A square prism has a height of 15 centimeters and a volume of 960 cubic centimeters. What is the measure of the width of the square base

Answer:

Distributive Law : x= [tex]\frac{11}{10}[/tex]

Step-by-step explanation:

5(2x - 1) = 6

Using Distributive law on right hand side we get

5*2x - 5 * 1 = 6

10x - 5 = 6

Now we add 5 on both hand sides

10x-5+5=6+5

10x= 11

Now we divide both sides by 10

[tex]\frac{10x}{10} = \frac{11}{10}[/tex]

Hence we get

x= [tex]\frac{11}{10}[/tex]

Answer: 13

Step-by-step explanation:

Divide 325 by 25

Answer: x=3

Step-by-step explanation: First we do distributive property in the parentheses. Next we subtract both sides by 6. Lastly we divide both sides by 3. Algebraic Rules!!!

Work:

3(x+2)=15

3x+6=15

3x+6-6=15-6

3x=9

3x/3=9/3

x=3

Multiply the bracket by 3

3x+6=15

3x+6-6=15-6

3x=9

divide by 3 for 3x and 9

3x/3=9/3

x=3

Check answer by using substitution method

3(x+2)=15

3(3+2)= 15

Multiply the bracket by 3

9+6= 15

15= 15

Answer is x= 3

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Final answer:

The graph of an equation reveals all possible solutions, and a system of equations can be solved graphically by finding the intersection points of their lines. Changing the slope or intercept allows manipulation of these lines, and growth rates show the rate of increase as perce

Explanation:

The graph of an equation illustrates the relationship between two variables and reveals the set of all possible solutions that satisfy the equation. When graphing a line, the slope dictates the direction and steepness of the line, while the intercept indicates where the line crosses the y-axis. To manipulate a line on a graph, you can change the slope or the intercept, altering its position and angle.

To solve a system of equations using graphs, plot each equation on the same set of axes. The point where the lines intersect represents the solution to the system, which is the set of values that satisfies all equations simultaneously. If using tables, input different values for one variable and solve for the other to find ordered pairs. When the pairs from different equations match, you've found an approximate solution. A growth rate can be determined by calculating the percentage change and can be interpreted as the rate at which a quantity increases over time.

Learning how to read and manipulate a graph is critical to interpret and express equations visually. Graphs not only convey solutions but also the behavior of equations, such as trends and growth rates, which are essential in understanding and communicating mathematical concepts effectively.

Answer:

3 terms. All of the numbers are considered terms.

Step-by-step explanation:

If it asked for variables, it would be 2.

FICA taxes on a W-2 form include Social Security and Medicare taxes, summed up at a standard rate of 7.65% of gross wages. To know the total FICA taxes paid, one must multiply the gross wages by 7.65% based on the provided rates.

The question is asking for the total FICA taxes paid, which includes both Social Security and Medicare taxes. The information provided indicates that the employee pays 6.2% for Social Security and 1.45% for Medicare, which are standard rates for FICA tax deductions. To calculate the total amount of FICA taxes, add these percentages together to get a combined rate of 7.65%. If you know the gross wages, you multiply this amount by 7.65% to find the total FICA tax contribution on your W-2 form. If the actual gross wages earned are unknown, the calculation cannot be completed without this figure.

It is important to note that your employer also matches the FICA tax contributions, and some economists argue that this employer contribution effectively reduces employees' wages, meaning that employees might bear the total cost of these taxes indirectly.

Answer:

The final angle is 124°

Step-by-step explanation:

1. Getting the total sum of all angles:

The general rule to get the sum of all interior angles is as follows:

sum of interior angles = (n-2)*180

where n is the number of sides

We know that a heptagon has 7 sides, therefore:

sum of interior angles of a heptagon = (7-2)*180 = 5 * 180 = 900°

2. Getting the missing angle:

We know that the total sum of all 7 angles is 900°

We also know that the sum of 6 of those angles = 776°

This means that:

measure of the last angle = 900 - 776

measure of last angle = 124°

The final angle is 124°

Hope this helps :)

Answer:

124 degrees

Step-by-step explanation:

Answer:

The best function represented by the scatter plot is f(x) = -5 + 0.5 x ⇒ 1st answer

Step-by-step explanation:

* Lets talk about the scatter plot

- Scatter plots are similar to line graphs in that they use horizontal and

 vertical axes to plot data points

- Scatter plots show how much one variable is affected by another.

- The relationship between two variables is called their correlation

- There are three types of correlation:

  positive: one variable increases so the other increase

  negative: as one variable increases, the other decreases

  no correlation:  there is no clear relationship between the variables

* Lets solve the problem

- The scatter plot shows the relationship between the leaf length (x)

  and leaf width f(x)

- Some leaves of a tree are ordered pairs:

# (11 , 0.5) , (12 , 1) , (13 , 1.5) , (14 , 2) , (15 , 2.5) , (16 , 3) , (17 , 3.5) ,

  (18 , 4) , (19 , 4.5) , (20 , 5) , (21 , 5.5) , (22 , 6)

∵ The scatter plot is similar to the line graph

- Lets find the equation which represents the relation between

 x and f(x)

∵ The form of the linear equation is y = mx + c, where m is the slope

  of the line and c is the y-intercept

- The rule of the slope of the line which passes through points (x1 , y1)

 and (x2 , y2) is: [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

- Chose any two points to find the slope of the line

∵ (12 , 1) and (14 , 2) are two points on the line

∴ [tex]m=\frac{2-1}{14-12}=\frac{1}{2}=0.5[/tex]

- Substitute the value of m in the equation

∴ y = 0.5 x + c

- To find c use any point from above and substitute x and y by its

  coordinates

∵ Point (16 , 3) lies on the line

∴ 3 = 0.5(16) + c ⇒ simplify

∴ 3 = 8 + c ⇒ subtract 8 from both sides

∴ 3 - 8 = c

∴ c = -5  

- Substitute the value of c in the equation

∴ y = 0.5 x - 5

* The best function represented by the scatter plot is f(x) = -5 + 0.5 x

Answer:

A. (-6, 5, 5)

Step-by-step explanation:

A suitable calculator can reduce the augmented matrix for the system.

Answer:

it is 0 because cosine is the x and sine is the y. Sin is 1 and cos is 0

[tex]\bf \begin{array}{ccll} miles&hours\\ \cline{1-2} 48&1\\ 30&x \end{array}\implies \cfrac{48}{30}=\cfrac{1}{x}\implies \cfrac{8}{5}=\cfrac{1}{x}\implies 8x=5 \\\\\\ x=\cfrac{5}{8}\qquad \textit{37 minutes and 30 seconds}[/tex]

Answer:

Option D.(60, 135)

Step-by-step explanation:

Let

x -----> the number of acres of peas

y ----> the number of acres of carrots

we know that

The inequality that represent the problem is equal to

[tex]x+y\leq 200[/tex]

so

Verify each case

case A) (-50,160)

substitute the value of x and the value of y in the inequality and then compare the result

[tex]-50+160\leq 200[/tex]

[tex]110\leq 200[/tex] ----> is true

The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number

case B) (80,160)

substitute the value of x and the value of y in the inequality and then compare the result

[tex]80+160\leq 200[/tex]

[tex]240\leq 200[/tex] ----> is not true

therefore

The point is not a solution

case C) (75,-200)

substitute the value of x and the value of y in the inequality and then compare the result

[tex]75-200\leq 200[/tex]

[tex]-125\leq 200[/tex] ----> is true

The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number

case D) (60,135)

substitute the value of x and the value of y in the inequality and then compare the result

[tex]60+135\leq 200[/tex]

[tex]195\leq 200[/tex] ----> is true

therefore

The point is a viable solution

Answer: First option.

Step-by-step explanation:

Knowing that the transformation T maps triangle XYZ onto triangle X'Y'Z', you can identifyfrom the figure that the triangle XYZ is the preimage, because it is the original shape and the triangle X'Y'Z' is the image, because is the shape obtained after the transformation.

You can observe in the figure that the image of the vertex X is the vertex X', the image of the vertex Y is the vertex Y' and the image of the vertex Z is the vertex Z'.

Therefore, the conclusion is: The image of Y is Y'.

Answer:

  1329

Step-by-step explanation:

A suitable calculator can tell you the minimum score is 1329.

Using the concept of z-scores and normal distributions, the lowest possible SAT score a student needs to qualify for acceptance into a top university, that requires top 5% of SAT scores, is approximately 1328.

The subject of your question falls under Mathematics, particularly statistics. The problem involves understanding SAT scores and how they apply to scholarships. The problem also asks for the understanding of z-scores and how they apply to normal distributions.

In this case, the SAT score requirement is stated to be within the top 5% of all test-takers. In terms of z-scores, this requirement matches with a z-score of approximately 1.64, since z-scores of this value represent the cut-off for the top 5% in a normal distribution.

To calculate the corresponding SAT score, we use the formula for z-score which is Z = (X - μ) / σ, where X is the SAT score, μ is the mean and σ is the standard deviation. We rearrange the formula to find X, where X = Z * σ + μ. Since we know the mean (μ = 1000), standard deviation (σ = 200), and Z (Z = 1.64), we can substitute these values to get X = 1.64 * 200 + 1000 = 1328.

Therefore, the lowest possible score a student needs to qualify for acceptance into the university is approximately 1328.

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Answer:

c

Step-by-step explanation:

c. positive 3 or 1; negative 1

Answer:

See below.

Step-by-step explanation:

The model may have the scale written somewhere. Try looking for it.

If you can't find it, then you can calculate this way.

Search online for the real motorcycle's length.

Then divide the scale model's length, 18 inches, by the real length. Express that as a ratio. That is the scale.

Let's say the length of a real motorcycle of this type is 90 inches.

Divide 18 inches by 90 inches.

18/90 = 1/5

The scale, then, is 1:5.

Answer:

The function in choice

A) [tex]h(t) = -16(t - 3)^{2} + 34[/tex]

could possibly represent this relationship.

Step-by-step explanation:

Consider the vertex form of parabolas with a local extrema at [tex](x_{0}, y_{0})[/tex].

[tex]y = a(x - x_{0})^{2} + y_0[/tex].

Note the minus sign in front of [tex]x_0[/tex] in this expression.

The coefficient [tex]a[/tex] cannot be zero. The value of [tex]a[/tex] depends on the direction and width of the parabola's opening:

For this parabola,

Among the four functions, only the function in A) meets the requirements.

Answer:

Step-by-step explanation:

area=6×11.4×13÷2=444.6 yd²

Final answer:

The area of a regular hexagon with an apothem of 11.4 yards and a side of 13 yards is approximately 444.6 square yards when rounded to the nearest tenth.

Explanation:

To find the area of a regular hexagon with a given apothem and side length, you can use the formula for the area of a regular polygon:

Area = (1/2) × Perimeter × Apothem

In this case, the perimeter of the hexagon can be calculated by multiplying the length of one side by 6 (since a hexagon has 6 sides). Therefore, the Perimeter = 13 yards × 6 = 78 yards.

Now, plug the values into the area formula:

Area = (1/2) × 78 yards × 11.4 yards

Area = (1/2) × 889.2 square yards

Area = 444.6 square yards

So, the area of the regular hexagon is approximately 444.6 square yards, when rounded to the nearest tenth.

Answer:

D

Step-by-step explanation:

(x + 5)x = 104

Distribute:

x² + 5x = 104

Subtract 104 from both sides:

x² + 5x − 104 = 0

Answer:

  1.5

Step-by-step explanation:

The coordinate values of point J are 1.5 times those of point A, so if dilation is about the origin, the scale factor is 1.5.

If the dilation is about some other point, this problem statement does not contain enough information to tell what the scale factor might be.

[tex]\boxed{x=1, \y=-1, \ z=2}[/tex]

We will use the Gaussian elimination method to solve this problem. To do so, let's follow the following steps:

Step 1: Let's multiply first equation by −2. Next, add the result to the second equation. So:

[tex]\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\~~ x&-~~~~~ y&+~~~~ z&~=~4\end{array}[/tex]

Step 2: Let's multiply first equation by −1. Next, add the result to the third equation. Thus:

[tex]\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&-~~~3~ y&+~~2~ z&~=~7\end{array}[/tex]

Step 3: Let's multiply second equation by −35, Next, add the result to the third equation. Therefore:

[tex]\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&&+~~\frac{ 1 }{ 5 }~ z&~=~\frac{ 2 }{ 5 }\end{array}[/tex]

Step 4: solve for z, then for y, then for x:

[tex] \frac{ 1 }{ 5 } ~ z & = \frac{ 2 }{ 5 } \\ \\ \boxed{z & = 2}[/tex]

[tex]-5y+3z &= 11\\-5y+3\cdot 2 &= 11\\ \\ \boxed{y &= -1}[/tex]

By substituting [tex]y=-1 \ and \ z=2[/tex] into the first equation, we get the [tex]x[/tex]. So:

[tex]x+2(-1)-2=-3 \\ \\ x-2-2=-3 \\ \\ \boxed{x=1}[/tex]

Answer:

X= 1, y= -1, z= 2

Step-by-step explanation:

let's take a peek at the graph.

the graph of the equation touches the x-axis at 1, 2 and 3, at 1 it crosses it, at 2 it crosses it, at 3 is doesn't cross it, it simply bounces off of it.

on the roots/solutions the graph crosses the x-axis, they have ODD multiplicity, on the solutions it bounces off of it, they have EVEN multiplicity, so then.

x = 1 => x - 1 = 0  <------ one  factor

x = 2 => x - 2 = 0 <------ another factor

x = 3 => x - 3 = 0  <------ another factor, BUT with even multiplicity

(x-1)¹(x-2)¹(x-3)² = f(x)

(x-1)(x-2)(x-3)² = f(x).

Answer:172

Step-by-step explanation:

24.5 times 6 is 157

Plus 15 for the paint is 172 for the TOTAL for ALL she spent

Answer:

Step-by-step explanation

Answer:

a) Let b represent the number of blue marbles placed in the second jar. Then 34-b is the number of yellow marbles in the second jar, and 25 - (34-b) is the number of yellow marbles remaining in the first jar. That value simplifies to b-9. The positive difference between b and (b-9) is 9.  

b) Let n, d, p represent the numbers of nickels, dimes, and pennies, respectively.  

.. (5n + 10d + p)/(n + d + p) = 7 ... the average value of the collection is 7 cents per coin  

.. (5(n-1) + 10d + (p+5))/((n-1) + d + (p+5)) = 6 ... replacing one nickel with pennies changes the average to 6 cents per coin  

Multiplying by the denominator and subtracting the right side of each resulting equation gives  

.. 10d + 5n + p = 7d + 7n + 7p  

.. 10d + 5n + p = 6d + 6n + 6p + 24  

Subtracting the second equation from the first gives  

.. 0 = d + n + p - 24 ... tells us the total number of coins is 24. This tells us the total value is $1.68 = 24*$0.07.  

This sum will consist of at least 3 pennies. If that is all the pennies, then the remaining 21 nickels and dimes must add to $1.65. If all were nickels, the value of the 21 coins would be $1.05. We have $0.60 more than that. For each nickel traded for a dime, we gain $.05, so 12 of the 21 nickels must be traded for dimes to raise the total coin value to $1.65.  

Alternatively, you can write two equations in the two unknowns:  

.. d + n = 21  

.. 10d + 5n = 165  

Subtracting 5 times the first equation from the second gives  

.. 5d = 60 ... which gives the same answer as reasoned above.  

There are 3 pennies, 9 nickels, 12 dimes. (If there are 8 pennies to start, then the number of nickels is zero, so it is impossible to trade one for 5 pennies. The solution shown is the only one.)

Answer:

A) 2k+4

Step-by-step explanation:

To solve for terms of x, we need to. she sure that x is on its own side while every other term is on the other side.

To start, we will cross multiply. If we have a/b=c/d, then ad=bc

We can perform the same calculation here,

6/x=3/(k+2)

6(k+2)=3x

Divide both sides by 3

2(k+2)=x

x=2k+4

Answer:

A

Step-by-step explanation:

The equation will be in the form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (2.5, 0) ← 2 points on the line

m = [tex]\frac{0-5}{2.5-0}[/tex] = - 2

The line crosses the y- axis at (0, 5) ⇒ c = 5

y = - 2x + 5 or

y = 5 - 2x → A

Answer:

  1/8 ft³

Step-by-step explanation:

Apparently cubic blocks that are 1/5 of 2 1/2 ft on a side are used to fill the cube that is 2 1/2 ft on a side. Then each edge of the block is ...

  (1/5) × (5/2 ft) = 1/2 ft

The volume of the block is the cube of that:

  (1/2 ft)³ = 1/8 ft³

The sculptures of great baseball sluggers are found in famous places of the city.

Here,

The sculptures of any famous personalities are installed in the places that are frequently visited by the public , so that the it will gain traction.

Thus,

The sculptures of famous baseball players will be available in city malls , museums , parks or baseball stadium.

The players coming to play baseball will be motivated by seeing their idols.

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Answer:

B.

Step-by-step explanation:

First thing to determine is how this parabola opens.  Up or down? Or left or right?  

*We see that the axis of symmetry is a line parallel to the y-axis; therefore, the axis of symmetry is an x =    line, making this an up or down parabola.  Now we need to determine how everything else all fits in.

The standard form of this type of parabola is

[tex]4p(y-k)=-(x-h)^2[/tex]

where p is the distance between the vertex and the focus.  If the vertex has a y coordinate of 3, and the focus has a y coordinate of -3, the vertical distance between those 2 numbers is 6.  Therefore, p = 6.  Filling in then:

[tex]4(6)(y-3)=-(x-4)^2[/tex]

and [tex]24(y-3)=-(x-4)^2[/tex]

Dividing both sides by 24 gives you what you are looking for:

[tex]y-3=-\frac{1}{24}(x-4)^2[/tex]

The equation of the parabola is:

⇒ y - 3 = -(1/24)(x - 4)²

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix.

We can use the standard form of the equation of a parabola with vertex (h, k) and axis of symmetry parallel to the y-axis, which is given by:

(x - h)² = 4p(y - k)

where (h, k) is the vertex and p is the distance between the vertex and the focus.

In this case, the vertex is (4, 3) and the focus is (4, -3).

Therefore, We get;

p = 3 - (-3)

p = 6.

Substituting the values of h, k, and p, we get:

(x - 4)² = 4(6)(y - 3)

Simplifying, we get:

(x - 4)² = 24(y - 3)

Now, we can simplify the equation to match it with the given options:

(x - 4)² = 24y - 72

(x - 4)² + 72 = 24y

y = (1/24)(x - 4)² + 3

Therefore, the equation of the parabola is:

B.) y - 3 = -(1/24)(x - 4)²

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Answer:

$.80 and 1.25

Step-by-step explanation:

hope this helps