Which equation can be used to calculate the surface area of the triangular prism net show below?
10 cm
13 cm
12 cm
5 cm
5 cm
[Not drawn to scale]

Answer:

A. [tex]h=\frac{SA-2B}{P}[/tex]

Step-by-step explanation:

We have been given a formula for the surface area of a container in shape of right prism. We are asked to solve for h for our given formula.

[tex]SA=Ph+2B[/tex]

First of all, we will switch sides for our given equation as:

[tex]Ph+2B=SA[/tex]

Now, we will subtract 2B from both sides of our equation.

[tex]Ph+2B-2B=SA-2B[/tex]

[tex]Ph=SA-2B[/tex]

Now, we will divide both sides of our equation by P.

[tex]\frac{Ph}{P}=\frac{SA-2B}{P}[/tex]

[tex]h=\frac{SA-2B}{P}[/tex]

Therefore, option A is the correct choice.

Answer:

A

Step-by-step explanation:We have been given a formula for the surface area of a container in shape of right prism. We are asked to solve for h for our given formula

First of all, we will switch sides for our given equation as:

Now, we will subtract 2B from both sides of our equation.

Now, we will divide both sides of our equation by P.

therefore its option A

okay so we need to solve for x.

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FIRST STEP:  12x^2+5x-4=12^2x+6 would turn into x2 + 5x - 4 = 2x + 6 so it'd have equal bases.

SECOND STEP: move any number with "x" in it to the left side. it ends up as  x2 + 3x - 4 = 6

THEN, we use the AC method to eliminate any unnecessary numbers.

you should end up with ( x - 2) (x + 5) = 0

SO, the answer is your third option. ( x = 2, x = -5)

Answer:

x=-5&x=2

Step-by-step explanation:

Since the bases on both sides of the equation are the same, they will cancel each other leaving the exponents

x²+5x-4 = 2x + 6

Collect like terms

x²+5x-2x-4-6=0

x²+3x-10=0

The highest power is 2 , so factorize

x²+5x-2x-10=0

x(x+5)-2(x+5)=0

(x+5)(x-2)=0

x = -5 or x = 2

Check

When x = -5

-5²+3*-5-10=0

25-15-10 =0

0=0

:.x=-5

When x=2

2²+3*2-10=0

4+6-10=0

0=0

This is a piecewise function because it is defined by more than two functions. Basically, we want to take the limit here. Recall that if a function [tex]f(x)[/tex]  approaches some value [tex]L[/tex]  as [tex]x[/tex]  approaches [tex]a[/tex]  from both the right and the left, then the limit of [tex]f(x)[/tex] exists and equals  [tex]L[/tex]. Here we won't calculate the limit, but apply some concepts of it. So:

a. [tex]as \ x \rightarrow +\infty, \ k(x) \rightarrow +\infty[/tex]

Move on the x-axis from the left to the right and you realize that as x increases y also increases without bound.

b. [tex]as \ x \rightarrow -\infty, \ k(x) \rightarrow 0[/tex]

Move on the x-axis from the right to the left and you realize that as x decreases to negative values y approaches zero.

c. [tex]as \ x \rightarrow 2, \ k(x) \rightarrow 0[/tex]

Since the function is continuous here, we can say that [tex]k(2)=0[/tex]

d. [tex]as \ x \rightarrow -2, \ k(x) \rightarrow 0[/tex]

The function is discontinuous here, but [tex]k(-2)[/tex] exists and equals 0 as the black hole indicates at [tex]x=-2[/tex].

e. [tex]as \ x \rightarrow -4, \ k(x) \rightarrow 2[/tex]

The function is also discontinuous here, but the black hole indicates that this exists at [tex]x=-4[/tex], so [tex]k(-4)=2[/tex]

f. [tex]as \ x \rightarrow 0, \ k(x) \rightarrow 4[/tex]

Since the function is continuous here, we can say that [tex]k(0)=4[/tex]

Answer:

B

Step-by-step explanation:

We can solve this by finding the slope of the function that passes through the points (2,15) and (3,26). We can use the "formula" rise over run.

So we have:

(26-15)/(3-2) which gives us 11 as our slope. Now we must find the y intercept!

It is -7.

So the answer is B

Answer:

the equation is y = 11x - 7

B is correct option.

Step-by-step explanation:

The function passes through the points (2, 15) and (3, 26)

Slope can be calculated by the formula

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

using this formula, the slope is given by

[tex]m=\frac{26-15}{3-2}\\\\m=\frac{11}{1}\\\\m=11[/tex]

The slope intercept form of line is y = mx+b

here, m = 11

hence, the equation is  y = 11x +b

Now, using the point (2,15) to find b

15=11(2)+b

15 = 22 +b

b = -7

Hence, the equation is y = 11x - 7

B is correct option.

Answer:

[tex]\large\boxed{y=4(x-3)^2+2\ \bold{vertex\ form}}\\\boxed{y=4x^2-24x+38\ \bold{standard\ form}}[/tex]

Step-by-step explanation:

The vertex form of a parabola:

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

(h, k) - vertex

We have the vertex at (3, 2) → h = 3 and k = 2.

Substitute:

[tex]y=a(x-3)^2+2[/tex]

The point (4, 6) is on athe parabola. Put the coordinates of this point to the equation:

[tex]6=a(4-3)^2+2[/tex]       subtract 2 from both sides

[tex]6-2=a(1)^2+2-2[/tex]

[tex]4=a\to a=4[/tex]

Finally:

[tex]y=4(x-3)^2+2[/tex]          vertex form

use (a - b)² = a² - 2ab + b²

[tex]y=4(x^2-6x+9)+2[/tex]          use the distributive property

[tex]y=4x^2-24x+36+2[/tex]

[tex]y=4x^2-24x+38[/tex]             standard form

Answer:

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

Step-by-step explanation:

Hopefully this helps :)

Answer:

This question is not complete.

Step-by-step explanation:

Hi, The question is not complete but i think the question was this:

Which of the following is the correct factorization of the polynomial below?

x^3 - 12

A. (x + 3)(x - 4)

B. (x - 3)(x + 4)

C. (x + 3)(x^2 - 4x + 4)

D. The polynomial is irreducible.

in which case, the answer will be this:

D as this polynomial can't be reduced

Answer:

x³ - 12 = (x - ∛12)(x² + x∛12 + 12²/³)

Step-by-step explanation:

Question is incomplete (options are missing);

However, I'll factorize the polynomial using identity

Given

x³ - 12

This can be factorized using the following identity

a³ - b³ = (a - b)(a² + ab + b²)

By comparison,

a³ = x³ and b³ = 12

a = x and b = ∛12

Replace a with x and b with ∛12 in the above equation

a³ - b³ = (a - b)(a² + ab + b²) becomes

x³ - 12 = (x - ∛12)(x² + x∛12 + ∛12²)

x³ - 12 = (x - ∛12)(x² + x∛12 + 12²/³)

This is as far as it can be factorized

So, the factorization of x³ - 12 using identity is (x - ∛12)(x² + x∛12 + 12²/³)

Final answer:

The volume of the core of the golf ball from Great Drive, with a diameter of 1.68 inches, is approximately 2.48 cubic inches. This is calculated using the formula for the volume of a sphere with the radius derived from the given diameter. The correct answer is 2.48 in³, which is option A.

Explanation:

The volume of a sphere is given by the formula V = (4/3) πr3, where π is pi (approximately 3.14159) and r is the sphere's radius. The diameter of the golf ball's core is given as 1.68 inches, so the radius is half of that, which is 0.84 inches. Plugging this into the formula gives us:

V = (4/3) π (0.84 inches)3 = (4/3) π (0.84 inches × 0.84 inches × 0.84 inches)

Doing the math, we find that:

V ≈ (4/3) π (0.592704 inches3) ≈ 2.48 in3

Therefore, the volume of the core of the ball rounded to the nearest hundredth is 2.48 cubic inches.

The correct answer is option A.

Answer:

[tex]\large\boxed{y=-\dfrac{2}{3}x+\dfrac{13}{3}}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\===============================[/tex]

[tex]\text{We have the point:}\\\\(5,\ 1)\ \text{and}\ (-4,\ 7).\ \text{Substitute:}\\\\m=\dfrac{7-1}{-4-5}=\dfrac{6}{-9}=-\dfrac{6:3}{9:3}=-\dfrac{2}{3}\\\\\text{We have the equation in form:}\\\\y=-\dfrac{2}{3}x+b\\\\\text{Put the coordinates of the point (5, 1) to the equation:}\\\\1=-\dfrac{2}{3}(5)+b\\\\1=-\dfrac{10}{3}+b\qquad\text{add}\ \dfrac{10}{3}\ \text{to the both sides}\\\\\dfrac{3}{3}+\dfrac{10}{3}=b\to b=\dfrac{13}{3}\\\\\text{Finally:}\\\\y=-\dfrac{2}{3}x+\dfrac{13}{3}[/tex]

Answer: -2,0 0,4

Step-by-step explanation:

let me know if you need help still UwU

Answer:

The function is positive from (-∞,-2) and (0,4).

Explanation:

To find the intervals where the function is positive, note where the line of the graph is above the x-axis.

As the functions goes toward negative infinity, the arrow of the graph is pointed up, so the function is positive starting from -∞ until x = -2, where it becomes negative.

The function once again goes above the x-axis at x = 0 and stays positive until x = 4. After this point, the function decreases forever, so (-∞,-2) and (0,4) are the only intervals where the function is positive.

Answer:

31 seats

Step-by-step explanation:

Let x be the smaller van, and y be the larger one.

We know that y = x + 14

We also know that 2x + y = 65

If we replace y by its value in the second equation we have:

2x + (x + 14) = 65, then we solve

2x + x + 14 = 65

3x + 14 = 65

3x = 51

x = 17

We now know the smaller van has 17 seats.

To find how many seats are in the big one, we take the first equation:

y = x + 14

y = 17 + 14

y = 31

Answer: [tex]\sqrt{32}\text{ mi}[/tex]

Step-by-step explanation:

The Pythagoras theorem of right triangle says that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

From the given figure , the hypotenuse of the right triangle = [tex]\sqrt{113}\text{ mi}[/tex]

Then According to Pythagoras theorem , we have

[tex](\sqrt{113})^2=x^2+(9)^2\\\\\Rightarrow\ x^2=113-81\\\\\Rightarrow\ x^2=32\\\\\Rightarrow\ x=\sqrt{32}\text{ mi}[/tex]

[tex]y=\dfrac{k}{x}[/tex]

1.

[tex]12=\dfrac{k}{13}\\\\k=156[/tex]

2.

[tex]y=\dfrac{156}{x}[/tex]

3.

[tex]y=\dfrac{156}{44}=\dfrac{39}{11}[/tex]

Answer:

A and B are the solutions....

Step-by-step explanation:

7 and 12 are smaller than 17.

Answer:

A. [tex]x=7[/tex]

B. [tex]x=12[/tex]

Step-by-step explanation:

Check each option individually.

A. [tex]17>7[/tex] is true, so it is a correct choice.

B. [tex]17>12[/tex] is true, so it is a correct choice.

C. [tex]17>17[/tex] is false, so it is an incorrect choice.

Answer: [tex]y=(x-1)^2-4[/tex]

Step-by-step explanation:

The vertex form of the equation of a parabola is:

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

Where (h,k) is the vertex.

To obtain this form, we need to complete the square:

Move the 3 to the other side of the equation:

[tex]y+3=x^2-2x[/tex]

Add this value to both sides of the equation: [tex](\frac{-2}{2})^2=1[/tex]

[tex]y+3+1=x^2-2x+1[/tex]

[tex]y+4=x^2-2x+1[/tex]

Then, rewriting:

 [tex]y+4=(x-1)^2[/tex]

Finally, we must solve for "y", getting the equation of the parabola in vertex form:

 [tex]y=(x-1)^2-4[/tex]

Answer:

[tex](f*g) (x) =2x^3-13x^2-7 [/tex]

Step-by-step explanation:

We have the following functions

[tex]f (x) = 2x+1[/tex]

[tex]g (x) = x^2-7[/tex]

To find [tex](f*g)(x)[/tex] we must multiply the function f (x) with the function g (x)

Then we perform the following operation

[tex](f*g) (x) =(2x+1)(x^2-7)[/tex]

Apply the distributive property

[tex](f*g) (x) =2x^3-14x^2+x^2-7 [/tex]

[tex](f*g) (x) =2x^3-13x^2-7 [/tex]

Finally we have that:

[tex](f*g) (x) =2x^3-13x^2-7 [/tex]

Answer:

l

Step-by-step explanation:

Answer: [tex]\frac{1}{(x+1)(x+y)}[/tex]

Step-by-step explanation:

Given the expression:

[tex](\frac{x-y}{x^2-1})(\frac{x-1}{x^2-y^2})[/tex]

The first step is to multiply the numerator of the first fraction by the numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction. Then:

[tex]=\frac{(x-y)(x-1)}{(x^2-1)(x^2-y^2)}[/tex]

Since [tex](x^2-1)[/tex] and [tex](x^2-y^2)[/tex] are perfect squares, you can factorize them in the form:

[tex]a^2-b^2=(a+b)(a-b)[/tex]

Then:

[tex]=\frac{(x-y)(x-1)}{(x+1)(x-1)(x+y)(x-y)}[/tex]

Simplifying, you get:

[tex]=\frac{1}{(x+1)(x+y)}[/tex]

Answer:

A: Line Segment WX

Step-by-step explanation:

100% on edge 2020

Answer:

WX is correct

Step-by-step explanation:

Got a 100 in edge quiz.

Answer:

x = -8

Step-by-step explanation:

-2x-2=14

We want to solve for x

Add 2 to each side

-2x-2+2 = 14+2

-2x=16

Divide each side by -2

-2x/-2 =16/-2

x = -8

Answer:

4,-2 and 1

Step-by-step explanation:

These are all quantities greater than -5

-5 < 4

-5 < -2

-5 < 1

So C, D and E

Answer:

A.) ∠3, ∠6, and∠7

If you have a protractor, that would help you alot :) but I hope this help you!

Answer:

A. ∠3, ∠6 and ∠7.

Step-by-step explanation:

Given,

r ║ s

Also, t is the common transversal of parallel lines r and s,

By the given diagram,

∠2 and ∠3 are vertical angles,

By vertically opposite angle theorem,

∠2 ≅ ∠3,

∠2 and ∠6 are corresponding angle,

By the corresponding angle theorem,

∠2 ≅ ∠6,

∠2 and ∠7 are alternate exterior angles,

By the alternate exterior angle theorem,

∠2 ≅ ∠7

Hence, Option 'A' is correct.

Answer:

1.Area of Porch =2.5m²

2.Number of people =3 people

Step-by-step explanation:

The porch area from the diagram has a dimension of 4 units by 10 units

One units =1cm

Thus the porch is drawn with dimensions of 4cm by 10 cm

Taking length is 10 cm and width as 4 cm, convert these dimensions according to the scale.

The scale is 1cm=0.25m

The width will be= 0.25×4=1 m

The length will be=0.25×10= 2.5m

Area of the porch is given by the formula;

length×width because its has a shape of a rectangle

Area of porch will be

=1m ×2.5m =2.5m²

2.

Find the dimensions of the tent

14 units by 10 units

Applying the scale on the dimensions by multiplying by 0.25

14×0.25=3.5m

10×0.25=2.5m

Width=2.5m

length=3.5m

Subtract the edge distance on both the length and width

Length will be=3.5-(0.25×2)=3.0m

Width will be=2.5-(0.25×2)=2.0m

Find the area remaining to be covered by the people while sleeping

=3.0×2.0=6m²

Area covered by sleeping bag and a ground mat

2m×1m=2m²

Number of people that can sleep in the tent

6m²÷2m²=3 people

Answer: Area of porch in metres [tex]= 2.5 m^{2}[/tex]

No. of people that can sleep in the tent = 0 (according to the given conditions)

Step-by-step explanation:

In the given figure we have the scale of 1 cm : 0.25 m which denotes that we have 0.25 m length in actual for every 1 cm on the figure. Also, each square in the figure measures 1 cm on each side.

From the fig. the dimensions of tent porch area are:

Length = 10 cm = [tex]10 \times 0.25[/tex]

[tex]= 2.5 m[/tex] on ground

Breadth= 4 cm = [tex]4 \times 0.25[/tex]

[tex]= 1 m[/tex] on ground

∴ Area of porch in metres = [tex]1\times 2.5[/tex]

Area of porch in metres [tex]= 2.5 m^{2}[/tex]

Answer:

106.90 cm

Step-by-step explanation:

Given

Angle=30 degrees

Base=92.58 cm

So,

We will have to use the triangular ratios to find the hypotenuse.

The triangular ratio that will be used for this will be cosine because we know the value of angle and base since it involves both cosine will be used.

cos⁡θ=Base/Hypotense

cos⁡30=92.58/Hypotenuse

0.8660=92.58/Hypotenuse

Hypotenuse=92.58/0.8660

=106.90 cm ..

Answer:

Hypotenuse = 107.02

Step-by-step explanation:

Points to remember

If angles of a triangle are 30°, 60° and 90° then the sides are  in the ratio

1 : √3 : 2

It is given a right angled  triangle with angles 30°, 60°, 90°

and height = 95.58 cm

To find the hypotenuse

From the figure we can write,

Base : Height : Hypotenuse = 1 : √3 : 2 = Base : 92.58 : Hypotenuse

Therefore Hypotenuse = (92.58 * 2)/√3

  = 107.02 cm

Answer:

288 square units

Step-by-step explanation:

The formula for the area of a square when you know its diagonal is: [tex]\frac{1}{2} d^2[/tex]

So, since we know the half diagonal is 12, we need to multiply that by 2 to get the diagonal, which is 24.

Put 24 into the formula. [tex]\frac{1}{2} * 24^2[/tex]

Simplify the exponent. [tex]\frac{1}{2} * 576[/tex]

Finally, multiply. [tex]288[/tex]

Answer:

7pi/2

Step-by-step explanation:

If was a full, the circumference or the arc length would be 2pi*r where r in this case is 7 so it would be 14pi.

Now this only a quarter of that, so this arc length is actually 14pi/4.

This can be reduced 14pi/4 =7pi/2

Answer:

3.5pi

Step-by-step explanation:

KA

The given line that passes through the points (7,-4) and (-1,3).

The slope is

[tex]m = \frac{3 - - 4}{ - 1 - 7} = - \frac{7}{8} [/tex]

The point-slope form is obtained using:

[tex]y-y_1= m (x-x_1) [/tex]

When (7,-4) is used the point-slope form is

[tex]y + 4= - \frac{7}{8} (x - 7) [/tex]

We expand now to get;

[tex]y = - \frac{7}{8}x + \frac{49}{8} - 4[/tex]

This implies that,

[tex]y = - \frac{7}{8}x + \frac{17}{8}[/tex]

Answer:

-6

Step-by-step explanation:

A(n)=-6+(1-1)(1)

simplified, this equals:

A(n) = -6+(0)(1)

A(n)=-6+0

A(n) = -6, for any given n term.

Answer:

16x² + 56x + 49

Step-by-step explanation:

First, expand:

(4x + 7)² = (4x + 7)(4x + 7)

Follow the FOIL method. FOIL = First, Outside, Inside, Last.

(4x)(4x) = 16x²

(4x)(7) = 28x

(7)(4x) = 28x

(7)(7) = 49

16x² + 28x + 28x + 49

Combine like terms:

16x² + (28x + 28x) + 49

16x² + (56x) + 49

16x² + 56x + 49 is your answer.

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