Step
1
try
Angle
m/IKL=54"
m/
CL
F
H
54°
Reason
Given
Select a Reason

The numerical length of GH = 20 units

FH is a line segment.

G is a point on the line segment.

Then G divides the line segment FH into two line segments FG and GH.

We are given the lengths of FH, FG and GH in terms of x.

That is,  FH=4x+8, FG=x and GH=5x

We need to find the numerical length of the line segment GH. We first need to find the x for this.

As G cuts the line segment FH into two parts, the length of the line segment FH is the sum of the lengths of the line segments FG and GH.

That is, FH = FG + GH

⇒ 4x+8 = x +5x

⇒ 4x+8 = 6x

⇒ 2x = 8

⇒ x = 4

So the numerical length of GH = 5x = 5 x 4 = 20 units

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Answer:

1.34 units.

Step-by-step explanation:

The line y = 2x - 5 has a slope of 2 so the line passing through the given point will be perpendicular to y= 2x - 5 and will have a slope of -1/2.

Let this line be y = -1/2x + c.

Its passes through (4, 6) so:

6 = -1/2*4 + c

6 = -2 + c

c = 6 + 2 = 8

So, equation of this line is y = -1/2x + 8.

Now we find the point where the 2 lines intersect:

y = 2x - 5

y = -1/2x + 8

2x - 5 = -1/2x + 8

2x + 1/2 x = 5 + 8

(5/2)x = 13

x = 26/5

  = 5.2.

and y = 2(5.2) - 5

          = 5.4.

So, the point of intersection is (5.2, 5.4)

and the distance between the point (4,6) and the line y = 2x - 5

= √((6 - 5.4)^2 + (4-5.2)^2)

= √(0.36 + 1.44)

= √1.8

= 1.34

There is a formula you can use directly to solve this.

Answer:

y = mx + b

y = 1/4x + 2

Step-by-step explanation:

m(slope) = rise/run = 1/4

b(y intercept) = 2

Answer: y = f (n 1)

Step-by-step explanation:

If we count interest rate = 5%

then if he earned 'y' amount in 1st year then in 2nd year he must earned

= y + 5% of y

== 1.05 y

here, y = f(n 1)

Answer: 60 inches in 5 feet

Step-by-step explanation:

5X12=60

An equivalent expression to given expression is 35(3 + m)

In this question, we have been given an expression 105 + 35m

We need to write an equivalent expression of given expression.

To find an equivalent expression we factorize given expression using the distributive property and the greatest common factor.

A common number for 35 and 105 is 35.

105 = 35 × 3

So, we can write given expression as,

105 + 35m

= (35 × 3) + 35m

= 35(3 + m)

Therefore, an equivalent expression to given expression is 35(3 + m)

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Answer:

(x,y)=(10,11)

Step-by-step explanation:

Drew actually has almost finished the equation. So I'm starting with the left part

[tex]2.5x+ 6= 31[/tex]

Cancel out 6 from both sides and divide both sides 2.5 which leaves us with

[tex]x=\boxed{10}[/tex]

Plug in the value of x into the second equation and simplify

y=-2.10+ 31

[tex]y=\boxed{ 11}[/tex]

Answer:

2; 6

Step-by-step explanation:

for the first shape there are 2 lines of symmetry

TWO

for the hexagon or the regular polygon there are 6 lines of symmetry

SIX

you can find lines of symmetry by drying a line down and seeing if when you fold them they will be exactly the same

Answer:

x=22

Step-by-step explanation:

Since a straight line is equal to 180 degrees,

(3x+3)+(5x+1) = 180

(3x+3)+(5x+1)-180=0

8x+4-180=0

8x-176=0

8x=176

x=176/8

x=22

Which also means that the first angle is (3(22)+3)=69 degrees

the second angle is (5(22)+1) = 111 degrees

111 + 69 = 180  

Answer: y=-47/5

Step-by-step explanation:

Yw

To withdraw money from the automated teller machine the numeric pattern required to complete the personal ID numbers is 2, 13, 24, 35,46,57,68.

As given in the question,

Using automated teller machine customers at the bank withdraw money

Numeric pattern given for the personal ID numbers is

2, 13, 24, 35

First term 'a'= 2

Common difference between consecutive terms are same

'd'=13 -2                                                  

   =11

It is an arithmetic progression series

nth term = a+ (n-1)d

5th term = 2 +(5-1)11

               =46

6th term =2+(6 -1)11

              =57

7th term= 2+ (7-1)11

             = 68

Therefore, to withdraw money from the automated teller machine the numeric pattern required to complete the personal ID numbers is 2, 13, 24, 35,46,57,68.

The complete question is:

The customers at the bank would like to withdraw money from the automated teller machine. Help them enter their personal ID numbers by completing the numeric patterns. 2, 13, 24, 35, ___, ___, ____.

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Price of key ring = £1.6

Price of purse = £3.2

The unitary approach is a strategy for problem-solving that involves first identifying the value of a single unit, then multiplying that value to figure out the required value.

Given Data

Vicky makes 8 purses and 9 key rings to sell for charity.

Vicky wants to get a total of exactly £40

Suppose the price of key ring be v

and the price of purses be 2v

£40 = £8(2v) + £9(v)

40 = 16v + 9v

40 = 25v

v = [tex]\frac{40}{25}[/tex]

v = 1.6

Price of key ring = £1.6

Price of purse = £3.2

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California is the most populated state, New York is the least populated, and 26% of Americans live in California, New York, and Texas.

Convert all statistics to percentages:

CA: 3 25 = 0.12 or 12%, 0.12 100 to calculate percentages.

NY: 3 50 = 0.06, or 6%, and 0.06 100 to get the percentage.

TX: 2 25 = 0.08 = 8%, 0.08 100 = percent

(A) California has the largest population of the three states.

(B) New York has the smallest population of the three states.

(C) USA = 100%, CA + NY + TX = 26%, so 74% of Americans do not live in these three states.

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     To prove this, we need to show that 2 is equal to x.

     Given:

2(x + 5) - 3x = 7x - 6

     Distribute:

2x + 10 - 3x = 7x - 6

     Combine like terms:

-1x + 10 = 7x - 6

     Add 1x to both sides of the equation:

10 = 8x - 6

     Add 6 to both sides of the equation:

16 = 8x

     Divide both sides of the equation by 8:

2 = x

     Reflexive property:

x = 2

       ✓

2(x + 5) - 3x = 7x - 6

x = 2

Answer: Alternate exterior angles

Step-by-step explanation:

Answer:

Terms: x, 4y, 32

variables: x, y

constant: 32

coefficients: 4, 1

Step-by-step explanation:

Hope this helps!

Answer:

16/5

Step-by-step explanation:

The direct variation equation (where k is the constant variation):

z = kw

First, we must solve for k:

k = w/z

Plug in -5 and 2:

k = 2/-5 = -2/5

Now plug k into the formula with 8 to solve for z:

z = -2/5 x 8 = 16/5

The linear equation in point-slope form of a line with a slope of 23 and point (3,-2) is y = 23x - 71.

The slope intercept formula is expressed as;

y = mx + b

Where m is the slope and b is the y-intercept.

Given the data in the question;

Point: (3,-2)

First, use the the formula for the equation of line to determine the y-intercept 'b'.

y = mx + b

Plug in slope m = 23 and point (3,-2)

-2 = (23)3 + b

-2 = 69 + b

b = -2 - 69

b = -71

Now that we have both the slope m ( 23 ) and y-intercept b ( -71 ), plug these values into y = mx + b to find the linear equation.

y = mx + b

y = 23x + (-71)

y = 23x - 71

Therefore, the equation of the line is y = 23x - 71.

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The value of x is found as 3 using the method of substitution.

For the given expression, use substitution method to solve.

2x + y = 7  ........eq 1

y = 2x - 5  ........eq 2

Substitute the value of y from eq 2 in eq 1.

2x + 2x - 5 = 7

Solving;

4x = 7 + 5

4x = 12

x = 3

Thus, the value of x is found as 3.

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The given coordinate pair, (10, -7) is not on the x–axis or the y–axis, but it is in Quadrant IV

A coordinate pair specifies a point on the coordinate plane.

The coordinates of points on the x–axis have a y–coordinate of 0

Therefore, the coordinates of a point that is on the x–axis can be expressed as (x, 0)

Points that are on the y–axis have a x–coordinate of 0, which gives the coordinates of the points located on the y–axis as (0, y)

The coordinates of the given point is (10, -7), therefore, the point is neither on the x or y–axis, but in one of the four quadrants.

The coordinate of points in the first quadrant can be represented generally as (x, y)

Points in the second quadrant have the general form of (-x, y)

The points in the third quadrant can be expressed generally in the form (-x, -y)

The coordinates of points on the fourth quadrant are of the form, (x, -y)

The given point is (10, -7), therefore it is in the fourth quadrant or Quadrant IV

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Answer:

x = 2

Step-by-step explanation:

x + 3 + 1/2 x + 3 +x + 1 = 12  Combine like terms

21/2 x + 7 = 12   Subtract 7 from both sides of the equation

2 1/2 x = 5

Another name for 2 1/2 is [tex]\frac{5}{2}[/tex]        ([tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{1}{2}[/tex])

[tex]\frac{5}{2}[/tex] x = 5  Multiply both sides of the equation by [tex]\frac{2}{5}[/tex]

[tex](\frac{2}{5})[/tex][tex](\frac{5}{2})[/tex]x = [tex]\frac{2}{5}[/tex][tex](\frac{5}{1})[/tex]

x = 2

Answer:

D

Step-by-step explanation:

the sum of the 3 angles in Δ DEF = 180° , that is

∠ D + 90° + 35° = 180°

∠ D + 125° = 180° ( subtract 125° from both sides )

∠ D = 55°

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

using the tangent and cosine ratios in the right triangle

tan35° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{DE}{EF}[/tex] = [tex]\frac{DE}{12}[/tex] ( multiply both sides by 12 )

12 × tan35° = DE , then

DE ≈ 8.40 ( to 2 dec. places )

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

cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{EF}{DF}[/tex] = [tex]\frac{12}{DF}[/tex] ( multiply both sides by DF )

DF × cos35° = 12 ( divide both sides by cos35° )

DF = [tex]\frac{12}{cos35}[/tex] ≈ 14.65 ( to 2 dec. places )

Answer:

‎

4 + (-125)‎

= 4 - 125‎

= -121‎

‎

The total distance climbed by Kristen and her family is 16 meters.

It is given in the question that Kirsten and family climb down to 8 meters below ground level. Then they climb the opposite of 8 meters to return to ground level.

We have to find the total distance climbed by Kristen and her family.

We know that,

Total distance climbed by Kristen and her family = Distance climbed down the cave + distance climbed up the cave to reach ground level

Hence, we can write that,

Total distance climbed by Kristen and her family = 8+8 = 16 meters.

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Answer:

x= -1, -13

Step-by-step explanation:

Answer: x=-13   x=-1

Step-by-step explanation:

[tex]x^2+14x=-13\\x^2+2(x)(7)+7^2-7^2=-13\\(x^2+2(x)(7)+7^2)-49=-13\\(x+7)^2-49=-13\\(x+7)^2-49+49=-13+49\\(x+7)^2=36[/tex]

[tex](x+7)^2-36=36-36\\(x+7)^2-36=0\\(x+7)^2-6^2=0\\(x+7+6)(x+7-6)=0\\(x+13)(x+1)=0\\x+13=0\\x+13-13=0-13\\x=-13\\x+1=0\\x+1-1=0+(-1)\\x=-1[/tex]

[tex]8 + 3x = 1 + 7.9x \\ \\ \implies 3x - 7.9x = 1 - 8 \\ \\ \implies - 4.9x = - 7 \\ \\ \implies \: x = \frac { \cancel{- 7}}{ \cancel{ - 4.9} } \\ \\ \implies \: x = 1.43[/tex]

choti bachi hô kya itne simp question ka answer kon puchta hai xD

Answer:

36

Step-by-step explanation:

24 customers dividend into 4 tables

so 24/4 = 6

then 6 customers can sit in 1 table

in case of 6 tables 6×6 =36

36 customers would sit in 6 tables

Answer:

3(2(4)(3)(2.8))

3(24(2.8))

3(67.2)

2016