Solve 2x - 1 < 7 and 5x + 3 < 3. {x | x < 0} {x | x < 4} {x | 0 < x < 4}

Answers

Answer 1
2x -1 <7 ; then, 2x < 8; then x < 4;
5x + 3 < 3; then, 5x < 0; then x < 0;
Finally, {x / x < 0};
Answer 2

Answer:

Solution for givrn system of inequalities: [tex]\{x ~| ~x < 0\}[/tex]

Step-by-step explanation:

We are given a system of two inequalities:

[tex]2x-1 < 7\\5x+3 < 3[/tex]

Solving the inequalities individually:

[tex]2x-1 < 7\\2x<7+1\\2x < 8\\x < 4\\\text{In interval notation: } x \in (-\infty, 4) \\\\5x + 3 < 3\\5x < 3-3\\5x < 0\\x< 0\\\text{In interval notation: } x \in (-\infty, 0)[/tex]

The intersection of the two solution will give us the solution to the system of inequalities:

[tex]x \in (-\infty, 4) \cap (-\infty, 0)\\ x \in (-\infty, 0) \\\{x ~| ~x < 0\}[/tex]


Related Questions

the table represents a function. what is the value of f(-1)?
f (-1) = - 3
f (-1) = - 1
f (-1) = 0
f (-1) = 6

Answers

f(-1)....this is basically saying that x = -1...and when x = -1 (according to ur chart), then f(-1) = 0 <==

The value of f(-1) from the table given is 0

Table of functions

Table of functions are used to find the relationship between variables. The variables x and y can be written as coordinate (x, y)

In order to determine f(-1), we need the value of f(x) at the point where x is 1. From the table, the value of f(-1) is 0

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two triangles.are.similar, solve for x if au=20x +108, ub=273, bc= 703, uv=444, AV = 372 and AC=589

Answers

If two triangles are similar then the corresponding sides are in proportion. Thus,

AB / AU = BC / UV = AC / AV

AB / (20x+108) = 703 / 444

Where AB is equivalent to:

AB = AU + UB

AB = 20x + 108 + 273

AB = 20x + 381

Therefore going back to the first equation:

(20x + 381) / (20x + 108) = 703/444

444 (20x + 381) = 703 (20x + 108)

8880x + 169164 = 14060x + 75924

14060x - 8880x = 169164 – 75924

5180 x = 93240

x = 93240 / 5180

x = 18          (ANSWER)

The correct value of x is [tex]\(\frac{1}{20}\)[/tex].

To solve for x, we need to use the properties of similar triangles. The sides of similar triangles are proportional. Given that triangles AU V and ABC are similar, we can set up the following proportion:

[tex]\[\frac{AU}{AB} = \frac{UV}{BC} = \frac{AV}{AC}\][/tex]

We are given the lengths of the sides as follows:

- (AU = 20x + 108)

- (UB = 273) (which is part of AB, since (AB = AU + UB)

- (BC = 703)

- (UV = 444)

- (AV = 372)

- (AC = 589)

Using the proportion involving the sides AU, UB, UV, and BC, we have:

[tex]\[\frac{AU}{UB} = \frac{UV}{BC}\][/tex]

Substituting the given values, we get:

[tex]\[\frac{20x + 108}{273} = \frac{444}{703}\][/tex]

Cross-multiplying to solve for x, we have:

[tex]\[(20x + 108) \cdot 703 = 444 \cdot 273\][/tex]

Expanding both sides gives us:

[tex]\[14060x + 76184 = 121172\][/tex]

Subtract (76184) from both sides to isolate the term with x:

[tex]\[14060x = 121172 - 76184\] \[14060x = 49888\][/tex]

[tex]\[x = \frac{49888}{14060}\][/tex]

Simplifying the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20, we get:

[tex]\[x = \frac{2494.4}{703}\][/tex]

Since (2494.4) is very close to (2496), and \(2496\) divided by (703) is (3.55), which is (20) times (0.1775), we can see that:

[tex]\[x = \frac{1}{20}\][/tex]

Therefore, the value of x is [tex]\(\frac{1}{20}\)[/tex].

A professor teaches a small lecture class with 25 students. For a certain class, 22 students attend the lecture. What is the experimental probability that a student is absent?

Answers

Your answer would be the fraction 3/25. If you're looking for a percentage, it would be 12%.
The probability would be 12%
If you're looking for the fraction.. I'm not sure about that part.. all I know is the percentage..
:)

A monkey is happy if it eats 3 types of fruit. There are 20 pears, 30 bananas, 40 peaches and 50 oranges. How do you distribute the fruit to make the most number of monkeys happy? What is this number?

Answers

you divide all the number by 5 to get you answer of 4 pears, 6 bananas, 8 peaches, and 10 oranges

To make the most monkeys happy we need 20 number of pair of pears, peaches, and oranges. and 20 number of pair of peaches bananas and oranges.

What is sampling distribution?

In statistics, sampling distribution refers to the study of multiple random samples drawn from a particular population depending on a specified property. The acquired data paint a clear picture of the changes in the likelihood of the outcomes determined. As a consequence, the analysts are aware of the outcomes ahead of time, allowing them to plan their actions accordingly.

Given, A monkey is happy if it eats 3 types of fruit. There are 20 pears, 30 bananas, 40 peaches, and 50 oranges. to formulate the equation we need to divide them by 10 and make the pair of three.

Hence,

2pears + 3 bananas + 4 peaches + 5 oranges

2(pears + oranges +  peaches)  + 2(banana + peach + oranges) + peach +1 orange.

Therefore to make the most monkey happy. we need to make 20 pairs of pears, oranges, and peaches and 20 pairs of banana peaches and oranges.

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Create a factorable polynomial with a GCF of 5z. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.

Answers

Final answer:

The original factorable polynomial 15z^2 + 10z can be rewritten in two different equivalent forms by factoring out the GCF to get 5z(3z + 2) and by applying the Zero Product Property to find its roots z = 0, -2/3.

Explanation:

To begin, we will create a factorable polynomial with a Greatest Common Factor (GCF) of 5z. An example might be: 15z^2 + 10z. This polynomial has two terms, and each term includes the GCF of 5z in its make up.

Now, let's rewrite this polynomial in two other equivalent forms using different methods of factorization and simplification.

Form 1: Factor by GCF

In this form, we factor out the GCF from the original polynomial. For our provided example, the GCF is 5z, so we get: 5z(3z + 2).

Form 2: Use the Zero Property

We can also rewrite this polynomial using the Zero Product Property. This naturally complements factoring because it allows us to set the factors equal to zero and solve for z. In this case, this provides the roots of the polynomial but not in factor form: z = 0, -2/3.

Therefore, the original polynomial and the different equivalent forms all represent the same relationship, just expressed in different manners.

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Final answer:

To create a factorable polynomial with a GCF of 5z, multiply it with another term like (4z+2). The resulting polynomial is 20z² + 10z. You can rewrite it in another equivalent form by factoring out the common term from each term, resulting in 2z(8z + 2) = 16z² + 4z.

Explanation:

To create a factorable polynomial with a GCF of 5z, we can start by multiplying 5z with another term. Let's say we multiply it with (4z+2). The polynomial becomes 5z(4z+2), which can be expanded to 20z² + 10z. This is one form of the polynomial.

To rewrite the polynomial in another equivalent form, we can factor out the common term from each term of the polynomial. Doing so, we get 5z(4z+2) = 5z * 4z + 5z * 2 = 20z² + 10z. Thus, the second equivalent form is 20z² + 10z.

The third equivalent form can be obtained by factoring out a common term, 2z, from each term: 5z(4z+2) = 2z * (2 * 4z + 2) = 2z(8z + 2) = 16z² + 4z.

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I NEED HELP ASAP!!!!!!

Answers

4 +12 = 16 crates

 16 x 32 = 512 juice boxes

 so both A & C are correct

What is the value of x in the equation 8 + x = 3? −5 5 11 24

Answers

8 + x = 3
To solve for this, we need to get x by itself on one side of the equation.
Currently, we have 8 being added to x, so we need to perform the opposite order of equations to get rid of 8.

The opposite of +8 is -8, so subtract 8.
Remember, if you add, subract, multiply or divide by any new number, you must do it to both sides of the equation.

8 + x = 3
Subtract 8 from both sides.
8 - 8 = 0
3 - 8 = -5

We're now left with:
x = -5

Your answer is A.) -5.

I hope this helps!
the answer is -5. Have a good day

Look at the cups shown below (please note that images are not drawn to scale): A cone is shown with width 3 inches and height 6 inches, and a cylinder is shown with width 3 inches and height 5 inches How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tent

Answers

Amount of juice that cup B will hold than cup A when both are completely full is A: 18.8 cubic inches.  therefore, Option A: 18.8 cubic inches.

Amount of juice hold by Cup B which is in the shape of a cylinder having width 2 inches that is radius 1 inches and height 7 inches

πr^2h = π × 1^2 ×7 = 7π  cubic inches

Amount of juice hold by cup A which is in the shape of a cone having width 2 inches that is radius 1 inches and height 3 inches

1/3 × π × r^2 h

1/3 × π × 1^2 × 3  =  πcubic inches

Amount of juice that cup B will hold than cup A when both are completely full  = 7π - π = 6π cubic inches

= 6 × 3.14

= 18.84 cubic inches

Option A: 18.8 cubic inches

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Question

Look at the cups shown below (please note that images are not drawn to scale):

A cone is shown with width 2 inches and height 3 inches, and a cylinder is shown with width 2 inches and height 7 inches.

How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth.

18.8 cubic inches

21.9 cubic inches

25.1 cubic inches

32.6 cubic inches

What is 3^ 2/3 equal to?

Answers

Final answer:

3^2/3 means squaring the number 3 to get 9, and then taking the cube root of 9, which is approximately 2.08008.

Explanation:

To calculate 3^2/3, we are dealing with an exponential expression where 3 is the base and 2/3 is the exponent. The exponent 2/3 means we must first square the base, which is 3, giving us 3 squared: 32 = 9. Next, we take the cube root (denominator of the fraction exponent) of this result since the exponent is 2/3, meaning the cube root of 9.

To find the cube root of 9, we look for a number which, when multiplied by itself three times, equals 9. Unfortunately, 9 is not a perfect cube, but using estimation or a calculator, we can find that the cube root of 9 is approximately 2.08008. Therefore, the exact expression for 32/3 remains (9)1/3 and the approximate decimal value is 2.08008.

The shaded area of the following shape can be found by subtracting the area of the circle from the area of the triangle. True False

Answers

It's true, because it is
True because you have to find what's in between

The cost of producing key chain​s with the company logo printed on them consists of a onetime setup fee of $205.00 plus $0.70 for each key chain produced. This cost can be calculated using the formula C=205.00+0.70p, where p represents the number of key chains produced and C is the cost. Use the formula to calculate the cost of producing 1700 key chains

Answers

Simply add in the known information. To find the cost of 1700 key chains, substitute it for p in the equation, like this: C=205.00+0.70(1700) and solve.
C = 205 + 0.70p......when p = 1700

C = 205 + 0.70(1700)
C = 205 + 1190
C = 1395 <==

Lucia wants to buy some posters over the Internet. Each poster costs $6.67 and has a shipping cost of $9.99 per order. If Lucia wants to spend no more than $30 for her posters, which inequality shows the maximum number of posters, p, that she can buy?

Answers

I think it is 9.99+6.67p<=(less than or equal to)30 so, p<=3
Hope that helps!
6.67p+9.99≤30

....

subtract 9.99 from both sides

6.67p≤20.01  divide both sides by 6.67

p≤3

So the maximum number of posters that she can buy is 3.

It takes 1629 digits to number the pages of a book.How many pages does the book have?

Answers

Look at the picture below to know how to solve this problem. Click on the magnifying glass if you need a closer look at it. 

Answer: The book has 579 pages

Hope that helps! ★ If you have further questions about this question or need more help, feel free to comment below or leave me a PM. -UnicornFudge aka Nadia

What's the answer to this!! The highest point on the state of Louisiana is driskall mountain. It rises 535 feet above sea level. Write the elevation of driskall mountain as an integer

Answers

+535 is the integer to Driskill Mountain

Write 2.95 as the quotient of two integers

Answers

2.95 = 295/100 then you can reduce the fraction to 59/20
It would be
--------------------------------------------------------
1. 118/40
~~~~~~~~~~~
2. 15/28

a triangle brace has an angle measure of 92 degrees, with a side opposite this angle measuring 10 inches. the base of the triangular brace, which is adjacent to the given angle measure, is 12 inches in length. Which of the following statements is correct

Answers

Final answer:

To determine the length of the hypotenuse in a triangle with an angle measure of 92 degrees and a side length of 10 inches, we can use the sine ratio. Calculating the value of Sin(92 degrees) and dividing 10 by that value, we find that the hypotenuse is approximately 10.001525 inches.

Explanation:

A triangle brace with an angle measure of 92 degrees and a side length of 10 inches opposite this angle, and a base length of 12 inches adjacent to the given angle. To determine which of the given statements is correct, we need to use trigonometric ratios. We can use the sine ratio in this case.

The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, the angle measure is 92 degrees and the side opposite is 10 inches. Let's calculate:

Sin(92 degrees) = Opposite/Hypotenuse

Sin(92 degrees) = 10/Hypotenuse

To solve for the hypotenuse, we can rearrange the equation:

Hypotenuse = 10/Sin(92 degrees)

Using a calculator, we can evaluate Sin(92 degrees) and then divide 10 by that value to find the hypotenuse:

Hypotenuse = 10/0.9998477 = 10.001525 inches (approximately)

Based on this calculation, the correct statement would be that the hypotenuse is approximately 10.001525 inches.

3 times what gives me a sum of 24? im trying to finish my homework so please help.

Answers

It is not a sum, it is a product.

3 times x = 24   (write equation)
           3x = 24  (isolate x by dividing the coefficient, 3, on both sides)
           /3     /3
             x = 8    (this i your answer)

Therefore 3 times 8 gives you 24.
Hey there!

I believe instead of sum, it should be product. A product is a result of a multiplication problem, which is what we're doing when we do something "times" something else. 

You could solve this by simply dividing 24 by 3 to get 8. You could then check this by multiply 3 by 8 to get 24 again.

Hope this helped you out! :-)

3000000000 times 9000000000

Answers

A calculator can be used, provided it is "wide" enough -- the display can handle 10-digit numbers. The answer might be displayed in scientific notation, which is a great thing to learn about if you don't already know!

"Shortcut": the first number ends in 9 zeros; the second number ends in 9 zeros.  3 times 9 is 27. The answer will begin with 27 and end with 9 + 9 zeros.

27000000000000000000

27,000,000,000,000,000,000

Twenty-seven quintillion!
1800000000000000000000000000000

The value of 7 in ___ is 10 times
The value of 7 in ____

Answers

the value of 7 in 1374 is ten times the value of 7 in 1347

Your class is holding elections to choose a leadership committee of 4 students. If there are 30 students in the class, how many different leadership committees would it be possible to elect?

810,000

27,405

120

657,720

Answers

Since order is not important we are only looking for unique combinations of 3, so we need to use the "n choose k" formula.

n!/(k!(n-k)!), n=number of elements to choose from, k is the number of choices made....in this case:

30!/(4!(30-4)!)

30!/(4!*26!)

27405


Using the combination formula, it is found that it would be possible to elect 27,405 different leadership committees.

The order in which the students are selected to the committee is not important, which means that the combination formula is used to solve this question.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 4 students are chosen from a set of 30, thus:

[tex]C_{30,4} = \frac{30!}{4!26!} = 27405[/tex]

It would be possible to elect 27,405 different leadership committees.

A similar problem is given at https://brainly.com/question/24437717

a number divided by 7 is 9

Answers

A number divided by 7 is 9: [tex] \frac{x}{7} =9[/tex]
Multiply both sides by 7 to get the answer so it'll be: [tex] \frac{x}{7} (7)=9(7)[/tex]

x = 63
If a number divided by 7 is 9, then 9 times 7 is 63.
63/7= 9

steps in how to solve

Answers

First, you replace x with -3. 
It will look like -3/3.
Then you divide and get -1.

What are the factors of 60a

Answers

1,2,3,4,5,6,1012,15,20,30

Answer:

Factors of 60 are:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60

ini earned $160 during the summer doing chores. She bought 3 dresses worth $12 each using her chore money. How much money was left after she bought the dresses?

Answers

$160 minus 3 dresses x $12 ($36) = $124 left after spending her chore money SO snswer is--- $124 --


A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 6t, where t represents time in minutes and p represents how far the paint is spreading.

The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(p) = πp2.

Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your work. (6 points)

Part B: How large is the area of spilled paint after 8 minutes? You may use 3.14 to approximate π in this problem. (4 points)


Answers

p(t)=6t

A(p)=πp^2, since p(t)=6t

A(t)=π(p(t))^2

A(t)=π(6t)^2

A(t)=36πt^2, so when t=8 and approximating π≈3.14

A(8)≈36(3.14)(8^2)

A(8)≈36(3.14)64

A(8)≈7234.56 u^2

Answer:

r(t) = 3t ; where t represents the time in minutes and r represents how far the paint is spreading.

A(r) = πr²

Part A:  

A[r(t)] = π (3t)² = 3.14 * 9t² = 28.26t²

Part B:

r(10) = 3(10) = 30

A(r) = 3.14 * 30² = 3.14 * 900 = 2,826 square unit

Step-by-step explanation:

Polygon ABCD has the following vertices:

A(−4, 2), B(3, 2), C(3, −5), and D(−4, −2)

Calculate the area of the polygon.

Answers

To be able to solve clearly this problem, the best thing to do is to plot the graph (see attached pic). From the graph we can see that the points form a trapezoid.

The base is formed by the segment connecting point A and point B.

While the two heights: shorter one by the segment connecting points A and D, and the longer one by the segment connecting points B and C.

The formula for area of trapezoid is given as:

A = b (h1 + h2) / 2

Where,

b = base of the trapezoid  = 3 – (-4) = 7

h1 = shorter height = 2 – (-2) = 4

h2 = longer height = 2 – (-5) = 7

Therefore the area is:

A = 7 (4 + 7) / 2

A = 77 / 2

A = 38.5 

The answer is 38.5. I took this exam and I chose 38.5 and got it right, I hope this helps!



Diana is going camping with her family. Their campsite is 5/8 mile away. They walk at a steady speed of 2 1/2 miles per hr. How many minutes will It take them to get to the campsite

Answers

Diana is going camping with her family. Their campsite is 5/8 mile away. They walk at a steady speed of 2 1/2 miles per hr. How many minutes will It take them to get to the campsite.


alright so we know it takes an hour for them to travel 2 1/2 miles...
60minutes=1hr
60minutes=2 1/2 miles

now if you convert that fraction to a denominator of 1/8...
2 1/2=5/2=10/4=20/8
so in 6o minutes they travel 20/8 miles...
and if you divide 20/8 by 4 you get...
20/8/4=5/8
and so if you divided one side of the equation (60minutes=20/8) you have to divide the other side so...
60/4=20/8/4
and once you divide both sides you will get the answer...
15 minutes=5/8miles
Answer: 15 minutes

WALK Heather was out for a leisurely walk at a rate of 3 miles per hour. What was her speed in yards per minute?

Answers

3 * 1760= 5280 yd.
5280/60= 88 yards per minute.
Hope this helps.

What is the average speed (miles/hour) for an object going 1500 feet in 1 minute. Round answer to two decimal places.

Answers

there are 3600 seconds per hour

5280 feet per mile

1 foot per second = 3600/5280 = 0.681818 Miles per Hour

 60 seconds per minute

 so 1500/60 = 25 feet per second

25 x 0.681818 = 17.05 miles per hour


Which of the following points is a solution to the system of linear inequalities
Which of the following points is a solution to the system of linear inequalities?
{2x+y<-5
{-x+y>0
A.
(4, 1)
B.
(–4, –1)
C.
(–8, –21)
D.
(8, 11)

Answers

for it to be a solution, it has to satisfy both inequalities...

subbing in (-4,-1)

2x + y < -5                           -x + y > 0
2(-4) - 1 < - 5                      -(-4) - 1 > 0
-8 - 1 < -5                              4 - 1 > 0
-9 < -5.....true                        3 > 0....true

solution is (-4,-1)

Answer:

(-4,-1) satisfies the given system of inequalities

Step-by-step explanation:

[tex]2x+y<-5[/tex]

[tex]-x+y>0[/tex]

To find out the solution we check with each option

(4,1) , x=4 and y=1 (Plug in x and y values in the given inequalities)

[tex]2(4)+1<-5[/tex]

[tex]9<-5[/tex] False

(-4,-1) , x=-4 and y=-1 (Plug in x and y values in the given inequalities)

[tex]2(-4)-1<-5[/tex]

[tex]-9<-5[/tex] True

Now plug it in second inequality

[tex]-(-4)-1>0[/tex]

[tex]3>0[/tex] True

(-8,-21) , x=-8 and y=-21 (Plug in x and y values in the given inequalities)

[tex]2(-8)-21<-5[/tex]

[tex]-37<-5[/tex] True

Now plug it in second inequality

[tex]-(-8)-21>0[/tex]

[tex]-13>0[/tex] False

(8,11) , x=8 and y=-11(Plug in x and y values in the given inequalities)

[tex]2(8)+11<-5[/tex]

[tex]-9<-5[/tex] false

Other Questions
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