Comparing and ordering integers

Hope it helps u.......

Answer:

y < (1/2)x + 2

Step-by-step explanation:

Recall that slope intercept form looks like

y = mx + b

we simply have to rearrange the given equation until it looks like the above

3x-6y>12   (subtract 3x from both sides and rearrange)

-6y > -3x + 12   (divide both sides by 6)

-y > (-3/6)x + (12/6)

-y > -(1/2)x + 2   (multiply both sides by -1, remember to flip the inequality)

y < (1/2)x + 2

Answer:

The two tires she bought is $35+$35 which then equals to $70. She spent $70 on tires. She then sold them for $65. She bought three rims, each $75... $75+$75+$75 which then equals her $225. And then sold them for $136. She then bought four headlight covers for $4 each... $4+$4+$4+$4, which equals her $16. Then sold them for $15. Her total profit is -$95. How i got that answer you say, well, if you calculate how much she spent on everything in total, she spent -$311 on everything. You then calculate how much she gained by selling everything she had bought, which was a total of $216. Add both of the total prices, -$311+216= you get -$95.

Step-by-step explanation:

Answer:

298

Step-by-step explanation:

35*2=70 65*2=130  130-70=60

75*3=225 136*3=408   408-225=183

5*4=20 15*5=75    75-20=55

55+60+183=298

Answer:

$8.50 per wk

Step-by-step explanation:

$8.50x6=$51.00+$24.00=$75.00.

Answer:

Manuel must save at least $ 8.5 each week ( 6x ≥ 75 - 24)

Step-by-step explanation:

He has to save more than $75 - $24 = $51 for the next 6 weeks to have enough money for class trip

X: the amount must save each week

6x ≥ 51   ... divide 3 both sides

2x ≥ 17

x ≥ 17/2

x ≥ 8 1/2

Answer:

Step-by-step explanation:

There are three congruence theorems for triangles and they are.

the assumptions made by the following theories are given below.

Step-by-step explanation:

  This theorem states that  triangles are congruent if any pair of corresponding sides and their angle are congruent.

    2. ASA theorem

  This theorem states that the triangles are congruent if any two angles and their sides are equal.

   3. SSS theorem

  This is the easiest among all three postulates. THIS theorem states that if all the sides of a triangle are congruent to the sides of the other triangle then the two triangles are congruent

Answer:

There are 32 pupils in the class

Step-by-step explanation:

Let's say there are N pupils in the class. Then each pupil must send N-1 cards - because it would make no sense to send one to themselves! So each of the N pupils send N-1 cards, which becomes 992 cards in total. In equation form, this is

[tex]N(N-1)=992\\N^2-N-992=0[/tex]

This is a second degree polynomial, which has the solutions

[tex]N=\frac{-b\pm \sqrt{b^2-4\cdot a \cdot c}}{2a}[/tex]

where [tex]a=1, b=-1, \text{and }c=-992[/tex]

If we insert these numbers in the equation,

[tex]N=\frac{-(-1)\pm \sqrt{1^2-4*1*(-992)}}{2*1}\\ = \frac{1\pm \sqrt{1+4*992}}{2}\\= \frac{1 \pm 63}{2}[/tex]

If we choose the solution with the minus sign, we get

N=-31

but this makes no sense! There can't be a negative number of pupils in the class!

So we choose the solution with the plus sign,

[tex]N=\frac{1+63}{2}\\ =\frac{64}{2}\\ =32[/tex]

So there are 32 pupils in the class

Answer:

number of pupils in the class = 32

Step-by-step explanation:

Let n be the number of students. So n-1 cards will be sent by each student.

n(n-1) =192

n² - n =192

n² - n - 192 = 0

n² - 32n + 31n - (31*32) = 0

n(n - 32) + 31 (n-32) = 0

(n-32)(n+31) = 0

n - 32 = 0    or n + 31 = 0

n = 32  or n = -31 is not possible because no. of students cannot be negative

n= 32

Answer:

The center of the circle is c=50 and radius of the circle is [tex]r=\sqrt{3}[/tex]

Step-by-step explanation:

Given circle equation is

[tex]x^2-4x+y^2+14y=-50\hfill(1)[/tex]

Equation (1) can be written as [tex]x^2-4x+y^2+14y+50=0\hfill(2)[/tex]

we know that the equation of the circle is of the form

[tex]x^2+y^2+2gx+2fy+c=0\hfill(3)[/tex]

with centre (-g,-f) and radius=[tex]\sqrt{g^2+f^2-c}[/tex]

when, g,f and c are constants

Now comparing the (2) and (3) equations we get 2g=-4

                                                                          [tex]g=\frac{-4}{2}[/tex]

                                                                          [tex]g=-2[/tex]

                                                                          [tex]2fy=14[/tex]

                                                                          [tex]f=\frac{14}{2}[/tex]

                                                                          [tex]f=7[/tex]

                                                                 and  [tex]c=50[/tex]

Now to find the centre and radius of the given circle equation, substituting the values of g,f,c in the formulae of centre and radius

                  centre=(-g,-f)

                             =(-(-2),-7)

                  centre=(2,7)

                  Radius=[tex]\sqrt{g^2+f^2-c}[/tex]

                              =[tex]\sqrt{(-2)^2+(7)^2-50}[/tex]

                             =[tex]\sqrt{4+49-50}[/tex]

                            =[tex]53-50[/tex]

                   Radius=[tex]\srqt{3}[/tex]

The center of the circle is c=50 and the radius of the circle equation [tex]r=\sqrt{3}[/tex]

Answer:

$720

Step-by-step explanation:

$1,200 divided by 2 (600) equals how many vanilla cupcakes there were.

40 people times 24 cupcakes each person (960) equals how many total cupcakes there were.

The total amount of cupcakes minus the amount of vanilla cupcakes equals the amount of chocolate cupcakes (960-600=360).

360 chocolate cupcakes times the amount each cupcake was sold for equals the amount of money raised from the chocolate cupcakes (360x2=720).

Answer:

$4250

Step-by-step explanation:

i = prt

or

p = i / rt

where,

i = $1,785

r = 6% = 0.06

t = 7 years

So, we can calculate initial vale by putting the values in above equation;

p = $1,785 / (0.06 x 7)

p = $1,785 / 0.42

p = $4,250

Hence the initial value will be $4250

Answer:

B

Step-by-step explanation:

Answer:

544.5π cm³ ≈ 1711 cm³

Step-by-step explanation:

Each cylinder has a bore (diameter) of 11 cm, and stroke (height) of 6 cm.

V = πr²h

V = π (11 cm / 2)² (6 cm)

V = 181.5π cm³

There are 3 cylinders, so the total volume is:

3V = 544.5π cm³

3V ≈ 1711 cm³

To calculate the total stroke volume of an inline 3-cylinder engine with an 11 cm bore and a 6 cm stroke, calculate the area of the bore, find the volume of one cylinder by multiplying by the stroke, and then multiply by the number of cylinders. The total stroke volume of the engine is 1710.6 cm³.

The student asked to calculate the total stroke volume of an inline 3-cylinder engine with an 11 cm bore and a 6 cm stroke. The formula to calculate the volume of a single cylinder is V =  rac{ ext{ extpi}}{4}  imes D^2  imes S, where V is the volume, D is the diameter of the bore, and S is the stroke. In this case, D would be 11 cm, and we would need to square this value, then multiply by  extpi/4 and by the stroke length of 6 cm, then multiply the result by the number of cylinders, which is 3, to get the total engine displacement.

Step by step, we first calculate the area of the bore (cylinder base):
Area =  extpi  imes (radius)² =  extpi  imes (5.5 cm)²
=  extpi  imes 30.25 cm²
= 95.0332 cm². Next, we calculate the volume of one cylinder: Volume = Area  imes Stroke = 95.0332 cm²  imes 6 cm = 570.1992 cm³. Finally, we find the total volume for all three cylinders: Total Volume = 570.1992 cm³  imes 3
= 1710.5976 cm³. Thus, the total stroke volume of the engine is 1710.5976 cm³ or rounded to 1710.6 cm³.

the true statements are:

- B. The difference in height between the pelican and the heron is 33 feet.

- C. The distance between the heights of the pelican and heron is 33 feet.

- E. The difference in height between the pelican and the trout is 40 feet.

- F. The distance between the heights of the pelican and the trout is 40 feet.

Let's calculate the differences and distances between the heights of the given objects.

Given heights:

- Heron: 50 feet above sea level

- Pelican: 17 feet above sea level

- Trout: 23 feet below sea level

Now, let's calculate the differences and distances:

A. The difference in height between the pelican and the heron is:

[tex]\[ \text{Difference} = \text{Height of pelican} - \text{Height of heron} \][/tex]

[tex]\[ \text{Difference} = 17 - 50 \][/tex]

[tex]\[ \text{Difference} = -33 \][/tex]

B. The difference in height between the pelican and the heron is:

[tex]\[ \text{Difference} = \text{Height of heron} - \text{Height of pelican} \][/tex]

[tex]\[ \text{Difference} = 50 - 17 \][/tex]

[tex]\[ \text{Difference} = 33 \][/tex]

C. The distance between the heights of the pelican and heron is the absolute value of their difference:

[tex]\[ \text{Distance} = |\text{Difference}| \][/tex]

[tex]\[ \text{Distance} = |-33| \][/tex]

[tex]\[ \text{Distance} = 33 \][/tex]

D. The difference in height between the pelican and the trout is:

[tex]\[ \text{Difference} = \text{Height of pelican} - \text{Height of trout} \][/tex]

[tex]\[ \text{Difference} = 17 - (-23) \][/tex]

[tex]\[ \text{Difference} = 17 + 23 \][/tex]

[tex]\[ \text{Difference} = 40 \][/tex]

E. The difference in height between the pelican and the trout is:

[tex]\[ \text{Difference} = \text{Height of trout} - \text{Height of pelican} \][/tex]

[tex]\[ \text{Difference} = -23 - 17 \][/tex]

[tex]\[ \text{Difference} = -40 \][/tex]

F. The distance between the heights of the pelican and the trout is the absolute value of their difference:

[tex]\[ \text{Distance} = |\text{Difference}| \][/tex]

[tex]\[ \text{Distance} = |-40| \][/tex]

[tex]\[ \text{Distance} = 40 \][/tex]

So, the true statements are:

- B. The difference in height between the pelican and the heron is 33 feet.

- C. The distance between the heights of the pelican and heron is 33 feet.

- E. The difference in height between the pelican and the trout is 40 feet.

- F. The distance between the heights of the pelican and the trout is 40 feet.

complete question given below:
A heron is perched in a tree 50 feet above sea level. Directly below the heron, a pelican is flying 17 feet above sea level. Directly below the birds is a trout, swimming 23 feet below sea level.

Select all the true statements.

A The difference in height between the pelican and the heron is -33 feet.The difference in height between the pelican and the heron is -33 feet.

B The difference in height between the pelican and the heron is 33 feet.The difference in height between the pelican and the heron is 33 feet.

C The distance between the heights of the pelican and heron is -33 feet.The distance between the heights of the pelican and heron is -33 feet.

D The difference in height between the pelican and the trout is -40 feet.The difference in height between the pelican and the trout is -40 feet.

E The difference in height between the pelican and the trout is 40 feet.The difference in height between the pelican and the trout is 40 feet.

F The distance between the heights of the pelican and the trout is 40 feet.

Answer:

C

Step-by-step explanation:

We have a linear equation in the form  y = mx

Where m is the slope

The slope is the change in y divided by change in x.

We can take any 2 points on the line and see the change in y and divide it by the change in x. We will get slope, m.

Lets take points (2,3) and (6,9).

The change in y is 9 - 3 = 6

The change in x is 6 - 2 = 4

So, the slope would be:

m = 6/4 = 3/2 = 1.5

So, the equation would be:

y = 1.5x

Correct answer is C.

Answer:

The answer is "The order ended segregation in the military."

Step-by-step explanation:

President Harry S. Truman is the 33rd president of the United States of America. He assumed the President's role after the death of Franklin D. Roosevelt (the 32nd president of the USA). Under his leadership, he was able to abolish the issues concerning the discrimination according to race or religion in the USA's military force. This was backed by the "Executive Order 9981," which he issued in 1948.

The "Executive Order 9981" ended the segregation in the military. Before it was issued, the Black Americans were trained differently from the White Americans. The White Americans were given more priority than the Black ones. This means that the Black Americans have to wait and train longer before they became qualified. Later, it was found out that there was actually no sense in segregating both Americans, since they both performed well in the wartime.

Thus, this explains the answer.

Answer:

its A

Step-by-step explanation:

Answer:

6 ft

Step-by-step explanation:

Use the formula for area of a parallelogram A = bh

b is for base and h is for height. A is for area.

Substitute b for 8 1/4 ft² and A for 49 1/2 ft². Isolate "h" to find the height of the deck.

A = bh

49 1/2 ft² = (8 1/4 ft²)h    Divide both sides by 8 1/4 ft² to isolate h

(49 1/2 ft²) ÷ (8 1/4 ft²) = (8 1/4 ft²)h ÷ (8 1/4 ft²)

(49 1/2 ft²) ÷  (8 1/4 ft²) = h

h = 6ft

Therefore the height of the deck is 6 feet.

[tex]5\frac{1}{3}[/tex] liters is the amount to be drained out and replaced

Solution:

40 % antifreeze solution in 16 liter radiator

Let "x" be the amount drained from radiation and replaced with pure antifreeze

To obtain a 60 % antifreeze solution

The original solution is 16 liter, 40% of which is antifreeze

You want the solution to be 60% antifreeze:

60 % x 16 = [tex]\frac{60}{100} \times 16 = 9.6[/tex]

You will remove x liters of the 40% solution and replace it with x liters pure (100%) antifreeze.

[tex]40 \% (16 - x) + 100 \% \times x = 60 \% \times 16[/tex]

Let us solve expression for "x"

[tex]\frac{40}{100} \times (16 - x) + \frac{100}{100} \times x = \frac{60}{100} \times 16\\\\0.4(16-x) + x = 0.6 \times 16\\\\6.4 - 0.4x + x = 9.6\\\\6.4 + 0.6x = 9.6\\\\0.6x = 3.2\\\\x = 5.33\\\\x = 5\frac{1}{3}[/tex]

Thus [tex]5\frac{1}{3}[/tex] liters is the amount to be drained out and replaced

Answer:

y=3/8

Step-by-step explanation:

-6y+13+9y=3y+13

3y+13=8y-3-6y+13+9y

3y+13=2y+9y-3+13

3y+13=11y+10

13=11y-3y+10

13=8y+10

8y=13-10

8y=3

y=3/8

First solving for log5(92):

log5(92) = log(92) / log(5) = 2.8095 = 2.810

Now to change to base 3:

log3(x) = log5(92)

Solve for x:

x = 3^(log5(92)

x = 3^2.810

x = 21.903

The answer would be the first one.

Answer:

I got A

Hope this helps

Step-by-step explanation:

Answer:

The inverse variation function can be written as:

[tex]f(x)=\frac{-200}{x}[/tex]

Step-by-step explanation:

Given :

[tex]f(x)[/tex] varies inversely with [tex]x[/tex]

when [tex]x=20[/tex], [tex]f(x)=-10[/tex]

To find the inverse variation equation.

Solution:

[tex]f(x)[/tex] varies inversely with [tex]x[/tex] can be represented as:

[tex]f(x)[/tex] ∝ [tex]\frac{1}{x}[/tex]

Thus, [tex]f(x)=\frac{k}{x}[/tex]

where [tex]k[/tex] represents the constant of proportionality.

We can determine the value of [tex]k[/tex] by plugging in the values given.

when [tex]x=20[/tex], [tex]f(x)=-10[/tex]

So, we have

[tex]-10=\frac{k}{20}[/tex]

Multiplying both sides by 20.

[tex]20\times (-10)=20\times \frac{k}{20}[/tex]

[tex]-200=k[/tex]

Thus  the inverse variation function can be written as:

[tex]f(x)=\frac{-200}{x}[/tex]

Answer:

1 compounding every 2 years

Step-by-step explanation:

Compounded bi-annually in mathematics refers to calculating interest twice a year, where the interest earned in the first six months is used to calculate the interest for the second six months.

The term compounded bi-annually refers to a method of calculating interest where the interest is added to the principal amount twice a year or every six months. This means that the interest you earn after the first six months will also earn interest for the second six months of the year. For example, if you have $1000 with an annual interest rate of 10% compounded bi-annually, after six months, you'd earn 5% interest of $50 making your total $1050. In the next six months, the interest would be calculated on $1050, giving you an another 5% of $52.5 for a total of $1102.5 for the year.

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Answer:

3/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find LCM  for 10, 4.  LCM = 20

3/10 = 3*2/10*2 = 6/20

3/4 = 3*5/4*5 = 15/20

6/20 < 15/20

3/4 is greater

OR

3/10 = 0.3

3/4 = 0.75

3/4 is greater

Answer:

I believe its 20% thats counting the 10% shipping cost

Step-by-step explanation:

Final answer:

Kedwin needs a minimum sale rate of approximately 24.29% in order to afford the headphones.

Explanation:

To calculate the minimum sale rate that Kedwin needs to be able to afford the headphones, we first need to calculate the total cost of the headphones including shipping. The headphones cost $175.00 and the shipping is 10% of the cost, which is $17.50. So the total cost is $175.00 + $17.50 = $192.50.

Next, we subtract Kedwin's current funds, $150.00, from the total cost, $192.50, to find the amount he still needs, which is $192.50 - $150.00 = $42.50.

Finally, we divide the amount he still needs by the original cost of the headphones and multiply by 100 to find the minimum sale rate. In this case, the calculation is ($42.50 / $175.00) * 100 = 24.29%. Therefore, Kedwin needs a minimum sale rate of approximately 24.29% in order to afford the headphones.

Answer:

B  [tex]x^4-x^3+x^2-x+1[/tex]

Step-by-step explanation:

Given,

Dividend = [tex](x^5+1)[/tex]

Divisor = [tex](x+1)[/tex]

Now According to the rule of Division.

Step 1: At first dividend is [tex](x^5+1)[/tex] and Divisor is [tex](x+1)[/tex] when it is divided for the first time the quotient will be [tex]x^4[/tex] and remainder will be [tex]-x^4+1[/tex]

Step: 2 Now the remainder of step 1 will be new dividend which is [tex]-x^4+1[/tex] and Divisor is [tex](x+1)[/tex]  so when it is divided the quotient will be [tex]x^4-x^3[/tex] and remainder will be [tex]x^3+1[/tex]

Step: 3 Now the remainder of step 2 will be new dividend which is [tex]x^3+1[/tex] and Divisor is [tex](x+1)[/tex]  when it is divided the quotient will be [tex]x^4-x^3+x^2[/tex] and remainder will be [tex]-x^2+1[/tex]

Step: 4 Now the remainder of step 3 will be new dividend which is [tex]-x^2+1[/tex] and Divisor is [tex](x+1)[/tex]  when it is  divided the quotient will be [tex]x^4-x^3+x^2-x[/tex] and remainder will be [tex]x+1[/tex]

Step: 5 Now the remainder of step 4 will be new dividend which is [tex]x+1[/tex] and Divisor is [tex](x+1)[/tex]  when it is divided the quotient will be [tex]x^4-x^3+x^2-x+1[/tex] and remainder will be 0.

Hence When the polynomial [tex](x^5+1)[/tex] is divided by  [tex](x+1)[/tex] the answer or quotient will be equal to  [tex]x^4-x^3+x^2-x+1[/tex] and remainder will be 0.

Answer:

y= -x+2

Step-by-step explanation:

given that line m, passes through (2,-7) and (4,-9)

(refer to attached)

slope of line m,

= [(-7) - (-9)] / (2- 4)

= (-7 +9) / (2- 4)

= (2) / (-2)

= -1

recall that the general form of a linear equation is

y = mx + b, where m is the gradient.

in this case, we found that m = -1, so look for the answer where the x-term has -1 as a coefficient, i.e the x-term is "-x"

By observation, we see that the only answer that has "-x" as part of the equation is A

Answer:

n=-2

Step-by-step explanation:

7/8+n/4=3/8

n/4=3/8-7/8

n/4=-4/8

-4/8=-1/2

n/4=-1/2

cross product

4*-1=2*n

-4=2n

n=-4/2

n=-2

Answer:

Step-by-step explanation:

7/8 +n/4 = 3/8

Multiply each term by 8

(8)7/8 +n/4(8) = 3/8(8)

7 + 2n = 3

2n = 3 - 7

2n = - 4

n = -4/2

n = -2

This question is incomplete. I found similar question with picture. Please refer to the attachment to relate with my answer

Full Question:

Various dilations of square A are shown. Which square was obtained by dilating square a by the scale factor of 3.

Answer:

E

Step-by-step explanation:

The square a is a 2 unit x 2 unit square. With scale factor of 3. Any unit length of the object must be multiplied by 3

In this case, since the object side is 2, the image side must be 2x3 = 6 units.

Therefore, the dilation of square A with factor of 3 is square E

A cell phone weighing 56 grams can be converted to kilograms by dividing by 1,000, resulting in a weight of 0.056 kilograms.

To convert the weight of a cell phone from grams to kilograms, one must utilize the metric system's conversion rate where 1 kilogram is equal to 1,000 grams.

Therefore, if a cell phone weighs 56 grams, to find the weight in kilograms, you would divide 56 by 1,000.

56 grams ÷ 1,000 = 0.056 kilograms.

Hence, the cell phone can weigh 0.056 kilograms.

It is important to note that in the metric system, expressing units in the most manageable form is advisable.

In this case, kilograms provide a more easily managed number for larger weights, whereas grams are suitable for smaller weights.

Answer:

(- 2, 5 )

Step-by-step explanation:

Given the 2 equations

3x + 4y = 14 → (1)

x = 2y - 12 → (2)

Substitute x = 2y - 12 into (1)

3(2y - 12) + 4y = 14 ← distribute and simplify left side

6y - 36 + 4y = 14

10y - 36 = 14 ( add 36 to both sides )

10y = 50 ( divide both sides by 10 )

y = 5

Substitute y = 5 into (2) for corresponding value of x

x = 2(5) - 12 = 10 - 12 = - 2

Solution is (- 2, 5 )

To find the point that satisfies both equations, substitute the value of x from the second equation into the first equation and solve for y. Then substitute the value of y into the second equation to find x. The point (-2, 5) satisfies both equations.

To find the point that satisfies both equations, we need to solve the system of equations:

3x + 4y = 14

x = 2y - 12

Substituting the value of x from the second equation into the first equation, we get:

3(2y - 12) + 4y = 14

6y - 36 + 4y = 14

10y = 50

y = 5

Substituting the value of y into the second equation, we get:

x = 2(5) - 12

x = 10 - 12

x = -2

Therefore, the point (-2, 5) satisfies both equations.

complete question given below:

3x+4y=14

x=2y-12

which point satisfies both equation