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2 years ago

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If the quantity 4 times x times y cubed plus 8 times x squared times y to the fifth power all over 2 times x times y squared is

completely simplified to 2xayb + 4xcyd, where a, b, c, and d represent integer exponents, what is the value of a? _______

1 answer:

MA_775_DIABLO [31]2 years ago

8 0

$\dfrac{4xy^3 + 8x^2y^5 }{2xy^2}$

$= \dfrac{4xy^3(1+2xy^2)}{2xy}$

$= 2y^2(1 + 2xy^2)$

$= 2y^2 + 4xy^4$

Answer: a = 1, b 2, c = 1, d = 4

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Which products result in a perfect square trinomial? Select three options.

Kazeer [188]

Answer:

Second option: $(xy+x)(xy+x)$

Third option: $(2x-3)(-3+2x)$

Fifth option: $(4y^2+25)(25+4y^2)$

Step-by-step explanation:

By definition, a perfect square trinomial can be obtained by squaring binomials.

Then:

$(a+b)^2=(a+b)(a+b)=a^2+2ab+b^2\\\\(a-b)^2=(a-b)(a-b)=a^2-2ab+b^2$

Knowing this, to obtain a perfect square trinomial, the binomials that you multiply must be equals.

Therefore, the products result in a perfect square trinomial are:

$(xy+x)(xy+x)=(xy+x)^2=(xy)^2+2(xy)(x)+x^2=x^2y^2+2x^2y+x^2$

$(2x-3)(-3+2x)=(2x-3)^2=(2x)^2-2(2x)(3)+3^2=4x^2-12x+9$

$(4y^2+25)(25+4y^2)=(4y^2+25)^2=(4y^2)^2+2(4y^2)(25)+25^2=16y^4+200y^2+625$

8 0

2 years ago

Read 2 more answers

Find the product. (a2)(2a3)(a2 – 8a + 9) 2a7 – 16a6 + 18a5 2a7 – 16a6 – 18a5 2a8 – 16a7 + 18a6 2a12 – 16a7 + 18a6 consider the d

Fofino [41]

Answer: $2x^7 -16a^6 +18a^5$

Step-by-step explanation: Given expression $(a^2)(2a^3)(a^2-8a + 9)$ .

The first factor $(a^2)$ has a degree of : 2 because power of a is 2.

The second factor $(2a^3)$ has a degree of : 3 because power of a is 3.

The third factor $(a^2-8a + 9)$ has a degree of : 2 because highest power of a is 2.

Let us multiply them now:

$(a^2)(2a^3)(a^2-8a + 9).$

First we would multiply $(a^2)(2a^3)$ .

According to product rule of exponents, we would add the powers of a.

Therefore,

$(a^2)(2a^3) = 2a^{2+3}= 2a^5$

Now, we need to distribute $2a^5$ over $(a^2-8a + 9)$

Therefore,

$(2a^5)(a^2-8a + 9)= 2a^{5+2} -16a^{5+1}+18a^5$

= $2x^7 -16a^6 +18a^5$

Highest power of resulting polynomial $2x^7 -16a^6 +18a^5$ is 7.

Therefore, The product has a degree of 7.

5 0

2 years ago

Read 2 more answers

The function f(theta) and g(theta) are sine functions where f(0) = g(0) = 0. The amplitude of f(theta) is twice the amplitude of

lana66690 [7]

Because the values of both functions is 0 at ∅ = 0, both have an equilibrium position of 0.
Next, we can use the given value of f(∅) to find the amplitude:
4 = Asin(π/4)
4 = A(√2 / 2)
A = 8 / √2
We halve this amplitude to find the amplitude of g(∅):
A = 4 / √2
The period is 2π/2 = π

g(∅) = 4sin(∅/2) / √2

6 0

2 years ago

Kyle works at a donut factory, where a 10-oz cup of coffee costs 95cents, a 14-oz cup costs $1.15, and a 20-oz cup costs

lianna [129]

Answer:

10Oz = 7 , 14Oz = 16, 20 OZ = 6

Step-by-step explanation:

There three equations that can be made here based on given data

Let number of 10 Oz cup be x

Let number of 14 Oz cup be y

Let number of 20 Oz cube be z

we can see that

x+y+z=29 ----- (i)

.95x + 1.15y + 1.5z = 34.05 ---- (ii)

10x+ 14y + 20z = 414 ---- (iiI)

We can solve these equations together to get the value of x and y and z (Done through calculator 3 variable equation function)

x= 7

y=16

z=6

5 0

2 years ago

an employer will do a 50% match on your investment to a 401k retirement plan. If you decide to contribute a monthly amount of $2

faltersainse [42]

Answer:

The amount that should be in the account after 15 years is $95,321.85

Step-by-step explanation:

According to the given data, we have the following:

monthly amount of $220=R

interest rate is fixed at 2.05%. We require the monthly ineterest rate, hence monthly interest rate= 2.05%/12=0.1708%=0.0017

t=15years×12=180 months

In order to calculate how much should be in the account after 15 years, we would have to use the following formula:

Ap=<u>R(1-(1+i)∧-t)</u>

i

Ap=<u>220(1-(1+0.0017)∧-180)</u>

0.0017

Ap=<u>162,04</u>

0.0017

Ap=$95,321.85

The amount that should be in the account after 15 years is $95,321.85

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6 0

2 years ago