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3 years ago

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The sum of two numbers is 40. If the larger is divided by the smaller, the quotient is 5 and the remainder is 4. Find the number

.

1 answer:

solmaris [256]3 years ago

6 0

Answer:

numbers are 33 and 7

Step-by-step explanation:

x+y=40

4y+5+y=40

5y+5=40

5y=35

y=7

x=4y+5=4(7)+5=28+5=33

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factor the polynomial completely and SHOW WORK i’ve been on it for the past 30 minutes and I want to cry 24x^3-78x^2+45x NO LINK

Svetllana [295]

9514 1404 393

Answer:

3(x)(4x -3)(2x -5)

Step-by-step explanation:

First of all, recognize that all coefficients are multiples of 3, and all terms have x as a common factor. This means your first factorization is ...

(3x)(8x^2 -26x +15)

Now, you can use the "X-method" or similar to factor the quadratic. Start by looking for factors of (8)(15) = 120 that have a total of -26. Both will be negative. Here is a list of the positive factor pairs.

120 = 1·120 = 2·60 = 3·40 = 4·30 = 5·24 = 6·20 = 8·15 = 10·12

The sums of these factor pairs are ...

121, 62, 43, 34, 29, 26, 23, 22

The pair with a sum of 26 is highlighted.

Using this information, you can complete the X-method diagram, or you can use these numbers to rewrite the quadratic x-term to have 2 parts:

8x^2 -20x -6x +15

Now, the quadratic can be factored by grouping:

= (8x^2 -20x) +(-6x +15)

= 4x(2x -5) +3(-2x +5)

Recognizing the sign difference between the parentheses contents, we can factor the quadratic to be ...

= (4x -3)(2x -5) . . . . . note the sign gets attached to the 3

So, the complete factorization of the original expression is ...

24x^3-78x^2+45x = 3(x)(4x -3)(2x -5)

3 0

3 years ago

GIVING BRAINLY JUST ANSWER CORRECTLY !!

Vinil7 [7]

Answer:

b. never

Explanation:

A fraction is always in the form p/q, where q is not 0; or can be converted in that form (in case of mixed fraction).

A number is said to be irrational, if it cannot be expressed in the form p/q, where q is not 0.

5 0

3 years ago

a stack of boards is 24 inches high. Each board is 3/8 of an inch thick. How many boards are in the stack?

meriva

To answer this we need to divide 24 by 3/8.

First we need to convert 24 to a fraction.

$\frac{24}{1}$

When dividing fraction, multiply the first fraction by the reciprocal of the second fraction. (A reciprocal is an upside down fraction)

$\frac{24}{1} * \frac{8}{3} = \frac{192}{3}$ (simplify:) 64

The answer is 64

Hopefully this helps! If you have any more questions or don't understand, feel free to DM me, and I'll get back to you ASAP! :)

4 0

3 years ago

Read 2 more answers

A books thickness in 31 millimeters what is the thickness in centimeters

Natasha2012 [34]

$\bf \begin{array}{ccllll}
cm&mm\\
\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\
1&10\\
x&31
\end{array}\implies \cfrac{1}{x}=\cfrac{10}{31}$

solve for "x"

6 0

3 years ago

Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position

stira [4]

Answer:

$v(t) = (2t+1) \mathbb{i} +3t^2 \mathbb{j} +4t^3 \mathbb{k}$

$r(t) = (t^2+t) \mathbb{i} +(t^3+2) \mathbb{j} +(t^4 - 3) \mathbb{k}$

Step-by-step explanation:

The velocity vector is the integral of the acceleration vector i.e.

$v(t) = \int a(t) dt$

$v(t) = \int (2 \mathbb{i}+6t \mathbb{j} 12t^2 \mathbb{k}) dt$

$v(t) = 2t \mathbb{i}+3t^2 \mathbb{j} 4t^3 \mathbb{k} + C_1$

When $t=0$ , $v(0) = \mathbb{i}$ . Inserting these values in $v(t)$ ,

$C_1= \mathbb{i}$

$v(t) = 2t \mathbb{i}+3t^2 \mathbb{j} 4t^3 \mathbb{k} + \mathbb{i}$

$v(t) = (2t+1) \mathbb{i}+3t^2 \mathbb{j} 4t^3 \mathbb{k}$

The position vector is the integral of the velocity vector i.e.

$r(t) = \int v(t) dt$

$r(t) = \int ((2t+1) \mathbb{i}+3t^2 \mathbb{j} 4t^3 \mathbb{k}) dt$

$r(t) = (t^2+t) \mathbb{i}+t^3 \mathbb{j} t^4 \mathbb{k} + C_2$

When $t=0$ , $r(t) =2\mathbb{j}-3\mathbb{k}$ . Inserting these values in $r(t)$ ,

$C_2=2\mathbb{j}-3\mathbb{k}$

$r(t)= (t^2+t) \mathbb{i}+t^3 \mathbb{j}+ t^4 \mathbb{k} + 2\mathbb{j}-3\mathbb{k}$

$r(t) = (t^2+t) \mathbb{i}+(t^3+2) \mathbb{j}+ (t^4-3) \mathbb{k}$

5 0

4 years ago