Sand Castles
Juan built a sand castle like the one shown. The castle is shaped like a rectangular prism with a rectangular pyramid on top. How much sand did it take Juan to build it?

The functions f and g that adds up to h(x) are:

f(x) = -2x+3 and g(x) = 7x-9

Step-by-step explanation:

Required output is:

h(x) = 5x-6

In order to find the required f and g functions we will see that which of the two functions add up to h(x)

In order to make our work easier we can see the functions f and g whose coefficients of  add up to 5x

Then we can select from the functions that produce h(x)

So,

Pair 1 whose coefficients of x add up to 5 is:

f(x) = -2x+6 and g(x) = 7x-9

Adding both functions

[tex](f+g)(x) = -2x+6+7x-9\\= 5x-3[/tex]

Pair 2 that adds up to 5x

f(x) = 8x+9 and g(x) = -3x-3

Adding both functions:

[tex](f+g)(x) = 8x+9-3x-3\\= 8x-3x+9-3\\=5x+6[/tex]

Pair 3 is:

f(x) = -2x+3 and g(x) = 7x-9

Adding both functions

[tex](f+g)(x) = -2x+3+7x-9\\= -2x+7x+3-9\\=5x-6[/tex]

Hence,

The functions f and g that adds up to h(x) are:

f(x) = -2x+3 and g(x) = 7x-9

Keywords: Functions, Sum of functions

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Answer:

(A) y+2=3(x-1)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-2)=3(x-1)

y+2=3(x-1)

Answer:

The student council from each box of candy will make the profit of $23.50.

Step-by-step explanation:

Given:

Each box of candy costs $50. Profit of 47% from each candy.

Now, to get the amount of how much profit from each box:

Amount of profit (A) = Profit% of cost of candy of each box

A = 47% of $50

[tex]A=\frac{47}{100}\times 50[/tex]

[tex]A=0.47\times 50[/tex]

[tex]A=23.50[/tex]

Amount of profit = $23.50

Therefore, the student council from each box of candy will make the profit of $23.50.

To find the product of 7 and 28 using place value and the distributive property, rewrite the product as 7(20 + 8). Distribute the 7 to both terms inside the parentheses and then add the resulting products.

To find the product of 7 and 28 using place value and the distributive property, we can rewrite the product as 7(20 + 8). This is because 28 can be decomposed into 20 + 8.

Using the distributive property, we can distribute the 7 to both terms inside the parentheses: 7(20) + 7(8).

The product of 7 and 20 is 140 and the product of 7 and 8 is 56. Therefore, the final product is 140 + 56 = 196.

The rectangle can be divided into  6 ways as, 1 × 56 or 56 × 1,  2 × 28 or 28 × 2, and 4 × 14 or 14 × 4.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.

Given:

Darren has a piece of wood that is 7 in by 8 in

The area of the rectangle can be given by,

[tex]Area = Length\times width[/tex]

Area = 7 × 8

Area = 56

You can now divide the length and width as shown below,

Rectangle =   1 × 56 or 56 × 1

Rectangle =   2 × 28 or 28 × 2

Rectangle =   4 × 14 or 14 × 4

Therefore, the rectangle can be divided into  6 ways as   1 × 56 or 56 × 1,  2 × 28 or 28 × 2, and 4 × 14 or 14 × 4.

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Answer:

120 50 pound bags

Step-by-step explanation:

first you see how much 50 pounds is to one ton which one 50 pound bag is equal to .025 tons

then you multiply .025 by 120 to get 3 (tons)

that shows that the answer is correct

The correct answer is A

Answer: B. 239 Square Feet

Step-by-step explanation:

Let y be the size of a kitchen that costs $3,824.00.

Given : The price of tiling a room varies directly as the size of the room.

Equation of direct variation between x and y : [tex]\dfrac{x_1}{x_2}=\dfrac{y_1}{y_2}[/tex]

If the tiling costs 4,224.00 for 264 square feet , to find the  size of a kitchen that costs $3,824.00.

We put [tex]x_1= 4224 \ \ ; \ y_1=264\ ; \x_2=3824\ ; \ y_2=y[/tex] , we get

[tex]\dfrac{4224}{3824}=\dfrac{264}{y}\\\\\Rightarrow\ y=\dfrac{264\times3824}{4224}=239[/tex]

Hence, the size of a kitchen that costs $3,824.00 is 239 Square Feet

The correct answer is B. 239 Square Feet

Answer:

52

Step-by-step explanation:

2200 / 42 = 52.381

You cannot bring a section of a carton, and 53 cartons is too much

53 * 42 = 2226. This goes over the weight limit.

52 * 42 = 2184. 2184 is less than 2200, so 52 is the greatest number you can bring

By dividing the elevator's weight capacity of 2200 pounds by the weight of one 42-pound carton, we find it can carry a maximum of 52 whole cartons simultaneously without exceeding the weight limit.

To solve this problem, we can use simple mathematical analysis. We need to calculate how many 42-pound cartons can fit into an elevator that has a maximum capacity of 2200 pounds without exceeding this limit.

We start with the equation:

Therefore, the elevator can safely carry 52 cartons at once, without any people in it.

A 100% increase means a value doubles, a 100% decrease means it drops to zero, and 100% error indicates complete inaccuracy. For increases and decreases, the percentage is calculated based on the ratio of change to the original amount multiplied by 100%. Percent error compares the experimental value with the accepted value to judge accuracy.

An example of a 100% increase would be if you have $50, and this amount doubles to $100. Here the final amount is 100% more than the original, as the increase ($50) is equal to the original value ($50). The formula used is % increase = (Amount of increase/original amount) x 100%. So, % increase = ($50/$50) x 100% = 100%.

A 100% decrease implies that something diminishes completely to zero. For instance, if you have 10 apples and all of them are taken away, the percent decrease is 100% since the decrease (10 apples) equals the original quantity (10 apples). The calculation would be % decrease = (Decrease/original amount) x 100%, which results in % decrease = (10/10) x 100% = 100%.

100% error in a measurement means the measurement is completely inaccurate. For example, if the accepted value of a length is 30 cm and the experimental measurement is 60 cm, then the percent error is calculated as: % error = (Absolute value of (Experimental value - Accepted value)/Accepted value) x 100%, which in this case is % error = (|60 cm - 30 cm|/30 cm) x 100% = 100%. This represents a complete deviation from the actual value.

Answer:

Nick gave 3 marbles to each of his 4 friends.

Step-by-step explanation:

Given:

Total Number of Marbles = 12

Number of Friends = 4

Let the number of marbles to be divided in each friend be x

Solution:

To find the number of marbles to be divided in each friend we have to divide Total Number of Marbles by  Number of Friends.

Hence number of marbles to be divided in each friend x = [tex]\frac{\textrm{Total Number of Marbles}}{\textrm{Number of friends}}= \frac{12}{4}=3[/tex]

Hence we can say that Nick gave 3 marbles to each of his 4 friends.

Answer:

21 miles

Step-by-step explanation:

Jeff drove [tex]=\dfrac{1}{2}[/tex] of the trip

Jason Joe drove [tex]=\dfrac{1}{4}[/tex] of the trip

Together Jeff and Jason Joe drove [tex]=\dfrac{1}{2}+\dfrac{1}{4}=\dfrac{2}{4}+\dfrac{1}{4}=\dfrac{3}{4}[/tex] of the trip

All trip [tex]=1[/tex]

Remaining trip [tex]=1-\dfrac{3}{4}=\dfrac{4}{4}-\dfrac{3}{4}=\dfrac{1}{4}[/tex]

Susan and Sharon divided the rest of the drive equally, so

Susan drove = Sharon drove [tex]=\dfrac{1}{4}:2=\dfrac{1}{4}\cdot \dfrac{1}{2}=\dfrac{1}{8}[/tex] of the trip.

The entire trip was 168 miles, then

Sharon drove [tex]=\dfrac{1}{8}\cdot 168=21\ miles[/tex]

Answer:

I'd say C.60but because of the half units its possibly B. but definitely not A or D.

Step-by-step explanation:

Because the short sides are approximately 6 units long and the long sides are 10 units long. You multiply it to find the area and you get 60.

hope this helps

The area of the graph rectangle is 60 sq. units.

The correct option is D) 60 sq. units.

The area of a rectangle is expressed as:

Area = length × width

First, we use the distance formula to find the length and width of the rectangle.

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

From the graph, the length is between the points (-1,1) and (8,-2):

Hence;

[tex]Length = \sqrt{(8-(-1))^2 + (-2 - 1)^2}\\\\Length = \sqrt{(8+1)^2 + (-2 - 1)^2}\\\\Length = \sqrt{(9)^2 + (-3)^2}\\\\Length = \sqrt{81 + 9}\\\\Length = \sqrt{90}\\\\Length = 3\sqrt{10}[/tex]

Next, we find the width which is between the points (-1,1) and (-3,-5):

[tex]Width = \sqrt{(-3 - (-1))^2 + (-5 - 1)^2}\\\\Width = \sqrt{(-3 + 1)^2 + (-5 - 1)^2}\\\\Width = \sqrt{(-2)^2 + (-6)^2}\\\\Width = \sqrt{4 + 36}\\\\Width = \sqrt{40}\\\\Width = 2\sqrt{10}[/tex]

Now, plug the values for the length and width into the above formula and solve for the area:

Area = length × width

Area = 3√10 × 2√10

Area = 3 × 2 × 10

Area = 60 sq. units

Therefore, the area measures 60 sq. units.

Option D) 60 sq. units is the correct answer.

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Answer:

Step-by-step explanation:

[tex]-\dfrac{2}{3}u=-4\qquad\text{change the signs}\\\\\dfrac{2}{3}u=4\qquad\text{multiply both sides by}\ \dfrac{3}{2}\\\\\dfrac{3\!\!\!\!\diagup^1}{2\!\!\!\!\diagup_1}\cdot\dfrac{2\!\!\!\!\diagup^1}{3\!\!\!\!\diagup_1}u=4\!\!\!\!\diagup^2\cdot\dfrac{3}{2\!\!\!\!\diagup_1}\\\\u=(2)(3)\\\\u=6[/tex]

Answer:

55/18

Step-by-step explanation:

f(x) = 2/3*12 +3

= 1/18 +3

=55/18

The value of f (12) will be;

⇒ f (12) = 11

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The function is,

⇒ f (x) = 2/3x + 3

Now,

Since, The function is,

⇒ f (x) = 2/3x + 3

Substitute x = 12 in above equation, we get;

⇒ f (x) = 2/3x + 3

⇒ f (12) = 2/3 × 12 + 3

⇒ f (12) = 2 × 4 + 3

⇒ f (12) = 11

Thus, The value of f (12) will be;

⇒ f (12) = 11

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Answer:

r = 0.93

Step-by-step explanation:

The correlation coefficient gives us the "strongness" of two variables associated.

This is the value "r".

It is positive if there is strong relationship (one goes up, another goes up and vice versa)

It is negative, if one goes up and another goes down (inverse relationship)

First of all, from the scatter points, we see that as x increases, y also tend to increase. And if we were to draw a line of best fit that goes through max points, we would see the line slopes UPWARD (means as x increases, y also increase).

Thus, the value of "r" will be positive. So we can eliminate first and second choice. Now remains the other two choices

0.64

0.93

The closer the value to 1, the more that line is slopier, and less that value from 1, the line will be less "slopy".

A perfect one would be a line with slope 1, as 1 unit increase in x, the y increases 1 unit as well.

So, if we were to draw a line, we would see that it will be very close to a value of 1. The value of 0.64 can be eliminated because the points are not much "relaxed" as it should be for 0.64.

So, the correct choice is the 4th choice, r = 0.93

Three other ordered pairs with θ between −360° and 360° that name the same point as (−3, 330°) are (−3, 30°), (−3, 690°), and (−3, -30°).

Given the ordered pair (−3, 330°), we can find three other ordered pairs that name the same point by adding or subtracting 360° from the given angle:

These three ordered pairs have angles between −360° and 360° and represent the same point as the given ordered pair.

Answer:

See above graph

Step-by-step explanation:

In between those whole numbers, each mark represents ⅕ [or 0,2], therefore you move one-fifth block to the right of 20 with an open circle, then shade everything to the left.

≥, ≤ → Solid Circle [●]

>, < → Blank Circle [○]

I am joyous to assist you anytime.

To graph the solution of the inequality, p < 20.2, one must draw a number line. Mark a point on the number line at 20.2 and shade or draw an arrow pointing to the left of this mark. Ensure to use an open circle at 20.2 to show that it itself is not part of the solution.

To graph the solution of the inequality p < 20.2 on a number line, you need to take the following steps:

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Answer:

Step-by-step explanation:

if y = 1/2x - 1 is the function

y = 1/2(-4) - 1

y = -2 - 1

y = -3

(-4, -3)

y = 1/2(2) -1

y = 1 - 1

y = 0

(2, 0)

y = 1/2(6) - 1

y = 3 - 1

y = 2

(6, 2)

the pictures should be in order

Answer:

[tex]\displaystyle 2 = f(6), 0 = f(2), -3 = f(-4)[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{1}{2}[6] - 1 = 3 - 1 = 2 \\ \\ \frac{1}{2}[2] = 1 - 1 = 0 \\ \\ \frac{1}{2}[-4] - 1 = -2 - 1 = -3[/tex]

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Answer: y+3 = 4( x + 1)

Step-by-step explanation:

The equation in point slope form is given as :

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] ) , where m is the slope

slope = 4

point given : (-1,-3)

Using the formula :

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )

and substituting the value , we have

y - (-3) = 4 (x -{-1} )

y+3 = 4( x + 1)

If the line is parallel to y=2x, the line must have the same slope.

So, the slope of your line is 2.

Now we need to find the y intercept. We should use the point given.

y=mx+b

-3=2(-4)+b

b=5

Equation: y=2x+5

Answer:

There was 62.23% change in radius as the ion formed.

Step-by-step explanation:

Given

Radius of Aluminium [tex](Al)[/tex] atom  = 143 pm

Radius of Aluminium [tex](Al^{3+})[/tex] atom  = 54 pm

Change is the radius =  Radius of Aluminium [tex](Al)[/tex] atom - Radius of Aluminium [tex](Al^{3+})[/tex] atom = 143 -54 = 89

Now to find % Change is the radius we will divide Change is the radius by Radius of Aluminium [tex](Al)[/tex] atom and multiply by 100 we get

% Change is the radius = [tex]\frac{\textrm{Change is the radius}}{\textrm{Radius of Aluminium (Al) atom}} \times 100 = \frac{89}{143}\times100= 62.23\%[/tex]

Hence there was 62.23% change in radius as the ion formed.

Answer:

The valid value of x is x=-2

Step-by-step explanation:

we know that

The sum of the interior angles of any quadrilateral must be equal to 360 degrees

so

[tex](7x^{2}-24x)+100+(24-46x)+(3x^{2}+56)=360[/tex]

solve for x

Combine like terms

[tex]10x^{2}-70x+180=360[/tex]

[tex]10x^{2}-70x-180=0[/tex]

Divide by 10 both sides

[tex]x^{2}-7x-18=0[/tex]

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2}-7x-18=0[/tex]

so

[tex]a=1\\b=-7\\c=-18[/tex]

substitute in the formula

[tex]x=\frac{-(-7)(+/-)\sqrt{-7^{2}-4(1)(-18)}} {2(1)}[/tex]

[tex]x=\frac{7(+/-)\sqrt{121}} {2}[/tex]

[tex]x=\frac{7(+/-)11} {2}[/tex]

[tex]x=\frac{7(+)11} {2}=9[/tex]

[tex]x=\frac{7(-)11} {2}=-2[/tex]

Remember that

The measure of the interior angle cannot be a negative number

For x=9

we have that the measure of one interior angle of quadrilateral  is

[tex]24-46x[/tex]

substitute the value of x

[tex]24-46(9)=-390\°[/tex]

therefore

The value of x=9 cannot be a solution

For x=-2

The measure of the interior angles are

[tex](7(-2)^{2}-24(-2))=76\°\\100\°\\(3(-2)^{2}+56)=68\°\\24-46(-2)=116\°[/tex]

therefore

The valid value of x is x=-2

Answer:

12Pi

Step-by-step explanation:

circumference of a circle can be worked out as Pi x diameter

Diameter = 2 x radius, therefore here d = 12 and circumference = 12 Pi

The circumference of the circle is C = 12π meters

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be r = 6 meters

Now , circumference of circle = 2πr

On simplifying , we get

C = 2π ( 6 )

C = 12π meters

Hence , the circumference is 12π meters

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Answer:

5,841 divided by 62 is 94.2

How much money did he have

Answer:

His profit would be $37 of the money he got back.

Step-by-step explanation:

Answer:

C) –|x| + 3

I got the answer correct!!!

Answer:

x equals plus or minus square root of 5 minus 1

Step-by-step explanation:

we have

[tex]x^{2} +2x=4[/tex]

Divide by 2 the coefficient of the x-term

[tex]2/2=1[/tex]

squared the number

[tex]1^2=1[/tex]

Adds both sides

[tex]x^{2} +2x+1=4+1[/tex]

[tex]x^{2} +2x+1=5[/tex]

Rewrite as perfect squares

[tex](x+1)^{2}=5[/tex]

take the square root both sides

[tex]x+1=(+/-)\sqrt{5}[/tex]

[tex]x=(+/-)\sqrt{5}-1[/tex]

therefore

x equals plus or minus square root of 5 minus 1

Answer - B. x = ± [tex]\sqrt{5[/tex] - 1

Answer:

4b = 8

Step-by-step explanation:

Given 12b = 24

This is written as (4 X 3)b = 24

⇒ 4b X 3 = 24

Dividing by 3 throughout, we have

4b = [tex]$ \frac{24}{3} $[/tex] = 8.

Therefore, the value of 4b is 8.

Answer:

An equation is a statement that maintains the equal value of two mathematical expressions. If the statement is true for all variable values, it is called an identity. ... An equation shows the equality of two variables while an inequality shows the inequality of two variables

An equation with a variable expresses a precise equality between expressions, while an inequality with a variable represents a range of possible values expressing that one value is greater or less than another. Equations typically have a definitive set of solutions, whereas inequalities signify a continuum of solutions that satisfy the relational condition.

The difference between an equation with a variable and an inequality with a variable lies in the relationship they describe between the variables. An equation states that two expressions are equal by means of the equal sign (=), implying a specific value or set of values for the variables involved. For example, in the equation of a line y = mx + b, where x and y are the variables on the horizontal and vertical axis respectively, and b and m represent the y-intercept and the slope, we can see a direct relationship between x and y that determines the position of a point on a Cartesian plane. Conversely, an inequality such as x > y or x < 10 indicates a range of possible values rather than a single specific value, expressing a relationship where one value is either greater than or less than another value, but not equal to it.

In the context of a graph, the independent variable typically plotted on the x-axis is assumed to be the cause or input which then determines the value of the dependent variable, depicted on the y-axis. The dependent variable changes in response to the independent variable, thereby showing their relationship. This is often represented by inequalities when a range of outcomes is possible, extending beyond the linear relationship that might be depicted with an equation.