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2 years ago

A road is inclined at an angle of 5°. After

Mathematics

1 answer:

Scorpion4ik [409]2 years ago

3 0

Answer:

464 feet

Step-by-step explanation:

The Sine of the angle of inclination gives the increase in altitude.

This is because the Sine of an angle is equal to the Opposite side divided by the Hypotenuse side. i.e

Sin Ф = Opposite ÷ Hypotenuse

Sin 5° = O ÷ 5328

0·08716 = O ÷ 5328

Make O the subject and multiply every fraction by 5328

(0·08716/1 × 5328)= (O/5328 × 5328)

464·388 = O

∴ The increase in altitude is 464·388 feet

This is supposed to be to the nearest foot so we round off

464·388 becomes 464 feet

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Which equation does the graph of the systems of equations solve?

mihalych1998 [28]

Answer:

$\text{B. }\frac{1}{3}x-3=-x+1$

Step-by-step explanation:

Let's start by taking a look at the blue line. The slope of any line that passes through two points is equal to the change in y-values over the change in x-values. We can see that the line passes through points (0, 1) and (1, 0). Assign these points to $(x_1,y_1)$ and $(x_2, y_2)$ (doesn't matter which you assign) and use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let:

$(x_1,y_1)\implies (0,1)\\(x_2,y_2)\implies (1, 0)$

The slope is equal to:

$m=\frac{0-1}{1-0}=\frac{-1}{1}=-1$

Therefore, the slope of this line is -1. In slope-intercept form $y=mx+b$ , $m$ represents slope, so one of the lines must have a term with $-x$ in it, which eliminates answer choices A and D.

For the second line, do the same thing. The red line clearly passes through (0, -3) and (3, -2). Therefore, let:

$(x_1,y_1)\implies (0,-3)\\(x_2,y_2)\implies (3, -2)$

Using the slope formula:

$m=\frac{-2-(-3)}{3-0}=\frac{1}{3}$

Thus, the slope of the line is 1/3 and the other line must have a term with $\frac{1}{3}x$ in it, eliminating answer choice C and leaving the answer $\boxed{\text{B. }\frac{1}{3}x-3=-x+1}$

*You can find the exact equation of each line by using the slope formula as shown and plugging in any point the line passes through into $y=mx+b$

7 0

2 years ago

Lara is putting lace trim around the border of a circular tablecloth. The tablecloth has a diameter of 1.2 meters. What is the l

mylen [45]

Answer:

3.8m

Step-by-step explanation:

Since Lara is putting lace trim around the border of a circular tablecloth, by the time she finishes she has covered the circumference.

The circumference of a circle is calculated using:

$C=\pi \: d$

where d is the diameter of the circle.

It was given that the diameter of the circular table cloth is 1.2 meters.

$C=3.14 \times 1.2$

$C=3.768$

Therefore the length of the lace she needed is 3.8m

6 0

2 years ago

What is the correlation

RideAnS [48]

Answer:

type=positive

Correlation refers to the degree of correspondence or relationship between two variables.

8 0

2 years ago

How can you construct perpendicular lines and prove theorems about perpendicular lines

omeli [17]

Answer:

See descriptions below.

Step-by-step explanation:

To construct a perpendicular bisector, draw a line segment. From each end of the line segment, draw arcs above and below which intersect from each side. Be sure to maintain the same radius on each. Where the arcs intersect above and below, mark points. Connect these two points. This is a perpendicular bisector.

To prove theorems about parallel lines, use angle relationships. For instance, when two parallel lines are cut by a transversal, specific angle are congruent. When these relationships are congruent, you must have parallel lines:

Alternate Interior
Alternate Exterior
Corresponding Angles
Same side interior add to 180

7 0

2 years ago

Help !! Picture ^^^^

nikitadnepr [17]

The answer is 78

If you multiply 17x6 you get 102
102 equals the whole rectangle after that you need to get rid of the part that’s not there
so you multiply 8x3 which equals 24
you then subtract 24 from 102 and get 78

6 0

2 years ago