Find the length of LM if L is the midpoint of NM. NL = 3x + 1, LM = 8x - 24.

Answers

Answer 1

Answer:

LM = 16

Step-by-step explanation:

From the question given:

L is the midpoint of NM

NL = 3x + 1

LM = 8x - 24

LM =?

Next, we shall determine the value of x.

This can be obtained as follow:

Since L is the midpoint of NM, it means that NL and LM are equal i.e

NL = LM

Thus, we can obtain the value of x as follow:

NL = 3x + 1

LM = 8x - 24

NL = LM

3x + 1 = 8x - 24

Collect like terms

3x - 8x = - 24 - 1

-5x = - 25

Divide both side by - 5

x = -25/-5

x = 5

Finally, we shall determine the length of LM as follow:

LM = 8x - 24

x = 5

LM = 8(5) - 24

LM = 40 - 24

LM = 16

Therefore, the length of LM is 16


Related Questions

find the midpoint of the line segment whose endpoints are
(5,9) (2,-1)?​

Answers

Answer:

(3.5,4)

Step by step explanation:

x coordinate =

[tex] \frac{5 + 2}{2} [/tex]

= 3.5

y coordinate =

[tex] \frac{ - 1 + 9}{2} [/tex]

= 4

midpoint = (3.5,4)

Answer:

(  3.5,4)

Step-by-step explanation:

To find the midpoint

Add the x coordinates together and divide by 2

(5+2)/2 = 7/2 = 3.5

Add the y coordinates together and divide by 2

(9+-1)/2 = 8/2 = 4

( 3.5,4)

Plz help I would appreciate it!

Answers

Answer:

(a) Triangles are similar if corresponding angles are congruent and the ratios of the lengths of corresponding sides are equal.

(b) x = 24

(c) y = 17; z = 51

Step-by-step explanation:

(a) Triangles are similar if corresponding angles are congruent and the ratios of the lengths of corresponding sides are equal.

(b)

15/45 = 8/x

1/3 = 8/x

x = 3 * 8

x = 24

(c)

a^2 + b^2 = c^2

x^2 + 45^2 = z^2

24^2 + 45^2 = z^2

576 + 2025 = z^2

z^2 = 2601

z = 51

15/45 = y/z

1/3 = y/51

3y = 51

y = 17

X=3816371/(27×63) solve for x

Answers

Answer:

X = 14,700

Step-by-step explanation:

you can use a calculator to get the x.

X=3816371/(27×63)

Please help me with this

Answers

verifying, by putting [tex] \theta=60^{\circ}[/tex]

LHS≠RHS

hence the question is FALSE

1. Given thatA={1,2,3,4,5} and B={3,5,10,11,12} and such that U= AUB. I) list down the elements of U,A' and A'UB'. ii) how many subsets do set A have?​

Answers

Answer:

U = {1, 2, 3, 4, 5, 10, 11, 12}A' = {10, 11, 12}A'∪B' = {1, 2, 4, 10, 11, 12}A has 32 subsets

Step-by-step explanation:

i) The union of the two sets is the list of elements that are in either. Duplicates are listed only once.

  U = {1, 2, 3, 4, 5, 10, 11, 12}

  A' = U - A = {10, 11, 12}

  A'∪B' = {10, 11, 12}∪{1, 2, 4} = {1, 2, 4, 10, 11, 12}

__

ii) A has 5 elements, so has 2^5 = 32 subsets, including the empty set and the whole set.

how many 6-digit numbers can be created using8, 0, 1, 3, 7, and 5 if each number is used only once?

Answers

Answer:

600 numbers

Step-by-step explanation:

For six-digit numbers, we need to use all digits 8,0,1,3,7,5 each once.

However, 0 cannot be used as the first digit, because it would make a 5-digit number.

Therefore

there are 5 choices for the first digit (exclude 0)

there are 5 choices for the first digit (include 0)

there are 4 choices for the first digit

there are 3 choices for the first digit

there are 2 choices for the first digit

there are 1 choices for the first digit

for a total of 5*5*4*3*2*1 = 600 numbers

Which expression is NOT equivalent to 4×38? A. 4×(3×18) B.(4×3)×18 C. (4×18)×3 D. (4×3)×(4×18)

Answers

Answer:

Every choice is not equivalent to 4✖️38.

Step-by-step explanation:

4✖️38=152

A. 54✖️4=216

B. 12✖️18=216

C. 72✖️3=216

D. 12✖️72=864

Every choice is not equivalent to 4✖️38.

simplify the equation. (5xE2 - 3x) - (5xE2 - 3x+1)

Answers

Answer:

[tex]\huge \boxed{\mathrm{-1}}[/tex]

Step-by-step explanation:

[tex](5xe^2 - 3x) - (5xe^2 - 3x+1)[/tex]

Distribute negative sign.

[tex]5xe^2 - 3x- 5xe^2 +3x-1[/tex]

Combine like terms.

[tex]0xe^2 +0x-1[/tex]

[tex]0-1=-1[/tex]

Select the equivalent expression.

Answers

C, because we multiply the exponents to get the answer.

Answer:

C

Step-by-step explanation:

Using the rule of exponents

[tex](a^{m}b^{n}) ^{p}[/tex] = [tex]a^{mp}[/tex] × [tex]a^{np}[/tex]

Thus

[tex](7^{2}5^{6})^4[/tex]

= [tex]7^{2.4}[/tex] × [tex]5^{6.4}[/tex]

= [tex]7^{8}[/tex] × [tex]5^{24}[/tex] → C

what is the coefficient of the variable in the expression 4-3x​

Answers

Answer:

As per the question,

We have to find what's the coefficient.

Let's start to seperate the expression.

Here,

x is the variable,

4 is a number.

-3 is also a number.

4, -3x

The number with x here is -3 in (-3x) as the coefficient is (-3) in the given equation.

Answer:

Hey there!

Rearrange the expression to: -3x+4

The coefficient would be -3.

Let me know if this helps :)

Please answer this question now

Answers

Answer:

m∠C = 102°

Step-by-step explanation:

This is is a cyclic quadrilateral

• The sum of opposite angles in a cyclic quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

If you look at the above diagram properly, you will notice there are are angles outside the circle. We refer to this an exterior or external angles in a cyclic quadrilateral

• Note that m∠B is Opposite the exterior angle m∠CDA

Hence,

m∠CDA = 2 × m∠B

m∠CDA = 2 × 100°

m∠CDA = 200°

• m∠CDA = m∠CD + m∠DA

m∠DA = m∠CDA - m∠CD

m∠DA = 200° - 116°

m∠DA = 84°

• Another external angle we need to find is m∠DAB

m∠DAB = m∠DA + m∠AB

We know that m∠DA = 84°, therefore,

m∠DAB = 84° + 120°

m∠DAB = 204°

• The final step is to solve for m∠C

m∠DAB is Opposite m∠C

Hence

m∠C = 1/2 × m∠DAB

m∠C = 1/2 × 204

m∠C = 102°

Select the correct answer.
The function g(x) = x^2 is transformed to obtain function h:
h(x) = g(x-3).
Which statement describes how the graph of h is different from the graph of g?
А. The graph of h is the graph of g horizontally shifted left 3 units.
B. The graph of h is the graph of g vertically shifted up 3 units.
C. The graph of his the graph of g vertically shifted down 3 units.
D. The graph of h is the graph of g horizontally shifted right 3 units.

Answers

Answer:

B The graft of h is the graft of g vertically shifted up 3 units

choose the answer based on the most efficient method. if the first step in the equation " -9 + x = 5x - 7" is subtract x, what should the next step be

Answers

Answer:

add 7 to both sides

Step-by-step explanation:

This is so because we are trying to solve the equation by seperating the variables from the real numbers. So as they remove all variables from the left side of the equation, we should remove any remaining numbers that are on the right side of the equation.

Hope this helps!

I need to know this fairly soon pleaseee​

Answers

Answer:

m<PQT= 94°

Step-by-step explanation:

If line QS bisect <PQR

m<PQS = m < SQR

7x-6= 4x+15

7x-4x= 15+6

3x= 21

X= 21/3

X= 7

m<PQS= 7x-6

m<PQS= 7(7)-6

m<PQS= 49-6

m<PQS= 43°

m<PQS= m<SQR

<mSQR=43°

m<PQR= m<PQS + m < SQR

m<PQR=43+43

m<PQR= 86°

BUT

m<PQR= m<TQW

m<PQT= m<RQW

m<PQR+m<TQW +m<PQT+ m<RQW

= 360°

Let m<TQW= x

86+86+x+x= 360

2x+172= 360

2x= 188

X= 94°

m<PQT= 94°

Simplify 2√28 - 3√63

Answers

Answer:

[tex]-5\sqrt{7}[/tex]

Step-by-step explanation:

2√28 - 3√63

4√7 - 9√7

- 5√7

Answer:

- 5√7

Step-by-step explanation:

without actually calculating the cubes find the value of each of the following (-28)^3+(12)^3+(16)^3 ​

Answers

Answer:

-16128

Step-by-step explanation:

This expression can be calculated by algebraic means, whose process is described below:

1) [tex](-28)^{3}+(12)^{3}+(16)^{3}[/tex] Given.

2) [tex](-12-16)^{3} + (12)^{3}+(16)^{3}[/tex] Definition of addition.

3) [tex](-12)^{3} + 3\cdot (-12)^{2}\cdot (-16)+3\cdot (-12)\cdot (-16)^{2}+(-16)^{3}+(12)^{3}+(16)^{3}[/tex] Cubic perfect binomial.

4) [tex](12)^{3}+[(-1)\cdot (12)]^{3}+(16)^{3} + [(-1)\cdot (16)]^{3}+3 \cdot (-12)^{2}\cdot (-16) + 3\cdot (-12)\cdot (-16)^{2}[/tex] Commutative property/[tex](-x)\cdot y = -x\cdot y[/tex]

5) [tex](12)^{3} + (-1)^{3}\cdot (12)^{3} + 16^{3} +(-1)^{3}\cdot (16)^{3} + (-3)\cdot [(-12)^{2}\cdot (16) +(-16)^{2}\cdot (12)][/tex] Distributive property/[tex](-x)\cdot y = -x\cdot y[/tex]/[tex]x^{n}\cdot y^{n} = (x\cdot y)^{n}[/tex]

6) [tex](12)^{3} + [-(12)^{3}]+(16)^{3} + [-(16)^{3}]+ (-3)\cdot [(-12)^{2}\cdot (16)+(-16)^{2}\cdot (12)][/tex] [tex](-x)\cdot y = -x\cdot y[/tex]

7) [tex](-3)\cdot [(-12)^{2}\cdot (16) + (-16)^{2}\cdot (12)][/tex] Existence of the additive inverse/Modulative property for addition.

8) [tex](-3) \cdot [(12)^{2}\cdot (16)+(16^{2})\cdot (12)][/tex] [tex]x^{n}\cdot y^{n} = (x\cdot y)^{n}[/tex]/[tex](-x)\cdot (-y) = x\cdot y[/tex]

9) [tex](-3)\cdot (12)\cdot (16)\cdot (12+16)[/tex] Distributive property.

10) [tex]-16128[/tex]     [tex](-x)\cdot y = -x\cdot y[/tex]/Definition of sum/Definition of multiplication/Result

can someone explain mean and median to me?

Answers

Answer:

Mean is obtained by adding of all of the term values by the number of terms in a given set of data. Mean is also called "average".

Median on the other hand is the arrangement of numerical data in chronological order from least to greatest and finding the middle number from that arranged set of data.

For a quadratic function y = ax² + bx + c, suppose the constants a, b, and c are consecutive terms of a geometric sequence. Show that the function does not cut the x axis.

Answers

Hello, because of the geometric sequence we can say that:

[tex]\alpha = \dfrac{b}{a}=\dfrac{c}{b}\\\\\dfrac{c}{a}=\dfrac{c*b}{a*b}=\dfrac{c}{b}\dfrac{b}{a}=\alpha^2\\\\\text{So the equation becomes.}\\\\ax^2+bx+c=0<=>x^2+\dfrac{b}{a}x+\dfrac{c}{a}=0\\\\<=>x^2+\alpha x+ \alpha^2=0\\\\\Delta=b^2-4ac = \alpha^2-4\alpha^2=-3\alpha^2 < 0[/tex]

So there is no real root, so the function does not cut the x axis.

Thank you

For the given quadratic function, the x-axis is not cut by the function because there is no true root.

What is a quadratic function?

To determine values for various parameters, quadratic functions are employed in a variety of scientific and engineering disciplines. A parabola is used to graphically illustrate them. The orientation of the curve is defined by the highest degree factor.

As per provided data in question,

α = b/a = c/b

c/a = (c × b)/(a × b) = (c/b) (b/a) = α²

For the equation,

ax² + bx + c = 0

x² + b/a(x) + c/a = 0

⇒ x² + ax + α² =0

Δ = b² - 4 ac = α² - 4α²

Δ = -3α² < 0, which means that no real root is there.

To know more about quadratic functions:

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42=−7(z−3)
solve for z
plzzz help me thxs a bunch
step by step if can thx

Answers

Answer:

z=-3

Step-by-step explanation:

1:open the brackets.

2:take 21 to the other side to be subtracted by 42

3:you get a -z but you can take it to the other side to get a +z but -21 divide to get the answer

42=-7(z-3)

-7(z-3)=42

-7z+21=42

-7z=42-21

-7z=21

therefore,

z=21\-7

that is, -21\7=-3

The perimeter of an isosceles triangle is 32 inches. If the base is longer than half of the two other equal sides by 2 inches, find the length of all sides of this triangle.

Write as a equation.​

Answers

Answer:

Step-by-step explanation:

Let equal sides of an isosceles triangle = a inches

Base = [tex]\frac{1}{2}a+2[/tex] inches

Perimeter  = 32 inches

a + a + [tex]\frac{1}{2}a+2[/tex] = 32

[tex]2a + \frac{1}{2}a+2 = 32\\\\\frac{2a*2}{1*2}+\frac{1}{2}a+2=32\\\\\frac{4a}{2}+\frac{1}{2}a+2=32\\\\\frac{5}{2}a+2 = 32\\\\[/tex]

Subtract 2 from both sides

[tex]\frac{5}{2}a=32-2\\\\\frac{5}{2}a=30\\\\a=30*\frac{2}{5}\\\\a=6*2[/tex]

a = 12 inches

base = [tex]\frac{1}{2}*12+2[/tex]

        = 6 + 2

Base = 8 inches

Thomas loves tomatoes. He plans to fill the container shown below with soil to grow his own tomato
plants. The dimensions of the container are shown in inches.
umi
ndo
20 in
geo
10 in-
How much soil will the container hold?
Either enter an exact answer in terms of or use 3.14 for .
inches?

Answers

Given that

Height of container is 20 inches .Radius of base is 10 inches .

To Find

Volume of container .

Formula

Volume of cylinder is πr²h

Solution

→ Volume = πr²h

Using π as 3.14

→ 3.14 × 10 × 10 × 20 = Volume

→ 314 × 20 = Volume

6280 inches² is the holding capacity of the container.

Answer:

6280

Step-by-step explanation:

this is correct on khan academy

Patrick raced round a 440 metre circular track and stopped suddenly after 900 metres . How far was she from the starting point at the 900 metre mark ? Solve

Answers

Answer:

20 meters

Step-by-step explanation:

The track is circular so it means that after Patrick raced the entire track he is back at the starting point. In other words, every 440 meters he is back to the beginning.

So we would have that, if he races round the track twice, he would run 440(2) = 880 meters and he would be back at the starting point.

The problem asks us how far is he from the starting point at the 900 meter mark. If at 880 meters he is at the starting point, then at 900 meters he would be [tex]900-880=20[/tex] meters from the starting point.

This is the new one! Please help I’m so lost

Answers

Answer:

(a) (f o g)(x) =  x^2 - 15x + 54

(b) (g o f)(x) = x^2 + 3x - 9

(c) (f o f)(x) = x^4 + 6x^3 + 12x^2 + 9x

(d) (g o g)(x) = x - 18

Step-by-step explanation:

f(x) = x^2 + 3x

g(x) = x - 9

(a)

(f o g)(x) = f(g(x)) = (g(x))^2 + 3(g(x)) = (x - 9)^2 + 3(x - 9)

(f o g)(x) = x^2 - 18x + 81 + 3x - 27

(f o g)(x) = x^2 - 15x + 54

(b)

(g o f)(x) = g(f(x)) = f(x) - 9 = x^2 + 3x - 9

(c)

(f o f)(x) = f(f(x)) = (x^2 + 3x)^2 + 3(x^2 + 3x)

(f o f)(x) = x^4 + 6x^3 + 9x^2 + 3x^2 + 9x

(f o f)(x) = x^4 + 6x^3 + 12x^2 + 9x

(d)

(g o g)(x) = g(g(x)) = x - 9 - 9 = x - 18

Help please on question 61!!

Answers

Answer:

r = 1

Step-by-step explanation:

2πr = x

πr² = y

x = 2y

2πr = 2πr²

r = 1

Find the value of x to the nearest degree.

A. 35
B. 28
C. 51
D. 55

Answers

Answer:

A

Step-by-step explanation:

First, we are already given the sides adjacent and opposite to ∠x. Therefore, we can use the tangent function. Recall that:

[tex]\tan(x)=opp/adj[/tex]

The opposite side is 20 while the adjacent side is 14.

Plug in the numbers. Use a calculator:

[tex]\tan(x)=20/14=10/7\\x=\tan^{-1}(10/7)\\x\approx55.0080\textdegree\approx55\textdegree[/tex]

Edits: Improved Answer. Removed Wrong Answer.

Answer:

55

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan x = 20/14

Taking the inverse tan of each side

tan ^-1 tan x = tan ^ -1 (20/14)

x =55.0079798

To the nearest degree

x = 55

PLS HELP ME ANSWER THIS QUESTION I DONT UNDERSTAND IT I WILL GIVE BRAINLIST AND A THANK YOU!!!!

Answers

Answer:

x=150°

Step-by-step explanation:

Using the vertical angle theorem, you can infer that AEC and DEB are in fact the same angle, 20°, and the same goes for FED and CEG, both 130°.

So, x spans AEC and CEG so is 20° + 130° = 150°

What transformation of the parent function f(x) is made to get f(3x)?

Answers

Answer: Vertically shifting it by 3

The transformation of a function is horizontally shrink by a factor of 3 .

What is a horizontal shrink?We can apply horizontal shrink to a function by multiplying its input values by a scale factor, a, where 0 < 1/a < 1.

Let’s go ahead and look at how f(x) = x2 will be affected by a scale factor of 1/2 and 1/3.

Below is a graph of the data.As we have expected, the graph stretches by a factor of 2 and 3. This is true for all horizontal stretches. The graph only stretches away from the y-axis when we horizontally stretch a graph.Horizontal stretch on other functions will exhibit similar properties. Let’s say we have f(x) = |x|, if this function’s graph is to be stretched horizontally to attain g(x), the new function’s expression can be expressed as |1/3 ∙ x| = |x/3|.

How do you horizontally shrink  by a factor of 3 ?

If g(x) = 3f (x): For any given input, the output of g is three times the output of f, so the graph is stretched vertically by a factor of 3. If g(x) = f (3x): For any given output, the input of g is one-third the input of f, so the graph is shrunk horizontally by a factor of 3.

Learn more about Transformation on :

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if the diameter is 20 cm what is the area based on pi

Answers

Answer:

[tex]\Large \boxed{\mathrm{100\pi \ cm^2 }}[/tex]

Step-by-step explanation:

[tex]\displaystyle area \ of \ circle \ = \ \pi (\frac{diameter}{2} )^2[/tex]

[tex]\displaystyle A \ = \ \pi ( \frac{20}{2} )^2[/tex]

[tex]\displaystyle A \ = \ \pi ( 10 )^2[/tex]

[tex]\displaystyle A \ = \ 100\pi[/tex]

I promise i will mark as brainiest

Answers

Answer:

The answer is option B

Step-by-step explanation:

The question above means that how many numbers can divide 2003 with a remainder of 23

That means all the numbers are less than 2003

The number of numbers that have this property are only

22 numbers

Hope this helps you

What is the perimeter of a square with an area of 441 cm2? A) 21 cm B) 42 cm C) 56 cm D) 84 cm

Answers

Answer:

D) 84cm

Step-by-step explanation:

Square area = √(441cm²) = 21 cm

perimeter = 4*21 = 84 cm

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