All categories

3 years ago

I need help with solving for x. Then find the measure of the base angle. Please

Mathematics

2 answers:

Paraphin [41]3 years ago

8 0

Answer:

x = 8 base angle = 81 degrees

Step-by-step explanation:

IRINA_888 [86]3 years ago

8 0

Answer:

x = 8

base angle = 81 deg

Step-by-step explanation:

we observe that because the given triangle is a isosceles triangle, the base angles must be the same.

Hence the missing base angle must also be (10x+1)°

recall that all internal angles of an triangle must add up to 180 deg,

hence

180° = sum of all internal angles

180° = 18° + (10x+1)° + (10x+1)°

180° = 18° + 2(10x+1)° (subtracting 18 from both sides)

180 - 18 = 2(10x+1)

162 = 2(10x+1) dividing both sides by 2)

162 / 2 = 10x + 1

81 = 10x + 1 (subtracting 1 from both sides)

81 - 1 = 10x

10x = 80 (divide both sides by 10)

x = 80/10

x = 8 (answer)

substituting x = 8 into the expression for the base angle

base angle = (10x+1)

= 10(8) + 1

= 10 + 1

= 81

You might be interested in

Choose the equation below that represents the line passing through the point (-5, 1) with a slope of three halves.

evablogger [386]

Correct answer is D.

Use equation of line which passes through the point $A(x_1,y_1)$ .
$y-y_1=m(x-x_1)$

$A(-5,1) \Rightarrow x_1=-5,y_1=1
\\ m= \frac{3}{2} 
\\
\\y-y_1=m(x-x_1) \\y-1= \frac{3}{2} (x-(-5))
\\y-1=\frac{3}{2} (x+5)
$

4 0

4 years ago

Read 2 more answers

Can someone go step by step to show me how to find the Slope of CD?

vazorg [7]

Use the slope formula. Y2-Y1/X2-X1. Give each coordinate a label. (X1,Y1), (Y2,Y1). Then plug the numbers in and solve. 4-1/9-12. So 3/-3, which equals -1.

6 0

3 years ago

Nathan earned $105,70 at his job when he worked for 7 hours. What was his

romanna [79]

Answer:

If it is $10,570 then the answer is 1510, but if you made a typo and meant 105,700, then the answer is 15100.

7 0

3 years ago

Read 2 more answers

Solve by quadratic equation

Ymorist [56]

<h2>Question :</h2>

$\tt \dfrac{x+2}{x-2} + \dfrac{x-2}{x+2} = \dfrac{5}{6}$

<h2>Answer :</h2>

$\large \underline{\boxed{\bf{x = \dfrac{\pm 2\sqrt{119}}{7}}}}$

<h2>Explanation :</h2>

$\tt : \implies \dfrac{x+2}{x-2} + \dfrac{x-2}{x+2} = \dfrac{5}{6}$

$\tt : \implies \dfrac{(x+2)(x+2) + (x-2)(x-2)}{(x-2)(x+2)} = \dfrac{5}{6}$

$\tt : \implies \dfrac{(x+2)^{2} + (x-2)^{2}}{(x-2)(x+2)} = \dfrac{5}{6}$

<u>Now, we know that</u> :

$\large \underline{\boxed{\bf{(a+b)^{2} = a^{2} + b^{2}+ 2ab}}}$
$\large \underline{\boxed{\bf{(a-b)^{2} = a^{2} + b^{2} - 2ab}}}$
$\large \underline{\boxed{\bf{(a+b)(a-b) = a^{2} - b^{2}}}}$

$\tt : \implies \dfrac{x^{2}+2^{2}+ 2 \times x \times 2 + x^{2}+2^{2} - 2 \times x \times 2 }{x^{2}-2^{2}} = \dfrac{5}{6}$

$\tt : \implies \dfrac{x^{2}+ 4 + \cancel{4x} + x^{2}+ 4 - \cancel{4x}}{x^{2}-4} = \dfrac{5}{6}$

$\tt : \implies \dfrac{x^{2} + x^{2} + 4 + 4}{x^{2}-4} = \dfrac{5}{6}$

$\tt : \implies \dfrac{2x^{2} + 8}{x^{2}-4} = \dfrac{5}{6}$

<u>By cross multiply</u> :

$\tt : \implies (2x^{2} + 8)6= 5(x^{2}-4)$

$\tt : \implies 12x^{2} + 48 = 5x^{2}-20$

$\tt : \implies 12x^{2} + 48 - 5x^{2} + 20 = 0$

$\tt : \implies 7x^{2} + 68 = 0$

$\tt : \implies 7x^{2} + 0x + 68 = 0$

<u>Now, by comparing with ax² + bx + c = 0, we have</u> :

a = 7
b = 0
c = 68

<u>By using quadratic formula</u> :

$\large \underline{\boxed{\bf{x = \dfrac{-b \pm \sqrt{b^{2} - 4ac}}{2a}}}}$

$\tt : \implies x = \dfrac{-(0) \pm \sqrt{(0)^{2} - 4(7)(68)}}{2(7)}$

$\tt : \implies x = \dfrac{0 \pm \sqrt{0 - 1904}}{14}$

$\tt : \implies x = \dfrac{\pm \sqrt{- 1904}}{14}$

$\tt : \implies x = \dfrac{\pm \sqrt{2\times 2\times 2\times 2\times 7\times 17}}{14}$

$\tt : \implies x = \dfrac{\pm \cancel{2} \times 2\sqrt{7\times 17}}{\cancel{14}}$

$\tt : \implies x = \dfrac{\pm2\sqrt{119}}{7}$

$\large \underline{\boxed{\bf{x = \dfrac{\pm 2\sqrt{119}}{7}}}}$

Hence value of $\bf x =\dfrac{\pm 2\sqrt{119}}{7}$

5 0

3 years ago

Read 2 more answers

Leslie mows lawns to earn money. For each customer, she charges $2.00 for gas and $3.00 per 12 hour of work. Let x represent the

RUDIKE [14]

Answer:

See Explanation

Step-by-step explanation:

Given

$Gas = \$2.00$

$Rate = \$3.00/12hr$

$\begin{array}{ccc}{Row} & {Hours} & {Earnings} & {A} & {2} & { } & {B} & {4} & { } & {C} & {6} &{ } \ \end{array}$ ---- Missing table

Required

Complete the table and plot the graph

First, we determine the equation of the table:

$Gas = \$2.00$

$Rate = \$3.00/12hr$ implies that:

$Rate = \$0.25/hr$

So:

$y = Gas + Rate * x$

$y = 2+ 0.25* x$

$y = 2+ 0.25 x$

To complete the table, we have:

$x = 2$

$y = 2+ 0.25 x = 2+0.25 * 2 = 2.5$

$x = 4$

$y = 2+ 0.25 x = 2+0.25 * 4 = 3$

$x = 6$

$y = 2+ 0.25 x = 2+0.25 * 6 = 3.5$

So, the complete table is:

$\begin{array}{ccc}{Row} & {Hours} & {Earnings} & {A} & {2} & {2.5} & {B} & {4} & {3} & {C} & {6} &{3.5} \ \end{array}$

See attachment for graph

6 0

3 years ago