The triangles are similar.


What is the value of x?


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The area of the considered parallelogram RTSU is given by: Option A: 21 sq. units

Area of a parallelogram  = (its height × its base) sq. units.

The shortest distance(length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units[/tex]

For this case, the missing diagram is attached below.

If we take the base as ST then as ST is parallel to y axis, the line perpendicular to ST would be parallel to x axis. The heigth of a parallogram  is the perpendicular distance between its base and top.

The base is ST and top is RU, the line segment US is perpendicular to both RU and US and its length,therefore, will serve as height as its length=perpendicular distance between the base and the top of the parallelogram.

Thus, we get:

Area of RTSU = Length of ST × Length of US

The coordinates of endpoints of ST are (4,-1), (4,-4)

Thus, the length of ST = distance between S and T = [tex]\sqrt{(4-4)^2 + (-1 - (-4))^2 }= 3[/tex]

The coordinates of endpoints of US are (-3,-1), (4,-1)

Thus, the length of US = distance between U and S = [tex]\sqrt{(-3-4)^2 + (-1 - (-1))^2 }= 7[/tex]

Thus, Area of RTSU = Length of ST × Length of US = 3 × 7 = 21 sq. units.

Thus, the area of the considered parallelogram RTSU is given by: Option A: 21 sq. units

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Answer:

21 square units I think

Step-by-step explanation:

Applying a subtraction operation, it is found that his new ERA was of 3.17.

ERA is a baseball concept, but understanding of baseball is not relevant to this question.

One year, a professional baseball pitcher had a 3.91 ERA. The next year, it was 0.74 points lower, hence it was given by the subtraction of 3.91 and 0.74, that is:

ERA = 3.91 - 0.74 = 3.17.

His new ERA was of 3.17.

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Answer:

more likely

Step-by-step explanation:

3/4 is 0.75 or 75%. I would describe it as likely.

elimination-

3/4 is not equal to 1 or 0.5 or 0. It is also not equal to 0.25

The total number of balls in a bag will be 4 in which 3 balls are red and 1 ball is blue.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

The probability of the event is 3/4.

Let the total number of balls be 4 of two colors that are red and blue and the probability of red color be 3/4.

There will be a total of 4 balls in the bag, 3 of which will be red and 1 blue.

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Answer:

find the value of 'c' sach that the point (1.5) 2,-3) and(C,7) are colliner?

Using the domain and range concepts, it is found that:

In a graph:

Hence:

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Answer:

r = 6.998 in

D = 13.996 in

C = 43.9697 in

Step-by-step explanation:

Area = π[tex]r^2[/tex]

153.86 = π[tex]r^2[/tex]

153.86/π = [tex]r^2[/tex]

sq root(153.86/π) = r ≈ 6.998 in

Diameter = 2r

D = 2(6.998) = 13.996 in

Circumference = 2πr

C = 2π(6.998)

C = 13.996π ≈ 43.9697 in

Hope this helps!

Answer:

400,000

Numbers given:

After rounding them to nearest hundredth thousand:

Difference:

Answer:

2.71

Step-by-step explanation:

Using this formula: Volume= 4 over 3 * π * r cubed.
then do R=(3V4π)⅓=(3·83.54·π)⅓≈2.71144
2.71144 rounded to the nearest 10 is 2.71

Answer:

I think the answer is twenve

The complete product is:

Every fraction has a numerator and a denominator separated by a horizontal bar known as the fractional bar.

As, the length of the painted area is 3 1/5 and width of the painted area is 2/3.

So, multiplication of length and width is as follows:

3 1/5 x 2/3

= 3 x 2/3 + 1/5 x 2/3

= 6/3 + 2 / 15

= 30 + 2 / 15

= 32/ 15

= 2 2/15

Thus, the required fraction is 2 2/15.

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Answer:

The answer is -8.

Step-by-step explanation:

1. Solve the upper half of the expression by following the order of operations:

10² - (100 + 8²)

10² - (100 + 64)

10² - 164

100 - 164

= -64

2. Solve the bottom half by multiplying 2 by itself three times:

2 · 2 · 2 = 8

3. Divide the now given values

[tex]\frac{-64}{8}[/tex]

= -8

hope this helps!

The total distance he travelled to the nearest hundredth of a mile is; B: 3.37 miles

Let F represents his starting point.

Let C represent his position from where he went to east direction.

Let H represent his position from where he went to left towards Florida Avenue.

We are given that;

FC = 0.75 miles

CH = 1.2 miles

∠FCH = 90°(This can be deduced from the question)

By Pythagoras theorem, we have;

FH = √(0.75² + 1.2²)

FH = 1.42

Thus;

Total distance he covered = FC + CH + FH

Total distance covered = 0.75 + 1.2 + 1.42

Total distance covered = 3.37 miles

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Answer:

31.25 %    or  5/16

Step-by-step explanation:

30 out of 96  chance

30/96 = 31.25%

Answer:The probability that a randomly chosen musician is a guitarist is 30/96.

Step-by-step explanation:

Answer:

119 cm^2

Step-by-step explanation:

To find the area of the white border, simply find the area of the outside rectangle and subtract the middle(dark) rectangle's area from that value.

White rectangle: 15x9 = 135

Dark rectangle: 8x2 = 16

135 - 16 = 119 cm^2
The unit is squared when finding the area of a two dimensional figure.

Answer:

The solution to the set of linear equations is:

[tex](5,-4)[/tex]

Step-by-step explanation:

Hey there!

In order to solve this system of equations, we can put the equations equal to each other since both equations are equal to y

[tex]6-2x=-4x+16[/tex]

Now we simplify

[tex]2x=10[/tex] ---> [tex]x=5[/tex]

So now that we know that x is equal to 5, we can find the value of y

let's substitute it in one of the equations

[tex]y=6-2(5)[/tex] ---> [tex]y=-4[/tex]

So now we know that the point where the two equations intersect is:

[tex](5,-4)[/tex]

This is going to be our solution

The graph is in an attachment below

Answer:

10 cubic inch is the volume of container

Answer:

5

Step-by-step explanation:

slope: increase in y ÷ increase in x

slope: (45-15)÷(9-3)

slope: 30÷6

slope: 5

Answer:

1 1/2 or 1.5

As a simplified fraction

If this helped pls give brainlest.

Answer:

Step-by-step explanation:

So, Lets find out if the solution is true or not, So first let us find the value of x.

⇒ 8 = -x + 10

We can rewrite the equation as,

⇒ -x + 10 = 8

Subtracting 10 from both sides we get :

⇒ -x + 10 – 10 = 8 – 10

⇒ -x = -2

Multiplying both sides by (-1) :

⇒ -1(-x) = -1(-2)

⇒ x = 2

Therefore,

Hey ! there

Answer:

Step-by-step explanation:

In this question we are given with an equation that is 8 = -x + 10 and we have also given its solution that is 2 .And We are asked to tell whether the solution of given equation is true or false .

For finding that we must have to solve the equation .

Solution : -

[tex]\longrightarrow \qquad \: 8 = -x + 10[/tex]

Step 1 : Flipping the equation so that there's ease in solving :

[tex] \longrightarrow \qquad \: - x + 10 = 8[/tex]

Step 2 : Subtracting with 10 on both sides :

[tex] \longrightarrow \qquad \: - x + \cancel{10 }- \cancel{ 10} =8 - 10[/tex]

On further calculations , We get :

[tex] \longrightarrow \qquad \: - x = - 2[/tex]

Step 3 : Multiplying with -1 on both sides :

[tex] \longrightarrow \qquad \: - x \times - 1 = - 2 \times - 1[/tex]

We get :

[tex] \longrightarrow \qquad \: \blue{\underline{\boxed{ \frak{x = 2}}}}[/tex]

Alternative Solution : -

There's another easy way to check whether 2 is solution of given equation or not . This is done by substituting value of x that is 2 in given equation that is 8 = -x + 10 . So substituting value of x ( solution ) in given equation :

As we can see that left side is equal to right side .

Answer:

4 square feet

Step-by-step explanation:

hope this helps :)

Answer:

A) $ = 2m + 26

B) $70

Step-by-step explanation:

For a, I know they already sold 13 for $2, meaning they made $26.  I know that for each muffin, they will make $2, meaning 2m + 26.

For b, you substitute 22 for m, and solve, getting $70.

Answer:

See below ↓↓↓

Step-by-step explanation:

Probability of getting heads

Probability of getting an odd number

The outcomes are equally likely because the probabiity of each outcome is the same.

Using relations in a right triangle, it is found that it's area is of 302.2 units squared.

The relations in a right triangle are given as follows:

In this problem, we have that the opposite side to the angle of 25º is of x, while the adjacent side is of 36, hence:

[tex]\tan{25^\circ} = \frac{x}{36}[/tex]

[tex]x = 36\tan{25^\circ}[/tex]

x = 16.79.

It is given by half the multiplication of it's sides, hence:

A = 0.5 x 16.79 x 36 = 302.2 units squared.

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The angle made by the apothem and the radius is 30 degrees. Then the correct option is B.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The apothem of a regular hexagon measures 8 cm.

Then the side length of the hexagon will be

[tex]\rm x = \dfrac{8}{\sin 60^o}= 9.24\ cm[/tex]

The perimeter of the hexagon will be

Perimeter = 6 × 9.24 = 55.43 cm

The area of the hexagon will be

Area = 0.5 × 8 × 9.24 = 36.95 cm².

The angle made by the apothem and the radius is 30 degrees.

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Answer:

2, 4, & 5

Step-by-step explanation:

I did it

Answer:

Here;

Step-by-step explanation:

The numbers greater than 10 are 11 and 12 on the dice meaning we've got 2 options out of 12.

So, 2/12 gives 1/6 in its simplest form

Answer:

pretty sure its y = 2x +1

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

84/7 = 12

Each person will get 12 ounces to drink.