Answer: π/180
Step-by-step explanation:
510 Degree (°) =. 8.90118 Radian (rad) Degree : A degree, a degree of arc or arc degree is a measurement of plane angle, on behalf of 1/360 of a full rotation. The symbol for degree is °. It is not an SI unit, however, it is accepted for use with SI. One degree is equal to π/180 radians.
Answer:
17pi/6 rad
Step-by-step explanation:
2 pi radians = 360 degrees
Divide both sides by 2.
pi radians = 180 degrees
From the statement above, you get the conversion factors:
(pi rad)/(180 deg) = (180 deg)/(pi rad) = 1
Both fractions above equal 1. Since multiplying by 1 does not change the number, multiply 510 deg by the fraction above that will cancel out degrees and will leave you with radians.
510 deg * (pi rad)/(180 deg) = 510pi/180 rad = 17pi/6 rad
What is the cube root of -729a9b6
ANSWER
[tex]\sqrt[3]{- 729{a}^{9} {b}^{6} } = - 9 {a}^{3} {b}^{2} [/tex]
EXPLANATION
We want to find the cube root of
[tex] - 729 {a}^{9} {b}^{6} [/tex]
We express this symbolically as:
[tex] \sqrt[3]{- 729 {a}^{9} {b}^{6} } [/tex]
The expression under the radical called the radicand.
We need to express this radical in exponential form using the property,
[tex] {x}^{ \frac{m}{n} } = \sqrt[n]{ {x}^{m} } [/tex]
Applying this rule gives us:
[tex]\sqrt[3]{- 729 {a}^{9} {b}^{6} } = ({- 729 {a}^{9} {b}^{6}})^{ \frac{1}{3} } [/tex]
[tex]\sqrt[3]{- 729{a}^{9} {b}^{6} } = ({- {9}^{3} {a}^{9} {b}^{6}})^{ \frac{1}{3} } [/tex]
Recall that
[tex] ({a}^{m} )^{n} = {a}^{mn} [/tex]
We apply this rule on the RHS to get,
[tex]\sqrt[3]{- 729{a}^{9} {b}^{6} } = ({- {9}^{3 \times { \frac{1}{3} } } {a}^{9 \times { \frac{1}{3} } } {b}^{6 \times { \frac{1}{3} } }})[/tex]
This simplifies to
[tex]\sqrt[3]{- 729{a}^{9} {b}^{6} } = - 9 {a}^{3} {b}^{2} [/tex]
Answer:
-9a3b2
Step-by-step explanation:
Translate the following phrase into an algebraic expression using the variable x to represent the cost of the puck. Do not simplify the cost of purchasing a hockey stick and puck if the stick costs $7 less than twice the cost of the puck
Final answer:
The algebraic expression for the cost of purchasing a hockey stick and a puck, where the stick costs $7 less than twice the cost of the puck, and using x to represent the cost of the puck, is x + (2x - 7).
Explanation:
To translate the given phrase into an algebraic expression using the variable x to represent the cost of the puck, let's follow the instructions provided in the phrase very carefully. The cost of the hockey stick is described as "$7 less than twice the cost of the puck." Therefore, we first consider "twice the cost of the puck" which is 2x, and then subtract 7 from it to account for the phrase "$7 less than." Hence, the final expression for the cost of the hockey stick is 2x - 7.
Now, to find the cost of purchasing both the hockey stick and the puck, we simply add the cost of the puck (x) to the expression for the cost of the hockey stick (2x - 7), giving us a total cost expression of x + (2x - 7).
Notice that we are not simplifying the expression; we're just writing the combined cost as requested. So the final untranslated expression for the cost of purchasing a hockey stick and a puck based on the given conditions is x + (2x - 7).
3.1x−16.3=−0.8
URGENT
find the value of x please
Answer:
x =5
Step-by-step explanation:
3.1x−16.3=−0.8
Add 16.3 to each side
3.1x−16.3+16.3=−0.8+16.3
3.1x = 15.5
Divide each side by 3.1
3.1x = 15.5/3.1
x =5
The cost of performance tickets and beverages for a family of four can be modeled using the equation 4x + 12 = 48, where x
represents the cost of a ticket. How much is one ticket?
$3.00
$4.00
$9.00
$15.00
Answer:
$9.00
Step-by-step explanation:
4x + 12 = 48 - First, subtract 12 from both sides.
4x = 36 - Then, divide each side by 4 to get x by itself.
x = 9 - After getting x by itself, we see that x = 9, so one ticket will
cost $9.00
For this case we have the following equation:
[tex]4x + 12 = 48[/tex]
Where the variable "x" represents the cost of a performance ticket.
Clear "x" of the equation to know the cost of a ticket.
Subtracting 12 on both sides of the equation:
[tex]4x = 48-12\\4x = 36[/tex]
Dividing between 4 on both sides of the equation:
[tex]x = \frac {36} {4}\\x = 9[/tex]
So, the cost of a ticket is $ 9.00
Answer:
Option C
What is the correct answer
Answer:
c
Step-by-step explanation:
just took the test
Answer:
B
Step-by-step explanation:
The domain of the function are the input values on the left and the corresponding values on the right are the output values, the range
domain is { 1, 2, 3, 4 }
Mahimi has x dollars for food. She wants to buy lunch and still have $2 left over to buy a snack later. How can mahimi represent how much she can spend on lunch
Answer:
x-2 dollars is the lunch money
The expression x-2 represents the spending amount on the lunch.
What is an expression?
One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given:
Mahimi has x dollars for food.
She wants to buy lunch and still have $2 left over to buy a snack later.
To find the spending amount on the lunch:
She spent on the lunch,
= $(x - 2).
Therefore, x -2 is the expression.
To learn more about the expression;
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Which expression is equivalent to 2x2 - 2x + 7?
- (4x+12) + (2x2–6x+5)
• (x2–5x+13)+(x2 +3X-6)
. (4x? -6x+ 11 ) + (2x² - 4x+4)
(5x® – 8x+120) + (-3x2 + 10x= 13)
Answer:
B) [tex](x^2 - 5x + 13) +(x^2 + 3x - 6)\\[/tex]
Step-by-step explanation:
Let's simplify the given options and find the correct answer.
The given expression is [tex]2x^2 - 2x + 7[/tex]
Let's take the option A and simplify.
[tex]-(4x + 12) + (2x^2 - 6x + 5)[/tex]
Distributing the negative sign and simplify.
[tex]-4x - 12 + 2x^2 -6x + 5[/tex]
Simplify the like terms.
[tex]2x^2 -10x - 7[/tex]
Which is not equal to the given expression.
Let's take the option B and simplify.
[tex](x^2 - 5x + 13) +(x^2 + 3x - 6)\\[/tex]
Simplify the like terms, we get
[tex]x^2 + x^2 -5x +3x +13 -6[/tex]
[tex]2x^2 -2x +7[/tex]
Which is equal to the given expression [tex]2x^2 -2x +7[/tex]
Therefore, the answer is B) [tex](x^2 - 5x + 13) +(x^2 + 3x - 6)\\[/tex]
Andy is learning to play the guitar. Last week he recorded the minutes per day that he practiced. Find the mean absolute deviation. Round to the nearest tenth.
Day S M T W T F S
Minutes 40 55 35 60 20 50 55
Answer:
11.4
Step-by-step explanation:
Step 1: Calculate the mean.
40, 55, 35, 60, 20, 50, 55
=
315
divided by 7
=
45
Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.
40 - 45 = 5
55 - 45 = 10
35 - 45 = 10
60 - 45 = 15
20 - 45 = 25
50 - 45 = 5
55 - 45 = 10
Step 3: Add those deviations together.
= 80
Step 4: Divide the sum by the number of data points.divided by 7
= 11.428
Step 5: Round to the nearest tenth.
= 11.4
Answer:
The mean absolute deviation is approximately is 11.43.Step-by-step explanation:
The means absolute deviations is define by:
[tex]D_{x} =\frac{\sum |x_{i}-x| }{N}[/tex]
From the formula, we observe that we need to find the mean, and then find the different between that mean and each element. Then, we have to sum all those differences and divide this by the total number of elements.
So, the mean is
[tex]x=\frac{\sum x_{i} }{N}\\ x=\frac{40+55+35+60+20+50+55}{7}=45[/tex]
Now, each difference would be
[tex]40-45=-5\\55-45=10\\35-45=-10\\60-45=15\\20-45=-25\\50-45=5\\55-45=10[/tex]
The sum of all differences, using their absolute value, would be:
[tex]5+10+10+15+25+5+10=80[/tex]
Then, we divide this result by the total number of elements which is 7:
[tex]\frac{80}{7} \approx 11.43[/tex]
Therefore, the mean absolute deviation is approximately is 11.43.
Paul needs to find 310% of 72. Which expression should he use
Answer:
3.10 * 72
Step-by-step explanation:
To find 310% of 72
Of means multiply and is means equal
310% * 72 = answer
Change to decimal form
3.10 * 72 = answer
223.20
Answer: (3.10)(72) is the correct answer
Step-by-step explanation:
5, 6, 7, 8, 9, 10, 11 What is the interquartile range of the data set?
Answer:
The IQR = 4.
Step-by-step explanation:
The median is the middle number so it is 8.
The lower quartile is 6 (the middle number of those less than 8).
In a similar way the upper quartile is 10.
The interquartile range is 10 - 6 = 4.
Final answer:
To find the interquartile range of the data set 5, 6, 7, 8, 9, 10, 11, we calculate Q3 (10) - Q1 (6), which results in an IQR of 4.
Explanation:
The question asks for the interquartile range (IQR) of the data set 5, 6, 7, 8, 9, 10, 11. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1) in a data set, representing the spread of the middle 50 percent of the data.
Step-by-step Calculation
First, arrange the data in ascending order, which has already been done: 5, 6, 7, 8, 9, 10, 11.
To find Q1, calculate the median of the lower half. Here, Q1 is 6 (the median of 5, 6, 7).
To find Q3, calculate the median of the upper half. Here, Q3 is 10 (the median of 9, 10, 11).
Finally, calculate the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 10 - 6 = 4.
Thus, the interquartile range of this data set is 4.
If you were asked to solve a system of equations in which there are no linear equation to start with you can sometimes begin by isolating and substituting a veritable there a square in both equations true or false
Answer:
The correct answer option is true.
Step-by-step explanation:
The given statement is true that if there is no linear equation to start with, you can isolate and substitute a variable that is squared in both the equation.
For instance, if we have a non linear equation, start by dividing both sides by coefficient of the variable.
Once you do that and isolate a variable, continue solving by substituting that variable into the other equation.
Multiply X to the 2/5 power times X to the 2/9 power
Answer:
[tex] x^{\frac{28}{45}} [/tex]
Step-by-step explanation:
To multiply powers with the same base, add the exponents.
[tex] x^{\frac{2}{5}} \times x^{\frac{2}{9}} = [/tex]
[tex] = x^{\frac{2}{5} + \frac{2}{9} [/tex]
[tex] = x^{\frac{2 \times 9}{5 \times 9} + \frac{2 \times 5}{9 \times 5}} [/tex]
[tex] = x^{\frac{18}{45} + \frac{10}{45}} [/tex]
[tex] = x^{\frac{28}{45}} [/tex]
Which equation represents the graphed function ?
Y= -2x+3
Y=2x+3
Y=1/2x +3
Y=-1/2x+3
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (1, 1)
m = [tex]\frac{1-3}{1-0}[/tex] = - 2
note the line crosses the y- axis at (0, 3) ⇒ c = 3
y = - 2x + 3 → A
Ify is 2.5 when x is 5 and y varies directly with x, find y when x is 10.
5
7.5
12.5
20
Answer:A
Step-by-step explanation:
Y varies directly as x
Y = kx
When y = 2.5, x = 5
Substitute the value of y and x
2.5 = k * 5
Make k the subject of the formula
k = 2.5/5
k = 1/2
:. The equation connectin y and x is
Y = 1/2x
When x = 10
Y = 1/2*10
Y = 10/2
Y = 5
Jeff is very tall he is 6 feet 5 inches tall how tall is he in inches
Answer:
77 inches
Step-by-step explanation:
1 foot=12 inches so what you have to do is 12x6=72 and since he is 6 foot 5 inches you add 5 to get 77.
Please mark brainliest and have a great day!
The equation of the circle whose center is at (2, 1) and radius is 3 is
Answer: The equation of the circle whose center is at (2, 1) and radius is 3 is [tex](x-2)^2+(y-1)^2=9[/tex]
Step-by-step explanation:
We know that the equation of a circle having center at (h,k) and radius r is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Given : The center of the circle : (2, 1)
The radius of the circle : 3 units
Then the equation of a circle with center at (2, 1) and radius is 3 is will be :-
[tex](x-2)^2+(y-1)^2=3^2\\\\\Rightarrow\ (x-2)^2+(y-1)^2=9[/tex]
What is another name for a relation that has each element in its domain
paired with exactly one element in its range?
Answer:
Step-by-step explanation:
A function is a relation in which each element of the domain is paired with exactly one element of the range.
A relation is a set of ordered pairs. The set of the first components of each ordered pair is called the domain and the set of the second components of each ordered pair is called the range. Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.
{(1,2),(2,4),(3,6),(4,8),(5,10)}
The domain is{1,2,3,4,5} and the range is{2,4,6,8,10}
So, this relation is a function.
what is 8^2 X8^3 as one base ?
Answer:
8^5
Step-by-step explanation:
What is the formula for scientific notation
Answer:General Formula of Scientific Notation. The general from of a number in scientific notation is: a ×10n where 1 ≤ a ≤ 10 and n is an integer. In other words the number that we'll call "a" is is multiplied by 10, raised to some exponent n.
Step-by-step explanation:
Final answer:
The formula for scientific notation involves expressing a number as the product of a coefficient (a number between 1 and 10) and a power of ten. The sign of the exponent is determined by the direction the decimal point is moved to create the coefficient.
Explanation:
The formula for scientific notation is a method of writing very large or very small numbers as a product of two parts: a coefficient and a power of ten. The coefficient must be a number greater than or equal to 1 and less than 10, while the power of ten reflects how many places the decimal point is moved to convert the number to the coefficient. In scientific notation, for example, the Earth's distance from the Sun, which is 150,000,000,000 meters, is expressed as 1.5 × 1011 m.
When converting a number to scientific notation, count the number of places you moved the decimal point to get a number between 1 and 10 for your coefficient. If the decimal point is moved to the left, the exponent will be positive, and if moved to the right, it will be negative. For instance, 2386 can be converted to 2.386 × 103 because the decimal is moved 3 places to the left.
If a circle has a diameter with end points: (4 + 6i) and (-2 + 6i),
1. Show me how you would determine the length of the diameter and radius.
2. Show me how you would determine the center of the circle.
3. Determine, mathematically, if (1+9i) lies on the circle. Show how you proved it mathematically.
4. Determine, mathematically, if (2-i) lies on the circle. Show how you proved it mathematically.
Answer:
Part 1) The diameter is [tex]D=6\ units[/tex] and the radius is equal to [tex]r=3\ units[/tex]
Part 2) The center of the circle is (1+6i)
Part 3) The point (1+9i) lies on the circle
Part 4) The point (2-i) does not lies on the circle
Step-by-step explanation:
Part 1) Show me how you would determine the length of the diameter and radius.
we have that
The circle has a diameter with end points: (4 + 6i) and (-2 + 6i)
we know that
The distance between the end points is equal to the diameter
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
(4 + 6i) ----> (4,6)
(-2 + 6i) ---> (-2,6)
substitute the values
[tex]d=\sqrt{(6-6)^{2}+(-2-4)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(-6)^{2}}[/tex]
[tex]d=6\ units[/tex]
therefore
The diameter is [tex]D=6\ units[/tex]
The radius is equal to [tex]r=6/2=3\ units[/tex] ---> the radius is half the diameter
Part 2) Show me how you would determine the center of the circle
we know that
The center of the circle is equal to the midpoint between the endpoints of the diameter
The circle has a diameter with end points: (4 + 6i) and (-2 + 6i)
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute
[tex]M(\frac{4-2}{2},\frac{6+6}{2})[/tex]
[tex]M(1,6})[/tex]
therefore
(1,6) ----> (1+6i)
The center of the circle is (1+6i)
Part 3) Determine, mathematically, if (1+9i) lies on the circle. Show how you proved it mathematically
Find the equation of the circle
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
we have
The center is (1+6i) -----> (1,6)
r=3 units
substitute
[tex](x-1)^{2}+(y-6)^{2}=3^{2}[/tex]
[tex](x-1)^{2}+(y-6)^{2}=9[/tex]
Verify if the point (1+9i) lies on the circle
Remember that
If a point lies on the circle, then the point must satisfy the equation of the circle
Substitute the value of x and the value of y in the equation and then compare the results
we have
the point (1+9i) -----> (1,9)
[tex](1-1)^{2}+(9-6)^{2}=9[/tex]
[tex](0)^{2}+(3)^{2}=9[/tex]
[tex]9=9[/tex] -----> is true
therefore
The point (1+9i) lies on the circle
Part 4) Determine, mathematically, if (2-i) lies on the circle. Show how you proved it mathematically
The equation of the circle is equal to
[tex](x-1)^{2}+(y-6)^{2}=9[/tex]
Verify if the point (2-i) lies on the circle
Remember that
If a point lies on the circle, then the point must satisfy the equation of the circle
Substitute the value of x and the value of y in the equation and then compare the results
we have
the point (2-i) -----> (2,-1)
[tex](2-1)^{2}+(-1-6)^{2}=9[/tex]
[tex](1)^{2}+(-7)^{2}=9[/tex]
[tex]50=9[/tex] -----> is not true
therefore
The point (2-i) does not lies on the circle
To determine the length of the diameter and radius, use the distance formula. The center of the circle can be found by finding the midpoint of the diameter's end points. To determine if a point lies on the circle, use the distance formula to compare the distance between the point and the center to the radius.
Explanation:1. Determining the length of the diameter and radius:
To find the length of the diameter, we can use the distance formula. The distance between two complex numbers (a + bi) and (c + di) is given by the formula √((c-a)^2 + (d-b)^2). In this case, the two end points of the diameter are (4 + 6i) and (-2 + 6i). Using the formula, the distance is √((-2-4)^2 + (6-6)^2) = √((-6)^2 + 0) = √(36) = 6.
The radius of a circle is half the length of the diameter. Therefore, the radius of this circle is 6/2 = 3.
2. Determining the center of the circle:
The center of the circle is the midpoint between the two end points of the diameter. To find the midpoint, we can take the average of the x-coordinates and the average of the y-coordinates. In this case, the x-coordinates of the end points are 4 and -2, and the y-coordinates are 6. Taking the averages, the x-coordinate of the center is (4 + (-2))/2 = 1 and the y-coordinate of the center is (6 + 6)/2 = 6. Therefore, the center of the circle is the complex number 1 + 6i.
3. Determining if (1 + 9i) lies on the circle:
To determine if a point lies on the circle, we can check if the distance between the center of the circle and the point is equal to the radius. Using the distance formula again, the distance between the center (1 + 6i) and the point (1 + 9i) is √((1-1)^2 + (9-6)^2) = √(0 + 9) = √(9) = 3. Since the distance is equal to the radius, we can conclude that (1 + 9i) does lie on the circle.
4. Determining if (2 - i) lies on the circle:
Using the same process, we find that the distance between the center (1 + 6i) and the point (2 - i) is √((2-1)^2 + (-1-6)^2) = √(1 + 49) = √(50). Since √(50) is not equal to the radius (3), we can conclude that (2 - i) does not lie on the circle.
24 people go to joe's birthday party.half walk and a quarter travel by bus all the others go by taxi. How many guests walk?
Answer:
12 guest walk
Step-by-step explanation:
Total number of people that went to the party= 24 (let this be represented as y)
Half of the people walk, this means 1/2 × y ----------- walk, where y=24 people
Hence half of 24= [tex]\frac{24}{2} =12[/tex]
12 people walked.
how do I write 6.741 in expanded form?
Answer:
6 + 0.7 + 0.04 + 0.001 = 6.741
6 x 1 + 0.1 x 7 + 0.01 x 4 + 0.001 x 1 = 6.741
The expression log1/3/log2 is the result of applying the change of base formula to a logarithmic expression. Which could be the original expression?
Answer:
Option C. [tex]log_{2}\frac{1}{3}[/tex]
Step-by-step explanation:
The given logarithmic expression is [tex]\frac{log(\frac{1}{3} )}{log2}[/tex]
Rule of logarithm says
[tex]\frac{log_{e}a }{log_{e}b}=log_{b}a[/tex]
So by this rule,
expression [tex]\frac{log(\frac{1}{3} )}{log2}[/tex] will become [tex]log_{2}\frac{1}{3}[/tex]
Therefore, Option C. [tex]log_{2}\frac{1}{3}[/tex] will be the answer.
To solve the problem we must know about the rule to change the base of any logarithmic expression.
The solution of the given expression [tex]\dfrac{log\dfrac{1}{3}}{log 2}[/tex] is [tex]\rm log_2\dfrac{1}{3}[/tex].
What is the rule for changing the base of a logarithm expression?The formula which helps us to change the base of any logarithm expression,
[tex]\rm log_ab = \dfrac{log_cb}{log_ca}[/tex]
Given to us
[tex]\dfrac{log\dfrac{1}{3}}{log 2}[/tex]
As we have already discussed the formula for the change of the base of any logarithm expression, comparing the formula with that expression,
[tex]\rm log_ab = \dfrac{log_cb}{log_ca} = \dfrac{log\dfrac{1}{3}}{log 2}[/tex]
[tex]\rm log_2\dfrac{1}{3} = \dfrac{log\dfrac{1}{3}}{log 2}[/tex]
Hence, the solution of the given expression [tex]\dfrac{log\dfrac{1}{3}}{log 2}[/tex] is [tex]\rm log_2\dfrac{1}{3}[/tex].
Learn more about Logarithm expression:
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Given ΔJKL : ΔXYZ, find x.
A)10
B)12
C)16
D)20
Answer: 12
Step-by-step explanation:
Triangle JKL is dilated by a scale factor of 1.5 to get triangle XYZ. You can find this out by dividing 9 by 6, which will give you 1.5. To get the answer, you multiply 8 by 1.5 to get 12
ANSWER
EXPLANATION
We have that ΔJKL is similar to ΔXYZ.
The corresponding sides will therefore
be in the same proportion.
This implies that,
[tex] \frac{XY}{JK} = \frac{YZ}{KL} [/tex]
From the diagram,XY=9, JK=6, KL=8, and YZ=x.
We plug in the known values into the formula to get:
[tex] \frac{9}{6} = \frac{x}{8} [/tex]
Multiply both sides by 8
[tex] \frac{9}{6} \times 8=\frac{x}{8} \times 8[/tex]
[tex]12 = x[/tex]
The correct answer is B.
This graph shows the solution to which inequality?
[tex]m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{2-(-6)}{3-(-3)} \\ \\ m=\frac{8}{6} \\ \\ m=\frac{4}{3}[/tex]
The y-intercept of the graph is -2
The graph is shaded upwards, so we will be using the greater than symbol, but since the line is dotted we will not be using any of the "equal to" symbols.
Hence, the solution of the graph is [tex]y>m=\frac{4}{3} x-2[/tex]
Option: C is the correct answer.
C. [tex]y>\dfrac{4}{3}x-2[/tex]
Step-by-step explanation:By looking at the graph we observe that the line is dotted this means that the inequality will be strict.
Also, this line passes through the point (-3,-6) and (3,2).
Hence, the equation of line is calculated by using a two point form i.e. a line passing through two points (a,b) and(c,d) is calculated with the help of formula as:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here (a,b)=(-3,-6) and (c,d)=(3,2)
i.e.
[tex]y-(-6)=\dfrac{2-(-6)}{3-(-3)}\times (x-(-3)}\\\\i.e.\\\\y+6=\dfrac{2+6}{3+3}\times (x+3)\\\\i.e.\\\\y+6=\dfrac{8}{6}\times (x+3)\\\\i.e.\\\\y+6=\dfrac{4}{3}\times (x+3)\\\\i.e.\\\\y+6=\dfrac{4}{3}x+4\\\\i.e.\\\\y=\dfrac{4}{3}x-2[/tex]
Also, the shaded region is towards the origin.
Hence, the inequality is:
[tex]y>\dfrac{4}{3}x-2[/tex]
the hastings family drove 12/25 of the distance to yellowstone national park on the first day of their vacation. what percent of the distance to the park remained for them to drive?
Step-by-step explanation:
They drove 12 out of 25, so the remaining is 13/25. To convert to percent:
13 / 25 = x / 100
x = 52
52% of the distance remains.
please help
What is the slope of the line that is represented by the equation y−15=−6(x+7)?
Answer:
m = -6
Step-by-step explanation:
Put this given equation into slope-intercept form:
y−15=−6(x+7) becomes y - 15 = -6x - 42.
Adding 15 to both sides results in y = -6x - 27,
and so the slope is -6. The y-intercept is -27, or (0, -27).
Answer:
slope m = -6
Step-by-step explanation:
y−15=−6(x+7)
y =−6(x+7) + 15
y =−6x +7(-6) + 15
y =−6x -42 + 15
y =−6x - 27
THis is in slope intercept form where slope m = -6
A. Jenna wants to buy a new tablet computer. Top Quality, an electronics store, is selling them at a 15% discount off the list price.
Using t as the list price of the tablet, write two different expressions representing the discounted price.
B. Explain how each expression represents the discounted price.
C. While at Top Quality, Jenna sees a smartphone on sale for 14 off its list price. Her friend tells her to wait and buy it at Big Value, a discount chain, where the same phone is selling for only 75% of the list price.
Should Jenna buy the smartphone at Top Quality or Big Value? Support your answer with mathematical evidence. (Assume that getting the lowest price is Jenna's only consideration.)
Answer:
Step-by-step explanation:
Part A
Cost = T - (15/100) * T
Cost = (85/100)*T
Part B
You are asked to take 15% off the cost of something. The first equation is very clear how to do that -- just take 15% of T away from T
The second part is not so obvious if you are not familiar with it, but the result will be the same.
Start with the first equation
Cost = T - (15/100) T Change 1 T to 100 / 100
Cost = 100*T/100T - 15/100T
Cost = 85 /100 * T
Part C
Cost = Phone - 14 at Top quality. Red in Graph below
Cost = 75/100 * Phone at Big value. Blue in Graph belos
The graph below is a good way to answer this. I won't solve it algebraically when the graph will give you a much better idea which phone to get.
Answer: Up to a phone cost of 55 dollars, the red phone is the better buy.
After 55$ the blue phone is better.
Try this with a couple of values for phone,
ne height of Zak is 1.86 metres.
The height of Fred is 1.6 metres.
Write the height of Zak as a fraction of the height of Fred.
Give your answer in its simplest form.
To write the height of Zak as a fraction of the height of Fred, divide Zak's height by Fred's height and simplify the fraction to its simplest form.
Explanation:To write the height of Zak as a fraction of the height of Fred, divide Zak's height by Fred's height. Zak's height is 1.86 metres and Fred's height is 1.6 metres. So the fraction becomes 1.86/1.6.
To simplify this fraction, find the greatest common divisor (GCD) of 1.86 and 1.6, which is 0.02. Divide both the numerator and denominator of the fraction by the GCD to write the height as a fraction in its simplest form.
The simplified fraction is 93/80.
Learn more about fractions here:https://brainly.com/question/20592980
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During the spring and summer, a concession stand at a community Little League baseball game field sells soft drinks and other refreshments. To prepare for the season, the concession owner refers to the previous year’s files, in which he had recorded the daily soft drinks sales (in gallons) and the average daily temperature (in degrees Fahrenheit). Using the coordinates of the two points (84,80) and (74,65), determine the slope of the line of best fit.
Answer:
1.5
Step-by-step explanation:
m=80-65/84-74
=15/10
1.5
*Since this is an application problem, we can use decimals.*
Answer:
The slope of the line is 1.5
Step-by-step explanation:
To know the slope of a line we can have the equation or to know points of the line. In this case from the graph we have to points (84,80) and (74,65). Having this and using the equation to calculate the slope, we have:
[tex]m=\frac{y2-y1}{x2-x1} \\[/tex]
Defining:
[tex](x1=84,y1=80)[/tex] and [tex](x2=74,y2=65)[/tex]
Now using the equation:
[tex]m=\frac{65-80}{74-84}[/tex]
[tex]m=\frac{-15}{-10} \\m=\frac{15}{10} =1.5[/tex]
The slope of the line is 1.5