Answers
Answer:
y-intercept = (0, 8)
x-intercepts = (4, 0) and (-2, 0)
vertex = (1, 9)
5th point = (2, 8)
Step-by-step explanation:
As the coefficient of x² is negative, the curve will be "n" shaped.
y-intercept
crosses the y-axis when x = 0
substitute x = 0 into the function and solve for y:
[tex]\implies y=-(0)^2+(2 \times 0)+8=8[/tex]
Therefore, y-intercept = (0, 8)
x-intercept
crosses the x-axis when y = 0
set the function to zero and solve for x:
[tex]\implies -x^2+2x+8=0[/tex]
[tex]\implies x^2-2x-8=0[/tex]
[tex]\implies (x-4)(x+2)=0[/tex]
[tex]\implies x=4, x=-2[/tex]
Therefore, x-intercepts = (4, 0) and (-2, 0)
vertex
vertex form: [tex]y=a(x-h)^2 +k[/tex], where (h, k) is the vertex
expand vertex equation: [tex]y=ax^2 -2ahx+ah^2 +k[/tex]
compare coefficients with original function: [tex]y=-x^2+2x+8[/tex]
[tex]\implies a=-1, h=1, k=9[/tex]
So vertex = (1, 9)
5th plot point
You can choose any value of x and input it into the equation for y, but for symmetry, I have chosen to find the other value of x (aside x = 0) when y = 8
[tex]\implies -x^2+2x+8=8[/tex]
[tex]\implies -x^2+2x=0[/tex]
[tex]\implies x^2-2x=0[/tex]
[tex]\implies x(x-2)=0[/tex]
[tex]\implies x=0, x=2[/tex]
5th point = (2, 8)
Related Questions
In the equation above, a is a constant. If the equation has the solutions x = -2 and 3 =
a
what is the value of a?
Answers
Answer:
a = 2
Step-by-step explanation:
ax² + 5x + 2 = 0
a ( - 2 )² +5 ( - 2 ) + 2 = 0
4a = 8
a = 2
x + y =7 What is the answer show your work
Answers
Answer:
x = 3y = 4.There are infinite solutions. I'll just give you this solution.Step-by-step explanation:
Given equation:
x + y = 7Solve for variables:
7 - x = y7 - 3 = 47 - y = x7 - 4 = 3.Answers:
x = 3y = 4.Riley’s Rug Warehouse purchases rugs from the manufacturer for $82.00 each. The manager marks the rugs up 150% and then includes a 10% sales tax. How much does a customer pay for 1 rug? (I ALREADY KNOW THE ANSWER. BUT I NEED THE WORK FOR THE ANSWER TO SHOW MY TEACHER) (the answer is $225.50)
Answers
82+82*1.5=205
205+205*0.1=$225.50
i need help 30 pionts if u help me!!!!
Answers
As so 2 x 9.6 x 10= 192
please help me to solve this problem
Answers
Answer:
1/x+2
Step-by-step explanation:
1/x−2 + 4/4-X^2
Factor 4−x^2
1/x−2 + 4/(x−2)(−x−2)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x−2 and (x−2)(−x−2) is (x−2)(−x−2).
Multiply : 1/x−2 TIMES −x−2/−x−2
−x−2/(x−2)(−x−2) + 4/(x−2)(−x−2)
Since −x−2/(x−2)(−x−2) and 4/(x−2)(−x−2) have the same denominator, add them by adding their numerators.
−x−2+4/(x−2)(−x−2)
Combine like terms in −x−2+4.
−x+2/(x−2)(−x−2)
Extract the negative sign in −x+2.
−(x−2)/(x−2)(−x−2)
Cancel out x−2 in both numerator and denominator.
1/X-2
Question 6 of 10
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
10
(-4, 8)
(0,0)
-10
10
10
0
A. y = 1/2 x
B. y = 4x
0
y
c. y = - 1/2 x
D. y
E. y = 2x
F. V = -2
Answers
Answer:
Y=-2X
Step-by-step explanation:
The equation of the line that passes through points (0, 0) and (-4, 8) is
y = -2x.
Option F is the correct answer.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
To find the equation of a line given two points, we can use the point-slope form of the equation of a line:
[tex]y - y_1 = m(x - x_1)[/tex]
where m is the slope of the line and (x_1, y_1) are the coordinates of one of the points on the line.
Given the coordinates (0, 0) and (-4, 8), we can find the slope of the line:
[tex]m = (y_2 - y_1) / (x_2 - x_1)[/tex]
= (8 - 0) / (-4 - 0)
= -2
Now that we have the slope of the line, we can choose one of the points to plug into the point-slope form.
Let's use (0, 0):
[tex]y - y_1 = m(x - x_1)\\y - 0 = -2(x - 0)\\y = -2x[/tex]
Therefore,
The equation of the line that passes through points (0, 0) and (-4, 8) is
y = -2x.
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6 x 2 7 x 2 8 x 2 3 x 3
Answers
[tex]6 \times 27 \times 28 \times 23 \times 3 = 312984[/tex]
Answer:
312984
Step-by-step explanation:
To solve the equation 6 x 27 x 28 x 23 x 3, you can follow these steps:
Start by multiplying the first two numbers: 6 x 27 = 162.
Then multiply the result by the next number: 162 x 28 = 4536.
Continue multiplying by the next number: 4536 x 23 = 104328.
Finally, multiply by the last number: 104328 x 3 = 312984.
The final result is 312984
The expression 17n + 11 represents the perimeter of the triangle.
Answers
Answer:
8n
Step-by-step explanation:
The third side of a triangle whose perimeter is 17n + 11 and the other two sides are (5n + 6) and (4n + 6) is 8n
A pool manager balances the pH level of a pool. The price of a bucket of chlorine tablets is $90, and the price of a pH test kit is $11. The manager uses a coupon that applies a 40% discount to the total cost of the two items. How much money does the pool manager pay for each item?
Answers
Answer:
The pool manager pay for each item is $60.6.
Step-by-step explanation:
Given:
A pool manager balances the ph level of a pool.
The price of a bucket of chlorine tablets is $90, and the price of a ph test kit is $11.
The manager uses a coupon that applies a 40% discount to the total cost of the two items.
Now, to find the money the pool manager pay for each item.
The price of a bucket of chlorine tablets is = $90.
The price of a ph test kit = $11.
So, to get the total price of both items we add both prices:
Total cost of two items = $101.
As, given a coupon that applies a 40% discount to the total cost of the two items.
Now, to get the total cost by applying discount:
Thus, the pool manager pay = $60.6.
Therefore, the pool manager pay for each item is $60.6.
Which polynomial is represented by the algebra tiles? 2x2 – 4x – 6 2x2 4x 6 –2x2 – 4x – 6 –2x2 4x 6.
Answers
Polynomials consist of both indeterminates and coefficients. The polynomial that is been represented by the algebra tiles is 2x²-4x -6.
What are polynomials?A polynomial consists of both indeterminates and coefficients and involves mathematical operations such as addition, subtraction, multiplication, and division.
In order to find the polynomial that is been represented by the tiles, we will simply, calculate the number of tiles for each variable,
As we can see in the image,
Number of tiles labeled as x² = 2
Number of tiles labeled as -x = 4
Number of tiles labeled '-' = 6
therefore, the polynomial can be written as 2x²-4x -6.
Hence, the polynomial that is been represented by the algebra tiles is 2x²-4x -6.
Learn more about Polynomials:
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Answer:
A. 2x2 – 4x – 6
Step-by-step explanation:
the volume of this sphere is 500pi/3 cubic inches. what's it's radius
Answers
Answer:
[tex]r= 5in[/tex]
Step-by-step explanation:
[tex]\frac{500\pi }{3} =\frac{4}{3} \pi *r^{3} \\r^{3} =\frac{500}{3} *\frac{3}{4} \\r^{3}=125\\r= 5 in[/tex]
{ Bring the number into the equation }
True or false: The function shown is not discrete because the domain is a finite set.
Answers
Answer:
false
Step-by-step explanation:
the domain can be discrete or continuous
a 65 foot ladder is leaning against a well. Its lower end is 25 feet away from the wall. How much farther away will it be if upper end is moved down 8 feet?
Answers
=====================================================
Explanation:
Check out the diagrams below.
We'll start with the left diagram (marked "before") which is a right triangle with the horizontal leg of 25 feet and hypotenuse 65 feet.
Use the pythagorean theorem to find the vertical side x.
a^2 + b^2 = c^2
25^2 + x^2 = 65^2
625 + x^2 = 4225
x^2 = 4225 - 625
x^2 = 3600
x = sqrt(3600)
x = 60
The top of the ladder is 60 feet high when placed against the wall in this configuration.
------------------
If the upper end is moved down 8 feet, then x-8 = 60-8 = 52 feet is the new height of the ladder. Refer to the "after" in the diagram below.
Like earlier, we'll use the pythagorean theorem to find the missing side.
a^2 + b^2 = c^2
y^2 + 52^2 = 65^2
y^2 + 2704 = 4225
y^2 = 4225 - 2704
y^2 = 1521
y = sqrt(1521)
y = 39
The horizontal distance from the ladder base to the wall is now 39 feet.
Earlier it was 25 feet, so it has increased by 39-25 = 14 feet.
Mckenzie has been saving her earnings from mowing the
neighborhood lawns. She has 22 dollars and wants to spend it
all on games. If each game costs 3 dollars, how many can
Mckenzie buy?
Answers
Answer:
7 games
Step-by-step explanation:
22 / 3 =
7.33
Mckenzie can buy 7 games
How do you find the maximum height of an object with only time
We have the formula h = 16t^2 - 80t
if you solve it you get 5 seconds for the time it is in the air. how do you find the maximum height from this
Answers
6000
Step-by-step explanation:
[tex]16t ^{2} - 80t[/tex]
substitute t to 5(seconds)
[tex]16(5) ^{2} - 80(5) \\ 6400 - 400 \\ = 6000[/tex]
What is 1942 divided by 33
Answers
Answer: 58.84
Step-by-step explanation: If you use a calculator that's the nroken down part.
500+6 (3+1)+(8-5) 3-2 (5+4)
Answers
Answer:
551
Step-by-step explanation:
500+6(4)+3(1)(5+4)
500+24+3(9)
524+27
551
Brainliest is much appreciated
Answer:
515, just evaluated it
2 of 10
Find the area of this semi-circle with radius, r = 95cm.
Give your answer rounded to 1 DP.
rcm
The diagram is not drawn to scale.
cm2
Answers
Solving steps:
*calculate area of the circle:
A = 9025 ∏
* Round A = 9025 ∏ to the required place:
A = 28352.9
I hope this helps you :)
Last Saturday, Ben and Dominic set up a lemonade stand to help their grandmother use
the lemons from her trees. They used 2 lemons for each cup of lemonade. By the end of the
day, the boys had sold 21 pitchers of lemonade. If each pitcher held 9 cups, how many
lemons did Ben and Dominic use?
Answers
Answer:
378 Lemons
Step-by-step explanation:
Because you use 2 lemons for every cup, you first need to find how many lemons per pitcher by multiplying 9 by 2 to get 18, so 18 lemons per pitcher, then multiply that by 21 because that's the total amount of pitchers to get 378 lemons
Write an equation for a line parallel to y=-3x + 11 and goes through the point (2,4)
Answers
Answer:
equation: y = -3x + 10
Step-by-step explanation:
y = -3x + 11
comparing the formula, y = mx + b
We can determine the slope is -3 and y-intercept is 11.
if the line passes (2,4)
use the formula:
y - y1 = m(x - x1)
y - 4 = -3(x - 2)
y = -3x + 6 +4
y = -3x + 10
which statement best explains whether y= 3x + 5 is a linear or non linear function( 50 POINTS) HURYY PLSS
Answers
Answer:
C the 3rd one
Step-by-step explanation:
that's the best explanation for me. I'm sorry if I'm wrong I wish you luck
What is the area of this polygon
A=220 cm^2
A=242 cm^2
A=248 cm^2
A=270 cm^2
Answers
Answer:
A = 220 cm²
Step-by-step explanation:
Area of a rectangle = width x heightArea of a triangle = 1/2 x base x heightArea of the rectangle = 11 x 18 = 198 cm²
Area of the triangle = 1/2 x (18 - 7) x (15 - 11) = 22 cm²
Therefore, area of the polygon = 198 + 22 = 220 cm²
Answer:
220 is The Correct Answer
Letter Choice (A)
Step-by-step explanation:
HERE'S MY PROOF AND MY RESEARCH
Area of a rectangle = width x height
Area of a triangle = 1/2 x base x height
Area of the rectangle = 11 x 18 = 198 cm²
Area of the triangle = 1/2 x (18 - 7) x (15 - 11) = 22 cm²
Therefore, area of the polygon = 198 + 22 = 220 cm²
Two poles meet at the top of the teepee. The angle at which they meet is equal to twice the complement of the angles that the poles form with the ground. What is the measure of the angle at which the two poles meet at the top of the teepee
Answers
The measure of the angle at which the poles meet at the top of the tepee is 180 degrees
Complementary anglesComplementary angles are angles which sum is equals to 90 degrees. Two angles complement each other when there sum is 90 degrees.
The two poles meet at the top of the tepee.
The angle at which they meet is equals to twice the complement of the angles that the poles form with the ground. Therefore,
Complement of the angles that the poles form on the ground = 90°
Then the measure of the angle at which the poles meet at the top of the tepee is as follows:
2(90) = 180°Therefore, the measure of the angle at which the poles meet at the top of the tepee is 180 degrees
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Theo wants to use a cookie recipe that makes 36 cookies but he wants to reduce the number of cookies to 24. If the recipe specifies using 4.5 cups of flour, how much flour should he use?
Answers
Answer:
3 cups
Step-by-step explanation:
[tex]36 : 24 = 4.5 : x[/tex]
where [tex]x[/tex] is the amount of flour he should use
Therefore,
[tex]\frac{36}{24} = \frac{4.5}{x}[/tex]
Cross multiply: [tex]36x = 4.5 \times 24[/tex]
[tex]\implies 36x = 108[/tex]
Divide both sides by 36: [tex]x = 108 \div 36 = 3[/tex]
Therefore, he should use 3 cups of flour
What is 45 minutes before 2:15
Answers
Answer:
1:30
Step-by-step explanation:
45 min = 15 min + 30 min
15 min before 2:15 is 2:00.
30 min before 2:00 is 1:30.
HELP Solve for w x and y
Answers
Step-by-step explanation:
take ∆PRT
angle prt = 30°(||sides, traversal, opp angles)
angle ptr = 45+y(|| sides, opp angles)
x+30+45+y = 180
x+y = 180-75= 105
x= 105-y
take triangle zrt
angle zrt =30(parallel sides and traversal with opp angles)
angle ztr = y(parallel lines)
30+y+w = 180
w = 150-y
angle pzt+azr = 360-300+2y=60+2y
pzt= 30+y
triangle pza
30+y + 45+30= 180
y = 180-105=75
w = 75
x=30
please I need the answers now
Answers
#a
[tex]\\ \tt\hookrightarrow 2(2x+1)=30[/tex]
[tex]\\ \tt\hookrightarrow 4x+2=30[/tex]
[tex]\\ \tt\hookrightarrow 4x=28[/tex]
[tex]\\ \tt\hookrightarrow x=7[/tex]
#b
[tex]\\ \tt\hookrightarrow 3(4x-3)=-12[/tex]
[tex]\\ \tt\hookrightarrow 12x-9=-12[/tex]
[tex]\\ \tt\hookrightarrow 12x=-3[/tex]
[tex]\\ \tt\hookrightarrow x=-1/4[/tex]
#c
[tex]\\ \tt\hookrightarrow 4(2x-7)=20[/tex]
[tex]\\ \tt\hookrightarrow 2x-7=5[/tex]
[tex]\\ \tt\hookrightarrow 2x=12[/tex]
[tex]\\ \tt\hookrightarrow x=6[/tex]
#d
[tex]\\ \tt\hookrightarrow 7(3x-4)=63[/tex]
[tex]\\ \tt\hookrightarrow 3x-4=9[/tex]
[tex]\\ \tt\hookrightarrow 3x=13[/tex]
[tex]\\ \tt\hookrightarrow x=13/3[/tex]
#e
[tex]\\ \tt\hookrightarrow 6(3x+3)=-72[/tex]
[tex]\\ \tt\hookrightarrow 18x+18=-72[/tex]
[tex]\\ \tt\hookrightarrow 18x=-90[/tex]
[tex]\\ \tt\hookrightarrow x=-5[/tex]
#f
[tex]\\ \tt\hookrightarrow -2(6x-3)=6[/tex]
[tex]\\ \tt\hookrightarrow 6x-3=-3[/tex]
[tex]\\ \tt\hookrightarrow 6x=0[/tex]
[tex]\\ \tt\hookrightarrow x=0[/tex]
The value of x is 7.
The value of x is -1/4.
The value of x is 7.
The value of x is 4 1/3.
The value of x is -5.
The value of x is 0.
What is the value of x in the equations?2(2x + 1) = 30
The first step is to divide both sides of the equation by 2
2x + 1 = 15
Combine similar terms
2x = 15 - 1
2x = 14
x = 7
3(4x - 3) = -12
The first step is to divide both sides of the equation by 3
4X - 3 = -12 /3
4x - 3 = -4
Combine similar terms
4x = -4 + 3
4x = - 1
x = -1/4
4(2x - 7) = 20
The first step is to divide both sides of the equation by 4
2x - 7 = 5
Combine similar terms
2x = 5 + 7
2x = 12
x = 6
7(3x - 4) = 63
The first step is to divide both sides of the equation by 7
3x - 4 = 9
Combine similar terms
3x = 9 + 4
3x = 13
x = 4 1/3
6(3x + 3) = -72
The first step is to divide both sides of the equation by 6
3x + 3 = - 12
Combine similar terms
3x = -12 - 3
3x = -15
x = -5
-2(6x - 3) = 6
The first step is to divide both sides of the equation by -2
6x - 3 = -3
Combine similar terms
6x = -3 + 3
6x = 0
x = 0
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A city employee is organizing a race down Broadway, from Beale Street to Grand Avenue. There will be a water station at the beginning and end of the race. There will also be water stations along the route, with no more than one mile between stations. What is the minimum number of water stations for this race
Answers
It can be deduced from the multiplication that the minimum number of water stations for this race will be 28.
How to calculate the number of water stationsYour information isn't complete as the figures aren't provided. Therefore, an overview will be given.
In this case, let's assume that there are 14 routes and that there will be a water station at the beginning and end of the routes.
From the scenario, if the racers are to run through all the routes, the number of water stations will be the value of 14 multiplied by 2. This will be:
= 14 × 2 = 28
In conclusion, the correct option is 28.
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en una clase de 2 de la eso hay el doble de chicas que de chicos. Si hay 30 alumnos, ¿cuantos chicos y chicas hay en clase?
hay que hacerlo mediante ecuaciones plis que alguien me ayude(todos las operaciones pls)
Answers
x = 2y
x + y = 30
Sustituímos en la segunda ecuación el valor de x que tenemos despejado en la primera:
2y + y =30
3y = 30
y = 30 : 3 = 10 chicos
x = 10 * 2 = 20 chicas
which one is greater 7,-7
Answers
Answer:
The 7 is the answer dear 7 is greater
Answer:
7 of course.
Step-by-step explanation:
Anything negative will always be smaller then a non-negative. It's like having a friend younger then you that will never be older. Could i get brainliest :D