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3 years ago

Solve the equation: 3y - 7 = 5y + 21? Question 1 options: -20 -14 -7/2 14

Mathematics

2 answers:

GrogVix [38]3 years ago

7 0

Y=-14 first subtract 3y to get -7=2y+21then subtract 21 to get -28=2y then divide 2

Paraphin [41]3 years ago

3 0

3y-7=5y+21
+7. +7
3y=5y+28
-5y -5y
-2y=28
Y= -14

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Pls hurry! Will make brainliest!! What is the formula that relates circumference and diameter?

Westkost [7]

Answer:

Circumference = πd

where d = diameter

Step-by-step explanation:

When using this formula you don't need to multiply by 2 like you do when using the radius because the diameter is twice the radius of a circle.

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3 years ago

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A student desired to invest $1,540 into an investment at 9% compounded semiannually for 6 years. With all else equal, what is th

irga5000 [103]

Answer:

The future value of this initial investment after the six year period is $2611.6552

Step-by-step explanation:

Consider the provided information.

A student desired to invest $1,540 into an investment at 9% compounded semiannually for 6 years.

Future value of an investment: $FV=P(1+r)^n$

Where Fv is the future value, p is the present value, r is the rate and n is the number of compounding periods.

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Therefore, the value of r is: $r=\frac{0.09}{2}=0.045$

Number of periods are: 2 × 6 = 12

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3 years ago

What is the completely factored form of f(x)=x3+5x2+4x−6?

Gre4nikov [31]

$f(x)=x^3+5x^2+4x-6$
$f(-3)=(-3)^3+5(-3)^2+4(-3)-6=0\implies x+3\text{ is a factor of }f(x)$

Synthetic division yields

-3 | 1   5   4   -6
.    |      -3 -6    6
- - - - - - - - - - - - -
.    | 1   2 -2    0

which translates to

$\dfrac{x^3+5x^2+4x-6}{x+3}=x^2+2x-2$

with remainder 0. Now by the quadratic formula,

$x^2+2x-2=0\implies x=\dfrac{-2\pm\sqrt{2^2-4(1)(-2)}}2=-1\pm\sqrt3$

and so

$f(x)=x^3+5x^2+4x-6=(x+3)(x-(-1+\sqrt3))(x-(-1-\sqrt3))$

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3 years ago

A market research team compiled the following discrete probability distribution, where X represents the number of automobiles ow

rodikova [14]

Answer:

The standard deviation of X is 0.7

Step-by-step explanation:

We are given the following distribution:

x: 0 1 2 3

P(x): 0.3 0.5 0.2 0.4

We have to find the standard deviation of X.

Formula:

$E(x) = \displaystyle\sum x_iP(x_i)\\\\E(x) =0(0.3) + 1(0.5) + 2(0.2) + 3(0.4)\\\\E(x) = 2.1\\\\E(x^2) = \displaystyle\sum x_i^2P(x_i)\\\\E(x^2) =0(0.3) + 1(0.5) + 4(0.2) + 9(0.4)\\\\E(x^2) = 4.9\\\\Var(x) = E(x^2) - (E(x))^2 = 4.9-(2.1)^2 = 0.49\\\\\sigma(x) = \sqrt{Var(x)} =\sqrt{0.49} = 0.7$

Thus, the standard deviation of X is 0.7

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3 years ago

Given f(x) = x ^ 2 - 6x + 8 and g(x) = x + 2 solve f(x) = g(x) . Use the tables below to help you, but please explain how you ca

Travka [436]

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = x² - 6x + 8 and g(x) = x + 2

To solve f(x) = g(x), equate the right sides, that is

x² - 6x + 8 = x + 2 ← subtract x + 2 from both sides

x² - 7x + 6 = 0 ← in standard form

(x - 1)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 6 = 0 ⇒ x = 6

These solutions can be verified from the tables, that is

f(x) = g(x) = 3 ← when x = 1

f(x) = g(x) = 8 ← when x = 6

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3 years ago