Khan help, please! Hanger stuff

What is the area of this triangle ?

oee [108]

Answer:

Area of triangle is 9.88 units^2

Step-by-step explanation:

We need to find the area of triangle

Given E(5,1), F(0,4), D(0,8)

We will use formula:

$Area\,\,of\,\,triangle =\sqrt{s(s-a)(s-b)s-c)} \\where\,\, s = \frac{a+b+c}{2}$

We need to find the lengths of side DE, EF and FD

Length of side DE = a = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Length of side DE = a = $=\sqrt{(5-0)^2+(1-8)^2}\\=\sqrt{(5)^2+(-7)^2}\\=\sqrt{25+49}\\=\sqrt{74}\\=8.60$

Length of side EF = b = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Length of side EF = b = $=\sqrt{(0-5)^2+(4-1)^2}\\=\sqrt{(-5)^2+(3)^2}\\=\sqrt{25+9}\\=\sqrt{34}\\=5.8$

Length of side FD = c = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Length of side FD = c = $=\sqrt{(0-0)^2+(8-4)^2}\\=\sqrt{(0)^2+(4)^2}\\=\sqrt{0+16}\\=\sqrt{16}\\=4$

so, a= 8.60, b= 5.8 and c = 4

s = a+b+c/2

s= 8.6+5.8+4/2

s= 9.2

Area of triangle= $=\sqrt{s(s-a)(s-b)s-c)}\\=\sqrt{9.2(9.2-8.6)(9.2-5.8)(9.2-4)}\\=\sqrt{9.2(0.6)(3.4)(5.2)}\\=\sqrt{97.5936}\\=9.88$

So, area of triangle is 9.88 units^2

4 0

4 years ago

Tell if the decimal on the left is less or greater than the decimal on the right. Use < or > 5.43123 5.43013

jok3333 [9.3K]

Proceed left to right. The larger number will have a larger digit in the corresponding place.

Here, the differing digits are 1 and 0 in the thousandths place. The appropriate sign is ">"

... 5.43123 > 5.43013

5 0

3 years ago

Mrs. Bailey gives a test, and her students’ scores range from 30 to 70. She decides to curve the scores, so that they range from

Harman [31]

Answer:

f(x) = x*3/4 + 42.5

Step-by-step explanation:

The original difference between the pair is 70 - 30 = 40

The new difference between the pair is 95 - 65 = 30

Since the differences are not the same, Mrs Bailey must first perform a (slope) multiplication by a factor of 30/40 or 3/4

Then 30 * 3/4 = 22.5

Then she can shift the scores up by 65 - 22.5 = 42.5 in order to get the range from 65 to 95

Therefore, f(x) = x*3/4 + 42.5. We can test that

f(30) = 30*3/4 + 42.5 = 65

f(70) = 70*3/4 + 42.5 = 95

8 0

3 years ago

Tomas and Tasha were hiking at a speed of 3.5 mph. On their way back, they were tired and their speed was 2 mph. How long was th

Anna35 [415]

To get the length of the route use the expression for speed,

Distance = Speed × Time

Length of the route is 7 miles.

It's given in the question,

Speed of Tomas and Tasha initially = 3.5 mph

Therefore, distance travelled by both with the speed of 2 mph one way will be,

Distance = 3.5t [Here, t = time ]

Speed of both while coming back = 2 mph

And the time taken = t + (1 hour 30 minutes)

= (t + 1.5) hours

Therefore, distance travelled while coming back = Speed × Time

= 2(t + 1.5)

Since, length of the route is same both ways,

3.5t = 2(t + 1.5)

3.5t = 2t + 3

3.5t - 2t = 3

1.5t = 3

t = 2 hours

Now substitute the value of t in the expression to get the distance of the route,

Distance = 3.5t

= 3.5 × 2

= 7 miles

Therefore, route was 7 miles long.

Learn more,

brainly.com/question/1955818

7 0

2 years ago

Read 2 more answers

The temperature falls from 0 degrees to Negative 12 and one-fourth degrees in 3 and one-half hours. Which expression finds the c

ANEK [815]

Answer:

The expression used to find the change in temperature per hour is Algebraic expression

Thus per hour; the temperature falls at the rate of $- 3\dfrac{1}{2}^0$

Step-by-step explanation:

A temperature falls from 0 to $- 12\dfrac{1}{4}$ in $3\dfrac{1}{2} \ hours$

Which expression finds the change in temperature per hour.

From the above given information;

The initial temperature is 0

The final temperature is $- 12\dfrac{1}{4}$

The change in temperature is $\Delta T = T_2 - T_1$

$\Delta T = -12\dfrac{1}{4} -0$

$\Delta T = -12.25$

Thus;

-12.25 ° = 3.5 hours

To find the change in x° per hour; we have;

x° = 1 hour

The expression used to find the change in temperature per hour is Algebraic expression

From above if we cross multiply ; we have;

(- 12.25° × 1 hour) = (x° × 3.5 hour)

Divide both sides by 3.5 hours; we have:

$\dfrac{-12.25^0*1 }{3.5}=\dfrac{ x^0 *3.5}{3.5}$

x° = - 3.5

x° = $- 3\dfrac{1}{2}$

Thus per hour; the temperature falls at the rate of $- 3\dfrac{1}{2}^0$

8 0

3 years ago