A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $ 63,042 . The variable costs will be $ 11.25 per book. The publisher will sell the finished product to bookstores at a price of $ 25.50 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

This is equivalent to x^2+8x+13

======================================================

Explanation:

The vertex of f is at (0,0). The vertex of g is at (-4, -3). The vertex has moved 4 units to the left and 3 units down.

To shift to the left, we replace x with x+4. So we have f(x) = x^2 turn into f(x+4) = (x+4)^2 so far.

Then we subtract off 3 to move everything 3 units down. We have

g(x) = (x+4)^2-3

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

Optionally we can expand things out like so

g(x) = (x+4)^2-3

g(x) = (x+4)(x+4)-3

g(x) = x(x+4)+4(x+4)-3

g(x) = x^2+4x+4x+16-3

g(x) = x^2+8x+13

Showing that (x+4)^2-3 is equivalent to x^2+8x+13

An apple orchard has an average yield of 32 bushels of apples per tree if tree density is 26 trees per acre. For each unit increase in tree density, the yield decreases by 2 bushels per tree. How many trees per acre should be planted to maximize the yield?

Answer:

Step-by-step explanation:

From the given information:

Let assume that  26+x trees per acre  are planted

then the  yield per acre will be (26+x)(32-2x)

However;

As x = 0 (i.e. planting 26 per acre), we have;

= (26+0) (32 - 2 (0))

= 26 × 32

= 832

As x = 1 (i.e planting 19 per acre), we have:

= (26+1) (32-2(1)

= 27 × 30

= 810

As x = 2 (i.e. planting 20 per acre), we have:

= (26 +2 ) ( 32 - 2(2)

= 28 × 28

= 784

The series continues in a downward direction for the yield per acre.

Thus,  for maximum plant 19 per acre, it can achieved by method of calculus given that the differentiation of the maximum point of x = 1

Finally, due to integer solution, it is not advisable to use calculus as such other methods should be applied.

Answer: S₁₉ = 855

Step-by-step explanation:

T₄ = a + ( n - 1 )d  = 5 , from the statement above , but n = 4

       a + 3d  = 5 -------------------------1

S₆ = ⁿ/₂[(2a + ( n - 1 )d]  =  10, where n = 6

    = ⁶/₂( 2a + 5d )         = 10

    = 3( 2a + 5d ) = 10

    = 6a + 15d      = 10 -----------------2

Now solve the two equation together simultaneously to get the values of a and d

   a + 3d     = 5

   6a + 15d = 10

from 1,

a = 5 - 3d -------------------------------3

Now put (3) in equation 2 and open the brackets

6( 5 - 3d )  + 15d = 10

30 - 18d + 15d      = 10

30 - 3d                 = 10

            3d            = 30 - 10

             3d           = 20

                         d = ²⁰/₃.

Now substitute for d to get a in equation 3

           a = 5 - 3( ²⁰/₃)

           a = 5 - 3 ₓ ²⁰/₃

              = 5 - 20

          a  = -15.

Now to find the sum of the first 19 terms,

we use the formula

S₁₉ = ⁿ/₂( 2a + ( n - 1 )d )

     = ¹⁹/₂( 2 x -15 + 18 x ²⁰/₃ )

     = ¹⁹/₂( -30 + 6 x 20 )

     = ¹⁹/₂( -30 + 120 )

     = ¹⁹/₂( 90 )

     = ¹⁹/₂ x 90

     = 19 x 45

     = 855

Therefore,

S₁₉ = 855

Answer:

Step-by-step explanation:

I answered this already a few minutes ago.

Answer:

yes you can

Step-by-step explanation:

you can write algebraic expressions and use variables for the unknown

Answer:

D

Step-by-step explanation:

The true statement is:

The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

As, per the graph and table is:

From the graph of f(x):

Axis of symmetry will be at x = 2

The maximum value of f(x) = 10

From the table of g(x):

Axis of symmetry will be at x = 2

The minimum value of g(x) = 4

thus, The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.

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Answer:

D

Step-by-step explanation:

[tex]4(x^2+3)-2y\\\\=4((-6)^2+3)-2(\frac{-1}{2} )\\\\=4(36+3)+1\\\\=4(39)+1\\\\=156+1\\\\=157[/tex]

The value of the expression 4(x² + 3) - 2y is 157, when x = -6 and y = -1/2.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

4(x² + 3) - 2y

Substitute x = -6 and y = -1/2 to find the value of expression,

= 4 ((-6)² + 3) - 2(-1/2)

= 4 (36 + 3) + 1

= 4 x 39 + 1

= 156 + 1

= 157

The required value of the expression is 157.

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Answer:

Step-by-step explanation:

The height on the side of the deck (h) can be found using the Pythagorean theorem. It tells you ...

  6^2 + h^2 = 10^2

  h = √(10^2 -6^2) = √64 = 8

The ladder touches the deck 8 feet above the ground. Tom is not afraid of that height.

Answer:

√(x)

Step-by-step explanation:

(1)/(x^-(1/2)) that's 3 goes into -3 leaving 1 and goes into 6 leaving 2

1/2 is same as 2^-1

so therefore we can simplify the above as

x^-(-1/2)

x^(1/2)

and 4^(1/2)

is same as √(4)

so we conclude as

√(x)

Answer:

Area = 18 square units

Step-by-step explanation:

To find the area of the triangle, let's go through the following steps:

(i) Let the vertices be;

A = (7, -3)

B = (4, -3)

C = (4, 9)

(ii) The sides of the triangle are therefore,

AB, BC and CA

(iii) Using the distance formula, calculate the lengths of AB, BC and CA

[tex]AB = \sqrt{(7-4)^2 + ( -3 - (-3))^2}[/tex]

[tex]AB = \sqrt{3^2 + (0)^2}\\[/tex]

[tex]AB = \sqrt{9}[/tex]

[tex]AB = 3[/tex]

[tex]BC = \sqrt{(4-4)^2 + ( -3 - 9)^2}[/tex]

[tex]BC = \sqrt{0^2 + (-12)^2}[/tex]

[tex]BC = \sqrt{144}[/tex]

[tex]BC = 12[/tex]

[tex]CA = \sqrt{(4-7)^2 + ( 9 - (-3))^2}[/tex]

[tex]CA = \sqrt{(-3)^2 + (12)^2}[/tex]

[tex]CA = \sqrt{9 + 144}[/tex]

[tex]CA = \sqrt{153}[/tex]

[tex]CA = 12.4[/tex]

(iv) Now that we have all the sides, let's calculate the area of the triangle using the Heron's formula.

Area = [tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex]

Where;

p = [tex]\frac{a + b + c}{2}[/tex]

a, b and c are the sides of the triangle.

In our case,

let

a = AB = 3

b = BC = 12

c = CA = 12.4

∴ p = [tex]\frac{3 + 12 + 12.4}{2}[/tex]

p = 13.7

Area = [tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex]

Area = [tex]\sqrt{13.7(13.7-3)(13.7-12)(13.7-12.4)}[/tex]

Area =  [tex]\sqrt{13.7(10.7)(1.7)(1.3)}[/tex]

Area =  [tex]\sqrt{323.9639}[/tex]

Area  = 17.999

Area = 18 square units

OR

To get the area of the triangle, we can use a much simpler approach.

Since the triangle is a right triangle,

(i) the hypotenuse, which is the longest side is CA = 12.4

(ii) the other two sides are AB and BC. These two sides will form the right angle.

Therefore, we can use the relation:

Area = [tex]\frac{1}{2}[/tex] x base x height

Where;

the base or height can either be AB or BC

Area = [tex]\frac{1}{2}[/tex] x 3 x 12

Area = 18 square units

PS: In a right triangle, the other two sides apart from the hypotenuse form the right angle.

Answer:

Confidence level  = 59.46%

Step-by-step explanation:

Given that:

An economist reports that 576 out of a sample of 1,200 middle-income American households participate in the stock market.

sample mean = 576

sample size = 1200

The sample proportion [tex]\hat p[/tex] = x/n

The sample proportion [tex]\hat p[/tex] = 576/1200 = 0.48

A confidence interval of [0.468, 0.492] was calculated. What confidence level was used in this calculation?

The  confidence interval level can be determined by using the formula:

[tex]M.E =Z_{critical} \times \sqrt{\dfrac{\hat p (1- \hat p)}{n}}[/tex]

If the calculated confidence interval was [0.468, 0.492]

Then,

[tex]\hat p[/tex]  - M.E = 0.468

0.48 -M.E = 0.468

0.48 - 0.468 = M.E

0.012 = M.E

M.E = 0.012

NOW;

[tex]0. 012 =Z_{critical} \times \sqrt{\dfrac{0.48 (1- 0.48)}{1200}}[/tex]

[tex]0. 012 =Z_{critical} \times \sqrt{\dfrac{0.48 (0.52)}{1200}}[/tex]

[tex]0. 012 =Z_{critical} \times \sqrt{\dfrac{0.2496}{1200}}[/tex]

[tex]0. 012 =Z_{critical} \times \sqrt{2.08\times10^{-4}}[/tex]

[tex]0. 012 =Z_{critical} \times 0.01442[/tex]

[tex]\dfrac{0. 012}{0.01442} =Z_{critical}[/tex]

[tex]Z_{critical} =0.8322[/tex]

From the standard normal tables,

the p - value at [tex]Z_{critical} =0.8322[/tex] =  0.7973

Since the test is two tailed

[tex]1 - \alpha/2= 0.7973[/tex]

[tex]\alpha/2= 1-0.7973[/tex]

[tex]\alpha/2= 0.2027[/tex]

[tex]\alpha= 0.2027 \times 2[/tex]

[tex]\alpha= 0.4054[/tex]

the level of significance = 0.4054

Confidence level = 1 - level of significance

Confidence level = 1 - 0.4054

Confidence level = 0.5946

Confidence level  = 59.46%

Answer:

[tex] \frac{2}{3} [/tex]

Step-by-step explanation:

Area of Octagon A = 4 m²

Side length of Octagon A = a

Area of Octagon B = 9 m²

Side length of Octagon B = b

The scale factor of their side lengths = [tex] \frac{a}{b} [/tex]

According to the area of similar polygons theorem, [tex] \frac{4}{9} = (\frac{a}{b})^2 [/tex]

Thus,

[tex] \sqrt{\frac{4}{9}} = \frac{a}{b} [/tex]

[tex] \frac{\sqrt{4}}{\sqrt{9}} = \frac{a}{b} [/tex]

[tex] \frac{2}{3} = \frac{a}{b} [/tex]

Scale factor of their sides = [tex] \frac{2}{3} [/tex]

Answer:

3:5

Step-by-step explanation:

square root of 9 is 3.

square root if 25 is 5.

therefore, 3:5.

Answer:

Step-by-step explanation:

Hello, this is pretty straight forward. Let me remind you the following.

The standard equation of a parabola is

[tex]y=ax^2+bx+c[/tex]

But the equation for a parabola can also be written in "vertex form":

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

In this equation, the vertex of the parabola is the point (h,k) .

So, here the vertex is the point (2, -25) and the axis of symmetry is x = 2

Thank you

Answer:

if anyone still needs the answer I added a pic

Step-by-step explanation:

Answer:

8,13

Step-by-step explanation:

Look at the pattern :

0,1,1,2,3,5,...,...,21,34,55.

As you see the number in the pattern was made by the sum of 2 numbers behind it. Then, the blanks must be filled by :

So, the blanks must be filled by 8 and 13

Answer:

In the two blanks would be 8, 13.

The pattern is practically the Fibonacci Code.

Step-by-step explanation:

The Fibonacci Code is a mathematical sequencing in which you start with two numbers and add them together to make the third number, then you add the third number and the second number together.  Practically you keep adding each new sum and the number before it in the sequence to find the next new sum.

After 55 in this pattern, the pattern would go 89, 144, 233, 377, 610, 987,...

Answer:

Step-by-step explanation:

Hello, the slope of the tangent is the value of the derivative.

f'(x) = 2*0.2x + 5 = 0.4x + 5

So we are looking for

[tex]-1\leq f'(x) \leq 1 \\ \\<=> -1\leq 0.4x+5 \leq 1 \\ \\<=> -1-5=-6\leq 0.4x \leq 1-5=-4 \\ \\<=> \dfrac{-6}{0.4}\leq 0.4x \leq \dfrac{-4}{0.4} \\\\<=> \boxed{-15 \leq x\leq -10}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval is (-15,-10).

It is given by the derivative at x = x_0, that is:

m = f'(x_0)

In this problem, the function is:

f(x) = 0.2x^2 + 5x − 12

Hence the derivative is:

f'(x) = 0.4x + 5

For a slope of -1, we have that,

0.4x + 5 = -1

0.4x = -6

x = -15.

For a slope of 1, we have that,

0.4x + 5 = 1.

0.4x = -4

x = -10

Hence it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval is (-15,-10).

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Answer:

B. the product of 7 and a number x

Step-by-step explanation:

7x is 7 multiplied by x.

Answer:

b is the product

Step-by-step explanation:

Answer:

[tex]\displaystyle \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV = \frac{\pi (17e^5 - 2)}{2}[/tex]

General Formulas and Concepts:
Calculus

Integration

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Integration Method [Integration by Parts]:
[tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]

Multivariable Calculus

Triple Integrals

Cylindrical Coordinate Conversions:

Spherical Coordinate Conversions:

Integral Conversion [Spherical Coordinates]:
[tex]\displaystyle \iiint_T {f( \rho, \phi, \theta )} \, dV = \iiint_T {\rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex]

Step-by-step explanation:

*Note:

Recall that φ is bounded by 0 ≤ φ ≤ 0.5π from the z-axis to the x-axis.

I will not show/explain any intermediate calculus steps as there isn't enough space.

Step 1: Define

Identify given.

[tex]\displaystyle \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV[/tex]

[tex]\displaystyle \text{Region E:} \ x^2 + y^2 + z^2 = 25 \ \text{bounded by first octant}[/tex]

Step 2: Integrate Pt. 1

Find ρ bounds.

Find θ bounds.

Find φ bounds.

Step 3: Integrate Pt. 2

We evaluate this spherical integral by using the integration rules, properties, and methods listed above:

[tex]\displaystyle \begin{aligned} \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV & = \int\limits^{\frac{\pi}{2}}_0 \int\limits^{\frac{\pi}{2}}_0 \int\limits^5_0 {e^{\rho} \rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta \\ & = \int\limits^{\frac{\pi}{2}}_0 \int\limits^{\frac{\pi}{2}}_0 {\bigg[ (\rho^2 - 2 \rho + 2) e^{\rho} \sin \phi \bigg] \bigg| \limits^{\rho = 5}_{\rho = 0}} \, d\phi \, d\theta\end{aligned}[/tex]

[tex]\displaystyle \begin{aligned}\iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV & = \int\limits^{\frac{\pi}{2}}_0 \int\limits^{\frac{\pi}{2}}_0 {(17e^5 - 2) \sin \phi} \, d\phi \, d\theta \\& = \int\limits^{\frac{\pi}{2}}_0 {\bigg[ -(17e^5 - 2) \cos \phi \bigg] \bigg| \limits^{\phi = \frac{\pi}{2}}_{\phi = 0}} \, d\theta \\& = \int\limits^{\frac{\pi}{2}}_0 {17e^5 - 2} \, d\theta \\& = (17e^5 - 2) \theta \bigg| \limits^{\theta = \frac{\pi}{2}}_{\theta = 0} \\& = \frac{\pi (17e^5 - 2)}{2}\end{aligned}[/tex]

∴ the given integral equals [tex]\displaystyle \bold{\frac{\pi (17e^5 - 2)}{2}}[/tex].

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Topic: Multivariable Calculus

Unit: Triple Integrals Applications

Answer:

The calculated Z= 10/4.61 = 2.169

The P value is 0.975 .

Since the calculated value of z= 2.169 falls in the rejection region we therefore reject the null hypothesis at 5 % significance level . On the basis of this we conclude that the students at University A do not spend more on textbooks then the students at University B.

Step-by-step explanation:

We set up our hypotheses as

H0 : x 1= x2 and Ha: x1 ≠ x2

We specify significance level ∝= 0.05

The test statistic if H0: x1= x2 is true is

Z =  [tex]\frac{x_1-x_2}\sqrt\frac{s_1^2}{n_1}+ \frac{s_2^2}{n_2}[/tex]

Z = 260-250/ √400/50 + 529/40

Z= 10 / √8+ 13.225

Z= 10/4.61 = 2.169

The critical value for two tailed test at alpha=0.05 is ± 1.96

The P value is 0.975 .

It is calculated by dividing alpha by 2 for a two sided test and subtracting from 1. When we subtract   0.025 ( 0.05/2)from 1 we get 0.975

Since the calculated value of z= 2.169 falls in the rejection region we therefore reject the null hypothesis at 5 % significance level . On the basis of this we conclude that the students at University A do not spend more on textbooks then the students at University B.

Answer:

A. y + 2= x

Step-by-step explanation:

Which equation is represented by the graph shown in the image?

A. y + 2= x

B. y + 1= x

C. y - 1= x

D. y - 2= x

Please show ALL work! <3

The graph shown has a slope of +1 and a y intercept of -2.

All given answer choices have a slope of +1, so that's not the problem.

We need one that has a y-intercept of -2, or the equation should be

y = x-2, or equivalently y+2 = x

which corresponds to answer choice A.

Answer:

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day

Step-by-step explanation:

We are given that a website developer wished to analyze the clicks per day on their newly updated website.

The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.

Let [tex]\mu[/tex] = mean number of clicks per day.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day

Here, the null hypothesis states that the mean number of clicks per day is 200 clicks a day.

On the other hand, the alternate hypothesis states that the mean number of clicks per day is different than 200 clicks a day.

Hence, this is the correct null and alternative hypotheses.

Answer: Null Hypothesis [tex]H_0:\mu=200[/tex]

Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]

Step-by-step explanation:

Let [tex]\mu[/tex] be the mean number of clicks per day.

Given, a website developer wished to analyze the clicks per day on their newly updated website.

The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.

i.e. he wants to check either [tex]\mu=200\text{ or }\mu\neq 200[/tex]

Since a null hypothesis is a hypothesis believes that there is no difference between the two variables whereas an alternative hypothesis believes that there is a statistically significant difference between two variables.

So,  Null Hypothesis [tex]H_0:\mu=200[/tex]

Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]

Hence, the required null and alternative hypotheses.

Null Hypothesis [tex]H_0:\mu=200[/tex]

Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]

Answer:

5443

Step-by-step explanation:

Order of Operations: BPEMDAS

Always left to right.

Step 1: Add 68 and 5042

68 + 5042 = 5110

Step 2: Add 5110 and 333

5110 + 333 = 5443

And we have our answer!

Answer:

26.75 units²

Step-by-step explanation:

Cube Area: A = l²

Triangle Area: A = 1/2bh

Step 1: Find area of biggest triangle

A = 1/2(3.5)(2 + 2 + 5)

A = 1.75(9)

A = 15.75

Step 2: Find area of 2nd biggest triangle

A = 1/2(5)(2)

A = 1/2(10)

A = 5

Step 3: Find area of smallest triangle

A = 1/2(2)(2)

A = 1/2(4)

A = 2

Step 4: Find area of cube

A = 2²

A = 4

Step 5: Add all the values together

A = 15.75 + 5 + 2 + 4

A = 20.75 + 2 + 4

A = 22.75 + 4

A = 26.75

Answer:

The answer is option C

Step-by-step explanation:

x² - 7x + 10

To factor the expression rewrite - 7x as a difference

That's

x² - 5x - 2x + 10

Factor out x from the expression

x( x - 5) - 2x + 10

Factor - 2 from the expression

x(x - 5) - 2( x - 5)

Factor out x - 5 from the expression

The final answer is

Hope this helps you

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

Area of rectangle = l × w

where

l is the length

w is the width

From the question

The length is twice its width is written as

l = 2w

Substitute this into the formula for finding the area of the rectangle

Area = 200 yd²

200 = 2w²

Divide both sides by 2

w² = 100

Find the square root of both sides

width = 10cm

Substitute this value into l = 2w

That's

l = 2(10)

length = 20cm

Perimeter of the rectangle is

2(20) + 2(10)

= 40 + 20

Hope this helps you

Answer:

a). BLUE color

b). 20%

Step-by-step explanation:

a). "Which color was chosen by approximately one fourth of the students?"

  Since one fourth of the students will be represented by one fourth area of the circle given.

That means color of choice represented by the quarter of the circle will be the color liked by one fourth students.

In the figure attached, BLUE color is the choice of one fourth students in the class.

b). Area represented by purple, green and other colors is a quarter of the circle.

If we divide this quarter into five equal sections, then the total of purple and green will be  [tex]4\times \frac{1}{5}[/tex] of the the quarter of the circle.

Measure of the angle defined by purple or green sections = [tex]\frac{4}{5}\times 90[/tex]

                                                                                                     = 72°

Percentage of the students who preferred purple or green = [tex]\frac{72}{360}\times 100[/tex]

                                                                                                     = 20%

Answer:

blue

20%

Step-by-step explanation:

Answer:

B All real numbers

hope you wil understand

Answer:

[tex]\boxed{\sf B. \ All \ real \ numbers}[/tex]

Step-by-step explanation:

The domain is all possible values for x.

[tex]f(x)=(\frac{1}{4} )^x[/tex]

There are no restrictions on the value of x.

The domain is all real numbers.

Answer:

Correct options are 2, 5 and 7.

Step-by-step explanation:

Consider the given vertices of triangle are A(-3,-3), B(-3,2) and C(1,2).

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using distance formula, we get

[tex]AB=\sqrt{(-3-(-3))^2+(2-(-3))^2}[/tex]

[tex]AB=\sqrt{(0)^2+(5)^2}[/tex]

[tex]AB=\sqrt{25}[/tex]

[tex]AB=5[/tex]

Similarly,

[tex]BC=\sqrt{(1-(-3))^2+(2-2)^2}=4[/tex]

[tex]AC=\sqrt{(1-(-3))^2+(2-(-3))^2}=\sqrt{16+25}=\sqrt{41}[/tex]

From the above calculation it is clear that AC>AB and AC>BC.

According to Pythagoras theorem, in a right angle triangle, the square of largest side is equal to the sum of squares of two small sides.

[tex]hypotenuse^2=base^2+perpendicular^2[/tex]

[tex]AC^2=(\sqrt{41})^2=41[/tex]

[tex]AB^2+BC^2=(5)^2+4^2=24+16=41=AC^2[/tex]

So, given triangle is a right angle triangle and AC is its hypotenuse.

Therefore, the correct options are 2, 5 and 7.

Answer:

d. 27 cubic feet

Step-by-step explanation:

volume of cube = s^3 = B * s

volume of pyramid = (1/3) * B * h

The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.

volume of pyramid = 9 cu ft

volume of cube = 3 * 9 cu ft = 27 cu ft

Answer: d. 27 cubic feet

Answer:

27 ft^3 (Answer d)

Step-by-step explanation:

Here the volume of the pyramid is (1/3) the volume of the cube:

Letting s represent the length of one side of the base,

(1/3)(s)^2(s) = 9 ft^3, equivalent to  s^3 = 27.

Solving for s, we get s = 3 ft.

Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)

Answer:

3 1/4

Step-by-step explanation:

Hey there!

Well if Cedarburg to Westford is 8 3/4 miles and Oxford to Westford is 5 1/2 miles, we can make the following,

CO = CW - OW

CO = 8 3/4 - 5 1/2

Make the denominators the same,

5 1/2

improper

11/2

*2

22/4

Proper

5 2/4

8 3/4 - 5 2/4

3 1/4 miles

Hope this helps :)

Answer:

The probability is 2,010,580/13,378,456

Step-by-step explanation:

Here is a combination problem.

We want to 7 cards from a total of 52.

The number of ways to do this is 52C7 ways.

Also, we know there are 12 face cards in a standard deck of cards.

So we are selecting 3 face cards from this total of 12.

So also the number of cards which are not face cards are 52-12 = 40 cards

Out of all these 40, we shall be selecting exactly 4. The number of ways to do this 40C4

Thus, the required probability will be;

(40C4 * 12C3)/52C7 = (91,390 * 220)/133,784,560

= 20,105,800/133,784,560 = 2,010,580/13,378,456

Answer:

C = pi sqrt(x)

Step-by-step explanation:

The area of a square is x

A = s^2 where s is the side length

x = s^2

Take the square root of each side

sqrt(x) = s

This would be the diameter of the inscribed circle

The circumference of a circle is given by

C = pi d

C = pi sqrt(x)

Answer:

See below.

Step-by-step explanation:

Assign the variable n to be the sides of the square.

Since a square has four equal sides, the area of the square is n^2 or x.

Therefore:

[tex]n=\sqrt{x}[/tex]

The largest circle that can be inscribed in the square will have the largest possible diameter. The largest possible diameter will be straight across the center of the circle. So, the largest possible diameter will be the side length, n.

Therefore, the radius will be n/2.

The circumference of a circle is:

[tex]C=2\pi r[/tex]

Plug in n/2 for the radius:

[tex]C=2\pi (\frac{n}{2})\\ C=n\pi[/tex]

Now, substitute n for the square root of x:

[tex]C=\pi\sqrt{x}[/tex]