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3 years ago

A student said that since -9 is less than 4, then |-9| is less than |4|. Is the student correct? Explain why or why not.

2 answers:

4 0

No, that is not true. The absolute value is the distance a number is from zero. The distance of -9 to 0 is 9. 9 is not less than 4.

bazaltina [42]3 years ago

3 0

Answer:

No.

Step-by-step explanation:

They are not correct because the "| |" signs mean absolute value. What ever is inside the signs must be positive. So -9 becomes 9 and 9 is greater than 4. So, the student is not correct.

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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

What is the amount of a $4,000.00 annuity due at 12 percent compounded semiannually for 3 years?

Dmitriy789 [7]

Answer:

$ 5674.076

Step-by-step explanation:

The question is on compound interest

The formulae = A= P(1+ r/n) ^nt .......where P is the principal amount, r is the rate of interest in decimal, n is number of compoundings per year and t is the total number of years.

Given; P= $4,000.00 , r=12/100=0.12, n=2 and t=3

Substituting values in the equation A= P(1+ r/n) ^nt

A= 4000 ( 1+0.12/2)^2×3

A=4000(1.06)^6

A=$ 5674.08

3 0

3 years ago

(-0.3) ÷ (-0.2)+(-2.56) In whole numbers with steps please

Valentin [98]

Answer:

-1 to the nearest whole number.

Step-by-step explanation:

(-0.3) ÷ (-0.2)+(-2.56)

Order of operations - the division is done first:

= 1.5 = (-2.56)

= 1.5 - 2.56

= -1.06.

6 0

3 years ago

At what points will Al be producing the most equal amounts of sandwiches and salads?

Neporo4naja [7]

Answer: D, Y, X

Step-by-step explanation:

The (salad, sandwich) coordinates are as follows:

A: (0, 10)

B: (1, 8)

C: (2, 6)

D: (3, 4) MOST EQUAL AMOUNTS

E: (4, 2)

F: (5, 0)

X: (4, 8) OUTSIDE OF THE PRODUCTION LINE

Y: (1, 3) UNDER THE PRODUCTION LINE

8 0

3 years ago

Read 2 more answers

Circle X is shown in the diagram.

GaryK [48]

Answer:

m<1 = 1/2(a+b)

Step-by-step explanation:

First, you have to add the two different side angles and then divide by two. I just took my quiz and got this.

7 0

3 years ago