Sam's total expenses last month were $1840. What was his total variable cost for last
month?
Expense
Amount
Rent
$100
Groceries and drinks
$1000
$10
Insurance premiums
Loan interest payment
Clothes
$30
$200
&
Utilities
$300
Home security fee
$200​

Answer:

x² is HCF (Height common factor)

Step-by-step explanation:

Given:

x² , x³

Find:

HCF (Height common factor)

Computation:

HCF (Height common factor) is uused to find Height common factor from the given numbers.

x² , x³

Takling x² as common

x² (1 , x)

So,

x² is HCF (Height common factor)

Answer:

histogram D

Step-by-step explanation:

From left to right, your frequencies (aka height of columns) should be 4, 8, 9, 8, and 3

Answer:

864 m²

Step-by-step explanation:

The area of a rectangle is given by the product of the length and the width

let A be the total area

A = 100*120

A = 12000 m²

Calculate the area of the small rectangles

Let A"' be the area of the road

A"' =A-A'

A"' = 12000-11136

A"' = 864 m²

Answer:

The nth term of the sequence is

Step-by-step explanation:

The sequence above is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

a = 1

d = 10 - 1 = 9 or 19 - 10 = 9 or 28 - 19 = 9

So the nth term of the sequence is

A(n) = 1 + (n - 1)9

= 1 + 9n - 9

= 9n - 8

Hope this helps you

Answer:

1. Factorization method

2. Formula method

3. Completing the square method

4. Graphical method

Step-by-step explanation:

There are four methods of solving quadratic equation:

1. Factorization method

2. Formula method

3. Completing the square method

4. Graphical method

1. Factorization method: Use factorization method when the quadratic equation can easily be factorize.

Example: x^2 - 4x - 12 = 0

(x-2)(x+6)

2. Formula method: This can be used when factoring the quadratic equation looks difficult or you are given instruction to use formula method

3. Completing the square method: Use completing the square method when you are instructed to do so.

4. Graphical method: This method is used when instructed to find x intercept.

Answer:

The correct option is;

(C) 28

Step-by-step explanation:

The information given are that;

The total number of students = 1000

The number of students in each row are consecutive positive numbers

Let the number of students in the first row be x,

Let the number of rows be 17

We have;

The number of students in  the last row = x + 16

The number of students in  the penultimate row = x + 15, we continue  to get;

n×x + n/2×(n-1) = 1000

(The term n/2×(n-1) is from the sum of an arithmetic progression formula)

Which gives;

17×x + 17/2×16 = 1000

17×x = 1000 - 17/2×16 = 1000 - 136 = 864

x = 864/17 = Which is not an integer,

We continue checking till we get to 25 rows which gives;

25×x + 25/2×24 = 1000

25×x + 300 = 1000

25×x  = 1000 - 300 = 700

x = 700/25 = 28

The number of student in the first row = 28 students.

Answer:

Marco will owe $ 23,360 once he graduates.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Principal of the loan = 20,000

Time in years = 4

Interest rate = 4.2%

2. What is the amount he will owe once he  graduates?

Let's use the formula of the interest simple, this way:

A = P * (1 + r * t)

where P is the principal of the loan, r the interest rate and t, the time in years.

Substituting with the values we know, we have:

A = 20,000 * (1 + 4 * 0.042)

A = 20,000 * 1.168

A = 23,360

Marco will owe $ 23,360 once he graduates.

Answer:

a) [tex]\boxed{-4}[/tex]

b) [tex]\boxed{26}[/tex]

c) [tex]\boxed{-12}[/tex]

d) [tex]\boxed{-9}[/tex]

e) [tex]\boxed{10}[/tex]

f) [tex]\boxed{-12}[/tex]

Step-by-step explanation:

1) [tex]\frac{41 - 3^2}{\sqrt{36}* 3-26 }[/tex]

=> [tex]\frac{41-9}{6*3-26}[/tex]

=> [tex]\frac{32}{18-26}[/tex]

=> [tex]\frac{32}{-8}[/tex]

=> -4

2) [tex]12+\sqrt[3]{8} * (9-2)[/tex]             ∴ [tex]\sqrt[3]{8} = 2[/tex]

=> [tex]12+2*(7)[/tex]

=> 12 + 14

=> 26

3) [tex]\frac{28-(7^2+3)}{-13+3*5}[/tex]

=> [tex]\frac{28-(49+3)}{-13+15}[/tex]

=> [tex]\frac{28-52}{2}[/tex]

=> [tex]\frac{-24}{2}[/tex]

=> -12

4) [tex]\frac{28}{4} - \sqrt[3]{8} * 2^3[/tex]

=> 7 - 2 * 8

=> 7 - 16

=> -9

5) [tex]7^2-5*8+1[/tex]

=> 49 - 40 + 1

=> 9 + 1

=> 10

6) [tex](2 * \sqrt{16} ) - (\sqrt[3]{27} * \sqrt{81} ) + 7[/tex]

∴  [tex]\sqrt{16} = 4, \sqrt[3]{27} = 3 , \sqrt{81} = 9[/tex]

=> (2 * 4) - (3 * 9) + 7

=> 8 - 27 + 7

=> -19 + 7

=> -12

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

Apply order of operations to solve each expression.

[tex]\frac{41-9}{6 \times 3-26}[/tex]

[tex]\frac{41-9}{18-26}[/tex]

[tex]\frac{32}{-8}=-4[/tex]

[tex]12+2\times 7[/tex]

[tex]12+14=26[/tex]

[tex]\frac{28-(49+3)}{-13+15}[/tex]

[tex]\frac{28-52}{2}[/tex]

[tex]\frac{-24}{2} =-12[/tex]

[tex]7-2 \times 8[/tex]

[tex]7-16=-9[/tex]

[tex]49-40+1[/tex]

[tex]=10[/tex]

[tex](2 \times 4)-(3 \times 9) +7[/tex]

[tex]8-27+7[/tex]

[tex]=-12[/tex]

Answer:

2 Candy bars

6 Mints

7 Gum

Step-by-step explanation:

Candy bars=x

mints=3x

gum=3x+1

10(x)+3(3x)+6(3x+1)=80

10x+9x+18x+6=80

37x=80-6

37x=74

x=2

SO:

cand bars = x = 2

mints = 3x = 6

gum = 3x+1 = 7

Answer:

2 candy bars, 6 mints, and 7 packages of gumm

Step-by-step explanation:

Answer:C

Step-by-step explanation:It’s C on edge

Answer:

-0.16

Step-by-step explanation:

Since it states g is equal to -3.57, we have to plug in -3.57 into the equation wherever it says g.

[tex]8-12(-3.57)-51[/tex]

We can multiply -12 and -3.57 to get 42.84.

[tex]8+42.84-51[/tex]

Now we can add 8 to 42.84 to get 50.84. Then, we subtract 51 from 50.84 to get our answer, -0.16!

Answer:

Statement 1. P

Reason 1. Theorem: The measure of an external angle of a triangle is equal to the sum of the measures of the remote interior angles.

Statement 2. 132 = 3x + 54

Statement 3. x = 26

Answer:

B

Step-by-step explanation:

-2   /  1        2     -3      1

         ____-2  _ 0_  _6_____

         1       0       -3      7

Write down the first number 1 as it is.

Step 2: Multiply 1 by  -2  ( 1*-2 = -2) and write under the next number. Then add

            2 +(-2) = 0

Step 3: Now  Multiply 0 by -2 ( 0 * -2 =0) and write under the next number ie, -3.

            -3 +0 = -3

Step 4: Multiply -3 by -2, ( -3*-2 = 6) and write under the number 1

            1 + 6  = 7

7 is the remainder

The remainder in the synthetic division problem given is 7.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given a synthetic division problem.

Put the first number straight down.

So 1 is taken down.

Multiplying 1 by -2, we get -2.

2 + (- 2) = 0

Multiplying 0 by -2, we get 0.

-3 + 0 = -3

Multiplying -3 by -2, we get 6.

1 + 6 = 7, is the remainder.

Hence the remainder is 7.

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Answer:

The rhombus ABCD has an area of 22 square units.

Step-by-step explanation:

The coordinates of rhombus ABCD are shown in the image attached below. The area of the rhombus can be found in terms of their diagonals, which are now calculated by Pythagorean Theorem:

[tex]AC = \sqrt{[6-(-4)]^{2}+[8-(-4)]^{2}}[/tex]

[tex]AC = 15.620[/tex]

[tex]BD = \sqrt{(4-6)^{2}+[0-(-2)]^{2}}[/tex]

[tex]BD \approx 2.828[/tex]

The area of the rhombus is: ([tex]AC = 15.620[/tex] and [tex]BD \approx 2.828[/tex])

[tex]A = \frac{AC\cdot BD}{2}[/tex]

[tex]A = \frac{(15.620)\cdot (2.828)}{2}[/tex]

[tex]A = 22.087[/tex]

The rhombus ABCD has an area of 22 square units.

Answer:

22 units

Step-by-step explanation:

Answer:

15.

Step-by-step explanation:

The new average will be 11 + 4 = 15.

Answer: The overall average will increase by 4 from 11 to 15

Step-by-step explanation: If each of the six integers is increased by four, that will add 6×4 to the total.

The original average was based on six numbers totaling 66, then divided by 6 to get the average, 11.

So add 66 + 24 = 90

Divide 90/6 = 15. The new average.

That is 4 more than the original 11.

Answer:

{y = 1/4x^2 − 2 y = −1/2x}

(0,0)

(-6,3)

Step-by-step explanation:

Rewrite as system of equations

y=-1/2x

1/4x^2-2y=-1/2x

Move expression to left and change its sign

y+1/2=0

1/4x^2-2y+1/2x=0

Multiply both sides of equation by 2

2y+x=0

1/4x^2-2y+1/2x=0

Sum the equation vertically and eliminate variable (2y)

3/2x+1/4x^2=0

Solve the equation

x=0

x=-6

Substitute the value of x into equation

y+1/2*0 = 0

y+1/2*(-6) = 0

Solve equation for y

y=0

y=3

so the solution is

(x1,y1)=(0,0)

(x2,y2)=(-6,3)

Answer:

1 -> D

2 -> C

3. -> F

4. -> E

5. -> A

6. -> B

Step-by-step explanation:

Match each function formula with the corresponding transformation of the parent function y = (x - 1)∧2

1. y = ( x - 1) 2 - 3    A. Reflected over the y-axis

2. y = - ( x - 1) 2      B. Translated up by 1 unit

3. y = ( x + 3) 2       C. Reflected over the x-axis

4. y = ( x - 2) 2        D. Translated down by 3 units

5. y = ( x + 1) 2        E. Translated right by 1 unit  

6. y = ( x - 1) 2 + 1    F. Translated left by 4 units

Using the standard transformation rules

f(x) -> a*g(bx-h) + k, we can obtain the following results

Answers:

1 -> D

2 -> C

3. -> F

4. -> E

5. -> A

6. -> B

Answer:

10

Step-by-step explanation:

We can do the ratio of 8:2:10. If we add it all up, we get 20. We do 100/20 and get 5, so each number equals 5. Then we do 2*5.

Sorry if this is wrong.

This is a linear equation in slope-intercept form. We can see that the slope is -1 and the y-intercept is -3 -- the line passes through (0, -3).

To graph this, we can simply plot the point (0, -3) and draw a line with slope negative 1 (this means that for every unit right, we have to move 1 unit down.

I have attached a picture of the graph.

Answer:

-56 + 3 sqrt(2) /2

Step-by-step explanation:

f(x) = x^2 +2/sqrt{x}.

2f(2) - f(8).

First find f(2)

f(2) = 2^2 +2/sqrt{2} = 4 + 2/ sqrt(2)

Then f(8)

f(8) = 8^2 +2/sqrt{8} = 64 + 2 / sqrt(4)sqrt(2) = 64+ 2/2sqrt(2) = 64 + 1/ sqrt(2)

2f(2) - f(8).

2 * (4 + 2/ sqrt(2)) - (64 + 1/ sqrt(2))

8 + 4/ sqrt(2)  - 64 - 1/ sqrt(2)

Combine like terms

-56 +  3 / sqrt(2)

Rationalizing the second term

-56 + 3/ sqrt(2) * sqrt(2)/sqrt(2)

-56 + 3 sqrt(2) /2

Answer:

(0.88, 0.65)

Step-by-step explanation:

Given that the two equations of the line are:

y =( -2/5)x + 1 and  y = 3x – 2. To find the solution, we have to solve the equations simultaneously.

y =( -2/5)x + 1       .             .            .      1)

y = 3x – 2             .            .             .      2)

Subtracting equation 1 from equation 2:

3.4x -3 = 0

3.4x = 3

Dividing through by 3.4

3.4x/3.4 = 3/3.4

x = 0.88

To find y, substitute x = 0.88 in equation 2:

y = 3(0.88) - 2

y = 2.65 - 2

y = 0.65

This means that the solution to the system of equations is the point of intersection of the two lines which is at (0.88, 0.65)

Answer:

(0.88, 0.65)

Step-by-step explanation:

i just took the test

Answer:

Step-by-step explanation:

The slant height of one side of this pyramid is 5, and the base of this side is 4.  Thus, the area of one slant side is (1/2)(5)(4) = 10 units^2.

There are 4 such sides.  Thus, the total slant surface area is 4(10 units^2), or 40 units^2.  

If you also want to include the base area, the total would be

40 units^2 + 16 units^2 = 56 units^2.

Answer:

3/32

Step-by-step explanation:

One approach to doing this probelm is to evaluate all three functions F, G and H at x = 2:

F(2) = 2(2) - 1 = 3

G(2) = 3(2) + 2 = 8

H(2) = (2)^2 = 4

                                                           3/8

Then (F/G)(2) = (3/8), and (F/G/H) = -------- = 3/32

                                                              4

Work Shown:

x = amount of rent paid per half year

2x = amount of rent paid annually

y = amount spent on groceries per quarter

4y = amount spent on groceries annually

z = amount spent on a transit pass monthly

12z = amount spent on transit pass annually

2x+4y+12z = total amount of money spent annually

Answer:

2x+4y+12z

Step-by-step explanation:

I just did the test and got it right

Answer:

120

Step-by-step explanation:

The total number of triangles that can be made are 120.

We have a circle and 10 points are placed on it.

We have to find how many possible triangles can be made such that their vertices will be the given points.

A combination can be defined as the number of possible arrangements of elements without taking into consideration the order of selection. The number of possible combinations can be given by -

[tex]\frac{n!}{(n-r)!r!}[/tex]

In the question given to us - we have 10 points on circle. Only three points are needed to make a triangle. The order does not matter here, therefore -

[tex]\frac{10!}{(10-3)!3!}\\\\\frac{10!}{7!\times3!} \\\\\frac{10\times9\times8\times7!}{7!\times3\times2\times1}[/tex]

10 x 3 x 4 = 120

Hence, the total number of triangles that can be made are 120.

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Answer: Yes, negative numbers can be written in scientific notation

Examples:

-1200 = -1.2 * 10^3

-1,897,000 = -1.897 * 10^6

We simply can ignore the negative at first, then convert to scientific notation (as you normally would with any positive number). Afterward, don't forget to put the negative back in.

Answer:

0.3 cm

Step-by-step explanation:

1 cm = 10 mm

1) Using proportion:

1 cm ----- 10 mm

x cm -----  3 mm

x = 1 cm * 3 mm/10 mm = 0.3 cm

2) 3 mm * 1cm/10mm = 0.3 cm

Answer:

3mm = 0.3 cm

Step-by-step explanation:

1 cm = 10 mm

3mm = 3/10 = 0.3cm

Answer: The fan catch the ball after 3 seconds.

Step-by-step explanation:

Given,  A baseball 4 feet off the ground is hit with an upward velocity of 52 feet per second.

The height of the baseball in feet after t seconds is given by the equation

[tex]h = - 16t2 + 52t + 4[/tex]

If a fan catches the ball 16 feet off the ground when it is coming  down.

then, at that time h= 16  feet

At h= 16

[tex]16=-16t^2+52t+4\\\\\Rightarrow\ 16t^2-52t+12=0\\\\\Rightarrow\ 4t^2-13t+3=0[/tex]

[tex]\Rightarrow\ 4t^2-t-12t+3=0\Rightarrow\ t(4t-1)-3(4t-1)=0\\\\\Rightarrow\ (4t-1)(t-3)=0\\\\\Rightarrow\ t=\dfrac{1}{4},\ t=3[/tex]

From the graph , it can be observe that when ball comes back , for height 16 feet the corresponding time t= 3 sec

So, the fan catch the ball after 3 seconds.

Answer:

P(odd) = 0.5

Step-by-step explanation:

There are 50 odd numbers for whole numbers 1-100, namely

{1,3,5,....97,99}

Therefore the probability that a single chosen number is odd is

P(odd) = 50/100 = 1/2

1/2 is the probability that the number is odd.

The probability is defined as the possibility of an event is equal to the ratio of the number of outcomes and the total number of outcomes.

Total number of possibilities = 100

We want to find Probability of selecting odd:

There are 50 odd numbers for whole numbers 1-100, namely

Favourable possibilities are:

{1,3,5,....97,99} (Total 5 possibilities).

Therefore Probability = 50/100 = 1/2 or 50%

P(odd) = 50/100 = 1/2

Hence, 1/2 is the probability that the number is odd.

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Answer:

45 mph

Step-by-step explanation: