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mash [69]
3 years ago
7

Isosceles trapezoid FGHJ has base angles that measure (8x+14) and (14x-15). Find x and the measure of each base angle.

Mathematics
1 answer:
lisov135 [29]3 years ago
7 0

Answer:

See below

Step-by-step explanation:

Remark

Base angles of Isosceles triangles are equal.

Equation

That means that 8x + 14 = 14x - 15

Solution

8x + 14 = 14x - 15              Add 15 to both sides

8x + 14+15 = 14x               Combine

8x + 29 = 14x                   Subtract 8x from both sides

8x - 8x + 29 = 14x - 8x    Combine

29 = 6x                            Divide by 6

x = 29/6

x = 4 5/6

Answer

x = 4 5/6 or 4.833

8x + 14 = 8 * (4 5/6)   +  14

8x + 14 = 38 2/3 + 14

8x + 14 = 52 2/3 or 52.6666

14x - 15 = 14 *(4 5/6) - 15

14x - 15 = 67 2/3   -15

14x - 15 = 52 2/3 or 52.666

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Help!!
Elza [17]

Answer:

(b)\ 2x - 9 = -1

(c)\ -2x + 12 = 4

(e)\ 2(x - 10) = -12

Step-by-step explanation:

Required

Which equals x = 4

(a)\ 2x + 6 = 2

Collect like terms

2x  = 2 - 6

2x  = -4

Divide both sides by 2

x = -2

(b)\ 2x - 9 = -1

Collect like terms

2x = -1 + 9

2x = 8

Divide both sides by 2

x = 4

(c)\ -2x + 12 = 4

Collect like terms

-2x =- 12 + 4

-2x =-8

Divide both sides by -2

x = 4

(d)\ 2(x + 2) = 10

Divide both sides by 2

x + 2 =5

Collect like terms

x = 5-2

x = 3

(e)\ 2(x - 10) = -12

Divide both sides by 2

x - 10 = -6

Collect like terms

x = 10 - 6

x = 4

Hence, the equations with the required solution are:

(b)\ 2x - 9 = -1

(c)\ -2x + 12 = 4

(e)\ 2(x - 10) = -12

3 0
3 years ago
In 1990 the average family income was about $ 39 , 000 , and in 2010 it was about $ 70 , 768 . Let x = 0 represent 1990, x = 1 r
iren2701 [21]

Answer:

<em />f(x) = 1588.4x + 39000<em />

f(15) = 62826

Step-by-step explanation:

Given

In 1990; Income= $39000

In 2010; Income= $70768

Solving (a): An equation in form of f(x) = ax + b

First, we need to determine the slope, a

a = \frac{y_2 - y_1}{x_2 - x_1}

Taking y as income and x as year index.

When x = 0; y = 39000

When x = 20; y = 70768

Substitute these values in the above formula

a = \frac{70768 - 39000}{20 - 0}

a = \frac{31768}{20}

a = 1588.4

Next, is to determine the formula using:

y - y_1 = a(x - x_1)

<em>Considering :When x = 0; y = 39000, we have</em>

<em />y - 39000 = 1588.4(x - 0)<em />

<em />y - 39000 = 1588.4x<em />

<em>Make y the subject of formula</em>

<em />y = 1588.4x + 39000<em />

<em />

<em>Express y as a function of x</em>

<em />f(x) = 1588.4x + 39000<em />

Solving (b): Income in 2005

<em>In 2005, x = 15</em>

So:

f(x) = 1588.4x + 39000 becomes

f(15) = 1588.4 * 15 + 39000

f(15) = 62826

3 0
3 years ago
One of the numbers was increased by 10 and the other remained the same. How did the average of the two numbers change?
Alexxandr [17]
10+0=10
10÷2=5
The average is 5.
6 0
3 years ago
Prove that if AC=DF and AB=DE then BC=EF
Step2247 [10]
In triangle ABC and DEF
AC =DF, [ given ]
AB =DE, [ given ]
angle A = angle D
by SAS
ABC congruent to triangle DFE
so
BC = EF, [ CPCTC]
hence proved
8 0
3 years ago
Michael opens a bag of Skittles and organizes them by color. He has 5 yellow, 6 green, 8
ELEN [110]

Answer:

I think 8:32 because there are 8 oranges and 32 in total

5 0
3 years ago
Read 2 more answers
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