Solve the inequality 5x < 16 + x. x < 1/4 x > 1/4 x < 4 x > 4

5x < 16 + x5x - x < 164x < 16x < 16/4=> x < 4

Solve the inequality 5x < 16 + x.
x < 1/4
x > 1/4
x < 4
x > 4

Answers

Answer 1

5x < 16 + x
5x - x < 16
4x < 16
x < 16/4
=> x < 4

Answer 2

Final answer:

To solve the inequality 5x < 16 + x, you first rearrange it to 4x < 16 by subtracting x from both sides. Then, divide by 4 to solve for x, which results in x < 4. This means any value less than 4 satisfies the inequality.

Explanation:

To solve the inequality 5x < 16 + x, you first need to rearrange the inequality so that all x terms are on one side of the inequality and the constant is on the other. You can start by subtracting x from both sides, which gives you 4x < 16.

Next, you can solve for x by dividing both sides by 4. Doing this gives you x < 4, which is your solution.

This means that any value less than 4 will satisfy the inequality. For example, if you insert 3 into the inequality (5*3 < 16 + 3), it holds true because 15 < 19.

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Related Questions

c+1/c-2 = 4/7 please show how you got the answer

Answers

C = 3 while c = 9

C + 1 = 4
c - 2 = 7

4 - 1 = C
C = 3

2+ 7 = c
c = 9

hope this helps

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jackson bikes 2 miles in 15 minutes. At this rate, how many miles will he bike in 45 minutes?

Answers

He will ride 6 miles in 45 minutes.

The height of a ball thrown directly up with a velocity of 10 feet per second from a initial height of of 100 feet is given by the equation h(t) = -16tsquared + 10t + 100, where t is the time in seconds and h is the ball’s height, measured in feet. When will the ball hit the ground? Round your answer to the nearest tenth.

Answers

The ball will hit the ground when h(t)=0 so:

-16t^2+10t+100=0

Using the quadratic equation:

t=(-10±√6500)/-32, and since t>0

t≈2.8 seconds (to nearest tenth of a second)

Answer:

The ball will hit at 2.83 seconds.

Step-by-step explanation:

It is given that,

Velocity with which a ball is thrown up is, v = 10 ft/s

Initial height, h = 100 ft

The equation for the height of an object as a function of t is given by :

[tex]h(t)=-16t^2+10t+100[/tex]...............(1)

Where

t is the time in seconds

h is the ball's height measured in feet

We have to find the time when the ball hits the ground. It can be calculated by solving the quadratic equation of equation (1). On solving we get the value of t as :

t = 2.832 seconds

So, at 2.83 seconds the ball will hit the ground. Hence, this is the required solution.

if O represents number of integers between 10,000 and 100,000 all of whose digits are odd, and E represents number of integers between 10,000 and 100,000 all of whose digits are even, what is the value of O - E?

Answers

i)
fist let's find O, that is the number of all numbers between 10,000 and 100,000, whose all digits are odd.

so we have to count: 11,111; 11,113; ... 99,999

we notice that all these numbers are 5 digit, and they are made up of the odd digits {1, 3, 5, 7, 9} with repetition allowed.

so there are in total [tex]5*5*5*5*5= 5^{5} [/tex] such numbers.

ii)

E is the total number, of 5-digit numbers formed from the set{0, 2, 4, 6, 8} with repetition allowed, and the first digit not equal to 0.

so [tex]E=4*5*5*5*5= 4*5^{4}[/tex]

iii) [tex]O-E=5^{5}-4*5^{4}=5^{4}(5-4)=5^{4}=625[/tex]

Answer: 625

A recipe for muffins calls for 3⁄5 of a cup of sugar and 4 cups of flour. If you want to make a bigger batch, using 5 cups of flour, how much sugar will you need?

Answers

(3/5) / 4 = x / 5
cross multiply
4x = 5(3/5)
4x = 3
x = 3/4....it would need 3/4 cups of sugar

Let set A = {odd numbers between 0 and 100} and set B = {numbers between 50 and 150 that are evenly divisible by 5}. What is A ∩ B? (2 points)

Answers

A = {odd numbers between 0 and 100}
A = {1, 3, 5, 7,...., 95, 97, 99}

B = {numbers between 50 and 150 that are evenly divisible by 5}
B = {50, 55, 60, 65, ..., 140, 145, 150}

The notation A ∩ B means the set of items that are in set A and also in set B. In terms of venn diagrams, it's the overlapping region between circle A and circle B

In this case, the following values are found in both set A and set B
{55, 65, 75, 85, 95}

So that's why
A ∩ B = {55, 65, 75, 85, 95}
which is the final answer

Which is a unit rate ? 4 dollars to 3 cans 5 students to 2 teachers 6 hours and 1 book 3 miles 2 days

Answers

6 hours to 1 book is a unit rate because the independent variable (books) is equal to 1.

Hope this helps!

Answer:

6 hours to 1 book

Step-by-step explanation:

Find the value of X in the problem below. Geometry

Answers

(3x+10) +14x = 180

17x +10 = 180

17x=170

x = 170/17 = 10

x = 10

0.75 = log x raise each side of the equation as power

Answers

Hi there!

0.75 = logx
I always flip them so that I can make sure I don't forget anything. FYI, this is one of the trick they used to force you make the mistake so make sure you always flip the equation (omg I talked too much)

--------------------------------------------------------------------------------
0.75 = logx
Flip it
logx = 0.75
We need to solve for the logarithm
log(x)= 0.75
Take exponent of both sides
10^logx =10^0.75
x = 10^0.75
x= 5.623413

I hope that helps!

Simplify the following expression: 2x − 6y + 3x2 + 7y − 14x. 3x2 + 12x + y 3x2 − 12x − y 3x2 − 12x + y 3x2 − 12x − 13y

Answers

3x2 − 12x + y would be your answer

The required simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x is 3x² -12x + y.

Given that,
To simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

= 2x − 6y + 3x² + 7y − 14x.
= 3x² + 2x -14x + 7y -6y
= 3x² -12x + y

Thus, the required simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x is 3x² -12x + y.

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Module 04.03 Exponential Functions and Models: Essential Questions:
1) How do the properties of exponents apply to exponential functions?
2)How are key features of graphs and tables used to model relationships between two quantities?
3)How can the average rate of a change be identified for a function?
*PLEASE HELP! NEED TO KNOW THIS.*

Answers

Final answer:

Properties of exponents are used to simplify and manipulate exponential functions. In graphing, growth rate, intercept, and asymptotes model relationships. The average rate of change for a function is calculated based on changes in output divided by input changes over an interval.

Explanation:Understanding Exponential Functions and Models

Exponential functions are mathematical expressions where a constant base is raised to a variable exponent. The properties of exponents, such as product, quotient, and power rules, apply to these functions and are used to simplify and manipulate expressions.

When modeling relationships between two quantities using graphs and tables, key features like the growth rate, y-intercept, and asymptotes are important. The growth rate can be understood from the steepness of the graph or how quickly the y-values increase as x increases. The y-intercept represents the starting value of the quantity being modeled when x equals zero.

The average rate of change for a function is identified by calculating the change in the function's output values (y-values) divided by the change in the input values (x-values) over the interval of interest. For exponential functions, this rate of change is not constant, but increases or decreases at a rate proportional to the function's current value.

An example of exponential growth in a natural population might be the rapid increase in a bacteria population in an ideal lab condition, where it doubles every fixed amount of time. In contrast, a logistic growth pattern occurs when the growth rate decreases as the population reaches carrying capacity, such as the population of sheep in a field with limited grass for food.

Exploring the Exponential Distribution

The exponential distribution is typically used to model the time between events in a memoryless process, where the probability of an event occurring is the same at any moment. In an exponential distribution, outcomes are not equally likely as not all intervals of time are equally likely to occur before the next event. The mean (m), often referred to as the expected value, and the standard deviation can be derived from the rate parameter, which is the reciprocal of the mean.

Understanding how to manipulate a linear equation, as well as interpret and compute growth rates, is foundational in various applications including those in economics, biology, and environmental science. The ability to read and manipulate graphs is crucial for clearly presenting data and drawing accurate conclusions.

If p-1 is a factor of p^4+p^2+p-k the value of k is

Answers

p=1
p^4+p^2+p-k=0

1+1+1-k=0 k=3

The value of k is 3 if p - 1 is a factor of [tex]p^4+p^2+p-k[/tex]

How to determine the value of k?

The expression is given as:

[tex]p^4+p^2+p-k[/tex]

The factor is given as:

p - 1

Set the factor to 0

p - 1 = 0

Add to both sides

p = 1

Substitute 1 for p in the expression and equate it to 0

[tex]1^4+1^2+1-k = 0[/tex]

Evaluate the exponents

1+1+1-k = 0

Evaluate the sum

3-k = 0

Add k to both sides

k = 3

Hence, the value of k is 3 if p - 1 is a factor of [tex]p^4+p^2+p-k[/tex]

Answers

6(y + 3)

The product of a constant factor of 6 and a factor with the sum of 2 terms

Answer: Hence, option '3' is correct.

Step-by-step explanation:

Since we have given that

[tex]6(y+3)[/tex]

This expression can be written in statement.

Here, we can see that there are two terms:

1) A constant factor of 6

2) Sum of two terms

So, according to options it can be written as :

The product of constant factor of 6 and a factor with the sum of two terms i.e. y and 3.

Hence, option '3' is correct.

11 POINTS GUYS PLZ
Answer 12 and 14

Answers

12) 10.77 + 2.09 + 0.75 = 13.61

13.61 x 1.07 = $14.56

total amount = $14.56

14) C shows the possible combinations

Please help me :) Thanks!

Answers

x^2+12x+5 = (x+6)^2 -31,

So the minimum value is y = -31. Dunno if -31 or you have to type =-31, I guess just '-31'?

With derivatives:

y' = 2x+12=0, x = -6, then y(-6) = 36-72+5 = -36+5 =-31

Just to be sure!!!! lol

The minimum value for y in the equation y = x² + 12x + 5 is (-6,-31). Here's how I figured it out:

Step 1: Figure out if the parabola is going up or down. If "a" is positive, the parabola will go up. If "a" is negative, the parabola will go down. In your case...

a = 1
Positive
Up
____________________________________________________________

Step 2: Find the Axis of Symmetry.

Formula: -b -12 -12
--------- = ------------ = ------------- = -6
2a 2(1) 2

The axis of symmetry is x = -6.
____________________________________________________________

Step 3: Plug in the value you found for the axis of symmetry for x into your original equation.

f(-6) = -6² + 12(-6) + 5
f(-6) = 36 - 72 + 5
f(-6) = -36 + 5
f(-6) = -31

The minimum gets written as an ordered pair: (-6,-31).
⊕ The axis of symmetry is the first number in the coordinate pair.
⊕ The answer that you get to step 3 is the second number in the pair.
____________________________________________________________

I hope that my answer helps you! This is the method that I use to solve these types of problems, but there are also other methods.

Solve the equation for the letter L: A=LW

L = AW
L equals W over A
L = A − W
none of the above

Answers

[tex] \frac{L}{A} =LW[/tex] ⇒ Multiply both sides by A
[tex] \frac{LA}{A}=LWA [/tex] ⇒ The terms 'A' on the LHS cancel each other
[tex]L=LWA[/tex] ⇒ Divide both sides by 'L'
[tex] \frac{L}{L}= \frac{LWA}{L} [/tex] ⇒ The terms 'L' on the LHS cancel each other to '1' and the terms 'L' on the RHS will also cancel each other
[tex]1= WA[/tex]

The correct answer is the last option = none of the above

2. If you have budgeted 12% of your monthly income for groceries, how much can you spend on groceries if you earn $950 bi-weekly?

Answers

bi weekly means you get paid every 2 weeks ( 2 times a month)

950*2 = 1900 per month for pay

1900*0.12 = 228 a month for food

Answer:

if you earn $950 bi-weekly, you earn 2 x 950 = $1900 per month. If you have budgeted 12% of your monthly income for groceries you need to find 12% of $1900: (1900 / 100) x 12 = 228. Answer: you can spend $228 a month on groceries.

how to write unit form for (2 tens 1 one) x 10

Answers

Numbers are arranged by their place values. Place values give a quantity of value to a certain digit in a number. Given a number, the rightmost number is the ones place, followed by the tens place, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, as so on and so forth. The place value of a certain digit is 10 times bigger than its adjacent digit to the right.

So for this problem, all you have to do is multiply the number of units of each place value, then multiple them all by 10.

(2(10) + 1(1))×10
21 × 10 = 210

Therefore, the number is equivalent and written as 210.

What is the area of a triangle that has a height of 4 feet and a base length of 9 feet? 18 feet2 36 feet2 144 feet2 324 feet2

Answers

18 feet.

9 x 4 = 36

36/2 = 18

18 feet is the answer hope this helps!!

An architectural drawing lists the scale as 1/4 = 1. If a bedroom measures 3 1/2 by 5 1/4 on the drawing, how large is the bedroom

Answers

The bedroom is 14x21. I hope this helps :)

Answer:

The measure of the bedroom is 14 by 21

Step-by-step explanation:

This scale represents the every measure in the drawing is a 1/4 of the original measure, so to find the original measure you must multiply the measure you find in the drawing by 4.

So for the beadroom (3 1/2, 5 1/4), you multiply each one by 4

The real measures of the beadroom are:

(3 1/2 * 4, 5 1/4 * 4)

(14,21)

The measure of the bedroom is 14 by 21

An angle measures 20° more than the measure of a complementary angle. What is the measure of each angle?

Answers

complementary angles, sum = 90
so
x + x + 20 = 90
2x = 70
x = 35

35 + 20 = 55

answer
the measure of each angle: 55 and 35

Arlene is comparing the prices of two truck rental companies. Company A charges $7 per hour and an additional $30 as service charges. Company B charges $8 per hour and an additional $40 as service charges.

Part A: Write an equation to represent each company's total charges for renting a truck for a certain number of hours. For both equations (one for Company A and one for Company B), define the variable used. (4 points)

Part B: Which company would charge less for renting a truck for 8 hours? Justify your answer. (3 points)

Part C: How much money is saved by using the services of Company A instead of Company B to rent a truck for 2 hours? (3 points)

Answers

Part A:
Company A: $7 per hour +$30 service charge =money spent
Company B: $8 per hour +$40 service charge =money spent

Part B:
Company A: $7(8)+$30 = $86
Company B: $8(8)+$40 = $104

Part C:
Company A: $7(2)+$30 = $44
Company B: $8(2)+$40 = $56
You would save $12 if you use Company A instead of Company B's truck rental.

Two trains leave stations 252 miles apart at the same time and travel toward each other. One train travels at 80 miles per hour while the other travels at 100 miles per hour. How long will it take for the two trains to meet?

Answers

First things first, distance = speed x time
So let's have "t" represent the time by both trains.
The first train shall be Train A and the other becoming Train B, so now we have Train A going 80t miles and Train B going 100t miles.

If two trains head toward each other, they will have traveled a total of 252 miles. The faster train will have traveled further (Train B), so the meeting point will be closer to the slower train's starting point (Train A).

So now we do 80t + 100t = 252
Which becomes 180t = 252
And by diving 252 by 180, you'll get that t is 1.4
This would mean they would meet at one hour and 24 minutes.

Final answer:

The time it takes for two trains traveling towards each other at speeds of 80 mph and 100 mph, and starting 252 miles apart, is found by dividing the distance by their combined relative speed. It takes them 1.4 hours or 1 hour and 24 minutes to meet.

Explanation:

To solve the problem of calculating the time it takes for two trains to meet, we need to understand the concept of relative speed in motion problems. When two objects move towards each other, their relative speed is the sum of their individual speeds. In this case, one train travels at 80 miles per hour and the other at 100 miles per hour, giving us a combined relative speed of 80 mph + 100 mph = 180 mph.

The distance between the two trains is 252 miles, and to find the time taken for the trains to meet, we divide the total distance by the relative speed:

Time = Distance / Relative Speed

Time = 252 miles / 180 mph

Time = 1.4 hours or 1 hour and 24 minutes for the two trains to meet.

Everett made 3/5 of the baskets he shot. Suppose he shot 60 baskets. How many did he make?

Answers

Everett made 36 shots

You have to multiply 5×12 to get 60. And whatever you do on the bottom you do on the top. So
you then multiply 3×12 and you
get 36. So he got 36 out of 60
shots.

3 (12) 36
-- = --
5 (12) 60

Solve the equation by completing the square. Round to the nearest hundredth if necessary? X^2+3x=24

Answers

x^2+3x=24, halve the linear coefficient, square it, and add it to both sides

In this case (3/2)^2=2.25

x^2+3x+2.25=26.25 now the left side is a perfect square...

(x+1.5)^2=26.25 take the square root of both sides

x+1.5=±√26.25 subtract 1.5 from both sides

x=-1.5±√26.25

x=-1.5-√26.25 and -1.5+√26.25

x≈ -6.62 and 3.62

can someone help with this

Answers

Hey There! :)

Solve for g.
[tex]g/20=12/48 [/tex]
Isolate the variable; Multiply both sides by 20.
[tex](g/20)*20=(12/48)*20 [/tex]
[tex]g=240/48 [/tex]
[tex]g=5[/tex]

Hope this helps.
-Benjamin

Write an equation ten times the sum of half a number and 6 is 8.

Answers

10(1/2x+6)=8
Is the equation. Hope this helped!

10(x/2+6)=8
the x/2 means x over two

Which is an obtuse angle?

∠CAB

∠BAC

∠BCA

∠ABC

Answers

BCA is an obtuse angle

Obtuse angle is an angle that is greater than 90° but less than 180°

∠BCA ← answer

How to simplify the expression 60/(-4)

Answers

Hey!

We could rewrite the problem as: [tex]\frac{60}{-4}[/tex]
Since we have a negative number, we could rewrite the fraction like this.
[tex]=-\frac{60}{4}[/tex]
Let's simplify it...
[tex]-\frac{60}{4}=-15[/tex]
Our answer would be:
[tex]=-15[/tex]

Thanks!
-TetraFish

Select the factors of 6ab + 3ay − 2bx − xy.

A. (3a − x)(2b + y)
B. (3a − y)(2b + x)
C. (2a − x)(3b + y)
D. (2a − y)(3b + x)

I need the answer I don't get it ...and this is a really long test ..but so far I only need help on this one . thanks to whoever helps me and give correct answer

Answers

answer
A. (3a − x)(2b + y)

cause

(3a − x)(2b + y) = 6ab + 3ay -2bx -xy (expand by using distributive property)

Answer:

The factors of given expression is (3a-x)(2b+y)

A is correct

Step-by-step explanation:

Given: [tex]6ab+3ay-2bx-xy[/tex]

We need to factor the given expression.

First we make two group

[tex]\Rightarrow (6ab+3ay)+(-2bx-xy)[/tex]

Factor each group

[tex]\Rightarrow 3a(2b+y)-x(2b+y)[/tex]

[tex]\Rightarrow (3a-x)(2b+y)[/tex]

So, we get two factor (3a-x) and (2b+y)

Hence, The factors of given expression is (3a-x)(2b+y)

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