The points I, J, K and L all lie on the same line segment, in that order, such that the ratio IJ:JK:KL is equal to 2:5:5 IfIL=60, find KL.

The measures of the angles D, F and B are 43°, 105° and 32°, respectively. (Correct choice: C)

Herein we find a geometric system generated by two parallel lines and two lines that pass through the two lines. The values of the missing angles by using triangle properties and concepts of alternating internal angles, supplementary angles and  vertical angles. Now we proceed to find the measures of the missing angles:

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Answer:

C

Step-by-step explanation:

For this problem you use the distributive property

the first expression should match the second

Answer: 24

Step-by-step explanation: 6 x 4 = 24
24 - 8 = 16

Answer:

The total cost of the laptop including tax will be $952.43.

Step-by-step explanation:

885.98 x 7.5%= $66.45

885.98 + 66.45= $952.43

Hope this helps!

The dimensions of the photograph are the length= 14 in  and the width= 5 in.

The rectangle is a quadrilateral.  The classification for quadrilaterals is given by the length of sides and angles. For a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

A rectangle is a geometric figure that has 4 sides called: base and height. Due to its characteristics, the rectangle presents two bases (B) and two heights (H).

The area of a rectangle is given by the multiplication between the base and the height.

The question gives:

Thenm

A= b * h

70 = (9 +w) * w

70= 9w +w²

w²+9w-70=0

[tex]w_{1,\:2}=\frac{-9\pm \sqrt{9^2-4\cdot \:1\cdot \left(-70\right)}}{2\cdot \:1}\\ \\ w_{1,\:2}=\frac{-9\pm \:19}{2\cdot \:1}[/tex]

Thus,  [tex]w_{1}=\frac{-9-\:19}{2\cdot \:1}=\frac{-28}{2}=-14[/tex] and [tex]w_{2}=\frac{-9+\:19}{2\cdot \:1}=\frac{10}{2}=5[/tex]

The dimensions should have positive values, then w=5.

If w=5, the length will be 5+9 = 14. With these dimensions, the area will be 14 * 5 = 70.

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Since the maximum height of the ball above the ground is 28 ft, the ball will never reach a height of 30 ft.

To determine if the ball will ever reach a hgeight of 30 ft, we need to determine the maximum height of the ball.

Using the equation of motion, v² = u² - 2gh where

So, making h subject of the formula, we have

h = (v² - u²)/-2g

Substituting the values of the variables into the equation, we have

h = (v² - u²)/-2g

h = ((0 ft/s)² - (40 ft/s)²)/-(2 × 32 ft/s²)

h = (0 ft²/s² - 1600 ft²/s²)/-(64 ft/s²)

h = - 1600 ft²/s²/-64 ft/s²

h = 25 ft

Since the ball is released from a height of 3 ft, its maximum height above the ground is H = 3 ft + h

= 3f + 25 ft

= 28 ft

So, we see that H = 28 ft < 30 ft.

Since the maximum height of the ball above the ground is 28 ft, the ball will never reach a height of 30 ft.

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The volume V(x) in cubic inches of the open-top box is (15[tex]x^{2}[/tex] - 2[tex]x^{3}[/tex])

and side of length x in inches of the square cutouts is

V(1) = 15 - 2 = 13

x ∠ 7.5

The vertical sides were 15 inches before we cut out the corners.  

The horizontal sides were 15 inches before we cut out the corners.

So now, if you fold all of the "tabs" up, you get a box that has a height of "x".  

The sides are now each missing a length of "x" from each end.  

So the longer edges of the box are now (15 - 2x) long.  

The shorter edges of the box are now (15 - 2x)

The volume of a box is given by V = (length)(width)(height)

 length = 15 - 2x

width and height of the box are equal to x in so

Multiply these together and get:

V(x) = (15 - 2x)(x)(x)

V (x)  =  (15[tex]x^{2}[/tex] - 2[tex]x^{3}[/tex])

let x = 1

V (x) =  (15[tex]x^{2}[/tex] - 2[tex]x^{3}[/tex])

V(1) = 15 - 2 = 13

First x must be greater than 0,

then, we have 2x ∠ 15

                          x ∠ 7.5

therefore, The volume V(x) in cubic inches of the open-top box is (15[tex]x^{2}[/tex] - 2[tex]x^{3}[/tex])

side of length x in inches of the square cutouts is

V(1) = 15 - 2 = 13

x ∠ 7.5

This unit has two parts:

The surface area of a box, and its volume

The length of the diagonal of a box

Each student should bring an empty cereal box (or some other box) to work on. (The length, width, and height of the box should all be different.)

Formula for the area of the surface

(a) If l, w, and h are the length, width, and height of a box, its surface area is given by surface area = 2*(l*w + l*h + w*h). (Do you see it?)

(b) Measurements

Measurements are made in inches and sixteenths of an inch, but they are recorded as decimals.

1/8 inch = .125 inch, ¼ inch = .25 inch, 3/8 inch = .375 inch, ½ inch = .5 inch, and so on.

Example:

length l = 8.375 inches

width w = 6.125 inches

height = 2.25 inches

(c) How to enter these measurements into a TI-108 calculator to get the surface area:

8.375*6.125 M+       51.29…

8.375*2.25 M+         18.84…

6.125*2.25 M+         13.78…

MRC * 2 =                167.84… square inches

We round this to 168 square inches (more or less)

Part 1b. We can also find the volume of the box:

volume = l*w*h = 8.375*6.125*2.25 = 115.4… cubic inches

If this were a hands-on unit, we would paper the box with square inch paper and fill the box with cubic inch blocks to see whether our computations are confirmed.

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3x = 3x is true for all values of x.

Hence, x| x is a set all real numbers. ( -∞,∞ )

Given the equation in the question;

Remove the parenthesis using the distributive property.

3(2x + 2) - 3x = 6 + 3x

3×2x + 3×2 - 3x = 6 + 3x

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

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

6x - 3x = 3x

3x = 3x

3x = 3x is true for all values of x.

Hence, x| x is a set all real numbers. ( -∞,∞ )

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The graph of the function is graph (b)

The equation of the graph is given as

f(x) = |x - 3|

The above equation is an absolute value function

An absolute value function is represented as

f(x) = a|x - h| + k

Where the vertex is

Vertex = (h, k)

From the given equation, we have

(h, k) = (3, 0)

a = 1

When a is positive, the graph opens up

From the graphs in the options, we have graph (b) that has the following features

(h, k) = (3, 0) and it opens upward

Hence, the graph of the function is graph (b)

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Answer:

7.66666666667

Step-by-step explanation:

I looked it up

Using the weighted mean, it is found that Trent can earn scores of at least 62 on the final exam to pass the course if he needs a "C" or better.

The complete problem is given as follows:

"Trent earns scores of 62, 86, and 80 on three chapter tests for a certain class.

His homework grade is 68 and his grade for a class project is 64.

The overall average for the course is computed as follows: the average of the three chapter tests makes up 50% of the course grade; homework accounts for 10% of the course grade; the project accounts for 20% of the course grade and the final exam accounts for 20% of the course grade.

What range of scores can Trent earn on the final exam to pass the course if he needs a "C" or better?

A "C" or better requires an overall course score of 70 or better, and 100 is the highest score that can be earned on the final exam."

The weighted mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.

For this problem, we have that:

Hence his weighted mean is given by:

76 x 0.5 + 68 x 0.1 + 64 x 0.2 + 0.2x = 57.6 + 0.2x.

For a grade C, he needs a score of at least 70, hence:

57.6 + 0.2x ≥ 70.

0.2x ≥ 12.4

x ≥ 12.4/0.2

x ≥ 62.

Hence Trent can earn scores of at least 62 on the final exam to pass the course if he needs a "C" or better.

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The coordinates of G after it is reflected over the x-axis are (4, -3)

The graph represents the given parameter

On the graph, we have the following point

G = (4, 3)

The rule of reflection across the x-axis is

(x, y) = (x, -y)

This means that

G' = (x, -y)

So, we have

G' = (4, -3)

Hence, the coordinates of G after it is reflected over the x-axis are (4, -3)

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Perimeter of the parallelogram = 210 in.

Area of parallelogram = 2,484 in.²

Perimeter of parallelogram = 2(a + b), where a and b are its sides.

Area of parallelogram = (b)(h), where h is its height and b is the length of one of its bases.

Given:

a = 51 in.

b = 54 in.

h = 46 in.

Perimeter of the parallelogram = 2(54 + 51) = 210 in.

Area of parallelogram = (b)(h) = (54)(46) = 2,484 in.²

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Answer:

[tex]\frac{1}{2}[/tex] hour later

Step-by-step explanation:

Since Mr.A has already traveled 25 miles there are 53 miles left to person B's house. In half an hour, Mr. A will have traveled 25 miles, while person b will have traveled 28. 25 + 28 = 53.

The solution to the given equation is x = 1, y = 2, z = 3. That is (1, 2, 3)

From the question, we are to solve the given system of linear equations

The given system of linear equation is

x + 2y -  z = 2       ----------- (1)

2x - 7y + 5z = 3    ----------- (2)

-4x + y + 2z = 4    ----------- (3)

From equations (1) and (2), eliminate z

5 × ( x + 2y -  z = 2      

1 × ( 2x - 7y + 5z = 3

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

5x + 10y -5z = 10

2x -7y + 5z = 3

Add the resulting equations

7x + 3y = 13 ----------- (4)

From equations (2) and (3), eliminate z

2 × ( 2x - 7y + 5z = 3    

5 × ( -4x + y + 2z = 4  

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

4x - 14y + 10z = 6

-20x + 5y + 10z = 20

Subtract the resulting equations

24x - 19y = -14 ---------- (5)

Now, solve equations (4) and (5) simultaneously

7x + 3y = 13

24x - 19y = -14

Eliminate y
19 × ( 7x + 3y = 13

3 × ( 24x - 19y = -14

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

133x + 57y = 247

72x - 57y = -42

Add the resulting equations

205x = 205

x = 205/205

x = 1

Substitute the value of x into equation (4)

7x + 3y = 13

7(1) + 3y = 13

7 + 3y = 13

3y = 13 - 7

3y = 6

c = 6/3

y = 2

Substitute the values of x and y into equation (1)

x + 2y -  z = 2

1 + 2(2) - z = 2

1 + 4 - z = 2

1 + 4 - 2 = z

3 = z

z =3

The solution to the given equation is x = 1, y = 2, z = 3. That is (1, 2, 3)

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The equation of the ellipse in standard form is equal to (y + 8)² / 25 + (x - 3)² / 16 = 1. (Correct choice: D)

In this problem we find the case of an ellipse whose center is located at a point distinct of the origin and whose major semiaxis is parallel to the y-axis. The standard form of the equation of the ellipse is:

(y - k)² / a² + (x - h)² / b² = 1

Where:

First, determine the coordinates of the center:

(h, k) = 0.5 · (3, - 3) + 0.5 · (3, - 13)

(h, k) = (3, - 8)

Second, calculate the length of the minor semiaxis:

a = 0.5 · [- 3 - (- 13)]

a = 5

c = 0.5 · [- 5 - (- 11)]

c = 3

b = √(a² - c²)

b = 4

Third, substitute all the parameters in the standard formula:

(y + 8)² / 25 + (x - 3)² / 16 = 1

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Using linear functions, it is found that 5 toppings would make the cost the same for all pizza.

A linear function is modeled by:

y = mx + b

In which:

For this problem, we have that:

Hence the cost functions are given as follows:

The costs will be the same when:

A(x) = B(x)

10 + 1.5x = 12.5 + x

0.5x = 2.5

x = 2.5/0.5

x = 5.

5 toppings would make the cost the same for all pizza.

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Answer:

29/5

Step-by-step explanation:

5 x 5 +4 = 29

now in fraction form it is 29/5.

The average value of function can be calculated using the formula →

[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex] and to find average rate of change of function can be calculated using → f '(x) =  [tex]$\frac{f(b)-f(a)}{b-a}[/tex].

We have a function (say f(x)).

We have to find the average value of a function and the average rate of change of function.

A function in mathematics is a relation involving two variables, such that one variable is dependent on the other for its value.

According to the question -

PART - A → Finding the Average value of a function.

The average (or the mean) value of f (x) on [a, b] is defined by -

[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex]

PART - B → Finding the Average Rate of Change of a function.

The average rate of change of function f(x) is found out as follows -

f '(x) =  [tex]$\frac{f(b)-f(a)}{b-a}[/tex]

Hence, to find the average value of function -

[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex]

and to find average rate of change of function -

f '(x) =  [tex]$\frac{f(b)-f(a)}{b-a}[/tex].

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Answer:

A

Step-by-step explanation:

Answer: A. 18

Step-by-step explanation:

Let the smallest number be x

Hence,

x+(x+2)+(x+4)+(x+6)=60

x+x+2+x+4+x+6=60

4x+12=60

4x+12-12=60-12

4x=48

Divide both parts of the equation by 4:

x=12

x+6=

12+6=

18

Answer: -152/9

Step-by-step explanation:

m−152=3+m10−3

m−152=3+10m−3

m−152=10m+3−3

m-152=10m

-152=9m

m=-152/9

Answer: D, E, A

Step-by-step explanation: By friend got rejected by them hopefully you don't.

Answer:

F, C, and D

Step-by-step explanation:

Yes, ∠2 and ∠3 are postulate or theorem that proves the condition is identified as supplementary.

∠1 and ∠2 are supplementary (Linear Pair Theorem)

m∠1 + m∠2 = 180◦ (Definition of supplementary ∠s)

∠1 ≈ ∠3 (Given)

m∠1 = m∠3 (Definition of ≈)

m∠3 + m∠2 = 180◦( Subst . prop . of ≈)

∠2 and ∠3 are supplements (Definition of supplementary ∠s)

An unsubstantiated claim that is assumed to be true is referred to as a postulate. A provable true assertion is referred to as a theorem. A line has at least two points, according to postulate 1. A plane has at least three noncollinear points, according to postulate 2.

Hence, postulate or theorem that proves j∥k and also ∠2 and ∠3 are supplementary.

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Answer:

40 pages

Step-by-step explanation:

10 pages per day times 4 days equals forty pages in four days.

Hope this helps! :)

Domain: (-infinity, 5)

Range; [-3, infinity)

Answer:

$38.02

Step-by-step explanation:

$36.73 × 1.035 = $38.02 (after rounding to two decimal places)

The measure of angle ABE is 63 degrees

The given parameters are

<AB = 63°

<BE = 0°

The measure of angle ABE is calculated using

<ABE = <AB + <BE

This is so because the angles AB and BE share a common point at B

So, we have

<ABE = 63 + 0

Evaluate the sum

<ABE = 63

Hence, the measure of angle ABE is 63 degrees

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Complete question

If AB = 63° and BE = 0°, what is the measure of <ABE?

The games that can be played for about places to cost the same is 3 games.

Let the number of games be represented by b.

The event charges $3 for bowling shoe rental and $10 per bowling. This can be represented as:

= 3 + 10b

MaxBowl charges $6 to run bowling shoes and $9 per bowling game. This will be:

= 6 + 9b

We will equate them together:

3 + 10b = 6 + 9b

Collect like terms

10b - 9b = 6 - 3

b = 3

Therefore, the games that can be played for about places to cost the same is 3 games.

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