Answer the questions.

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Work Shown:

[tex]y = \frac{4x+30}{x+5}\\\\y = \frac{4x+20+10}{x+5}\\\\y = \frac{(4x+20)+10}{x+5}\\\\y = \frac{4(x+5)+10}{x+5}\\\\y = \frac{4(x+5)}{x+5}+\frac{10}{x+5}\\\\y = 4+\frac{10}{x+5}\\\\[/tex]

Therefore, a = 10

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As an alternative approach, we could work in reverse like this:

[tex]y = 4+\frac{a}{x+5}\\\\y = 4*\frac{x+5}{x+5}+\frac{a}{x+5}\\\\y = \frac{4(x+5)}{x+5}+\frac{a}{x+5}\\\\y = \frac{4(x+5)+a}{x+5}\\\\y = \frac{4x+20+a}{x+5}\\\\[/tex]

Then notice that the 20+a must be 30, so solving 20+a = 30 leads to a = 10

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As yet another alternative approach (well I suppose it's actually 2 extra approaches) we could use either polynomial long division or synthetic division. Either way, you should end up with a remainder of 10, which corresponds directly to a = 10

Answer:

[tex]p \: \alpha \: \frac{1}{q} \\ p = \frac{k}{q} \\ k \: is \: a \: constant \: of \: proportionality \\ when \: p \: is \: 9.. \: \: q = 16 \\ 9 = \frac{k}{16} \\ k = 144 \\ when \: p \: is \: 18 : \\ 18 = \frac{144}{q} \\ q = \frac{144}{18} \\ q = 8[/tex]

Answer:

Second one

third one

fifth one

last one

Step-by-step explanation:

Based on the x intercepts we can write

a(x+1)(x-5)

where a is some constant

solve for a by plugging in some coordinates

let's plug in (1,-8)

-8=a(1+1)(1-5)

-8= -8a

a=1

therefore the quadratic is (x+1)(x-5)

expand this

x²-4x-5

To find out where something is decreasing/increasing it's easiest to take the first derivative

x²-4x-5= 2x-4

set this equal to 0

2x-4=0

2x=4

x=2

Which means that our two intervals are

(-∞,2)U(2,∞)

plug in any values in the intervals to see whether or not the function is increasing/decreation

Let's plug in 0 for (-∞,2)

2(0)-4

-4

It's negative so it's decreasing on this interval

DO the same thing with the other one

let's plug in x=3

2(3)-4

2

this is positive so it's increasing on this interval

Go back to the critical value of x=2 and plug this into the equation to find the max/min

(2+1)(x-5)= -9

This is a minimum because the cofeccient for the degree is positive

For the limit one notice that we have a positive, even degree which means the end behavior is positive, positive

what this means is as x approaches negative infinity it's infinity

and as x approaches infinity it's infinity

Answer:

[tex]60st \\ = (60 \times 5 \times - 3.7) \\ = - 1110[/tex]

Answer:

-1110

Step-by-step explanation:

given:

s = 5

t = -3.7

to find

60st

=60*s*t

=60*5*(-3.7)

=300*-3.7

=-1110

Answer:

A

Step-by-step explanation:

Answer:

ty

Step-by-step explanation:

mtj

Answer:

No

Step-by-step explanation:

This is because it's part of a whole.  It has to be an integer to be whole.

Answer:

no because Whole numbers include positive integers along with 0 and also  Whole numbers include natural numbers that begin from 1 onwards and also this a negative are not considered as a whole number so its a no

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

i got it right on my test

Answer:

Your solution is (6, -7)

Step-by-step explanation:

4x + 2y = 10

x - y = 13

We want to solve for one variable at a time.

Let's start with x.

x - y = 13

Add y to both sides.

x = 13 + y

Now we have an expression for x.

Plug this into each instance of x in the first equation.

4x + 2y = 10

4(13 + y) + 2y = 10

Distribute the 4 across the parentheses.

52 + 4y + 2y = 10

Combine like terms.

52 + 6y = 10

Subtract 52 form both sides.

6y = -42

Divide both sides by 6.

y = -7

Now that we know y, plug its value back into the expression for x.

x = 13 + y

x = 13 + (-7)

Simplify.

x = 13 - 7

Subtract.

x = 6

Your solution is (6, -7).

Hope this helps!

Answer:

7 is a answer

Step-by-step explanation:

2a+3b

2×2+3×1

4+3

7

hope it helps....

[tex] \sf a = 2,\: b = 1[/tex]

[tex] \sf Q) \:2a + 3b = {?}[/tex]

[tex] \sf \implies 2a + 3b[/tex]

[tex] \sf \implies 2(2) + 3(1)[/tex]

[tex] \sf \implies 4 + 3[/tex]

[tex] \sf \implies 7[/tex] is the required answer.

Answer:

median: 8

mode: 8, 10

mean: 8

The mean will help her predict how much she will walk in week six.

Step-by-step explanation:

First order the numbers:

4, 7, 8, 8, 8, 9, 10, 10

median: 8

mode: 8, 10

mean: 8

Which measure of central tendency will help her predict how much she will walk in week six. The mean will help her predict how much she will walk in week six.

Answer:

me :- mighty assassin-,-

xd

Answer:

log (1/6)

Step-by-step explanation:

Using the property that log a - log b = log(a/b), we get that log 4 - log 24 = log(4/24) = log (1/6)

I hope this helps! :)

Answer:

U got it correct

Step-by-step explanation:

Answer:

I think it's AA because the sum of a triangle is 180 and if you subtract the right angle and the other angle from 180 it gives you the same angle in the other triangle.

Step-by-step explanation:

180-(90+70)=20 The other angle in the first triangle

180-(90+20)=70 The other angle in the second triangle

These angles show that they're similar

Answer:

about 1587

that is the answer to the question

Step-by-step explanation:

I just typed it in a calculator

Answer: D

Step-by-step explanation:

Area is pi x r^2

Diameter is 2r

46.7/2 = 23.35

3 x 23.35^2 =  1635.67 or closest to D

Answer:

180 square inches

Step-by-step explanation:

let separate the figure and form two rectangles

first rectangle

length = 10 in

breadth = 9 in

let's find its area

area =l*b

=10*9

=90 in.^2

second rectangle

length = 15 in.

breadth = 6 in.

area =l*b

=15 *6

=90 in.^2

area of a whole he painted =area of first rectangle + area of second rectangle

=90 + 90 in.^2

=180 in .^2

Answer:

the answer is the alphabet a

Answer:

[tex]\frac{\sqrt{2} }{6}[/tex]

Step-by-step explanation

[tex]\frac{1}{\sqrt{18} } \\\frac{1}{\sqrt{18} } *\frac{\sqrt{18} }{\sqrt{18} } \\\frac{1*\sqrt{18} }{(\sqrt{18} )^2} \\\frac{1\sqrt{18} }{18} \\\frac{3\sqrt{2} }{18} \\\frac{\sqrt{2} }{6}[/tex]

Answer:

B

Step-by-step explanation:

B

Answer:

C-true

Step-by-step explanation:

A-false

B-false

C-true

D-false

used substitution

The product of the two expressions (m - n)(m + n) gives x² - 4

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the expression (m - n)(m + n):

Multiplying the two expressions gives:

m² + mn - mn - n²

This gives:

m² - n²

The product of the two expressions (m - n)(m + n) gives x² - 4

Find out more on equation at: https://brainly.com/question/2972832

#SPJ2

Answer:

8

Step-by-step explanation:

Since the first decimal place is greater than 5, it rounds to 8, because 8 is the next whole number to 7.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

36 inches

Step-by-step explanation:

Given data

Area of triangle =2 1/4 square inches

Area =9/4 square inches

Height of triangle =1/8 inches

We know that the expression for the area of triangle is

Area = 1/2Base *Height

9/4=1/2*Base *1/8

9/4=Base/16

Cross multiply

16*9=Base*4

144=Base*4

Base =144/4

Base=36 inches

Answer:

G

Step-by-step explanation:

36+36=72

180-72=108

360-(108×2)

144

144÷2

72

Answer:

1, 2, 6

Step-by-step explanation:

The z score shows by how many standard deviations the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \ \sigma=standard\ deviation[/tex]

Given that mean (μ) = 130 texts, standard deviation (σ) = 20 texts

1) For x < 90:

[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{90-130}{20} =-2[/tex]

From the normal distribution table, P(x < 90) = P(z < -2) = 0.0228 = 2.28%

Option 1 is correct

2) For x > 130:

[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{130-130}{20} =0[/tex]

From the normal distribution table, P(x > 130) = P(z > 0) = 1 - P(z < 0) = 1 - 0.5 = 50%

Option 2 is correct

3) For x > 190:

[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{190-130}{20} =3[/tex]

From the normal distribution table, P(x > 3) = P(z > 3) = 1 - P(z < 3) = 1 - 0.9987 = 0.0013 = 0.13%

Option 3 is incorrect

4)  For x < 130:

[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{130-130}{20} =0[/tex]

For x > 100:

[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{100-130}{20} =-1.5[/tex]

From the normal table, P(100 < x < 130) = P(-1.5 < z < 0) = P(z < 0) - P(z < 1.5) = 0.5 - 0.0668 = 0.9332 = 93.32%

Option 4 is incorrect

5)  For x = 130:

[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{130-130}{20} =0[/tex]

Option 5 is incorrect

6)  For x = 130:

[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{160-130}{20} =1.5[/tex]

Since 1.5 is between 1 and 2, option 6 is correct

Answer:

Ans = 65

Step-by-step explanation:

2x3 + 5x + 9

2x3 + 5x10 + 9

6 + 50 + 9

56 + 9

= 65