Answer:
[tex]f(x)=-4(x-2)(x+7)[/tex]
Or, in standard form:
[tex]f(x)=-4x^2-20x+56[/tex]
Step-by-step explanation:
We can use the factored form of a quadratic equation:
[tex]f(x)=a(x-p)(x-q)[/tex]
Where a is the leading coefficient and p and q are the zeros of the quadratic.
We know that the x-intercepts are at (2, 0) and (-7, 0).
So, let's substitute 2 for p and -7 for q. This yields:
[tex]f(x)=a(x-2)(x+7)[/tex]
Now, we need to determine a.
We know that it passes through the point (1, 32). In other words, if we substitute 1 for x, we should get 32 for f(x). Therefore:
[tex]32=a(1-2)(1+7)[/tex]
We can now solve for a. First, compute:
[tex]32=a(-1)(8)[/tex]
Multiply:
[tex]32=-8a[/tex]
Divide both sides by -8:
[tex]a=-4[/tex]
So, the value of a is -4.
Therefore, our entire equation is:
[tex]f(x)=-4(x-2)(x+7)[/tex]
Notes:
We can expand this into standard form:
[tex]f(x)=-4(x-2)(x+7) \\ f(x)=-4(x^2+5x-14) \\ f(x)=-4x^2-20x+56[/tex]
2 cartons of juice in the month of January. In the month of February, she drank twice as many cartons of juice as in
January. How many cartons of juice did she drink in February?
Answer:
She drank 4 cartons in February.
Step-by-step explanation:You multiply 2x2 because it doubles.
how to write this numbers in word 23.13
Answer:
twenty three and 13 hundredths
Answer:
Twenty three point thirteen
Pls help me on 21 , 22 , and 23
9514 1404 393
Answer:
21. perpendicular
22. neither
23. parallel
Step-by-step explanation:
It can help to plot the points on a graph and draw lines through them. This can also let you count grid squares, which can make it easier to find the slope.
21. See attachment 1. The lines are perpendicular.
QR has a slope of -3/2. ST has a slope of 2/3, the opposite reciprocal.
__
22. See attachment 2. The lines are neither parallel nor perpendicular.
__
23. The x-coordinates of Q and R are the same, so this is a vertical line at x=-1. The x-coordinates of S and T are also the same, so it is a vertical line at x=11. The two vertical lines are parallel to each other.
_____
Additional comment
When you have a number of problems that all require similar arithmetic, it can be useful to embed that arithmetic in a spreadsheet. You have to enter the numbers somewhere to "show work" or perform a calculation, so you may as well enter them into a spreadsheet that does the calculation for you.
Of course, the slope formula is ...
m = (y2 -y1)/(x2 -x1)
If you simply show the values of m for each pair of points, you can see if they are equal (lines are parallel). You can also have the spreadsheet compute their product to see if it is -1 (lines are perpendicular). If you get a #DIV/0! error, it means the line is vertical (and the product will also give an error). You can avoid error messages by making the spreadsheet more sophisticated, but that isn't necessary for the purpose here.
Someone please help me!
please help . imagine ^^
Answer:
A
Step-by-step explanation:
PLEASE MARK BRAINLIEST
find the quotient 5/6 divided by 2
Answer:
0.41666666666
Step-by-step explanation:
I used a calculator.
-2x + 4 < 16
Help me please I didn’t pay attention
Answer:
I think it’s done like this, I’m not sure
First, collect the like terms
-2x<16-4
-2x<12
x<12/-2
x<-6
So, you substitute -6 instead of x to find which is greater
12+4<16
16<16
Which makes it false
Step-by-step explanation:
I hope I explained well, please give me brainliest
The solution of the inequality - 2x + 4 < 16 will be;
⇒ - 6 < x
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ - 2x + 4 < 16
Now,
Solve the expression as;
⇒ - 2x + 4 < 16
Subtract 4 both side, we get;
⇒ - 2x + 4 - 4 < 16 - 4
⇒ - 2x < 12
Divide by 2 , we get;
⇒ - x < 6
Multiply by - 1, we get;
⇒ x > - 6
⇒ - 6 < x
Thus, The solution of the inequality - 2x + 4 < 16 will be;
⇒ - 6 < x
Learn more about the inequality visit:
https://brainly.com/question/25275758
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A piece of glass with an initial temp of 99 degrees Celsius is cooled at a rate of 3.5 degrees Celsius per minute. Concurrently, a piece of copper with an initial temp of 0 degrees Celsius is heated at 2.5 degrees Celsius per minute. Which of the following systems of equations can be used to solve for the temp, T, in degrees Celsius, and the time, m, in minutes, when the glass and copper reach the same temp?
Answer:
T= 99 - 3.5m
T= 2.5m
Step-by-step explanation:
HELP PLS
What is the slope of the line that passes through (1, 4) and (-3, -3)?
Answer:
y=7/4x+9/4
Step-by-step explanation:
You want to find the equation for a line that passes through the two points:
(1,4) and (-3,-3).
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (1, 4), point #1, so the x and y numbers given will be called [tex]x_1[/tex] and [tex]y_1[/tex]. Or,
Also, let's call the second point you gave, (-3,-3), point #2, so the x and y numbers here will be called [tex]x_2[/tex] and [tex]y_2[/tex]. Or,
Now, just plug the numbers into the formula for m above, like this:
m=
[tex]\frac{-3-4}{-3-1}[/tex]
m= 7/4
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
y=7/4x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(1,4). When x of the line is 1, y of the line must be 4.
(-3,-3). When x of the line is -3, y of the line must be -3.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=7/4x+b. b is what we want, the 7/4 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specifically passes through the two points (1,4) and (-3,-3).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.
You can use either (x,y) point you want..the answer will be the same:
(1,4). y=mx+b or 4=7/4 × 1+b, or solving for b: b=4-(7/4)(1). b=9/4.
(-3,-3). y=mx+b or -3=7/4 × -3+b, or solving for b: b=-3-(7/4)(-3). b=9/4.
See! In both cases we got the same value for b. And this completes our problem.
The equation of the line that passes through the points
(1,4) and (-3,-3)
is
y=7/4x+9/4
twice the sum of k and 9 is 4
Answer:
2(k + 9) = 4
Step-by-step explanation:
Use distributive property.
2 x k = 2k
2 x 9 = 18
Equation:
2k + 18 = 4
Subtract 18 from both sides
2k = -14
Divide both sides by 2
k = -7
Answer:
-7
Step-by-step explanation:
First, we need to write this an equation
2(k+9)=4
2k+18=4
-18 -18
2k=-14
/2 /2
k=-7
Jim wants to put carpet in four identical rooms. Each room is 14 ft by 20.5 ft. A
roll of carpet will cover 200 square feet. How many rolls will he need? *
3 rolls
4 rolls
5 rolls
6 rolls
Answer: Jim will need 6 rolls
Step-by-step explanation: 14*20.5 is 287 I rounded 287 to 300 and then muttplied 300 by 4 and got 1200 that would be 6 rolls
Solve this problem.
Don't answer if you don't know. NO IMPROPER ANSWERS.
Answer: 9.
Step-by-step explanation: First take 6 and divide it by 2, and then multiply by 3. This gets to the correct answer of 9.
Answer: The answer is 9.
Step-by-step explanation: First I take 6 divided by 2 and then I multiply by 3 to get the correct answer of 9. Or I could show you an equation that looks like this from: 6÷2(1+2) to 3*3=9; therefore, 1 is incorrect answer because it has an order of operations and 9 is the correct answer because it doesn’t have an order of the operations. I hoped this helps you! :D
Find the expected value of the
random variable with the
following probability distribution:
Х
2
3
4
5
6
7
8
9
10
11
12
Р
1/36
1/18
1/12
1/9
5/36
1/6
5/36
1/9
1/12
1/18
1/36
[?]
Answer:
1/36 hope this helps
Step-by-step explanation:
Marla's brainlist pls
please I need help I will mark brainiest
Answer:
sorry i looked and i tried, but i dont know the answer.
Step-by-step explanation:
Find 6,650/35. please help me i tried using calculator but it put 0.19
Answer:
113
i did it in the caculater and this is what showed.
Answer:
That's odd, the actual answer is 6650 / 35 = 190
Good luck! Hope this helped :)
q is the midpoint of segment pr. pq=2x+1 and qr= 3x-5. what is the length of segment pr
Add
to each side x2 - 8x = 9 to complete
the square.
Answer:
the correct answer is 16
Step-by-step explanation:
Add ⇒ 16 to each side x2 – 8x = 9 to complete the square.
Can yall help me on this?
Answer:
y = 3x - 2
Step-by-step explanation:
Step 1: Look at the "y" axis and see what it is going through (-2)
Step 2: Check if the line if a positive slope or a negative slope (positive)
Step 3: Since we now know this is a positive slope, it cancels out "D" and "A".
Step 4: This would not be B because the rise is "1" and the run is "3"
Final Ansr: "C" because the rise is "3" and the run is "1" with a "-2" y-intercept.
Austin makes $7.75 per hour at his job at the car wash. How many full hours does Austin need
to work to make $100?
Answer:
13 full hours
Step-by-step explanation:
Divide.
100 / 7.75 ≈ 12.9
He needs to work FULL hours, so round up.
12.9 -> 13
Best of Luck!
Answer:
He would need to work 13 hours.
Explanation:
If you divide 7.75 from 100 you will get a decimal of 12.9032258065 but if we round then it would be 13 meaning that the answer is 13 hours.
Jen and Brandy are studying soil. They each collected a sample of soil from the front yard of the school and then analyzed its components. Finally, they compared their results and found that they were very different. Their findings are recorded in the chart below.
How should Jen and Brandy proceed?
A.They should discuss their results and try to figure out why they are different.
B. They should ignore the differences in their results and complete their lab report.
C. They should argue about which student is right.
D. They should ask their teacher which set of results are more accurate.
Answer:
c.
Step-by-step explanation:
:)
Answer:
A
Step-by-step explanation:
i did the quiz and got a 96%
A pile of 100 $5coins is 150 mm high. One coin is______mm thick
Answer:
1.5mm
Step-by-step explanation:
100x = 150. x = height is one $5 coin
x = 150/100
x = 1.5
A relay race is 1 3 4 miles long. Each relay team has 4 runners. If each runner runs the same distance in the race, how far will each runner run? Choose the correct answer.
Answer: 7/16
Step-by-step explanation:
Distance of the relay race = 1 3/4 miles
Number of runners for the relay team = 4 runners
Distance to be run by each runner will be:
= Distance of the relay race / Number of runners
= 1 3/4 ÷ 4
= 7/4 ÷ 4
= 7/4 × 1/4
= 7/16
Each runner will run 7/16 miles
Please help its7to10 I be waiting like two hours
Answer:
Please check the explanation!
Step-by-step explanation:
Important factors to remember regarding the like terms:
'Like terms' are terms whose variables such as 2x and 6x are the same. Also if the variables contain the exponents such as 4 in x⁴, they must be the same too.Since the coefficient doesn't affect likeness, therefore we can say that all constant terms would be treated as the like terms.Question 7
Given the terms
2b b⁶ b x⁴ 3b⁶ 2x²
From the list of terms, there are two groups of like terms which are:
2b b (Like terms containing the variable b)
b⁶ 3b⁶ (Like terms containing the variable b with the same exponents)
The remaining two x⁴ and 2x² terms are different from each other and the rest of the termsQuestion 8
Given the terms
6 2n 3n² 3m² n/4 7
From the list of terms, there is one group of like terms which are:
6 7 (Constants Like terms)
2n n/4 (The terms with the same variable n)
All the remaining terms such as 3n², 3m² are all different from each other and the rest of the terms.Question 9
Given the terms
10k² m 3³ p/6 2m
From the list of terms, there are there is one group of like terms which are:
m 2m (The terms withe same variable m)
All the remaining terms such as 10k², 3³, p/6 are all different from each other and the rest of the terms.Question 10
Given the terms
6³ y³ 3y² 6² y 5y³
From the list of terms, there are two groups of like terms which are:
y³ 5y³ (The terms withe same variable m and exponent)
6³ 6² (Constant like terms. Plz don't confuse the power as all are the same constant terms)
All the remaining terms such as y and 3y² are all different from each other and the rest of the terms.I need help please
When the weight is greater than 15 pounds, the cost will be greater than $10.
Answer:
muy bien ami si me funciono la pregunta
Una limusina cuesta $ 85 para alquilar por 3 horas más un 7% de impuesto sobre las ventas. Cúal es el costo total
alquilar una limusina por 6 horas?
Answer:
$181.9
Step-by-step explanation:
Si cuesta 85 dólares por 3 horas, queremos duplicarlo para obtener la cantidad por 6 horas, que es 170 dólares. Esto es antes del impuesto a las ventas. Puede encontrar la cantidad después del impuesto a las ventas multiplicando 170 por 1.07. Hace esto porque el 100 por ciento del costo sería 170 por 1 y el 7 por ciento es .07, por lo que si desea el 107 por ciento del costo, debe hacerlo 170 por 1.07. Esto funciona porque toma el 7 por ciento de 170 y lo agrega al costo total. También puede hacer esto 170 veces .07. Luego suma el producto a 170. 181,9 es la respuesta final.
English- If it costs 85 dollars for 3 hours we want to double that to get the amount for 6 hours which is 170 dollars. This is before sales tax. You can find the amount after sales tax by multiplying 170 by 1.07. You do this because 100 percent of the cost would be 170 times 1, and 7 percent is .07, so if you want 107 percent of the cost you want to do 170 times 1.07. This works because it takes 7 percent of 170 and adds it to the total cost. You could also do this by 170 times .07. Then add the product to 170. 181.9 is the final answer.
What is 230% of 90?
A 207
B 237
C 320
D 227
Answer:
207 or option a is the answer
Answer:
Option A) [tex]207[/tex]
Step-by-step explanation:
[tex]230\%[/tex] can be written as [tex]\frac{230}{100}[/tex] which is equivalent to the decimal form [tex]2.3[/tex]. The word of indicates that you will need to use the multiplication operation:
[tex]230\%[/tex] of [tex]90 = 2.3\times90[/tex]
[tex]= 207[/tex]
∴ [tex]230\%[/tex] of [tex]90[/tex] is [tex]207[/tex].
Hope this helps :)
A is what percent of B?
A = 2 qt, B = 2 gal
Step-by-step explanation:
4qt=1gal
8qt=2gal
percent of b=a
x%times b=a
x%=a/b
x%=2/8
x%=1/4=25%
answer" 25%.
What is the value of 3/8 divided by 9/10
Answer:
0.41666666666
Step-by-step explanation:
Answer:
The value is 5/12
I have 2 questions
Transform the equation.
Stretch y=5x by a factor of 3
What is the transformed equation?
Transform the equation.
Shift y=5√x+5 horizontally, 5 units to the right and a stretch by a factor of 4
What is the transformed equation?
Answer:
1. I assume that stretching vertically by factor of 2 means that every point on the transformed curve is twice as far from the x axis as the original curve.
Imagine that you have plotted y=5x. you want to change the y scale so that each point on the original curve is two times as high. For example, one point on the original curve is (1,5). This point must be relocated to (1,10). Similarly, the point (2,10) on the original curve must be relocated to (2,20).
You can see that these relocations are accomplished if we transform the function to y=2(5x)=10x.
Step-by-step explanation:
hope this helps! even though it's just the first one...