A building casts a shadow 48 feet long. At the same time, a 40-foot-tall flagpole casts a shadow 9.6 feet long what is the height of the building?

Answer:

They can suffer from a lot of stress and their relationships won't last.

Step-by-step explanation:

Hope this helps!

Answer:

It's 117

Step-by-step explanation:

The first team has a total of 515 and the second 398

so you subtract 398 from 515 and you will get 117

Option A : The lines that best approximate the directrices of the ellipse are x= -4.6 and x = 4.6, which are the closest to x = -5 and x = 5.

The directrices of an ellipse are lines that are equidistant from the two foci. In this case, the foci of the ellipse are located at (-5,0) and (5,0). The distance between the foci is 2c, where c is the distance from the center to a focus, and can be found using the equation \(c^2 = a^2 - b^2\), where a and b are the lengths of the major and minor axes, respectively.

From the given diagram, we can see that the length of the major axis is 10 and the length of the minor axis is 8. Therefore, a = 5 and b = 4. The value of c can be found as follows:

\(c^2 = a^2 - b^2\)

\(c^2 = 5^2 - 4^2\)

\(c^2 = 9\)

c = 3

Therefore, the directrices are the vertical lines that pass through (-5,-3) and (5,-3) and are equidistant from the foci. These lines are given by x = -5 and x = 5.

Therefore, the lines that best approximate the directrices of the ellipse are A. x= -4.6 and x = 4.6, which are the closest to x = -5 and x = 5.

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Which lines best approximate the directrices of the ellipse? Round to the nearest tenth.

A. x= -4.6 and x = 4.6

B. x = -3.5 and x = 3.5

C. y=-4.6 and y = 4.6

D. y = -3.5 and y = 3.5

Noting that the tip is one among the total sum charged on the bill is the best strategy for computing the required 20% tip using fractions.

aggregate attempting to determine the whole amount, time, or quantity. The amount at issue or under investigation is very active. the overall outcome, significance, or import. a third accounting, the principal, and the interest. There are word forms for quantities, amounting, and amounted. adaptable noun A thing's quantity is how much of it there is, that however much someone have, the amount you require or how much you can get. He needs that much money to make ends meet.

given

You can use a fraction to express the percentage 20%.

This is inferred from the fact that the sign for percentage,% means to divide by 100.

Therefore, it is important to understand that 20% equals 20/100, or 1/5.

As a result, the 20% tip represents one-fifth of the total.

Noting that the tip is one among the total sum charged on the bill is the best strategy for computing the required 20% tip using fractions.

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Answer:

The Burnets spent .22 × $5,825 = $1,281.50 on taxes and insurance.

Answer:

sinB= 3.8(sin16/2.4) or ~0.45162

[Note: ~ means about]

Step-by-step explanation:

To solve this problem, we need to use the Law of Sines. The Law Of Sines states that sinA/a = sinB/b. Since we know the value of A,a, and b, we can plug our known values in to find our unknown value, sinB.

sinA/a = sinB/b   [Plug in known values]

sin16/2.4 = sinB/3.8

Now, we want to just find the value of sinB. To do this, we will need to multiply both sides by 3.8, so the right side just reads sinB.

sin16/2.4 = sinB/3.8   [Multiply by 3.8]

3.8(sin16/2.4) = sinB

Now, if we want the exact answer, we can leave it as is. If you are looking for a decimal answer, let's continue to see what we would get:

3.8(sin16/2.4) = sinB

3.8(0.27563/2.4) ~ sinB

3.8(0.11484) ~ sinB

0.43642 ~ sinB

B ~ 0.45162

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To calculate the interest for 1/2 a month over a period of 8 years, we first need to calculate the total number of months in 8 years:

Total number of months = 8 years x 12 months/year = 96 months

Next, we can calculate the interest for half a month:

Interest = Principal x Rate x Time

Where:

- Principal = $90,900.00

- Rate = 8.25% (annual interest rate)

- Time = 0.5/12 years (half a month, expressed in years)

Rate needs to be converted to a monthly rate, so we divide it by 12:

Rate = 8.25% / 12 = 0.6875% (monthly interest rate)

Time needs to be expressed in years, so we divide it by 12:

Time = 0.5/12 years

Now we can calculate the interest:

Interest = $90,900.00 x 0.006875 x 0.0416667

Interest = $25.08 (rounded to the nearest cent)

Therefore, the interest for 1/2 a month on a principal of $90,900.00 with an annual interest rate of 8.25% over a period of 8 years is $25.08.

Answer:

The interest for 1/2 month is $312.47, and the total interest for 8 years is $30, 032.64

Step-by-step explanation:

Make a plan:

Draw the conclusion:

Hope this helps!

Answer:

6 3/16 in²

Step-by-step explanation:

Area of rectangle = width x length

Given:

width = 2 3/4 in

length = 2 1/4 in

⇒ area = 2 3/4 × 2 1/4 = 11/4 × 9/4 = 99/16 = 6 3/16 in²

The probability that the second card is a diamond given that the first card is not a diamond is 13/68.

Probability is the odds that a random event would happen. The odds that the random event happens has a probability value that lies between 0 and 1. The more likely it is that the event happens, the closer the probability value would be to 1.

There are 4 shapes in a deck of cards. Each shape has 13 cards each.

Total number of cards that are diamonds = 13

Total number of cards that are not diamonds = 39

Total number of cards in a deck of cards = 52

Probability that the second card is a diamond given that the first card is not a diamond = (number of cards that are not diamonds / total number of cards) x (number of diamonds / number of cards -1)

= (39 / 52) x (13 / 51) = 13/68

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Answer:

3x-9

Step-by-step explanation:

Answer:

does this help?........

Part 1

The equation is \(y=a(x+8)(x-72)\).

Using the point \((62, -490)\) to solve for \(a\),

\(-490=a(62+8)(62-72) \implies a=\frac{7}{10}\\\\\therefore \boxed{y=\frac{7}{10}(x+8)(x-72)}\)

Part 2

When \(x=-8\), \(y=0\).

When \(x=2\), \(y=-490\).

So, the average rate of change is \(\frac{-490-0}{2-(-8)}=\boxed{-49}\)

The answer is x-3. We don't know the brother's height, so we make it into a variable. You may pick any variable, but x is a common choice. We then subtract 3 from x, which would give us Aria's height. Since we don't know the height of the brother, we won't know Aria's height.

The period of the sound wave created by the tuba is approximately 0.0134 seconds.

The speed of sound in air is given as 343 meters per second. The formula relating the speed of sound, wavelength, and period of a wave is:

v = λ × f

Where:

v = speed of sound (343 m/s)

λ = wavelength (4.61 m)

f = frequency (unknown)

To find the period, we need to determine the frequency of the sound wave. The period (T) is the reciprocal of the frequency (f), so we can rewrite the formula as:

v = λ / T

Rearranging the equation to solve for the period (T), we get:

T = λ / v

Substituting the given values, we have:

T = 4.61 m / 343 m/s

Calculating the value, we find:

T ≈ 0.0134 seconds

Therefore, the period of the sound wave created by the tuba is approximately 0.0134 seconds.

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By answering the presented question, we may conclude that As a result, inequality the cost difference between one pencil and one rubber is £0.08.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many basic inequalities may be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are split or added on both sides. Exchange left and right.

To determine the cost difference between one pencil and one rubber, we must first determine the cost per item for each product.

The price of a pencil is 1.56 / 6 = £0.26.

The price of a rubber is 2.72 / 8 = £0.34.

Therefore the cost difference between one pencil and one rubber is:

£0.34 - £0.26 = £0.08

As a result, the cost difference between one pencil and one rubber is £0.08.

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Answer:

Perimeter, P = 5.2 cm

Step-by-step explanation:

Perimeter is the sum of all the sides.

All sides of a square is equal. Here, the side of a square is 1.3 cm.

The perimeter of a square is given by :

P = 4 × side

It means,

P = 4 (1.3 cm)

P = 5.2 cm

Hence, the perimeter of the square is 5.2 cm.

Answer:

Step-by-step explanation:

sin (B) = \(\frac{2}{5}\)

The product when +2, -5, +4 and -3 are 10 multiplied is 1200

From the question, we have the following parameters that can be used in our computation:

+2, -5, +4 and -3 are 10 multiplied?

This is represented as

Product = +2 * -5 * +4 * -3 * 10

Remove the positive signs

So, we have the following representation

Product = 2 * -5 * 4 * -3 * 10

Lastly, we evaluate the products

Product = 1200

Hence, the product of the numbers is 1200

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In circle the length of PQ = 24 inches.

What is Circle?

A circle is a closed, two-dimensional object in which all points in the plane are equally spaced apart from the centre. The line of reflection symmetry is formed by each line that traverses the circle. Additionally, it possesses rotational symmetry around the centre for each angle.

Since AB= 25 inches and AC = 16 inches then

=> BC = AB-AC = 25-16 = 9 inches.

∠APB is a right angle because it is inscribed in a semicircle.

The three right triangles ᐃAPB, ᐃACP and ᐃPCB are all similar

because their corresponding angles are equal.  Therefore

=> \(\frac{AC}{PC}=\frac{PC}{BC}\)

=> \(\frac{16}{PC}=\frac{PC}{9}\)

=> \(PC^2 = 25*9 = 144 = 12^2\)

=> PC = 12 inches

By symmetry , PC = QC then,

=> PQ = 12*2 = 24 inches.

Hence the length of PQ is 24 inches.

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Answer:

\(\pm 9in^2\)

Step-by-step explanation:

We are given that

Radius of end of a log, r= 9 in

Error, \(\Delta r=\pm 1/2\)in

We have to find the error in computing the area of the end of the log by using differential.

Area of end of the log, A=\(pi r^2\)

\(\frac{dA}{dr}=2\pi r\)

\(\frac{dA}{dr}=2\pi (9)=18\pi in^2\)

Now,

Approximate error in area

\(dA=\frac{dA}{dr}(\Delta r)\)

Using the values

\(dA=18\pi (\pm 1/2)\)

\(\Delta A\approx dA=\pm 9in^2\)

Hence, the possible propagated error in computing the area of the end of the log\(=\pm 9in^2\)

Answer:

\(A = (254.34 \pm 28.26) in^2\)

Step-by-step explanation:

radius, r = 9 inches

error = 0.5 inch

The area of the end is

A = 3.14 x r x r = 3.14 x 9 x 9 = 254.34 in^2

\(A = \pi r^2\\\\\frac{dA}{dr}=2\pi r\\dA = 2 pi r dr \\\\dA = 2 \times 3.14\times 9\times 0.5 = 28.26\)

So, the area is given by

\(A = (254.34 \pm 28.26) in^2\)

The size of the exterior angle in the given 7-sided shape, as shown in the image attached below is: x = 46°.

To calculate the size of the exterior angle in a polygon when the interior angle is known, we can use the following relationship:

Interior angle + Exterior angle = 180°

Given that the interior angle measures 134°, as shown in the image below, we can substitute it into the equation:

134° + Exterior angle = 180°

To isolate the exterior angle, we subtract 134° from both sides of the equation:

Exterior angle = 180° - 134°

Simplifying further:

Exterior angle = 46°

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The sine and cosine of the angle of point P are sin θ = 143/145 and cos θ = -24/145 respectively. Option b. is the answer

Given the coordinate of the point as P (-24/145, 143/145)

This implies x = -24/145 and y =  143/145

To determine the sine and cosine of the angle of point P, we can make a sketch using this information (see attached image).

opposite = 143/145, adjacent = -24/145

hypotenuse = √[(-24/145)² + (143/145)²] = √1 = 1

Using trigometric ratios:

sin θ =   (143/145) / 1 = 143/145    [sin θ = opposite/ hypotenuse]

cos θ =  (-24/145) / 1 = -24/145    [cos θ = adjacent/ hypotenuse]

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Answer:

there is 92.25

Step-by-step explanation:

15x2=30

then you have to find out 5% out of 45 because you need to get 35 not 30.

The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.

To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.

Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:

For car service A: y_A = 0.60x + 300 (in cents)

For car service B: y_B = 0.75x (in cents)

To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:

0.60x + 300 = 0.75x

Subtracting 0.60x from both sides:

300 = 0.15x

Dividing both sides by 0.15:

x = 300 / 0.15

x = 2000

Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:

y_A = 0.60(2000) + 300

y_A = 1200 + 300

y_A = 1500 cents or $15.00

So, when each car travels 2000 miles, the charges will be equal at $15.00.

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Answer:

(3, 25)

Step-by-step explanation:

The symmetry of a parabola means that if you have two y coordinates which are the same, the axis of symmetry is going to be in the middle of the x-coordinates. So in this case it's the middle number of -2 and 8. So to find the midpoint of these two numbers, you simply add them together and divide it by 2. This gives you the equation: \(\frac{-2+8}{2}=\frac{6}{2}=3\). This means that the axis of symmetry is at: \(x=3\), and as you may know, this axis of symmetry passes through the vertex. So this means the x-axis of the vertex is 3, so to find the y-value simply plug in 3 as x

y = (-2-3)(3-8)

y = (-5)(-5)

y = 25

So this means the vertex is at (3, 25)