2x - 3
M+
X + 4
X =
?

Answer:

a) The axis of symmetry is the line, y = 2

b)  The vertex  of a parabola is (-3, 2)

c) The focus of the parabola is (0, 2)

d) The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola

Step-by-step explanation:

a) The function for the parabola can be expressed as follows;

12·(x + 3) = (y - 2)²

The general form of the equation of the parabola is x = a·(y - k)² + h

The axis of symmetry is the line, y = k

By comparison, with the given equation of the parabola, we have;

12·(x + 3) = (y - 2)²

x = (1/12)·(y - 2)² - 3

Therefore;

a = (1/12), k = 2, h = -3

The axis of symmetry is y = k

∴ The axis of symmetry is the line, y = 2

b) The vertex  of a parabola = (h, k)

∴ The vertex  of a parabola = (-3, 2)

c) The focus of a parabola is [tex]\left(h + \dfrac{1}{4\cdot a} , \ k\right)[/tex]

Therefore, the focus of the parabola is [tex]\left(-3 + \dfrac{1}{4\cdot \dfrac{1}{12} } , \ 2\right)[/tex] = (0, 2)

The focus of the parabola = (0, 2)

d) The directrix of a parabola is [tex]h - \dfrac{1}{4\cdot a}[/tex]

[tex]\therefore h - \dfrac{1}{4\cdot a} = -3 - \dfrac{1}{4\cdot \dfrac{1}{12} } = -3 - 3 } = -6[/tex]

The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola, showing the vertex, focus, directrix, and axis of symmetry, created with Microsoft Excel

The axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6

It is given that the parabola equation is  [tex]\rm 12(x+3)=(y-2)^2[/tex]

It is defined as the graph of a quadratic function that has something bowl-shaped.

We know the standard form of a parabola is:

[tex]\rm x= a(y-k)^2+h[/tex]  .........(1)

We have the equation of parabola:

[tex]\rm 12(x+3)=(y-2)^2\\\\\rm x+3 =\frac{1}{12} [(y-2)^2]\\\\\rm x =\frac{1}{12} [(y-2)^2]-3\\[/tex]........(2)

a) Axis of symmetry: the axis of symmetry is a straight line that divides the parabola into two identical parts.

By comparing the equation (1) and (2), we get:

Axis of symmetry ⇒ (y - k) = 0 ⇒ (y - 2) = 0 ⇒ y = 2.

b) Vertex of the parabola = (h,k): (-3, 2)

c) The focus of the parabola is [tex]\rm (h+\frac{1}{4a} ,k)[/tex],

[tex]\rm h = -3, a = \frac{1}{12} , k= 2[/tex]

∴ [tex]\rm (-3+\frac{1}{4\times(\frac{1}{12}) } ,2)\\\\\rm (0,2)[/tex]

The focus of the parabola is (0, 2)

d) The directrix of a parabola is [tex]\rm x = h-\frac{1}{4a}[/tex]

[tex]\rm x = -3-\frac{1}{4\times\frac{1}{12} }\\\\\rm x= -3-3\\\rm x= -6[/tex]

The directrix of a is x = -6

e) Shown in the below picture: graph of the parabola and vertex, focus, directrix, and axis of symmetry

Thus, the axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6

Know more about the parabola here:

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Answer:

The maximum value is (2,9) I can't really see the question well btw

Answer:

7()=11

8()=42

I could barely see the answer for number 9 sorry :(

Step-by-step explanation:

the 7() is 2(3)+5

2(3)=6

6+5=11

Question (8)

c^2+3a x b

c(6)^2+ 3(3) x 2/3

36+9 x 2/3

36+6=42

Answer:

(7)=11

(8)=42

Step-by-step explanation:

here

Answer:

x = 17

Step-by-step explanation:

area = L x W

45 = (x-2)(x-14)

45 = x² - 14x - 2x + 28

simplify:

x² -16x - 17 = 0

(x + 1)(x -17 ) = 0

x = -1    not applicable

x = 17

Proof:

(17-2)(17-14) = 45

15 x 3 = 45

45 = 45

Pen is 3 x 2 = 6

Pencils s 4 x 3 = 12

Answer:

5^-2

Step-by-step explanation:

When you multiply exponents, you can add them if they have like bases.

-4 + 2 = -2

Answer:

It would be x over 25

Answer:

[tex]BA = 6.0[/tex]

[tex]BC = 13.4[/tex]

Step-by-step explanation:

Given

The attached triangle

Solving (a) BA

Considering the tangent of angle C, we have:

[tex]tan\ C = \frac{BA}{AC}\\[/tex]

This gives:

[tex]tan\ 25 = \frac{BA}{12}[/tex]

Make BA the subject

[tex]BA = 12 * tan\ 25[/tex]

[tex]BA = 12 * 0.4663[/tex]

[tex]BA = 6.0[/tex] --- approximated

Solving (a) BC

Using Pythagoras theorem

[tex]BC^2 = BA^2 + AC^2[/tex]

[tex]BC^2 = 6.0^2 + 12^2[/tex]

[tex]BC^2 = 180[/tex]

Square root of both sides

[tex]BC = \sqrt{180[/tex]

[tex]BC = 13.4[/tex]

Answer:

2400

Step-by-step explanation:

x+y+z=147

x+(x+1)+(x+2)=147

3x+3=147

3x=144

x=48

The three consecutive positive numbers are 48, 49, and 50.

48 • 50 = 2400

Answer:

2400 just believe me I’m correct

Answer:

y = 4

Step-by-step explanation:

use the distributive property

9y - 36 = 0

     +36  +36

9y = 36

divide by 9

y = 4

Hope this helped! Have a nice day! Plz mark as brainliest!!! :D

-XxDeathshotxX

Answer is in the photo. I can't attach it here, but I uploaded it to a file hosting. link below! Good Luck!

tinyurl.com/wpazsebu

Answer:

The answer is y=-1x+8 or you can write it this way y=-x+8 either way will work fine.

Step-by-step explanation:

y=mx+b

m=-1

y-y=m(x-x¹)

y-1=-1(x-7)

y-1=-1x+7

+1 +1

y=-x+8

I hope this helps:)

Answer:

-2, 1, 4

Step-by-step explanation:

Answer:

There are 1.6875,  2/3's in 9/8

Step-by-step explanation:

To figure this out you would take 9/8 and divide it by 2/3.

(9/8)/(2/3)=1.6875

Answer:

4

Step-by-step explanation:

Use PEMDAS. Use a calulator to solve 3 and 1/3 times 1.9+19.5 divided by 4 and 1/2 and after you solve that solve 62/75- 0.16. Divided the first answer by the second. Now move to 3.5+4 and 2/3+ 2 and 2/15 then solve. Next solve 0.5 times ( 1 and 1/20+ 4.1) and with the answer you got from the equation above divided that by the answer just solved. Now divided the number on the left with the number on the right and you should get 4.

Answer:

4

Step-by-step explanation:

Answer:

Total Depth: 64.28m

Step-by-step explanation:

Assuming that the submarine is travelling at a constant rate, then we can use the information provided and apply a Rule of Three since it is basically a ratio problem. In this rule, you simply need to multiply the diagonal values of the ratio and divide by the last value to get the variable, which would be the depth after 110m

70min  <=======>  25 m

110min  <=======>  x m

(110 * 25) / 70 = x

2750 / 70 = x

39.28 = x

We can see that at 110min the depth would be 39.28 m but since this is an additional period of time that the submarine travelled we need to add this distance to the initial 25 m to get the total depth of the submarine.

39.28m + 25m = 64.28m

Answer:

OMG IM ON THE SAME QUESTION

Step-by-step explanation:

Answer: v-(kx8)

Step-by-step explanation: plz mark me brainliest

Answer:

The appropriate alternative hypothesis if he wanted to substantiate his suspicion would be [tex]H_{a}: \mu > 238[/tex]

Step-by-step explanation:

At the null hypothesis, we test that the mean is equal to a certain value.

At the alternate hypothesis, we test that the mean is different, less than or more than the mean value tested at the null hypothesis.

The historical U.S. mean unemployment insurance benefit was reported to be $238 per week.

This means that the null hypothesis is:

[tex]H_{0}: \mu = 238[/tex]

A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was above the national level.

This means that the alternate hypothesis is:

[tex]H_{a}: \mu > 238[/tex]

Answer:

16x^10+16x^8+4x^6

The expanded and simplified form of [tex](2x^3 + 4x^5)^2[/tex] is  [tex]4x^6 + 16x^8 + 16x^10[/tex].

when we combine all the like terms.

To expand and combine like terms for the expression [tex](2x^3 + 4x^5)^2,[/tex] we need to square each term inside the parentheses and then combine like terms.

Using the FOIL method (First, Outer, Inner, Last) to multiply the terms, we have:

[tex](2x^3 + 4x^5)^2 = (2x^3)^2 + 2(2x^3)(4x^5) + (4x^5)^2[/tex]

Simplifying each term:

[tex](2x^3)^2 = 4x^6\\2(2x^3)(4x^5) = 16x^8\\(4x^5)^2 = 16x^10[/tex]

Combining like terms, we have:

[tex](2x^3 + 4x^5)^2 = 4x^6 + 16x^8 + 16x^10[/tex]

Therefore, the expanded and simplified form of [tex](2x^3 + 4x^5)^2[/tex] is [tex]4x^6 + 16x^8 + 16x^10.[/tex]

To know more about  "expression."  here

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Full Question

Expand and combine like terms: (2x^3+4x^5)^2 by simplication.

(No graph needed)

The answer would be B) Awesome Ansel's Farm 1 cow for every 5 chickens.

Answer:

452.39

Step-by-step explanation:

Answer:

21 is 84% to 25, so there would be 25 total questions on the test

Answer:

58 units

Step-by-step explanation:

I decided that one side is 37 units and another is 2 units, since that would make the area 37 units. (you can also use 74 units and 1 unit)

Then I multiplied 37 by 5/4, which equals a new length of 46.25 units, and I also multiplied 2 by 5/4, which equals a new length of 2.5 units.

Finally, I solve for the area of the triangle:

1/2(46.25 x 2.5) ≈ 58 units (rounded to the nearest whole number)

Answer:

1. C(n) = 2.25n + 120

2. R(n) = 3.51n

3. P(n) = 1.26n - 120

1. 96 frozen bananas must be sold in order to make a positive profit.

2. In order to make a profit, I have to sell a minimum of 96 frozen bananas.

Step-by-step explanation:

1. Write a function, C(n), to represent your total costs for the week if you sell n frozen bananas.

Total cost is the addition of total variable cost and total fixed cost. Therefore, the function is as follows:

C(n) = 2.25n + 120

Where 2.25n is the total variable cost while 120 is the total fixed cost.

2. Write a function, R(n), to represent the revenue from the sale of n frozen bananas during the week.

Revenue is equal to selling price per unit multiplied by the number of units sold. Therefore, the function is as follows:

R(n) = 3.51 * n

R(n) = 3.51n

Where 3.51 is the selling price per unit while n the number of units sold.

3. Write a function, P(n), that represents the profits for selling n frozen bananas in a given week.

Profit is equal to total revenue minus total cost. Therefore, the function can be derived as follows:

P(n) = R(n) - C(n)

P(n) = 3.51n - 2.25n + 120

P(n) = 1.26n - 120

1. How many frozen bananas must you sell in order to make a positive profit? Write your answer as a whole number.

This can be obtained by equating the profit function to zero and solve for n as follows:

P(n) = 0 => 1.26n - 120 = 0

Therefore, we have:

1.26n = 120

n = 120 / 1.26

n = 95.2380952380952 frozen bananas

Writing it as a whole number, we have:

n = 95 frozen bananas

However, using this whole number will result in a negative profit by substituting it into the profit function as follows:

P(n) = (1.26 * 95) - 120 = -$0.30

Therefore, n has to be increased by one to 96 which is also a whole number to have a positive profit as follows:

P(n) = (1.26 * 96) - 120 = $0.96

Therefore, 96 frozen bananas must be sold in order to make a positive profit.

2. Complete the following sentence to explain the meaning of #1:

In order to make a profit, I have to sell a minimum of 96 frozen bananas.

Answer:

It can be concluded that at 5% significance level that there is no difference in the amount paid by chain A and chain B for the job under consideration

Step by Step Solution:

The given data are;

Chain A 4.25, 4.75, 3.80, 4.50, 3.90, 5.00, 4.00, 3.80

Chain B 4.60, 4.65, 3.85, 4.00, 4.80, 4.00, 4.50, 3.65

Using the functions of Microsoft Excel, we get;

The mean hourly rate for fast-food Chain A, [tex]\overline x_1[/tex] = 4.25

The standard deviation hourly rate for fast-food Chain A, s₁ = 0.457478

The mean hourly rate for fast-food Chain B, [tex]\overline x_2[/tex] = 4.25625

The standard deviation hourly rate for fast-food Chain B, s₂ = 0.429649

The significance level, α = 5%

The null hypothesis, H₀:  [tex]\overline x_1[/tex] = [tex]\overline x_2[/tex]

The alternative hypothesis, Hₐ:  [tex]\overline x_1[/tex] ≠ [tex]\overline x_2[/tex]

The pooled variance, [tex]S_p^2[/tex], is given as follows;

[tex]S_p^2 = \dfrac{s_1^2 \cdot (n_1 - 1) + s_2^2\cdot (n_2-1)}{(n_1 - 1)+ (n_2 -1)}[/tex]

Therefore, we have;

[tex]S_p^2 = \dfrac{0.457478^2 \cdot (8 - 1) + 0.429649^2\cdot (8-1)}{(8 - 1)+ (8 -1)} \approx 0.19682[/tex]

The test statistic is given as follows;

[tex]t=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{S_{p}^{2} \cdot \left(\dfrac{1 }{n_{1}}+\dfrac{1}{n_{2}}\right)}}[/tex]

Therefore, we have;

[tex]t=\dfrac{(4.25-4.25625)}{\sqrt{0.19682 \times \left(\dfrac{1 }{8}+\dfrac{1}{8}\right)}} \approx -0.028176[/tex]

The degrees of freedom, df = n₁ + n₂ - 2 = 8 + 8 - 2 = 14

At 5% significance level, the critical t = 2.145

Therefore, given that the absolute value of the test statistic is less than the critical 't', we fail to reject the null hypothesis and it can be concluded that at 5% significance level that chain A pays the same as chain B for the job under consideration

Answer:

A.

Step-by-step explanation:

✔️Find the Mean and Mean Absolute Value of the first data set:

Write out the data values:

1, 2, 4, 4, 5, 5, 6, 7, 9, 9, 9, 11

Mean = sum of all data values ÷ number of data values in the data set

Mean = 72 ÷ 12 = 6

M.A.D = sum of |data value - mean| ÷ the number of data values

|1 - 6| = 5

|2 - 6| = 4

|4 - 6| = 2

|4 - 6| = 2

|5 - 6| = 1

|5 - 6| = 1

|6 - 6| = 0

|7 - 6| = 1

|9 - 6| = 3

|9 - 6| = 3

|9 - 6| = 3

|11 - 6| = 5

Sum of |data value - mean| = 30

M.A.D = 30 ÷ 12 ≈ 2.5.

✔️Find the mean and M.A.D of the second data set following the same steps and formula:

Write out the data:

1, 3, 4, 6, 6, 6, 7, 9, 9, 10, 10, 13

Mean = 84 ÷ 12 = 7

Sum of |data value - mean| = 32

M.A.D = 32 ÷ 12 = 2.7

✔️Comparing both data sets,

The difference of the means = 7 - 6 = 1

Thus, the value of this difference, 1, is less than half of the M.A.D of both sets, 2.5 and 2.7.

Answer:

Franklin Delano Roosevelt, often referred to by his initials FDR, was an American politician who served as the 32nd president of the United States from 1933 until his death in 1945. A member of the Democratic Party, he won a record four presidential elections and became a central figure in world events during the first half of the 20th century. Roosevelt directed the federal government during most of the Great Depression, implementing his New Deal domestic agenda in response to the worst economic crisis in U.S. history. As a dominant leader of his party, he built the New Deal Coalition, which defined modern liberalism in the United States throughout the middle third of the 20th century. His third and fourth terms were dominated by World War II, which ended shortly after he died in office.

Step-by-step explanation:

to this ‘Great Man Theory’ it can be said that Franklin Delano Roosevelt upheld his victorious and highly regarded government through means of social, economic and political reforms, as well as ambitious personal and strategic decisions that have successfully remained influential to American society today and maintained his image as a prominent historic leader.