The pie chart below shows how the annual budget for a certain company is divided by department. If the amount budgeted for sales and research combined is 75,000,000. What is the total annual budget?

Given:

Ethan is 23 years older than Evan

So, let Ethan is (x) years old

And Evan is (y) years old

So, the difference between them is 23 years old

so, x - y = 23

And the sum of Ethan and Evan's age is 43

so, x + y = 43

So, we have the following system of equations:

add the equations to eliminate (y):

Now, substitute with (x) into the second equation to find (y):

So, the answer will be:

Ethan's age = x = 33

Evan's age = y = 10

The solutions to the quadratic trigonometric equation are given as follows:

x = kπ, k = ± 1, ± 3, ± 5, ± 7.

The quadratic trigonometric equation is defined as follows:

cos²(x) + cos(x) = 4cos(x) + 4.

Then the following transformation is applied to solve the equation:

y = cos(x).

Hence:

y² + y = 4y + 4

y² - 3y - 4 = 0

(y - 4)(y + 1) = 0.

Applying the Factor Theorem, the solutions are given as follows:

However, we want the solutions for x, hence they are obtained as follows:

cos(x) = 4.

x = arccos(4), which has no solution, as there are no angles with a cosine of four.

cos(x) = -1.

x = arccos(-1)

x = kπ, k = ± 1, ± 3, ± 5, ± 7

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A 90 degree counterclockwise rotation about point A, a reflection across the y-axis, and a translation 20 units down may be used on quadrilateral ABCD to demonstrate that it is congruent to quadrilateral GHIJ.

A quadrilateral in geometry is a four-sided polygon with four edges and four corners. A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words quadri, which means four, and latus, which means side, were combined to create the English term quadrilateral. A four-sided polygon with four angles is known as a quadrilateral. Parallelogram, rhombus, kite, rectangle, trapezoid, square, and isosceles trapezoid are the seven different forms of quadrilaterals.

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Answer:

This statement is True.

Step-by-step explanation:

5/8 is equal to 0.625 in decimal form. Use our fraction to decimal calculator to convert any fraction to a decimal and to know if it is a terminating or a recurring (repeating) decimal. It is, a so called, 'terminating' decimal. To convert this fraction to a decimal, just divide the numerator (5) by the denominator (8).

Recall that the interior angles of a regular quadrilateral add up to 360 degrees, and a right angle has a measure of 90 degrees.

Let x° be the measure of the fourth angle, then we can set the following equation:

Adding like terms we get:

Subtracting 220 degrees from the above result we get:

Answer:

Answer: Slope of 1.

Step-by-step explanation:

    First, we will put the equation into slope-intercept form.

x - y = 4

x = y + 4

y = x - 4

    Our slope, when the line is written as y = mx + b, is the m value. Our m value here is one, so the slope of a line parallel to the line whose equation is x - y = 4 is 1.

Data:

• Cumulative probability of -2.18 ,: 0.0146

• Cumulative probability of 3.74 ,:, ,0.9999

Procedure:

0. Using the following formula we can get our probability.

Step-by-step explanation:

a)

(6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)(2x + 3 - 7x - 11)

[tex] \sf \frac{(6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)}{(2x + 3 - 7x - 11)}[/tex]

[tex] \sf = \frac{(6(10)^3 + 9(10)^2 + 4(10) + 7 - 17(10)^2 - 8(10) + 8)}{(2(10) + 3 - 7(10) - 11)}[/tex]

[tex] = \frac{ - 5175}{58}[/tex]

4x^2 - 7 + 1/(2x + 3 - 7x - 11)

[tex] \sf{ 4x^2 - 7 + \frac{1}{(2x + 3 - 7x - 11)}}[/tex]

[tex] \sf{ 4(10)^2 - 7 + \frac{1}{(2(10) + 3 - 7(10) - 11)}}[/tex]

[tex] = \sf \frac{22793}{58}[/tex]

Since we have that y = 10, then:

Then

In the first part, we need to sum 15 to both sides of the equation.

In the second part, we divide both sides by 5.

Then, x = 19.

The apple that costs the least per pound is Apple B.

The cost per pound for each apple will be calculated as:

= Cost / Weight

Apple A:

= Cost / Weight

= 4.90 / 4

= $1.25 per pound

Apple B:

= Cost / Weight

= $1 / 10

= $0.1 per pound

Apple C:

Cost / Weight

= $0.45 / 0.5

= $0.9 per pound

Therefore, apple B is the cheapest

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t - the number of years the money is invested for
P = $16,000
m =2
t = 12 yr
r = 8% or .08
FV = 16,000* ( 1+ .08/2) 2*12 = 16000 (1.04) 24 = 16000* (2.5633041) = $41012.8656
FV - the future value of the investment = $41012.87 is answer

The value of the function f(7/3)-h(-2) is 30

Functions are simply defined as theorems, laws, equation or rules that holds true for the relationship between two variables in a given expression.

The variables are known as;

Given the functions as;

To determine f(73), substitute the value as x in the function, we have;

f(7/3) = 3(7/3) - 1

expand the bracket

f(7/3) = 7 -1

f(7/3) = 6

For h(-2), substitute the value as x in the function, we have;

h(-2) = -2(-2)² + 3(-2) - 9

expand the bracket

h(-2) = -8 -6 - 9

Subtract the values

h(-2) = -23

Now, f(7/3)-h(-2) = 7 --23

f(7/3)-h(-2) = 30

Hence, the value is 30

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Note:

For similar shapes, the ratio of their areas is equal to the square of the ratio of sides.

That is:

The value of X is 36

[tex]\cos \theta=\frac{x}{16} \implies x=16 \cos \theta \\ \\ \sin \theta=\frac{y}{16} \implies y=16 \sin \theta[/tex]

The total cost with taxes included is given by

which is equal to

which gives

then, we have $880.3581. By rounding to the nearest cent, the answer is $880.36

a)

The slope intercept equation of a line is expressed as

y = mx + c

where

m is the slope

c is the y intercept

The given equation is

x + y = 3

y = - x + 3

By comparing both equations,

m = - 1

If two equations are parallel, it means that they have the same slope. Thus, the slope of the parallel line passing through the point (- 3, 2) is - 1

We would find the y intercept by substituting x = - 3, y = 2 and m = - 1 into the slope intercept equation. It becomes

2 = - 1 * - 3 + c

2 = 3 + c

c = 2 - 3

c = - 1

By substituting m = - 1 and c = - 1 into the slope intercept equation, the equation of the line is

y = - x - 1

b) If two equations are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line Thus, the slope of the perpendicular line passing through the point (- 3, 2) is - - 1/1 = 1

We would find the y intercept by substituting x = - 3, y = 2 and m = 1 into the slope intercept equation. It becomes

2 = 1 * - 3 + c

2 = - 3 + c

c = 2 + 5

c = 5

By substituting m = 1 and c = 5 into the slope intercept equation, the equation of the line is

y = x + 5

a) y = - x - 1

b) y = x + 5

To determine the post image coordinates after a dilation centered about the origin, we will simply multiply each of the coordinates by the given scale factor of 1/3.

Let's start with Point A.

The post image coordinate of A is at (-4, 8).

Moving on to Point B.

The post image coordinate of B is at (-10, 0).

Lastly to Point C.

The post image coordinate of C is at (-12, 12).

Hello there. To solve this question, we'll have to remember some properties about scatter plots and slope of a line.

Given the scatter plot of the data information, we have to determine the slope of the line.

For this, we could determine it numerically using the least squares method, if we knew the data (the coordinates of the points we're plotting the best fit).

In this case, we simply need to find, by inspection, two points contained in the line and use the slope formula.

Given two points (x0, y0) and (x1, y1) that a line L passes through, then the slope m of this line is given by:

By inspection, we can easily spot the points (16, 12) and (28, 20).

Plugging these coordinates in the formula, we get:

Add the numbers and simplify the fraction

This is the slope of this line.

We have to do a diagram with the following characteristics.

• VX has to intersect UW at V.

• VX is perpendicular to UW.

• U, V, and W are collinear.

Based on the given information, we have the following diagram

The image above shows the answer.

From the figure given in the question, we are asked to find the area and perimeter.

(a) Area:

Since the figure is a trapezoid, the formula for the area of a trapezoid is:

Area = (a + b)h

2

Where:

a = 2

b = 5

h = 4

Area = (2 + 5)4

2

Area = 7/2 * 4

Area = 3.5 * 4

Area = 14 cm²

(b) Perimeter:

To get the perimeter, we will have to add all the side length.

But we will have to find the missin side length first.

Using pythagoras:

a² + b² = c²

Where:

a = 4

b = 3

c² = 4² + 3²

c² = 16 + 9

c² = 25

Taking square of both sides:

c = √25

c = 5

Since we have gotten the missing side length as 5cm, we can now add all the given side length to get the perimeter.

Perimeter = 4 + 2 + 5 + 5

Perimeter = 16 cm

(a) Option B, 30

(b) 60, Option A

Answer:

3 1/13

Step-by-step explanation:

rate(time) of one pipe + rate(time) of the other pipe = 1 job

The rate would be the the number of jobs over the time

The rate of the first pipe is 1/5 and the rate of the second pipe is 1/8.

Together:

1/5t + 1/8t = I job

t(1/5 + 1/8) = 1

t(8/40 + 5/40) = 1

t(13/40) = 1  multiply each side by 40/13

t(40/13)(13/40) = 1(40/13)

t = 40/13

t = 3 1/13

Yo bro, I'm just doing this for the rewards for my homework. please don't read this or take it serious

Answer:

Solutions below.

Step-by-step explanation:

This question is asking us to find the points of intersection, which means its asking to find the x-intercept abd y-intercept.

To find the x-intercept, we know that y = 0.

Therefore we can substitute y = 0 into the line equation:

[tex]0 = - \frac{1}{4} x + 2 \\ - \frac{1}{4} x = - 2 \\ x = - 2 \div - \frac{1}{4} \\ = 2 \times 4 \\ = 8[/tex]

Therefore the point of the x-intercept is (8,0).

Likewise to find the y-intercept, we know x = 0.

Therefore we can substitute x = 0 into the line equation:

[tex]y = - \frac{1}{4} (0) + 2 \\ = 0 + 2 \\ = 2[/tex]

Therefore the point of the y-intercept is (0,2).

Answer:

x-intercept:  (8, 0)

y-intercept:  (0, 2)

Step-by-step explanation:

Given equation:

[tex]y=-\dfrac{1}{4}x+2[/tex]

The graph intersects the y-axis when x = 0.  

To find the graph's y-intercept, substitute x = 0 into the equation and solve for y:

[tex]\begin{aligned}x=0 \implies y&=-\dfrac{1}{4}(0)+2\\y&=0+2\\y&=2\end{aligned}[/tex]

Therefore, the coordinates of the point of intersection with the y-axis are:

The graph intersects the x-axis when y = 0.  

To find the graph's x-intercept, substitute y = 0 into the equation and solve for x:

[tex]\begin{aligned}y=0\implies \-\dfrac{1}{4}x+2&=0\\-\dfrac{1}{4}x&=-2\\x&=8\end{aligned}[/tex]

Therefore, the coordinates of the point of intersection with the x-axis are:

The given expression is : 2 × 4/3

Answer :

Out of $205000, the total commission earned by the agent will be $12300.

A commission is a fee paid to a salesperson in exchange for services in facilitating or completing a sale transaction. Mathematically -

Commission [C] = Sales revenue [R] x commission rate [rc]

Given is an agent who lists a sellers house for 6% commission. The final agreed sales price is $205,000.

The total sales price = [P] = $205000

The commission on house = [C] = 6%

Now, the money agent gets as a commission will be = [M] -

[M] = 6% of 205000

[M] = (6/100) x 205000

[M] = 6 x 2050

[M] = 12300

Therefore, out of $205000, the total commission of the agent will be $12300.

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Multiply the coordinates by the scale factor (5)

T'= (-1 x 5 , 5x5) = (-5,25)

T' = (-5,25)

The value of m is -6/5.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.

Given:

2m -3 = 3/10 (5m - 12)

Now, cross multiplying

10( 2m -3)= 3( 5m -12)

20m -30 = 15m - 36

20m- 15m= -36 + 30

5m = -6

Divide both side by 5

m= -6/5

Verification:

LHS = 2m-3

=2(-6/5)-3

=-12/5-3

=-27/5

and, RHS

= 3/10( 5m -12)

=3/10(5 x (-6/5) -12)

=3/10 (-6 - 12)

=3/10 x -18

= -54/10

= -27/5

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The value is x≤1 or x>2

Equations don't always need to have a "equal to" symbol on both sides to be balanced. Sometimes it can be about a "not equal to" relationship, meaning that something is superior to or inferior to another. In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.

2x +6≤8 or 2x + 8 > 12

2x +6≤8

2x ≤2

x≤1

2x +8>12

2x>4

x>2

The value is x≤1 or x>2

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