Fill in the blank. In the triangle below, x =

Can u guys pls help me with this homework

gladu [14]

The value of √(7 * 23 - 1)/8 is 4.47, the values of a, b and c are -14/11, -10/11 and 3, respectively and the area of the shape is 5√5 + 5 square meters

<h3>How to evaluate the radical expression?</h3>

The question goes thus:

If √5 = 2.236, evaluate √(7 * 23 - 1)/8

We have:

√(7 * 23 - 1)/8

Evaluate the product of 7 and 23

√(7 * 23 - 1)/8 = √(161 - 1)/8

Evaluate the difference of 161 and 1

√(7 * 23 - 1)/8 = √160/8

Evaluate the quotient of 160 and 8

√(7 * 23 - 1)/8 = √20

Express 20 as the product 4 and 5

√(7 * 23 - 1)/8 = √(4 * 5)

Expand the product

√(7 * 23 - 1)/8 = √4 * √5

Express √4 as 2

√(7 * 23 - 1)/8 = 2 * √5

Substitute √5 = 2.236

√(7 * 23 - 1)/8 = 2 * 2.236

Evaluate the product

√(7 * 23 - 1)/8 = 4.472

Approximate

√(7 * 23 - 1)/8 = 4.47

Hence, the value of √(7 * 23 - 1)/8 is 4.47

<h3>How to simplify the radical expression?</h3>

The expression is given as:

(3√2 + 5√6)/(3√2 - 5√6)

Rationalize the above expression

(3√2 + 5√6)/(3√2 - 5√6) * (3√2 + 5√6)/(3√2 + 5√6)

Evaluate the product

(3√2 + 5√6)²/((3√2)² - (5√6)²)

Simplify the denominator

(3√2 + 5√6)²/(18 - 150)

This gives

[(3√2)² + (5√6)² + 2 *(3√2) * (5√6)]/(-132)

Simplify the numerator

[168 + 120√3]/(-132)

Simplify the fraction

-14/11 - 10√3/11

Hence, the values of a, b and c are -14/11, -10/11 and 3, respectively

<h3>How to determine the area?</h3>

The area is calculated as:

A = 1/2 * (Sum of parallel bases) * Height

So, we have:

A = 1/2 * (4 + 3√5 + 6 - √5) * √5

Evaluate the like terms

A = 1/2 * (10 + 2√5) * √5

Evaluate the product

A = (5 + √5) * √5

Evaluate the product

A = 5√5 + 5

Hence, the area of the shape is 5√5 + 5 square meters

Read more about rational expressions at:

brainly.com/question/8008240

#SPJ1

6 0

1 year ago

Student council expects $150 students for a dance and spends $10 on food for each student. The council expects the number of stu

Natalija [7]

Answer:

$A) S(t)=150(1.08)^{t-1}$ $B) A(t)=10(0.96)^{t-1}$

$C) If\:t = 1\\E(t)=150\times10\\ \\If\:t >1\\E(t)=150(1.08)^{t-1}\times10(0.96)^{t-1}$

Step-by-step explanation:

Considering that The Student Council expects to 150 students for a dance, and spends $10 per student.

If the expectancy is that the number of students increases by 8%

Then since the growth is 8%

we can write the the Predicted Number of Students as a Geometric Sequence,

A.

$a_{1}=150\\a_{2}=150\times 1.08 =162\\a_{3}=162\times 1.08= 174.96\approx 175\\a_{4}=175\times1.08=189\\a_{5}=189\times 1.08=204.12\approx 204\\$

Therefore,

$S(t)=150(1.08)^{t-1}$

B) If we spend $10 per student on the 1st year, but the Council wants to reduce the expenditure 4% yearly. Since we want to reduce 4% we must multiply by 96%.

$b_{1}=10\\b_{2}=10*(0.96)=9.6\\b_{3}=9.6*(0.96)=9.22\\b_{4}=9.22*(0.96)=8.85\\b_{5}=8.85*(0.96)=8.50$

Therefore we can write:

$A(t)=10(0.96)^{t-1}$

C)

The total expenditure for food must be reduced, by 4%. As long as the public goes increasing by 8% yearly this

So,

$If\:t = 1\\E(t)=150\times10\\ \\If\:t >1\\E(t)=150(1.08)^{t-1}\times10(0.96)^{t-1}$

7 0

3 years ago

8x + 6x - 5x I need help

attashe74 [19]

The solution is 9X

Like if I am right

7 0

3 years ago

Read 2 more answers

What is 3×9-10÷2 please help

Anettt [7]

3x9-10/2

First take mind of PEMDAS

First multiply 3x9

27-10/2

now divide 10 by 2

27-5

22

so 3x9-10/2=22

8 0

3 years ago

Find the value of W please help me

Aleonysh [2.5K]

Answer:

w=58 degrees

Step-by-step explanation:

The sum of all angles in a triangle should add up to 180 [ its a fact]

and the square-like shape inside the triangle represents the fact that that angle is 90 degrees.

So, we can make an equation

32+90+w=180

122+w=180 [if u add 32+90, u'll get 122]

w=180-122 [subtract 122 from both sides to isolate "w"]

w=58

5 0

3 years ago