9. If LK MK, LK = 7x - 10, KN = x + 3, MN = 9x - 11, and KJ = 28, find LJ.

9. If LK MK, LK = 7x - 10, KN = X + 3, MN = 9x - 11, And KJ = 28, Find LJ.

Answers

Answer 1

Answer:

[tex] LJ = 46 [/tex]

Step-by-step explanation:

Given:

[tex] LK = MK [/tex]

[tex] LK = 7x - 10 [/tex]

[tex] KN = x + 3 [/tex]

[tex] MN = 9x - 11 [/tex]

[tex] KJ = 28 [/tex]

Required:

LJ

Solution:

Step 1: create an equation to find the value of x

Since we are given that LK = MK, and LK = 7x - 10, let's find the expression for MK to get an equation.

[tex] MK + KN = MN [/tex] (segment addition postulate)

[tex] MK = MN - KN [/tex] (Subtract KN from each side)

[tex] MK = (9x - 11) - (x + 3) [/tex] (subtitution)

[tex] MK = 9x - 11 - x - 3 [/tex]

[tex] MK = 9x - x - 11 - 3 [/tex]

[tex] MK = 8x - 14 [/tex]

LK = MK, therefore,

[tex] 7x - 10 = 8x - 14 [/tex]

Subtract 8x from each side

[tex] 7x - 10 - 8x = 8x - 14 - 8x [/tex]

[tex] -x - 10 = -14 [/tex]

Add 10 to both sides of the equation

[tex] -x - 10 + 10 = -14 + 10 [/tex]

[tex] -x = -4 [/tex]

Divide both sides by -1

[tex] x = 4 [/tex]

Step 2: Find LJ

[tex] LJ = LK + KJ [/tex] (segment addition postulate)

[tex] LJ = (7x - 10) + (28) [/tex]

Plug in the value of x

[tex] LJ = 7(4) - 10 + 28 [/tex]

[tex] LJ = 28 - 10 + 28 [/tex]

[tex] LJ = 46 [/tex]


Related Questions

A calculus exam that was taken by 94 students is recorded and normally distributed. The mean score on the exam is 78 and the standard deviation is 2.4. What percent of the scores are in the 70.8 and 85.2 range?

Answers

Answer:

99.73%

Step-by-step explanation:

If you have a calculator with distribution functions, this problem boils down to using a single command:

norm(70.8, 85.2, 78, 2.4) = 0.9973

This tells us that 99.73% of the scores are in the 70.8-85.2 range.

Evaluate
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Answers

Answer:

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Step-by-step explanation:

X×(-6)×(-4)=24

two negatives cancel out and turn the 24 to a positive number

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Answers

Answer:

4(1+2)/2 = 6

Step-by-step explanation:

Think about multiples of 6 (I thought of 12)

"Think 'What' x 'what' will make the lowest multiple of 6"

the answer would be 4(1+2)/2=6

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Answer:

A=a2/ a squared

Charles’ law describes the relationship between the initial and final temperature and volume of a gas held at a constant pressure. [tex]\frac{v_{i} }{V_{f} }=\frac{t_{i} }{t_{f} }[/tex] A). Solve the equation for [tex]v_{f}[/tex] B). Solve the equation for [tex]t_{f}[/tex] Show Step by Step

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Step-by-step explanation:

Solve for f(-7).
f(x) = 5 - X
f(-7) = [?]
Enter

Answers

f(-7)=5-(-7)
f(-7)=5+7
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Answer:

[tex]f(-7)=12[/tex]

Step-by-step explanation:

[tex]f(x)=5-x\\\\\text{Substitute 'x' for '-7' and solve.}\\\\f(-7)=5-(-7)\\\\f(-7)=5+7\\\\\boxed{f(-7)=12}[/tex]

Hope this helps.

describe the relaationship between two place value positions

Answers

Answer:

Any place-value position is 10 times greater than the position to its right and / of the position to its left.

NEED ASAP

Change the percent to a decimal.0.4% =
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C 4.0
D 0.04

Answers

Answer:

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If you do the math you should get this answer

oweikeme has 2500 Naira and bought the following items from the bookshop: 60 ballpoint pens at 15 Naira each, two dozen of exercise books at 5 Naira each,8 drawing books at 80 Kobo each how much has he have left​

Answers

Answer:

1480

Step-by-step explanation:

60x15=900

24x5=120

there is no mention of qweikeme having any kobo

At a picnic there are 7 pieces of fruit for every 4 vegetables. If there are 28 pieces of fruit, how many vegetables are there?

Answers

Step-by-step explanation:

There are 7 fruits for every 4 vegetables.

If there are 28 fruits, the number of fruits have multiplied by 4. This means that the number of vegetables have multiplied by 4 as well.

=> 4 * 4 = 16 vegetables.

Hence there are 16 vegetables.

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Answers

Answer:

6

Step-by-step explanation:

M=2*2*3*5*5=300

N=2*2*2*3*3*7=504

Common factors between the two numbers are 2 and 3

The GCF(greatest common factor):

2×3 = 6

To see if it is true:

300/6 = 50

504/6 = 84

6 is the answer to the question.

Which rule describes the relationship between the input and output pairs in the following table?
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10
5
10
20
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B)Multiply the input by 2 to get the output

C)Multiply the input by 3 then subtract 5 from the result to get the output

Answers

Answer:

B)Multiply the input by 2 to get the output

Step-by-step explanation:

5x2=10

10x2=20

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:


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Answers

Answer:

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Step-by-step explanation:

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Mane and Seth are working on a lab activity where they are tracking some leaves that are
floating past them in a rain runoff channel near their home. They have to measure how far the
leaves travel in different amounts of time. They place a long tape measure along side of the
runoff channel to measure distance A borrowed stopwatch will let them record the amount of
time. They plan to have time intervals that begin at two seconds, and increase by two's until
they get to 20 seconds. The data they recorded is below.
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Answers

Answer:

Independent = time intervals

Dependant = how far the leaves travel

Step-by-step explanation:

independent = what you change

dependent = what you measure

Answer

a tape measure

Step-by-step explanation:

Solve for the distance from point A to point B. Round your answer to
nearest tenth.
A(5,4) and B(-4,-3)

Answers

Answer:

11.4

Step-by-step explanation:

Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

1. [tex]d=\sqrt{(-4-5)^2+(-3-4)^2}[/tex]

2. [tex]d=\sqrt{(-9)^2+(-7)^2}[/tex]

3. [tex]d=\sqrt{81+49}[/tex]

4. [tex]d=\sqrt{130}[/tex]

5. [tex]d=11.4017[/tex]

6. [tex]d=11.4[/tex]

-2a>6, then a is what?

Answers

Answer: a < -3

Step-by-step explanation:

-2a > 6    Divide both sides by -2 and remember if you divide both sides  of an inequality by a negative number the sign switches.

-2a > 6  

a < -3

Answer:

a < -3

Step-by-step explanation:

It less than -3

a family uses 1303 kWh of electric energy in a month. if the power company charges $0.08 cents per kilowatt, what is the total electric bill for the month?

Answers

$104.25 is the electric bill for the month

not sure how to complete this, info is in the photo.

Answers

The answers are...
1. 4
2. 7
3. 17

3. Simplify. *
5m3 + 2m– 7m3 – 8m

Answers

Step-by-step explanation:

5m³ + 2m - 7m³ - 8m

= -2m³ -6m

= -2m(m² + 3)

Solve 2|x - 1| >= 10

Answers

Answer:

               [tex]\bold{\underline{x\in(-\infty\,,\,-4\big>\cup\big<6\,,\,\infty)}}[/tex]

Step-by-step explanation:

[tex]\bold{2|x-1|\geqslant10}\\\\{}\ \div2\qquad\div2\\\\\bold{|x-1|\geqslant5}\\\\\bold {x-1\geqslant5\qquad\quad\vee\qquad x-1\leqslant-5}\\\\\bold {x\geqslant6\qquad\qquad\vee\qquad\ \ x\leqslant-4}\\\\\bold{\underline{x\in(-\infty\,,\,-4\big>\cup\big<6\,,\,\infty)}}[/tex]

brody is working two summer jobs, making $10 per hour

Answers

thiis isnt specific but if hes working two summer jobs and making 10 per hour than Brody would be making less than min. wage

This isn’t a really helpful description but if he’s working two summer jobs he should be making about five dollars per both jobs so he’s making minimum-wage on both jobs

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X
2x
3x
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Answers

Step-by-step explanation:

x+2x+3x=180

6x=180

divide both sides by 6

x=30°

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Answers

(0,-4) 2-2=0. -7+3=-4




Ans; (0,-4)

Method ; x-axis: 2 – 2 = 0
y-axis: -7 + 3 = -4

1. Here is a map that shows parts of Texas and

a. About how far is it from Amarillo to Oklahoma City?
b. Driving at a constant speed of 70 miles per hour, will it be possible to make this
trip in 3 hours?

Answers

Answer:

a). 240 miles (Approx)

b). Trip can't be covered in 3 hours with a constant speed = 70 miles pr hour

Step-by-step explanation:

a). As the scale has been given at the bottom. Length of the scale represents the distance between two points.

  Now by measuring the distance between these stations, approximate distance between Amarillo and Oklahoma = 4(length of the scale)

  = 4×60

  = 240 miles.

b). Driving at a constant speed = 70 miles per hour

   Distance covered in 3 hours = 70 × 3

                                                   = 210 miles

Therefore, distance of 240 miles between these stations can't be covered with the driving speed 70 miles per hour in 3 hours.

The perimeter of the tennis court is 228 feet. What are the dimensions of the court? Write the equation for the situation: What is the width of the court? What is the length of the court?

Answers

Answer:

It’s 36 by 78 tennis court

width = 36 ft.

length = 78 ft.

Step-by-step explanation:

2(w+2w+6)=228 feet

2w+4w+12=228

6w=228-12

6w=216

w=36

So, 2w+6=78

It’s 36 by 78 tennis court

width = 36 ft.

length = 78 ft.

The dimensions of the tennis court can be determined by solving the equation system: width (w) = 42 feet and length (l) = 96 feet.

To find the dimensions of the tennis court, we can set up a system of equations based on the given information:

Equation for the perimeter:

The perimeter of a rectangle is given by the formula:

P = 2(length + width).

In this case,

the perimeter is 228 feet, so the equation gives:

228 = 2(l + w)

Equation relating length and width: It is stated that the width (w) is equal to the length (l), which can be expressed as:

w = l

To solve the system of equations:

Substitute the value of l from the second equation into the first equation:

[tex]228 = 2((2w + 6) + w)[/tex]

Simplifying the equation:

[tex]228 = 2(3w + 6)[/tex]

Divide by 2 on both sides

[tex]114 = 3w + 6[/tex]

Subtract by 6 on both sides

[tex]108 = 3w[/tex]

Divide by 3 on both sides

[tex]w = 36[/tex]

Substituting the value of w back into the second equation:

[tex]l = 36[/tex]

Therefore, the width of the tennis court is 36 feet, and the length is 96 feet.

Learn more about solving equations here:

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17. The length of a rectangle is 3 inches greater than its width. The perimeter is 28 inches.
Find the dimensions of the rectangle.

Answers

Answer:

[tex] \boxed{ \bold{ \sf{ width \: of \: a \: rectangle = 5.5 \: inches}}}[/tex]

[tex] \boxed{ \bold{ \sf{length \: of \: a \: rectangle =8.5 \ \: \: inches}}}[/tex]

Step-by-step explanation:

Let the width of a rectangle be 'w'

Length of a rectangle = w + 3

Perimeter of a rectangle = 28 inches

To find : dimensions of the rectangle ( length and width )

Finding the width of a rectangle ( w )

[tex] \boxed{ \sf{perimeter \: of \: a \: rectangle = 2(l + w)}}[/tex]

[tex] \dashrightarrow{ \sf{28 = 2(w + 3 + w)}}[/tex]

[tex] \dashrightarrow{ \sf{28 = 2(2w + 3)}}[/tex]

[tex] \dashrightarrow{ \sf{28 = 4w + 6}}[/tex]

[tex] \dashrightarrow{ \sf{4w + 6 = 28}}[/tex]

[tex] \dashrightarrow{ \sf{4w = 28 - 6}}[/tex]

[tex] \dashrightarrow{ \sf{4w = 22}}[/tex]

[tex] \dashrightarrow{ \sf{ \frac{4w}{4} = \frac{22}{4} }}[/tex]

[tex] \dashrightarrow{ \sf{w = 5.5 \: inches}}[/tex]

Width of a rectangle = 5.5 inches

Now, replacing / substituting the value of w in order to find the length of a rectangle

[tex] \sf{ length = 3 + w}[/tex]

[tex] \dashrightarrow{ \sf{length = 3 + 5.5}}[/tex]

[tex] \dashrightarrow{ \sf{length = 8.5 \: \: inches}}[/tex]

Length of a rectangle = 8.5 inches

Hope I helped!

Best regards! :D

Expand
Your answer should be a polynomial in standard form -4w(w^2-9)

Answers

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ - 4 {w}^{3} + 36w}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ - 4w( {w}^{2} - 9})[/tex]

Distribute -4w through the parentheses

[tex] \dashrightarrow{ \sf{ - 4 {w}^{3} + 36w}}[/tex]

Hope I helped!

Best regards! :D

The standard form of the polynomial -4w(w²-9) will be -4w³+36w.

What are polynomials?

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

The highest degree of terms is written first, followed by the next degree, and so on, to represent a polynomial in standard form.

The given expression can be converted to the standard form as below,

P = -4w(w²-9)

P = ( -4w) x (w²) + ( 4 x 9w)

P = -4w²+36w

Therefore, the standard form of the polynomial -4w(w²-9) will be -4w³+36w.

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Write g(x) in terms of f(x) after reflecting the graph of f(x) across the y-
axis. *

Answers

Answer:

g(x)=f(-x) , the dot on the x axis is negative so multiply it by a another negative to get a positive

The middle value of the data set is

Answers

Answer:

The middle value of the data set is called/labled the median

Step-by-step explanation:

if there is a odd (1,3,5...)number of number in the data set circle the middle two and add them and divide by two and that will be your median

hope it helps:)

Also, just look at the number in the middle of the data set to figure out the median

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