What is the ratio of the area of the inner square to the area of the outer square?

(a−b)²+b²/a²

a²−b²/a²

(a−b)²/(a+b)²

(ab)²/(a+b)²

Answer:

A. Every tenth person working for the largest corporation in town

Step-by-step explanation:

We are given that,

'Valeriya wants to determine the likely voting outcome for the new town council election'.

It is required to find the most biased outcome.

Now, from the options, we see that,

'Every tenth person working for the largest corporation in town'.

will yield the most biased result, as the people working in the largest corporation may have different opinions and benefits.

So, it is most likely that the voting result for this sample may result in the outcome beneficial to only the people working in the large corporations and not for others.

Thus, sample A will yield a most biased result.

Answer:

Option A is correct.

AA similarity postulate justifies that [tex]\triangle HEF \sim \triangle HGE[/tex]

Step-by-step explanation:

The sum of the measures of a angles in a triangle add up to 180 degree.

In the triangle HGE:

[tex]\angle EHG+\angle EGH+\angle GEH = 180^{\circ}[/tex]

Substitute the given values;

[tex]90^{\circ}+37^{\circ}+\angle GEH = 180^{\circ}[/tex]

[tex]127^{\circ}+\angle GEH = 180^{\circ}[/tex]

Simplify:

[tex]\angle GEH = 180 -127 = 53^{\circ}[/tex]

In triangle HEF and triangle HGE

[tex]\angle FHE = \angle GHE = 90^{\circ}[/tex]   [Angle]

[tex]\angle EFH = \angle GEH = 53^{\circ}[/tex]  [Angle]

AA (Angle-Angle) similarity postulates states that two triangle are similar if they have two corresponding angles that are congruent or equal.

by AA similarity postulates;

[tex]\triangle HEF \sim \triangle HGE[/tex]

Answer:

Length is 19 feet.

Width is 13 feet.

Step-by-step explanation:

Let the length of the rectangle be = L feet

The width is 6 feet less than its length, so width is = L-6 feet

The area of the rectangle is 247 square feet, means length x width = 247

[tex]L(L-6)=247[/tex]

[tex]L^{2} -6L=247[/tex]

[tex]L^{2} -6L-247=0[/tex]

Now here a = 1, b = -6 and c = -247

So, putting these in quadratic equation formula, we get

[tex]L=\frac{-(-6)+\sqrt{(-6)^{2}-(4)*(1)*(-247) } }{2*1}[/tex]

This gives L=19 or -13

As it is a dimension, so we will neglect the negative value.

Hence, L = 19 feet

Width = [tex]19-6[/tex] = 13 feet

Mr. Archer was going at a speed of approximately 67 mph and Mr. Sassoon was going at a speed of 47 mph (rounded to the nearest whole number).

This problem is a typical distance-rate-time problem. Firstly, we can infer based on the travel times for Mr. Archer and Mr. Sassoon that Mr. Archer traveled for 7 hours (from 9 am to 4 pm) and Mr. Sassoon traveled for 3 hours (from 1 pm to 4 pm) to reach Joshua.

Equalizing the distance travelled by both individuals, we have: its clear that 20 mph * 7 hours = Mr. Sassoon's speed * 3 hours. From this, we can easily infer that Mr. Sassoon's speed is [tex]20*7/3 = 46.67[/tex] mph

Since Mr. Archer travelled 20 mph faster than Mr.Sassoon, Mr.Archer's speed was [tex]46.67 + 20 = 66.67[/tex] mph. Therefore, Mr. Archer was going at a speed of approximately 67 mph and Mr. Sassoon was going at a speed of 47 mph (rounded to the nearest whole number).

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-3(m-2n)=5m             (distribute the negative 3)

-3m+6n=5m                 (add 3m to both sides)

6n= 8m                           (now divide by 8 to solve for m)

6n/8=m                           you can simplify

3/4n=m

Answer:

Position of ball from top of tower after 1 second is 4.9 m

Position of ball: [tex]y=-4.9t^2+122.5[/tex]

Step-by-step explanation:

An object falls from rest on a high tower and takes 5.0 s to hit the ground.

Let position of object from top of tower be y

Using formula, v =u - gt

[tex]v=0-9.8\times 5[/tex]

[tex]v=49\ m/s[/tex]

Speed of object when hit the ground.

Height of tower, H₀

[tex]H_0=\dfrac{49^2-0}{2\times 9.8}=122.5\ m[/tex]

Velocity of ball after 1 s

[tex]v=0-9.8\times 1[/tex]

[tex]v=-9.8\ m/s[/tex]

Using formula, [tex]s=\dfrac{v^2-u^2}{2g}[/tex]

[tex]y=\dfrac{9.8^2-0^2}{2\times 9.8}[/tex]

[tex]y=4.9\ m[/tex] From top of tower

Now find position of ball from top of tower.

[tex]y=-\dfrac{1}{2}\times 9.8\times t^2+122.5[/tex]

[tex]y=-4.9t^2+122.5[/tex]

Please find the attachment for graph.

Answer:The radius r used in below equations would equal 2in because it is half the given diameter of 4in.

The volume of the cone would be

The volume of a cylinder with the same dimensions would be

The cylinder is 24 - 8 = 16 cubic inches greater.

Step-by-step explanation:

The correct unit cost per car is $1.83.

To find the unit cost per car, we need to divide the total cost by the number of cars built. Since each student builds three mouse trap cars and spends an average of $5.50, the total cost for one student is $5.50.

Let's denote the unit cost per car as [tex]\( C \)[/tex]. The equation representing the total cost for one student is:

[tex]\[ 3C = \$5.50 \][/tex]

Now, we solve for [tex]\( C \)[/tex] to find the unit cost per car:

[tex]\[ C = \frac{$5.50}{3} \][/tex]

[tex]\[ C = $1.8333... \][/tex]

Rounding to two decimal places, the unit cost per car is approximately $1.83.

The decimal .66667 is approximately equivalent to the fraction 2/3. It is understood by recognizing that fractions are essentially divisions, and .66667 is the result of 2 divided by 3.

The decimal value of .66667 can be expressed as a fraction. In this case, .66667 is approximately equal to 2/3. To derive this, understand that fractions are a division operation. The decimal .66667 is a result of division where the numerator is smaller than the denominator, which is a characteristic of fractions between 0 and 1. So, if you divide 2 by 3, you will get 0.66667 proving that .66667 is a representation of the fraction 2/3.

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Answer:

D. a reflection across point R of pre-image

Step-by-step explanation:

Considering this question is over 4 years old I highly doubt you're going to see this question, or maybe you're not even in school anymore. Even after all that being said, I'm still going to ask this:

May I have brainliest please? :)

There are 9 thirds in 3 hours, since each hour is made up of 3 thirds.

To find out how many thirds are in 3 hours, we consider that 1 hour is equal to 3 thirds (since 1 divided by 1/3 equals 3). Therefore, if 1 hour equals 3 thirds, then 3 hours would contain 3 times as many thirds. We calculate this as follows:

1 hour = 3 thirds
3 hours = 3 hours × 3 thirds/hour = 9 thirds

Thus, there are 9 thirds in 3 hours.

The equation of the line in point-slope form is y = -2x + 7.

To find the equation of the line passing through the point (2, 3) with a slope of -2, we can use the point-slope form of a linear equation:

[tex]\[y - y_1 = m(x - x_1)\][/tex]

where m is the slope and [tex]\((x_1, y_1)\)[/tex] is a point on the line.

Given that the point [tex]\((x_1, y_1)\)[/tex] is (2, 3) and the slope m is -2, we substitute these values into the point-slope form:

y - 3 = -2(x - 2)

Now, we can simplify the equation:

y - 3 = -2x + 4

Next, we can move the constant term to the other side:

y = -2x + 4 + 3

y = -2x + 7

So, the equation of the line in point-slope form is y = -2x + 7.

Answer:

Climbing and descending add to the flight 416 m

Step-by-step explanation:

The plane must climb to 10 km during the first 200 km. This forms a right triangle, where 10 and 200 are its legs and the hypotenuse is the distance travelled by the airplane. From Pythagorean theorem, that distance is:

√(10² + 200²)

The plane must descend 10 km during the final 300km. This forms a right triangle, where 10 and 300 are its legs and the hypotenuse is the distance travelled by the airplane. From Pythagorean theorem, that distance is:

√(10² + 300²)

If the airplane climbed during 300 km and descended during 200 km, then during 1500 - 200 - 300 = 1000 km it doesn't climb or descend.

The distance added by climbing and descending is:

1000 + √(10² + 200²) + √(10² + 300²) - 1500 = 0.416 km or 416 m