Mathematics High School


[02.05]
Solve for x: 4 − (x + 2) < −3(x + 4) (1 point)


x < −7

x > −7

x < −9

x > −9

Answers

Answer 1
first, get rid of the paranthesis:
4-x-2<-3x-12 => 2-x<-3x-12
next, eliminate x on one side. here I'll eliminate -3x by adding 3x on both side:
2+2x<-12
2x<-14
x<-7

Answer 2

 Option A

x<-7

Given :

[tex]4 - (x + 2) < -3(x + 4)[/tex]

Explanation :

Solve the given inequality for x by applying algebraic properties

We use order of operation to simplify the left and right side of inequality

[tex]4- (x + 2) < -3(x + 4)\\4-x-2<-3x-12\\-x+2 < -3x -12\\Add\; 3x \; on \; both \; sides\\2x+2<-12\\Subtract\; 2\; from \; both \; sides\\2x<-14\\Divide \; both \; sides \; by 2\\x<-7[/tex]

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Related Questions

What point is the image of (3,4) if it is reflected over the y axis?A. (-3,-4)B. (3,-4)C. (-3,4)D. (3,4)

Answers

point is the image of (3,4) if it is reflected over the y axis is (-3,4)
answer
C. (-3,4)

If point is the image of (3,4) if it is reflected over the y axis, then the resulting point is (-3,4) (option c)

When a point is reflected over the y-axis, its x-coordinate changes sign while the y-coordinate remains the same. In other words, if we have a point (x, y), its image after reflection over the y-axis will be (-x, y).

Let's apply this rule to the given point (3, 4). When we reflect it over the y-axis, the x-coordinate changes sign, but the y-coordinate remains the same. Therefore, the image of (3, 4) after reflection over the y-axis will be (-3, 4).

So, the correct Answer: C. (-3, 4)

To know more about reflection here

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A local hamburger shop sold a combined total of 445 hamburgers and cheeseburgers on Tuesday. There were 55 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Tuesday?

Answers

Let x represent the number of hamburgers sold, and (x - 55) represent the number of cheeseburgers sold.

Set up an equation:
hamburgers + cheeseburgers = total number of burgers

x + (x-55) = 445

solve for x: 
2x - 55 = 445

2x = 445 + 55

2x = 500

x = 500÷2

x = 250

This means 250 hamburgers were sold on Tuesday.

Hope this helps!

-Jabba


To solve for the number of hamburgers sold, two equations were setup: H + C = 445 and C = H - 55. Substituting the second equation into the first and solving for H results in finding that 250 hamburgers were sold on Tuesday.

The question asks us to find out how many hamburgers were sold on Tuesday given that a total of 445 hamburgers and cheeseburgers were sold, and there were 55 fewer cheeseburgers than hamburgers. Let's denote the number of hamburgers as H and the number of cheeseburgers as C. We have two equations here: H + C = 445 and C = H - 55. Plugging in the second equation into the first, we get H + (H - 55) = 445, which simplifies to 2H - 55 = 445. Adding 55 to both sides gives us 2H = 500, and dividing both sides by 2 gives us H = 250. Therefore, on Tuesday, the hamburger shop sold 250 hamburgers.

One number is four times another. the greater number is xx. write an expression for the lesser number.

Answers

xx/4=y Y is the lesser number. xx is the greater number. Since xx is four times y, you need to divide xx by four to find y. To find xx, you would need to multiply y times four, and the resulting expression would be 4y=xx.

i think its D but who knows HEEEEELELELLELEELEP

Answers

you plus 4 friends = 5 people

 them multiply 5 by m sp you get 5m

D is the correct answer


Calculat the length of the circumference of a circle with diameter of 8cm.
Use [tex] \pi [/tex] = 3

Answers

Hello there!

The formula for finding the circumference of a circle is 2[tex] \pi [/tex]r (or 2*3*r in your terms). Although we don't have the radius yet, we can certainly find it pretty easily. Keep in mind that the radius will always be half the diameter. So, let's find the radius.

8 / 2 = 4; now we have everything we need to solve for the circumference.

2*3*4 is our expression. Now let's simplify it.
2 * 3 = 6
6 * 4  = 24

Your circumference is 24cm.

I hope this helps!

Sharon writes this sentence:

Seven less than two times a number is 29.



Enter the equation that represents Sharon's sentence into the box.

Use x for the variable.

Answers

The answer is 2x-7=29

Answer:

your answer would be 2x-7+29



What is f(-3) if f(x) =|2x-1|-5

Answers

f(x) = |2x-1|-5

f(x) = |2*(x)-1|-5

f(-3) = |2*(-3)-1|-5 ... replace every x with -3

f(-3) = |-6-1|-5

f(-3) = |-7|-5

f(-3) = 7-5

f(-3) = 2 which is the final answer

Side Note: the vertical bars mean "absolute value" which represents distance. Negative distance makes no sense which is why absolute value results are never negative.

The value of a function is gotten from the input variable

The value of f(-3) is 2.

We have:

[tex]f(x) = |2x - 1| -5[/tex]

Substitute -3 for x

[tex]f(-3) = |2 \times -3 - 1| -5[/tex]

Multiply 2 and -3

[tex]f(-3) = |-6 - 1| -5[/tex]

[tex]f(-3) = |-7| -5[/tex]

Remove absolute bracket

[tex]f(-3) = 7 -5[/tex]

[tex]f(-3) = 2[/tex]

Hence, the value of f(-3) is 2.

See attachment for the graph of [tex]f(x) = |2x - 1| -5[/tex]

Read more about absolute functions at:

https://brainly.com/question/1389494

Macs farm has a total of 18 horses and 27 cows. what is the ratio of horses to cows in simplest form?

Answers

The ratio is basically finding the quotient of two numbers. If you want to find the ratio of horses to cows, divide the number of horses to that of cows.

Ratio = 18/27

When expressing it to its simplest form, make sure it is reduced. 18 and 27 are both factors of 9. So,

Ratio = 9*2/9*3
Cancelling out 9, the ratio at its simplest form is: 2/3

Answer:

2/3

Step-by-step explanation:

Suppose there are n students in a class what is the probability at least two students have same birthday

Answers

I don't have enough info to solve this
P(at least two have same birthday) =
1 - (1/2)^(n).

Since no specific number of students is given, we only get an expression.

Y’all I am struggling. Help me out please I’ll give 15 points! #7

Answers

Since the angles in triangle ACM indicate that it is a 30-60-90 triangle, we know that the other two sides of triangle ACM are 20 and 10 (30-60-90 triangles have a very specific side coefficient). This means that the sides of this triangle have side lengths 40, 10, and [tex]20\sqrt{3}[/tex]. Adding these together you get 50+[tex]20\sqrt{3}[/tex]. Hope this helps!

The function graphed represents the amount of water in a container, in gallons, x minutes after a drain is opened.

What is the meaning of each key feature of the graph?

Drag the answer into the box to match each item.

Answers

The x-intercept: The number of minutes it takes for the container to empty
The y-intercept: The number of gallons in the container before the drain is open

Hope this helps!!

Let

x-------> the time in minutes

y-----> the function that represent the amount of water in gallons

Step 1

Find the x-intercept

we know that

The x-intercept is the value of x when the value of the function is equal to zero

In this problem (see the graph)

For [tex]y=0[/tex]

the value of x is [tex]15\ min[/tex]

so

the x-intercept is the point [tex](15,0)[/tex]

that means

The number of minutes it takes for the container to empty  is [tex]15\ min[/tex]

Step 2

Find the y-intercept

we know that

The y-intercept is the value of the function y when the value of x is equal to zero

In this problem (see the graph)

For [tex]x=0[/tex]

the value of the function y is [tex]120\ gal[/tex]

so

the y-intercept is the point [tex](0,120)[/tex]

that means

The number of gallons in the container before the drain is open is [tex]120\ gal[/tex]

therefore

the answer in the attached figure


You can jog around the block twice and the park once in 10 min. You can jog around the block twice and the park 3 times in 22 min. Write a system of linear equations that represents this situation. How long does it take to jog around the park?

Answers

b = block     p = park

2b + p = 10 min                2 runs around the block takes 10 minutes
2b + 3p = 22 min        2 runs around the block plus 3 runs around the park                                                       takes 22 minutes

To solve, I will use substitution. First, I will divide the first equation by 2 to get b by itself and subtract p from both sides to get b by itself. Then, substitute 5 - 1/2p in for b in the second equation because they have equal values. Then, subtract 10 from both sides to eliminate it. Divide by 2 to both sides to get 'p' by itself.

2b + p = 10 min ---------→b + 1/2p = 5 ----------→ b = 5 - 1/2p

2(5 - 1/2p) + 3p = 22 ---------→ 10 -p + 3p = 22 --------→ 10 + 2p = 22

10 + 3p = 22 ----------→ 2p = 12

2p = 12 -------------→ p = 6

It takes 6 minutes to jog around the park

Hope this helps!

In a zoo there are 17 more monkeys than lions and 30 more lizards than lions. If there were 151 monkeys, lions and lizards in total, how many of each kind are there?

Answers

If the amount of monkeys is m, lions is a, and lizards is b, then a+b+m=151, 17+a=m (since there are 17 more monkeys than lions), and 30+a=b. Substituting those values in (17+a=m and 30+a=b), we have 30+17+a+a+a=151=47+3a. Subtracting 47 from both sides, we get 104=3a. Next, we can divide both sides by 3 to get 104/3=a (the number of lions), 104/3+17=the number of monkeys, and 104/3+30=the number of lizards. Somehow we end up with a fraction (not a whole number), so there are 2/3rds of monkeys floating around using this logic.


Jose receives a $10 gift card for downloading music and wants to determine how many songs he can purchase. Each downloaded song costs $1.19. Write and solve an inequality to determine how many songs Jose can purchase. What does the solved inequality represent?

Answers

Final answer:

To determine the number of songs Jose can purchase using his gift card, the inequality 1.19x ≤ 10 is solved, resulting in x ≤ 8.4, meaning Jose can purchase a maximum of 8 songs.

Explanation:

Jose's gift card scenario:

Let's denote the number of songs he can purchase as x.

The inequality to represent this situation is: 1.19x ≤ 10 (the total cost of the songs cannot exceed the value of the gift card).

Solving for x, we get x ≤ 8.4. Since he can't purchase a fraction of a song, Jose can purchase a maximum of 8 songs using the gift card.

Ana wants to paint her dogs doghouse. She has 4 colors: Green, Maroon, Blue and Wheat. One color will cover the walls, and another color will be used for the trim. (For example, green walls with wheat trim = GW.) Which one of these answers show all of the possible color combinations?

A. BW, BM, BG, BB, MW, MB, MG, MM, GW, GB, GM, GG
B. GM, GB, GW, MG, MB, MW, BG, BM, BW, WG, WM, WB
C. MM, MG, WB, WM, WG, BB, BG, BM, WB, GB, GM, GW

Answers

Let us take this one by one. One color can pair with three colors.

 

Green = Maroon, Blue, Wheat = GM, GB, GW

Maroon = Green, Blue, Wheat = MG, MB, MW

Blue = Green, Maroon, Wheat = BG, BM, BW

Wheat = Green, Maroon, Blue = WG, WM, WB

 

So the combinations are:

 

GM, GB, GW, MG, MB, MW, BG, BM, BW, WG, WM, WB

 

Which is letter B.

The awnser is b trust I got it right thank you for your time nd day

15. How much less would a 25 year old male pay for a $50,000 policy of 20 y life insurance @ $5.84 per $1000, than a straight life policy @ $15.66 per $1000? (Points : 1)
$783
$491
$292
$415

Answers

The man would pay $491 less for a policy of 20 year life insurance than a straight life policy. So, the answer is the second one.

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

Amount for policy = $50,000

If he opt for life insurance @$5.84 per $1000,

then, his amount of premium will be

[tex]50000\times \frac{5.84}{1000}=\$292[/tex]

If he opt for straight policy @ $15.66 per $1000,

then, his amount of premium will be

[tex]50000\times \frac{15.66}{1000}=\$783[/tex]

Difference in both the cases will be

[tex]783-292=\$491[/tex]

Hence, Second option is correct.

Find the dimensions of the rectangle with largest area that can be inscribed in an equilateral triangle with sides of 1 unit, if one side of the rectangle is on the base of the equilateral triangle.

Answers

Maximum area = sqrt(3)/8 Let's first express the width of the triangle as a function of it's height. If you draw an equilateral triangle, then a rectangle using one of the triangles edges as the base, you'll see that there's 4 regions created. They are the rectangle, a smaller equilateral triangle above the rectangle, and 2 right triangles with one leg being the height of the rectangle and the other 2 angles being 30 and 60 degrees. Let's call the short leg of that triangle b. And that makes the width of the rectangle equal to 1 minus twice b. So we have w = 1 - 2b b = h/sqrt(3) So w = 1 - 2*h/sqrt(3) The area of the rectangle is A = hw A = h(1 - 2*h/sqrt(3)) A = h*1 - h*2*h/sqrt(3) A = h - 2h^2/sqrt(3) We now have a quadratic equation where A = -2/sqrt(3), b = 1, and c=0. We can solve the problem by using a bit of calculus and calculating the first derivative, then solving for 0. But since this is a simple quadratic, we could also take advantage that a parabola is symmetrical and that the maximum value will be the midpoint between it's roots. So let's use the quadratic formula and solve it that way. The 2 roots are 0, and 1.5/sqrt(3). The midpoint is (0 + 1.5/sqrt(3))/2 = 1.5/sqrt(3) / 2 = 0.75/sqrt(3) So the desired height is 0.75/sqrt(3). Now let's calculate the width: w = 1 - 2*h/sqrt(3) w = 1 - 2* 0.75/sqrt(3) /sqrt(3) w = 1 - 2* 0.75/3 w = 1 - 1.5/3 w = 1 - 0.5 w = 0.5 The area is A = hw A = 0.75/sqrt(3) * 0.5 A = 0.375/sqrt(3) Now as I said earlier, we could use the first derivative. Let's do that as well and see what happens. A = h - 2h^2/sqrt(3) A' = 1h^0 - 4h/sqrt(3) A' = 1 - 4h/sqrt(3) Now solve for 0. A' = 1 - 4h/sqrt(3) 0 = 1 - 4h/sqrt(3) 4h/sqrt(3) = 1 4h = sqrt(3) h = sqrt(3)/4 w = 1 - 2*(sqrt(3)/4)/sqrt(3) w = 1 - 2/4 w = 1 -1/2 w = 1/2 A = wh A = 1/2 * sqrt(3)/4 A = sqrt(3)/8 And the other method got us 0.375/sqrt(3). Are they the same? Let's see. 0.375/sqrt(3) Multiply top and bottom by sqrt(3) 0.375*sqrt(3)/3 Multiply top and bottom by 8 3*sqrt(3)/24 Divide top and bottom by 3 sqrt(3)/8 Yep, they're the same. And since sqrt(3)/8 looks so much nicer than 0.375/sqrt(3), let's use that as the answer.
The area of the rectangle is equal to L x W where L is the length and W is the width. 

               A = L x W

If we let L be the length and given that the triangle is equilateral with sides equal to 1, the value of W should be (0.5 - L/2)(tan 60)

           W = (0.5 - L/2)(tan 60)

Simplifying the expression for the width,
          W = 0.866 - 0.866L

The area now becomes,
      A = (L)(0.866 - 0.866L)

Simplifying,
    
   A = 0.866L - 0.866L²

Derive and equate to zero for the maximum value of L. 
   dA = 0.866 - 2(0.866)(L) = 0

The value of L from the equation should be 0.5. 
           W = 0.866 - 0.866(0.5) = 0.433

Answer: L = 0.5
             W = 0.433

find three consecutive odd integers such that the square of the first plus the square of the third is 170

Answers

Here is the set up:

x
x + 2
x + 4

x^2 + (x + 2) + (x + 4)^2 = 170

Take it from here.

A store offers customers two ways to pay for a new TV. Option 11: Pay $1,500$1,500 today. Option 22: Pay nothing today, and take out a simple interest loan to pay a total of $1,650$1,650 one year from now. What is the simple interest rate on the loan in option 22?

Answers

Let's solve for the simple interest rate on the loan in option 2. We formulate an equation by enumerating the following: 
Option 1: If the customer pays today, the amount needed is only $1500. 
Option 2: If the customer pays after 12 months, the total amount is $1650. 
The equation is $1500+ ($1500x%charge) =$1650. Solve for % charge after 12 months, %charge = ($1650-$1500) /$1500 %charge =0. 1 or 10%

Therefore, the percent charge after 12 months is 10%.

find the root of 6x-48=0

Answers

undistribute 6
(6)(-48)=0
set to zero
x-8=0
add 8 to both sides
x=8
the root is at x-8
Find the roots of 6x-48=0 by solving for x.

X=8

A garden table and a bench cost $573 combined. The garden table costs $77 less than the bench. What is the cost of the bench?

Answers

just do 573 minus 77

Because the total cost is $573.00, subtract the cost of the garden table from the total. 

• 573 - 77 = 496

So, the bench costs $496.00.

Hope this helps! :D

~PutarPotato

A store sells small notebooks for ​$8 and large notebooks for ​$10. if a student buys 6 notebooks and spends ​$56​, how many of each size did he​ buy?

Answers

The first thing you have to do is find a way to make the last digit 6 (since its $56). So that would be $8×2=16, so there are 2 small notebooks. Then, she needs another $40 to get $56, so 40÷10=4, so she bought 4 large notebooks.

Answer: 2 small, 4 large
I would approach this from a Guess and Check Strategy. Take combinations of two numbers when added equal six: 0 + 6 1+ 5. 2+ 4, 3 + 3, 4 + 2, 5 + 1, 6 + 0. Take a combination like 3 + 3. If the student bought 3 notebooks at $8  each and 3 notebooks at $10 each it would be $24 + $30 = $54 which is just short of $56. You could use each of the combinations in the same way until you match $56. In the end the combination of 2 + 4 would solve the problem. Two notebooks at $8 each plus four notebooks at $10 each would be: $16 + $40 which does equal $56. So the student bought 2 notebooks at $8 each and 4 notebooks at $0 each.

Solve this Multi-Step Equation

-3(t + 5) + (4t + 2) = 8

Answers

-3t-15+4t+2=8
-3t+4t=8+15-2
t=21
Im guessing you just want to know what t equals so, t=21

A vending machine needs to be programmed to accept any combination of coins totaling 0.75, excluding pennies, and half dollars. How many combinations are possible?

Answers

Combination 1: 3 quarters (25 cent).

Combination 2: 2 quarters and 5 nickels.

Combination 3: 2 quarters, 2 dimes, 1 nickel.

Combination 4: 15 nickels

Combination 5: 7 dimes and 1 nickel.

Combination 6: 1 quarter, 5 dimes

Combination 7: 1 quarter, 1 dime, 7 nickels.

Combination 8: 1 quarter, 2 dimes, 6 nickels.

Combination 9: 1 quarter, 3 dimes, 4 nickels.

Combination 10: 1 quarter, 4 dimes, 2 nickels.

I believe those are all the possible combinations.

I hope that helped you! :)

You know that you can ride your bike 8 miles in 20 minutes. At the same pace, how many miles would you go in 2 hours?

Answers

Hello there,
2 hrs= 160 minutes
20 minutes= 8 miles
160 minutes= ? miles
As you can see 20 x 8 = 160 miles 
So, you need to multiply 8 in both sides (meaning- 20 x 8 & 8 x 8)
160 minutes= 64 miles

Hope this helps

~Top 

Martha took 48 pictures of flowers and 36 pictures of beautiful scenery.she wants to display the pictures so there are the same number of each kind of picture in each display.what is the greatest number of displays she can make?

Answers

Well if you have 48 pics of flowers and 36 pictures of scenery and you want an equal amount of pictures of the scenery, you want to start out by just seeing what number divides evenly into both, in this case, it is four.

Where do the graphs of y = 3x and y= 3x + 4 intersect the y -axis and what is the relationship between the two lines?

Answers

y=3x should intersect the y-axis at 0,0 (technically it is y=3x+0) and for y=3x+4, (0,4) is where the equation intersects the y-axis. Because both these equations share the same slope, this means the two lines are parallel to each other. Hope this helps!
The equations y = 3x and y = 3x + 4 can not intersect because they have the same slope meaning they are both parallel lines.

Hope I helped :)

What is the LCM of 5 and 6?

Answers

Answer: 30

Explanation: To find the least common multiple of lcm of 5 and 6, we begin by listing the first few multiples of each number.

Multiples of 5

1 x 5 = 5

2 x 5 = 10

3 x 5 = 15

4 x 5 = 20

5 x 5 = 25

6 x 5 = 30

Notice that we skipped 0 x 6 in our list of multiples. That's because 0 x 6 is 0 and our least common multiple can't be 0.

Next we list the multiples of 6. When we list the multiples of 6, it's a good idea to keep an eye on the list of multiples for 6 so that we know when we have found a least common multiple.

Multiples of 6

1 x 6 = 6

2 x 6 = 12

3 x 6 = 18

4 x 6 = 24

5 x 6 = 30

Notice that 30 appears in both lists so we can stop here.

This means that the least common multiple of 5 and 6 is 30.

Answer:

30

Step-by-step explanation:

both 6 and 5 go into 30 :)

Find the greatest common factor of 16, 27 and 20

Answers

Can you list the factors of each of those numbers (the numbers that divide evenly into them)? Of those three lists, what's the highest number present in all three?
The greatest common factor for 16, 27, and 20 is 1.
The factors for 16 are 1,2,4,8,16.
The factors for 27 are 1,3,9,27.
The factors for 20 are 1,2,4,5,10,20.

The length of a quarter is 0.955 inch.Round the length of a quarter to the nearest tenth of an inch

Answers

0.955 rounded to the nearest tenth is 0.1

0.955 rounded to the nearest tenth would be 1.0


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