Answers
a) y-intercept
The y-intercept is the point where it crosses the y axis so x would 0.
So putting in 0 for x:
y = x^2 - 8x + 7
y = 0^2 - 8(0) + 7
y = 0 - 0 + 7
y = 7
The y intercept is at the point (0,7).
b)
The zeroes are the points where it crosses the x axis so it’s when the y is set to 0.
0 = x^2 - 8x + 7
Since it’s a quadratic equation we have to factor it. We fill in 2 numbers that add to -8 and multiplied to equal 7.
(x +____)(x+ ____)
The 2 numbers are 7 and -1 because -1*-7=7 and -7+(-1)=-8. So:
0 = (x-7)(x-1)
So now we have x-7 and x-1 equaling some quantity. If either of those happens to equal zero, it makes the whole equation 0, because (x-7)0=0 and 0(x-1)=0
So we can set each of it separately to 0 to solve for x.
x-7=0
x= 7
x-1=0
x= 1
The zeroes are at the points (1, 0) and (7, 0)
C.
The Vertex Form of a Quadratic is:
y = a(x-h)^2 + k. And the vertex is (h, k)
y = x^2 - 8x + 7
y - 7 = x^2 - 8x
We want to complete the square by adding some number to both sides of the equation so that when we factor it we are going to get (x-a)(x-a).
So take half of 8 to get two equal numbers that would be our “a”. 8/2=4 so we want (x - 4)(x- 4).
(x-4)(x-4) multiplies out to x^2 - 8 + 16.
continuing,
y - 7 = x^2 - 8x
Add 16 to both sides.
y - 7 + 16 = x^2 - 8x + 16
y + 9 = (x-4)(x-4)
y + 9 = (x-4)^2
y = (x-4)^2 - 9 is the vertex form.
The vertex is at the point (4, -9). So the axis of symmetry is at the line x = 4.
D. The vertex is solved in C as the point (-4, -9).
Related Questions
which is greater? -1 17/20 or -1 8/10PLSSS HELP ASAPplsss show work aswell
Answers
8 * 2 = 16
10 * 2 = 20
New fraction: 16/20
-1 17/20 vs. - 1 16/20
-1 16/20 (-1 8/10) is greater. (For negative numbers, you can tell which one is greater by determining which one is closest to zero.)
The product of four and a number C is decreased by five?
Answers
Divide. Express your answer in simplest form. 2 1/2 ÷ 2 1/6
13/15 5 5/12 26/30 1 2/13
Answers
Answer:
[tex] \frac{15}{13} = 1 \frac{2}{13} [/tex]
Step-by-step explanation:
[tex]2 \frac{1}{2} \div 2 \frac{1}{6} \\ \\ \\ \frac{5}{2} \div \frac{13}{6} \\ \\ \\ \frac{5}{2} \times \frac{6}{13} \\ \\ \\ \frac{5}{1} \times \frac{3}{13} \\ \\ \\ = \frac{15}{13} \\ \\ \\ = 1\frac{2}{13} [/tex]
I hope I helped you^_^
Answer:
[tex]2 \frac{1}{2} /2 \frac{1}{6} = \frac{5}{2} / \frac{13}{6} [/tex]
[tex] = \frac{5}{2} \times \frac{6}{13 } = \frac{5 \times 6}{2 \times 13} [/tex]
[tex] = \frac{5 \times 3}{1 \times 13} [/tex]
[tex] = \frac{15}{13} [/tex]
[tex] = 1 \frac{2}{13} [/tex]
Step-by-step explanation:
Thank you!!!!!!!!!!!
What is the value of the expression3+3⋅72−9⋅103+3⋅72−9⋅10 ?
Answers
-7.763 will be the total to the answer.
20 POINTS !!!!!!!!!
Solve the quadratic equation by completing the square.
x^2 - 18x + 68 = 0
First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Answers
Answer:
x = x = 9 ±[tex]\sqrt{13}[/tex] or x ≈ 12.61 or x ≈ 5.39
Step-by-step explanation:
x² - 18x + 68 Solve by completing the square.
x² - 18x = - 68
Now complete the square and add that number to both sides of the equation.
1/2 (of the coefficient of the x term)² = (1/2 · -18)² = 81 .
x² - 18x + 81 = -68 + 81
(x - 9) (x - 9) = 13 Now find the square root of both sides
[tex]\sqrt{(x - 9)(x - 9)}[/tex] =[tex]\sqrt{13}[/tex] Solve
x - 9 = ±[tex]\sqrt{13}[/tex] Solve for x
x = 9 ±[tex]\sqrt{13}[/tex]
x = 9 + [tex]\sqrt{13}[/tex] or x = 9 - [tex]\sqrt{13}[/tex]
x ≈ 12.61 or x ≈ x 5.39
At a school dance, the ratio of girls to boys is 8:3. If there are 528 students at the dance, how many are boys and how many are girls?
Answers
Answer:
144 boys and 384 girls
Step-by-step explanation:
8 girls to every 3 boys. You can make an equation to solve this: 8x + 3x = 528. 528 = 11x. Then divide 528 by 11 to get 48. x=48. 8(48) = 384 girls. 3(48) = 144 boys.
Hooke’s Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 180 newtons stretches a spring 5 cm, how much will a force of 270 newtons stretch the same spring?
Answers
Answer:
7.5m
Step-by-step explanation:
Set up a proportion and cross multiply to find the unknown
Hope this helps
The elongation of spring by 170 newtons force maintaining the given ratio is 7.5 cm.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given question,
Elongation of spring in 180 newtons = 5 cm
The ratio of elongation to force applied = 5/180
The force the second time is 270 newtons.
Let's say the elongation at this time is x cm.
The ratio of elongation to force applied = x/270
Both ratios must be the same.
Therefore, x/270 = 5/180
x = 270/36 = 7.5 cm
Hence "The elongation of spring by 170 newtons force maintaining the given ratio is 7.5 cm".
For more information about ratios and proportions,
brainly.com/question/26974513
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Jenna is having her birthday party at the ice cream palace. The ice cream party palace charged 2.49 for each ice cream cone and 24.99 for a birthday cake Jenna decides to buy a birthday cake and an ice cream cone for each of her friends. Jenna needs to determine the total cost for her birthday party.
Answers
Answer:
multiply the cost of the ice cream cones by the amount of friends then add the cost of the birthday cake.
example: (2.49 × n) + 24.99 = a
I would give you an answer but I dont have enough information, I'm sorry for the inconvenience.
Which division sentence is represented by the model?
Number Line
6÷69=9
19÷6=23
19÷23=6
Answers
The modal represent the division is 6 ÷ 6/9 = 9.
What is division?One of the most fundamental operations in arithmetic is division, in which a larger number is divided into smaller groups with the same number of items. Dividing a large group into smaller groups so that each group has the same number of items is called division. In math, it is an operation that equalizes sharing and grouping.
Given the number line in figure,
shows the number is divided in 9 equal parts
1/9, 2/9, 3/9, ..........9/9
and from 0 to 6/9 parts are marked,
there are 6 parts in 0 to 6/9
the division model for equation is
6 ÷ 6/9
and division is 6 ÷ 6/9 = 9
Hence the division sentence is represented by the model is 6 ÷ 6/9 = 9.
Learn more about division;
https://brainly.com/question/2273245
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The question is incomplete, complete question is attested in image
ΔABC is similar to ΔDEF. The length of segment AC is 12 cm. The length of segment BC is 18 cm. The length of segment DF is 10 cm.
What is the length of segment EF?
Question 1 options:
15
14
10
9
Answers
Answer:
It's 15
i took the test
Step-by-step explanation:
√80+√20 find it ......
Answers
Answer:
Approximately 13.41
Step-by-step explanation:
First do square root of each, which is finding what number multiplies by its self to get the number.
For example: The square root of 80 is approximately 8.94, and the square root of 20 is approximately 4.47.
So: 8.94 + 4.47 = 13.41 (Add normally, but remember to put the decimal in the right place).
Hope this helped :)
I need help!!! Can you figure this out?
Answers
Answer:
128 degrees
Step-by-step explanation:
38+90=128
Plzzz help!! just atleast look at my question!! plzz I really need help!
Answers
no
Step-by-step explanation:
-2 - -3 doesn't equal -5
Answer:
no
Step-by-step explanation:
-2 - -3 = 1 not 5
A drill press operator requires 1 2/3 minutes to drill through 1 inch of steel. How long will it take him to drill through four-fifths inch of the same steel?
Answers
Answer: It will take him 1.3
Step-by-step explanation:
1 2/3 divided by 5 is 0.333
0.333 times 4 is 1.3
-9 + ( -16) =
( -4) – (-6) + (-5) – (8) =
( 3) – (-9) + (-3) – (-2) =
- ( 5) – (-7) + (-8) =
- ( -8) – (-9) + (-4) – (-1) =
( -5) – (-11) + (10) – (8) =
( -1) – (-2) + (-3) – (-6) =
( -4) – ( 4) – (6) + (-5) – (-8) =
(-6) + (-5) – (-8) =
Answers
Answer:
-9 + ( -16) = -25
( -4) – (-6) + (-5) – (8) =-11
( 3) – (-9) + (-3) – (-2) =11
- ( 5) – (-7) + (-8) =-6
- ( -8) – (-9) + (-4) – (-1) =14
( -5) – (-11) + (10) – (8) =8
( -1) – (-2) + (-3) – (-6) =4
( -4) – ( 4) – (6) + (-5) – (-8) =-11
(-6) + (-5) – (-8) =-3
Step-by-step explanation:
Hope it helps
Answers:
-9 + ( -16) = -25
( -4) – (-6) + (-5) – (8) = -11
( 3) – (-9) + (-3) – (-2) = 11
- ( 5) – (-7) + (-8) = -6
- ( -8) – (-9) + (-4) – (-1) = 14
( -5) – (-11) + (10) – (8) = 8
( -1) – (-2) + (-3) – (-6) = 4
( -4) – ( 4) – (6) + (-5) – (-8) = -11
(-6) + (-5) – (-8) = -3
Find the missing side of each triangle. Round your answers to the nearest tenth if necessary. (Please Show)
Answers
7249jwnsnjdkwlskjeiwiwo1ñwlld
Answer:
I think it's about 15 to 22.
Step-by-step explanation: So first I checked the length for the unknown number and I added the 12 and 10 together but that didn't work and so i'm just estimating the number for x yo.
Sorry if I didn't helped you yo.
HELP ASAP!! Im being timed!!
Answers
Answer:
im pretty sure its a
Step-by-step explanation:
3x(6x + 5)
4x(2x-3y)
Answers
Step-by-step explanation:
1) 3x(6x+5)
= 18x+15x
= 33x Answer
2) 4x(2x-3y)
= 8x-12xy Answer
Cannot be solved because it has unlike terms
Which graph shows the solution to this system of inequalities? y ≤ x + 1 y > -3x – 2
Answers
x - 4 < 4y
1/4x -1
it is y > so the area is above the line y = 1/4x -1 so D is not right
second one
y < x + 1
a video store is selling previously owned dvds for 40% off the regular price of $15. what is the sale price of the dvds.
Answers
Answer:
$9
Step-by-step explanation:
A video store is selling previously owned DVDs for 40% off the regular price of $15. What is the sale price of the DVDs?
40% = 0.4
15 * 0.4 = $6 (Discount)
15 - 6 = $9 (Sale Price)
Therefore the Answer is: $9
Simplify.
15 20 24+20
Answers
Answer:
-5 divide by 28
Step-by-step explanation:
so the question supposed be " 15-20 divided by 2(4) + 20
15-20 which is also 15 + (-20)= -5
2(4)=8, 8+20=28
so it can simplify into -5 / 28
(hope it helps :)
Can someone pls help me
Answers
Answer:
I'm not sure, but I'll try
Step-by-step explanation:
(Side)^2 = (Hypotenuse)^2 - (Side)^2
(Side)^2 = (9)^2 - ( √ 65 )^2
(Side)^2 = (81) - (65)
(Side)^2 = 16
Take root of answer
Side = √16
Side = 4
Answer = 4
_________
[tex] \: [/tex]
a² = c² - b²
a² = 9² - (√65)²
a² = 81 - 65
a² = 16
a = √16
a = 4
The equation y=2x+3 represents the cost y (in dollars) of mailing a package that weighs x pounds. a. Graph the equation. b. Using the graph, which is the best estimate for the cost to mail the package?
a. Graph the equation.
b. Using the graph, which is the best estimate for the cost to mail the package?
the packedge is 1.126 lb
c. Use the equation to find how much it costs to mail the package.
Answers
Answer:
B. Slightly more than $5
Step-by-step explanation:
y = 2x + 3
Firstly we check variables to make sure we understand.
y = dollars
x = pounds
On the scale, it says 1.126 lb. Which means 1.126 pounds.
And so, x = 1.126
y = 2x + 3
y = 2(1.126) + 3
y = 2.252 + 3
y = 2.252
The graph for part a and park b. It is underneath. I wrote 1.1, because it is rounded down from 1.126 lb, which is part b. The one with one line and no dots is part a.
Hi plz answer this I'll give u more points if u do
Answers
Answer:
6 feet in the distance
Step-by-step explanation:
t^(5)-10t+1=0 find the answer (≈)
Answers
Answer:
t: -1.80244705, 0.100001, 1.75234772
2
Rearrange terms
3
Subtract
6
6
6
from both sides of the equation
4
Simplify
5
Divide both sides of the equation by the same term
6
Simplify
answer pls 8 + 40 ÷ (10 × 2)
Answers
Answer:
10
8+40÷20=8+2=10
,.,.......
Is each number correctly expressed in scientific notation? Choose Yes or No.
Number Scientific Notation
4,836,000,000 4.836 × 106
Choose...
0.0000005812 5.812 × 10–7
Choose...
546,000,000,000 5.46 × 1011
Choose...
Answers
Answer:
NoYesYesStep-by-step explanation:
The first one is incorrect because would be 4,836,000 instead of 4,836,000,000. The correct notion would be [tex]4.836*10^9[/tex]
5%x52?524526235+36285
Answers
Answer:
The answer is 7,878,684,378
LOL
Step-by-step explanation:
Find the domain and range of the function
Answers
Step-by-step explanation:
using set notation
domain [-3,3]
range[-1,3]
what is the circumference of a circle that has a diameter of 15m?
a.) 47.1m
b.) 23.55m
c.) 94.2m
d.) 50.3m
Answers
Answer:
47.1
Step-by-step explanation:
c=pie d
c=3.14×15
47.1
Answer:
Step-by-step explanation:
So, as you know u got a the diameter.
-Given:
d = 15.
circle (Pi) = 3,14159265359 (But we use always 3.14)
Find: we need to find circumference.
C=Pi * d = 3,14 * 15 = 47,1m.
I hope this answers your question, sir.