Answer:
f(x) = -x² + 20x - 96Step-by-step explanation:
Parabola f(x) = ax² + bx + c passing through points (8,0) and (12,0) means that 8 and 12 are its root and (x-8) and (x-12) are its factors
So we get:
f(x) = a(x - 8)(x - 12)
The parabola passes through point (13, -5) that means if x=13 then f(x)=-5
So:
-5 = a(13 - 8)(13 - 12)
-5 = a(5)(1)
-5 = 5a
a = -1 {<0 so parabola opens down}
Therefore:
f(x) = -(x - 8)(x - 12)
And expanding:
f(x) = -(x² - 12x - 8x + 96)
So the standard form equation of the parabola:
f(x) = -x² + 20x - 96
In Aunt Peggy’s backyard there are cows and chickens. There are 20 more chickens than cows. The total number of legs is 130. How many chickens and how many cows are there? (Each cow has 4 legs, each chicken has 2 legs.)
Answer:
There's 15 cows and 35 chickens.
Step-by-step explanation:
Take 20 and multiply it by 2. The answer is 40. Then subtract 40 from 130. The answer will be 90. The cow has double the amount of legs than the chicken, so the cow is equivalent to 2 chicken. Divide 90 by 3. The answer is 30. Then divide 30 by 2 the answer is 15. Add 15 and 20 and the answer is 35 chickens. Divide 30 by 2 and the answer is 15.
You will get 35 chicken and 15 cows as your answer. Happy Election Night, and I hope this helps! ;)
Write an equation in slope-intercept form for the line that passes through (6,- 3) and is parallel to y = -2x + 4 *
Write an equation in slope-intercept form for the line that passes through (6,- 3) and is parallel to y = -2x + 4.
__________________________________________________________
Parallel lines are lines with the same slope but different y-intercept.
Slope-intercept form is written as y=mx+b, where m is the slope and b is the y-intercept.
__________________________________________________________
The given line is y=-2x+4. A line parallel to this would have the same slope, which is -2. To find the y-intercept, plug the point into an equation in point-slope form.
[tex]\displaystyle \text{Point-Slope Form} \rightarrow y-y_{1}=m(x-x_{1})[/tex]
m is the slope, and since the slope is the same as the given line, m will be equal to 2.
The line is supposed to pass through a point, which is written as (x, y). In this line, it is supposed to pass (6, -3). x₁ will be the x value of the point, and y₁ will be the y value of the point. That means x₁ is 6 and y₁ is -3.
Substitute the values into the formula:
[tex]y-y_{1}=m(x-x_{1}) \rightarrow y-(-3)=2(x-6)[/tex]
When subtracting a negative number from a number or variable, the sign will change, and the number will become positive.
[tex]y-(-3)=y+3[/tex]
Here is the new equation:
[tex]y-3=2(x-6)[/tex]
Distribute the 2 to everything in the parentheses. It will be 2 times x and 2 times -6. Remember that a positive number multiplied by a negative number is negative.
Positive(+) times(×) positive(+) = positive(+) Positive(-) times(×) negative(-) = negative(-) Positive(+) divided(÷) by positive(+) = positive(+) Positive(+) divided(÷) by negative(-) = negative(-)[tex]2 \times x=2x\\2 \times -6=-12\\\\2(x-6)=2x-12[/tex]
Rewrite the equation:
[tex]y-3=2x-12[/tex]
Lastly, you need to move -3 to the other side, as slope-intercept form is written as y=mx+b. You can move it by adding three(+3) to both sides, which is simply doing the opposite of it(-3+3=0).
[tex]\displaystyle y-3+3=2x-12+3[/tex]
[tex]y=2x-9[/tex]
The answer to your question is [tex]\bf \displaystyle y=2x-9[/tex].
If the factors of a quadratic function are (x + 2) and (x − 9), what are the x-intercepts of the function?
A.
(-9,0) and (-2,0)
B.
(-2,0) and (9,0)
C.
(2,0) and (9,0)
D.
(-9,0) and (2,0)
Answer:
The x-intercepts of the function are:
(-2,0) and (9,0)Step-by-step explanation:
As
[tex]( x + 2 ) ( x - 9 ) = 0[/tex]
so
Either
( x + 2 ) = 0
or
( x - 9 ) = 0
solving ( x + 2 ) = 0
[tex]x + 2 = 0[/tex]
[tex]x = 0 - 2[/tex]
[tex]x = -2[/tex]
solving ( x - 9 ) = 0
[tex]x-9=0[/tex]
[tex]x=9[/tex]
We also know that to get x-intercepts by setting y=0.
Therefore, the x-intercepts of the function are:
(-2,0) and (9,0)Answer:
The correct answer is (-2,0) and (9,0)
Step-by-step explanation:
PLATOOOOOOOOOOOO!!!!!!!!!!!!!!!
Triangles B and C have been built by dilating Triangle A
Pleas im so close to failing class and can't mess up on this project
Wish you a GREAT Thanksgiving :)
I hope this helps !! =)
a) A
b) 3
c) 1/3
d) 2
Answer:
The answer is d
Step-by-step explanation:
Because it can be combined in the equation
Find the area of the figure
Answer:
area=18
Step-by-step explanation:
draw a dotted line so it separates the top part from the bottom and then the area of the bottom part is 6x2 which is 12 and then the area of the top is 3x2 which is 6
6+12=18
Use a model to divide 2
Answer:
2/2 divided by 1/3 becomes 2/2 * 3/1 by using keep change flip. 2/2 * 3 is 6.
i need help pls anyone
Answer:
[tex]5\geq m[/tex] - put a closed dot on 5, then an arrow pointing to the left
Step-by-step explanation:
You have to solve the equation. After solving, you should end up with [tex]5\geq m[/tex]
Dorian buys 2 pounds of almonds for $21.98 and 3 pounds of dried apricots for 26.25 which is less expensive per pound how much less expensive
Answer:
The apricots are $2.24 less expensive per pound.
Step-by-step explanation:
To find the price per pound of each product divide the price Dorian by the number of pounds Dorian bought:
Almonds: 21.98 ÷ 2 = 10.99
Almonds cost $10.99 per pound.
Apricots: 26.25 ÷ 3 = 8.75
Apricots cost $8.75 per pound.
The apricots are less expensive per pound. To find how much less expensive they are compared to the almonds, subtract the cost of the apricots per pound from the cost of the almonds per pound:
10.99 - 8.75 = 2.24
The apricots cost $2.24 less per pound than the almonds do.
x − 2y = 14 x + 3y = 9 what is the system of equations?
answer
(12, -1)
hope this helps :)
Answer:
(12,-1)
I got it right on my test
You buy a 5-pound bag of sugar. What is its mass in grams?
Answer:
2270 grams
Step-by-step explanation:
Answer:
5 pounds = 2267.96 grams
What tool do I use on this? (picture needed)
Answer:
a screw driver
Step-by-step explanation:
you can use an electric one if you want to.
Answer:
Allen key
Step-by-step explanation:
In which number does the digit 7 have a value that is 10 times as great as the digit 7 in the number 0.9750
PLEASE PLEASE HELP I WILL GIVE BRAINALSIT
Answer:
Veggie soup
Step-by-step explanation:
Plz Mark as brainliest!!!
help now give me like yuuuuh
Answer:
Step-by-step explanation:
D
The Math Club is renting a banquet room for a party with door prizes. The banquet room costs
$125 to reserve and the door prizes each cost $8.50. Find the possible number of door prizes that
can be purchased if the club decides to use no more than $250 to reserve the banquet room and
the purchase the door prizes.
Answer:
14
Step-by-step explanation:
1/2 w + 2 ; w = 1/9 what is the answer because i have been on this problem for an hour
Answer:
its -1/5
Step-by-step explanation:
Answer:
Step-by-step explanation:
1/2 (1/9) + 2=
1/18 + 2=
2 1/18
kx^2 + 6x + k = 0 find k
Answer:
Step-by-step explanation:
kx^2 + 6x + k = 0
k= 6x/x^2+1
-7/9 greater or less than -5/8?? help me quick please!
Answer:
-7/9 is less than -5/8.
Step-by-step explanation:
-5/8 in decimal form is -0.625.
-7/9 in decimal form is -0.777777778.
1. What is the median weight of the Welsh corgis? What does the median tell you about their weights?
Answer:
Male: 22–31 lbs (10–14 kg), Female: 22–29 lbs (10–13 kg)
Step-by-step explanation:
Median tells the average weight. Like, what your corgi might weight.
The median tells us about the center level of all the weights.
What is Median?The median is a statistical measure that represents the central value of a dataset when it is arranged in ascending or descending order. It is the value that separates the higher half of the data from the lower half.
From the given table, we can determine that the median weight of the Welsh corgis is 27.3. The median represents the middle value of a dataset when it is arranged in ascending or descending order.
In this case, it tells us that half of the Welsh corgis in the sample have weights below 27.3, and the other half have weights above 27.3.
So, the median tells us about the center level of all the weights.
Learn more about Median here:
https://brainly.com/question/20757070
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State the slope and the y-intercept for the graph of the equation. y = x – 3 a. ; 3 b. –; 3 c. ; 3 d. 3;
It is given that AD = 4x + 8 and DB = 6x - 3. Solve for x.
Answer:
x=18
Step-by-step explanation:
Watch help video
In ARST, the measure of angel T=90°, ST = 7.7 feet, and RS = 9.7 feet. Find the measure
of Angel R to the nearest degree.
Answer: 53
Step-by-step explanation:
what is the output value of (4x+2)(x-5)/2 using input value of x=2
(4x+2)(x-5)/2
(4 . 2 + 2)(2 - 5)/2
(8 + 2)(- 3)/2
10/2 . (- 3)
5 . (- 3)
- 15
Answer: - 15
Answer:
-15
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
(4x + 2)(x - 5) / 2
x = 2
Step 2: Evaluate
Substitute: (4 · 2 + 2)(2 - 5) / 2Parenthesis - Multiply: (8 + 2)(2 - 5) / 2Parenthesis - Add: 10(2 - 5) / 2Parenthesis - Subtract: 10(-3) / 2Multiply: -30 / 2Divide: -15Match each data relationship with a type of correlation
Answer:
Y tends to increase as x increases: positive correlation
Step-by-step explanation:
Y tends to decrease as x increases: negative correlation.
Y does not change bases on changes in x: No correlation.
I
The actual packing volume in cubic feet, p(s), within a packing crate depends on the length of the side of the base, s, in feet, and of the square-based supports by spanning placed at each corner. This relationship is represented by the table.
If the bases of the supports never have dimensions greater than feet by feet, which statements describe the function represented in the table and the given information? Select two options.
The function is cubic.
D = {R} and R = {R}
R = {15.625 ≤ p(s) ≤ 91.125}
The function has constant second differences.
Answer:
B and D sorry
Step-by-step explanation:
Got it right on my test :)
Answer:
2 and 4
Step-by-step explanation:
Determine the vertex form of g(x) = x2 + 2x – 1. Which graph represents g(x)? On a coordinate plane, a parabola opens up. It goes through (negative 2, 3), has a vertex at (negative 1, 2), and goes through (0, 3). On a coordinate plane, a parabola opens up. It goes through (negative 1, 2), has a vertex at (1, negative 2), and goes through (3, 2). On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (1, 2), and goes through (2, 3). On a coordinate plane, a parabola opens up. It goes through (negative 3, 2), has a vertex at (negative 1, negative 2), and goes through (1, 2).
Answer:
the last one I think
Step-by-step explanation:
The vertex form of the quadratic equation is:
[tex]g(x) = (x + 1)^2 - 2[/tex]
And the graph can be seen at the end
How to get the vertex form of the quadratic equation?
For a quadratic equation with leading coefficient a, and with vertex (h, k), the vertex form is:
[tex]y = a*(x - h)^2 + k[/tex]
Here we have:
[tex]g(x) = x^2 + 2x - 1[/tex]
First, we need to find the vertex. by using the known formula we get:
[tex]h = -2/(2*1) = -1[/tex]
To get the value of k, we need to evaluate g(x) in x = -1.
[tex]g(-1) = (-1)^2 + 2*-1 - 1 = 1 - 2 - 1 = -2[/tex]
So the vertex is (-1, -2), which means that the vertex form is:
[tex]g(x) = (x + 1)^2 - 2[/tex]
And its graph can be seen below.
If you want to learn more about quadratic equations:
https://brainly.com/question/1214333
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Hank works at an auto repair shop. He has a customer that spent $415 on parts for the repair. Hank
charges $30 an hour in labor costs. If he has quoted the customer that it will be no more than $550, how many hours, h, will the work take
him?
Answer:
Auto repair labor rates vary widely across the country, and even within the same city. As of January 17, 2017, auto repair shops in the AAA Approved Auto Repair network charged between $47 and $215 per hour, based primarily on the shop's cost of doing business.
Is this congruent by SSS, SAS, AAS, ASA? Please help!
Answer:
SSS
Step-by-step explanation:
There is two given congruent angles
Functions Question (image attached)
Answer:
[tex]x {}^{2} \times + 4x[/tex]
Step-by-step explanation:
[tex]f(x + 4) = (x + 4) {}^{2} - 3(x + 4) - 4 \\ = x {}^{2} + 8x + 16 - 3x - 12 - 4 \\ = x {}^{2} + 4x[/tex]
What is the solution to the equation shown below? (2/3)x + 5 = 1
Answer:
The solution is x = −6.
Step-by-step explanation: