What is the slope of the line in the graph?

for an 8 foot ramp need to be elevated at an angle measure 10 degree to level with a step approximately how far does the ramp ne

d1i1m1o1n [39]

Answer:

7.878 ft far

Step-by-step explanation:

Given:

- A ramp is to be lifted to an angle Q = 10 degrees

- The total length of the ramp L = 8 ft

Find:

- how far does the ramp need to be away to hit the edge of the step

Solution:

- The question asks in "other words" the horizontal distance (d) from the ramp pivot on the floor to the edge of the step when it is lifted 10 degrees.

- We will use trigonometry to solve a right angle triangle: The horizontal distance is a projection of Length L on to the flat ground surface. Hence, we have:

cos(Q) = d / L

d = L*cos(Q)

- Plug in values:

d = 8*cos(10)

Answer: d = 7.878 ft

8 0

3 years ago

At a store, apples cost $0.80 $0.80 each and oranges cost $0.95 $0.95 each. Harry buys some apples and oranges and spends $9.55

gregori [183]

Answer:

Harry buys 6 apples and 5 oranges at the store.

Step-by-step explanation:

Given:

Cost of each apples = $0.8

Cost of each oranges = $0.95

Total money spend =$9.55

Number of fruits bought= 11

We need to find the number of apples bought and number of oranges were bought.

Solution:

Let the number of apples bought be 'a'.

Let the number of oranges were bought be 'o'.

Number of fruits bought= 11

So we can say that;

Number of fruits bought is equal to sum number of apples bought and number of oranges were bought.

framing in equation form we get;

$a+o=11$ ⇒ equation 1

Now we can say that;

Total money spend is equal to number of apples bought multiplied by Cost of each apples plus number of oranges were bought multiplied by Cost of each oranges.

framing in equation form we get;

$0.8a+0.95o=9.55$ ⇒ equation 2

Now Multiplying equation 1 by 0.8 we get;

$0.8(a+o)=0.8\times11$

$0.8a+0.8o=8.8$ ⇒ equation 3

Subtracting equation 3 from equation 2 we get;

$0.8a+0.95o-(0.8a+0.8o)=9.55-8.8\\\\0.8a+0.95o-0.8a-0.8o=0.75\\\\0.15o=0.75$

Dividing both side by 0.15 we get;

$\frac{0.15o}{0.15}=\frac{0.75}{0.15}\\\\o=5$

Substituting the value of o in equation 1 we get;

$a+o=11\\\\a+5=11\\\\a=11-5=6$

Hence Harry buys 6 apples and 5 oranges at the store.

3 0

3 years ago

Derek has a bank account that pays 2.1% simple interest. The balance is $910. When will the account grow to $1,000?

swat32

Answer:

The account will grow to 1,000 in 5 years.

Step-by-step explanation:

Since the account will become 1000, the interest is 90 dollars. I=p*r*t.

90=910*.021*t

90=19.11*t.

t=4.71, so it will take 5 whole years.

3 0

2 years ago

Calculate the number of subsets and the number of proper subsets for the set.

arlik [135]

A set of n elements has 2ⁿ subsets. One of these subsets is the set itself, so this set would have 2ⁿ - 1 <em>proper</em> subsets.

The given set has 4 elements, so it has 2⁴ = 16 subsets and 2⁴ - 1 = 15 proper subsets.

Just to illustrate the claim, we have

• subsets of size 0 (1 of these):

{ } (empty set)

• subsets of size 1 (4 of these):

{1/6}, {1/7}, {1/8}, {1/9}

• subsets of size 2 (6 of these):

{1/6, 1/7}, {1/6, 1/8}, {1/6, 1/9}, {1/7, 1/8}, {1/7, 1/9}, {1/8, 1/9}

• subsets of size 3 (4 of these):

{1/6, 1/7, 1/8}, {1/6, 1/7, 1/9}, {1/6, 1/8, 1/9}, {1/7, 1/8, 1/9}

• subsets of size 4 (1 of these):

{1/6, 1/7, 1/8, 1/9}

and the last one is the only subset that is not a proper subset, because that subset = the set.

6 0

2 years ago

PLEASE HELP!! DUE SOON :( #40

Allisa [31]

Answer:

Types of polygon

Polygons can be regular or irregular. If the angles are all equal and all the sides are equal length it is a regular polygon.

Regular and irregular polygons

Interior angles of polygons

To find the sum of interior angles in a polygon divide the polygon into triangles.

Irregular pentagons

The sum of interior angles in a triangle is 180°. To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°.

Example

Calculate the sum of interior angles in a pentagon.

A pentagon contains 3 triangles. The sum of the interior angles is:

180 * 3 = 540

The number of triangles in each polygon is two less than the number of sides.

The formula for calculating the sum of interior angles is:

(n - 2) * 180 (where n is the number of sides)

6 0

2 years ago