Solve the inequality 9y+5(y+3)<4y−35 and write the solution in interval notation.

Answers

Answer 1

Answer:

( −∞,−5) interval notation, and inequality solution y < -5 ,

Step-by-step explanation:

Answer 2

Answer:

y<-5

Your Interval Notation would be an open circle and the arrow would be pointing to the left. (<-- (-6) --- (-5) --- (-4) -->) This will be your # line.

Step-by-step explanation:

9y+5(y+3) < 4y-35

1) Distribute the 5 in 5(y+3).

9y+5y+15 < 4y-35

2) Combine like terms. 9y and 5y.

9y+5y= 14y

14y+15 < 4y-35

3) MY TIP is to keep the variables on the left side, bc if you don't at the end you will have to flip the sign. so.. Subtract 4y from both sides

14y+15 < 4y-35

-4 -4

10y+15 < -35

3) Then you will subtract 15 from both sides

10y+15 < -35

-15 -15

10y < -50

4) Last is to divide to get your variable by itself.

10y < -50

÷10 ÷10

Answer : y < -5

Interval Solution: Open circle, -5 in the middle of the line and you will shade in the numbers to the left. .


Related Questions

Use the graph to find the slope. What is the runners speed?

Answers

The formula for the slope is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{20-10}{2-1}[/tex]

[tex]m=\frac{10}{1}[/tex]

[tex]m=10[/tex]

Hope this helps.

頑張って!

Answer:

The answer is 10 minutes per mile!

Step-by-step explanation:

I hope this helped! :)

Evaluate the limit with either L'Hôpital's rule or previously learned methods.lim Sin(x)- Tan(x)/ x^3x → 0

Answers

Answer:

[tex]\dfrac{-1}{6}[/tex]

Step-by-step explanation:

Given the limit of a function expressed as [tex]\lim_{ x\to \ 0} \dfrac{sin(x)-tan(x)}{x^3}[/tex], to evaluate the following steps must be carried out.

Step 1: substitute x = 0 into the function

[tex]= \dfrac{sin(0)-tan(0)}{0^3}\\= \frac{0}{0} (indeterminate)[/tex]

Step 2: Apply  L'Hôpital's rule, by differentiating the numerator and denominator of the function

[tex]= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ sin(x)-tan(x)]}{\frac{d}{dx} (x^3)}\\= \lim_{ x\to \ 0} \dfrac{cos(x)-sec^2(x)}{3x^2}\\[/tex]

Step 3: substitute x = 0 into the resulting function

[tex]= \dfrac{cos(0)-sec^2(0)}{3(0)^2}\\= \frac{1-1}{0}\\= \frac{0}{0} (ind)[/tex]

Step 4: Apply  L'Hôpital's rule, by differentiating the numerator and denominator of the resulting function in step 2

[tex]= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ cos(x)-sec^2(x)]}{\frac{d}{dx} (3x^2)}\\= \lim_{ x\to \ 0} \dfrac{-sin(x)-2sec^2(x)tan(x)}{6x}\\[/tex]

[tex]= \dfrac{-sin(0)-2sec^2(0)tan(0)}{6(0)}\\= \frac{0}{0} (ind)[/tex]

Step 6: Apply  L'Hôpital's rule, by differentiating the numerator and denominator of the resulting function in step 4

[tex]= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ -sin(x)-2sec^2(x)tan(x)]}{\frac{d}{dx} (6x)}\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^2(x)sec^2(x)+2sec^2(x)tan(x)tan(x)]}{6}\\\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^4(x)+2sec^2(x)tan^2(x)]}{6}\\[/tex]

Step 7: substitute x = 0 into the resulting function in step 6

[tex]= \dfrac{[ -cos(0)-2(sec^4(0)+2sec^2(0)tan^2(0)]}{6}\\\\= \dfrac{-1-2(0)}{6} \\= \dfrac{-1}{6}[/tex]

Hence the limit of the function [tex]\lim_{ x\to \ 0} \dfrac{sin(x)-tan(x)}{x^3} \ is \ \dfrac{-1}{6}[/tex].

What’s the perimeter of the tabletop in feet?

Answers

Answer:

Perimeter = 14.0942 ft       (aprox)

Step-by-step explanation:

1 ft = 12 inches

1 inch = 1/12 = 0.08333 ft

4 inch = 4*0.08333 = 0.3333 ft

then:

there are:

4 quarters of circle = 4/4 = 1 complete circle

        perimeter = 2π r

         π = 3.1416

         r = radius

         perimeter = 2*3.1416*0.3333ft

         perimeter = 2.0942 ft       (aprox)

4 sides  (3ft each)

       perimeter = 4*3ft

        perimeter = 12ft

Total perimeter:

2.0942ft +´12ft = 14.0942 ft

Can you please please help me with this please it’s so hard and i will give you a branlist

Answers

i think it’s the parallel sides “b”

The value of the digit 9 is ten times as much as the 9 in 893,417.

Answers

Answer: 943,212

Step-by-step explanation:

Suppose that you want to know the value of a given digit in a given number, where the digit is x.

Now, you should count the position of this digit, starting at the decimal point and counting to the left.

This position, a number n, will give the value of our digit as:

Value = x*10^(n-1)

in the number 893,417 the digit 9 is in the fifth place (counting from right to left).

Then the value of this 9 is:

9*10^(5 - 1) = 90,000

Now, if we want something ten times larger than this, we have:

N = 10*90,000 = 900,000

Now the 9 is in the sixth place, then we must find a number with a 9 in the sixth place, for example, 943,212.

The sum of two even consecutive integers is 114. What is the smallest integer?

Answers

Answer:

56

Step-by-step explanation:

The sum of two even consecutive integers is 114.

Let's let the first even integer be 2n, where n is some integer: it doesn't matter what n is, but if we multiply n by 2, we are certainly getting an even number. This is because any integer multiplied by 2 is even.

So, this means that the second number is 2n+2.

Their sum is 114. In other words:

[tex](2n)+(2n+2)=114[/tex]

Solve for n.

Combine like terms:

[tex]4n+2=114[/tex]

Subtract 2 from both sides:

[tex]4n=112[/tex]

Divide both sides by 4:

[tex]n=28[/tex]

So, n is 28.

This means that the first number is 28(2) or 56.

And the second number is 58.

So, the smallest integer is 56.

And we're done!

Brenda received $25 for babysitting for 3 hours. If she is paid proportionally, how much should she get for 7.5 hours?​

Answers

Answer:

$187.5

Step-by-step explanation:

25 times 7.5 is 187.7

Derrick and Samantha are selling tickets for their school musical. Floor seats cost $7.50 and balcony seats cost $5.00. Samantha sells 60 floor seats and 70 balcony seats, Derrick sells 50 floor seats and 90 balcony seats. Write an expression to show how much money Samantha and Derrick have collected for tickets.

Answers

F(x) = 7.50x
B(x) = $5.00x

F(x) = 7.50(90)
B(x) = 5.00(160)

$7.50(90) = $675

$5.00(160) = $800

Techside Real Estate, Inc. is a research firm that tracks the cost of apartment rentals in Southwest Virginia. In mid-2002, the regional average apartment rental rate was $895 per month. Assume that, based on the historical quarterly surveys, it is reasonable to assume that the population standard deviation is $225. In a current study of apartment rental rates, a sample of 180 apartments in the region provided the apartment rental rates.
a. Do the sample data enable Techside Real Estate, Inc. to conclude that the population mean apartment rental rate now exceeds the level reported in 2002? The sample mean is $915 and the sample standard deviation is $227.50. Make your decision based on α=0.10.
b. What is the P-value?

Answers

Answer:

1) we will fail to reject the null hypothesis and conclude that the population mean apartment rental rate does not exceed the level reported in 2002

2) P - value = 0.116435

Step-by-step explanation:

We are given;

Population mean; μ = $895

Sample mean; x' = $915

Population standard deviation; σ = $225

Sample standard deviation; s = $227.50

Sample size; n = 180

Let's state the hypothesis;

Null hypothesis;H0: μ ≤ $895

Alternative hypothesis;Ha: μ > $895

Now, the z-score formula is;

z = (x' - μ)/(σ/√n)

Thus, we are making use of the population standard deviation

z = (915 - 895)/(225/√180)

z = 20/16.7705

z = 1.193

From online p-value from z-score calculator attached, with α = 0.10, one tail, we have;

The P-Value is 0.116435

This is more than the significance level of 0.1, thus we will fail to reject the null hypothesis and conclude that the population mean apartment rental rate does not exceed the level reported in 2002

What is 12 raised to the first power?

Answers

Answer:

12^1 = 12

Step-by-step explanation:

Any number raised to the power of one equals the number itself.

A recipe for chocolate chip cookies calls for 2 2/3 cups of flour. If you are making 1 1/4 recipes how many cups of flour are needed

Answers

Answer: 10/3 or 3 1/3 cups of flour
The ratio is (8/3 cups of flour : 1 batch or recipe)
In order to make 1 1/4 recipes you have to multiply the 1 by 1 1/4. But then in order to keep the ratio equivalent, you also have to multiply the other side by the same number.

2 fraction bars. The first bar is labeled 1 with 8 boxes underneath that are labeled one-eighth. The second bar is labeled 1 with 8 boxes underneath that are labeled one-eighth. Use the drop-down menu to complete the statement. To find the quotient of 2 ÷ 3 8 , circle groups of ------

Answers

Answer:

1/3

Step-by-step explanation:

hope this helps  

Answer:

It is 3/8

Step-by-step explanation:

I got it right on Edge 2021.

In a class of 50 statistics​ students, 27
students received an A. What fraction of the class received an​ A?

Answers

Answer:

Fraction of the number that received an A= = 27/50

Step-by-step explanation:

In a class of 50 statistics​ students, 27

students received an A.

Total number of students=50

Number that received an A= 27

Fraction of the number that received an A= Number that received an A/Total number of students

Fraction of the number that received an A= = 27/50

Help i dont understand this someone help me pls :(

Answers

Answer:

X=7

Step-by-step explanation:

(2) means time 2 so use 5 times 2 and get 10 and take away 3 you get 7 and 7 is X

to prove I am right use 7x5-3/2=16-3x2=10

hey bro I was joking at first

Answer:

f(2) = 5(2) -3

         10 - 3

f(2) = 7

What is the volume of the cube shown?

6 3/4
11 25/64
30 3/8
8 1/64

Please help !

Answers

Answer:

11 25/64 in ^3

Step-by-step explanation:

Volume of a cube is given by

V = s^3

s = 2 1/4 = 9/4

V = (9/4) ^3

  = 729/64

  =11 25/64 in ^3

Look at the correlation between Risk-Taking (R) and Relationship Happiness (HAPPY). Use the standard alpha level of 5%. How would you describe the relationship?

1. The relationship is non-significant.

2. There is a significant negative relationship.

3. There is a significant positive relationship.

4. The correlation is zero.

Answers

Image of the correlation between Risk-Taking (R) and Relationship Happiness (HAPPY) is missing, so i have attached it.

Answer:

Option 1 - The relationship is non - significant

Step-by-step explanation:

From the image attached, we can see that under the correlations table;

For correlation between relationship happiness and risk taking;

σ(sigma) = 0.053

Similarly, for correlation between risk taking and relationship happiness;

σ(sigma) = 0.053

.

Now,σ(sigma) = 0.053 is more than the standard alpha level of 5%(0.05). Thus, we fail to reject the null hypothesis since it is non - significant.

The point (0, –4) is located

Answers

I'm going to assume you're asking where the point is located on a coordinate plane.

We have x = 0 and y = -4.

So, we start at (0, 0) and move down 4 units.

Best of Luck!

Petra is making necklaces to sell at craft. the hardware for each necklace is 3.75 and each bead costs 0.50. The number of beads Petra needs depends on the design she chooses. which expression gives the total cost to make 30 necklaces.

Answers

Answer:

T=112.5+0.50*b (since there was not a given number of beads)

Fruit juice in 4/5 pint cartons is sold by the park in 5/6 pint mugs. How many mugs are in a​ carton?

Answers

Answer:

Number of mugs in cartoon = 24 / 25

Step-by-step explanation:

Given:

Pints of cartoon = 4/5

Pints of mugs = 5/6

Find:

Number of mugs in cartoon

Computation:

Number of mugs in cartoon = Pints of cartoon / Pints of mugs

Number of mugs in cartoon = (4/5) / (5/6)

Number of mugs in cartoon = 24 / 25

Find the value of the expression for the given values.
6x-2 for x = -2, x = 6, and x = -5
If x= - 2. then 6x - 2 =
If x = 6, then 6x - 2 =
If x= - 5. then 6x-2=

Answers

Answer:

If x= - 2. then 6x - 2 = -14

If x = 6, then 6x - 2 = 34

If x= - 5. then 6x-2= -32

Step-by-step explanation:

You have to substitute the value of x in the expression.

If x = -2,

6x-2 = 6*(-2) - 2 = -12-2 = -14

PLEASE HELP ME

A map has a scale of
2 in. = 17 mi. If you measured the distance between two cities to
be 19 in. on the map, how many miles would it actually be?
If necessary, round your answer to the nearest tenth.

Answers

Answer:

  161.5 miles

Step-by-step explanation:

19 inches is 9.5 times 2 inches. So, the actual distance is 9.5 times 17 miles:

  9.5 × 17 miles = 161.5 miles

To make fruit salad,Maria bought 2 1/4 pounds of apples,and 1 1/3 pounds.How much fruit salad did this make

Answers

Answer:

If this was all the fruit, 3 and 7/12

Step-by-step explanation:

1/4 and 1/3 LCM is 12

1/4=3/12

1/3=4/12

2+1=3

3/12+4/12=7/12

3+7/12= 3 7/12

a regular polygon of 2 k + 1 sides has 140 as
size of each interior angle find K​

Answers

Hope this can help.

Explain why the graph of the equation g(x) = -(x + 1 ) - 3 would be a parabola opening downward.

Answers

Answer: Because the a-value is negative.

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(x - h)² + k    where

"a" is the vertical stretch-a is a reflection over the x-axish is the horizontal shift (positive = right, negative = left)k is the vertical shift (positive = up, negative = down)

Given: g(x) = - (x + 1)² - 3

                    ↓

                 a= -1

Since the a-value is negative, the parabola will be reflected over the x-axis which will change the curve from (U-shaped) to (∩-shaped).

23^0 is equal to _____. 0 1 1/23 23

Answers

Answer:

1

Step-by-step explanation:

Anything to the power is 0 is equal to 1.

Answer:

the answer is 1

Step-by-step explanation:

2/3 * 9 = ? PLEASE HELP

Answers

Answer:

6

Step-by-step explanation:

Which of state of matter has no definite shape but does have a definite volume? (A) Liquid B) Element OC) Solid OD) Gas​

Answers

Answer:

Liquid

Step-by-step explanation:

solids :have definite shape and definite volume.

Liquids :have definite volume and shape of the container.(or no definite shape)

Gas: has no definite volume and no definite shape.

The answer would have to be liquid

Please help. I’ll mark you as brainliest if correct!

Answers

Answer:
Width: 4
Length: 12

Work:
Length=Width times 2 + 4

Simplify. Please provide steps on how to solve so I can learn.

Answers

Answer: Choice C

[tex](xy)^{1/2}[/tex] which is equivalent to [tex]\sqrt{xy}[/tex]

===============================================

Explanation:

The exponent for the y term inside the parenthesis is 1/6 and then that expression is raised to the 3rd power. The exponents multiply to (1/6)*3 = 3/6 = 1/2

This means [tex]\left(y^{1/6}\right)^3 = y^{1/2}[/tex]

Having an exponent of 1/2 is the same as applying the square root, so,

[tex]\sqrt{x} = x^{1/2}[/tex]

Meaning,

[tex]y^{1/2}\sqrt{x} = y^{1/2}x^{1/2} = (xy)^{1/2} = \sqrt{xy}[/tex]

what is 3.825 as a fraction with a guide?

Answers

Answer:

153/40

Step-by-step explanation:

The first step to finding the fraction is to get rid of the decimal points as fractions do not have decimals. To do this we can multiply it by 1000 which gives us 3825. To have this equal to the original number we add ÷1000 on the denominator which gives us 3825/1000 which is a fraction still equal to the original number (3825÷1000=3.825). Which can further be simplified to 153/40 (both numbers divisible by 25). This is the simplest fraction which can express the number 3.825 (153/40=3.825).

Hope this helped!

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