Answer:
The solved expression is [tex]x=3+\sqrt{2}[/tex] and [tex]x=3-\sqrt{2}[/tex]
Therefore [tex]x=3\pm\sqrt{2}[/tex]
Step-by-step explanation:
Given quadratic equation is [tex]x^2-6x+7=0[/tex]
To solve the given equation by using completing the square :
[tex]x^2-6x+7=0[/tex]
Rewritting the above equation as below :
[tex]x^2-6x+7+2-2=0[/tex]
[tex](x^2-6x+7+2)-2=0[/tex]
[tex](x^2-6x+9)-2=0[/tex]
[tex](x^2-6x+3^2)-2=0[/tex]
[tex](x^2-2(x)(3)+3^2)-2=0[/tex] ( it is of the form of [tex](a-b)^2=a^2-2ab+b^2[/tex] heere a=x and b=3 )
[tex](x-3)^2-2=0[/tex]
[tex](x-3)^2=2[/tex]
Taking square root on both sides we get
[tex]\sqrt{(x-3)^2}=\pm\sqrt{2}[/tex]
[tex]x-3=\pm\sqrt{2}[/tex]
[tex]x=\pm\sqrt{2}+3[/tex]
[tex]x=3\pm\sqrt{2}[/tex]
Therefore [tex]x=3+\sqrt{2}[/tex] and [tex]x=3-\sqrt{2}[/tex]
-10 + 5b = -35...I want to know the answer to this question pls...or else I will fail the 3rd quarter
Answer:
-5
Step-by-step explanation:
-10+5b=-35
5b=-35-(-10)
5b=-35+10
5b=-25
b=-25/5
b=-5
Find the value (1.2) power 3
Answer:
1.728 is the correct answer
????????????????????????
Answer:
Step-by-step explanation:
P(7) = No.of possibilities for getting 7/Total outcomes
=1/8
Answer:
1/8
Step-by-step explanation:
there is 8 "slices" and 1 7
A translation is shown on the grid below in which triangle A is the pre-image and triangle B is the image.
Which rule describes the x-coordinates in the translation?x+0
x+6
x-6
x+4
Answer:
x+6
Step-by-step explanation:
just took it on edge
x-6 is the rule which describes the x-coordinates in the translation
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Graph transformation is the process by which a graph is modified to give a variation of the proceeding graph.
Horizontally translating a graph is equivalent to shifting the base graph left or right in the direction of the x-axis.
In the given graph B is the image and A is the preimage.
The image B is shifted to left by six units.
x-6 is the rule which describes the x-coordinates in the translation
Hence, x-6 is the rule which describes the x-coordinates in the translation
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Write the following quadratic in standard form. Then identify a, b, and c.
y² - 7y + 6 = -6
Answer:
Therefore,
[tex]y^{2}-7y+12=0[/tex] ....Standard form.
[tex]a=1\\b=-7\\c=12[/tex] ......Numerical Coefficients.
Step-by-step explanation:
Given:
[tex]y^{2}-7y+6=-6[/tex]
To Find:
a ,b , c
Solution:
Quadratic:
A quadratic equation is an equation of the second degree.
Meaning it contains at least one term that is squared.
The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable.
Here it is given as
[tex]y^{2}-7y+6=-6[/tex]
Adding 6 on both the side we get
[tex]y^{2}-7y+6+6=-6+6[/tex]
[tex]y^{2}-7y+12=0[/tex]
Which is Quadratic Equation in STANDARD form Where,
[tex]a=1\\b=-7\\c=12[/tex]
Therefore,
[tex]y^{2}-7y+12=0[/tex] ....Standard form.
[tex]a=1\\b=-7\\c=12[/tex] ......Numerical Coefficients.
The graph shows the number of hours per day spent on social media by a group of teenagers and the number of hours per day spent exercising. A line of best fit for the data is shown.
A scatterplot is shown in the xy-plane. The horizontal axis is labeled as Social Media Hours Per Day and the vertical axis is labeled as Exercising Hours Per Day. The values on the horizontal axis range from 0 to 1.6 in increments of 0.2 and the values on the y-axis range from 0 to 2 in increments of 0.2. The line of best fit intersects the x-axis at a point just to the left of 1 decimal point 4 and y-axis at a point just below 1.1. Majority of the data points are concentrated between 0.3 and 0.6 on the horizontal axis and 0.6 and 0.9 on the vertical axis and two points are marked on the line.
Use the graph to determine how many hours a teenager would spend exercising in one day if they spent 0.25 hours on social media.
Use the graph to determine how many hours a teenager would spend exercising in one day if they spent 1.38 hours on social media.
Do you think the predictions from part (a) and part (b) are reliable? Explain your reasoning.
a)Exercise hour per day is 0.903
b) Exercise hour per day is 0.01573
c) The predicted values are closer to given data points.
What line of best fit?
The line of best fit is a straight line that minimizes the sum of squared differences between observed and predicted values.
From the graph we can find the line equation.
Social media hours per day/1.4 + Exercise hour per day/1.1 = 1
a) If 0.25 hours were spent on social media per day.
0.25/1.4 + Exercise hour per day/1.1 = 1
Exercise hour per day = (1 - (0.25/1.4))*1.1
Exercise hour per day = 0.8215*1.1
= 0.903
b) Social media hours per day/1.4 + Exercise hour per day/1.1 = 1
Given that 1.38 hours were spent on social media
1.38/1.4 + Exercise hour per day/1.1 = 1
Exercise hour per day/1.1 = 1 -(1.38/1.4))
Exercise hour per day = 0.0143*1.1
= 0.01573
c) The predictions from a) and b) are correct because the line almost fits the data points. The line on the data point is minimum error. The line gives the estimated values not the actual values. The predicted values are closer to given data points.
Complete question
The sum of 2 consecutive odd integers is 92. Find the numbers.
If x represents the smaller integer, then the larger integer is
Answer: If x is odd then x + 2 is going to be the next odd integer
Step-by-step explanation:
Set up the equation and solve.
x + x + 2 = 92 This is the equation. Collect like terms.
2x + 2 = 92 Subtract 2
2x = 90 divide by 2
x =45
x + 2 = 47
45 + 47 = 92.
So x + 2 is the next odd number after x.
Answer:
x + 2
Step-by-step explanation:
Rachel has a rope that is 5 meters long . She cuts away a piece that is 1.32 meters long . How long is the remaining piece
Determine whether a triangle with the given side lengths is a right triangle,
Side lengths
Right triangle
Not a right
triangle
Not enough
information
7, 24, 25
12, 16, 20
18. 32.40
4,7,8
To determine whether a triangle with given side lengths is a right triangle, we can use the Pythagorean theorem. If the sum of the squares of the two shorter sides equals the square of the longest side, then the triangle is a right triangle.
Explanation:To determine whether a triangle with given side lengths is a right triangle, we can use the Pythagorean theorem. According to the theorem, if the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse), then the triangle is a right triangle.
For the side lengths 7, 24, 25, we have 7² + 24² = 49 + 576 = 625, which is equal to 25². Therefore, this triangle is a right triangle.For the side lengths 12, 16, 20, we have 12² + 16² = 144 + 256 = 400, which is not equal to 20². Therefore, this triangle is not a right triangle.For the side lengths 18, 32, 40, we have 18² + 32² = 324 + 1024 = 1348, which is not equal to 40². Therefore, this triangle is not a right triangle.For the side lengths 4, 7, 8, we have 4² + 7² = 16 + 49 = 65, which is not equal to 8². Therefore, this triangle is not a right triangle.a number c increased 6 by is less than or equal to -26
Answer:
c ≤ - 32
Step-by-step explanation:
It will be less than or equal to - 26 if a number c is increased by 6.
Now, we have to solve the inequality for c.
The inequality is, c + 6 ≤ - 26
⇒ c + 6 - 6 ≤ - 26 - 6 {Subtracting 6 from both the sides}
⇒ c ≤ - 32
Therefore, the solution of the inequality is that c is less than or equal to - 32. (Answer)
Rachel has 3 times as many roses as carnations. She has 12 fewer carnations than daisies. There are 15 daisies. How many flowers does Rachel have in all
Answer:
27 flowers
Step-by-step explanation:
Let
x ----> the number of roses
y ----> the number of carnations
z ----> the number of daisies
we know that
[tex]x=3y[/tex] ----> equation A
[tex]y=z-12[/tex] -----> equation B
[tex]z=15[/tex] -----> equation C
substitute the value of z in equation B
[tex]y=15-12=3[/tex]
substitute the value of y in equation A
[tex]x=3(3)=9[/tex]
so
Rachel have 9 roses, 3 carnations and 15 daisies
In total
9+3+15=27 flowers
Rachel has 15 daisies, 3 carnations, and 9 roses, giving her a total of 27 flowers.
Let's break down the information provided:
Rachel has 3 times as many roses as carnations.She has 12 fewer carnations than daisies.There are 15 daisies.Step-by-Step Solution:
1. Start with the number of daisies: 15 daisies.
2. Rachel has 12 fewer carnations than daisies:
15 daisies - 12 = 3 carnations.
3. Rachel has 3 times as many roses as carnations:
3 carnations * 3 = 9 roses.
4. Add up all the flowers she has:
15 daisies + 3 carnations + 9 roses = 27 flowers in total.
Therefore, Rachel has a total of 27 flowers.
The ratio of the price of a tv to the price of a computer is 13:15 if the tv 400 dollars cheaper than the computer, how much does the computer cost.
The computer cost is $3000
Step-by-step explanation:
The given is:
The ratio of the price of a tv to the price of a computer is 13 : 15The tv 400 dollars cheaper than the computerWe need to find the cost of the computer
Assume that the price of the computer is $x
∵ The ratio between the prices of the tv and the computer is 13 : 15
∵ The price of the computer is $x
∵ The price of the tv 400 dollars cheaper than the computer
- That means the price of the tv is less than the price of the
computer by $400
∴ The price of the tv is $(x - 400)
By using the ratio method
→ tv : computer
→ 13 : 15
→ (x - 400) : x
By using the cross multiplication
∴ 15(x - 400) = 13(x)
- Simplify the left hand side
∴ 15x - 6000 = 13x
- Add 6000 to both sides
∴ 15x = 13x + 6000
- Subtract 13x from both sides
∴ 2x = 6000
- Divide both sides by 2
∴ x = 3000
The computer cost is $3000
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What is the constant of proportionality in the equation y = 3x?
constant of proportionality
Answer:
Step-by-step explanation:
y = mx + b
in this form, the constant of proportionality is also known as the slope....and it can be found in the m position
y = 3x.....is actually y = 3x + 0....so the slope (constant of proportionality is gonna be 3
Answer:
the constant proportionality it gonna be 3
Step-by-step explanation:
the starting equation is y=mx+b
plug in the numbers and get your answer
my photo math said it is x = 0 lol
guy is pouring a new patio for his house.
He rents a concrete mixer for $50 per day plus $12.50 per hour. If he is charged $143.75, how long did guy have the concrete mixer?
Answer:
Step-by-step explanation:
50 + 12.50h = 143.75....where h = # of hrs
12.50h = 143.75 - 50
12.50h = 93.75
h = 93.75 / 12.50
h = 7.5 (or 7 1/2) hrs <====
Find the slope and the equation for the line passing through the point (−5,−0.75)(−5,−0.75) with x-intercept at x=−6
Answer:
Slope is -0.75
Step-by-step explanation:
When calculating slope you can use the formula [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex] to find the slope. In this case that formula is using the 2 points (-5, -0.75) and (-6, 0). When those points are put in the equation becomes [tex]\frac{0+0.75}{-6+5}=\frac{0.75}{-1}=-0.75[/tex]. This means that the slope is -0.75.
What is the length of a rectangle when the length of the rectangle is 2(x+1) meters and the perimeter is 60 meters
Step-by-step explanation:
Given,
The length of a rectangle(l) = 2(x + 1) meters and
The perimeter of a rectangle = 60 meters
To find, the width of a rectangle(b) = ?
We know that,
The perimeter of a rectangle = 2(l + b)
⇒ 2(2(x + 1) + b) = 60
⇒ 2(x + 1) + b =[tex]\dfrac{60}{2} =30[/tex]
⇒ b = 30 - 2(x + 1)
⇒ b = 30 - 2x - 2
⇒ b = 28 - 2x
⇒ b = 2(14 - x)
∴ The width of a rectangle(b) = 2(14 - x)
Hence, the width of a rectangle(b) = 2(14 - x)
Help me please I need to know the answer to this question in under an hour :-)
Answer:
7/15
Step-by-step explanation:
You can put in your graphing calculator if you have one
Answer:
Step-by-step explanation:
36(1/3)^n-1 first five term of the sequence
Answer:
Step-by-step explanation:
first term: put n = 1
36(1/3)^n-1 = 36(1/3)^1-1 =12 - 1 = 11
2nd term: put n = 2
36(1/3)^n-1 = 36(1/3)^2-1 = 19.784
3rd term: put n = 3
36(1/3)^n-1 = 36(1/3)^3-1 = 0.3333
4th term: put n = 4
36(1/3)^n-1 = 36(1/3)^4-1 = -0.5555
5th term: put n = 5
36(1/3)^n-1 = 36(1/3)^5-1 =-0.85185
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Damian rides his bike 38 miles each week for 15 weeks.
How many total miles does he ride in 15 weeks?
Enter your answer in the box.
____ miles
Answer:
570 miles in 15 weeks
Step-by-step explanation:
trust me
Answer:
570
Step-by-step explanation:
because 38 miles x 15 weeks is 570 miles
Your $54200 2 year car loan is at 15.1% compounded annually. What will you have paid for your car after 2 years?
To find the total amount paid for the car after 2 years, we use the compound interest formula [tex]A = P(1 + r)^n[/tex], where P is the initial loan amount, r is the interest rate, and n is the number of years. Substitute in the given values to calculate the final amount.
Explanation:To calculate the total amount paid for the car after 2 years, we apply the formula for compound interest. The formula is[tex]A = P(1 + r)^n[/tex], where A is the final amount, P is the principal (or initial amount), r is the interest rate, and n is the number of periods. In this case, P = $54200, r = 15.1% or 0.151, and n = 2.
Plugging these values into the formula:
[tex]A = $54200 * (1 + 0.151)^2[/tex].
Once you solve the equation, you will find the total amount paid for the car after 2 years.
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Final answer:
Using the compound interest formula, you will have paid $71,787.31 for a $54,200 car loan at 15.1% interest compounded annually after 2 years.
Explanation:
To calculate the total amount paid for a car after 2 years on a loan of $54,200 with an interest rate of 15.1% compounded annually, we'll use the formula for compound interest:
[tex]A = P (1 + r/n)^{(nt)}[/tex]
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money)r is the annual interest rate (decimal)n is the number of times that interest is compounded per yeart is the time in yearsFor this car loan:
P = $54,200r = 15.1% = 0.151n = 1 (since interest is compounded annually)t = 2 yearsSubstitute the values into the formula:
A = $54,200 (1 + 0.151/1)^(1*2)
A = $54,200 (1 + 0.151)^2
A = $54,200 (1.151)^2
Calculate the amount:
A = $54,200 * (1.151)^2
A = $54,200 * 1.324301
A = $71,787.31
After 2 years, you will have paid $71,787.31 for your car.
(a) Write 389% as a decimal.
(b) Write 0.005 as a percentage.
Answer:
a)3.89 b)0.5%
Step-by-step explanation:
389%= 389/100
0.005*100%
=0.5%
Consecutive odd integers of 201
Question :
The sum of three consecutive odd integers is 201. Find the integers.
Answer:
The Integers are 65,67,69.
Step-by-step explanation:
Let x be any number. when it is multiplied by 2 it becomes an even number.
So, 2x is an even number. Now adding an odd number to 2x , it becomes an odd number
so
First odd number be 2x+1
Second odd number be 2x+3
Third odd number be 2x+5
Now the sum of these three odd number gives 210,
That is
(2x+1) +(2x+3) +(2x+5) = 201
2x+1+2x+3+2x+5 =201
6x + 9 = 201
6x = 201- 9
6x = 192
[tex]x =\frac{192}{6}[/tex]
x = 32
Hence
The first odd number is (2x+1) = (2(32)+1) = 64+1 =65
The second odd number is (2x+3) = (2(32)+3) = 64+3 =67
The third odd number is (2x+1) = (2(32)+5) = 64+5 =69
If y = 2x2 – 4x, what is the value of y when x equals 5.
A.10
B.30
C.80
D.480
Answer:
The value of y in the given equation is B. 30.
Step-by-step explanation:
y = 2x² - 4x x = 5
y = 2(5)² - 4(5) Plug 5 in for x
y = 2(25) - 20 Square 5 and multiply 4 by 5
y = 50 - 20 Multiply 2 by 25
y = 30
Hope this helps,
❤A.W.E.S.W.A.N.❤
3(x-2)=5x+8 ; solve for x
Answer:
see attached picture please
Answer:
3x² -- 5x -- 8
Step-by-step explanation:
For a polynomial of the form
a
x
2
+
b
x
+
c
, rewrite the middle term as a sum of two terms whose product is
a
⋅
c
=
3
⋅
−
8
=
−
24
and whose sum is
b
=
−
5
.
Tap for fewer steps...
Factor
−
5
out of
−
5
x
.
3
x
2
−
5
(
x
)
−
8
Rewrite
−
5
as
−
8
plus
3
3
x
2
+
(
−
8
+
3
)
x
−
8
Apply the distributive property.
3
x
2
−
8
x
+
3
x
−
8
Factor out the greatest common factor from each group.
x
(
3
x
−
8
)
+
1
(
3
x
−
8
)
Factor the polynomial by factoring out the greatest common factor,
3
x
−
8
.
(
3
x
−
8
)
(
x
+
1
)
A nurse must mix a 20% solution of medication in an existing container of water. The container currently holds 12 ounces of water how many ounces of medication should the nurse add to make the proper solution?
Answer:
3 ounces of medication to be added to get 20%solution of medication
Step-by-step explanation:
To find:
The amount of medication to be added to 12 ounces of water to get a 20% solution
Let the amount of medication to be added =x
So total amount of mixture = amount of water + amount of medication
= 12+x
% medication = (amount of medication÷total amount of the mixture)× 100
Therefore
% medication =( x÷12+x)×100
20 =( x÷12+x)×100
[tex]20 =\frac{x}{12+x}[/tex] X 100
20(12+x) =100x
240+20x =100x
100x-20x =240
80x =240
x =240÷80
x=3
so 3 ounces of medication to be added to get 20%solution of medication
James is planning on driving his car to the family reunion. The distance to the
meeting place is 892 miles. If his car gets 29 mpg, how many gallons of gas
will he need?
A. 42.7
O B. 38.9
O C. 36.1
O D. 30.8
Answer:
"D" (and any subsequent words)
Step-by-step explanation:
Answer:
its D
Step-by-step explanation:
Help giving brainliest
Answer:
i think 2m
Step-by-step explanation:
3 plus 3 is 6 minus 8
What is the probability that she draws a card less than 5
Answer:
Number of favourable outcomes i.e. ‘a card of diamond’ is 13 out of 52 cards. Therefore, probability of getting ‘a card of diamond’ Number of favorable outcomes P(D) = Total number of possible outcome = 13/52 = 1/4 (v) a king or a queen. Total number of king is 4 out of 52 cards. Total number of queen is 4 out of 52 cards
Step-by-step explanation:
Answer:
4/13
Step-by-step explanation:
16/52 = 4/13
A model of an airplane has a length of 2.5 feet. If the scale used to create the model was 1 foot = 250 feet, what is the actual length of the airplane?
Answer:
Step-by-step explanation:
1 ft = 250 feet....so 2.5 ft = (2.5 * 250) = 625 feet <==
The actual length of airplane using the scale factor is; 625 feet.
What is the scale factor?The scale factor states the scale or measurement by which a figure is bigger or smaller than the other figure. The size by which the figure would be reduced or enlarged is called its scale factor.
We are given that;
Length of Airplane = 2.5 feet
Now, we want to find the actual length of the airplane with a scaled length of 2.5 feet.
1 foot = 250 feet,
Thus, the actual length of airplane= (2.5 x 250)
the actual length of airplane= 625 ft
Hence, The actual length of airplane using the scale factor is; 625 feet.
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Tully ran 7\10 mile and Maggie ran 3\5 mile who ran farther explain
Answer:
Tully ran farther
Step-by-step explanation:
tully maggie
7/10 | 3/5
find the LCD. the LCD is 10.
7/10 | 3x2/5x2
7/10 | 6/10