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3 years ago

1. Write the ratio in the simplest form. (1 point) 45:15 9:3 3:1 1:3 4:1

Mathematics

1 answer:

TEA [102]3 years ago

7 0

Answer:

45:15=9:3=3:1

9:3=3:1

3:1 stays the same.

1:3 stays the same.

4:1 stays the same.

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Find the polynomial of minimum degree, with real coefficients, zeros at

drek231 [11]

Answer:

$\huge\boxed{p(x)=4x^3-20x^2+4x+300}$

Step-by-step explanation:

$\text{If}\ x=4\pm3i\ \text{and}\ x=-3\ \text{are the zeros of a polynomial, then it has a form:}\\\\p(x)=\bigg(x-(4-3i)\bigg)\bigg(x-(4+3i)\bigg)\bigg(x-(-3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x-4+3i)(x-4-3i)(x+3)\bigg(r(x)\bigg)\\\\p(x)=\underbrace{\bigg((x-4)+3i\bigg)\bigg((x-4)-3i\bigg)}_{\text{use}\ (a+b)(a-b)=a^2-b^2}(x+3)\bigg(r(x)\bigg)\\\\p(x)=\bigg((x-4)^2-(3i)^2\bigg)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2$

$p(x)=(x^2-2(x)(4)+4^2-3^2i^2)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ i^2=-1\\\\p(x)=(x^2-8x+16-9(-1))(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+16+9)(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+25)(x+3)\bigg(r(x)\bigg)\qquad\text{use FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\p(x)=\bigg((x^2)(x)+(x^2)(3)+(-8x)(x)+(-8x)(3)+(25)(x)+(25)(3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x^3+3x^2-8x^2-24x+25x+75)\bigg(r(x)\bigg)\qquad\text{combine like terms}\\\\p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)$

$\text{The y-intercept is at 300}.\\\\\text{For}\ w(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0\\\\\text{y-intercept is}\ a_0\\\\\text{Therefore for}\ p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)\\\\\text{y-intercet is}\ 75\bigg(r(x)\bigg)\\\\75\bigg(r(x)\bigg)=300\qquad\text{divide both sides by 75}\\\\r(x)=4\\\\\text{Finally:}\\\\p(x)=(x^3-5x^2+x+75)(4)\qquad\text{use the distributive property}\\\\p(x)=(x^3)(4)+(-5x^2)(4)+(x)(4)+(75)(4)\\\\p(x)=4x^3-20x^2+4x+300$

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4 years ago

Customers arrive at a bank at a rate of 12/hour. It takes the clerk on average 4 minutes to help each customer. a. What is the a

-Dominant- [34]

Answer:

Step-by-step explanation:12 customers per hour..

4minutes per customer..

Time customers must wait= 12customers ×4minutes =48 minutes.. The clerk use 48minutes to attend to 12customers in one hour leaving him with 12spare minutes.

(B)since the clerk has 12 minute to spare it means each customer have a minute to wait before getting attention..

(C)number of customers waiting =12/2=6customers...

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3 years ago

There are 7/8 kilograms of salt in the kitchen. Mrs. Jackson used 2/15 of salt when preparing dinner . How much salt did she use

neonofarm [45]

so since Mrs Jackson used 2/15 of 7/8, the amount she used is simply their product.

$\bf \stackrel{\textit{how much is }\frac{2}{15}\textit{ of }\frac{7}{8}?}{\cfrac{7}{8}\cdot \cfrac{2}{15}}\implies \cfrac{7}{15}\cdot \cfrac{2}{8}\implies \cfrac{7}{15}\cdot \cfrac{1}{4}\implies \cfrac{7}{60}$

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3 years ago

-3x+2=-7 What does x equal? And how do you solve it?

Liono4ka [1.6K]

Answer:

x = 3

Step-by-step explanation:

Given

- 3x + 2 = - 7 ( subtract 2 from both sides )

- 3x = - 9 ( divide both sides by - 3 )

x = 3

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3 years ago

What is <br> g(x)= 7/8(7) - 1/2

laila [671]

Answer: g=3/56

Hope this helps you

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3 years ago