Find each angle measure in the triangle.

Answer:

(1) TRUE.

(2) FALSE.

(3) FALSE.

(4) TRUE.

(5) FALSE.

Step-by-step explanation:

(1) [tex]\sqrt{32} = 2^{\frac{5}{2} }[/tex]

[tex]2^{\frac{5}{2} } = (\sqrt{2} )^5 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 4\sqrt{2}\\\\\sqrt{32} = \sqrt{16 \ \times \ 2}\ = \ \sqrt{16} \ \times \ \sqrt{2} \ = \ 4\sqrt{2}[/tex]

Thus, the equation is TRUE.

(2) [tex]16^{\frac{3}{8} } = 8^2[/tex]

[tex]16^{\frac{3}{8} } =(2^4)^{\frac{3}{8} } = 2^\frac{3}{2} }= (\sqrt{2} )^3 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 2\sqrt{2} \\\\8^2 = 64[/tex]

Thus, the equation is FALSE.

(3) [tex]4^{\frac{1}{2} } = \sqrt[4]{64}[/tex]

[tex]4^{\frac{1}{2} }= \sqrt{4} = 2\\\\\sqrt[4]{64} = (64)^{\frac{1}{4} } = (2^6)^{\frac{1}{4} }= 2^{\frac{6}{4} } = 2^{\frac{3}{2} }=(\sqrt{2} )^3 = (\sqrt{2} \times \sqrt{2} \times \sqrt{2} ) = 2\sqrt{2}[/tex]

Thus, the equation is FALSE.

(4) [tex]2^8 = (\sqrt[3]{16} )^6[/tex]

[tex]2^8 = 256\\\\ (\sqrt[3]{16} )^6 = (16)^{\frac{6}{3} } = (2^4)^{\frac{6}{3} } = (2)^{\frac{24}{3} } = 2^8 = 256[/tex]

Thus, the equation is TRUE.

(5) [tex](\sqrt{64} )^{\frac{1}{3} } = 8^{\frac{1}{6} }\\\\[/tex]

[tex]8^{\frac{1}{6} } = (2^3)^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} } = \sqrt{2} \\\\(\sqrt{64} )^{\frac{1}{3} } = (2^6)^{\frac{1}{3} } = 2^{\frac{6}{3} } = 2^2 = 4[/tex]

Thus, the equation is FALSE.

Answer:

Please find attached the required flow chart proof created using Microsoft Visio

Step-by-step explanation:

The given parameters are;

[tex]\overline {BD}[/tex] bisects ∠ADC and ∠ABC

Required to proof that ΔABD ≅ ΔCBD

The two column proof is given as follows;

Statement                [tex]{}[/tex]            Reason

[tex]\overline {BD}[/tex] bisects ∠ADC    [tex]{}[/tex]           Given

∠ADB ≅ ∠CDB    [tex]{}[/tex]                Definition of angle bisector

[tex]\overline {BD}[/tex] bisects ∠ABC    [tex]{}[/tex]           Given

∠ABD ≅ ∠CBD    [tex]{}[/tex]                Definition of angle bisector

[tex]\overline {BD}[/tex] ≅ [tex]\overline {BD}[/tex]            [tex]{}[/tex]                Reflexive Property

ΔABD ≅ ΔCDB    [tex]{}[/tex]                ASA

The Angle-Side-Angle ASA, ASA, congruency postulate, states that if two angles and the included side of one triangle is congruent to two angles and the included side of another triangle, then the two angles are congruent.

Answer:  9 ab is the area of the garden.

No scale or dimensions are given, so

Estimating to get a practical, reasonable answer:

Using typical walkway widths to 6 ft, it is reasonable to calculate the area the red triangle to be 486 square feet

and the area of the garden to be about 4400 square feet, rounding up.

OR

Using a metric standard of 2 meters, The area of the red triangle would be 54m²

The area of the garden would be about 500m²

Step-by-step explanation:

The area of the red triangle is [tex]A = \frac{ab}{2}[/tex]  That is assuming that it is a right triangle and side a is the altitude or height of the triangle and side b is the base.  

The measurements of the triangle are approximately in the proportion of 3, 4, 5, a typical "Pythagorean Triple" right triangle.

Estimating from rough measurements of the triangle and the dimensions of the garden as shown, it appears that the area of the garden is about 18 times the area of the red triangle.

The area of the triangle is half the area of a rectangle with the same side lengths a & b, so 9 ab is a good estimate of the area of the garden.

If  the walkways are the typical 6 foot width found in many public gardens, and the length side b is the about 6 of those widths, and side a is about 4.5 of those widths, we can estimate the altitude to be 27 and the base to be 36 (in the proportion 3:4).

Area of the triangle estimate: A = 36ft × 27ft /2 = 486 square feet

OR

Using a metric standard, estimate  a 2 meter wide sidewalk, the area of the triangle can be reasonably calculated to be A = 9m × 12m /2 = 54 m²

The area of the garden would be 9 × 54 = 486m² rounded reasonably to 500m²

Answer: 5400

Step-by-step explanation:The area of the triangle is defined as the product of half the base and the height of the triangle. The area of the triangle = 1/2 x b x h It is given that the length of the sides are as A= 90 B=120 C=150.

So, The area of the triangle = 1/2 x b x h = b x h/2  = 120 x 90/2 = 10800/2 = 5400

Answer:

Tell ur teacher to stop ignoring you 23

Step-by-step explanation:

ur welcomw 32

Answer:

Simplifying

(4 + 2k) * 6 + 3k = 0

Reorder the terms for easier multiplication:

6(4 + 2k) + 3k = 0

(4 * 6 + 2k * 6) + 3k = 0

(24 + 12k) + 3k = 0

Combine like terms: 12k + 3k = 15k

24 + 15k = 0

Solving

24 + 15k = 0

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-24' to each side of the equation.

24 + -24 + 15k = 0 + -24

Combine like terms: 24 + -24 = 0

0 + 15k = 0 + -24

15k = 0 + -24

Combine like terms: 0 + -24 = -24

15k = -24

Divide each side by '15'.

k = -1.6

Simplifying

k = -1.6

Step-by-step explanation:

Answer:

x=(-6)

Step-by-step explanation:

Answer:

x= -6

Step-by-step explanation:

5x-10= -40

add 10 to both sides

5x= -30

divide both sides by 5

x= -6

Answer:

$518

Step-by-step explanation:

The total gross payment = full-time payment + part-time payment

Given that:

She worked 46 hours for her full-time payment and time-and-a-half for anything and she is being paid $9 per hour;

and also worked for 7 hours for her part-time payment and she is being paid $11 per hour and time-and-a-half for anything

Then, the total gross payment = $46(9 1/2) + $7(11  1/2)

The total gross payment = $46(9.5) + $7(11.5)

The total gross payment = $437 + $80.5

The total gross payment = $517.5

The total gross payment ≅ $518

Answer:

24

Step-by-step explanation:

The area of a parallelogram is A=

The area of triangle is A=1/2 so this means if the area of the parallelogram is 48 m then the area of a triangle is 24 m

Answer:

C

Step-by-step explanation:

10/4=2.5

2.5x38=95

95 minutes= 1 hour 35 minutes

Answer:

y=-1/2x+1

Step-by-step explanation:

Answer:

f(5) = 3

Step-by-step explanation:

f(x) is the y coordinate at x.

At x = 5, y = 3, so f(5) = 3.

Answer:

23.28 inches (im not sure if this is correct because you need length, height, and width.)

Step-by-step explanation:

lwh

3

The graph of the function f and graph of the function g(x) have the different y-intercept but have the same end behavior option (C) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a graph of a function f and a function g(x) is:

[tex]\rm g(x) = (2)2^x[/tex]

If draw a graph of g(x) on the coordinate plane, it will be a exponential function.

For y intercept of g(x):

x = 0,

y = 2

But graph of a function f and graph of a function g(x) has same end behavior.

Thus, the graph of the function f and graph of the function g(x) have the different y-intercept but have the same end behavior option (C) is correct.

Learn more about the function here:

brainly.com/question/5245372

#SPJ2

Answer:

(−1)(5x+2)

Step-by-step explanation:

I googled it

Answer:

(x-1)(5x+2)

Step-by-step explanation:

5[tex]x^{2}[/tex] + 2x - 5x - 2

(5[tex]x^{2}[/tex] + 2x) (- 5x - 2)

x(5x + 2) -1(5x + 2)

(x-1)(5x+2)

Answer: No the ratios are NOT related  

Step-by-step explanation:

Answer:

$40 in euros!

Step-by-step explanation:

Answer:

it b

Step-by-step explanation:

Answer:

0.156

Step-by-step explanation:

Answer:

5/32

Step-by-step explanation:

[tex] \frac{5}{8} \div 4 \\ \\ = \frac{5}{8} \times \frac{1}{4} \\ \\ = \frac{5 \times 1}{8 \times 4} \\ \\ = \frac{5}{32} [/tex]

Answer:

$600

Step-by-step explanation:

because 40 hours at a rate of $15/hours adds up to $600.

(40*15= 600)

Answer:

-12x -15

Step-by-step explanation:

3(-4x-5)

3*-4x -3*5

-12x -15

Answer:

-12x-15

Step-by-step explanation:

expand and simplify

-12x-15

Answer:

1.345

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  

10 . If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

I think it’s 11 but not sure

Step-by-step explanation:

Answer:

11.4017543

(round if you're supposed to)

Step-by-step explanation:

It is a right triangle so you can use the pythagoreum theorem.

a(a) + b(b) = c(c)

a and b: legs

c: hypostenuse

9 and 7 are legs

the unknown is the hypostenuse

9(9) + 7(7) = c(c)

81 + 49 = c(c)

130 = c(c)

square root of 130 is 11.4017543

c(c) = 130

c = 11.4017543

Answer:

Diameter is 11cm, and the radius is 5.5

Step-by-step explanation:

To get the radius, just divide the size of the circle by 2

Diameter is the same size as the circle

Answer:

Number of gallons consumed by first car = 15 gallons

Number of gallons consumed by second car = 25 gallons

Step-by-step explanation:

Given that:

Fuel efficiency of first car = 30 miles per gallon

Fuel efficiency of second car = 15 miles per gallon

Total distance traveled = 825 miles

Total gas consumption = 40 gallons

To find:

Number of gallons consumed by each car = ?

Solution:

Let the number of gallons consumed by first car = [tex]x[/tex] gallons

As per question statement, number of gallons consumed by second car:

[tex]40-x[/tex]

Number of miles covered by a car = Fuel efficiency [tex]\times[/tex] Number of gallons consumed

Number of miles covered by first car = 30 [tex]\times[/tex] [tex]x[/tex]

Number of miles covered by second car = 15 [tex]\times[/tex] ([tex]40-x[/tex])

Using the given statement:

[tex]30x+15(40-x)=825\\\Rightarrow 30x+600-15x=825\\\Rightarrow 15x=225\\\Rightarrow x =15\ gallons[/tex]

Therefore, Number of gallons consumed by first car = 15 gallons

Number of gallons consumed by second car = 40 - 15 = 25 gallons

Given:

Jeffery babysits for 4 dollars per hour and works as a math tutor for 7 dollars per hour.

He is only allowed to work 13 hours total per week.

He wants to make at least 65 dollars.

To find:

The system of inequalities to represent this situation.

Solution:

Let x be the number of hours he babysits per week and y be the number of hours h works as a math tutor.

He is only allowed to work 13 hours total per week.  It means sum of x and y must be less than or equal to 13.

[tex]x+y\leq 13[/tex]

He wants to make at least 65 dollars. It means total earnings must be greater than or equal to 65.

[tex]4x+7y\geq 65[/tex]

Number of hours can not be negative.

[tex]x\geq 0, y\geq 0[/tex].

Therefore, the required system of inequalities contains some equations,  [tex]x+y\leq 13,4x+7y\geq 65[/tex] and [tex]x, y\geq 0[/tex].

Answer:84

Step-by-step explanation:

Answer:

x^2+3x-28

Step-by-step explanation:

Answer:

The answer is x^2  3x 28

Step-by-step explanation:

Answer:

9/100.

Step-by-step explanation:

9% is equal to about 9/100. 9/100 is the simplest form.