Which expression is equivalent to 7a2b + 10a2b2 + 14a2b3?

Answers

Answer 1

Answer: The given expression can be simplified in many ways by grouping like terms. The simplest form is obtained by factoring out a²b which gives us the following expression.

a²b(7 + 10b +14b²)

Answer 2

Answer:

Answer:

a²b(7 + 10b +14b²)

Step-by-step explanation:

$7a^2b + 10a^2b^2 + 14a^2b^3$

To find out equivalent expression we need to factor the given expression

To factor it first we find out GCF(greatest common factor)

7 a^2b -------> 7*a*a*b

10a^2b^2 ----->5*2 * a*a*b*b

14a^2b^3 -------> 7*2 *a*a*b*b*b

To get GCF we look at the factors that are in common

GCF = a*a*b that is a^2b

We factor out GCF a^2b, write a^2b outside and divide all the terms by a^2b

$a^2b(7 +10b +14b^2)$

7+10b+14b^2 cannot be factor . its prime

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Find 3 consecutive numbers where the product of the smaller two numbers in 19 less than the square of the largest number?

Answers

Answer is 5, 6, & 7

x = smallest number
y = x + 1
z = x + 2

(x)(y) = z^2 - 19
(x)(x+1) = (x + 2)^2 - 19
(x^2 + x) = (x^2 + 4x + 4) - 19
x^2 + x = x^2 + 4x + 4 - 19

x^2 term drops out from both sides

x = 4x + -15
15 = 4x - x
15 = 3x
15/3 = x
x = 5
y = x + 1 = 6
z = x + 2 = 7

Confirm by substituting back in for the variables:
(x)(y) = z^2 - 19
(5)(6) = (7)^2 - 19
30 = 49 - 19
30 = 30 [OK]

A moving company had one seven of a ton of a weight to move across town. If they wanted to split it equally amongst 8 trip,how much weight they have on each trip?

Answers

so 1/7 divided by 8

equals to 1/ 56 tons per trip

Miguel’s steps in evaluating an expression are given below. 32 ÷ 2(23 – 4) Step 1: = 32 ÷ 2(8 – 4) Step 2: = 32 ÷ 2(4) Step 3: = 32 ÷ 8 Step 4: = 4 What, if any, was Miguel’s mistake?

Answers

Answer:

its actually c he did a mistake on step 3 i just took the test and got it right

Step-by-step explanation:

Miguel incorrectly multiplied before dividing in step 3

Answer:

C. Miguel incorrectly multiplied before dividing in step 3.

Step-by-step explanation:

look at picture down below

Please Help! Geometry!

Answers

Answer:

x = 109.349

x = 110 (to the nearest tenth)

Step-by-step explanation:

We can solve for "x" using the sine formula.

Sine formula is expressed as:

sinA / a = sinB/b = sinC/c

Where A, B and C are the values of the given angles

a, b, and c are the values of the corresponding length of the sides to each angles of the triangle.

Let's proceed to applying the sine formula.

sin33 / 59.2 = sin73/ x

Let's cross Multiply and solve for "x"

x * sin33° = 59.2 * sin73°

(Punch your calculator)

sin 33° = 0.545

sin 73° = 0.956

Therefore: let's substitute the value of sin33° and sin73°

x * 0.545 = 59.2 * 0.956

x = 59.595 / 0.545

x = 109.349

x = 110 (to the nearest tenth)

Which of the following is a solution of 4x2 = − 9x − 4?

Answers

get all on one side
add 9x+4 both sides
4x^2+9x+4=0
use quadratic formula
in form
ax^2+bx+c=0
x= $\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}$

a=4
b=9
c=4

x= $\frac{-9+/- \sqrt{9^(2)-4(4)(4)} }{2(4)}$
x= $(-9+/- √(81-64) )/(8)$
x= $(-9+/- √(17) )/(8)$
x= $(-9+ √(17) )/(8)$ or $(-9- √(17) )/(8)$

aprox
x=-1.64039 or -0.6096

4 x 2 = − 9x − 4

Multiply 4 and 2. Add 4 to both sides.
8 + 4 = -9x

Divide both sides by -9.
(8 + 4)/-9 = x

Simplify
-12/9 = x

When you add 18 to 1/4 of a number, you get the number itself.

Answers

$(1)/(4)x +18=x \n 18= -(4)/(1) x+x \n 18= (3)/(4) x\n 24= x$

$(1)/(4) x+18=x \ \ \ \ \ /*4 \n x+72=4x \ \ \ \ /-x \n 72=3x \n 3x=72 \ \ \ /:3 \n x=24$

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