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3 years ago

Please help I always get stuck, some of the steps don't make sense to me ?

Mathematics

1 answer:

harina [27]3 years ago

6 0

Answer:

If the kid walks for the dotted line, the distance is 36ft.

Now, you can see that this is a triangle rectangle, then we must have that:

x^2 + (x + 6)^2 = 36^2 (the Pythagorean theorem)

Now we must solve this for x.

x^2 + x^2 + 2*6*x + 36 = 36^2

2*x^2 + 12*x -1260 = 0

The solutions for this equation are:

$x = \frac{-12 +-\sqrt{12^2 +2*4*1260} }{2*2} = \frac{-12 +-101.1}{4}$

the solutions are:

x = (-12 - 101.1)/4 = -28.78

x = (-12 + 101.1)/4 = 22.3

Then we have x = 22.3 ft

The lenght of the path following the cathetus is:

D = x + x + 6 = 2*22.3ft + 6ft = 50.6ft

Then the difference between the distances is:

Diff = 50.6ft -36ft = 14.6ft

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Answer:

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Step-by-step explanation:

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

Calculate the speed in km/hour of a car that travels 24 km in 120 minutes

bonufazy [111]

Answer:

Step-by-step explanation:

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3 years ago

Read 2 more answers

The skittles jar has a radius of 3.5 cm and a height of 11.5 cm. using the two given boxes for reference what would be a good es

Bond [772]

C) 1059 skittles

Step-by-step explanation:

We know that the first container held 192 skittles. Knowing the dimension of the container we can calculate the volume of 192 skittles:

Volume of 192 skittles = 5 × 4 × 4 = 80 cm³

Volume of 1 skittle = 80 / 192 = 0.42 cm³

We also know that the second container held 258 skittles. Knowing the dimension of the container we can calculate the volume of 258 skittles:

Volume of 258 skittles = 12 × 3 × 3 = 108 cm³

Volume of 1 skittle = 108 / 258 = 0.42 cm³

We found that the volume of 1 skittle is equal to 0.42 cm³. Now we calculate the volume of the skittles jar:

volume of cylinder = π × radius² × height

volume of skittles jar = 3.14 × 3.5² × 11.5 = 442 cm³

Now we can calculate the number of skittles in the jar:

number of skittles in the jar = volume of the jar / skittle volume

number of skittles in the jar = 442 / 0.42 = 1052 which is close the C) 1059

Learn more about:

volume of cylinder

brainly.com/question/12748872

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3 years ago

Use two different methods to find an explain the formula for the area of a trapezoid that has parallel sides of length a and B a

evablogger [386]

Answer:

Formula of Trapezoid:

A = (a + b) × h / 2

The formula can be derived in different ways. for now, we have discussed two ways:

1. By using the formula of a triangle

2. By dividing into different sections

Step-by-step explanation:

1. By using the formula of a triangle

One of the ways to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.

Assume a trapezoid PQRS with lower base SR and upper base PQ (they are parallel) and sides PS and QR.

The image is attached below.

Connect vertices P and R with a diagonal.

Consider triangle ΔPQR as having a base PQ and an altitude from vertex R down to point M on base PQ (RM⊥PQ).

Its area is

S1= $\frac{1}{2} *PQ*RM$

Consider triangle ΔPRS as having a base SR and an altitude from vertex P up to point N on-base SR (PN⊥SR).

Its area is

S2= $\frac{1}{2} *SR*PN$

Altitudes RM and PN are equal and constitute the distance between two parallel bases PQ and SR.

They both are equal to the altitude of the trapezoid h.

Therefore, we can represent areas of our two triangles as

S1= $\frac{1}{2}*PQ*h$

S2= $\frac{1}{2}*SR*h$

Adding them together, we get the area of the whole trapezoid:

S=S1+S2= $\frac{1}{2} (PQ+SR)h,$

which is usually represented in words as "half-sum of the bases times the altitude".

2. By dividing into different sections

Trapezoid PQRS is shown below, with PQ parallel to RS.

Figure 1 - Trapezoid PQRS with PQ parallel to RS(image is attached below.)

We are going to derive the area of a trapezoid by dividing it into different sections.

If we drop another line from Q, then we will have two altitudes namely PT and QU.

Figure 2 - Trapezoid PQRS divided into two triangles and a rectangle. (image is attached below.)

From Figure 2, it is clear that Area of PQRS = Area of PST + Area of PQUT + Area of QRU. We have learned that the area of a triangle is the product of its base and altitude divided by 2, and the area of a rectangle is the product of its length and width. Hence, we can easily compute the area of PQRS. It is clear that

=> $A_{PQRS} = (\frac{ah}{2}) + b_{1}h + \frac{ch}{2}$