what is the absolute value of

Answer: 18

Step-by-step explanation:

3 times 6

Answer:

A

Step-by-step explanation:

given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the given condition x = 24 and y = 360

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{360}{24}[/tex] = 15

Hence y = 15x is the equation → A

Answer: A

Step-by-step explanation:

Answer: a - add 3 to both sides

Step-by-step explanation: you want to have the variable with the number all to itself to solve for x, so you have to add 3 to both sides to get 3/4x=-15. then divide by 3/4 to both sides and you will get a final answer.

Answer:

A = 53.34 [tex]units ^ 2[/tex]

Step-by-step explanation:

To find the length of the rectangle we solve the PLA triangle

Using the Pythagorean theorem we find the PL side.

[tex]PL = \sqrt{4^2+12^2}\\PL = \sqrt{16+144}\\PL = 12.65[/tex]

Then the length of the rectangle is 12.65

Now we solve the MALU triangle. Where MU = PL

We use the Pythagorean theorem:

[tex]MU^2+LU^2 = (MA + AL)^2\\12.65^2+LU^2 = (MA+12)^2[/tex]

Where LU and MA are unknown.

Finally we solve the triangle MPA

[tex]MA^2 + PA^2 = PM ^2[/tex]

Where PM = LU

So:

[tex]MA^2 + 4^2 = LU^2[/tex]

Now we have two equations and two unknowns. So we solve the system.[tex]12.65^2 + LU^2 = (MA + 12) ^2[/tex]  (i)

[tex]MA^2+4^2 = LU^2[/tex]  (ii)

We introduce (ii) in (i)

[tex]12.65^2 + MA^2+16=MA^2+24MA+144[/tex]

Now we clear MA

[tex]160.02+16-1 44 = 24MA[/tex]

[tex]32.02 = 24MA[/tex]

[tex]MA = \frac{32.02}{24}[/tex]

MA = 1.3342 (iii)

Now we introduce (iii) in (ii)

1.3342^2 + 4^2 = LU^2

LU = 4.2166

Now we have the length of the rectangle and also its width.

The area A of a rectangle is:

A = l*w

Where

 l = length

w = width

A = 4.2166*12.65

A = 53.34 [tex]units^2[/tex]

Answer:

He would make $4391.92

The constant of proportionality is 14.6

Step-by-step explanation:

If Daniel works 213 hours and makes $1820.00

(I assume that is a typo and he made 1820. not 18.20)

How much does he make per hour

$1820/213 = $8.54 per hour

Now if he works 514 hours

514 * 8.54/hour = $4391.92

y = kx, where k is the constant of proportionality

a = 14.6h,

The constant of proportionality is 14.6

To find the total loudness of three earphones with a given ratio is 1176 decibels.

The ratio of loudness of the earphones is 6:5:3. Given that Polina's earphones have a loudness of 420 decibels, we can find the loudness of Lala's and Goffy's earphones. Let the loudness of Lala's earphones be 6x, Polina's is 5x, and Goffy's is 3x.

Adding the loudness of all three earphones, we have: Lala's (6x) + Polina's (420) + Goffy's (3x). Substituting 5x = 420 and solving gives 5x = 420, x = 84. Therefore, the total loudness of all three earphones is 6(84) + 420 + 3(84) = 504 dB + 420 dB + 252 dB = 1176 decibels.

Answer: a=2 b=5 c=-7

parabola equation is y = 2x^2+5x-7 = 0

Step-by-step explanation:

Substitute (x,y) into y = a x^2 + b x + c

(2,11)      11 = 4a + 2b + c

(-1,-10)  -10 = a - b + c

(-4,5)      5 = 16a -4b + c

Solve the linear system in a, b, c

Det[{{4,2,1},{1,-1,1},{16,-4,1}}] = 54

Det[{{11,2,1},{-10,-1,1},{5,-4,1}}] = 108

Det[{{4,11,1},{1,-10,1},{16,5,1}}] = 270

Det[{{4,2,11},{1,-1,-10},{16,-4,5}}] = -378

a = 108/54 = 2

b = 270/54 = 5

c = -378/54 = -7

parabola equation is y = f(x) = 2x^2+5x-7

f(2) = 8+10-7 = 11 ✔

f(-1) = 2-5-7 = -10 ✔

f(-4) = 32-20-7 = 5 ✔

Answer: The volume of a block of ice is 9 meters

You have to LxWxH

Answer: I am pretty sure your answer is 208 cm. Whenever you see a percentage immediately change it to a decimal like in this case 0.070 and multiply it by 400. 400x0.070 is equal to 280. Hope this helps :)

Answer: h = -4

Step-by-step explanation:

-9h-6+12h+40=22

-9h+12h=22+6-40 "collect all unknown values in a side and collect numbers in other side "

"Don't forget to Change signs"

3h= -12

3h/3 = -12/3 "dividing by 3 in both sides"

h= -4

[tex]-9h-6+12h+40=22\qquad\text{combine like terms}\\\\(-9h+12h)+(-6+40)=22\\\\3h+34=22\qquad\text{subtract 34 from both sides}\\\\3h=-12\qquad\text{divide both sides by 3}\\\\\boxed{h=-4}[/tex]

Answer:

y = -2x+11

Step-by-step explanation:

If we have a slope and a line, we can use the slope intercept form of a line

y-y1 = m(x-x1)

where (x1,y1) is the point and m is the slope.

Substitute in what we know

y-5 = -2 (x-3)

We want it in slope intercept form which is y = mx+b

Distribute the -2

y-5 = -2x+6

Add 5 to each side

y-5+5 = -2x +11

ANSWER:

y = -2x + 8

ABOUT POINT SLOPE FORM:

ABOUT SLOPE INTERCEPT FORM:

y - Y1 = m (x - X1)

y - 5 = -2 (x - 3)

y - 5 = -2x + 3

 + 5           + 5

y = -2x + 8 --- IN SLOPE INTERCEPT FORM

Hope this helps you!!! :)

You can use same operations on both sides such that both sides' x value come on one side and rest of the values go on other side so that you get what is equal to x.

The value of x is 6

It is because [tex]a^x[/tex] where x is a variable and "a" is a constant, is a function. A function only outputs single value to each input.

If for x = p and x = q, we get same value, then we will have  [tex]a^x[/tex]  not being a function. Thus, for that to be a function, we need those inputs same too for output to be same.

Thus,  [tex]a^p = a^q \implies p = q[/tex]

Remember that we need base to be same(here a is base and p and q are exponents)

We can use the fact that 64 is cube of 3 and can use the above stated fact.

Thus, we have:

[tex]4^{(x+30)} = 64^{(2x)}\\4^{x+30} = 4^{3^{2x}} \\\\\text{since power of power will multiply, thus,}\\\\4^{x + 30} = 4^{6x}\\\\or\\\\x+30 = 6x\\\\\text{Subtracting x on both sides}\\\\30 = 5x\\\\\text{Dividing by 5 on both sides}\\\\6 = x\\x = 6[/tex]

Thus, The value of x is 6

Learn more about base and exponent here:

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Answer:

13 y^2 - 9 x y + 3 x^2

Step-by-step explanation:

Simplify the following:

6 x^2 - 7 x y + 8 y^2 - (x^2 - 3 x y - y^2) - (2 x^2 + 5 x y - 4 y^2)

-(x^2 - 3 x y - y^2) = -x^2 + 3 x y + y^2:

6 x^2 - 7 x y + 8 y^2 + -x^2 + 3 x y + y^2 - (2 x^2 + 5 x y - 4 y^2)

-(2 x^2 + 5 x y - 4 y^2) = -2 x^2 - 5 x y + 4 y^2:

6 x^2 - 7 x y + 8 y^2 - x^2 + 3 x y + y^2 + -2 x^2 - 5 x y + 4 y^2

Grouping like terms, 6 x^2 - 7 x y + 8 y^2 - x^2 + 3 x y + y^2 - 2 x^2 - 5 x y + 4 y^2 = (8 y^2 + y^2 + 4 y^2) + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2):

(8 y^2 + y^2 + 4 y^2) + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2)

8 y^2 + y^2 + 4 y^2 = 13 y^2:

13 y^2 + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2)

x y (-7) + x y 3 + x y (-5) = -9 x y:

13 y^2 + -9 x y + (6 x^2 - x^2 - 2 x^2)

6 x^2 - x^2 - 2 x^2 = 3 x^2:

Answer:  13 y^2 - 9 x y + 3 x^2

Answer:

She need 72 index cards.

Step-by-step explanation:

Ms. James has a 6 square foot bulletin board and a 12 square food bulletin board and she wants to cover both boards with index cards without gaps or overlaps.

Each index card has an area of [tex]\dfrac{1}{4}[/tex] square foot.

Dividing the area of each board with the area of the index card will yield the the number of cards she needs to cover up completely.

Let us assume T₁ and T₂ are the number of cards she needs to cover 6 square feet food bulletin board and 12 square feet food bulletin board respectively. So

[tex]T_1=\dfrac{6}{\frac{1}{4}}=24,\\\\T_2=\dfrac{12}{\frac{1}{4}}=48[/tex]

Therefore, in total she need 24+48=72 index cards.

Answer:

if a polygon is square,then it is also a rectangle is correct

Step-by-step explanation:

1)if a polygon has 4 right angles,then it is a square is wrong since in the statement a square has all its angles as right angles but it need not imply that it is a square as it could also be a rectangle

2) polygon need not have four right angles eg:rhombous with angles 60°,60°,120°,120° is also a polygon

3)every polygon need not be a rectangle as it could be square

4)if a polygon is square, then all its angles are right angles and if all its angles are right then it is rectangle.

hence option 4 is true.

Answer:

$120.96

Step-by-step explanation:

So the area of the room is 14*12. So the area of the room is 168ft^2. So now we multiply it by .72 because it costs .72 per square foot. So the cost is 120.96

To calculate the cost of installing wallpaper around a rectangular room measuring 14 feet by 12 feet, you first find the perimeter, which is 52 feet, then multiply by the cost per foot, $0.72, leading to a total cost of $37.44.

The formula for the perimeter P of a rectangle is P = 2(length + width). In this case, the length is 14 feet and the width is 12 feet.

P = 2(14 feet + 12 feet) = 2(26 feet) = 52 feet.

Now that we have the perimeter, we multiply it by the cost per foot of the wallpaper to find the total cost. The wallpaper costs $0.72 per foot.

Total cost = Perimeter × Cost per foot = 52 feet × $0.72/foot = $37.44.

Hence, it will cost $37.44 to install the wallpaper around the rectangular room that measures 14 feet by 12 feet.

Answer:

p = 10t - 100

Step-by-step explanation:

Perform the indicated multiplication:  p = 10t - 100.

The equivalent form of the algebraic equation p = 5(2t - 20) is p = 10t - 100, which is a simplified linear representation of the original equation.

The student is looking for an equivalent form of the algebraic equation p = 5(2t - 20). By distributing the 5, we obtain p = 10t - 100. This is now a simplified linear equation representing the same rule as the original equation. It's also similar to manipulating a quadratic equation to find the value of t, as shown in the other examples provided. However, this linear equation doesn't require solving for t; rather, we're simply rewriting it in a more straightforward format.

Answer:

D

Step-by-step explanation:

Answer: We can say that (a/b)^2 is a rational number

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

Proof:

Rational means the number is a ratio of two whole numbers

If 'a' is rational, then a = p/q for some whole numbers p,q (eg: p = 2, q = 3 so p/q = 2/3)

The same applies for b, which I'll let b = r/s, with r & s being whole numbers.

To avoid division by zero, I'm going to make p,q,r,s nonzero which leads to 'a' and 'b' being nonzero.

Now let's divide 'a' over b to get

a/b = (p/q) divided by (r/s)

a/b = (p/q) * (s/r)  .... flip the second fraction; multiply

a/b = (ps)/(qr)

The new numerator is p*s which is a whole number (because the product of two whole numbers is also a whole number). The same goes for q*r in the denominator. So a/b is rational if both 'a' and 'b' are rational together.

We can extend this to (a/b)^2 as well

(a/b)^2 = [ (ps)/(qr) ] ^2

(a/b)^2 = [ (ps)^2 ]/[ (qr)^2 ]

(a/b)^2 = (p^2*s^2)/(q^2*r^2)

p is a whole number, and so is p^2. Same for s and s^2. Overall, the final numerator p^2*s^2 is also a whole number. Similarly, q^2*r^2 is a whole number.

So we have yet another ratio of two whole numbers proving that (a/b)^2 is a rational number.

Answer:

136 ounces

Step-by-step explanation:

So you take 8.5 lbs and multiple it by the second number in the ratio this only works if the first number is 1 and it represents what you are starting with  

8.5*16=136

To convert pounds to ounces, multiply the number of pounds by 16. An 8.5 pound baby weighs 136 ounces.

To convert pounds to ounces, you need to multiply the number of pounds by 16 because there are 16 ounces in 1 pound.

In this case, an 8.5 pound baby would be equivalent to:

8.5 pounds x 16 ounces/pound = 136 ounces

Therefore, an 8.5 pound baby weighs 136 ounces.

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Answers are attached in the pictures. Solutions are in RED.

Answer:

12. 7.5

13. 0.224

14. 193.5

15. 2/3

16.  5/7

17. -10

18. 2:1

19. 16

20. 150

21. 46,200

22. 4

23. 18

24. 5.29

25. 7.07

26. 19.80

27. 15.87

28. 9.80

29. 6.71

30. 1.26

Step-by-step explanation:

12. 5/8 = x/12

  8x = 60

   x = 7.5

13. x/1.11 = 1/5

  5x = 1.12

   x = 0.224

14. 6x /27 = 43

      6x = 1161

         x = 193.5

15. x+2)/3 = 8/9

   9x + 18 = 24

   9x = 6

  x = 2/3

16. (3x -5)/4 = -5/7

     21x - 35 = -20

     21x = 15

     x = 5/7

17. (x-2)/4 = (x+4)/2

    2x - 4 = 4x + 16

    -2x = 20

     x = -10

18.  9 grams of fat.

      6 grams are saturated.

     9-6 = 3 grams are cheese.

  ratio of saturated to cheese = 6:3

                                                   = 2:1

19. goats to sheep = 4:7

     7/11 x = 28

     x = 28 × 11/7

     x = 44

   goats = 44-28 = 16

20. 280:4 = 10,500:x

   280/4 = 10,500/x

  280x = 42000

     x = 150

21. 42:2 = x:2200

   42/2 = x/2200

   92,400 = 2x

    x = 46,200

22. √(2×8) = √16 = 4

23. √(9×36) = √324 = 18

24. √(4×7) = √28 = 5.29

25. √(5×10) = √50 = 7.07

26. √(28×14) = √392 = 19.80

27. √(7×36) = √252 = 15.87

28. √(8×12) = √96  = 9.80

29. √(3×15) = √45 = 6.71

30. √4/5 × 2) = √8/5 = 1.26

Answer:

7.0

Step-by-step explanation:

If we had the number 7.1  the 1 is the tenth digit. .

So 7 to the nearest tenth is written 7.0.

Answer:

7.5 is exactly halfway between 7 and 8. Therefore, 7.5 rounds to 8.

Step-by-step explanation:

To round to the nearest tenth using a number line, look at the tenth place value closest to the number you are rounding.

Answer:

D

Step-by-step explanation:

Answer:

D) 67  

Step-by-step explanation:

 j = 4N + 11

N = 14           Insert the value of N

j = 4×14 + 11    

j = 56 + 11

j = 67

Jupiter has 67 moons.

Answer:

1.301 × 10⁴ ft  

Step-by-step explanation:

Difference = h₂ - h₁

Difference = 20 320 - 7310

Difference = 13 010 ft

To convert the number to scientific notation, we move the decimal point four places to the left and make the exponent of 10 equal to +4.

Difference = 1.301 × 10⁴ ft

Answer:1 and a half

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

There are one in 1/2

Answer:

100;200

There are 200 total flips and to find probability we would have to divide it by two. Doing so, should give you something like this 100;200.

If it's a graph: Solutions are points of intersection

The same line means infinitely many solutions

Parallel lines = never intersects = no solution

1 point of intersection = 1 solution

If it's a system of equations:

If you get _*x = _(a number), 1 solution (divide by the coefficient, and get only 1 possible value)

If you get x = x, infinitely many solutions (x can be anything and still equal itself)

If you get two different constants equaling (such as 1 = 2), there is no solution because no value of x can make those two values equal.