a) f(x) = -⅙(x+3)²+6

b) f(x)=-⅙(x-3)²+6

c) f(x) = -6 (x+3)² +6

d) f(x) = -6 (x-3)² + 6

**Answer:**

a.) f(x) = -⅙(x+3)²+6

**Step-by-step explanation:**

The maximum value, our vertex, is at point (-3,6).

We can insert this value into the vertex form of a quadratic function and then solve for a as follows...

[tex]4.5 = a(0 +3)^2 +6\\4.5=a(9)+6\\-1.5 = 9a \\-.17=a\\a = -1/6[/tex]

a equals -1/6... We can input this into the original equation we used...

f(x) = -1/6(x+3)^2+6

Good luck on the bellwork ;)

PLEASE HELP ASAP A group of 8th and 9th graders were surveyed about whether they use social media to communicate with their friends. The results are shown below in the conditional relative frequency table by row. A 4-column table with 3 rows. The first column has no label with entries 8th grade, 9th grade, total. The second column is labeled do not use with entries 0.06, 0.19, 0.38. The third column is labeled use with entries 0.84, 0.81, 0.62. The fourth column is labeled total with entries 1.00, 1.00, 1.00. Which conclusions can be drawn from the results of the survey? Check all that apply. There is no association between using social media and grade level. The probability a student uses social media, given that he or she is in 9th grade, is 81%. A student who is more likely to not use social media is in 8th grade. An 8th grader is more likely to use social media than not. Knowing a student’s grade level does not help determine if he or she uses social media.

Options A, B, D, and E are correct answers such that the **probability** of the usage of social media by 8th and 9th-grade students is given.

A. There is no association between using social media and grade level.

B. The **probability** a student uses social media, given that he or she is in 9th grade, is 81%.

D. An 8th grader is **more likely** to use social media than not.

E. Knowing a student’s grade level does not help determine if he or she uses social media.

What is Probability?**Probability** is the **ratio** of the favorable outcomes to the total outcomes.

Given that, a group of 8th and 9th graders were **surveyed** about whether they use social media to communicate with their friends.

We can see that, there is **no relationship** between the usage of social media and grade level so, we can say that there is no association between using social media and grade level.

**Probability** of using social media by a 9th grader is-

P(9) = 0.81 / 1 x 100 = 81%

**Probability** of using social media by a 8th grader is-

P(8) = 0.84 / 1 x 100 = 84%

We **cannot define** the usage of social media depending on the grade level.

Thus, Options A, B, D, and E are correct answers.

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The table is attached

Find the perimeter of the following quadrilateral.

Write your answer as a mixed number in simplest form.

Be sure to include the correct unit in your answer.

**Answer:**

Plus all the fractions together .

Which equals to 35/4 cm

**Step-by-step explanation:**

hope it helps you !!

The **perimeter **of the **quadrilateral **is P = 8 3/4 cm

Given data:

The **perimeter **of a quadrilateral is the sum of the lengths of all its sides. A quadrilateral is a polygon with four sides. The formula for finding the perimeter of a **quadrilateral **depends on the specific type of quadrilateral.

So, the sides of the **quadrilateral **is represented as:

AB = 3 1/2 cm

BC = 2 cm

CD = 1 4/5 cm

DA = 1 9/20 cm

So, the **perimeter **is P = 3 1/2 cm + 2 cm + 1 4/5 cm + 1 9/20 cm

On simplifying ,

P = 3.5 cm + 2 cm + 1.8 cm + 1.45 cm

P = 8.75 cm

Hence , the **perimeter **is P = 8 4/3 cm

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can you please help me fill this out thanks

**Answer: **[tex]\sqrt{2}[/tex]

**Step-by-step explanation:**

In a 45 45 90 triangle the two sides are 1 wile the hypothenuse is [tex]\sqrt{2}[/tex]

Find the height of a rectangular prism if the surface are is 288 square centimetres and the base has a length of 4 centimetres and a width of 9 centimetres.

The rectangular prism below is made up of 6 rectangular faces, and the faces opposite to each other are have an equal area.

The area of one of the faces is lxh or lh, and the area of the face opposite to it is also equal, so the area of those two equal faces is 2lh.

The area of the base of the prism is lxw, and the area of its opposite face is equal, so the area of those two equal faces is 2lw.

The area of the face in the left side of the prism is wxh, and the area of the face opposite to it is also equal, so their combined area is 2wh.

So, to find the total surface area of a rectangular prism, we’d add the sum of all the rectangular faces, so the formula of finding the surface area of a rectangular prism=

2lh+2lw+2wh

=2(lh+lw+wh)

Given,

Surface area of the rectangular prism=288 cm^2

2(lh+lw+wh)=288

2[4h+(4x9)+9h)]=288

4h+(4x9)+9h=288/2

4h+(4x9)+9h=144

13h+36=144

13h=144-36

13h=108

h=108/13

h=8.308 cm

Hope this helps!

The area of one of the faces is lxh or lh, and the area of the face opposite to it is also equal, so the area of those two equal faces is 2lh.

The area of the base of the prism is lxw, and the area of its opposite face is equal, so the area of those two equal faces is 2lw.

The area of the face in the left side of the prism is wxh, and the area of the face opposite to it is also equal, so their combined area is 2wh.

So, to find the total surface area of a rectangular prism, we’d add the sum of all the rectangular faces, so the formula of finding the surface area of a rectangular prism=

2lh+2lw+2wh

=2(lh+lw+wh)

Given,

Surface area of the rectangular prism=288 cm^2

2(lh+lw+wh)=288

2[4h+(4x9)+9h)]=288

4h+(4x9)+9h=288/2

4h+(4x9)+9h=144

13h+36=144

13h=144-36

13h=108

h=108/13

h=8.308 cm

Hope this helps!

The **height **of a rectangular **prism **is 8.3 cm.

The area is the **space occupied **by a two-dimensional **flat surface**. It is expressed in square units. The surface area of a three-dimensional object is the area occupied by its outer surface.

We have,

**Surface Area **= 288 square cm

Base **length **= 4 cm and **width **= 9 cm

So, SA of rectangular prism

288 = 2(lw+ wh + lh)

144 = (36 + 9h + 4h)

13h = 144- 36

13h = 108

h = 8.30 cm

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Timmy has 6 pennies. Sara steals 3 pennies from Timmy. How many pennies does Timmy have now ?

**Answer:**

Timmy has 3 pennies.

**Step-by-step explanation:**

If Timmy has 6 pennies at first, and Sarra takes away 3

then 6-3=3, so timmy has three left.

3 because she stole 3. 6-3=3

What is the answer to this

Answer:

im pretty sure it's c

Step-by-step explanation:

**Answer:**

its C

**Step-by-step explanation:**

Solve for 2.

Write the smaller solution first, and the larger solution second.

(3x – 6)(-x + 3) = 0

smaller x =

larger x =

**Answer:**

(3x – 6)(-x + 3) = 0

=> 3x - 6 = 0 => x = 6/3 = 2

and

=> -x + 3 = 0 => x = 3

Hope this helps!

:)

Ben and Tom each take their driving test. The probability that ben and tom will pass is 0.8 and 0.7, respectively. Work out the probability that only one of them will pass their driving test.

Answer:

Pr(only one of them will pass the driving test) = 0.38

Step-by-step explanation:

The probability that Ben will pass = 0.8

Let Pr = pribability

Pr(Ben pass) = 0.8

Pr(Ben fail) = 1 - Pr(Ben pass) = 1-0.8

Pr(Ben fail) = 0.2

The probability that Tom will pass = 0.7

Pr (Tom pass) = 0.7

Pr (Tom fail) = 1 - Pr (Tom pass) = 1-0.7

Pr (Tom fail) = 0.3

Pr(only one pass) = Pr(Ben pass and Tom fail) + Pr (Tom pass and Ben fail)

Pr(only one pass) = (0.8 × 0.3) + (0.7 × 0.2)

Pr(only one pass) = 0.24 + 0.14

Pr(only one pass) = 0.38

**Answer:0.38**

**Step-by-step explanation:**

What is the area of rectangle with side lengths of 5/12 foot and 2/3 foot?

**Answer:**

The answer is 5/18

**Step-by-step explanation:**

The **area **of a **rectangle **with side **lengths **of **5/12** foot and **2/3** foot is **5/18 square feet** and this can be determined by using the formula of the **area **of a **rectangle**.

Given :

Lengths of 5/12 foot and 2/3 foot.

The **area **of the **rectangle **is given by the formula:

A = W [tex]\times[/tex] L

where **A **represents the **area **of the rectangle, **W **represents the **width** of the rectangle, and **L **is the **length **of the rectangle.

So, the **area **of a **rectangle **with side **lengths **of **5/12** foot and **2/3** foot is given by:

[tex]\rm A = \dfrac{5}{12}\times \dfrac{2}{3}[/tex]

Further, **simplify **the above expression

[tex]\rm Area = \dfrac{10}{36}[/tex]

[tex]\rm Area = \dfrac{5}{18}[/tex]

The **area **of a **rectangle **with side **lengths **of **5/12** foot and **2/3** foot is **5/18 square feet**.

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A person invests 10000 dollars in a bank. The bank pays 5.5% interest compounded

monthly. To the nearest tenth of a year, how long must the

person leave the

in the bank until it reaches 27400 dollars?

leave the money

r

A = P(1 + -)nt

n

Answer:

The answer is 18.4 months.

What is 0.83¯¯¯¯ expressed as a fraction in simplest form?

Enter your answer in the box.

**Answer: 5/6**

**Step-by-step explanation:**

**Answer:**

the answer is

100÷83

**Step-by-step explanation:**

hope this helps

Please can people help??!!

Photo below

i think this is the method for solving it

Right triangle RST is shown below with the dimensions given in feet

(ft)

Which is closest to the measure of ZR?

Select one

15.1

15.7

74.3

74.9

**Answer:**

As the triangle is right angled ,

sinR = 17/63

Angle R = 15.7⁰

The **closest value** of the **measure **of ∠R is,

⇒ ∠R = 15.7°

What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

**Right triangle** RST is shown below with the dimensions given in feet.

Now, By **trigonometric **formula;

tan x = Opposite / Adjacent

Here, Opposite side of angle R = 17 ft

And, Adjacent side = 63 ft

Hence, We get;

tan x = Opposite / Adjacent

tan R = 17 / 63

tan R = 1/9

R = 15.7°

Thus, The **closest value** of the **measure **of ∠R is,

⇒ ∠R = 15.7°

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3. A regular hexagon has six equilateral triangles with a common

endpoint. If the height of one of those triangles is 8 inches explain

why the perimeter of the hexagon is 55.43 inches.

**Answer:**

if the height of the triangle is 8 in, its side is 9.2379, and this side is also the side of the hexagon, so the perimeter is 6*9.2379 = 55.43 in

**Step-by-step explanation:**

As the hexagon is regular, each of those triangles will also be regular.

So if the height of one triangle is 8 inches, we can find the side of the triangle with the height formula of a regular triangle:

height = side * sqrt(3)/2

8 = side * 0.866

side = 8/0.866 = 9.2379

The side of the triangle will also be the side of the hexagon. So the perimeter of the hexagon will be:

P = 6 * 9.2379 = 55.43 inches

The area of a swimming pool is 120 sq meters. The width of the pool is 8 meters. what is the length of the pool in centimeters ?

120/8 = 15m

15m = 150cm

Answer 150cm

15m = 150cm

Answer 150cm

Select The decimal that is equivalent to 7/8

**Answer:**

0.875

**Step-by-step explanation:**

look at the fraction as a division problem

8÷7

I don’t know how to do this

**Answer:**

See attachment

**Step-by-step explanation:**

how to make a dot plot

**Answer:**

draw a a big L and put your numbers

Draw a line horizontally and make values and put dots

HELP!!! Cumulative Exam!! Which is the simplified form of m Superscript negative 8 p Superscript 0? StartFraction 1 Over m Superscript 8 Baseline p EndFraction StartFraction 1 Over m Superscript 8 EndFraction StartFraction p over m Superscript 8 EndFraction m Superscript 8

**Answer:**

(B)[tex]\dfrac{1}{m^8}[/tex]

StartFraction 1 Over m Superscript 8 EndFraction

**Step-by-step explanation:**

We want to find the simplified form of: [tex]m^{-8}p^0[/tex]

[tex]m^{-8}p^0=m^{-8}$ X p^0\\p^0=1\\m^{-8}=\frac{1}{m^8} \\$Therefore:\\m^{-8}$ X p^0=\dfrac{1}{m^8} X 1\\=\dfrac{1}{m^8}[/tex]

The correct option is B.

**Answer:**

I am 80% sure its 1 if not then its 1/p

**Step-by-step explanation:**

Jen has a newer car than Amelie, and it has One-third the miles of Amelie’s car. Amelie’s car has 45,000 miles. Which of the following equations model this situation? Select all that apply.

3(m) = 45,000

1/3 + m = 45,000

m = (1/3) (45,000)

m = 3(45,000)

m = 1/3 = 45,000

**Answer:**

Its 1rst and 3rd

**Step-by-step explanation:**

I took the assignment. Its correct.

**Answer:**

1 and 3

**Step-by-step explanation:**

on edge just got it right :)

it was found that out of 45 girls,10 joined singing but not dancing and 24 joined dancing . how many joined but not singing ? how many joined both

11 are in both singing and dancing.

45-10 singing= 35 not singing

45-24 dancing = 21 not dancing

24+10= 34 in singing OR dancing,

Subtract the 34 from 45

which leaves 11 in both singing AND dancing.

45-10 singing= 35 not singing

45-24 dancing = 21 not dancing

24+10= 34 in singing OR dancing,

Subtract the 34 from 45

which leaves 11 in both singing AND dancing.

**21 girls joined** **but** **not singing** and **14 girls **joined **both singing and dancing.**

**Arithmetic operations **can also be specified by the, **subtract**, **divide**, and **multiply** built-in** functions.**

**Total** no. of girls =** 45**

No. of girls are** dancing **=** 24**

No. of girls are** singing but not dancing** =** 10**

No. of girl are** both singing and dancing **= 24-10 =** 14**

No. of girls are **dancing but not singing** = 45-24=**21**

Hence, **21 girls joined** **but** **not singing** and **14 girls **joined **both singing and dancing.**

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If Nick used 56 feet of fence to enclose a square garden.How long,in feet was each side of Nicks garden?

**Answer:**

Each side is 14 ft.

**Step-by-step explanation:**

If there are 4 equal sides, you divide 56 by 4. That equals 14.

what is 5 + 5 /2 - 4 x 10

**Step-by-step explanation:**

use bodmas

start with multiplication

-4*10 = -40

5+5/2 - 40

addition next

5 + 5/2 = 7.5

7.5 - 40 = -32.5

Expand. Your answer should be a polynomial in standard form. (x - 7)(x - 3)

**Answer:**

x^2-10x+21

**Step-by-step explanation:**

**Answer:**

The answer is x^2-10x21

f(x) = (x-6)(x + 5)

What are the zeros of the quadratic?

**Answer:**

x=6 x=-5

**Step-by-step explanation:**

f(x) = (x-6)(x + 5)

To find the zeros, set the function equal to zero

0 = (x-6)(x + 5)

Using the zero product of property

0 = x-6 0=x+5

x=6 x=-5

Which table represents a linear function?

**Answer: **C

**Step-by-step explanation:**

when x increases by 1 y increases by 2 and is consistent

hope this helps :3

Kate recorded the length of her last six workouts. Workout Length (minutes) 1 49 2 29 3 32 4 55 5 42 6 29 What is the median of the lengths of Kate's workouts? (Round, if necessary.) A. 6 minutes B. 29 minutes C. 39.33 minutes D. 37 minutes Reset

**Answer:**

1, 2, 3, 4, 5, 6, 29, 29, 32, 42, 29, 55

median = 29

**Step-by-step explanation:**

median is the middle number in a list of numbers from least to greatest.

The numbers $1,$ $2,$ $\dots,$ $10$ are to be entered into the 10 boxes shown below, so that each number is used exactly once: \[P = (\square + \square + \square + \square + \square)(\square + \square + \square + \square + \square).\]What is the maximum value of $P$? What is the minimum value of $P$?

**Hint**

If we define x to be the value of one of the factors, since 1 + 2 + 3 + 4 + 5 ... + 10 = 11(5) = 55, the value of the other factor has to be 55-x.

To maximize P, you'd like to make x as close as possible to the vertex you found. What if you want to minimize P? Remember x must be an integer.

I hope this helps :)

The function f(x) = (x - 4)(x-2) is shown.

What is the range of the function?

1:01

all real numbers less than or equal to 3

all real numbers less than or equal to - 1

all real numbers greater than or equal to 3

all real numbers greater than or equal to -1

6+

4

2

10.-

-6

-4

8

10

X

-2

-2

-4

-6

-10

Save and Exit

Next

Submit

Mark this and return

**Answer:**

the range for f(x) = (x-4) (x-2) is [-1,∞)

**Step-by-step explanation:**

all real numbers greater than or equal to -1

The **range **of the **function **is all real numbers greater than or equal to -1

The **domain **of a **function **is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The **range **is the set of outputs of a relation or **function**. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the **function **be represented as A

Now , the value of A is

f ( x ) = ( x - 4 ) ( x - 2 ) be equation (1)

On simplifying , we get

f ( x ) = x ( x - 2 ) - 4 ( x - 2 )

f ( x ) = x² - 2x - 4x + 8

f ( x ) = x² - 6x + 8

Now , the **range **of the **function **is set of possible y values

The vertex of the parabola is at ( 3 , -1 )

So , the **range **of the **function **is f ( x ) ≥ -1 and the interval is [ -1 , ∝ ]

Hence , the **range **of the **function **is f ( x ) ≥ -1

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distance between two points: what is the distance between 2, -3 and 8, -9?

Answer:

6sqrt(2) units

Step-by-step explanation:

Distance² = (-9 - -3)² + (8 - 2)²

Distance² = (-6)² + 6²

Distance² = 36 + 36

Distance² = 72

Distance = 6sqrt(2)

sqrt: square root

The distance between 2 and -3 is 5, and the distance between 8 and -9 is 17

Por qu Gabriel no quiere salir con Rosa?Porque Rosa es su hermanaPorque ella es su primaPorque est muy chiquitaPorque ya es su novia
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