The width of a room is 7 feet, and the area of the room is 77 square feet. Find the room's length.

If GF is a midsegment of CDE, find CD. A. 3.4 B. 6.8 C. 13.6 D. 14

bogdanovich [222]

Answer:

C

Step-by-step explanation:

Triangle CGF and triangle CED are similar. Hence, the ratio of their corresponding sides are equal. Thus we can write:

$\frac{5x+4}{2x+3}=\frac{CD}{3x+0.8}$

We can now cross multiply and solve for CD:

$\frac{5x+4}{2x+3}=\frac{CD}{3x+0.8}\\(5x+4)(3x+0.8)=(2x+3)(CD)\\15x^2+4x+12x+3.2=(2x+3)(CD)\\15x^2+16x+3.2=(2x+3)(CD)\\CD=\frac{15x^2+16x+3.2}{2x+3}$

Since GF is a midsegment of CDE, CD is double of CF. So we can write:

$CD=2CF\\\frac{15x^2+16x+3.2}{2x+3}=2(3x+0.8)\\\frac{15x^2+16x+3.2}{2x+3}=6x+1.6\\15x^2+16x+3.2=(6x+1.6)(2x+3)\\15x^2+16x+3.2=12x^2+18x+3.2x+4.8\\15x^2+16x+3.2=12x^2+21.2x+4.8\\3x^2-5.2x-1.6=0$

By using quadratic formula $\frac{-b+-\sqrt{b^2-4ac} }{2a}$ and with a=3, b= -5.2, and c= -1.6, we find the value of x to be:

$\frac{5.2+-\sqrt{(-5.2)^2-4(3)(-1.6)} }{2(3)}=2$

Since the expression for CD is $\frac{15x^2+16x+3.2}{2x+3}$ , we plug in $x=2$ into this expression to find value of CD:

$\frac{15(2)^2+16(2)+3.2}{2(2)+3}=13.6$

The correct answer is C

6 0

3 years ago

Read 2 more answers

A church building fund has invested some money in two ways: part of the money at 7% interest and four times as much at 11%. Find

aliya0001 [1]

Answer: he invested $15000 in part 1 and $60000 in part 2

Step-by-step explanation:

Let x represent the amount of money invested in part one.

Let 4x represent the amount of money invested in part 2 .

Total amount of money invested in part 1 and part 2 is

x + 4x = 5x

The formula for simple interest is expressed as

I = PRT/100

Where

P is the principal or initial amount.

T is the duration in years

R is the number rate.

For part 1

R = 7%

T = 1 year

P = x

I = (x × 7 × 1)/100 = 0.07x

For part 2,

R = 11%

T = 1 year

P = 4x

I = (4x × 11 × 1)/100 = 0.44x

if the total annual income from interest is 7650. This means that

0.44x + 0.07x = 7650 - - - - - - - -2

0.51x = 7650

x = 7650/0.51

x = 15000

Amount invested in part 1 is $15000

Amount invested in part 2 is 4×15000 = $60000

4 0

3 years ago

In a classic Conan Doyle story, Sherlock Holmes solves a crime mystery by recognizing that a guard dog didn't bark. Therefore, t

ohaa [14]

Answer:

G. Modus tollens

Step-by-step explanation:

This question used the inference called modus tollens.

Modus tollens is a a valid form of argument that is of this form below:

If S, then T

if not S, then not T.

S = dog doesn't know perpetrator

Not S = dog knows who the perpetrator is

T = the dog barked

Not T = the dog did not bark.

So if we put this into the statement in bold letters, we would have:

The dog doesn't know perpetrator, so it barked.

And,

The dog didn't bark, so it knows the perpetrator.

3 0

3 years ago

Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the g

Ede4ka [16]

Answer:

y=-3x-13

Step-by-step explanation:

Plug in the -2 and -4 for the y and x. The slope is the same

1) -4 = -3 (-3)+b

2) -4=9+b

3) -4-9=b

4) -13=b

The equation is y=-3x-13

5 0

3 years ago

Read 2 more answers

Colleen is searching for online air tickets to weeks ago the cost to fly from Orlando to Denver was $300 now the cost is $375 wh

rodikova [14]

Answer:

7.69% (round if need be)

Step-by-step explanation:

325. 25 times 13 is 325. 12/13 represents the original 300. 1/13 represents the decimal that changed. Multiply by 100 to get the percentage

3 0

3 years ago