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3 years ago

Anya says, 62,996 rounds to 63,000 select all the places to which she could have rounded the number

1 answer:

6 0

<span>She could round this number may it be in the tens and hundreds place. When rounding off a number, one should consider the place of the digit he or she would like to round it off to. One should consider what number is placed at the right of the rounding number. If the number is below 5, then that digit should remain and the rest of the digits to the right should be turned to 0s. </span>

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What are the solutions to the following system?

bija089 [108]

The solutions are $(\sqrt{2},-1) \text { and }(-\sqrt{2},-1)$ .

Solution:

Given equation:

$-2 x^{2}+y=-5$

Add $2 x^{2}$ on both sides.

$-2 x^{2}+y+2 x^{2}=-5+2 x^{2}$

$y=-5+2 x^{2}$ -------- (1)

$y=-3 x^{2}+5$ (given) -------- (2)

Equate (1) and (2).

$-5+2 x^{2}=-3 x^{2}+5$

Add $3 x^{2}$ on both sides.

$-5+2 x^{2}+3 x^{2}=-3 x^{2}+5 +3 x^{2}$

$-5+5x^{2}=5$

Add 5 on both sides.

$-5+5x^{2}+5=5+5$

$5x^{2}=10$

Divide by 5 on both sides, we get

$x^{2}=2$

Taking square root on both sides, we get

$x=\sqrt{2}, x=-\sqrt{2}$

Substitute $x=\sqrt{2}$ in (1).

$y=-5+2(\sqrt{2})^2$

$y=-5+4$

$y=-1$

Substitute $x=-\sqrt{2}$ in (1).

$y=-5+2(-\sqrt{2})^2$

$y=-5+4$

$y=-1$

Therefore the solutions are $(\sqrt{2},-1) \text { and }(-\sqrt{2},-1)$ .

Option C is the correct answer.

6 0

3 years ago

How many of the first 1000 positive integers are multiples of both 4 and 5 but not 6 ?

castortr0y [4]

Let's begin by breaking each number down into its prime factors: 4 = 2 x 2 5 = 5 6 = 2 x 3 Next, let's determine the Lowest Common Multiple (LCM) of the numbers 4, 5, and 6 by multiplying all common and unique prime factors of each number: common prime factors: 2 unique prime factors: 2,5,3 LCM = 2 x 2 x 5 x 3 = 60 Next, let's determine how many times 60 goes into 10,000 (excluding remainder): 10,000/60 = 166 and 2/3 Multiples of ALL 3 numbers (4,5,6) = 166 Next, let's determine the Lowest Common Multiple (LCM) of the numbers 4 and 5 by multiplying all common and unique prime factors of each number: common prime factors: none
unique prime factors: 2 x 2 x 5
LCM = 2 x 2 x 5 = 20 Next, let's determine how many times 20 goes into 10,000:
10,000/20 = 500
Multiples of BOTH numbers (4 and 5) = 500 Finally, let's subtract the multiples of ALL three numbers (4,5,6) from the multiples of BOTH numbers (4 and 5) to get our answer: Multiples of ONLY numbers 4 and 5 (excluding 6): 500 - 166 = <span>334</span>

5 0

3 years ago

A uniform bar of length l and weight w is attached to a wall with a hinge that exerts a horizontal force hx and a vertical force

maria [59]

The answer is Hx = ½ Wsin θ cos θ
The explanation for this is:
Analyzing the torques on the bar, with the hinge at the axis of rotation, the formula would be: ∑T = LT – (L/2 sin θ) W = 0
So, T = 1/2 W sin θ. Analyzing the force on the bar, we have: ∑fx = Hx – T cos θ = 0Then put T into the equation, we get:∑T = LT – (L/2 sin θ) W = 0

4 0

3 years ago

Hi I’ll appreciate it if you help me!

dexar [7]

The answer would be 30in.
Reasoning: if the two figures are proportional, you would set it up in a proportion. It would be 36/x=12/10. Then cross multiply, so it would be 12x and 36(10). Afterwords you’ll have 12x=360, then divide both sides by 12 and you’ll end up with 30.

4 0

3 years ago

20 points! Thank you

julsineya [31]

$HEY THERE !!$

Factorization of the trinomial
3x^3 +6x^2 -24x
will be :-

taking common 3x

=>3x(x^2+2x-12)......1️⃣

now the factorization of (x^2+2x-12) will be
(x-2)(x+4).......2️⃣

so your answer from 1️⃣and 2️⃣ is (A) 3x(x-2)(x+4).

Hope it helped you.

3 0

3 years ago

Read 2 more answers