Values that can makes an inequality a true statement are called the ____________.

Answers

Answer 1

Answer: Values that can makes an inequality a true statement are called the solution set. It is the set of values that satisfy a given set of equations or inequalities. Hope this answers the question. Have a nice day. Feel free to ask more questions.

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What is the weights maximum displacement? Please help and explain!

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according to the graph, the displacement goes from a maximum position of 14 at time 0.75 to a minimum of -14 at time 2.25 s, hence the maximum displacement is:

14 + 14 = 28 units

14 positive side, 14 negative side.

Does a central angle and its intercepted arc have the same measure?

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Yes my dear. And here is the explanation: The measure of each inscribed angle is exactly half the measure of its intercepted arc. As they have the same intercepted arc,then we can say that they have the same measure.

The angles of a triangle are in the ratio 1 : 4 : 5. Work out the size of the smallest angle?

Answers

Answer:

18°

Step-by-step explanation:

sum the parts of the ratio, 1 + 4 + 5 = 10 parts

The sum of the 3 angles in a triangle = 180° , then

180° ÷ 10 = 18° ← value of 1 part of the ratio

Since 1 is the smallest part of the ratio it represents the smallest angle, thus

smallest angle = 18°

Solve for x
3x+1/14=2x/8

Answers

3x+(1/14)= 2x/8
24x+(4/7)=2x ( i multiplied everything by 8)
22x+4/7=0 ( i subtracted 2x to both sides)
22x= -4/7 ( i subtracted 4/7 to both sides)
x= (-4/7)/ 22
x= -2/77

$3x + (1)/(14) = (2x)/(8)$

First, you multiply everything by 8, so you get:
$8(3x + (1)/(14)) = 8( (2x)/(8))$

Then, you develop, and you get:
$24x + (8)/(14) = 2x$

You simplify $(8)/(14)$ by dividing by 2, and you get:
$24x + (4)/(7)$ = 2x

Then, you put known numbers apart (numbers without x), and unknown numbers apart (numbers with x), which means you move 2x to the other part (and it become -2x), and $(4)/(7)$ to the other part ( and it become $- (4)/(7)$ ), so you get:
$24x - 2x = - (4)/(7)$

you subtract and you get:
$22x = - (4)/(7)$

then, you move 22 to the other part, and since it's a multiplication, it become a division, so you get:
$x = ( - (4)/(7) )/(22)$

As you know, $22 = (22)/(1)$ , and dividing 2 fraction is equal to multiplying the first fraction by the inverse of the second fraction, so you get:
$-(4)/(7) * (1)/(22) = x$

You multiply and you get:
$- (4)/(154) = x$

4 and 154 have a common factor which is 2, so you divide each one by 2, and you get:
$-(4/2)/(154/2) = x$

you divide, and you get:
$-(2)/(77) = x$

So, $x = -(2)/(77)$

Hope this Helps! :D

Which polynomial is prime? 3x3 + 3x2 – 2x – 2 3x3 – 2x2 + 3x – 4 4x3 + 2x2 + 6x + 3 4x3 + 4x2 – 3x – 3

Answers

Answer: $3x^3-2x^2+3x-4$

Step-by-step explanation:

We know that a polynomial is said to be prime if it does not factorize into polynomials.

1. $3x^3+3x^2-2x-2\n=3x^2(x+1)-1(x+1)\n=(x+1)(3x^2-1)$

This is not prime as it can factorize.

2. $3x^3-2x^2+3x-4\n=x^2(3x-2)+1(3x-4)$

$(3x-2)\ and\ (3x-4)$ are not same , thus we cannot factorize the above polynomial.

Therefore this polynomial is prime.

3. $4x^3+2x^2+6^x+3=2x^2(2x+1)+3(2x+1)\n=(2x+1)(2x^2+3)$

This is not prime as it can factorize.

4. $4x^3+4x^2-3x-3\n=4x^2(x+1)-3(x+1)\n=(x+1)(4x^2-3)$

This is not prime as it can factorize.

The correct answer is B. 3x3 – 2x2 + 3x – 4 :D

have a good day!

Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping?x2(4x + 1) – 2(4x + 1)
x2(4x – 1) + 2(4x – 1)
4x2(x + 2) – 1(x + 2)
4x2(x – 2) – 1(x – 2)