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2 years ago

Jacob walks 1.5 miles north. He turns and walks 0.8 miles west. How far is he from his starting point?

Mathematics

1 answer:

Flura [38]2 years ago

7 0

Answer:

1.7 miles

Step-by-step explanation:

Given that,

Jacob walks 1.5 miles north.

He turns and walks 0.8 miles west.

We need to find how far is he from his starting point. Let he is at a distance of x miles from the starting point. It can be calculated as follows :

$x=\sqrt{1.5^2+0.8^2} \\\\x=1.7\ \text{miles}$

Hence, he is 1.7 miles from his starting point.

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What is the volume of the right rectangular prism? Enter your answer in the box.

Nutka1998 [239]

Answer:

1000 cm²

Step-by-step explanation:

Given:

Length = 10 cm
Width = 12.5 cm
Height = 8 cm

Formula:

$\text{Volume = Length} \times \text{Width} \times \text{Height}$

Substitute the length, width, and the height of the prism to determine the volume of the prism.

$\implies \text{Volume = 10} \times 12.5 \times 8$

Simplify the right hand side of the equation, as needed;

$\implies \text{Volume = 10} \times 12.5 \times 8$

$\implies \text{Volume =}\ 125 \times 8$

$\implies \boxed{\text{Volume =}\ 1000 \ \text{cm}^{2} }$

Therefore, the volume of the prism is 1000 cm².

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2 years ago

50% of cheese pizza 40% pepperoni pizza 270 students bought lunches how many lunches are sold on Friday

Sindrei [870]

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3 years ago

A machine produces 312 bolts in 30 minutes. At the same rate, how many minutes would it takes to produce 260 bolts.

myrzilka [38]

Hi

312 bolts ⇒ 30 min
260 bolts ⇒ x min

312x = 30·(260)
312x = 7800
x = 7800/312
x = 25 min

Answer: 25 minutes

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3 years ago

Read 2 more answers

Plzzz solve this for me with steps!!!! I will give you brainliest

Vinvika [58]

Step-by-step explanation:

Left hand side:

tan 203° + tan 22° + tan 203° · tan 22°

From angle sum identities, we know:

tan (α + β) = (tan α + tan β) / (1 − tan α · tan β)

Therefore:

tan (203° + 22°) = (tan 203° + tan 22°) / (1 − tan 203° · tan 22°)

tan (225°) = (tan 203° + tan 22°) / (1 − tan 203° · tan 22°)

1 = (tan 203° + tan 22°) / (1 − tan 203° · tan 22°)

tan 203° + tan 22° = 1 − tan 203° · tan 22°

Substituting:

1 − tan 203° · tan 22° + tan 203° · tan 22°

3 0

3 years ago

Acute △ABC with angles α, β, and γ is inscribed in a circle. Tangents to the circle at points A, B, and C intersect in points M,

SOVA2 [1]

Answer:

The measures of angles of triangle MNP are

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the measure of arcs AB, BC and AC

we know that

The inscribed angle is half that of the arc it comprises.

$\gamma=\frac{1}{2}[arc\ AB] ----> arc\ AB=2\gamma\\\alpha=\frac{1}{2}[arc\ BC] ----> arc\ BC=2\alpha\\\beta=\frac{1}{2}[arc\ AC] ----> arc\ AC=2\beta$

step 2

Find the measure of angle M

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

$M=\frac{1}{2}[arc\ AB+arc\ BC-arc\ AC]$

substitute

$M=\frac{1}{2}[2\gamma+2\alpha-2\beta]\\M=[\gamma+\alpha-\beta]$

step 3

Find the measure of angle N

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

$N=\frac{1}{2}[arc\ AC+arc\ BC-arc\ AB]$

substitute

$N=\frac{1}{2}[2\beta+2\alpha-2\gamma]\\N=[\beta+\alpha-\gamma]$

step 4

Find the measure of angle P

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

$P=\frac{1}{2}[arc\ AC+arc\ AB-arc\ BC]$

substitute

$P=\frac{1}{2}[2\beta+2\gamma-2\alpha]\\P=[\beta+\gamma-\alpha]$

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3 years ago