XZ¯¯¯¯¯¯¯¯ has a point Y between points X and Z. XY=17, YZ=4x+9, and XZ=11x−9.

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.

To know more about slope or gradient:

https://brainly.com/question/25748640

#SPJ9

Prove that Tringle ABC is congruent to tringle GEC

Answer:

35  5/9 cm total

Step-by-step explanation:

24 +   8   +  8/3  +    8 / 9   =  35  5/9 cm

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.

To learn more on distance click:

https://brainly.com/question/15172156

#SPJ1

Answer:

x=W/k

Explanation:

Given the equation

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

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

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.

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

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.

To know more about function refer to https://brainly.com/question/16404442

#SPJ1

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]

Here, we want to deduce the equation of the blue graph

From what we have, we can see that the image of the f(x) was moved 2 units to the right and 1 unit upwards

What this mean is that, we have 1 added to the y value and 2 added to the x value

So, the equation of the blue graph is

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.

Learn more about fraction additions:

https://brainly.com/question/11562149

#SPJ1

Solution:

The equation in the question is given below as

Step 1:

Expand the brackets in the qu

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

(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)

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:

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.

Learn more about algebra here:

https://brainly.com/question/24875240

#SPJ1

We have to differentiate f(x).

We can do this as:

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

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

Read more about difference quotient at

https://brainly.com/question/27771773

#SPJ1

Complete question

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

ANSWER:

STEP-BY-STEP EXPLANATION:

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

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%

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

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

The way in which this data-collection method produce bias in obtaining an estimate of all drivers who are satisfied with the company’s truck drivers is that: D. This sample may lead to voluntary response bias because drivers can choose to call the phone number and register an opinion.

A sampling bias can be defined as a type of bias in which members of an intended population are selected in such a way that some members have a higher or lower sampling probability (chances) than the other members.

This ultimately implies that, a sampling bias would occur when members of an intended population are selected incorrectly and as such resulting in a sample that is not representative of the entire population.

Generally speaking, a voluntary response sample is a data-collection technique (method) that is always biased because it only include individuals who choose to volunteer, unlike a simple random sample.

Read more on sampling bias here: https://brainly.com/question/15062060

#SPJ1

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.

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 =

According to the commutative property, the numbers we use can be moved around or swapped around without changing the solution. For addition and multiplication, the principle is true, but not for division or subtraction.

4x-3

 Is x=2

4(2)-3

This uses the ___ attribute?

Answer:

(5,-5) commutative property of subtraction property is used.

Example:

It can be commutative if you retain the negative with the 2 and the positive with the 5. Edited: Subtraction is not a commutative operation; for example, 5-2=3 and 2-5=-3. The order of addition or subtraction does not important, though, if you maintain the sign of the integer, as in +5-2=3 and -2+5=3, for example. 

To learn more about commutative property refer to:

https://brainly.com/question/778086

#SPJ13

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.

Answer:

x = 4.8

Step-by-step explanation:

Area = Length times width

12 = 2.5x  Divide both sides by 2.5

4.8 = x