The dimensions for a rectangular prism are x + 3 for the length, x + 2 for the width, and x for the height. What is the volume of the prism? Enter your answer as a polynomial in standard form.

Question 4

[tex]\sin 30^{\circ}=\frac{y}{14\sqrt{3}}\\\\\frac{1}{2}=\frac{y}{14\sqrt{3}}\\\\\boxed{y=7\sqrt{3}}\\\\\\\\\cos 30^{\circ}=\frac{x}{14\sqrt{3}}\\\\\frac{\sqrt{3}}{2}=\frac{x}{14\sqrt{3}}\\\\\boxed{x=21}[/tex]

Question 5

[tex]\cos 45^{\circ}=\frac{x}{28}\\\\\frac{1}{\sqrt{2}}=\frac{x}{28}\\\\x=\frac{28}{\sqrt{2}}\\\\\boxed{x=14\sqrt{2}}\\\\\\\\\sin 45^{\circ}=\frac{y}{28}\\\\\frac{1}{\sqrt{2}}=\frac{y}{28}\\\\y=\frac{28}{\sqrt{2}}\\\\\boxed{y=14\sqrt{2}}[/tex]

Answer:

x = 2/5

y = 3/5

Step-by-step explanation:

**Disclaimer** Hi there! I assumed the question to be a system of equations. The following answer is a method for solving a system of equations. Thus, if it is not, please let me know and I will modify my answer.

Given information:

[tex]\frac{x}{2}+y=\frac{4}{5}[/tex]

[tex]x+\frac{y}{2} =\frac{7}{10}[/tex]

Eliminate fractions by multiplying 10 on both sides of the first equation:

[tex]10*\frac{x}{2}+10*y=10*\frac{4}{5}[/tex]

[tex]5x+10y=8[/tex]

Eliminate fractions by multiplying 10 on both sides of the second equation:

[tex]10*x+10*\frac{y}{2} =10*\frac{7}{10}[/tex]

[tex]10x+5y=7[/tex]

Current system:

[tex]5x+10y=8[/tex]

[tex]10x+5y=7[/tex]

Multiply the second equation by 2:

[tex]5x+10y=8[/tex]

[tex]20x+10y=14[/tex]

Subtract the first equation from the second equation:

[tex](20x+10y)-(5x+10y)=14-8[/tex]

[tex]20x+10y-5x-10y=6[/tex]

[tex](10y-10y)+20x-5x=6[/tex]

[tex]0+15x=6[/tex]

[tex]\boxed{x=\frac{2}{5} }[/tex]

Substitute the x value back to one of the equations to get the y value:

[tex]x+\frac{y}{2} =\frac{7}{10}[/tex]

[tex](\frac{2}{5}) +\frac{y}{2} =\frac{7}{10}[/tex]

[tex](\frac{2}{5}) +\frac{y}{2}-\frac{2}{5} =\frac{7}{10}-\frac{2}{5}[/tex]

[tex]\frac{y}{2} =\frac{3}{10}[/tex]

[tex]\frac{y}{2}*2 =\frac{3}{10}*2[/tex]

[tex]\boxed{y=\frac{3}{5} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The answer is x = 2/5, y = 3/5 or (2/5, 3/5)

First, in order to avoid fractional values during calculation, multiply both equations by 10 to simplify.

Multiply the 1st equation by 10 and 2nd equation by 5.

    3. 10 (5x +  10y) = 10 (8) ⇒ 50x + 100y = 80

    4. 5 (10x + 5y) = 5 (7) ⇒ 50x + 25y = 35

Subtract : 3rd equation - 4th equation

Now, substitute for x in the 1st equation to find y.

The solution of the fraction given as -8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16) is determined as 4 or - 0.25.

A fraction represents a part of a whole or, more generally, any number of equal parts.

A fraction  can also be described as how many parts of a certain size there are, in a given whole.

The fraction given can be written as follows;

-8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16)

-8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y - 4)(y+4)

-8/(2y - 8)  = [5(y - 4) - (7y + 8)] /(y-4)(y + 4)

-8/(2y - 8)  = (5y - 20 + 7y + 8)/(y-4)(y + 4)

-8/(2y - 8)  = (12y - 12)/(y-4)(y + 4)

cross and multiply both sides of the equation;

-8((y-4)(y + 4)) = (12y - 12)(2y - 8)

-8(y² - 16) = 24y² - 96y - 24y + 96

-8y² + 128 =  24y² - 120y + 96

0 = 32y² - 120y - 32

solve the quadratic equation using formula method;

a = 32, b = -120, c = - 32

y = 4 or -0.25

Thus, the solution of the fraction given as -8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16) is determined as 4 or - 0.25.

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y=6

for the eqution

[tex]\frac{-8}{2y-8} =\frac{5}{y+4} -\frac{7y+8}{y^{2}-16 } \\[/tex]

Answer:

1000xm

Step-by-step explanation:

1 meter = 3.2808 feet, hence. 9.8424 x 10^8 feet in 1 second. 1 foot in x seconds. hence it takes 1 / (9.8424 x 10^8) = 0.10168 x 10^(-8) seconds. ➡️1km = 1000xm⬅️

It will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.

To find out how long it will take light to travel one meter, we need to convert the given distance of 10,000 km to meters and the time of 3.0 x 10² seconds to seconds.

Given:

Distance traveled by light = 10,000 km

Time taken by light = 3.0 x 10² seconds

To convert km to meters, we know that 1 km = 1 x 10³ m, so:

10,000 km = 10,000 x 1 x 10³ m = 1 x 10⁷ m

Now, we can find the time taken to travel one meter by dividing the total time by the total distance:

Time taken to travel one meter = Total time / Total distance

Time taken to travel one meter = (3.0 x 10² seconds) / (1 x 10⁷ m)

To simplify the expression, we can cancel out one factor of 10 from the numerator and denominator:

Time taken to travel one meter = (3.0 x 10) / (1 x 10⁶ m)

Now, we get the final answer:

Time taken to travel one meter = 3.0 x 10⁻⁵ seconds

So, it will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.

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The attached graph is the graph of the function f(x) = -2sin(x)

The function is given as:

f(x) = -2sin(x)

The above function is a sine function that has an amplitude of 2

Next, we plot the graph of the sine function f(x) = -2sin(x) using a graphing calculator

See attachment for the graph of f(x) = -2sin(x)

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Answer:

f(t)=250(1-0.12)^t

or

f(t)=250(0.88)^t

Step-by-step explanation:

Use the formula f(t)=P(1+b)^t

Plug in the information.

f(t)=250(1-0.12)^t

or

f(t)=250(0.88)^t

The only thing I did in the second equation is I subtract 0.12 from 1.

Hope this helps!

Multiplying both sides of an inequality by a negative number reverses the inequality symbol.

The table of values is given as:

A: (-16 > -4) (-16 < -4) (-16 = -4)

B: (40 > 8) (40 < 8) (40 = 8

C: (-45 > 15) (-45 < 15) (-45 =15)

D: (35 > -20) (35 < -20) (35 = -20)

In the above list of inequalities, the true inequalities are

-16 < -4 --- because -16 is less than -4

40 > 8 --- because 40 is greater than 8

-45 < 15 --- because -45 is less than 15

35 > -20 --- because 35 is greater than -20

Lastly, when an inequality is multiplied or divided by a negative number, the inequality sign changes

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Answer:

-16 < -4

40 > 8

-45 < 15

35 > -20

Reverses

Step-by-step explanation:

hope this helps

Answer:

2(7x + 2)

Step-by-step explanation:

Perimeter of a Rectangle = 2 x Length + 2 x Width.

Given Length = 4x, Width = 3x + 2,

Perimeter of Rectangle = 2(4x) + 2(3x + 2)

= 8x + 6x + 4

= 14x + 4 (Degree one polynomial)

= 2(7x + 2)

Answer:

7a + b

Step-by-step explanation:

5a + 2a + 3b - 2b

= 7a + 3b - 2b

= 7a + b

The first table is a quadratic function while the second table is a linear function.

1) For the first table, we have;

x y

0 5

1 0

2 -3

3 -4

4 -3

x = 2  and x = 4 have same value of y = -3  and as such it will be a Quadratic Function.

y = x²  - 6x + 5

2) For the second table, we have;

x y

2 5

5 14

6 17

8 23

10 29

This table is a Linear function because  slope is same and equal to 3 all through. Thus, the equation is y = 3x - 1  

3) For the third table, we have;

x y

-3 8

-2 4

-1 2

0 1

1 0.5

This is an exponential function because equation can be modelled by;

y = 2⁻ˣ

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Answer:

Step-by-step explanation:

Step-by-step explanation:

15 r blue marbles

20- 5 = 15

To make x² + 6x = 7 a perfect square, we add 16 to the equation.

In the question, we are asked for the term that must be added to the equation x² + 6x = 7, to make it into a perfect square.

The given equation can be shown as:

x² + 6x = 7,

or, x² + 6x - 7 = 0.

To make it a perfect square, we need to find the b² term as per the 2ab term for the formula, (a + b)² = a² + 2ab + b², where a is x.

This can be shown as:

x² + 6x - 7 = 0,

or, x² + 2(x)(3) - 7 = 0, where we get b = 3.

Thus, b² = 3² = 9, can be obtained by adding 16 to the equation, as -7 + 16 = 9.

Thus, we add 16 to both sides of the equation, to get:

x² + 2(x)(3) - 7 + 16 = 16,

or, x² + 2(x)(3) + 9 = 16,

or, (x + 3)² = 16, which gives us the required perfect square.

Thus, to make x² + 6x = 7 a perfect square, we add 16 to the equation.

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Answer:

A' (-15, -5)

B' (10, -10)

C' (-5, -20)

Answer:

A ' (-15, -5)

B ' (10, -10)

C ' (-5, -20)

Step-by-step explanation:

The scale factor is [tex]K=5[/tex]. This tells us to multiply each coordinate, of each point, by the scale factor (5) to get the dilated points.

Point A is at [tex](-3,-1)[/tex] and moves to [tex]A ' (-15, -5)[/tex] after multiplying the x and y coordinates by 5. The same applies to points B and C as well.

Point B moves from [tex](2,-2)[/tex] to [tex]B' (10,-10)[/tex] because [tex]2*5=10[/tex] and [tex]-2*5=-10[/tex]. This also means that Point C moves from [tex](-1,-4)[/tex] to [tex]C' (-5,-20)[/tex] because  [tex]-1*5=-5[/tex] and [tex]-4*5=-20[/tex].

The dilation rule can be written as [tex](x, y)[/tex] → [tex](5x, 5y)[/tex]

As a result of the dilation, triangle A'B'C' has sides that are 5 times longer compared to the corresponding sides of triangle ABC.

The new price after the price increase of Nu 40 will be Nu 840.

The price of a pant after n Nu 40 price increases will be:

= 800 + 40

= 840

The expected weekly sales as a function of the number of price increases will be:

= n - 1) × 800

= (30 - 1) × 800

= 29 × 800

= 23200

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F(x)= 2(x-2)^2 + 2 is the correct equation of F(x)

A quadratic function is a polynomial function of the second degree. The general form of a quadratic function is this: f (x) = ax^2 + bx + c, where a, b, and c are real numbers and a≠ 0.

Graphs of quadratic functions

The term "parabola" refers to the graph of a quadratic function. A parabola essentially resembles the letter "U," yet it can be inverted or exactly this shape depending on the situation. The leading coefficient determines whether the graph of a quadratic function opens up or down; if it is more than zero, the parabola opens up; if it is less than zero, the parabola opens down.

It is given that graph of F(x), shown below, resembles the graph of G(x) = x^2, but it has been changed somewhat.

We need to find the equation of F(x)

In the figure, parabola opens up, the leading coefficient is greater than zero ,So option (d) is correct

Hence the equation of F(x) is 2(x-2)^2 + 2

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The volume of the solid is 900 cubic unit given that the solid lies between planes perpendicular to the x-axis at x = 0 and x = 19, the cross sections perpendicular to the x-axis on the interval 0 ≤ x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x. This can be obtained by finding the area of the square using the length of the diagonal.

Given that, diagonals that run from the parabola y = - 2√x to the parabola   y = 2√x

D = 2√x - (-2√x)

D = 4√x

D² = s² +  s², where s is the side of the square

(4√x)² = 2s²

16x = 2s²

s² = 8x

s² is the area

Thus,

V = [tex]\int\limits^{15}_0 {8x} \, dx[/tex]

V =  [tex]8\int\limits^{15}_0 {x} \, dx[/tex]

V = 4 (15² - 0)

V = 4×225

⇒ V = 900 cubic unit

Hence the volume of the solid is 900 cubic unit given that the solid lies between planes perpendicular to the x-axis at x = 0 and x = 19, the cross sections perpendicular to the x-axis on the interval 0 ≤ x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x.

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: A solid lies between planes perpendicular to the x-axis at x = 0 and x = 19. The cross sections perpendicular to the x-axis on the interval         0 ≤x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x. Find the volume of the solid.

Answer:

B, cos(0)=1

Step-by-step explanation:

cos(0)=1

Coordinate A is at point (1,0)

Answer: [tex]\frac{\sqrt{6}}{2}[/tex]

Step-by-step explanation:

By the Pythagorean theorem,

[tex]2^2 + (MN)^2 = (\sqrt{10})^2\\\\4+(MN)^2 = 10\\\\(MN)^2 = 6\\\\MN=\sqrt{6}\\\\\implies \tan L=\frac{\sqrt{6}}{2}[/tex]

Answer:

Below.

Step-by-step explanation:

x^2 + 4x  = 18

x^2 + 4x + (2)^2 = 15 + 2^2

x^2 + 4x + 4 = 18 + 4

(x + 2)^2 = 22

x  + 2 = +/- √22

x = -2 + √22 and x =  -2 + √22

x = 2.7  and -6.7  to nearest tenth.

Answer:

5.373 cm

Step-by-step explanation:

Divide the volume by the length to find the area of the equilateral triangle

100/8 = 12.5

Area of equilateral triangle = sqrt(3) / 4  *  s^2   = 12.5

   s^2 = 12.5 *4  / sqrt3

    s = 5.373 cm

The simplified form of the expression is x-4 + 2/x-2

Given the following fraction below

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

Using the long division as shown below;

        x + 4

x-2 |  x^2 + 2x - 6

        x^2 - 2x

_________________

                4x   - 6

                 4x   - 8

___________________

                         2

Hence the simplified form of the expression is x-4 + 2/x-2

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Answer:

C. 7

Step-by-step explanation:

The answer is 7. Use the power of a power property. To use it you have to multiply the power inside the parenthesis to the one outside of the parenthesis. 1/5 * 5 = 1. Since the power is 1, you do not need to write the power.

Hope this helps!

Answer: Read the explanation

Step-by-step explanation:

If the points of a figure are all moved the same, they are congruent.

Point A is moved 9 points right, and 7 points down.

Point B is moved 9 points right, and 7 points down.

Point C is moved 9 points right, and 7 points down.

So, they are congruent.

Answer:

[tex]m_{1} =1/2\\m_{2} =5[/tex]

Step-by-step explanation:

[tex]2m^{2} -11m+5=0[/tex]

[tex](2m-1)(m-5)=0[/tex]

[tex]2m-1=0\\2m=1\\m_{1} =1/2[/tex]

[tex]m-5=0\\m_{2} =5[/tex]

Hope this helps

What is a Venn Diagram?

Explain : A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.

How to draw a Venn Diagram?

Explain : To create an intersecting Venn diagram, draw three circles that overlap in the middle. You'll be able to show which attributes are unique to each circle, which overlap between two, and which are common characteristics of all three groups. Two circles overlapping is a classic venn diagram

What is a venn Diagram mostly used for?

Explain : A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.

Set notations: The concepts illustrated in Venn ...

Scaled Venn Diagram: Also called Area Propo...

Reuleaux Triangle: Shape formed from the int...

Intersection: The items that overlap in the sets. ...

Here's some question for Venn Diagrams!

A. What's the first step creating a Venn Diagram? https://www.math-only-math.com/practice-test-on-Venn-diagrams.html

B. What's the last step to create a Venn Diagram? https://www.purplemath.com/modules/venndiag4.htm

C. What does a Venn Diagram looks like?

( Try using those questions to partice more about Venn Diagrams! )

( Also, thank you for the points! )

The equation of the function is −3<x<1. See the explanation below.

Given the graph of function f is a parabola,

Thus, equation of parabola  is y=(x+3)(x+1)

⇒y=x² +4x+3

⇒y−3+2²

= x²+2× x ×2+2²

⇒y+1=(x+2)²

We can rewrite this as

 (x+2)² =4× (1/4) ×(y+1)

Comparing the above equation to the equation of a parabola, (x−h)² =4a(y−k), where (h,k) is the coordinates of vertex of parabola, we have,

(h,k)≡(−2,−1)

Hence, the x coordinate of the vertex is −2 which lies in the interval −3<x<1

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Answer:

C.) [tex]x^{\frac{3}{2} } y^{\frac{19}{2} }[/tex]

Step-by-step explanation:

To simplify the expression, you need to:

1.) Rewrite [tex]\sqrt{xy^{3} }[/tex]

    -----> [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]

2.) Distribute the exponents

    -----> When an exponent is raised to another exponent, they should be multiplied

3.) Create common denominators

4.) Combine the variables

    -----> When two variables with exponents are being multiplied, the exponents should be added