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3 years ago

Can someone help me with my algebra?

Mathematics

1 answer:

SIZIF [17.4K]3 years ago

4 0

Answer:

The top graph

Solutions:

-2

Step-by-step explanation:

The given quadratic function in factored form is

$f(x) = - (x + 2)(x - 2)$

This is a parabola that has x-intercepts at (-2,0) and (2,0)

This parabola opens downward because the leading coefficient is less than 1.

The second function is

$g(x) = 2 |x + 2|$

This is an absolute value function with vertex at (-2,0).

Therefore the graph that shows the solution to f(x)=g(x) is the top graph.

Hence the solution is x=-2,x=0

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Section 5.2 Problem 17:

Elina [12.6K]

This DE has characteristic equation

$4r^2 - 12r + 9r = (2r - 3)^2 = 0$

with a repeated root at r = 3/2. Then the characteristic solution is

$y_c = C_1 e^{\frac32 x} + C_2 x e^{\frac32 x}$

which has derivative

${y_c}' = \dfrac{3C_1}2 e^{\frac32 x} + \dfrac{3C_2}2 x e^{\frac32x} + C_2 e^{\frac32 x}$

Use the given initial conditions to solve for the constants:

$y(0) = 3 \implies 3 = C_1$

$y'(0) = \dfrac52 \implies \dfrac52 = \dfrac{3C_1}2 + C_2 \implies C_2 = -2$

and so the particular solution to the IVP is

$\boxed{y(x) = 3 e^{\frac32 x} - 2 x e^{\frac32 x}}$

8 0

2 years ago

. name four rays shown?

Aliun [14]

The rays shown in the pictur: Ray VX, YZ , XY, ZV..... Plus more!

4 0

2 years ago

John is building a fence around his home currently his fence measures 14 feet on each side but he wants to increase only the wid

nalin [4]

Answer:

The dimensions of rectangular fence are 14 feet and 20 feet.

Step-by-step explanation:

We are given the following in the question:

Length of rectangular fence = 14 feet

Width of fence = (14+x) feet

Area of rectangular field = 280 square feet

Area of rectangular field =

$A= \text{Length}\times \text{Width}$

Putting the values, we get,

$280 = 14(14+x)\\\\14 + x = \dfrac{280}{14}\\\\14 + x = 20\\x =20-14\\x = 6$

Thus, the dimensions of rectangular fence are 14 feet and 20 feet.

7 0

2 years ago

Find the greatest number that will divide 63, 45 and 69 so as to leave the same remainder.

jeka57 [31]

Answer:

Step-by-step explanation:

Let n be unknown divisor and a be the same remainder, then

$63=q_1\cdot n+a\\ \\45=q_2\cdot n+a\\ \\69=q_3\cdot n+a$

Subtract a from all equalities:

$63-a=q_1\cdot n\\ \\45-a=q_2\cdot n\\ \\69-a=q_3\cdot n$

Subtract them:

$63-45=(q_1-q_2)n\Rightarrow 18=(q_1-q_2)n\\ \\69-63=(q_3-q_1)n\Rightarrow 6=(q_3-q_1)n\\ \\69-45=(q_3-q_2)n\Rightarrow 24=(q_3-q_2)n$

The greatest number is 6. When you divide numbers 63, 45, 69 by 6, you'll get remainders 3, 3, 3, respectively.

7 0

2 years ago

96 customers come into the store over 3 days. How many customers came to the store per day?

Minchanka [31]

Answer:

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers