y=x
y=-6x–14

(substitution method)

Answer:

The perimeter of an equilateral triangle that has a height of 24m is

Option C : 48 square root 3

Step-by-step explanation:

Given:

Height of the triangle =24 m

To Find:

The perimeter of an equilateral triangle  = ?

Solution:

Perimeter of the equilateral  triangle  =  3a

where a is the side of the triangle

Here the height is given as 24 m

Then from the figure

[tex]Sin(60^{\circ}) = \frac{opposite}{hypotenuse}[/tex]

[tex]Sin(60^{\circ}) = \frac{24}{x}[/tex]

[tex]x = \frac{24}{Sin(30^{\circ})}[/tex]

[tex]x= \frac{24}{\frac{\sqrt{3}}{2}}[/tex]

[tex]x = \frac{24 \times2}{\sqrt{3}}[/tex]

[tex]x = \frac{48}{\sqrt{3}}[/tex]

Now

The perimeter is

=> 3x

=>[tex]3 \times \frac{48}{\sqrt{3}}[/tex]-------------------------(1)

Now we know that 3 = [tex]\sqrt{3} \times \sqrt{3}[/tex]--------------------(2)

Substituting (2) in (1)

=>[tex](\sqrt{3} \times \sqrt{3}) \times \frac{48}{\sqrt{3}}[/tex]

=>[tex]48\sqrt{3}[/tex]

Answer:

200 = 20

470 47

The number of year 10 students over the total number of students

Can y’all help me I have no points and what is 5/7times28

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

1) Make into multiplication problem

1a) Keep Change flip(multiply by the reciprocal): 50/ 2/3 to 50*3/2

2) Solve 50*3/2

2a) 50*3=150

2b)150/2=75

3) 75

Answer:

[tex]\frac{7}{12}[/tex]  of an hour is remaining for Mariko's social studies class

Step-by-step explanation:

Given:

Total duration of Mariko's social studies class = 5/6 of an hour.

Only 3/12 of an hour has passed.

To Find:

Fraction of an hour remains for Mariko's social studies class =?

Solution:

Converting into minutes

5/6 of an hour =  [tex]\frac{5}{6} \times (60)[/tex]

=>[tex]\frac{300}{6}[/tex]

=>50 minutes

So the total duration of  Mariko's social studies = 50 minutes

If  3/12 of an hour passes means

Converting into  minutes

=>[tex]\frac{3}{12} \times 60[/tex]

=>[tex]\frac{180}{12}[/tex]

=>[tex]\frac{180}{12}[/tex]

=> 15 minutes

15 minutes has passed

Remaining time left is

50 minutes - 15 minutes = 35 minutes left

Now converting into 35 minutes into hours we get

=> [tex]\frac{35}{60}[/tex]

=>[tex]\frac{7}{12}[/tex]

Subtracting the time passed from the total class time gives us the remaining time. The calculation involves simplifying the time passed fraction and finding a common denominator to subtract fractions. In the end, we find that 7/12 of an hour remains for Mariko's social studies class.

This is a question about subtracting fractions to calculate remaining time. Mariko's social studies class lasts 5/6 of an hour and 3/12 of an hour has passed. To find out how much time remains, you need to subtract the time that has passed from the total class time.

First, you simplify the fraction of the time that has passed. 3/12 simplifies to 1/4, since 3 and 12 are both divisible by 3.

Then, you subtract 1/4 from 5/6 to calculate the time remaining. To do this, you need to find a common denominator, which is 12 in this case.

Converting 5/6 and 1/4 into twelfths gives you the fractions 10/12 and 3/12 respectively.

Then, subtract 3/12 from 10/12 which is 7/12.

So, the answer is 7/12 of an hour remains for Mariko's social studies class.

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Step-by-step explanation:

Input:

Input is generally defined as the information that is sent or passed to a computer or the information what is taken.  The devices that are used to give or offer such information is know as Input devices.

For example:  

We usually use keyboard to type and give a specific data to the computer and hence it can be considered as an Input device.

Output:

Output is generally defined as the source of information that is received or processed by the computer or the information what is given back. The devices that are used to give back such information is know as Output devices.

Example:

Printers takes the input from us,process it and gives back the output in the form of printed sheets,Hence it can be considered as Output device.

Answer:

96-8k = 3k+63

96 - 11k = 63      

(you get -11 by bringing the +3k to the other side which changes the sign to -3k ;   -8k-3k = 11k)

-11k = 63 - 96

-11k = -33

k = -33/-11

k= 3

Answer:

options A and D

Step-by-step explanation:

Given x² - 3x - 28

By factor the given function:

x² - 3x - 28 = (x - 7) (x + 4)

So, comparing the results with the given options.

The answer is options A and D

A. X-7

D. X+4

Answer:

B and C are the correct answers

To find the median of Gary's monthly car sales, we arrange the numbers in ascending order and find the average of the two middle numbers since there's an even number of observations. The median number of cars sold is 10.5.

The subject of this question is Mathematics and it pertains to the concept of calculating the median in statistics. Gary's monthly car sales in ascending order were: 5, 9, 10, 11, 12, 14. When calculating the median of a set of numbers, we first put the numbers in order from least to greatest. If there is an odd number of observations, the median is the middle number. If there is an even number of observations, the median is the average of the two middle numbers.

In this case, Gary's sales were an even number of months, so we find the average of the two middle numbers (10 and 11). To calculate the average, we add the two numbers together and then divide by 2: (10+11)/2 = 10.5. So, the median number of cars Gary sold per month is 10.5.

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Answer:

0=0

Step-by-step explanation:

Simply,there is no solution.

Answer:

The number of cows in farmhouse shelter is 16

The number of chickens in farmhouse shelter is 2   .

Step-by-step explanation:

Total number of animals in farmhouse shelters = 18

Total number of legs of both animals = 68 legs

Let The number of cows = C

Let The number of chickens = c

∵  the number of legs does each cow has = 4

And, The number of legs does each chicken has = 2

According to question

∵Total number of animals in farmhouse shelters = 18

i.e number of cows + number of chickens = 18

Or, C + c = 18                       .....1

Again

∵ Total number of legs of both animals = 68 legs

i.e  number of cows × number of legs does each cow has + number of chickens × number of legs does each chicken has = 68

Or, C × 4 + c × 2 = 68

i.e 4 C + 2 c = 68                     ........2

Solving eq 1 and eq 2 , we get

(4 C + 2 c ) - 2 × (C + c) = 68 - 2 × 18

Or, (4 C - 2 C) + (2 c - 2 c) = 68 - 36

Or, 2 C + 0 = 32

∴  C = [tex]\dfrac{32}{2}[/tex]

i.e C = 16

So, The number of cows in farmhouse shelter = C = 16

Again

Put the value of C into eq 1

∵ C + c = 18

Or, c = 18 - C

Or, c = 18 - 16

i.e c = 2

So, The number of chickens in farmhouse shelter = c = 2

Hence, The number of cows in farmhouse shelter is 16 and The number of chickens in farmhouse shelter is 2   . Answer

Answer:

Step-by-step explanation:

so he needs at least 35 and he already knows 18...

k + 18 > = 35 (thats a greater then or equal sign)

k > = 35 - 18

k > = 17

so he would have to learn at least 17 more

Answer:

k + 18 > = 35 (thats a greater then or equal sign)

k > = 35 - 18

k > = 17

so he would have to learn at least 17 more

Answer:

  this sequence has no common ratio

Step-by-step explanation:

The ratios of successive terms are ...

  4/2 = 2

  8/4 = 2

  -16/8 = -2

  32/-16 = -2

  -64/32 = -2

2 is not the same as -2, so this sequence has no common ratio.

___

The sequence 2, -4, 8, -16, 32, -64 will have a common ratio of -2 using the same method to find it.

Answer:

3 quarters and 7 pennies

Step-by-step explanation:

You can write equations, but you can also use the trial and error method.

Guess 1:

1 quarter = 25 cents

82 - 25 = 57

57 pennies = 57 cents

25 cents + 57 cents = 82 cents

57 - 1 = 56

He has 56 more pennies than quarters, so this is not the answer.

Guess 2:

2 quarters = 50 cents

82 - 50 = 32

32 pennies = 32 cents

50 cents + 32 cents = 82 cents

32 - 2 = 30

He has 30 more pennies than quarters, so this is not the answer.

Guess 2:

3 quarters = 75 cents

82 - 75 = 7

7 pennies = 7 cents

75 cents + 7 cents = 82 cents

7 - 3 = 4

He has 4 more pennies than quarters, so this is the answer.

Answer: 3 quarters and 7 pennies

The boy has 3 quarters and 7 pennies.

To solve this problem, we can set up a system of equations. Let's say that the number of quarters the boy has is q. Since he has 4 more pennies than quarters, the number of pennies he has is q + 4. We know that 1 quarter is equal to 25 cents and 1 penny is equal to 1 cent. So, the total value of the coins can be expressed as 25q + (q + 4) = 82.

Simplifying the equation, we have 25q + q + 4 = 82.

Combining like terms, we get 26q + 4 = 82.

Subtracting 4 from both sides, we have 26q = 78.

Dividing both sides by 26, we find that q = 3. Therefore, the boy has 3 quarters and 3 + 4 = 7 pennies.

Final answer:

In the expression 4(5 + x), the factors are 4 and (5 + x), which can be determined by understanding the distributive property of multiplication over addition.

Explanation:

The question asks, "What are the factors in the expression 4(5 + x)?" To understand this, we need to realize that a factor is something multiplied by another thing that results in a given expression. In this case, the factors of the expression 4(5 + x) are 4 and (5 + x). This is evident from the distributive property of multiplication over addition, which essentially breaks down the expression into its multiplied components. For instance, multiplying 4 by each term inside the parentheses (5 and x) would result in the same expression, 4×5 + 4*x, which shows that 4 and (5 + x) are indeed the factors of the given expression.

Answer:

The surface area of Rectangular prism is [tex]358 \ cm^2[/tex].

Step-by-step explanation:

Given:

Length of the rectangular prism = 7 cm

Width of the rectangular prism = 5 cm

Height of the rectangular prism = 12 cm

we need to find the surface area of rectangular prism.

Solution:

the surface area of rectangular prism is equal to 2 times sum of length times width and width times height and length times height.

framing in equation form we get;

the surface area of rectangular prism = [tex]2(l\times w+w\times h+h\times l)[/tex]

the surface area of rectangular prism = [tex]2(7\times5+5\times12+12\times7) = 2(35+60+84) = 2\times179 = 358\ cm^2[/tex]

Hence The surface area of Rectangular prism is [tex]358 \ cm^2[/tex].

Answer:

[tex]\frac{2}{5}[/tex](3 + y)

Step-by-step explanation:

y = -x - 1 is the equation of the line that passes through (2,-3) and is perpendicular to y = x - 5

Solution:

Given that we have to write the equation of the line that passes through (2,-3) and is perpendicular to y = x - 5

The equation of line in slope intercept form is given as:

y = mx + c ------ eqn 1

Where, "m" is the slope of line and "c" is the y intercept

Given equation of line is:

y = x - 5

On comparing the above equation with eqn 1,

m = 1

We know that,

Product of slope of line and slope of line perpendicular to given line is equal to -1

Therefore,

[tex]1 \times \text{ slope of line perpendicular to given line } = -1\\[/tex]

Slope of line perpendicular to given line = -1

Now we have to find the equation of line with slope -1 and passing through (2, -3)

Substitute m = -1 and (x, y) = (2, -3) in eqn 1

-3 = -1(2) + c

-3 = -2 + c

c = -3 + 2

c = -1

Substitute m = -1 and c = - 1 in eqn 1

y = -x - 1

Thus the equation of line is found

Answer:

-40/33

Step-by-step explanation:

Answer:

-6/11 > -2/3

Step-by-step explanation:

6/11 = 18/33

2/3 = 22/33

Since 18/33 < 22/33  then 6/11 < 2/3 then -6/11 > -2/3

Hence, the value of the expression is 36.

Solution:

Step 1: Given expression is [tex]4(10-4)^{2} \div 4[/tex].

BODMAS means do Bracket, Of, Division, Multiplication, Addition, Subtraction

Step 2: Using BODMAS rule first simplify the expression which is in bracket.

⇒ [tex]4(10-4)^{2} \div 4=4(6)^2\div4[/tex]

Step 3: Squaring of the number 6.

⇒ [tex]4(6)^2\div4=4\times36\div4[/tex]

Step 4: Using BODMAS rule, divide 36 by 4.

⇒ [tex]4\times36\div4=4\times9[/tex]

Step 5: Using BODMAS rule, multiply 4 with 9.

⇒ [tex]4\times9=36[/tex]

Hence, the value of the expression is 36.

903 kg of potatoes will be delivered to stores in Bronx

Solution:

Given that, lamar has 1354.5 Kilograms of potatoes to deliver equally to 18 stores

12 of the stores are Bronx

Number of stores in Bronx = 12

From given,

Kilograms of potatoe = 1354.5 kg

Total number of stores = 18

Let us first find the kilograms of potato delivered to 1 store

[tex]\text{kg of potato to 1 store } = \frac{\text{Total kg of potato}}{\text{ total number of stores}}[/tex]

Substituting the values we get,

[tex]\text{kg of potato to 1 store } = \frac{1354.5}{18} = 75.25[/tex]

Thus 75.25 kg potato is delivered to 1 store

How many kilograms of potatoes will be delivered to stores in Bronx

Number of stores in bronx is 12, so multiply 75.25 by 12

[tex]\rightarrow 12 \times 75.25 = 903[/tex]

Thus 903 kg of potatoes will be delivered to stores in Bronx

Answer:

holdup in the yard when two clothespins held up a pair of pants

Step-by-step explanation:

I had this as my asignment, so if anybody wants the full answers I can give them it. It's the 6.3 puzzle time, just message me!

The Volume of the Cylinder is shown below:

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc.

Given:

As, We know that the Volume of Cylinder

= πr²h

1. r= 12 inch, h= 4 inch

So, Volume of Cylinder = πr²h

                                       = 3.14 x 12 x 12 x 4

                                       = 1808.64 in³

2. r= 6 inch, h= 7 inch

So, Volume of Cylinder = πr²h

                                       = 3.14 x 6x 6x 7

                                       = 791.28 in³

3.  r= 3 inch, h= 13 inch

So, Volume of Cylinder = πr²h

                                       = 3.14 x 3 x 3 x 13

                                       = 367.38 in³

4.  r= 9 inch, h= 11  inch

So, Volume of Cylinder = πr²h

                                       = 3.14 x 9 x 9 x 11

                                       = 2,797.74 in³

5.  r= 8 inch, h= 15  inch

So, Volume of Cylinder = πr²h

                                       = 3.14 x 8 x 8 x 15

                                       = 3,014.4 in³

6.  r= 10 inch, h= 7 inch

So, Volume of Cylinder = πr²h

                                       = 3.14 x 10 x 10 x 7

                                       = 2,198 in³

7.  r= 3 inch, h= 9 inch

So, Volume of Cylinder = πr²h

                                       = 3.14 x 3 x 3 x 9

                                       = 254.34 in³

8.  r= 8 inch, h= 15  inch

So, Volume of Cylinder = πr²h

                                       = 3.14 x 8 x 8 x 15

                                       = 3,014.4 in³

9.  r= 14  inch, h= 15 inch

So, Volume of Cylinder = πr²h

                                       = 3.14 x 14 x 14 x 15

                                       = 9,231.6 in³

10.  r= 6 inch, h= 21 inch

So, Volume of Cylinder = πr²h

                                       = 3.14 x 6 x 6 x 21

                                       = 2,373.84 in³

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The price will increase 8024 dollars.

The price of next model will be $67,024.

Step-by-step explanation:

Given,

Cost of current model = $59,000

Increase in new model = 13.6% of cost of current model

Amount of increase = [tex]\frac{13.6}{100}*59000[/tex]

Amount of increase = 0.136 * 59000

Amount of increase = $8024

The price will increase 8024 dollars.

Cost of next model = Cost of current model + Amount of increase

Cost of next model = 59000 + 8024 = $67,024

The price of next model will be $67,024.

Keywords: addition, division

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Answer:

The population after 10 years will be 10975

Step-by-step explanation:

Given:

Initial population :  7000

Growth rate per year = 4.6 percent

To Find:

Population in 10 years = ?

Solution:

The population after 10 years  can be found by

where

[tex]P = P_0 (1+ \frac{r}{100})^t[/tex]

P is population after 10 years

t is the times

r is the rate of interest

[tex]P_0[/tex] is the initial population

On substituting the values,

[tex]P(t) = 7000(1+ \frac{4.6}{100})^{10}[/tex]

[tex]x(t) = 7000(1+ 0.046)^{10}[/tex]

[tex]x(t) = 7000 (1.046)^{10}[/tex]

x(t) = 7000(1.567)

x(t) = 10975

Answer

(8-2×2) to the power of 2 is 16

Work: 2×2=4

8-4=4

4 to the power of 2 =16

Answer:

144

Step-by-step explanation:

in pemdas always do parenthesis first so it will be 8-2x2= 144 because

Answer: 5

Step-by-step explanation:

Range = highest value - lowest value

The highest value from the data set given = 1

The lowest value = -4

Therefore :

Range = 1 - (-4)

Range = 1 + 4

Range = 5

Debra needs 126 cups of fertilizer for her garden.

To solve this problem, we need to follow these steps:

1. Calculate the area of Debra's rectangular garden.

2. Convert the area from square yards to square feet.

3. Determine the total amount of fertilizer needed in cups.

Let's start:

1. Calculate the area of the rectangular garden:

  Length = 9 1/3 yards

  Width = 12 yards

  Area = Length × Width

       = (9 1/3) × 12

  First, let's convert 9 1/3 to an improper fraction:

[tex]\( 9 \frac{1}{3} = \frac{(9 \times 3) + 1}{3} = \frac{27 + 1}{3} = \frac{28}{3} \)[/tex]

  Now, multiply the fractions:

  Area = [tex]\( \frac{28}{3} \times 12 \)[/tex]

       = [tex]\( \frac{28 \times 12}{3} \)[/tex]

       = [tex]\( \frac{336}{3} \)[/tex]

       = 112 square yards

2. Convert the area from square yards to square feet:

  1 square yard = 9 square feet

  Area in square feet = 112 square yards × 9

                      = 1008 square feet

3. Determine the total amount of fertilizer needed in cups:

  Given that 1/8 cup of fertilizer is needed per square foot.

  Total cups of fertilizer = Area in square feet × (1/8)

                           = 1008 × (1/8)

                           = 126 cups

So, Debra needs 126 cups of fertilizer for her garden.