Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
This is a triangle. side a has a length of 6 yards. side b has a length of 10 yards. side c has a length of 14 yards. The altitude to side c has a length of X yards. what is x

Answer:

Look Below

Step-by-step explanation:

Now if you are looking what percent 15 is in 150, then it'll be 22.5%

Just Multiply 150 with 15 (add a 0. before adding the 15) then multiply 150 x 0.15, and you get 22.5, to which that is 22.5%.

a. If G(t) = a (1 + r)ᵗ, then G(0) = a corresponds to the starting area of the glacier, which is given to be 142 acres. So a = 142.

The area of the glacier shrinks by 4.4% each year. This means that after 1 year, the area is reduced to

142 - (4.4% of 142) = 142 (1 - 0.044) ≈ 135.75 acres

After another year,

135.75 - (4.4% of 135.75) = 135.75 (1 - 0.044) ≈ 129.78 acres

or equivalently, 142 (1 - 0.044)² acres.

And so on. After t years, the glacier would have an area of

G(t) = 142 (1 - 0.044)ᵗ   ⇒   G(t) = 142 × 0.956ᵗ

b. If the year 2007 corresponds to t = 0, then 2012 refers to t = 5. Then the area of the glacier is

G(5) = 142 × 0.956⁵   ⇒   G(5) ≈ 113.39 acres

c. Simply take the difference between G(5) and G(0) :

G(5) - G(0) ≈ 142 - 113.39 ≈ 28.61 acres

d. The average rate of change of G(t) from 2007 to 2012 is given by the difference quotient of G(t) over the interval 0 ≤ t ≤ 5 :

[tex]ARC_{[2007,2012]} = \dfrac{G(5) - G(0)}{5 - 0} \approx \dfrac{113.39 - 142}5[/tex]

so that ARC ≈ -5.72 acres/year. This rate tells us that a little less than 6 acres of glacial ice is lost each year, based on the reduction over the first 5 years.

e. The year 2017 refers to t = 10, so now we compute

[tex]ARC_{[2012,2017]} = \dfrac{G(10) - G(5)}{10 - 5} \approx \dfrac{90.55-113.39}5[/tex]

which comes out to about ARC ≈ -4.57 acres/year. Since this rate is smaller than the ARC between 2007 and 2012, this means that the glacial ice is disappearing at a slower rate in later years.

Answer: 1 cup of water with 1 1/2 teaspoons of powdered drink.

Step-by-step explanation:

I know this, because if 1 cup is 1 1/2 teaspoons of powdered drink, then 2 cups of water would have 3 teaspoons of powdered drink mix, so the second option is out. And, the third option is out because it less than 1 cup of water with 1 1/2 teaspoons of powered drink mix.

The parking lot is located along the front and one side of the school

building.

Reasons:

The given dimensions in the compound are;

Length of the school and the old parking lot = 300 + 75

Width of the school and the old parking lot = 165 + 75

Length of the school, the old and new parking lot = 300 + 75 + x

Width of the school and the old and new parking lot = 165 + 75 + x

Area of the new parking lot the school wants = Double the old parking lot

In terms of areas, we have;

New compound - School = 2 × (old compound - school)

Which gives;

(300 + 75 + x) × (165 + 75 + x) - 300 × 165 = 2 × ((300 + 75) × (165 + 75) - 300 × 165)

2 × (375 × 240 - 49,500) = (375 + x) × (240 + x) - 49,500

Simplifying gives;

81,000 = x² + 615·x + 40,500

x² + 615·x + 40,500 - 81,000 = 0

x² + 615·x - 40,500 = 0

Factorizing with a graphing calculator gives;

(x - 60)·(x + 675) = 0

Therefore;

x = 60 or x = -675

Given that x is a natural number, we have, the correct value is; x = 60;

The distance with which the lot should be expanded, x = 60 feet.

Learn more about writing equations here:

https://brainly.com/question/20475360

https://brainly.com/question/7107994

The dimensions of the dilated image is 125 millimeters by 300 millimeters.

An image is dilated if the dimensions of the image is resized in a way that does not change the shape of the image. When an image is dilated, it is made larger.

The scale factor is 2.5. This means that the dimensions are 2.5 larger. Dimensions of the dilated image : 50 x 2.5 and 120 x 2.5 = 125 mm by 300 mm

To learn more about dilation, please check: https://brainly.com/question/3457976

Answer:

2

Step-by-step explanation:

0.6m-1.2+m=2

1.6m-1.2=2

1.6m=3.2

m=2

Answer:

Kim is younger than 6 years

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Y= x-10

Step-by-step explanation:

M= Y2-Y1/X2-X1

  = -7-(-9)/3-1

  = 2/2

  = 1

sub x=1 and y=-9 into Y=MX + C

-9=1+C

-9-1=1+C-1

C=-10

Answer:

x/3 ≤ 5

I'm not sure if this is what you were looking for. If not, please be more specific in your questions!

Answer: only has one solution

Step-by-step explanation:  If you find the answer for 7x+3x-8, youll get 10x+8. This will be the same answer for 2(5x-4). Making them equal and having only one solution

Answer:

x has infinite values.

Step-by-step explanation:

7x+3x-8 = 2(5x-4) = 7x+3x-8 = ||10x-8 = 10x-8||

In this case this we have the same eqations on both sides, x = anything.

In other words, x have infinite values.

Answer:

0.35*4=1.40

Step-by-step explanation:

Think of doing 35*4 but dividing the result by 100, or 2 decimal places to the left:

35*4 = 35*2*2 = 70*2 = 140

140/100 = 1.40

So, 0.35*4=1.40

Answer:

1.4

Step-by-step explanation:

You can use a calculator or you can try it using this method:

4 * 0.05 = 0.2

4 * 0.3 = 1.2

1.2 + 0.2 = 1.4

Answer:

$7.50 per hour

Step-by-step explanation:

after 2 hours, she earns $15

after 4 hours, she earns $30

after 8 hours, she ears $60

15/2 = 30/4 = 60/8 = 7.5/1

Answer:

Its not linear

Step-by-step explanation: Linear means it travels in a perfect line

Answer:

£39.20

Step-by-step explanation:

2+1+5=8

£78.40/8 = 9.8

9.8*5= 49

49-9.8= 39.2

Step-by-step explanation:

2⋅13⋅(3−9)−1⋅25(10−15)=⋅3−3⋅3−3(−3)−3

\frac{2 \cdot 1}{3} \cdot (3x-9y)-1 \cdot \frac{2}{5}(10x-15y)=a \cdot 3y-3xb \cdot 3x-3yc(-3)x-3y

Here is my answer. I hope it is helpful.

Step-by-step explanation:

24 cans cost $8.

so, 1 can is 1/24 if the total, and that applies then also to the price.

so, the cost of 1 can is 8/24 = 1/3 ≈ $0.33

Answer:

Cost per can = $0.33.

Step-by-step explanation:

8 / 24

= 1/3

= 0.333....

Answer:

 3x - 20

Step-by-step explanation

          simplify 1/2

STEP 3

Pulling out like terms

3.1     Pull out like factors :

6x + 10  =   2 • (3x + 5)

Equation at the end of step

3 (3x + 5) -  25

Final result : 3x - 20

By the fundamental theorem of calculus,

[tex]\displaystyle F(x) = \int_0^x \cos(t^2) \, dt \implies F'(x) = \cos(x^2)[/tex]

and so F'(1) = cos(1).

i have to write 20 characters so there is ur answer

Answer:

  a) m = 60°, n = 30°

  b) m = 20°, n = 45°

Step-by-step explanation:

The top and bottom horizontal lines are parallel, so angle m is an alternate interior angle congruent to the interior angle(s) of the equilateral triangle. Those angles are all 60°.

Angle n is the complement of angle m, so is 90°-60° = 30°

  m = 60°, n = 30°

__

The base angles of the isosceles right triangle are n = 45°. (This should be a memorized fact. It is computed as (180° -90°)/2 = 45°.)

The base angles of the isosceles acute triangle are (180°-50°)/2 = 65°. Angle m is the difference between one of these and angle n.

  m = 65° -45° = 20°

  m = 20°, n = 45°

_____

Additional comment

The sum of angles of a triangle is 180°. The "base" angles of an isosceles triangle (one with two equal sides) are equal. If 'a' is the third angle, and 'b' are the base angles, you have ...

  a + 2b = 180°

  2b = 180° -a

  b = (180° -a)/2 . . . . . . the relation used above

[tex]\huge \rm༆ Answer ༄[/tex]

Let's rearrange the terms to convert the equation into slope - intercept form ~

I hope it helps ~

Answer:

y = - 3x

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 2 ← is in slope- intercept form

with slope m = - 3

Parallel lines have equal slopes , then

y = - 3x + c ← is the partial equation

To find c substitute (- 1, 3 ) into the partial equation

3 = 3 + c ⇒ c = 3 - 3 = 0

y = - 3x ← equation of parallel line

Answer:

y = -3x

Step-by-step explanation: