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3 years ago

A. the sum of two numbers is 52. One number is three less than quadruple the other number. What are the two numbers?

Mathematics

1 answer:

avanturin [10]3 years ago

3 0

1st number: x

2nd number: 4x - 3

(x) + (4x - 3) = 52

5x - 3 =52

5x = 55

x = 11

2nd number: 4x - 3 = 4(11) - 3 = 44 - 3 = 41

Answer: 11 and 41

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In the given figure △ABC ≅△DEC. Which of the following relations can be proven using CPCTC ?

Serhud [2]

Option B:

$\overline{A B}=\overline{D E}$

Solution:

In the given figure $\triangle A B C \cong \triangle D E C$ .

If two triangles are similar, then their corresponding sides and angles are equal.

By CPCTC, in $\triangle A B C \ \text{and}\ \triangle D E C$ ,

$\overline{AB }=\overline{DE}$ – – – – (1)

$\overline{B C}=\overline{EC}$ – – – – (2)

$\overline{ CA}=\overline{CD}$ – – – – (3)

$\angle ACB=\angle DCE$ – – – – (4)

$\angle ABC=\angle DEC$ – – – – (5)

$\angle BAC=\angle EDC$ – – – – (6)

Option A: $\overline{B C}=\overline{D C}$

By CPCTC proved in equation (2) $\overline{B C}=\overline{EC}$ .

Therefore $\overline{B C}\neq \overline{D C}$ . Option A is false.

Option B: $\overline{A B}=\overline{D E}$

By CPCTC proved in equation (1) $\overline{AB }=\overline{DE}$ .

Therefore Option B is true.

Option C: $\angle A C B=\angle D E C$

By CPCTC proved in equation (4) $\angle ACB=\angle DCE$ .

Therefore $\angle A C B\neq \angle D E C$ . Option C is false.

Option D: $\angle A B C=\angle E D C$

By CPCTC proved in equation (5) $\angle ABC=\angle DEC$ .

Therefore $\angle A B C\neq \angle E D C$ . Option D is false.

Hence Option B is the correct answer.

$\Rightarrow\overline{A B}=\overline{D E}$

5 0

3 years ago

Show how to use the distributive property to find 7 x 1214

Sophie [7]

Answer:8498

Step-by-step explanation:

(7*1000)+(7*200)+(7*10)+(7*4)

7000+1400+70+28

8498

8 0

3 years ago

-(x+3) = 2x-6 what is x

Makovka662 [10]

Answer:

x=1

Step-by-step explanation:

So, first you make sure to multiply the parenthesis by the negative so then it would be,

-x-3=2x-6

Then you add the -3 from the right to the other side

so, -x=2x-3

Then you want all the X variables to one side so you subtract the 2x to both sides.

so, -3x=-3

divide both by -3

x=1

7 0

3 years ago

A scientist conducted an experiment. Due to chemical reaction, the temperature of a compound rose 1/10 degree every 1/4 hour for

klio [65]

Answer:

The rate is $\frac{2}{5}$ degree per hour.

Step-by-step explanation:

Given : A scientist conducted an experiment. Due to chemical reaction, the temperature of a compound rose $\frac{1}{10}$ degree every $\frac{1}{4}$ hour for a limited time.

To find : What was the rate, in degrees per hour that the temperature of the compound rose ?

Solution :

In every $\frac{1}{4}$ hour the temperature of a compound rose $\frac{1}{10}$ degree

To get the rate, in degrees per hour,

In every 1 hour the temperature of a compound rose is

$r=\dfrac{\frac{1}{10}}{\frac{1}{4}}$ degree

$r=\dfrac{4}{10}$ degree/hr

$r=\dfrac{2}{5}$ degree/hr

Therefore, the rate is $\frac{2}{5}$ degree per hour.

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3 years ago

There is 3/4 of a box of cereal remaining. You eat 2/5 of the remaining cereal. What fraction of the box do you eat? Hint: What

Len [333]

Answer:I think it’s 7/20

Step-by-step explanation:

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3 years ago