Mathematics Middle School

write the function:
[tex]f(x) = - 5 {x}^{2} - 60x - 181[/tex]
in vertex form, and identity its vertex

Answers

Answer 1
Notice that our function [tex]f(x)[/tex] is a parabola, and the vertex form of a parabola is:[tex]f(x)=a(x-h)^{2} +k[/tex] where (h,k) are the coordinates of its vertex.
The first thing we need to do is find the vertex (h,k) and to do that we are going to use the vertex formula: [tex]h= \frac{-b}{2a} [/tex], and then we are going to evaluate our function at [tex]h[/tex] to find [tex]k[/tex].
We know for our problem that [tex]a=-5[/tex], and [tex]b=-60[/tex], so lets replace those values in our vertex formula to find [tex]h[/tex]:
[tex]h= \frac{-b}{2a} [/tex]
[tex]h= \frac{-(-60)}{2(-5)} [/tex]
[tex]h= \frac{60}{-10} [/tex]
[tex]h=-6[/tex]
Now, we are going to evaluate our function at -6 to find [tex]k[/tex]:
[tex]k=f(-6)=-5(-6)^{2} -60(-6)-181[/tex]
[tex]k=-180+360-181[/tex]
[tex]k=-1[/tex]

Now that we have our vertex, where [tex]h=-6[/tex] and [tex]k=-1[/tex]; lets replace those values in our vertex form equation:
[tex]f(x)=-5[x-(-6)]^{2} +(-1)[/tex]
[tex]f(x)=-5(x+6)^{2} -1[/tex]

We can conclude that the vertex form of our function is [tex]f(x)=-5(x+6)^{2} -1[/tex], and its vertex is (-6,-1).

Related Questions

A recipe calls for 1/3 cup of honey for every 1/2 cup of cream. Complete each statement. For every 1 cup of honey, the recipe calls for cup(s) of cream. For every 9/2 cups of cream, the recipe calls for cup(s) of honey.

Answers

For every 1/3 cup of honey, we need 1/2 cup of cream.

Since 3 times of 1/3 cup will make a 1 while cups, we multiply the ratio above by 3.

1 cup of honey will need 1/2 x 3 cups of cream. 

1/2 x 3 = 3/2 = 1 1/2 cups

So 1 cup of honey will need 1/2 cup of cream.

---------------------------------------------------------------
To answer the next part, we start again from the original ratio given.

For every 1/2 cup of cream, we need 1/3 cup of honey.

We need to find 9/2 cups of cream. 9/2 cups is 9 times of 1/2 cup. So we multiply the ratio above by 9.

9/2 cups of cream will need 1/3 x 9 cups of honey.

1/3 x 9 = 3

So 9/2 cups of cream need 3 cups of honey.

-------------------------------------------------------------------
Answer:
(a) 1 cup of honey needs 1/2 cup of cream
(b) 9/2 cups of cream need 3 cups of honey.
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a wheel has a radius of 5 ft what is the minimum number of complete revolutions that the wheel must make it to roll at least a 1,000 feet? use pi=3.14

A. 64
B. 31
C. 32
D. 63

Answers

If the radius is 5 ft, the circumference is 10 pi or about 31.4

1000 divided by 31.4 = 31.8

So, it should make a minimum of 32 revolutions to reach 1000 feet.

The minimum number of complete revolutions that the wheel must make it to roll at least a 1,000 feet is 32.

What is circumference of a circle?

The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant π and the diameter of the circle.

Given that, a wheel has a radius of 5 ft.

We know that, the formula to calculate circumference of a circle is 2πr.

So, circumference of wheel is 2×3.14×5

= 31.4 feet

Number revolutions to roll at least a 1,000 feet is

1000/31.4

= 31.84

≈ 32

Therefore, the minimum number of complete revolutions that the wheel must make it to roll at least a 1,000 feet is 32.

Learn more about the circumference here:

brainly.com/question/28757341.

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Azul spun a tri-color spinner twice. What is the probability that the spinner landed on the colors blue and green in any order?

Answers

The spinner is tri-colored, which means there are 3 sections on the spinner. One section is colored blue, one is colored green. Let the third section be colored x.

The outcomes on spinning the spinner twice will be:
(Blue, Blue), (Blue,Green), (Blue,x), (Green, Green), (Green, Blue), (Green, x), (x,x), (x,Blue), (x, Green)

Total number of outcomes = 9

We want to find the probability that spinner lands on the colors blue and green in any order. The favorable outcomes thus will be:
(Blue, Green) and (Green, Blue)

Number of favorable outcomes = 2

The probability that the spinner landed on the colors blue and green in any order = 2/9 

So, this means there are a 2 in 9 chances that the spinner landed on the colors blue and green in any order?

Answer:2/9

Step-by-step explanation:

You paint 1/3 of a wall in 1/4 of an hour at this rate how long will it take for you to paint one whole wall

Answers

Hi!
your answer is 3/4 of an hour or 60/4*3
3/4 of an hour because you add 2/4

Which quadrants have an abscissa and ordinate that has the same sign?

A. Quadrants I and II

B. Quadrant II and IV

C. Quadrants I and III

Answers

The answer would be C. Quadrants I and III!
C for sure it would make the most sense

Why does it take 4 copies of 1 tenth to equal 2 copies of 1 fifth?

Answers

4(1/10) = 2(1/5)

1/10 x 4/1
1 x 4 = 4
10 x 1 = 10
4/10 = 2/5

1/5 x 2/1
1 x 2 = 2
5 x 1 = 5
2/5


2/5 = 2/5

A point undergoes two transformations. The x-coordinate's sign changes and the y-coordinate increases. What were the transformations?

The point was reflected over the y-axis and translated down.
The point was reflected over the x-axis and translated to the right.
The point was reflected over the y-axis and translated up.
The point was reflected over the x-axis and translated to the left.

Answers

The answer is that the point was reflected over the y-axis and translated up.

Answer:

(C) The point was reflected over the y-axis and translated up.

Step-by-step explanation:

Find the next three terms of the sequence.

–6, –24, –96, –384, . . . (1 point)
–768, –1,536, –3,072
–768, –3,072, –12,288
–1,536, –6,144, –24,576
–1,536, –9,216, –36,864

Answers

Next terms 147,456 589,824 2,359,296
Hope this helps:


6, 24, 96, 384, 1536, 6144

you are multiplying each term by 4 to get the next term,

so (384)(4) = 1536 and (384)(4)(4) = 6144 would be the next two terms.

1,2,5,6,9,10,13 (you are to add 1, you add 3, you add 1, you add 3, ...) 











1st: 6
2nd: 6*-4 = -24
3rd: 6*(-4)^2 = 96

4th: 6^(-4)^3 -384
5th: 6*(-4)^4
6th: 6*(-4)^5
7th: 6*(-4)^6






SOMEONE HELP MEE!!!!

Answers

To find the score she got, we will have to find the total number of questions.

254+23 = 277

Now you will divide the right number of questions by the total and multiply it by 100.

(254/277) * 100 = 91.71 %

Hope this helps :)
Okay. So we see the number correct and incorrect. First, let's add the numbers to find the total amount of quesstions. 254 + 23 is 277. There was a total of 277 questions on the assesment. Now, all we have to do is divide the amount correct by the total number of questions. 254/277 is 0.9169675 and other numbers behind it or 0.92 when rounded to the nearest hundredth. Multiply that by 100 to convert to a percent 0.92 * 100 is 92. There. Sue's score was about 92%.

Help me (system of equations)

Answers

There would be no solution because when you multiply the bottom equation by 2 it would equal to -8x +2y = 6. So when you add that equation to 8x - 2y = 1, 0x or 0y would not equal to 7.

Hope this helps :)

Explain how the identity property in the problem, 5/6 (1) = 1(5/6) = 5/6 is the same with any rational number.

PLEASE HELP!!

Answers

Hi there!

Since any number multiplied by the number 1 is the same number, we can conclude that the identity of 5/6 stays the same since it has been multiplied by 1. 

Hope this helps!

The dot plot shows the number of visitors. Deter the median of the data set

Answers

Where is the dot plot? Otherwise, the median is determined by finding out what is the middle number. 
Do you have an attachment for this problem? You can find the median by putting the numbers in order and finding out which is the middle number. If there are two numbers in the middle, add them, and divide it by 2, and you can find your answer. 

Solve the equation n+6.5=20. Then write a real-world problem that involves adding these two quantities

Answers

A. n + 6.5 = 20.0.
     -6.5     -6.5
n       =     13.5.

B. Soni was counting how much money was in her piggy bank. After inserting $6.50, the total of her savings was $20.0. How much money did Soni have before she inserted the $6.50? ($13.50)

Which of the following describes a correct method for finding the sum -7/2+3/4

A. Write the sum of the numerators over the sum of the denominators. Simplify.

B. Rewrite using the LCD. Write the sum of the numerators over the sum of the denominators. Simplify

C. Rewrite Using the LCD. Write the sum of the numerators over the common denominator. Simplify

D. Rewrite using the LCD. Write the difference of the numerators over the common denominator. SImplify

Answers

Answer : (C) Rewrite Using the LCD. Write the sum of the numerators over the common denominator. Simplify


Rewrite Using the LCD
-7/2+3/4 = -14/4 + 3/4

Write the sum of the numerators over the common denominator:
-14/4 + 3/4 = 11/4

Simplify
11/4 = 2 3/4

The graph shows the distance a car travels at a constant speed. What is the speed of the car?

Answers

at 1 hour the dot is on 40  so that is equal to 40 miles per hour

r = d x t

The sum of the three Romano brothers is 63. If there ages can be represented as consecutive integers, what is the age of the middle brother.

Answers

Let the age of the middle bother be x.
The oldest brother is 1 year older than the middle brother,so his age is x + 1.
The youngest brother is 1 year younger than the middle bother, so his age
is x - 1.

Add the three ages and get 63.
x - 1 + x + x + 1 = 63

3x = 63

x = 21

Answer: The age of the middle brother is 21.

Mike owns two hardware stores. The scatterplots show the number of items sold at a specific price for each store for one week. Which store has more sales revenue ($$)?

A) Store #1

B) Store #2
C) The stores bring in the same amount of sales.
D) This cannot be determined from the scatterplots.

Answers

Your answer is D. This cannot be determined from the scatter plots.
 

The revenue from store1 is more. The correct option is A.

What is a scatter plot?

A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed.

As per the given Scatter plot the revenue for a store can be calculated by adding the revenue collected by the shop from each particular product.

And to calculate the revenue collected by the store from each particular product, multiplying the cost of a single item to its corresponding price.

Therefore, the revenue from each of the store are:

The revenue collection for store1 is $35,100.

The revenue collection for store2 is $29,800.

Since 35,100>29,800, therefore, the revenue from store1 is more.

Learn more about Scatter Plot:

https://brainly.com/question/13984412

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The complete question is:

Mike owns two hardware stores. The scatterplots show the number of items sold at a specific price for each store for one week. Which store has more sales revenue ($$)?

A) Store #1

B) Store #2

C) The stores bring in the same amount of sales.

D) This cannot be determined from the scatterplots.

The Scatterplot for the two stores are mentioned in the images.

Rewrite the following equation in slope-intercept form. 17x + 15y = 5 Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:
y = [tex] \frac{-17}{15} x[/tex] + [tex] \frac{1}{3} [/tex]

Explanation:
The slope-intercept form of the equation has the following formula:
y = mx + c
where:
m is the slope
c is the y-intercept

The given is:
17x + 15y = 5

To put it in the slope-intercept formula, we should isolate the y as follows:
17x + 15y = 5
15y = -17x + 5
y = (-17/15) x + (5/15)
y = [tex] \frac{-17}{15} x[/tex] + [tex] \frac{1}{3} [/tex]
where:
m is the slope = -17/15
c is the y-intercept = 1/3

Hope this helps :)

Final answer:

Slope-intercept form of the equation 17x + 15y = 5 is y = (-17/15)x + 1/3, with a slope of -17/15 and a y-intercept of 1/3.

Explanation:

To rewrite the equation 17x + 15y = 5 in slope-intercept form, which is y = mx + b where m is the slope and b is the y-intercept, follow these steps:

Subtract 17x from both sides of the equation: 15y = -17x + 5.Divide both sides of the equation by 15 to solve for y: y = (-17/15)x + 5/15.Simplify the fractions to get the final form: y = (-17/15)x + 1/3.

Here, the slope (m) of the line is -17/15, and the y-intercept (b) is 1/3.

Kallisto built a rectangle sign that measured 2 3/4 feet in length by 1 1/2 feet in width. To find the area multiply the length and width. What is the area of the sign in square feet to write any Quetion to solve. Please help me this is due tomorrow.

Answers

It's 6/11 square feet

Mixed number form is 3 7/10

Don’t know if you needed that, just though I’d put it out there, though.

Erwin is purchasing a $190,000 home and is making a 20% down payment toward the cost. He is also buying 2 points in order to lower his interest rate. The appraisal fee is $400, the title is $300, and the processing fee is $575. Including the down payment, what are his total closing costs?

Answers

His total closing costs are $42,315.

Each point on a mortgage is 1% of the loan value.  Since he is paying 20% down, the loan amount will be after this is paid.  20% of 190000 = 0.2(190000)=38000.  The remaining loan will be 190000-38000=152000.  2 points will be 2% of this loan amount; 0.02(152000)=3040.  This means his upfront costs are:

38000 down payment
3040 for points
400 appraisal fee
300 title
575 processing fee

for a grand total of 42315.
The answer would be $42,315

Hope this helps :)

Simplify 2(x+3)-4 showing each step

Answers

To simplify this, we first need to distribute the 2 into the parenthesis.

= 2 * x + 2 * 3 - 4

Now, we can simplify:

= 2x + 6 - 4
= 2x + 2

Hope this helps!
Okay, we want to start with having the original expression for the first step.

2(x+3)-4
We can use distributive property to get rid of the parenthesis. So I will be multiplying everything inside the parenthesis by the 2.

2x + 6 - 4
The reason I didn’t multiply the four by two was because the four is outside of the parenthesis. Right now, we can add like terms. Four is basically negative since it has a subtraction sign outside of it and six is positive ( this is the same as doing 6-4, I’m just calling it negative because as you get used to simplifying expressions, you have to think of it that way).

6+(-4)=6-4=2
Now we have all the like terms added, we can find our simplified expression.
2x+2

tom works for a manufacturing plant and makes $7.00 per hour. Last week he worked 49 hours.for the hours above 40,he receives time-and-a-half. what did tom earn last week?

Answers

well due to my calculations Tom should have gotten 311.5 dollars last week.

40×7=280
7÷2=3.5
9×3.5=31.5
31.5+280=311.5

Or You could do this
(40×7)+(3.5×9)=311.5

HELP PLZ ASAP I WILL GIVE BRAINLIEST ANSWER PLZZZZZ

Answers

We use the Pythagorean Theorem: 6² - 4² = TQ², TQ = 2√5 ≈ 4
The length of each side of the square is about 4 units and the length of it's diagonal is about 4√2 ≈ 6 units.
---
Hope this helps!
--------------------------------------------
Find TQ :
--------------------------------------------

a² + b² = c²
4² + TQ² = 6²
TQ² = 6² - 4²
TQ² = 36 - 16
TQ² = 20
TQ = 2√5 units  or 4.47 units (nearest hundredth)

The length of TQ is 2√5 units

--------------------------------------------
Find the diagonal of the square :
--------------------------------------------

a² + b² = c²
(2√5)² + (2(√5)² = c²
c² = 20 + 20 
c² = 40
c = √40
c = 2√10 units or 6.32 units (nearest hundredth)

The diagonal of the square is 2√10 units

The perimeter of a square is at most 22 feet. Let N represent the length of one side of the square

Part A:
Write and inequality that represents the situation.
( I think it’s N is greater than or equal to 22 , but just making sure ;) )

Part B:
Of the lengths 2.5 ft , 4.8 ft , 5.2 ft , 5.8 ft , and 6 ft , which could be the side length of the square.
Write all that apply.

Please explain your answers and show your work.

Thanks!!!

Answers

Part A

P = perimeter of square
P = add up the four sides
P = N+N+N+N
P = 4*N
where N is the side length of the square

The perimeter of the square is at most 22 ft, which means 22 ft is the largest the perimeter can be. Think of it as the ceiling. 

So P = 22 or P < 22. We can combine those two ideas to get [tex]P \le 22[/tex] (P is less than or equal to 22)

Replace P with 4N and solve for N
[tex]P \le 22[/tex]

[tex]4N \le 22[/tex] 

[tex]\frac{4N}{4} \le \frac{22}{4}[/tex] divide both sides by 4

[tex]N \le \frac{11}{2}[/tex]

[tex]N \le 5.5[/tex]

The side length N can be 5.5 ft or smaller

-----------------------------------------------------------------------------------------------

Part B

The result we got from part A above was [tex]N \le 5.5[/tex] which means N can be equal to 5.5 or it can be smaller than 5.5

So this describes N = 2.5, N = 4.8, and N = 5.2
The values N = 5.8 and N = 6 are too big

So the answers to part B are 2.5 ft, 4.8 ft, and 5.2 ft

PLZ HELP!!!!!! (WILL GIVE BRAINLIEST!!!!)

Answers

3 x 2 is 6. 6 x 5 is 30.. There you go, the answer is 30.

if someone could help me, it’d be great!

Answers

ABC has
A as the first letter
B as the second letter
C as the third letter
The order is important

Similarly with EFG we hae
E as the first letter
F as the second letter
G as the third letter
The order is also important

Based on the orderings, we can say
A corresponds to E
B corresponds to F
C corresponds to G

Which means
A rotates to E
B rotates to F
C rotates to G

The final answer is choice C) Angle C
since we're looking for the angle that rotates or maps to angle G

which benchmark fraction could you use to estimate the prodict of 36 x 11/16

Answers

we know that
benchmark fractions are commonly used for estimation.
[1/2 1/3 1/4 3/4 2/3]------------> are all benchmark fractions

we have that
36 x 11/16
11/16 is about 12/16 which is 3/4 

the answer is 3/4

what is the area of this shape

Answers

A = (14)(18) + 1/2(18)(13)
A = 252 + 117
A = 369

answer
369 m^2

hope it helps

The distance from Caleb's house to the school is 1.5 miles, and the distance from Ashley's house to the school is 3520 feet. Who lives closer to the school, Caleb or Ashley? Use numbers and words to support your answer.

Answers


Hi there!

To solve this problem, first we need to convert everything into feet.

1.5 mi = 7920 ft

Since
7920 is greater than 3520,

Ashley lives closer to the school.

Hope this helps!

what is the anwser to x^2-9x-22=

Answers

it = 0 ok if this is helps just tell me 
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