10. Given: BD || CE25= 26Prove: AC = AE(a) BD ICE(b) AC AE(c) 25* LC; 26 = LE(d) 25 = 26(e) LC= LE6DE

Answer:

29,378 people

Step-by-step explanation:

[tex]28337 \times {1.0121}^{3} = 29378[/tex]

Answer:

9 is the answer

Answer: 9 cubes

Step-by-step explanation:

9 * 9 is 81 which makes the floor of it

since its a cube, we multiply 81 by 9, giving 729

We have to differentiate f(x).

We can do this as:

The answer is f'(x)=60x-25.

The blue car has traveled the greater distance on one gallon of gasoline

The formula for calculating the unit rate is expressed as shown:

For the blue car

Distance = 39.5miles

Gallons of gasoline = 1.25 gallons

Get the unit rate:

The unit rate of the blue car as a mixed fraction is 31 3/5 miles per gallon

For the red car

Distance traveled = 22.4 miles

Gallons of gasoline = 0.8 gallons of gasoline

Get the unit rate of the red car;

From the unit rates, we can see that the blue car has traveled the greater distance on one gallon of gasoline since its unit rate is greater than that of the red car.

Answer:

x=W/k

Explanation:

Given the equation

To solve for x, we divide both sides of the equation by k.

She received 19 purple and 6 blue marbles, so the total number of marbles is 19 + 6 = 25

Percentage of purple marbles = 100 * 19/25 = 1900/25 = 76%

Percentage of blue marbles = 100 * 6/25 = 600/25 = 24%

Answer:

Percentage of purple marbles = 76%

Percentage of blue marbles = 24%

The age for two men is 39.5 and 42.5.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific variables in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables.

Given:

Average of 6 men = 35

Average of 4 men  = 32

So, Total age of 6 men

=6x35

=210 years

and, Total age of 4 men

=32  x 4

=128 years

Then, the remaining age for 2 people

= 210 - 128

=82 years

Let the age for two be x and y

then , x+ y=82

and x-y=3

On solving

2x =85

x=42.5 years

and y=39.5 years

Hence, the age for two men is 39.5 and 42.5.

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Distance is the total movement of an object without any regard to direction. Total distance jogged by Linsey is 420 yards.

What is distance?

Distance is the total movement of an object without any regard to direction

Given data

vertex 1 is at ( -4, - 1)

vertex 2 is at ( - 4, 5)

vertex 3 is at (2,5)

vertex 4 is at ( 2, -1 )

Lindseys jogs along the edge of the park in order from vertex 1 to the vertex 2 , vertex 2 to vertex 3 and vertex 3 to vertex 4 and then back to vertex 1. One unit in the coordinate grid is 20 yards.

Let us calculate distance vertex 1 and vertex 2of (-4,-1) and (-4,5)

x₁=-4,x₂=-4, y₂=5, y₁=-1

Distance=√(x₂-x₁)²+(y₂-y₁)²

Substitute the values x₁=-4,x₂=-4, y₂=5, y₁=-1 in distance formula

=√(-4+4)²+(5-(-1))²

=√6²

=6

Since 1 one unit on the coordinate gride equal 20 yd.

so 6×20=120 yards.

Now for four vertices we get 4×120=480 yards.

So total distance jogged by Linsey is 420 yards.

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Mason added 19/12 cups of chips to his sundae.

We know that Mason has a sundae and he put:

To get the total number of chips, we just need to add these fractions (except the one for the milk chocolate chips, as these are removed).

Then we will get:

Total = 1/3 + 3/4 + 1/2 = 4/12 + 9/12 + 6/12 = 19/12

Where we used the common denominator 12 to add the fractions.

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A histogram is a representation that organizes a group of data points into specified ranges.

For the given data:

4, 18 , 20, 17, 16, 23, 19, 14, 8, 8, 6, 12, 20, 14, 18

The equation for g(x) is g(x) = x²-3

When x=0, f(x)= 0 and so has a vertex at (0,0)

Given that g(x) is a shifter version of f(x) and has a vertex at (0,-3), g(x) must be shifted down the y axis such that g(x)= x2+c when x=0 and g(x)= -3 -3=0+c c=-3 when x=3.

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The most appropriate choice for speed will be given by-

Speed of the flying carpet is 15.2 mph

What is speed?

The distance travelled by the body per unit time is called speed of the body.

If d is the distance travelled by the body and t is the time taken, then

speed = [tex]\frac{d}{t}[/tex]

Speed is a scalar quantity as the direction is not taken into account.

Here,

Let the speed of the flying carpet be [tex]x[/tex] miles

A flying carpet flies 2.4 miles with the wind

Time taken flying with the wind = [tex]\frac{2.4}{x +4}[/tex]

The flying carpet flies 1.4 miles against the wind

Time taken flying against the wind = [tex]\frac{1.4}{x - 4}[/tex]

By the problem,

                         [tex]\frac{2.4}{x +4} = \frac{1.4}{x-4}[/tex]  

                         [tex]2.4(x - 4) = 1.4(x + 4)\\2.4 x - 9.6 = 1.4 x + 5.6\\2.4 x - 1.4 x = 9.6 + 5.6\\[/tex]

                          [tex]x = 15.2[/tex] mph

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Yes. Because Mound 1 and Mound 2 form a pair of corresponding angles with that red transversal line (lane). Corresponding angles are congruent and parallel to each other.

1) Since both mounds share the same measure of the angle, then we can say that those mounds are yes, parallel to the lane since they both corresponding angles, and corresponding angles are parallel and congruent to each other.

2) So the answer is :

Yes. Because each mound 1 and Mound 2 form a pair of corresponding angles with that red transversal line. Corresponding angles are congruent and parallel to each other.

Answer:

3√2

Step-by-step explanation:

[tex] \sqrt{ {(6 - 9)}^{2} + {(9 - 6)}^{2} } [/tex]

[tex] \sqrt{ {( - 3)}^{2} + {3}^{2} } [/tex]

[tex] \sqrt{9 + 9} = \sqrt{2 \times 9} = \sqrt{2} \sqrt{9} = 3 \sqrt{2} [/tex]

The system of linear equations has one and only one solution.

x = 3 and y = 2.

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

We have,

x - 3y = -3 _____(1)

4x + 3y = 18 ______(2)

We will solve the equation to check its solutions.

x - 3y = -3 can be written as:

x = -3 + 3y ____(3)

Putting in (2) we get,

4(-3 + 3y) + 3y = 18

-12 + 12y + 3y = 18

15y = 18 +12

15y = 30

y = 2

Putting in (3)

x = -3 + 3 x 2 = -3 + 6 = 3

x = 3

We see that,

x = 3 and y = 2

Putting in the equation it is satisfied.

x - 3y = -3

3 - 3 x 2 = -3

3 - 6 = -3

-3 = -3

4x + 3y = 18

4x3 + 3x2 = 18

12 + 6 = 18

18 = 18

Thus,

The system of linear equations has one and only one solution.

x = 3 and y = 2.

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Using percentages, we can conclude that the total cost of the meal is approximately $33.

So, the total cost of the meal:

Sales tax on the bill: 9%

18% tip of the bill:

Total cost of meal: $27.5277 + $5 = $32.5277

Therefore, using percentages, we can conclude that the total cost of the meal is approximately $33.

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The difference quotient of the function f(x) = 4x² + 3x - 5 is [f(x + h) - f(x)]/h = 8x + 4h + 3

The function is given as

f(x) = 4x² + 3x - 5

Start by calculating the function f(x + h)

So, we have the following

f(x + h) = 4(x + h)² + 3(x + h) - 5

Expand

f(x + h) = 4(x² + 2xh + h²) + 3(x + h) - 5

Open the brackets

f(x + h) = 4x² + 8xh + 4h² + 3x + 3h - 5

The difference quotient is then calculated as

[f(x + h) - f(x)]/h

This gives

[f(x + h) - f(x)]/h = (4x² + 8xh + 4h² + 3x + 3h - 5 - 4x² - 3x + 5)/h

Evaluate the like terms

[f(x + h) - f(x)]/h = (8xh + 4h² + 3h)/h

Evaluate the quotients

[f(x + h) - f(x)]/h = 8x + 4h + 3

Hence, the value of [f(x + h) - f(x)]/h is 8x + 4h + 3

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Complete question

If f(x) = 4x² + 3x - 5, then [f(x + h) - f(x)]/h is equal to which of the following?

From the problem, we are given a point (8, -6) and an equation y = 4x + 7

The equation we are to obtain is perpendicular to y = 4x + 7

In Mathematical terms, it means the slope of the given equation and the one we are to find follow the relation:

slope of the given equation = 4

The required equation passes through a point (8,-6)

The formula for obtaining the equation with a given slope that passes through a point is given as :

By substituting;

The equation in slope-intercept form is y = -0.25x - 4

Step 1

Rearrange the expression to bring like terms together.

Step 2

Simplify to get the final answer

Hence the right answer is option C

Observe the given graph carefully.

In a circle graph, the circle is divided into different sectors, each characterized by its central angle.

The complete circle measures 360 degrees. So the complete distribution (100% data) corresponds to 360 degrees.

In the given problem, we are concerned with the budget,

(a)

Consider the following,

So, one-fourth of the budget will correspond to the department which covers the 90-degree sector of the circle graph.

As observed from the graph, the most suitable department under this criteria is the Engineering Department.

Thus, Engineering Department gets approximately one-fourth of the annual budget.

(b)

Consider that the departments Engineering and support combiningly cover a little more than one-third of the area of complete circle.

Consider the following,

Note that the area covered by the department is a little more than one-third, so the corresponding percentage value must also be a little more than 33.33%.

From the available options, 40% is the value available next to 33.33%, so this should be the most suitable choice.

Thus, it can be concluded that approximately 40% of the annual budget goes to the departments Engineering and Support combined.

Therefore, option (b) is the correct choice.

Given:

The distance to the door from your desk is d meters.

Your first step is 1/6 that distance =

Each successive step is 1/6 the previous distance.

so, the second step =

The third step =

And so on,

So, for the step number n, the formula will be :

So, for 8 steps

You will have traveled =

For 12 steps =

For 20 steps =

For n steps =

Prove that Tringle ABC is congruent to tringle GEC

SOLUTION

Given the following

Consider the image below

To solve the right triangle, we need to find the following:

To find B, we use the sum of angles in a triangle

hence

Substituting into the equation we have,

Subtract 136.5 from both sides

hence

B = 43.5°

To find b, we use the trigonometry ratio for tangent

From the triangle above

Substituting into the equation

Then

hence

b = 1.8in to 1 decima place

To find c, we also apply trigonometry ratio for sine of an angle

Substituting the values into the equation we have,

Divide both sides by 1.9, we have

hence

c = 2.6 in

Therefore, to solve the right triangle, we have

Answer; B = 43.5°, b = 1.8in, c = 2.6 in

The first error Rafael made was that he made six arcs instead of taking the perpendicular bisector of the diameter and then making 4 arcs.

A square is constructed first by taking the perpendicular bisector of the diameter and making the four arcs and then joining them to make the square.

Answer: C

Step-by-step explanation: A is definitely not correct. not b. not d

The money was distributing un equally. Because of the great depression, the lower classes made less money

Solution:

Let x be the number of antifreeze solution. Thus;

We would solve for x;

Hence, the amount needs to be drained out is;

Answer: 1.15 gallon

The slope can be calculated as the quotient between the difference in the y-coordinates of two points, and the difference in the x-coordinates of the same two points.

We pick any 2 known points, like (0,2) and (5,4).

We calculate the slope as:

Answer:

The slope is m=2/5=0.4

You have the equation:

To solve this equation you have to clear the variable x. You can clear the variable x, as follow:

You multiply both sides of the equation by 5.

Then the solution is:

(7,-8)

1) Considering that f(x-2) is a transformation of f(x). Precisely, a horizontal translation to the right.

2) So, we can write out the following:

Note that a horizontal translation just "pushes to the right". So there was no vertical shift.

3) Hence, the answer is (7,-8)

The slope of a ramp with a height-to-distance ratio of 1 to 12 feet is 4.76 degrees.

The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The tangent relation or the height-to-distance ratio helps to determine the slope of the line.

It is given that the height-to-distance ratio of a slope is given as 1 to 12 feet.

So,

[tex]\tan \alpha = 1/12\\\alpha= \tan^{-1}1/12\\\alpha= 4.76^\circ[/tex]

So, the slope of the ramp is about 4.76 degrees.

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