∠E and ∠F are vertical angles with m∠E=5x+10 and m∠F=7x−12 .

What is the value of x?

The width of the rectangle is 6.1 in.

That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.

Perimeter of the rectangle = 2(L + W) unit

WE have been given that  length of a rectangle is 3 inches less than 4 times the width.

Length = 4x-3

width = x

If the perimeter is 55 inches, then

Perimeter of the rectangle = 2(L + W) unit

55= 2(4x-3 +x)

55 = 2(5x-3)

27.5 = 5x-3

27.5+3 = 5x

30.5/5 = x

6.1=x

Thus, Width is 6.1 in

The length (4 x 6.1 -3) = 21.4

Hence,  the width of the rectangle is 6.1 in.

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g + m = 32

g = 3m

3m + m = 32

4m = 32

m = 32/4

m = 8  (Mikhail's age)

g = 3m

g = 3(8)

g = 24 (Gabrielle's age)

:To find out a person's age, all you need is that person's 12 months of beginning. After this, all you want to do now's subtract the beginning 12 months from the continuing modern year and you will have the age. this can help you to calculate the age from the date of delivery. Age= 2020- 1966 = 54.

Your age in the total range of days is calculated as a variety of years, x, with twelve months = 365x plus. a number of years, y, with three hundred and sixty-six days = 366y plus. a number of days in the remaining partial yr.

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As per the radius and given angle the length of the arc will be equal to 2.09 cm.

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the given information in the question,

Radius, r = 4 cm

Angle, θ = 30°

The formula for an arc's length is stated as:

= 2πr(θ ÷ 360)

So,

The length of arc = 2π(4)(30/360)

The length of the arc = 2.09 cm.

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Final answer:

Mario can talk for up to 384 minutes on his $50 prepaid phone plan. We use the inequality 0.13m ≤ 50 and solve for m to find the maximum number of whole minutes Mario can use.

Explanation:

To solve this problem, we need to set up an inequality that represents the constraints of Mario's prepaid phone plan budget. The inequality will help us determine the maximum number of minutes Mario can talk on this plan.

Let's use m to represent the number of minutes Mario can talk. We know that each minute of talk time costs $0.13, and Mario's prepaid plan is $50. Our inequality should reflect the fact that the total cost of talking m minutes cannot exceed his budget of $50.

The inequality will look like this:

0.13m ≤ 50

To solve for m, we divide both sides of the inequality by 0.13:

m ≤ 50 / 0.13

When we calculate 50 divided by 0.13, we get approximately 384.6154. Since Mario cannot talk for a partial minute on his prepaid plan, we round this number down to the nearest whole minute, which is 384 minutes.

Therefore, Mario can talk for up to 384 minutes on his prepaid phone plan.

To find the number of minutes Mario can talk on the prepaid phone plan, we can set up an inequality: 0.13x <= 50. Solving this inequality, we find that Mario can talk for a maximum of 384 minutes.

To find the number of minutes Mario can talk on the prepaid phone plan, we can set up an inequality based on the cost. Let x represent the number of minutes. The cost of the phone plan is $50, and each minute costs $0.13. So, the inequality is: 0.13x <= 50. To solve this inequality, we divide both sides by 0.13 to isolate x and find: x <= 50 / 0.13. Using long division or a calculator, we can find that x is approximately 384.61, but since we can't have a fraction of a minute, the maximum number of minutes Mario can talk on this plan is 384 minutes.

Answer:

All of the above is the answer

Step-by-step explanation:

Answer:

Length is 20 meters and width is 16 meters.

Step-by-step explanation:

Given: Perimeter of parallelogram is 72 meters.

            Width of the parallelogram is 4 meters less than its length.

To find: Length and width of the parallelogram.

Solution: Let the length of the parallelogram be x meters. So, width of the parallelogram is [tex]x-4[/tex] meters.

As per question,

[tex]x+x+x-4+x-4=72[/tex]

[tex]4x-8=72[/tex]

[tex]4x=72+8[/tex]

[tex]4x=80[/tex]

[tex]x=\frac{80}{4}[/tex]

[tex]x=20[/tex]

Hence, length of the parallelogram is 20 meters, and width of the parallelogram is [tex]20-4=16[/tex] meters.

Complementary angles are angles that add up to 90 degrees but may not have the same measure. A counterexample to the statement would be two angles that are complementary but not congruent.

Complementary angles are angles that add up to 90 degrees. Congruent angles are angles that have the same measure.

A counterexample is a situation where the statement is false. In this case, a counterexample would be two angles that are complementary but not congruent.

For example, let's consider a 45-degree angle and a 45-degree angle. These angles are complementary because their sum is 90 degrees. However, they are not congruent because they have different measures.

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Answer:

A

Step-by-step explanation:

A segment with endpoints X (6, 2) and Y (- 1, - 3) when rotated 90 degrees about the origin will result in new endpoints X' (-2, 6) and Y' (3, -1).

This problem deals with the concept of point rotation in a 2D coordinate plane around the origin. When any point (X, Y) is rotated 90 degrees counter-clockwise about the origin, the new position, let's say (X', Y'), can be calculated by using the formulas X' = -Y and Y' = X. Therefore, applying these rotations to the points X(6,2) and Y(-1,-3), we get X'(-2, 6) and Y' (3, -1). So, the endpoints X Prime and Y Prime of the rotated segment are (-2, 6) and (3, -1) respectively.

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After rotating a 90-degree rotation about the origin, the coordinates of X (6, 2) and Y (-1, -3) transform to X' (-2, 6) and Y' (3, -1) respectively.

When a point (x, y) is rotated 90º counterclockwise about the origin, it transforms to (-y, x). Let's apply this rule to the endpoints X (6, 2) and Y (-1, -3).

The coordinates of X prime would be (-2, 6) that is, (-y, x).

The coordinates of Y prime would be (3, -1) that is, (-y, x).

Thus, the transformed coordinates for X and Y would be (-2, 6) and (3, -1) respectively after a 90-degree rotation about the origin.

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Final answer:

Using the formula L = 0.8T², we find that a pendulum 30 ft long has a period of approximately 6.1 seconds, which corresponds to Option D.

Explanation:

The question is about finding the period, T, in seconds for a pendulum that is 30 ft long, using the formula L = 0.8T2. First, to solve for T given that L = 30, we rearrange the equation to T = √(L/0.8). Plugging in L = 30, we have T = √(30/0.8), which simplifies to T = √(37.5).

Calculating further, we find T ≈ 6.12 seconds. Therefore, the answer closest to the period in seconds for a pendulum that is 30 ft long is 6.1 seconds (Option D).

Answer:

The answer is 4.5 cups of cereal and 1.5 cups of mixed nuts

Step-by-step explanation:

Let 'c' be the number of cups of cereal.

Let 'n' be the number of cups of mixed nuts.

One batch of his recipe makes 6 cups of snack mix, so equation becomes:

[tex]c+ n=6[/tex]     ..... (1)

Also given that Brad uses 3 times as much cereal as mixed nuts, so equation becomes:

[tex]c=3n[/tex]     ......(2)

Substituting (2) in (1)

[tex]3n+n=6[/tex]

=> [tex]4n=6[/tex]

=> [tex]n=1.5[/tex]

Since c = 3n, then

[tex]c=3*1.5=4.5[/tex]

So, the answer is 4.5 cups of cereal and 1.5 cups of mixed nuts.

Answer:

this is a multiple choice question with 4 answers

Yes, it specifies the population

No, it does not specify the population

Yes, it anticipates enough variability in responses

No, it does not anticipate enough variability in responses

I think the answer is.......... (Drum roll please)........... D.

Step-by-step explanation:

There is not any variability in this question it is just a yes or no question. If the question was "How long does an average person exercise for "

These two equations do not have the same solution. x = 4 for the first equation and x = -4 for the second equation.

In the equation 5x + 10 = 30, we are adding 10 to the product of 5 and x. To find x, we can first subtract 10 from both sides of the equation to get 5x = 20. Then we divide both sides of the equation by 5 to solve for x, giving us x = 4.

5x + 10 = 30

5x = 30 - 10

5x = 20

x = 20/5 = 4

In the equation 5(x + 10) = 30, we are first adding x and 10 together, then multiplying the result by 5. To solve for x, we can start by dividing both sides of the equation by 5 to get x + 10 = 6. Then we subtract 10 from both sides to solve for x, giving us x = -4.

5(x + 10) = 30,

5x + 50 = 30

5x = 30 - 50

5x = -20

x = -20/5 = -4

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Answer:

Hence, the value of x is [tex]x\leq -18[/tex]

Step-by-step explanation:

Consider the provided inequity.

[tex]\frac{x}{3}\leq -6[/tex]

We need to solve the above inequity of x.

Multiply both the side by 3.

[tex]3\times\frac{x}{3}\leq 3\times -6[/tex]

[tex]x\leq -18[/tex]

Hence, the value of x is [tex]x\leq -18[/tex]

The number 5.78778778 is a rational number because it has a repeating decimal pattern that can be expressed as the fraction 573/99.

The number 5.78778778 is a rational number. Rational numbers are those that can be expressed as a fraction where both the numerator and the denominator are integers.

In this case, the number 5.78778778 has a repeating decimal pattern, which is a hallmark of rational numbers.

We can convert this repeating decimal into a fraction by setting it equal to a variable, say x, subtracting a shifted version of x to isolate the repeating part, and then solving for x to find its fractional equivalent.

If we perform this process, we can turn 5.78778778... into a fraction. For example:

→ Let x = 5.78778778...

→ Multiply both sides of the equation by 100 to shift the decimal two places: 100x = 578.78778778...

→ Subtract the original x from this new equation: (100x - x) = (578.78778778... - 5.78778778...)

→ This simplifies to 99x = 573

→ Divide both sides by 99 to solve for x: x = 573/99

→ This fraction represents the decimal number 5.78778778..., confirming it is rational.

x = the age of Heather

One half of Heather's age two years from now plus one-third of her age three years ago is twenty years

(x + 2)/2 + (x - 3)/3 = 20

by solving the equation we find

x = 24 years