two-column proof
Given: GH || FJ

m ∠ G=m ∠J=90

Prove: ΔH J F ≅ Δ F G H

Answer:

E could be located at 7.9cm.

The ratio of the volumes of two similar cylinders with heights of 35 meters and 25 meters, respectively, is 2.744.

Solids of the same type that have proportional corresponding linear

measures are similar solids. In the case of similar cylinders:

height of A/ height of B = radius of A/radius of B

If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

volume of A/ volume of B = (height of A/ height of B)^3 = (radius of A/radius of B)^3

If two similar cylinders have heights of 35 meters and 25 meters, then the ratio of the volume of the large cylinder to the volume of the small cylinder is:

height of larger cylinder / height of smaller cylinder = 35 meters / 25 meters = 7/5

volume of larger cylinder/ volume of smaller cylinder = (height of larger cylinder / height of smaller cylinder)^3 = (7/5)^3 = 2.744

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When an angle exists encircled by a circle, its measure exists equivalent to the intercepted arc's measure divided by two.

The measure of m WX is 66.

The arc that is inside the inscribed angle and whose endpoints are on the angle is known as the intercepted arc. Anywhere on the circle that the sides of an inscribed angle intersect to produce an intercepted arc can serve as the angle's vertex.

Angles with vertices on a circle and that cross an arc on the circle are said to be inscribed angles. Half of the intercepted arc's length and half of the central angle's length intersecting that same arc make up the measure of an inscribed angle. Congruent inscribed angles are those that intersect the same arc.

According to the Inscribed Angle Theorem, an inscribed angle's measure is equal to half of its intercepted arc's measure. Congruent inscribed angles are those that intersect the same arc.

In the given diagram, XY is a semi-circle. So,

m XWY = 180

m WX + m WY = 180

If an angle is inscribed in a circle, then the measure of the angle equals  one half the measure of its intercepted arc. 

m WY = 2(m ∠X)

m WY = 2(m ∠X) = 114

Therefore, m WX = 180 - m WY = 66.

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Answer:

48.65x6.2=301.63

Step-by-step explanation:

Answer:

down below

Step-by-step explanation:

301.63

It's a bit difficult to type this in a mobile so I won't put it. If you would like the explanation, I can always go back and edit my answer

Hope this helps! :)

The number of gallons required for 280 million cars is 1,555,556 gallons.

Given that, 1 ton makes 90 cars, there are 280 million cars needed

and 1 ton = 500,000 gallons of water.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Let the number of gallons of water needed for 280 million cars be x.

Now, 90 : 500,000 :: 280 : x

⇒ 90x=500,000 × 280

⇒ x = 14,00,00,000/90

⇒ x = 1,555,555.555≈1,555,556 gallons

Therefore, the number of gallons required for 280 million cars is 1,555,556 gallons.

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Answer:

75

Step-by-step explanation:

If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel

x + 25 + 80 = 180

x = 180 - 80 - 25

x = 75

Answer:

1/8

Step-by-step explanation:

We can state that ΔJML ≅ ΔMJK under SSS condition.

So,

Given: KJ || LM, JL || KM

To Prove: ΔJML ≅ ΔMJK

So, ΔJML ≅ ΔMJK under SSS condition.

Therefore, ΔJML ≅ ΔMJK.

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==================================================

Work Shown:

m = slope

m = (y2 - y1)/(x2 - x1)

m = (5 - 3)/(j - 8)

m = 2/(j - 8)

Plug in the given slope of -1/4 and solve for j

m = 2/(j - 8)

-1/4 = 2/(j - 8)

-1*(j-8) = 4*2

-j + 8 = 8

-j = 8-8

-j = 0

j = 0

The slope through (8,3) and (0,5) is -1/4

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

Check:

m = (y2 - y1)/(x2 - x1)

m = (5-3)/(0-8)

m = 2/(-8)

m = -1/4

The answer is confirmed.

Answer:

j = 0

Step-by-step explanation:

Slope-intercept form of a linear equation:

[tex]\large\boxed{y=mx+b}[/tex]

where:

Given:

Substitute the given slope and point into the formula and solve for b:

[tex]\begin{aligned}y & = mx+b\\\implies 3 & = -\dfrac{1}{4}(8)+b\\3 & = -2+b\\3+2&=-2+b+2\\5&=b\\\implies b & =5\end{aligned}[/tex]

Substitute the given slope and found value of b into the formula to create an equation for the line:

[tex]\boxed{y=-\dfrac{1}{4}x+5}[/tex]

Substitute the point (j, 5) into the equation and solve for j:

[tex]\begin{aligned}y&=-\dfrac{1}{4}x+5\\\implies 5&=-\dfrac{1}{4}j+5\\5-5&=-\dfrac{1}{4}j+5-5\\0&=-\dfrac{1}{4}j\\\implies j&=0\end{aligned}[/tex]

Solution

Therefore, the value of j is 0.

The solution to given equation 0.2(x + 8) - 3.4 = 2.4 is x = 21

In this question, we have been given an equation 0.2(x+8)-3.4=2.4

We need to solve given equation.

0.2(x + 8) - 3.4 = 2.4

0.2x + 1.6 - 3.4 = 2.4

0.2x - 1.8 = 2.4

0.2x = 2.4 + 1.8

0.2x = 4.2

x = 21

We need to check above solution.

Substitute x = 21 in LHS of given equation.

LHS

= 0.2(21 + 8) - 3.4

= 0.2(29) - 3.4

= 5.8 - 3.4

= 2.4

= RHS

Therefore, the solution to given equation 0.2(x + 8) - 3.4 = 2.4 is x = 21

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If TU = 14 feet, then the radius of the circle is 7 feet.

The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually represented by the letters 'R' or 'r'.

A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more modern usage, it is also their length.

Simply dividing the circle's diameter in half yields the radius formula. If we connect the points on the circle's circumference to the exact center.

Let the radius of the circle be TU = 14 feet

Radius of the circle = c/2

Where, c = 14 then substitute the value in the above equation, then

r = 14/2

r = 7 feet

Therefore, the radius of the circle is 7 feet.

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Answer:

4

Step-by-step explanation:

PR -  QR = PQ

27 -  3 = 24 =PQ

24=6n

n=4

Answer:

The sweaters are now $20.

Step-by-step explanation:

$25 × .8 = $20

The equation that represent the number of days it will take phoebe to finish the novel is: x= number of pages left to be read / pages to be read per day

Information about the problem:

To solve this problem, we have to write the equation in order to calculate (x) the number of days it will take phoebe to finish the novel with the given information:

number of pages left to be read = novel’s pages - read pages

number of pages left to be read = 368 – 53

number of pages left to be read = 315 pages

Knowing the number of pages left to be read we can write the following equation:

x = number of pages left to be read / pages to be read per day

x = 315 pages /35 pages/day

x = 9 days

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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Answer: 2.82842712 or 2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

A circle is a curve sketched out by a point moving in a plane. The radius and the diameter of the circle are 59.73 cm and 119.46 cm, respectively.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

Given that circumference of the circle as 375.3 cm. Therefore, the radius and the diameter of the circle can be written as,

Circumference of circle = 2 × π × (Radius of the circle)

375.3 cm = 2 × π × (Radius of the circle)

(Radius of the circle) = 375.3cm/ (2 × π)

The radius of the circle = 59.73 cm

Diameter of circle = 2 × (Radius of the circle)

                              = 2 × 59.73 cm

                              = 119.46 cm

Hence, the radius and the diameter of the circle are 59.73 cm and 119.46 cm, respectively.

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Answer:

add the red and the blue balloons

45+85=130

The equation of the line, with slope equal to 5 and passing through the point located at (0 , 2), is 5x - y = -2.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values to set up the equation.

(y - y1) = m(x - x1)

where m = 5 and (x1 , y1) = (0 , 2)

(y - 2) = 5(x - 0)

y - 2 = 5x

In slope-intercept form, the equation of the line is:

y - 2 = 5x

y = 5x + 2

In standard form, the equation of the line is:

y = 5x + 2

5x - y = -2

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The equation y = -3x - 19 (slope-intercept form) in Ax + By = C form is 3x + y = 19.

The slope-intercept form of a linear equation is a way to express a linear equation in the form y = mx + b, where y represents the dependent variable, x represents the independent variable, m represents the slope of the line, and b represents the y-intercept.

According to the given information:

The given equation, y = -3x - 19, is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. However, to write it in the Ax + By = C form, also known as the standard form of a linear equation, we need to rearrange it.

The standard form of a linear equation is Ax + By = C, where A, B, and C are constants, and A is usually required to be a positive integer or zero.

To convert y = -3x - 19 into standard form, we can follow these steps:

Step 1: Move all the terms to one side of the equation.

y + 3x = -19

Step 2: Multiply all the terms by -1 to make the coefficient of x positive.

-1(y + 3x) = -1(-19)

-y - 3x = 19

Step 3: Rewrite the equation with positive coefficients for x and y.

3x + y = 19

So, the equation y = -3x - 19 in Ax + By = C form is 3x + y = 19.

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Answer:

Please give brainliest if it applies!

w = 20m

l = 60m

Step-by-step explanation:

P = 2l + 2w

We know the perimeter = 160 and we know that l = 3w, so write what we know and solve for w.

P = 2l x 2w

160 = 2(3w) + 2w

160 = 6w + 2w

160 = 8w

Divide both sides by 8

20 = w

Now we can figure out the length, which is 3(w) or 3 x 20 = 60

Answer:

6000 Newtons

Step-by-step explanation:

just multiply 3000 by 2

Answer: angle BCD is 77°

Step-by-step explanation:

       BDC+CDA=119°

-5x+52°-2x+32°=119°

            -7x+84°=119°

                   -7x=35°

                      x=-5°

Then substitute x in the equation for BDC

-5(-5)+52°=BDC

   25+52°=BDC

       BDC=77°

The probability of rolling a number less than or equal to 3 is 0.5.

What is the probability of rolling a number less than 3?

Event: The collection or the set of outcomes in an experiment is called as an event.

Outcomes: The possible results of a trail in an experiment are called as outcome.

Probability:

The ratio of the number of favorable outcomes to certain event and the total number of possible outcomes is called as the probability of an event.

The probability of rolling a number less than or equal to 3 is obtained by taking the ratio of the number of favorable outcomes by the total number of outcomes. It is expected about 50% of times that rolling a number less than or equal to 3.

The probability of rolling a number less than or equal to 3 is 0.5.

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Answer:

-7<x<10

Step-by-step explanation:

trust :)

The equation that could be used to prove the lines are parallel is: D. (c - a)/b = d/e

Parallel lines are lines that do not converge at any point and have the same slope.

Slope (m) = change in y / change in x

Slope of the first line = (c - a)/0 - b

Slope of the first line = (c - a)/b

Slope of the second line = (0 - (-d))/(e - 0)

Slope of the second line = d/e

Thus, if both line are parallel, then (c - a)/b = d/e. This is because parallel lines have the same slope.

The equation is: D. (c - a)/b = d/e

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The solution of the given linear equation in one variable t - 2(3 - 2t) = 2t + 9 is at t = 5.

According to the given question.

We have a linear equation in one variable.

t -2(3-2t) = 2t + 9

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the linear equation in one variable  t -2(3-2t) = 2t + 9 is given by

t - 2(3 - 2t) = 2t + 9

⇒ t - 6 + 4t = 2t + 9          (by distributive rule)

⇒ 5t - 6 = 2t + 9

⇒ 5t - 2t = 9 + 6

⇒ 3t = 15

⇒ t = 15/3

⇒ t = 5

Hece, the solution of the given linear equation in one variable t - 2(3 - 2t) = 2t + 9 is at t = 5.

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Answer:

D. 1

Step-by-step explanation:

16+2x = 10+8x

6 = 6x

x = 1

BC and AD parallel and congruent (=) to each other

The perpendicular bisector of a segment is a line that passes through the midpoint of a segment and is perpendicular to the segment.

A perpendicular bisector is a line that intersects and passes through the midpoint of a given segment at a 90° angle.

A triangle's median is a line segment that connects a vertex to the opposing side's midpoint. Every triangle has three medians, one from each vertex, and they all cross at the triangle's centroid.

A triangle's altitude is a line segment that passes through a vertex and is perpendicular to the baseline.

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