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3 years ago

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The map shows the intersection of three roads. Malcom Way intersects Sydney Street at an angle of 162°. Park Road intersects Syd

ney Street at an angle of 87°. Find the angle at which Malcom Way intersects Park Road.

1 answer:

Y_Kistochka [10]3 years ago

6 0

Answer:

The angle at which malcom Way intersects Park Road = 111 °

Step-by-step explanation:

Malcom Way intersects Sydney Street at $\theta_{1}$ = 162 °

Park Road intersects Sydney Street at $\theta_{2}$ = 87 °

The angle at which Malcom Way intersects Park Road $\theta_{3}$ = ?

We know that

$\theta_{1} + \theta_{2} + \theta_{3} = 360$

$\theta_{3} = 360 - \theta_{1} - \theta_{2}$

$\theta_{3} = 360 - 162 - 87$

$\theta_{3} = 111$ °

Therefore the angle at which malcom Way intersects Park Road = 111 °

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Given: angle 1 and angle 2 form a linear pair,

iris [78.8K]

Answer:

Look at the proof down

Step-by-step explanation:

The given is;

→ ∠1 and ∠2 form a linear pair

→ ∠1 ≅ ∠3

We want to prove;

→ ∠2 and ∠3 are supplementary

<em>We will write the proof in like a table</em>

1. ∠1 and ∠2 formed a linear pair ⇒ 1. Given

2. m∠1 + m∠2 = 180° ⇒ 2. Sum of angles on a straight line

3. ∠1 and ∠2 are supplementary angles ⇒ 3. Supplementary angles add up to 180°

4. ∠1 ≅ ∠3 ⇒ 4. Given

5. m∠2 + m∠3 = 180° ⇒ 5. Substitution method

6. ∠3 is a supplement of ∠2 ⇒ 6. Supplement of equal angles

7. ∠2 and ∠3 are supplementary ⇒ 7. Proved

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4 years ago

A painter is paid a standard hourly rate and makes $41.25 for five hours of painting. How much is the painter paid for eight hou

Y_Kistochka [10]

41.25/ 5= 8.25 per hour. 8.25 x 8= $66.00

7 0

3 years ago

What is the value of x in the equation below 6 (x - 8) equals 72

olga_2 [115]

Here is the equation:

$6(x-8)=72$

In the equation, 6 is being multiplied by x - 8. There are two ways to solve this equation.

FIRST METHOD

<h3> $6(x-8)=72$ </h3>

You need to remove the parentheses by multiplying everything in the parentheses by 6.

$6(x-8) = (6\times x) + (6 \times -8)$

Multiply:

$6 \times x = 6x\\6 \times -8 = -48$

Remember:

NEGATIVES

Negative(-) times(×) negative(-) = positive(+)

Negative(-) times(×) positive(+) = negative(-)

Negative(-) divided(÷) by positive(+) = negative(-)

Negative(-) divided(÷) by negative(-) = positive(+)

POSITIVES

Positive(+) times(×) positive(+) = positive(+)

Positive(-) times(×) negative(-) = negative(-)

Positive(+) divided(÷) by positive(+) = positive(+)

Positive(+) divided(÷) by negative(-) = negative(-)

Now combine the two values and rewrite the equation:

$6x+-48 \rightarrow 6x-48=72$

Since you're looking for x alone, you will need to remove the -48. This can be done by adding 48 to both sides, -48+48=0, which cancels it out).

$6x-48+48=72+48\\6x=120$

Lastly, divide both sides by 6 to leave x alone.

$\frac{6x}{6} = \frac{120}{6}$

$x=20$

SECOND METHOD

While the first step is somewhat complicated, there is a much easier way.

$6(x-8)=72$

Start by dividing both sides by 6 to remove the number next to the parentheses.

$\frac{6(x-8)}{6} =\frac{72}{6}$

$x-8=12$

(The 6 is cancelled out since 6 divided by 6 equals 1, and 1 × any number is that number).

Now you need to leave the variable alone, which can be done by adding 8 to both sides(-8+8=0 and -8 is cancelled out).

$x-8+8=12+8\\$

$x=20$

Either method can be used, but the second one is definitely shorter!

The answer is x = 20.

8 0

3 years ago

Read 2 more answers

A bricklayer needs to order 6300kg of building sand

luda_lava [24]

Answer:

$9\times 10^7\ \text{grains of sand}$

Step-by-step explanation:

Given that,

A bricklayer needs to order 6300kg of building sand.

1 grain of this sand weighs $7\times 10^{-5}\ kg$ .

We need to find how many grains of sand are there in 6300 kg.

It can be just calculated as follows :

1 grain of sand = $7\times 10^{-5}\ kg$

$6300\ kg=\dfrac{6300}{7\times 10^{-5}}\\\\=9\times 10^7\ \text{grains of sand}$

or

= 90000000 grans of sand

So, 6300 kg is equal to $9\times 10^7\ \text{grains of sand}$ .

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3 years ago

O is the midpoint of segment IU. If I is (-7, 2) and O is (5, -8), what are the coordinates of U?

vaieri [72.5K]

Answer:

(17 , -18)

Step-by-step explanation:

5 = (-7 + x) / 2

x = 17

-8 = (2 + y) / 2

y = -18

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3 years ago