4) The hospital and the fire department are 46 meters apart. From a window in the hospital,
the angle of elevation to the top of the fire department is 730. From the same window, the
angle of depression to the ground at the base of the fire department is 640. Find the height
of the fire department to the nearest tenth.

Answer: The answer is 904.32

Answer:

x=20

Step-by-step explanation:

Right angle triangle ABC

ac^2=ab^2+bc^2

or (x+9)^2=x^2+(x+1)^2

or x^2+81+18x=x^2+x^2+1+2x

or 80= X^2-16x

or x^2-16x-80=0

x^2-20x+4x-80=0

x(x-20)+4(x-20)=0

(x+4)(x-20)=0

either x=-4 or x=20

since x is a length it can not be negative

Answer:

$51,282

Step-by-step explanation:

100*1.75%=1.75*504 months (42 years)=882

100*504 months (42 years)=50,400

50,400+882=$51,282

Hope this is correct, and helps you out :)

He will have $74,356.50 in his account.

Interest is the price you pay to borrow money or the cost you charge to lend money.

Initial investment (PV)= $100

Number of periods (n)=42 years

Interest rate (i)= 1.75%

So, FV= P(1+r/100)^(nt) -1)) / (r/n)

FV= 100(1+0.0175/100)^(12*42) -1)) / (0.0175/12)

FV= $74,356.50

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Answer:

Step-by-step explanation:

-43.6F/-37.4F/-17/37.3/51.9/52

Answer:

the first answer is correct

Step-by-step explanation:

Answer:

The correct function is

A. y = -0.5x+100

Answer:

y

=

4

(

x

+

11

)

2

−

484

Step-by-step explanation:

Answer:

-4,2

Step-by-step explanation:

Answer

Q=(4,2)

Step-by-step explanation:

In X axis, count 4 units to the right

In Y axis, count 2 units up

Graph would look like this.

the anwser is 23 dregrees

Answer:

x=12

Step-by-step explanation:

x+3=15

move constant to the right

x=15-3

subtract 15 to 3

x=12

Answer:

X =12

Step-by-step explanation:

X+3 =15

subtract 3 from each side

X+3-3 =15-3

X = 12

Answer:

Step-by-step explanation:

volume of sphere = (4/3)πr³

Difference= [(4/3)*π*6³]-[(4/3)*π*3³]

[tex]=\pi*[(\frac{4}{3}*6*6*6) - (\frac{4}{3}*3*3*3)]\\\\=\pi*[(4*2*6*6)-(4*3*3)]\\\\=\pi *[288-36]\\\\=252\pi[/tex]

The kids have to wait for 1 hour to get their bags.

Step-by-step explanation:

Given that,

A bus with kids and a truck with their bags started moving from the school to the camp at the same time.

To find the distance traveled by the bus :

⇒ Distance = Speed × Time

⇒ 60 × 3

⇒ 180 m

∴ The distance is 180 m.

To find the time taken by the truck to reach the camp :

Time taken = distance / speed.

⇒ 180 / 45

⇒ 4 hours.

∴ The time taken by the truck to reach the camp is 4 hours.

To find how long the kids have to wait for their bags :

The time taken by the truck to reach the camp - the time it took for the kids to arrive.

⇒ 4 hours - 3 hours

⇒ 1 hour.

∴ The kids have to wait for 1 hour to get their bags.

The bus traveled 180 miles to the camp in 3 hours at 60 mph, while the truck took 4 hours at 45 mph to cover the same distance. Hence, the kids had to wait 1 hour for their bags to arrive.

Travel Time and Waiting Time

To determine how long the kids had to wait for their bags, we need to calculate the time it took for the truck to reach the camp.

The bus travels at a speed of 60 mph and it took the kids 3 hours to reach the camp. The distance to the camp can be calculated using the formula:

Next, we calculate the time it took for the truck, traveling at 45 mph, to cover the same distance:

Therefore, the kids had to wait for 1 hour for their bags to arrive.

Answer:

2/8 or 1/4

Step-by-step explanation:

2/8 or 1/4 because the spots on the spinner are blue out of 8 is 2/8 or 1/4

Answer:

2/6

Step-by-step explanation:

This should have been simple because you don't include the blue parts

Answer:

(x+2)(x+3)(x+4)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

none of the others are graphically correct

Answer:

C, "Will's destination was 160 miles from where he started."

Step-by-step explanation:

The first and second choices are absurd. It doesn't give any reason or evidence that he stopped during that time. The time does not line up either. D, does not make sense because he only traveled 40 miles in 2 hours. But from hour 3 to 5 he traveled 120 miles.

Answer:

V=0.45

V=0.06

V=0.39

V=7.77

Answer:

Step-by-step explana

a= 1

b= 1/16 or .0625

c= 1/256 or .00390625

Step-by-step explanation:

The answer is 15

Answer:

y = x² + 2x + 1

Step-by-step explanation:

Same y value at x = -2 & x = 0

So line of symmetry is at:

x = (-2+0)/2

x = -1

Vertex: (-1,0)

y = a(x - -1)² + 0

y = a(x + 1)²

At x = 1, y = 4

4 = a(1 + 1)²

4 = 4a

a = 1

y = (x + 1)²

y = x² + 2x + 1

The general form of the equation of the quadratic function is x² + 2x + 1

The formula expressing the equation of the quadratic function will be expressed as:

y = a(x -h)² + k

From the table shown, we can see that the y-values are the same at where x = -2 and 0

Get the line of symmetry:

[tex]x =\frac{-2+0}{2}\\x=\frac{-2}{2} \\x=-1[/tex]

We can see that when x = -1, y = 0. Hence the vertex will be at (-1, 0)

h = -1

k = 0

Substitute into the formula y = a(x -h)² + k

y = a(x -(-1))² + 0

y = a(x+1)²

From the table at where x = 1, y = 4. On substituting to get "a" we have:

4 = a(1+1)²

4 = 4a

a = 1

Get the required quadratic function by substituting the parameters into the general formula as shown:

y = a(x -h)² + k

y = 1(x +1)² + 0

y = (x+1)²

y = (x+1) (x+1)

y = x² + x +x + 1

y = x² + 2x + 1

Hence the general form of the equation of the quadratic function is x² + 2x + 1

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Answer:

s ≥ 170

Step-by-step explanation:

The problem raises the following statement: "The cruising speed of the bullet train will be at least 170 miles per hour"

Which means that the train has a speed of 170 miles for now or higher, knowing this we can pose the inequality.

Knowing that "s" is the train's cruising speed (in miles per hour), we have to:

s ≥ 170

This would be the inequality that the statement represents.

The inequality representing the bullet train's cruising speed being at least 170 miles per hour is s ≥ 170.

The situation described involves finding an inequality for the train's cruising speed. To represent the train's cruising speed in miles per hour, we use the variable s.

Given that the cruising speed of the bullet train will be at least 170 miles per hour, we need an inequality that expresses this condition.

The inequality is:

s ≥ 170

This means that the cruising speed s can be 170 miles per hour or higher.

Answer:

hello i dont even know how to do this

Step-by-step explanation:

Answer:

he measure of each interior angle of a regular polygon with 14 sides is about 154.3.

Step-by-step explanation:

Answer:

Option C

7

Step-by-step explanation:

The coordinate point of K is (-2,5) and H(-2,-2)

[tex]KH =\sqrt{ {(x2 - x1)}^{2}+{(y2 - y1)}^{2} } [/tex]

[tex] = \sqrt{ {( - 2 - 5)}^{2} + {( - 2 + 2)}^{2} } [/tex]

[tex] = \sqrt{ {( - 7)}^{2} + {(0)}^{2} } [/tex]

[tex] = \sqrt{49} = 7[/tex]

Answer:

5x = - 10

5. 5

x = 2

y = -10

its easyyy

Answer:

64 70% and 16 45%

Step-by-step explanation:

it's 4 70% and 1 45% to make 5 pints of 65% so 64 70% and 16 45%

Answer:

18

Step-by-step explanation:

because there where two houses each invited 9 guests and 9 + 9 = 18

The length of arc QS in circle R is approximately 22.9 units. This is determined by using the formula for arc length in a circle, which is the radius times the angle (in radians). The angle was first converted from degrees to radians.

To find the length of arc QS in circle R, we need to use the formula for the arc length. The arc length of a circle is given by the formula Length = radius * angle (in radians). The angle is provided as 82 degrees, and the radius QR is given as 16 units.

First, we need to convert the angle from degrees to radians. We use the formula: radians = degrees * (π / 180). Hence, 82 degrees is approximately 1.43117 radians.

Now, let's substitute our values into the formula. Length = 16 units * 1.43117 radians.

Hence, the arc length of QS is approximately 22.9 units when rounded to the nearest hundredth.

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Answer: 1256cm

Step-by-step explanation:

Final answer:

When Josie doubles the radius of the bird bath to build a larger one, the new surface area will be 1256 cm², as surface area quadruples when doubling the radius of a circle.

Explanation:

Josie calculated that the surface area of her small bird bath with a radius of 10 cm is 314 cm^2. If she doubles the dimensions for a larger bird bath, the new radius will be 20 cm. To find the surface area of the larger bird bath, we use the formula for the area of a circle, A = πr².

Plugging in the new radius:

A = 3.14 × (20 cm)^2

A = 3.14 × 400 cm^2

A = 1256 cm2

This means the surface area for the larger bird bath Josie plans to build will have 1256 cm^2 for bird bathing. This calculation demonstrates how the surface area of a circle quadruples when the radius is doubled, which is consistent with the principle that surface area scales with the square of the dimension changes.