To solve the given system of inequalities, we need to find the values of x that satisfy both inequalities. The solution is x ≤ 5.
Explanation:To solve the given inequalities, we need to find the values of x that satisfy both inequalities. Let's start with the first inequality:
3x - 8 ≤ 23
Adding 8 to both sides, we get:
3x ≤ 31
Dividing both sides by 3, we get:
x ≤ 31/3
Now, let's move on to the second inequality:
-4x + 26 ≥ 6
Subtracting 26 from both sides, we get:
-4x ≥ -20
Dividing both sides by -4 (and reversing the inequality sign since we're dividing by a negative number), we get:
x ≤ 5
Therefore, the solution to the system of inequalities is x ≤ 5. Answer choice B is correct.
Which equation relates f(x) with g(x)?
A. g(x) = f(x) + 5
B. g(x) = f(x + 5)
c. g(x) = f(x) - 5
D. g(x) = f(x - 5)
Answer:
g(x)=f(x-5)
Step-by-step explanation:
I did this question for my EOC & got it correct.
The equation that relates f(x) with g(x) is g(x) = f(x - 5).
Explanation:The equation that relates f(x) with g(x) is option D. g(x) = f(x - 5).
Option D represents a translation of the function f(x) in the positive x-direction by a distance of 5 units. This means that every y-value of f(x) at x will now be the y-value of g(x) at (x + 5). The equation g(x) = f(x - 5) precisely captures this relationship between f(x) and g(x).
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Problem Set
1. Use the set of ordered pairs below to answer each question.
{(4,20), (8,4),(2,3), (15,3), (6,15),(6,30), (1,5),(6,18),(0,3)}
a. Write the ordered pair(s) whose first and second coordinate have a greatest common factor of 3.
b. Write the ordered pair(s) whose first coordinate is a factor of its second coordinate.
c. Write the ordered pair(s) whose second coordinate is a prime number.
a) (15, 3) and (6, 15) and (0, 3) are the ordered pairs whose first and second coordinate have a greatest common factor of 3
b) The ordered pair(s) whose first coordinate is a factor of its second coordinate are (4, 20) and (6, 30) and (1, 5) and (6, 18)
c) (2 , 3) and (15, 3) and (1, 5) and (0, 3) are ordered pair(s) whose second coordinate is a prime numbers
Solution:
Given that,
Use the set of ordered pairs below to answer each question.
{(4, 20), (8, 4), (2, 3), (15, 3), (6, 15), (6, 30), (1, 5), (6, 18), (0, 3)}
a. Write the ordered pair(s) whose first and second coordinate have a greatest common factor of 3So we must find GCF of the ordered pairs
GCF of 4 and 20:
The factors of 4 are: 1, 2, 4
The factors of 20 are: 1, 2, 4, 5, 10, 20
Then the greatest common factor is 4
GCF of 8 and 4:
The factors of 4 are: 1, 2, 4
The factors of 8 are: 1, 2, 4, 8
Then the greatest common factor is 4
GCF of 2 and 3:
The factors of 2 are: 1, 2
The factors of 3 are: 1, 3
Then the greatest common factor is 1
GCF of 15 and 3:
The factors of 3 are: 1, 3
The factors of 15 are: 1, 3, 5, 15
Then the greatest common factor is 3
GCF of 6 and 15:
The factors of 6 are: 1, 2, 3, 6
The factors of 15 are: 1, 3, 5, 15
Then the greatest common factor is 3
GCF of 6 and 30:
The factors of 6 are: 1, 2, 3, 6
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
Then the greatest common factor is 6
GCF of 1 and 5:
The factors of 1 are: 1
The factors of 5 are: 1, 5
Then the greatest common factor is 1
GCF of 6 and 18:
The factors of 6 are: 1, 2, 3, 6
The factors of 18 are: 1, 2, 3, 6, 9, 18
Then the greatest common factor is 6
GCF of 0 and 3:
The factors of 0 are: All Whole Numbers
The factors of 3 are: 1, 3
Then the greatest common factor is 3
Summarizing the results:
(15, 3) and (6, 15) and (0, 3) are the ordered pairs whose first and second coordinate have a greatest common factor of 3
b. Write the ordered pair(s) whose first coordinate is a factor of its second coordinate.So let us find the factors of second cordinate and check
For (4, 20) , the factors of 20 are 1, 2, 4, 5, 10, 20
Thus first coordinate 4 is factor of second cordinate
For (8, 4) the factors of 4 are 1, 2, 4
Thus first coordinate is not a factor of second cordinate
For (2, 3), the factors of 3 are 1, 3
Thus first coordinate is not a factor of second cordinate
For (15, 3), the factors of 3 are 1 and 3
Thus first coordinate is not a factor of second cordinate
For (6, 15) , the factors of 15 are 1, 3, 5, 15
Thus first coordinate is not a factor of second cordinate
For (6, 30), the factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
Thus first coordinate 6 is factor of second cordinate
For (1, 5) , the factors of 5 are 1 and 5
Thus first coordinate 1 is a factor of second cordinate
For (6, 18) , the factors of 18 are 1, 2, 3, 6, 9, 18
Thus first coordinate 6 is factor of second cordinate
For (0, 3) , the factors of 3 are 1 and 3
Thus first coordinate is not a factor of second cordinate
Summarizing the results:
The ordered pair(s) whose first coordinate is a factor of its second coordinate are (4, 20) and (6, 30) and (1, 5) and (6, 18)
c. Write the ordered pair(s) whose second coordinate is a prime number.A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.
Therefore,
(2 , 3) and (15, 3) and (1, 5) and (0, 3) are ordered pair(s) whose second coordinate is a prime numbers
To find the ordered pairs with a GCF of 3, divide the second coordinate by the first to find pairs where the first is a factor of the second, and check the second coordinate for prime numbers.
Explanation:To find the ordered pairs whose first and second coordinates have a greatest common factor of 3, we can go through each pair and check the GCF. The pairs that have a GCF of 3 are (6, 15), (6, 30), and (0, 3).
To find the ordered pairs whose first coordinate is a factor of its second coordinate, we need to divide the second coordinate by the first coordinate and check if the result is a whole number. The pairs that meet this condition are (2, 3), (15, 3), and (0, 3).
To find the ordered pairs whose second coordinate is a prime number, we need to check if the second coordinate is divisible only by 1 and itself. The pair that meets this condition is (2, 3).
solve 9 is subtracted from 2 times the sum of 7 and 4
2×11+9
22+9
31
This the the way to solve this answer
Answer:77
Step-bystep explanation:
[9-2] * [7+4]
[7] * [11]
7*11=77
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which rate describes a unit price?
$1.00 for 2 lemons
3.00 for every pound
$4.00 for 3 slices of pizza
$6.00 for every 6 bottles
I'm assuming there should be a dollar sign here. This is the same as saying "$3 for one pound". A unit rate has some amount per 1 unit of something else. In this case, the 1 unit is 1 pound.
A different example of a unit rate is writing 40 miles per hour. This is the same as saying the car drives 40 miles in 1 hour. The unit here is the "1 hour".
Answer:
Given: $1.00 for 2 lemons $3.00 for every pound $4.00 for 3 slices of pizza $6.0
Step-by-step explanation:
Solve the system by elimination. 4x+6y=10 6x=9y−3
Answer:
x=1, y=1. (1, 1).
Step-by-step explanation:
4x+6y=10
6x=9y-3
-----------------
4x+6y=10
9y-6x=3
-----------------
4x+6y=10
-6x+9y=3
---------------
simplify -6x+9y=3 into -2x+3y=1
------------------------
4x+6y=10
-2x+3y=1
---------------
4x+6y=10
2(-2x+3y)=2(1)
-----------------------
4x+6y=10
-4x+6y=2
---------------
12y=12
y=12/12
y=1
4x+6(1)=10
4x+6=10
4x=10-6
4x=4
x=4/4=1
To solve the system of equations by elimination, multiply one equation by a constant that will create opposite coefficients for one of the variables. Then, combine the equations and solve for the remaining variable.
Explanation:To solve the system of equations by elimination, we need to eliminate one of the variables by adding or subtracting the equations.
In this case, let's eliminate y. We can do this by multiplying the first equation by 3 and the second equation by 6, so that the coefficients of y will be the same but opposite in sign. This gives us:
12x + 18y = 30
36x = 54y - 18
Now subtract the second equation from the first equation:
(12x + 18y) - (36x) = (30) - (54y - 18)
12x + 18y - 36x = -54y + 48
-24x + 18y = -54y + 48
Collect like terms:
-24x - 18y = -54y + 48
Rearrange the equation:
-24x + 54y = 48
The resulting equation is -24x + 54y = 48.
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√−100 = ___ +_____i
...
The square root of -100 is 0 + 10i or simply 10i in the form of a complex number, representing the imaginary part along the complex plane's imaginary axis.
Explanation:The square root of a negative number is not a real number, but rather a complex number denoted by the imaginary unit i for the square root of -1. To find the square root of -100, express -100 as the product of its prime factors: [tex]\(-100 = -1 \times 2^2 \times 5^2\)[/tex]. Then, applying the properties of square roots, break it down: [tex]\(\sqrt{-1} \times \sqrt{2^2} \times \sqrt{5^2}\)[/tex].
The square root of -1 is represented as i, while the square roots of [tex]\(2^2\)[/tex] and [tex]\(5^2\)[/tex] are 2 and 5, respectively. Combining these results, the square root of -100 is 0 + 10i, or simply 10i in complex number form, indicating that it lies on the imaginary axis of the complex plane.
It's important to note that the square root of a negative number results in a complex number with a real part of 0 and an imaginary part that represents the square root of the positive value of the number. In this case, the square root of -100 yields an imaginary component of 10i, indicating the distance from 0 along the imaginary axis in the complex plane, demonstrating the nature of complex numbers when dealing with square roots of negative values.
which expression is equivalent to 2/5(4x+9)
Answer:
d
Step-by-step explanation:
because 2/5 × 4x=8/5 and 2/5×9=18/5
ita in d
Ralph and Homer read a total of 33 books over the summer. Ralph read three more than four times as many as Homer. How many books did each person read?
Help Please! Add work.
Ralph read 27 books and Homer read 6 books.
Step-by-step explanation:
Given,
Total books read = 33
Let,
Books read by Ralph = x
Books read by Homer = y
According to given statement;
x+y=33 Eqn 1
Ralph read three more than four times as many as Homer.
x = 4y+3 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex](4y+3)+y=33\\4y+3+y=33\\5y=33-3\\5y=30[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{30}{5}\\y=6[/tex]
Putting y=6 in Eqn 2
[tex]x=4(6)+3\\x=24+3\\x=27[/tex]
Ralph read 27 books and Homer read 6 books.
Keywords: linear equation, substitution method
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In which quadrant does 0 lie given that sin 0<0 and cos 0<0
Answer:
[tex]\theta[/tex] must be in the third quadrant so that [tex]\sin \theta < 0[/tex] and [tex]\cos \theta < 0[/tex].
Step-by-step explanation:
We have to determine that in which quadrant the angle [tex]\theta[/tex] lies if [tex]\sin \theta < 0[/tex] and [tex]\cos \theta < 0[/tex].
The horizontal axis i.e. x-axis and the vertical axis i.e. y-axis divides the coordinate plane into four zones, the zone with x and y both positive is the first quadrant and rotating about the origin in anticlockwise we will find 2nd, 3rd and 4th quadrant one by one.
In the first quadrant all the trigonometrical functions [tex]\sin \theta[/tex], [tex]\cos \theta[/tex] and [tex]\tan \theta[/tex] are positive.
In the second quadrant only [tex]\sin \theta[/tex] is positive.
In the third quadrant only [tex]\tan \theta[/tex] is positive i.e. [tex]\sin \theta[/tex] and [tex]\cos \theta[/tex] are negative.
In the fourth quadrant only [tex]\cos \theta[/tex] is positive.
Therefore, [tex]\theta[/tex] must be in the third quadrant so that [tex]\sin \theta < 0[/tex] and [tex]\cos \theta < 0[/tex]. (Answer)
If both sin 0 and cos 0 are negative, the angle 0 lies in the third quadrant because only in this quadrant are both sine and cosine functions negative.
Explanation:The question asks in which quadrant does 0 lie given that sin 0<0 and cos 0<0. In the context of trigonometric functions in the Cartesian coordinate system, the sin of an angle is negative in the third and fourth quadrants, and the cos function is negative in the second and third quadrants. As such, if both sin 0<0 and cos 0<0, it indicates that the angle 0 must lie in the third quadrant. This is because it is the only quadrant where both the sin and cos of an angle are negative. Therefore, the angle 0 lies in the third quadrant.
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sin^-1 0.42 find the nearest degree
Answer:
[tex]25^o[/tex]
Step-by-step explanation:
Let
x ----> the angle in degrees
we know that
[tex]sin(x)=0.42[/tex]
Find the measure of angle x
Using a calculator
[tex]x=sin^{-1}(0.42)=24.83^o[/tex]
Round to the nearest degree
[tex]x=25^o[/tex]
A garden has an area of 240ft^2. Its length is 14ft. More then it’s width. What are the dimensions of the garden?
Answer:
width of garden=b=10 ft
length of garden=l=10+14=24 ft
Step-by-step explanation:
given area of garden=240 ft^2
length of garden=l
width of garden=b
ac/ ques, l=b+14
area of garden=lb
240 ft^2=(b+14)b
put b=10 form hit and trial method
240=(10+14)10=(24)10=240
width of garden=b=10 ft
length of garden=l=10+14=24 ft answer
-16/1296 in simplest form
Pls someone help!
Answer:
-1/81
Step-by-step explanation:
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Answer:
-1/81
Step-by-step explanation:
There are 178 7th grade students and 20 chaperones going on the field trup to the equarium.each bus holds 42 people how many buses will the group have to take? Inequality
Answer:
The group will need to take a minimum of 5 buses to carry all the people to the trip
Step-by-step explanation:
Given:
Number of 7th grade students going on the trip = 178
Number of chaperones going on the trip = 20
Number of people each bus can hole = 42
To find the number of buses the group will have to take.
Solution:
Let minimum number of buses the group will have to take = [tex]x[/tex]
using unitary method:
If 1 bus can hold = 42 people
Then, [tex]x[/tex] buses can hold = [tex]42x[/tex] people
Total number of people for the trip = [tex]178+20=198[/tex]
The total number of people that can go in [tex]x[/tex] buses must be greater than or equal to 198 in order to carry all the people to the trip.
Thus we have the inequality:
[tex]42x\geq198[/tex]
Solving for [tex]x[/tex]
Dividing both sides by 42.
[tex]\frac{42x}{42}\geq\frac{198}{42}[/tex]
[tex]x\geq4.71\approx 5[/tex] [As number of buses must be in whole number]
Thus, the group will need to take a minimum of 5 buses to carry all the people to the trip.
The number of buses needed for a field trip is 5 buses.
To determine how many buses are needed for 178 7th grade students and 20 chaperones going to the aquarium, where each bus holds 42 people, we first calculate the total number of passengers: 178 students + 20 chaperones = 198 people. We then divide this total number by the bus capacity. However, since we can't have a fraction of a bus, if there is any remainder after division, we must round up to the next whole number. So the inequality to represent this situation is:
Calculate total passengers:
178 students + 20 chaperones = 198 people
Divide by bus capacity to find the number of buses needed:
198 ÷ 42 = 4.714...
Round up to the next whole number, which means 5 buses will be needed.
Which line most accurately represents the line of best fit for the scatter plot?
A graph shows numbers from 0 to 14 on the x axis at increments of 2 and the numbers 0 to 112 on the y axis at increments of 16. Scatter plot shows ordered pairs 0, 32 and 2, 48 and 3.5, 56 and 4, 72 and 6, 75 and 8, 90 and 9, 96 and 10, 110. A line labeled A joins ordered pair 0, 32 and 4, 112. A line labeled B joins the ordered pairs 0, 32 and 10.5, 112. A line labeled C joins the ordered pairs 0, 32 and 14, 96. A line labeled D joins the ordered pairs 0, 32 and 14, 64.
Line A
Line B
Line C
Line D
Answer:
Hence two ordered pairs can be joined to best draw the line of best fit for this scatter plot are (0, 14) and (10, 1)
Option B is correct.
Step-by-step explanation:
How do I draw a tape diagram showing the equivalence of 24:32 and 48:64
Start by simplifying both fractions
[tex]
\dfrac{24}{32}=\dfrac{12}{16}=\dfrac{6}{8}=\dfrac{3}{4} \\
\dfrac{48}{64}=\dfrac{24}{32}=\dfrac{12}{16}=\dfrac{6}{8}=\dfrac{3}{4}
[/tex]
As you can see both fractions simplify to a same value hence the equality
[tex]\dfrac{24}{32}=\dfrac{48}{64}[/tex]
stands.
Hope this helps.
ANYONE GOOD IN MATH TRANSLATIONS??
Answer:
(x, y ) → (x + 2, y - 4 )
Step-by-step explanation:
Compare the coordinates of 2 corresponding points in the original and the image, that is
B(- 5, 4 ) → B'(- 3, 0 )
To translate from B → B'
We require a shift of 2 units right in the x direction and 4 units down in the y direction, that is
(x, y ) → (x + 2, y - 4 ) ← translation rule
A store sells two different packages of glue sticks as described below. Package A : 18 glue sticks. Package B : 12 glue sticks.
Answer:
Package A: [tex]g=18p[/tex] and Package B: [tex]g=12p[/tex]
Step-by-step explanation:
Here is the complete question: A store sells two different packages of glue sticks as described below. Package A : 18 glue sticks. Package B : 12 glue sticks. Write an equation for package A and B that represents the total number of glue sticks is "g" in "p" package.
Given: There are 2 packages .
Package A has 18 glue sticks
Package B has 12 glue sticks
As given let "g" be the total number of glue sticks in "p" packages.
Package A:
Total number of glue sticks in "P" packages= [tex]Total\ number\ of\ glue\times p[/tex]
∴ [tex]g=18\times p= 18p[/tex]
∴ [tex]g=18p[/tex]
Package B:
Total number of glue sticks in "P" packages= [tex]Total\ number\ of\ glue\times p[/tex]
∴ [tex]g=12\times p= 12p[/tex]
∴ [tex]g=12p[/tex]
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Find KL.
x=____
KL=___
KL is equal to JM because the quadrilateral is a parallelogram.
7x-2=12x-22
5x=20
x=4
KL=7(4)-2=26
answer: x=4, KL=26
Question 5) Which of the following equations is equivalent to 5 - 2x + 7y = 4 ?
abel
Aly- - Ex-1
labey
Bv=zx -
sebep
Cy=x+
adol
y = 2
PLEASE HELP!!!!!
Answer:
B
Step-by-step explanation:
Given
5 - 2x + 7y = 4 ( subtract 5 from both sides )
- 2x + 7y = - 1 ( add 2x to both sides )
7y = 2x - 1 ( divide all terms by 7 )
y = [tex]\frac{2}{7}[/tex] x - [tex]\frac{1}{7}[/tex] → B
Answer:
B. [tex]y=\frac{2}{7}x-\frac{1}{7}[/tex]
Step-by-step explanation:
We have been given an equation [tex]5-2x+7y=4[/tex]. We are asked to choose the equation that is equivalent to our given equation.
We will convert our given equation in point-slope form of equation.
[tex]5-2x+2x+7y=4+2x[/tex]
[tex]5+7y=4+2x[/tex]
[tex]5-5+7y=4-5+2x[/tex]
[tex]7y=-1+2x[/tex]
[tex]7y=2x-1[/tex]
Divide both sides by 7:
[tex]\frac{7y}{7}=\frac{2x}{7}-\frac{1}{7}[/tex]
[tex]y=\frac{2}{7}x-\frac{1}{7}[/tex]
Therefore, equation [tex]y=\frac{2}{7}x-\frac{1}{7}[/tex] is equivalent to our given equation and option B is the correct choice.
3. Put the polynomial in standard form.
5x-3x + 1+ 6x?
1+ 6x² + 5x+3x?
6x² + 5x - 3x +1
-3x? + 5x+ 6x² + 1
-3x2 + 6x² + 5x + 1
The polynomial in standard form is [tex]\( -3x^3 + 6x^2 + 5x + 1 \)[/tex], which corresponds to option A.
Here are the step-by-step instructions to put the given polynomial in standard form:
1. Rearrange the terms by descending order of exponents: Start by rewriting the polynomial with the terms arranged from highest degree to lowest degree.
[tex]$$ -3x^3 + 6x^2 + 5x + 1 $$[/tex]
2. Check for any missing terms: Make sure that each degree of x from highest to lowest is represented. In this case, all terms are present.
3. Double check the arrangement: Ensure that the terms are arranged correctly with respect to their exponents.
[tex]$$ -3x^3 + 6x^2 + 5x + 1 $$[/tex]
Thus, the polynomial in standard form is:
[tex]\[ -3x^3 + 6x^2 + 5x + 1 \][/tex]
Therefore, the correct answer is option A.
Complete Question:
Put the polynomial in standard form
[tex]$$5 x-3 x^3+1+6 x^2$$[/tex]
Choose the correct option
A: [tex]$-3 x^3+6 x^2+5 x+1$[/tex]
B: [tex]$1+6 x^2+5 x-3 x^3$[/tex]
C: [tex]$6 x^2+5 x-3 x^3+1$[/tex]
D: [tex]$-3 x^3+5 x+6 x^2+1$[/tex]
Mrs. Burke wants to get family portraits taken and is comparing prices between two different photography studios. Cameron Photography charges $33 per portrait sheet, plus $51 for the session fee. Lasting Memories Company charges $99 for the session fee and $29 per portrait sheet. If Mrs. Burke plans to purchase a certain number of portrait sheets, the cost will be the same at either studio. How many portrait sheets would that be? What would the total cost be? If Mrs. Burke orders portrait sheets, the portrait session will cost $ at either studio.
Answer:
12 portrait sheets with total cost of $447
Step-by-step explanation:
x sheets ordered
Cameron: 33x + 51 = Lasting Memory : 29x + 99
33x + 51 = 29x + 99
33x - 29x = 99 -51
4x = 48
x = 12 sheets ordered
Total cost: 33 * 12 + 51 = 447
check: 29 * 12 + 99 = 447
Final answer:
Mrs. Burke needs to purchase 12 portrait sheets for the cost to be the same at either studio, and the total cost would be $495.
Explanation:
Mrs. Burke is comparing the costs of family portraits between Cameron Photography and Lasting Memories Company to find out how many portrait sheets will result in the same total cost at either studio. To solve this, we can set up an equation where the total cost at Cameron Photography equals the total cost at Lasting Memories.
Let x be the number of portrait sheets. The total cost at Cameron Photography is given by the expression 33x + 51 (where 33 is the cost per portrait sheet and 51 is the session fee). The total cost at Lasting Memories is expressed as 29x + 99 (with 29 being the cost per portrait sheet and 99 is the session fee).
To find the number of portrait sheets that results in equal costs, we set the two expressions equal to each other:
33x + 51 = 29x + 99
Subtracting 29x from both sides, we get:
4x + 51 = 99
Subtracting 51 from both sides, we get:
4x = 48
Dividing by 4, we find that x = 12. So, Mrs. Burke would need to purchase 12 portrait sheets for the cost to be the same at either studio. Plugging x back into either original cost equation, we find that the total cost at either studio will be 33(12) + 51 = 99(12) + 99 = $495.
Which equation represents the line that passes through the points (-1,-2)and(3,10)
Answer:
y= 3x +1
Step-by-step explanation:
Let's write the equation of the line in slope-intercept form. That is, y= mx +c, where m is the slope and c is the y-intercept.
Start by finding the slope with the formula below:
[tex]\boxed{\text{slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]
Slope
[tex]=\frac{10-(-2)}{3-(-1)}[/tex]
[tex]=\frac{10+2}{3+1}[/tex]
[tex]=\frac{12}{4}[/tex]
= 3
Substitute m= 3 into the equation:
y= 3x +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= -1, y= -2,
-2= 3(-1) +c
-2= -3 +c
c= -2 +3
c= 1
Thus, the equation of the line is y= 3x +1.
_______
Alternatively, we can write the equation in the point-slope form.
[tex]\boxed{y-y_1=m(x-x_1)}[/tex]
Substitute m= 3 and a pair of coordinates into [tex](x_1,y_1)[/tex]:
y -10= 3(x -3)
Additional:
For more questions on writing equations of line, check out:
https://brainly.com/question/25549430The equation which passes through the points (-1,-2)and(3,10) will be y= 3x +1
What is an equation?An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Let's write the equation of the line in slope-intercept form. That is, y= mx+c, where m is the slope and c is the y-intercept.
Start by finding the slope with the formula below:
[tex]\rm Slope =\dfrac{y_1-y_2}{x_1-x_2}[/tex]
Slope
[tex]\rm Slope =\dfrac{10-(-2)}{3-(-1)}[/tex]
[tex]\rm Slope=\dfrac{12}{4}[/tex]
Slope = 3
Substitute m= 3 into the equation:
y = 3x + c
To find the value of c, substitute a pair of coordinates into the equation.
When x= -1, y= -2,
-2 = 3(-1) + c
-2= -3 + c
c = -2 + 3
c = 1
Thus, the equation of the line is y = 3x + 1.
Alternatively, we can write the equation in the point-slope form.
y - y₁ = m ( x - x₁ )
Substitute m= 3 and a pair of coordinates into :
y - 10 = 3 ( x - 3 )
Therefore the equation which passes through the points (-1,-2)and(3,10) will be y= 3x +1
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What is the perimeter of the parallelogram?
(2, 2), (5,2), (4,4), (1,4)
Answer:
10.5 units (3 s.f.)
Step-by-step explanation:
Please see attached picture for full solution.
Note that AB and CD are horizontal lines because A and B have the same y coordinate, and C and D have the same y coordinate. As a result, I can simply subtract their x coordinate values to find length of AB and CD.
GIVING BRAINLIEST!!! STATEMENT REASONING NEEDED!!! 100 POINTS!!!
Answer:
See explanation
Step-by-step explanation:
a1) Given
[tex]\angle A\cong \angle C\\ \\\angle ABD\cong \angle CDB[/tex]
Statement Reason
1. [tex]\angle A\cong \angle C[/tex] - Given
2. [tex]\angle ABD\cong \angle CDB[/tex] - Given
3. [tex]\overline{BD}\cong \overline{DB}[/tex] - Reflexive property
4. [tex]\triangle ABD\cong \triangle CDB[/tex] - AAS postulate
5. [tex]\overline {AB}\cong \overline{CD}[/tex] - Congruent triangles have congruent corresponding parts
6. [tex]AB=CD[/tex] - Definition of congruent segments
a2) Given
[tex]\overline{H O}\parallel \overline{E N}\\ \\H W=N W[/tex]
Statement Reason
1. [tex]H W=W N[/tex] - Given
2. [tex]\overline{H O}\parallel \overline{E N}[/tex] - Given
3. [tex]\angle O H W\cong \angle E N W[/tex] - Alternate interior angles theorem (two parallel lines H O and E N are cut by transversal H N)
4. [tex]\angle H W O\cong \angle N W E[/tex] - Vertical angles theorem
5. [tex]\triangle H O W\cong \triangle N E W[/tex] - ASA postulate
b) Given
[tex]PO=PR\\ \\OS=RS\\ \\\angle O\cong \angle R\\ \\m\angle P=90^{\circ}[/tex]
Statement Reason
1. [tex]m\angle P=90^{\circ}[/tex] - Given
2. [tex]\triangle OPE, \triangle RPN[/tex] are right triangles - Definition of right triangles
3. [tex]\angle O\cong \angle R[/tex] - Given
4. [tex]PO=PR[/tex] - Given
5. [tex]\triangle POE\cong \triangle PRN[/tex] - HA postulate
6. [tex]OS=RS[/tex] - Given
7. [tex]\angle O\cong \angle R[/tex] - Given
8. [tex]\angle OSN\cong \angle SRE[/tex] - Vertical angles theorem
9. [tex]\triangle SON\cong \triangle SRE[/tex] - ASA postulate
c1) Given
[tex]\overline{SA}\parallel \overline{NE}\\ \\\overline{SE}\parallel \overline{NA}[/tex]
Statement Reason
1. [tex]\overline{SA}\parallel \overline{NE}[/tex] - Given
2. [tex]\angle ENS\cong \angle ASN[/tex] - Alternate interior angles theorem (two parallel lines SA and NE are cut by transversal SN)
3. [tex]\overline{SE}\parallel \overline{NA}[/tex] - Given
4. [tex]\angle ESN\cong \angle ANS[/tex] - Alternate interior angles theorem (two parallel lines SE and NA are cut by transversal SN)
5. [tex]\overline{SN}\cong \overline{NS}[/tex] - Reflexive property
6. [tex]SN=NS[/tex] - Definition of congruent segments
7. [tex]\triangle ENS\cong \triangle ASN[/tex] - ASA postulate
8. [tex]\overline{SA}\cong \overline {NE}[/tex] - Congruent triangles have congruent corresponding parts
9. [tex]SA=NE[/tex] - Definition of congruent segments
c2) Given
[tex]\angle BTO\cong \angle IWE\\ \\\overline{WI}\cong \overline{BT}\\ \\\overline{OW}\cong \overline{ET}[/tex]
Statement Reason
1. [tex]\angle BTO\cong \angle IWE[/tex] - Given
2. [tex]\overline{WI}\cong \overline{BT}[/tex] - Given
3. [tex]\overline{OW}\cong \overline{ET}[/tex] - Given
4. [tex]\overline{WT}\cong \overline{TW}[/tex] - Reflexive property
5. [tex]WI=BT[/tex] - Definition of congruent segments
6. [tex]OW=ET[/tex] - Definition of congruent segments
7. [tex]WT=TW[/tex] - Definition of congruent segments
8. [tex]OT=OW+WT[/tex] - Segment addition postulate
9. [tex]WE=WT+TE[/tex] - Segment addition postulate
10. [tex]OW+WT=ET+WT[/tex] - Substitution property
11. [tex]OT=WE[/tex] - Substitution property
12. [tex]\triangle BOT\cong \triangle IEW[/tex] - SAS postulate
Answer:
What he said
Step-by-step explanation:
A principal of $4000 is invested at 8.75% interest, compounded annually. How many years will it take to accumulate $14,000 or more in the account?
Answer:
The number of years will it take to accumulate the amount in the account is 15 years .
Step-by-step explanation:
Given as :
The principal invested = p = $4000
The rate of interest = r = 8.75% compounded annually
The amount accumulate after t years = A = $14,000
Let The years of accumulation = t years
From Compounded Interest
Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, $14000 = $4000 × [tex](1+\dfrac{\textrm 8.75}{100})^{\textrm t}[/tex]
Or, [tex]\dfrac{14000}{4000}[/tex] = [tex](1.0875)^{\textrm t}[/tex]
Or, 3.5 = [tex](1.0875)^{\textrm t}[/tex]
Taking log both side
[tex]Log_{10}[/tex]3.5 = [tex]Log_{10}[/tex] [tex](1.0875)^{\textrm t}[/tex]
Or, 0.54 = t [tex]Log_{10}[/tex]1.0875
or, 0.54 = t × 0.036
∴ t = [tex]\dfrac{0.54}{0.036}[/tex]
I.e t = 15
So, The number of years will it take = t = 15 years
Hence, The number of years will it take to accumulate the amount in the account is 15 years . Answer
What is the cube of 27x18
Answer:
114791256
Step-by-step explanation:
27*17=486
486^3=114791256
Answer:
114791256
Step-by-step explanation:
27*17=486
486^3=114791256
Factor completely 2x^2 - 98
Answer:
Step-by-step explanation:
2x^2 - 98 = 2 * ( x^2 - 49)
= 2 * (x^2 - 7^2)
= 2 * (x+7) * (x-7) {a²-b² = (a+b)(a-b)}
h=-16t^2+96t+4
solve by factoring
Answer:
6 plus or minus square root of 37/2
Step-by-step explanation:
Is the quadratic formula allowed or no?
Answer:
t = 3 ± ½√37
Step-by-step explanation:
0 = -16t² + 96t + 4
This isn't factorable, so complete the square or use quadratic formula. Completing the square:
16t² − 96t = 4
t² − 6t = 1/4
t² − 6t + 9 = 1/4 + 9
(t − 3)² = 37/4
t − 3 = ±½√37
t = 3 ± ½√37
Find the time required for an investment of $6000 to triple if the interest rate of 5.5% is compounded continuously.
Answer: t ≈ 20 years
Step-by-step explanation:
Since it is compounded continuously , we will use the compound interest formula:
A = P[tex]e^{rt}[/tex]
Where A is the amount when tripled
P is the initial amount
r is the rate
t is the time
since the investment is tripled , it means the A = 3P.
From the question:
A = 3P
P = $6000
r = 5.5%
t = ?
Substituting into the formula , we have
3P = P[tex]e^{rt}[/tex] , that is
3(6000) = 6000[tex]e^{0.055t}[/tex]
Dividing through by 6000 , we have
3 = [tex]e^{0.055t}[/tex]
Take the In of both sides in order to remove the exponential , that is
In 3 = 0.055t
divide through by 0.055
t = In 3 / 0.055
Therefore :
t = 19.97476888
t≈ 20 years
Kyle ran for 27 minutes on Tuesday. On Wednesday, Kyle ran for n fewer minutes than he ran on Tuesday. On Friday, Lee ran for 3 times longer than Kyle ran on Wednesday. Kyle wrote this expression to show how long Lee ran.
Answer:
(27 - n) times 3 is the expression Kyle should use.
Step-by-step explanation:
If Lee ran for 3 times longer than Kyle ran on Wednesday, then we have to figure out how long Kyle ran on Wednesday. If Kyle ran n fewer minutes than he ran on Tuesday, then we need to figure out how long he ran on Tuesday. If Kyle ran 27 minutes on Tuesday, the we need to subtract n from that to get how long Kyle ran on Wednesday. We can't figure that out with an undefined variable, therefore, that will just have to be 27 - n in the equation. If Lee ran for 3 times that, we need to multiply that by 3. 27 - n would have to be done first, so we will put that in parenthesis. We put all of that together to get (27 - n) times 3. Hope this helps!