All categories

2 years ago

In the rectangle below, SU= 4x-2, RT = 5x-10, and m ZSVT= 84º.

Mathematics

1 answer:

stepladder [879]2 years ago

3 0

Answer:

RV = 15, ∠ VUR = 48°

Step-by-step explanation:

The diagonals of a rectangle are congruent , so

RT = SU , that is

5x - 10 = 4x - 2 ( subtract 4x from both sides )

x - 10 = - 2 ( add 10 to both sides )

x = 8

Then

RT = 5x - 10 = 5(8) - 10 = 40 - 10 = 30

The diagonals bisect each other , then

RV = 0.5 × 30 = 15

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

∠ RVU = ∠ svt = 84° ( vertical angles )

RV = UV ( diagonals are congruent and bisect each other )

Then Δ RVU is isosceles with base angles congruent , then

∠ VUR = $\frac{180-84}{2}$ = $\frac{96}{2}$ = 48°

You might be interested in

Marvin Martian, Aly Alien, and Hank Human are all looking for a hidden spaceship. Their probabilities of

never [62]

Answer: Aly , Marvin, Hank

Step-by-step explanation:

Aly has the lowest with 20, Marvin has 30, and hank has 50. it says least to mostly likely to win

7 0

3 years ago

Read 2 more answers

I think of a number. If I divide the sum of 6 and the number by 3,the result is 4 more than one quarter of the number. Find the

Alex17521 [72]

Answer:

Step-by-step explanation:

Let the number be x.

Sum of the number and 6: $6+x$

Divide it by 3: $\frac{6+x}{3}$

Result is 4 more than one quarter of the number:

$\frac{6+x}{3} =4+\frac{1}{4} x$

Multiply both sides by 12:

$\frac{6+x}{3}\cdot \:12=4\cdot \:12+\frac{1}{4}x\cdot \:12$

Simplify:

$4\left(x+6\right)=48+3x$

Expand:

$4x+24=48+3x$

Subtract 24 from both sides:

$4x+24-24=48+3x-24$

$4x=3x+24$

Subtract 3x from both sides:

$4x-3x=3x+24-3x$

$x=24$

The number is 24.

7 0

2 years ago

What was the population in 2008? Can someone explain this to me?

Bas_tet [7]

Answer:

UNITED STATES ITALY DEM. REP. CONGO

Population mid-2008 305 million 60 million 67 million

Population 2050 (projected) 438 million 62 million 189 million

Lifetime births per woman 2.1 1.3 6.5

Percent of population below age 15 20% 14% 47%

Percent of population ages 65+ 13% 20% 3%

Life expectancy at birth 78 years 81 years 53 years

Annual births 4.3 million 568,120 2.9 million

Annual deaths 2.4 million 575,300 0.8 million

Annual births minus deaths 1.9 million -7,200 2.1 million

Percent of population undernourished <2.5% <2.5% 74% hope this helps!

6 0

2 years ago

Read 2 more answers

I need help with solving this problem please!!!

KATRIN_1 [288]

3 is 23 degree
8 is 157 degree

7 0

2 years ago

Read 2 more answers

What is the slope of the line?

shtirl [24]

Answer:

$m=\frac{1}{3}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (2, -1)

Point (-4, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute [SF]: $m=\frac{-3+1}{-4-2}$
Add/Subtract: $m=\frac{-2}{-6}$
Simplify: $m=\frac{1}{3}$

4 0

2 years ago