The sum of two numbers is 8. The difference of the same two numbers is 4. What are the two numbers?

5x+7y=25

5x-2y=-65

subtract both of the equations

5x-5x=0

7y--2y= 7y+2y=9y

25--65=25+65=90

0+9y=90

9y=90

divide both sides by 9 to get y by itself

9y/9=90/9

cross out 9 and 9 which becomes 1*1*y=y

90/9=10

y=10

find x by using the substitution method

5x+7y=25

5x+7(10)=25

5x+70=25

move +70 to the other side

sign changes from +70 to -70

5x+70-70=25-70

5x=-45

divide both sides by 5 to get x by itself

5x/5=-45/5

cross out 5 and 5 then becomes 1*1*x=x

-45/5=-9

x=-9

answer:

(-9,10)

Answer: Any number less than 9.

Step-by-step explanation: The inequality is x is less than 9, that’s what < means, so you can say x is 8, 7, 6, 6.9, etc, x is anything less than 9.

The equation that relates x and y for the Fusion hybrid is y = k + x

So,

y = k + x

Therefore, the equation that relates x and y for the Fusion hybrid is y = k + x

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A record's key field is the field whose contents make the record unique among all records in a file.

In computer science and database management, a record's key field, also known as a primary key, is a unique identifier that is used to distinguish one record from another in a database. A key field can be a single field or a combination of fields that uniquely identify a record.

For example, in a database of employee records, the social security number or employee ID number may be used as the key field to identify each employee record. This key field must be unique for each record in the database, and it is typically indexed to allow for faster searching and sorting of records.

The key field plays a crucial role in ensuring data integrity and consistency in a database. It is used to enforce data constraints and relationships between tables, and it is often used as a reference by other tables in a database.

In summary, a record's key field is an important component of a database that uniquely identifies each record and allows for efficient management and organization of data.

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Answer: 46 and 80l degreesx 23+b

Step-by-step explanation:

Answer: I just did the ones that did not already have an answer

Section A:

7. 1.5 hours

9. 480 meters

10. 10 km

Section B:

1. 40 mph

2. 160 miles

3. 168 miles

4. 5.2 mph

5. 26.25 km/h

The angle of elevation of the sun is 38.24 degrees (rounded to two decimal places).

The ratio of the height of the tree and the length of the shadow can be found by using the formula for tan which is given by:

tan(x) = (opposite/hypotenuse)

In the given problem statement, the height of the tree is opposite to the angle we are trying to find and the length of the shadow is the hypotenuse of the right-angled triangle. Therefore, we can say that:

tan(x) = opposite/hypotenuse = 86/110

We can use the inverse tangent function to find the value of x. This is because tan is the ratio of the opposite side (height of the tree) to the adjacent side (length of the shadow), and the inverse tangent function gives the angle that has that ratio.

So, tan x = 86/110 => x = tan⁻¹ (86/110) = 38.24 degrees (rounded to two decimal places). Therefore, the angle of elevation of the sun is 38.24 degrees.

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To find the number that should be divided by 54.88 to get 9.87, you can multiply 54.88 by 9.87. The result is 541.7656. So, 541.7656 divided by 54.88 equals 9.87.

To find the number that should be divided by 54.88 to get 9.87, we can use the formula for solving a proportion: if a/b = c/d, then a = (b * c) / d. In this case, we have 54.88/x = 9.87/1, so x = (54.88 * 1) / 9.87 = 541.7656. To verify the answer, we can divide 541.7656 by 54.88 and see that the result is approximately 9.87, which confirms that 541.7656 is the correct number.

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A t-shirt company offers four different sizes of shirts: small (S), medium (M), large (L), and extra-large (XL). Additionally, the shirts are available in five different colors: blue, red, white, black, and gray.

A random shirt is selected and a tree diagram is used to depict the sample space. The root of the tree diagram represents the selection of a shirt. There are four possible outcomes: S, M, L, and XL.

Each of these outcomes branches out to the five color choices: blue, red, white, black, and gray. This yields 20 different outcomes. The tree diagram will look like this:To compute the probability of any given outcome, divide the number of favorable outcomes by the total number of outcomes. Since there are 20 total outcomes, the probability of any one outcome is 1/20.

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The account balance after 9 years is $528.28. The result is obtained by adding the interest to the initial deposit.

The simple interest of an amount of money can be counted by the following formula.

I = P₁ - P

I = P × r × t

Where

We have

Find the final account balance!

After 9 years, the simple interest of the savings is

I = P × r × t

I = $425.00 × 2.7% × 9 years

I = $3,825.00 × 0.027

I = $103.28

The final account balance would be

I = P₁ - P

$103.28 = P₁ - $425.00

P₁ = $425.00 + $103.28

P₁ = $528.28

Hence, after 9 years, the account balance would be $528.28.

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He worked 43 hours to earn Rs. 23250

His basic pay is Rs. 18000 for a basic 36 hours a week. His salary is

Rs. 23250. This proves that he has worked extra time. So the amount earned in the extra hours equals Rs. 23250 - Rs. 18000 = Rs.5250.

Amount per hour earned in basic pay = 18000/36 = Rs.500 a hour.

∴ Amount per hour earned in extra hours = 1.5 x 500 = 750  per hour.

So number of hours he worked in extra time =  Rs.5250/750 = 7 hours.

Thus total number of hours = 36 + 7 = 43 hours.

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If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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Michael is now (B) 6 years old.

Let's start by defining variables for the current ages of Norman and Michael.

Let N be Norman's current age, and M be Michael's current age.

From the problem statement, we know that N = M + 12 (Norman is 12 years older than Michael).

We also know that in 6 years, Norman will be twice as old as Michael.

So we can set up the following equation:

N + 6 = 2(M + 6)

Substituting N = M + 12 into the equation, we get:

M + 12 + 6 = 2(M + 6)

Simplifying:

M + 18 = 2M + 12

M = 6

Therefore, Michael is currently 6 years old.

Answer: (B) 6

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Answer:

B. 180 degrees

Step-by-step explanation:

The straight angle represents 180°. Hence, option (B) is the correct answer.

Answer:

t = 610

Step-by-step explanation:

668 - 58 = 610

610 + 58 = 668

Answer:

t=610

Step-by-step explanation:

you need to get the exponent by itself, to do this:

t+58=668 becomes t=610 by subtracting 58 from both sides to balance it out (what you do to one side you have to do to the other)

The change that Angie will receive from an $100 bill is $38.944.

Angie went to the store and bought 3 pairs of tennis shoes that each cost $24. The total cost will be:

= 3 × $24 = $72

Sales tax was then calculated at 6%. This will be:

= 6% × $72

= $4.32

Total cost = Cost + Tax

= $72 + $4.32

= $76.32

Coupon off = 20% × $76.32 = $15.264

Total amount paid = Cost - Coupon

= $76.32 - $15.264

= $61.056

The change gotten will be:

= $100 - $61.056

= $38.944

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Answer:

6) x = 3, y = -1 or (3, -1)

8) x = -1, y = ½ or (-1, ½)

Step-by-step explanation:

I will only demonstrate problems 6 and 8 since the process of solving for the solution is practically similar for problems 6 and 7.

Given the following systems of linear equations with two variables:

\(\displaystyle\mathsf{\left \{{{Equation\:1:\:x\:+\:y=2} \atop {Equation\:2:\:2x\:-\:y=7}} \right. }\)

First, isolate y from Equation 1:

x + y = 2

x - x + y = -x + 2

y = -x + 2

Substitute the value of y in the previous step into Equation 2:

2x - (-x + 2) = 7

2x + x - 2 = 7

3x - 2 = 7

Add 2 to both sides:

3x - 2 + 2 = 7 + 2

3x = 9

Divide both sides by 3 to solve for x:

\(\displaystyle\mathsf{\frac{3x}{3}\:=\:\frac{9}{3}}\)

x = 3

Substitute the value of x into Equation 1 to solve for y:

x + y = 2

3 + y = 2

3 - 3 + y = 2 - 3

y = -1

Therefore, the solution to the given system is: x = 3, y = -1 or (3, -1).

\(\displaystyle\mathsf{\left\{Equation\:1:\:3(6x\:-\:4y)\:=24} \atop{Equation\:2:\:3x\:-\:2y\:=4}} \right.}\)

For Equation 2, divide both sides by -3:

\(\displaystyle\mathsf{\frac{-3(6x-4y)}{-3}=\frac{24}{-3} }\)

6x - 4y = -8

Add 6x to both sides:

6x + 6x - 4y = 6x - 8

- 4y = 6x - 8

Divide both sides by -4 to isolate y:

\(\displaystyle\mathsf{\frac{-4y}{-4}=\frac{6x\:-\:8}{-4} }\)

\(\displaystyle\mathsf{y=-\frac{3}{2}+2}\)

Substitute the value of y from the previous step into Equation 2:

3x - 2y = -4

\(\displaystyle\mathsf{3x\:-\:2\Big(-\frac{3}{2}+2\Big)\:=-4}\)

3x + 3 - 4 = -4

3x - 1 = -4

3x - 1 + 1 = -4 + 1

3x = -3

Divide both sides by 3 to solve for x:

\(\displaystyle\mathsf{\frac{3x}{3}=\frac{-3}{3}}\)

x = -1

Substitute the value of x into Equation 2 to solve for y:

3x - 2y = -4

3(-1) - 2y = -4

-3 - 2y = -4

Add 3 to both sides:

-3 + 3 - 2y = -4 + 3

-2y = -1

Divide both sides by -2 to isolate y:

\(\displaystyle\mathsf{\frac{-2y}{-2}=\frac{-1}{-2}}\)

y = ½

Therefore, the solution to the given system is: x = -1, y = ½ or (-1, ½).

Answer:

Answer is B

Step-by-step explanation:

\(12x - y = 25 \\ 9x + y = 17 \\ x = \frac{17 - y}{9} \\ 12( \frac{17 - y}{9} ) - y = 25 \\ \)

\(\frac{204}{9} - \frac{12}{9} y - y = 25 \\ \frac{204}{9} - \frac{21y}{9} = 25 \\ - \frac{21y}{9} = 25 - \frac{204}{9} \\ - \frac{21y}{9} = 2.33 \\ - 21y = 20.997 \\ y = - 0.99\)

\(y = - 1 \\ x = \frac{17 - y}{9} \\ x = \frac{17 - - 1}{9} = \frac{18}{9} \\ x = 2\)

Answer:

37

Step-by-step explanation:

you multiply 3 times 5 to get area for the rectangle that is higher. than you multiply 2 times 11 to get the area of lower rectangle. at the and you add them together. so 15+22=37

The classroom should have 28-42 pots.

To find the number of pots needed for a classroom, you first need to determine the total floor space in square feet. If the classroom has a length of 35 feet and a width of 40 feet, the total floor surface area is 35 feet * 40 feet = 1400 sq ft.

The scientist suggests providing two or three pots of flowers for every 100 sq ft of floor space. To find the number of pots needed for 1400 sq ft of floor space, you can divide 1400 sq ft by 100 sq ft/pot.

So 1400 sq ft / 100 sq ft/pot = 14 pots

The researcher suggests a minimum of 2 pots per 100 sq ft of floor space, therefore, the classroom needs at least 2 pots. The researcher also suggested a maximum of 3 pots per 100 sq ft of floor space,

Therefore, the classroom should have between 2 and 3 pots of flowers per 100 sq ft of floor space, which means that the classroom should have between 28 and 42 pots of flowers.

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The slope of the perpendicular line is 1/5

The equation of the line is given as

5x + y = -4

The equation of a line can be represented as

y = mx + c

Where

Slope = m

So, the first step is to make the variable y the subject in 5x + y = -4

This gives

y = -5x - 4

By comparing the equations, we have the following

m = -5

This means that the slope of 5x + y = -4 is -5

So, we have

Slope 1 = -5

The slopes of perpendicular lines are opposite reciprocals

i.e.

Slope 2 = -1/Slope 1

This gives

Slope 2 = -1/-5

Evaluate

Slope 2 = 1/5

Hence, the perpendicular line has a slope of 1/5

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Answer:

$25

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 5%/100 = 0.05 per year,

putting time into years for simplicity,

12 months ÷ 12 months/year = 1 years,

then, solving our equation

I = 500 × 0.05 × 1 = 25

I = $ 25.00

The simple interest accumulated

on a principal of $ 500.00

at a rate of 5% per year

for 1 years (12 months) is $ 25.00.

Answer:

The approximate age of the bone is approximately 11552 years.

Step-by-step explanation:

The current proportion of carbon-14 with respect to its original amount is defined by following formula:

\(\frac{y}{a} = e^{-0.00012\cdot t}\) (1)

Where:

\(y\) - Current amount of carbon-14, no unit.

\(a\) - Initial amount of carbon-14, no unit.

\(t\) - Time, in years.

If we know that \(\frac{y}{a} = 0.25\), then the approximate age of the bone is:

\(t = -8333.333\cdot \ln \frac{y}{a}\)

\(t\approx 11552.453\,yr\)

The approximate age of the bone is approximately 11552 years.

We know the equation.

We also know the y-intercept, which is -3.

All we need to find is the slope. Once the slope is found, our equation is set.

Since the slope has been found, the equation is y = -x/2 - 3.

Hoped this helped.

\(-BrainiacUser1357-\)

Answer:

The image is the answer i couldn't type that in so i took a screenshot

Step-by-step explanation:

Noneya

Answer:

Step-by-step explanation:

Answer:

For First Question i had answered

The attachment is the answer

Step-by-step explanation:

For question 1 i am not sure

Hope It Helps!!!

7 days would the skier have to go skiing in order to make the season pass less expensive than the daily​ passes.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. Every mathematical equation begins with L.H.S = R.H.S.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Let s be the cost of skiing per day.

So,  the season pass plus ski rentals equates to daily skiing plus ski rentals

450 + 20s = 64s + 20s

450 = 64s

7.03 ≈ s

Hence, 7 days would the skier have to go skiing in order to make the season pass less expensive than the daily​ passes.

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There is 4 bottles in each of the packs when Andre and Jillian were shopping at the same grocery store for bottles of sports drinks for their kickball teams. Andre bought 3 packs of bottled drinks, plus 11 single bottles. Jillian purchased 5 packs, plus 3 singles. Andre and Jillian discovered that they had purchased the same number of bottles

The bottles in each of the packs can be calculate as follows:

Expressions that indicate the total number of bottles purchased

The formula 3p + 11 can be used to express how many bottles André purchased.

The formula that can be used to express how many bottles Jillian purchased is 5p + 3

Where:

P is the number of bottles in the purchased packs.

Counting how many bottles are in the pack

The expressions of Andre and Jillian would be equal if they each had the same number of bottles.

3p + 11 = 5p + 3

Take the subsequent actions to find the value of p:

Combine related words

5p - 3p = 11 - 3

2p = 8

Subtract 2 from both sides of the equation.

p = 4

Your question is incomplete but most probably your full question was

Andre and Jillian were shopping at the same grocery store for bottles of sports drinks for their kickball teams. Andre bought 3 packs of bottled drinks, plus 11 single bottles. Jillian purchased 5 packs, plus 3 singles. Andre and Jillian discovered that they had purchased the same number of bottles. How many bottles were in each of the packs? (All of the packs have the same number of bottles.)

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Answer:

I can't help sorry which grade ??