The congruence theorem that can be used to
prove ABAE = ACAD is
SSS.
O ASA.
SAS.
HL.
what is the answer?

Answer:

The length is 7 m

The width is 10 m

Step-by-step explanation:

length = x

width = 2x - 4

length * width = area

It is given that the area is 70 [tex]m^{2}[/tex]

From there

x * (2x - 4) = 70

[tex]2x^{2}[/tex] - 4x = 70

[tex]2x^{2}[/tex] - 4x - 70 = 0

[tex]x^{2}[/tex] - 2x - 35 = 0

Now we have a quadratic equation, which is  a[tex]x^{2}[/tex] + bx + c = 0, where a [tex]\neq[/tex] 0

In this equation a = 1, b = -2 and c = -35

Discriminant (D) formula is b² - 4ac

D = [tex]-2^{2}[/tex]  - 4 * 1 * (-35) = 144 > 0

This discriminant is more than 0, so there are two possible x

Their formulas are  [tex]\frac{- b - \sqrt{D} }{2a}[/tex] and [tex]\frac{- b + \sqrt{D} }{2a}[/tex]

[tex]x_{1}[/tex] =  [tex]\frac{- (-2) - \sqrt{144} }{2}[/tex] = -5 < 0 (the length of the rectangle has to be more than 0, so we don't use this x)

[tex]x_{2}[/tex] = [tex]\frac{- (-2) + \sqrt{144} }{2}[/tex] = 7 > 0 (this one is right)

Calculating the dimensions

length = x = 7 (m)

width = 2x - 4 = 2 * 7 - 4 = 10 (m)

Answer:

K would equal to:

K= 50

Hope that helps! :)

Step-by-step explanation:

$0.0972

I think.

Um this is to make it long enough to post. lol

Answer:

Approximately $0.10 per ounce

Step-by-step explanation:

Hi! :) I'm assuming this problem is asking for the price per ounce? If not, I apologize.

So, in order to determine the price of cereal per ounce we would simply divide $3.50 by 36 to find the cost per ounce.

$3.50 / 36 = approximately $0.09722222 which we can round up to $0.10.

Hope this helps!

Answer: 378 the second option

Step-by-step explanation:

Answer:

378

Step-by-step explanation:

Multiply 9 and 12 then divide by 2 to get the area of the triangle then multiple by 7 to get the volume

Answer:

Step-by-step explanation:

If f(x)=x+1 and g(x)=2x then

g(f(x))=2(x+1)

g(f(x))=2x+2

Answer:

Student B's score has a greater variation from the mean than student A's score

Step-by-step explanation:

Student A : standard deviation = 5.4

Student B : standard deviation = 10.6

The standard deviation is used to measure the degree of variability of a measured value from the mean or average value of the set. The higher the value of standard deviation, the greater the variabilityabiut the mean. Hence for the question given above, Student B's score varies greatly from the mean Than student A's score.

Answer:

Step-by-step explanation:

Given the following values a=−15 and b=−5.

We are to find a/b

a/b = -15/-5

a/b = 15/3

a/b = 5*3/5*1

a/b = 5/5 * 3

a/b = 1*3

a/b = 3

Hence a divided b will be 3

Answer:

D because non of them work lol

Step-by-step explanation:

Hope this Helped

Answer:

C: 191.

Step-by-step explanation:

The total area of this is a little less than 15 x (3+4+10) = 15 x 17 = 255.

So then we subtract that by 36, which is the rectangle that is missing from the shape. So 255-36 = 219.

So now we have to guess. The triangle seems a little small, so it has to be the largest option, which is C: 191.

Answer:

The numbers are 20 and 45

Step-by-step explanation:

Let the two numbers be a and b

The ratio of the two is 4:9

That means;

a/b = 4/9

9a = 4b •••••(i)

secondly;

Subtracting 5 from each gives a ratio of 3:8

(a-5)/(b-5) = 3/8

8(a-5) = 3(b-5)

8a - 40 = 3b - 15

3b - 15 + 40 = 8a

3b + 25 = 8a

a = (3b + 25)/8 •••(ii)

Insert this into 1

9(3b + 25)/8 = 4b

27b + 225 = 32b

32b - 27b = 225

5b = 225

b = 225/5

b = 45

From i;

9a = 4b

9a = 4 * 45

a = 4 * 45/9

a = 20

Answer:

27

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find out - 'e'

Given,

90 % of e = 30

[tex] = > \frac{90}{100} \times e = 30[/tex]

[tex] = > e = 30 \times \frac{100}{90} [/tex]

[tex] = > e = \frac{100}{3} [/tex]

=> e = 33.3333......

=> e = 33.3 (approx. ) (Ans)

Answer:  

11/9

hope this helped :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

11 / 12 = 0,91 and a periodic 6

3 / 4 = 0,75

11 / 12 = 3 / 4 = 0,916 ÷ 0,75

Answer:

Hello!

A parallel line must equal 180 degrees. Thus, 6y plus 120 degrees must equal 180. First, subtract 120 from 180. This gives us 60. To find y, we divide 60 by 60. This gives us 10. So, our answer is y=10. This means that y is being multiplied 6 times to equal 60.

I hope this answer helped you! If it did, please rate it and give it a Thanks so other people can learn from it too!

Have a great day!

Answer:

x is 122

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

[tex]DE=.5*BC=.5*26=13[/tex]

Answer:

no solution

Step-by-step explanation:

when you distribute, the 6x on each side cancel out leaving there to be no solution to the problem. I attached a photo of my work as well.

Answer:

The answer is False meaning it's no solution

Step-by-step explanation:

1. Distribute 3 through the parentheses which will be 6x+12=6x+10

2.Cancel equal terms on both sides of the equation and you will get 12=10 which isn't a true statement.

Answer:

30000

Step-by-step explanation:

when dividing the powers, you subtract them.

Answer:

first you simplify the first part which will be

(15)^2-(18+9)*(6)

225-27*6

225-162

Answer will be 63

I showed my work :)

[tex]s = 50d + 25[/tex]

[tex]55 = 50d + 25[/tex]

[tex]55 - 25 = 50d + 25 - 25[/tex]

[tex]30 = 50d[/tex]

[tex] \frac{30}{50} = \frac{50d}{50} [/tex]

[tex]0.6 = d[/tex]

Your car would slide a distance of 0.6 feet.

Answer:

The variables are: x and y

The coefficients are: 1/4 and 3

The constants are: -23 and 42

Step-by-step explanation:

Given equation:

1/4x + 3y − 23 = 42

The variables are: x and y

The coefficients are: 1/4 and 3

The constants are: -23 and 42

Answer:

2(3x+1)(x+1)

Step-by-step explanation:

First, we factor out the common term, which is 2.

2(3x²+4x+1)

Then, we factor the polynomial inside the parenthesis.

2(3x+1)(x+1)

Answer:

2(3x + 1)(x + 1)

Step-by-step explanation:

Given

6x² + 8x + 2 ← factor out 2 from each term

= 2(3x² + 4x + 1) ← factor the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 3 × 1 = 3 and sum = 4

The factors are + 3 and + 1

Use these factors to split the x- term

3x² + 3x + x + 1 ( factor the first/second and third/fourth terms )

= 3x(x + 1) + 1(x + 1) ← factor out (x + 1) from each term

= (3x + 1)(x + 1) , then

3x² + 4x + 1 = (3x + 1)(x + 1)

and

6x² + 8x + 2 = 2(3x + 1)(x + 1) ← in factored form

Answer:

1/3

Step-by-step explanation:

Answer: 1/3

Step-by-step explanation: