Are you able to find the area of the following figure?

A: Yes the area can be found by adding four and the seven and dividing by two
B: No you are not able to find the area because one side length is missing
C: Yes the area can be found by multiplying the 4 and 7 and then dividing the product by two.
D: No you are not able to find the area because the numbers are both irrational numbers

Answer:

Step-by-step explanation:

To find the difference A - B', we need to first find the complement of B, denoted by B', which is the set of all elements in U that are not in B.

Given that U = {1, 2, 3, 4, 5, 6, 7, 8, 9},

B = {1, 4, 6, 9},

then B' = {2, 3, 5, 7, 8}.

Next, we find A - B' by looking for the elements that belong to A and not to B':

A - B' = {2, 4, 6, 8} - {2, 3, 5, 7, 8} = {4, 6, 8}.

The equation which is more appropriate for modeling this DATA is y = 64 × (1.25)^x

The correct answer choice is option A.

y = 64 × (1.25)^x

when,

x = 1

substitute into the equation

y = 64 × (1.25)¹

= 64 × 1.25

= 80

y = 79 × 1.25^x

when x = 1

= 79 × 1.25¹

= 79 × 1.25

y = 98.75

79 + 1.25x

when x = 1

= 79 + 1.25(1)

= 79 + 1.25

= 80.25

64 + 22x

when x = 1

= 64 + 22(1)

= 64 + 22

= 86

Therefore, y = 64 × (1.25)^x is the equation which is more appropriate to represent the data.

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Answer: y=-7x-0 if solving for literal y or x=y+0/-7 if solving for literal x.

Step-by-step explanation:

-7x-y=0

add (+) 7x to both sides

-y=7x+0

then divide by -1

y=-7x-0

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

for literal X

-7x-y=0

add y to both sides

-7x=y+0

then divide by -7\

x=y+0/-7

It take the man 19.83 seconds to fall to 130 feet

From the question, we have the following parameters that can be used in our computation:

h(t) = 12.5(0.2t − 1)^2 + 20

When the man reaches 130 feet, we have

h(t) = 130

Substitute the known values in the above equation, so, we have the following representation

12.5(0.2t − 1)^2 + 20 = 130

Using a graphing calculator, we have

t = 19.83

Hence, the time is 19.83 seconds

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Answer:

y= -4x+2

Step-by-step explanation:

diff in y / diff in x = slope

so the slope is (-2-2) /(1-0) = -4

intercept is whatever is on Y axis, it's 2

so y= -4x+2

Answer:

Step-by-step explanation:

Divide 100 by 16 and write the answer as a mixed number. Reduce the

fraction part of the mixed number.  6 1/4 here u go.

The total amount of Investment A is $6,348.58.

What is the compound interest?

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

To find the total amount of investment A, you can use the formula for compound interest:

A = P * (1 + r/n)⁽ⁿᵗ⁾

Where P is the initial investment ($5,000), r is the annual interest rate (6%), n is the number of times interest is compounded per year (2 times), and t is the number of years invested (4).

A = 5000 * (1 + 0.06/2)⁽²*⁴⁾

= 5000 * (1 + 0.03)⁸

= 5000 * 1.03⁸

= 5000 * 1.269716

= $6,348.58

Hence, The total amount of Investment A is $6,348.58.

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(a) The perimeter of the rectangle in centimeter is 2,800 cm.

(b) The area of the rectangle is 450,000 cm².

The perimeter of the rectangle in centimeter is calculated as follows;

P = 2 ( L + B )

where;

The length of the rectangle = 9 m = 900 cm

The breadth of the rectangle = 5 m = 500 cm

Perimeter = 2 ( 900 cm + 500 cm ) = 2,800 cm

The area of the rectangle is calculated as follows;

A = LB

A = 900 cm  x  500 cm

A = 450,000 cm²

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Answer:

JN = 16

Step-by-step explanation:

Since diagonals in parallelograms bisect each other, JN = [tex]\frac{1}{2}[/tex]JL

Answer:

To find JN in parallelogram JKLM when JL is 32, you can draw a line from J to L, and then extend the line to find JN. The length of JN will be equal to 32.

The solution is, the system represents the situation is, x+y= 20

and, 2x+3y = 48.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Each button has a diameter of either 2 or 3 centimeters.

The combined diameters of all buttons is 48 cm.

If x is the number of 2 cm buttons,

and y is 3 cm buttons.

Kate has a collection of 20 buttons.

So, the system represents the situation is,

x+y= 20

and, 2x+3y = 48.

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These values do not satisfy the requirement that x, y, and z be positive numbers, so the problem does not have a solution.

What is a three-variable linear equation?

When a, b, and c are constants, a linear equation in two variables has the form ax + by + c = 0. (real numbers). Similar to this, a three-variable linear equation has the form ax by c z plus d = 0, where a, b, c, and d are constants.

Let's call the three numbers x, y, and z, where x is the largest number and z is the smallest number. Then, we have the following information:

x + y + z = 54

x - z = 46

y + z = 13

From the second equation, we can find z:

z = x - 46

Substituting this into the third equation:

y + x - 46 = 13

y = 13 + 46 - x

Substituting both of these into the first equation:

x + (13 + 46 - x) + (x - 46) = 54

Expanding the parentheses:

2x = 154

Dividing both sides by 2:

x = 77

Substituting this value of x into the equation for z:

z = x - 46 = 77 - 46 = 31

And substituting it into the equation for y:

y = 13 + 46 - x = 13 + 46 - 77 = -18

Note that these values do not satisfy the requirement that x, y, and z be positive numbers, so the problem does not have a solution.

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The relative frequency of rolling a three is 14/40 or 0.35.

Answer14/40 or 0.35

Step-by-step explanation:

Number of times dice is rolled= 40

Number of times three comes up= 14

Relative frequency(Probability) = 14/40 or 0.35

Answer: If you can explain the question a little bit more i would be happy to help!

Step-by-step explanation:

Answer:

TW = 9

Step-by-step explanation:

WY is the perpendicular bisector of TZ with TY ≅ ZY , then

Δ TWZ is isosceles with ZW ≅ TW , that is

3x = x + 6 ( subtract x from both sides )

2x = 6 ( divide both sides by 2 )

x = 3

Then

TW = x + 6 = 3 + 6 = 9

The cost of a box of pencils is $4.

The cost of a ream of paper is $7.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 1 = 6 is an equation.

We have,

Pencils = x

Reams of paper = y

Now,

Natalie:

3x + 9y = 75 _____(1)

Ronnie:

8x + 5y = 67 _____(2)

From (1) and (2)

Multiply 8 on (1)

Multiply 3 on (2)

24x + 72y = 600

24x + 15y = 201

(-)     (-)       (-)      

      57y = 399

           y = 7

Now,

3x + 9y = 75

3x + 9 x 7 = 75

3x + 63 = 75

3x = 75 - 63

3x = 12

x = 4

Thus,

The cost of a box of pencils and a ream of paper are $4 and $7.

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Answer:

4x + 3 = y

Step-by-step explanation:

Answer:

4x+3

there is no actual explanation

Three added= +3

four times a number= 4*x=4x

The measure of m∠EFG in triangle CDE is equal to 93 units.

In Mathematics, the midpoint theorem states that in a triangle, the line segment which joins the midpoints of any two (2) sides of the triangle must be parallel to the third side and congruent to half of the length of the third side.

By applying the midpoint theorem to triangle CDE, the measure of m∠EFG can be calculated as follows;

m∠ECD = m∠EFG

12 + 9x = −2x + 111

9x + 2x = 111 - 12

11x = 99

x = 99/11

x = 9.

For line segment m∠EFG, we have the following:

m∠EFG = −2x + 111

m∠EFG = −2(9) + 111

m∠EFG = −18 + 111

m∠EFG = 93 units.

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Answer: The amount invested at 6% was $1393.57, the amount invested at 9% was $306.13, and the amount invested at 15% was $1393.57 + $306.13 + $100 = $1800.70.

Step-by-step explanation:

Let's denote the amount invested at 6% as "x". Then, the amount invested at 9% would be "y", and the amount invested at 15% would be "z".

According to the problem, we have the following information:

x + y + z = $7500 (the total amount invested)

0.06x + 0.09y + 0.15z = $867 (the total annual income)

And,

z = x + y + $100 (the amount invested at 15% was $100 more than the amounts invested at 6% and 9% combined)

We can substitute the third equation into the first equation to get:

x + y + x + y + $100 = $7500

Simplifying:

2x + 2y + $100 = $7500

2x + 2y = $7400

Next, we can substitute "z = x + y + $100" into the second equation:

0.06x + 0.09y + 0.15(x + y + $100) = $867

Expanding:

0.06x + 0.09y + 0.15x + 0.15y + 0.15 * $100 = $867

0.21x + 0.24y + $15 = $867

0.21x + 0.24y = $852

Finally, we can solve for x and y using the equations "2x + 2y = $7400" and "0.21x + 0.24y = $852".

We can use elimination method to find x:

2x + 2y = $7400

0.21x + 0.24y = $852

Multiplying the first equation by 0.21:

0.42x + 0.42y = $1557.8

Subtracting the second equation from the first:

0.42x + 0.42y - 0.21x - 0.24y = $1557.8 - $852

0.21x - 0.03y = $705.8

Dividing both sides by 0.21:

x = $705.8 / 0.21 + 0.03y / 0.21

x = $3357.14 / 0.24 + y

Finally, substituting x back into the equation "2x + 2y = $7400":

2($3357.14 / 0.24 + y) + 2y = $7400

Expanding:

$6714.29 + 2.24y = $7400

Solving for y:

2.24y = $7400 - $6714.29

y = $685.71 / 2.24

y = $306.13

And finally, substituting y back into the equation "x = $3357.14 / 0.24 + y":

x = $3357.14 / 0.24 + $306.13

x = $1393.57

Therefore, the amount invested at 6% was $1393.57, the amount invested at 9% was $306.13, and the amount invested at 15% was $1393.57 + $306.13 + $100 = $1800.70.

The difference in rainfall between the wettest and driest days is 3/8 inches.

The intensity of the rain is typically categorized as light, moderate, or heavy. Light precipitation is defined as less than 0.10 inches per hour. Rainfall that is considered moderate ranges from 0.10 to 0.30 inches per hour. More than 0.30 inches of rain per hour is considered heavy rainfall. under 0.5 mm per hour. Greater than 0.5 mm per hour but less than 4.0 mm per hour is considered moderate rain. Greater than 4 mm per hour but less than 8 mm per hour is considered heavy rain. greater than 8 mm per hour of extremely intense rain.

Rainfall in Rainiest day = 5/8

Rainfall in driest day = 2/8

So, The Difference = 5/8 - 2/8 = 3/8 inches

Hence, rainfall on the rainiest day 3/8 more than driest day

Proper fraction = 3/8

Mixed fraction = 8/2 inches.

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Answer:

398

Step-by-step explanation:

40*2q-p

=40*2*5-2

=400-2

=398

Answer:

2008

Step-by-step explanation:

since p=2

q=5

therefore, 402(q)-p

=402(5)-2

=2,010-2

=2008

1. The company’s degree of operating leverage is 4.

2. The degree of operating leverage is 3.34.

3. The new contribution is $17, 280.

How much a company's operating income alters in reaction to a change in sales is measured by the level of operating leverage.

1. Degree of operating leverage = Contribution /Net Operating Income

and, Contribution = 54,000

Net Operating Income = $13,500

Thus, operating Leverage = 54000/ 13500  = 4

2. If Company's sales increase by 7% then contribution also increases by 7%,

Revised Contribution = $54000 + 7% = $57780

and, Revised net Operating income = $57780- $40500

                                                            = 17280

Degree of operating leverage = 57780 / 17280  = 3.34

3. Contribution format income statement:

Sales = $90000+ 7% = $96,300

Less: Variable Cost 36, 000 + 7% = $38520

So, New Contribution = 57780 - 40500 = $17, 280.

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Answer:

The first one is 76°, second one is 38°, third one is 66°

Step-by-step explanation:

Suppose the second one is x, given the first one is twice of the second one, so the first one is 2x.

2x+x+(28°+x)=180°

4x=152°

x=38

So, the first one is 76°, second one is 38°, third one is 66°

The solution is the original price was 93.33.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

An game is on sale for $28, which is 30% off the original price.

let,

the original price was x

ATQ,

x*30% = 28

x = 280/3

x=93.33

Hence, The solution is the original price was 93.33.

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Answer:

Angle A is 90, angle B is 50, angle C is 90, and angle D is 40.

Answer:

<A = 90

<B = 50

<C = 90

<D = 40

Step-by-step explanation:

C:

vertical angles are congruent so the angle left of C is 40.  The angle right to C is 50 because alternate interior angles are congruent

The three angles together are supplemental

180 - 50 - 40 = 90

A:

A = C vertical angles are congruent

A = 90

D:

A, D and 50 are supplemental

180 -90-50 = 40

B

The sum of the interior angles of a triangle are 180

180 - 40 - 90 = 50

The given cubic equation has no roots.

Traditionally, a cubic problem can be solved by converting it into a quadratic equation, which can then be solved by factoring or the quadratic formula. A cubic equation has three roots, just like a quadratic equation has two. Three real roots or one real root and two imaginary roots are both possible for a cubic equation. Cubic equations must also always be arranged in their standard form first.

The following strategies can be used to resolve a cubic equation:

Using Graphical Method to Find Integer Solutions with Factor Lists

Given that the cubic equation is: 8x²-5x³+7-12x

Regrouping the equation in standard form:

- 5x³ + 8x² - 12x + 7

Here, the constant is 7. Take the factors of the constant.

7 = 1, 7

Substitute the value of the factors as follows:

G(1) = - 5(1)³ + 8(1)² - 12(1) + 7 = -5 + 8 - 12 + 7 ≠ 0

G(7) = -5(7)³ + 8(7)² -12(7) + 7 = -1715 + 392 - 84 + 7 ≠ 0

Hence, the given cubic equation has no roots.

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Answer:

the slope is -6

the y-intercept is 2

Step-by-step explanation:

y=mx+b where m is the slope and b is the y-intercept

a) Slope: -6;

b) y-intercept: 2, which means that the line touches the "y" axis on point (0, 2).

Given equation: [tex]y = -6x + 2[/tex].

Here's a little tip that will help you quickly find the slope and y-intercept.

First, solve the equation for "y". This equation is already solved for "y", this is called "slope-intercept form". Now, take a look at the attached image and identify the values. As you can tell, for the given equation, values are:

a) Slope: -6;

b) y-intercept: 2, which means that the line touches the "y" axis on point (0, 2).

You may verify this information using the algebraic methods (slope formula and substituting "x" by 0 and calculate "y"). It'll give you the same answer, this is just a faster way to find the values.

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Answer:

The length of a is 36 mm.

Step-by-step explanation:

Similar rectangles have the same shape, but can have different sizes. The ratio of the lengths of corresponding sides of similar rectangles is always the same.

Given that b = 18 mm, c = 24 mm, and d = 36 mm, the ratio of the lengths of corresponding sides of the two rectangles is c/d = 24/36 = 2/3.

So, the length of a is equal to b * (c/d) = 18 * (2/3) = 36 mm.