2x - y = -13
2x + y = 1

Step-by-step explanation:

We have,

[tex]\dfrac{6}{7} \times 42.21[/tex]

To find, the value of [tex]\dfrac{6}{7} \times 42.21[/tex] = ?

∴ [tex]\dfrac{6}{7} \times 42.21[/tex]

= [tex]\dfrac{6}{7} \times \dfrac{4221}{100}[/tex]

We know that,

The properties of rational numbers,

[tex]\dfrac{a}{b} \times \dfrac{c}{d} =\dfrac{a\times c}{b\times d}[/tex]

= [tex]\dfrac{6\times 4221}{7\times 100}[/tex]

= [tex]\dfrac{25326}{700}[/tex]

= 36.18

Thus, the value of [tex]\dfrac{6}{7} \times 42.21[/tex]= 36.18

The population in this situation is all the terms that the teacher taught this semester and that are represented in the note cards and put in the paper bag.

Explanation:

The population in this situation of Mr Wilson is all the terms that the teacher taught this semester and that are represented in the note cards and put in the paper bag. The sample is every set of 5 note cards that is selected by the students.

The data is representative of the population because they are selected randomly without bias. Every of term has the same probability of being selected. Also it given that the cards are replaced every time, so all the students will face the same population when they are going to select a sample.

Answer:

900 g

Step-by-step explanation:

Increase by 20% means 120% of the value

120/100 × 750

900g

Answer:

D

Step-by-step explanation:

Answer:

I believe the answer is -15, I calculated it and thats what i got

Step-by-step explanation:

Tessa's account balance is $-15.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that Tessa had $90 in her checking account. She paid her cable/internet bill for $75.She deposited $50 from her part-time job before writing a check for $80 to pay her credit card bill.

The remaining amount is calculated as:-

Balance = 90 + 50 - 75 -80

Balance = $-15

Hence, the account balance is $-15.

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Answer:

22.7

Step-by-step explanation:

First write 18% as a decimal by moving the decimal point two places to the left to get .18.

The word "of" means multiply, so we have (.18)(75) which is 13.5.

Answer:

13.5

Step-by-step explanation:

18% of 75

18% /100% x 75

0.18 x 75

13.5

15° and 165°

Step-by-step explanation:

Step 1 :

Let x and y denote the angles with x as the smaller angle and y as the larger angle

When 2 angles are supplementary, the sum of both the angles is 180 degrees.

Hence x + y = 180

Step 2:

Given that the larger angle is 15 more than 10 times the smaller angle

Hence y = 15 + 10 x

Step 3 :

Solving for the 2 equations we have

11x = 165 => x = 15

=> y = 180-15 = 165

Hence the 2 angles are 15 and 165 degrees.

Answer:

52 / 27

Step-by-step explanation:

To multiply mixed numbers, convert them into improper fractions. Multiply the two improper fractions together and simplify the result.

To multiply mixed numbers, we first convert them into improper fractions. To convert 1 1/3 into an improper fraction, we multiply the whole number (1) by the denominator (3) and add the numerator (1). This gives us 4/3. Similarly, to convert 1 4/9 into an improper fraction, we multiply the whole number (1) by the denominator (9) and add the numerator (4). This gives us 13/9.

Now, we can multiply the two improper fractions together. 1 1/3 times 1 4/9 equals (4/3) * (13/9). To multiply fractions, we multiply the numerators together and multiply the denominators together. So, (4/3) * (13/9) equals (4 * 13) / (3 * 9), which simplifies to 52/27.

Therefore, 1 1/3 times 1 4/9 in fraction form is equal to 52/27.

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Answer:

yes

Step-by-step explanation:

when addi g the ones place it would result in 14 so u would need to regroup the 1 into the tens place

Answer:

Here is a similar question:

A bakery uses 10 1/5 ounces of icing for every 1/4 of a cake. What is the unit rate in ounces of icing per cake.

The unit rate in ounces of icing per cake = 40 4/5 ounces

Step-by-step explanation:

Given:

Ounces of ice used for every 1/4 cake = 10 1/5

We have to find the unit rate.

Let the unit rate be 'x' .

Unit rate is the rate when we use unit 'one' as our reference to find any value.

Lets convert the mixed fraction of ounces.

⇒ [tex]10\frac{1}{5} = \frac{(10\times 5)+1}{5} =\frac{51}{5}[/tex]

Portion of the cake used = [tex]\frac{1}{4}[/tex]

To find the unit rate here we must divide :

⇒ [tex]x=\frac{number\ of\ ounces\ used}{portion\ of\ the\ cake}[/tex]

⇒ [tex]x=[/tex] [tex]\frac{51}{5}[/tex]  ÷  [tex]\frac{1}{4}[/tex]

⇒ [tex]x=[/tex] [tex]\frac{51}{5}\times \frac{4}{1}[/tex]

⇒ [tex]x=[/tex] [tex]\frac{51\times 4}{5}[/tex]

⇒ [tex]x=[/tex] [tex]\frac{204}{5}[/tex]

⇒ [tex]x=[/tex] [tex]40\frac{4}{5}[/tex]  Or [tex]40.8[/tex]  

Hence, the unit rate in ounces of icing per cake = 40 4/5 ounces.

Answer:

Another similar question:

A bakery uses 10 3/5 ounces of icing for every 1/4 of a cake. What is the unit rate in ounces of icing per cake?

Step-by-step explanation:

Answer is 42 2/5

10 3/5 ÷ 1/4 = 53/5 ÷ 1/4

= 53/5 x 1/4

= 212/5

= 42 2/5

Answer:

y=-1/3x-8

Step-by-step explanation:

y-y1=m(x-x1)

y-(-9)=-1/3(x-3)

y+9=-1/3x+3/3

y+9=-1/3x+1

y=-1/3x+1-9

y=-1/3x-8

The dimensions of the rectangle shown on the coordinate plane is The base is 9 units and the height is 4 units.

Option: B.

Step-by-step explanation:

We are given with the coordinate points of a rectangle.

The points are  (1, -1), (10, -1), (10, -5), (1, -5).

From the given graph, the bigger side is the base and the height is the smaller side.

The points  (1, -1), (10, -1) and (1, -5), (10, -5) can be used to find the base of the rectangle.

The points (10, -1), (10, -5) and  (1, -1), (1, -5) can be used to find the height of the rectangle.

Let us find the base using coordinate point (1, -5), (10, -5) .

Since the base runs horizontally on the x-axis, we have to find the run.

run = [tex]x_2-x_1[/tex].

run = 10-1.

run (base)= 9 units.

Let us find the base using coordinate point (10, -1), (10, -5) .

Since the height runs vertically on the y-axis, we have to find the rise.

rise = [tex]y_2-y_1[/tex].

rise = -5-(-1).

rise=-5+1.

rise (height)= 4 units.      ( Units are always measured in positive.)

∴ The base is 9 units and the height is 4 units.

Answer:

The answer is 24

Step-by-step explanation:

If each person eats 1/3 of the pizza then that means it takes 3 people to eat a whole pizza so you multiply three times 8 and you get twenty four.

The simplified expression is x^2 - 14xy + 49y^2.

To multiply the expression (x - 7y)^2 using the Special Product Formula, we can use the formula (a - b)^2 = a^2 - 2ab + b^2.

In this case, a = x and b = 7y. Plugging these values into the formula, we get:

(x - 7y)^2 = x^2 - 2(x)(7y) + (7y)^2

Simplifying further:

= x^2 - 14xy + 49y^2

So, the simplified expression is x^2 - 14xy + 49y^2.

Answer:

1.Distribute values

(3x+12)-(2x+8)

2.Add common terms

x+4

Answer:

The answer is b

Step-by-step explanation:

I took the test

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

If QPS is a right angle we know a right angle equals 90 degrees. so you can find your answer by doing 90-35.

Therefore getting 56.

Hope this helps :)

The relation {(5 , 11) , (-9 , 3) , (0 , 9) , (-6 , 11)} is a function ⇒ C

Step-by-step explanation:

Let us revise the relation and the function:

A. {(11 , 5) , (3 , -9) , (11 , -6)

∵ The input 11 has two outputs 5 and -6

∵ In the function each input has only one output

∴ The relation is not a function

B. {(0 , 11) , (-9 , 3) , (0 , 9) , (-9 , -6)

∵ The inputs 0 and -9 have two outputs 11 , 9 and 3 , -6

∵ In the function each input has only one output

∴ The relation is not a function

C. {(5 , 11) , (-9 , 3) , (0 , 9) , (-6 , 11)}

∵ Each input has only one output

∵ In the function each input has only one output

∴ The relation is a function

D. {(5 , 11) , (-9 , 3) , (0 , 9) , (0 , -6)}

∵ The input 0 has two outputs 9 and -6

∵ In the function each input has only one output

∴ The relation is not a function

The relation {(5 , 11) , (-9 , 3) , (0 , 9) , (-6 , 11)} is a function

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Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

6.3g + 14

Answer:

6.3g + 14

Step-by-step explanation:

3(4x + 2)

= 3 . 2(2x + 1)

= 6(2x + 1)

proof

• 3(4x + 2)

= 3(4(2) + 2)

= 30

• 6(2x + 1)

= 6(2(2) + 1)

= 30

The measure of m∠KPN is 68°.

Step-by-step explanation:

From the given diagram, we are given with lines passing through a point P creating different angles.

Data given,

m∠KPN = 4x°.

m∠NPO = (x+5)°.

And m∠KPO= 90°.

The m∠KPO is spitted into m∠KPN and m∠NPO.

Thus the sum of m∠KPN and m∠NPO will be m∠KPO.

⇒m∠KPN + m∠NPO =m∠KPO.

Substitute the values to find x value.

4x°+(x+5)°= 90°.

(°5x+5)=90°.

5x°=90°-5°.

5x°=85°.

x=[tex](\frac{85}{5} )[/tex].

x= 17.

⇒m∠KPN = 4x°.

=4(17)°.

m∠KPN =68°.

Thus the measure of m∠KPN is 68°.

The expression for the new function (fog(x)) = x⁸ + 8x⁴

What is a composite function?

A composite function some called function of a function is a process whereby two functions produce a third function.

Let assume there is a function f(x) and g(x), a composite function fog(x) read  as f of g of x, produces a third function h(x).

In the given question, we are to find (fog) (x), we will replace the value of the function g(x) for x in f(x).

i.e.

f(g(x) = x² + 8x  

[tex]f(g(x) = (x^4)^2+8(x^4)[/tex]

[tex]f(g(x)) = x^8+8x^4[/tex]

Answer:

$3.19

Step-by-step explanation:

so he starts with $18.90 and we know that he spent $2.95. So we will subtract  $2.95 from $18.90. So we are left with $15.95. But now its says he bought 5 items with $15.95. So we will divide 15.95 by 5. So the price of the item that he bought 5 of is $3.19

If you are at a higher level you can use this method:

make and equation of: 5x + 2.95 = 18.90

with this you would subtract 2.95 and then divide by 5 just like we did above.

Answer:

d. 15.95

Step-by-step explanation:

So if one item cost $2.95 and he bought 5 other items that were the same price, we first have to subtract $2.95 from the total which is $18.90.

18.90 - 2.95 = 15.95

Now, to find the cost of the other five items we divide the amount of money left by 5.

15.95 / 5 = 3.19

So each of the other five items costs $3.19.

To find the total cost of the five items together, we multiply 3.19 by 5.

3.19 x 5 = 15.95

To solve this, you need to isolate/get the variable "c" by itself in the equation:

4c + 8c = -55 + 3c    You can first combine like terms (4c and 8c)

12c = -55 + 3c         Subtract 3c on both sides

9c = -55       Divide 9 on both sides

[tex]c=-\frac{55}{9}[/tex]

Answer:

the correct answer is d

Step-by-step explanation:

The Area of rectangle is 30 sq. unit.

The distance between two points A( a,b) and B(c, d) in coordinate plane is

D= √(c- a)² + (d- b)²

Given:

From the figure the coordinates of rectangle are A(3, 8), B(6, 11), C(11, 6) and D(8, 3).

Using Distance Formula

length: l = √(8-3)² + (3-8)² = √25 + 25 = √50

width: w= √(6-3)² + (11- 8)² = √9+9 = √18

So, the area of rectangle = l x w

                                          = √50 x √18

                                          = √50 x √18

                                          = √900

                                          = 30 sq. unit.

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As, the Questions figure is not given. So, this question is solved with different figure but with same method of solving.

Answer: has because 1/4 is 25 and 3/4 is 75

Step-by-step explanation:

Answer:

2/5 with an exponent of 3 is 8/125 or 0.064

Step-by-step explanation:

Given:

A fraction = 2/5

Exponent = 3

To find the value of the fraction using the exponent.

We know that :

⇒ [tex](a)^3=a\times a\times a[/tex]  

The exponents is the number of times a number is multiplied.

So,

⇒ [tex](\frac{2}{5})^3[/tex]

⇒ [tex]\frac{2\times 2\times 2}{5\times 5\times 5}[/tex]

⇒ [tex]\frac{8}{125}[/tex]

On further division the number can be written as 0.064

Answer:

False

Step-by-step explanation:

Whichever has more heat (in this case the stove) has more thermal energy