Solve for X and Y

Picture above

Answer:

Domain:  { x ∈ R | x ≠ -2, 3 }

Step-by-step explanation:

[tex]f(x)=\dfrac{(x+2)(x-1)}{(x-3)(x+2)}[/tex]

The domain (x-values) of a rational function is all real numbers of x with the exception of those for which the denominator is 0.   Therefore, to find the values of x that need to be excluded from the domain, equate the denominator to zero and solve for x.

The denominator for the given function is [tex](x - 3)(x + 2)[/tex]

[tex]\implies (x - 3)(x + 2)=0[/tex]

[tex]\implies (x - 3)=0\implies x=3[/tex]

[tex]\implies (x + 2)=0 \implies x=-2[/tex]

There will be a hole at x = -2 and an asymptote at x = 3.

So the values of x that need to be excluded from the domain are:

x = 3 and x = -2

Therefore, the domain of the given rational function is:  { x ∈ R | x ≠ -2, 3 }

Answer:

50%.

Step-by-step explanation:

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The numbers which should be placed in the boxes from left to right, when Juanita factor the expression, is 6 and 3 respectively.

The factor of a polynomial is the terms in linear form, which are, when multiplied together, give the original polynomial equation as a result.

Juanita begins to factor an expression as shown.

[tex]x^2+ 3x-18=(x+ \;\;)(x-\;\;)[/tex]

To find the value of blank, we have to factor the left-hand side expression using the split the middle term method as,

[tex]x^2+ 3x-18\\x^2+ 6x-3x-18\\x(x+6)-3(x+6)\\(x+6)(x-3)[/tex]

Hence, the numbers which should be placed in the boxes from left to right, when Juanita factor the expression is 6 and 3 respectively.

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Answer:

okay so the answer is 70°

Step-by-step explanation:

the triangle has two sides equal meaning its a scalene triangle. now bases scalene triangles have two angles equal. hence sum of angles in the triangle sum up to 180° please. rate. me brainliest. if I'm. right

[tex]55 + 55 + x = 180 \\ 110 + x = 180 \\ x = 180 - 110 \\ x = 70degrees[/tex]

Answer:

3,295.4

Step-by-step explanation:

to the nearest tenth is 3,295.4

Ohhh, interest problems. I haven't done an equation like this in a long time, but I will attempt.

I would say that the answer is the 2nd option. The equation is i = (5200)(0.06)(2.5).

The traditional interest formula is I = (P)(R)(N).

P = the original amount of money given

R = interest rate

N = the amount of time

I hope this answers your question (and that I understood the question correctly!).

-Toremi

Answer: 44.85 in decimal and 44 Rem 52

Step-by-step explanation: Check my file for long calculation. You can stop when the remainder is 52 Or continue to divide further with decimal

Step by Step Explanation:

Here, to find the slope of line passing through two points x₁,x₁ and y₁,y₂ is given by:-

[tex]\sf m=\frac{y_2 - y_1}{x_2 - x_1} [/tex]

where,

x₁ = 2

x₂ = 9

y₁ = 5

y₂ = 8

Therefore putting the values , we get

[tex] \sf \: m=\frac{y_2 - y_1}{x_2 - x_1} \\ \\ : \longrightarrow \: \frac{8 - 5}{9 - 2} \\ \\ : \longrightarrow \: \frac{3}{7} [/tex]

Hence, the slope of line passes through the points (2, 5) and (9, 8) is 3/7.

The amount of each monthly installment is $1,294 and the hire purchase of the car​ is: $4,158.

a.  Monthly installment

2 1/2 years=30 months

First step

Amount payable=[49,500×(1-.30)] /30 months

Amount payable=(49,500×.70)/30 months

Amount payable=$34,650/30 months

Amount payable=$1,155

Second step

Amount of monthly installment=[$1,155×(1+0.12)

Amount of monthly installment=$1,155×1.12

Amount of monthly installment=$1,293.6

Amount of monthly installment=$1,294 (Approximately)

b. Hire purchase

Hire purchase=$1,155×.12×30 months

Hire purchase=$4,158

Therefore the amount of each monthly installment is $1,294 and the hire purchase of the car​ is: $4,158.

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The decimal equivalent of 7 half’s is the number in decimal form

The exact decimal equivalent of 7 half’s is 3.5

A decimal number is a number represented by an integer and a fractional part

The number is given as:

7 halves

Express as product

7 * 1/2

Evaluate the product

3.5

Hence, the exact decimal equivalent of 7 half’s is 3.5

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5 red, 4 yellow, 9 blue, 2 pink, 4 purple

5 + 4 + 9 + 2 + 4 = 24 people

Calculate persons of each color

Total:&

Answer:

500

Step-by-step explanation:

let's say charlie sends x messages per month

he spends $50 + 0.05 for each x (message), which comes out to less than or equal to $75.

as an equation, this is

50 + 0.05 x ≤ 75

subtract both sides by 50 to isolate the variable and its coefficient

0.05 x ≤ 25

multiply both sides by 1/0.05 to isolate x

x ≤ 500

the maximum is therefore x = 500 messages

[tex]~~~~\sec\left(y+\dfrac{\pi}2 \right) = -2\\\\\\\implies \left[\cos \left( y+ \dfrac{\pi}2 \right) \right]^{-1} = -2\\\\\\\implies \left( \cos y \cos \dfrac{\pi}2 -\sin y \sin \dfrac{\pi}2 \right)^{-1} =-2\\\\\\\implies \left(0- \sin y \right)^{-1} =-2\\\\\\\implies \left(-\sin y \right)^{-1} = -2\\\\\\\implies \sin y = \dfrac 12\\\\\\\implies y = n\pi + (-1)^{n} \dfrac{\pi}6\\\\\text{In the interval, }~(0,\pi)\\\\\\y= \dfrac{\pi}6, ~\dfrac{5\pi}6[/tex]

Answer:

For B it is A92B but for a

Step-by-step explanation:

I got it right on my test!

Answer:

Answer:

1900

Step-by-step explanation:

i took the est

Answer:

Step-by-step explanation:

The bodybuilder gains 1.5 each week for 5 weeks.

If the bodybuilder gains 1.5 for 5 weeks, how many pounds did he gain?

1.5 * 5 = 7.5

Answer:

D. Neither A not B is true.

Step-by-step explanation:

The solutions of the equations are none among the given answers..So, it's neither a not b.

You have marked the right option:D

Hope it helps:)

Answer: B, Randomly select 6 graduate students and 24 undergrad students for the survey.

Step-by-step explanation: This guarantees that each type is proportionately represented in the survey.

Not A because it risks too many or too few graduate students. It is not C because again, it risks too many or too few graduate students. It is not D because each section has about 50 students and the professor only wants 30 in his sample.

Answer:

Step-by-step explanation:

B

In this exercise we have to calculate the value of the water depth, so we have: d=5.5Cos(12t)+6

A periodic wave is a wave with a repeating continuous pattern that determines its wavelength and frequency

Putting together some information given in the statement we have:

Knowing that the formula will be given by an equation similar to:

[tex]d=acos(bt)+k[/tex]

Where:

The amplitude difference is given by:

[tex]8.75-3.25=5.5\ m[/tex]

The mean depth is:

[tex]k=\dfrac{(3.25+8.75)}{2}=6\ m[/tex]

Then writing the equation with;

[tex]d=acos(bt)+k\\\\d=5.5cos(12t)+6[/tex]

Hence the value of water depth will be d=5.5Cos(12t)+6

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Answer:

I cannot answer this question because it is not complete. Please use complete sentences and questions.

The quadratic equation which matches given solution is x² + 3x + 3 = 0. Then the correct option is C.

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

We know that the formula

[tex]\rm x = \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

The solutions are given below.

[tex]\rm x = \dfrac{-3 \pm \sqrt3 \iota }{2}[/tex]

Then

1)  2x² + 6x + 9 = 0, the zeroes of the equation will be

[tex]\rm x = \dfrac{-6\pm 6\iota}{4}\\\\x = \dfrac{-3\pm 3 \iota}{2}[/tex]

2)  x² + 3x + 12 = 0, the zeroes of the equation will be

[tex]\rm x = \dfrac{-3\pm \sqrt{39}\iota}{2}[/tex]

3)  x² + 3x + 3 = 0, the zeroes of the equation will be

[tex]\rm x = \dfrac{-3\pm \sqrt3\iota}{2}[/tex]

4)  2x² + 6x + 3 = 0, the zeroes of the equation will be

[tex]\rm x = \dfrac{-6\pm 2\sqrt{3}}{4}\\\\x = \dfrac{-3\pm \sqrt3 }{2}[/tex]

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The composite figure includes a rectangle and trapezoid

The area of the composite figure is 810.5cm².

From the complete question, we have the following parameters:

Shapes: Rectangle and trapezoid

The area of the rectangle is:

Area = Length × Width

So, we have:

Area = 15 × 23

Area  = 345cm²

The area of the trapezium

Area = 0.5 × (a + b) ×h

So, we have:

Area = 0.5 × (15 + 34) × 19

Area = 0.5 × 49 × 19

Area = 465.5cm²

Add both areas to calculate the area of the composite figure

Total area = 345cm² + 465.5cm²

Total area  = 810.5cm²

Hence, the area of the composite figure is 810.5cm².

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Answer:

484 meters squared

Step-by-step explanation:

Area is Length times Width.

You're dealing with a square meaning all sides are equal.

You simply need to do 22m x 22m = 484m squared

The volume of any shape is the amount of space in it.

The volume of the cylinder is 1570 square units

The question is incomplete. Assume the following parameters

Shape = Cylinder

Radius, r = 10

Height, h = 5.

The volume of a cylinder is:

V = πr^2h

So, we have:

V = 3.14 * 10^2 * 5

Evaluate the product

V = 1570

Using the assumed values, the volume of the cylinder is 1570 square units

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Answer:

The answer is given in the picture

Step-by-step explanation:

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