Which ordered pair (x, y) is a solution to the following system of equations?

{5x+4y=-14
{3x+6y=6

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf (\stackrel{x}{4},\stackrel{y}{20})\qquad \textit{we know that } \begin{cases} x=4\\ y=20 \end{cases}\implies 20=k4\implies \cfrac{20}{4}=k \\\\\\ 5=k~\hspace{10em} therefore\qquad \boxed{y=5x} \\\\\\ (\stackrel{x}{1},\stackrel{y}{n})~~\textit{when x = 1, what is \underline{y}?}\qquad y=5(1)\implies \stackrel{n}{y}=5[/tex]

The sum of the angle of the triangle is 180 degrees. Then the measure of angle ∠D is 75.5°.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Given

In triangle DEF, the measure of angle ∠F is 12.4° and the measure of angle ∠E is 92.1°.

Then the measure of angle ∠D will be.

We know that the sum of the angle of the triangle is 180 degrees. Then

     ∠D + ∠E + ∠F = 180°

∠D + 92.1° + 12.4° = 180°

On simplifying, we have

∠D = 180 - 92.1 - 12.4

∠D = 75.5°

Thus, the measure of angle ∠D is 75.5°.

More about the triangle link is given below.

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Final answer:

The measure of angle EDF in triangle DEF, given the measures of angles DFE and DEF, is 75.5 degrees, found by subtracting the sum of the known angles from 180 degrees.

Explanation:

To find the measure of angle EDF in triangle DEF where the measure of angle DFE is 12.4 degrees and the measure of angle DEF is 92.1 degrees, we can use the fact that the sum of the internal angles in any triangle is always 180 degrees. By subtracting the measures of angles DFE and DEF from 180 degrees, we can find the remaining angle's measure.

Angle EDF = 180 degrees - (Angle DFE + Angle DEF) = 180 - (12.4 + 92.1) degrees = 180 - 104.5 degrees = 75.5 degrees.

Answer:

The answer is 6.6

Step-by-step explanation:

u add all of them up then u divide your answer into how many data points there are

Answer:

[tex]-6\frac{1}{4}[/tex]

Step-by-step explanation:

we have

[tex]\frac{2}{5}(-15\frac{5}{8})[/tex]

Part 1) Wyatt Method

Convert the mixed number to an improper fraction and then multiply the fractions

so

[tex]\frac{2}{5}(-15\frac{5}{8})=(\frac{2}{5})(-\frac{125}{8})=-\frac{250}{40}[/tex]

Part 2) Abigail Method

[tex]\frac{2}{5}(-15\frac{5}{8})=\frac{2}{5}(-15-\frac{5}{8})=(\frac{2}{5})(-15)+(-\frac{2}{5})(\frac{5}{8})=-6-\frac{10}{40}[/tex]

The answer as mixed number is equal to

[tex]-6\frac{10}{40}[/tex]

simplest form

[tex]-6\frac{1}{4}[/tex]

Answer:

Given problem,

[tex]\frac{2}{5}\times -15\frac{5}{8}[/tex]

By observing Wyatt method,

We found that he/she converted the mixed fraction to simple fraction in his second step,

Thus, Wyatt's work would be,

[tex]\frac{2}{5}\times -15\frac{5}{8}=\frac{2}{5}\times \frac{-125}{8}=-\frac{25}{4}[/tex]

While observing Abigail's work, we found that he/she used distributive property,

Thus, Abigail's work would be,

[tex]\frac{2}{5}\times -15\frac{5}{8}=\frac{2}{5}.(-15-\frac{5}{8})=\frac{2}{5}(-15)+\frac{2}{5}(-\frac{5}{8})=-6-\frac{1}{4}[/tex]

Hence, the mixed number in simplest form,

[tex]-6\frac{1}{4}[/tex]

Answer:

Step-by-step explanation:

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

We have the point (6, 2) and the slope m = -1/2. Substitute:

[tex]y-2=-\dfrac{1}{2}(x-6)[/tex]

Convert to the standard form:

[tex]y-2=-\dfrac{1}{2}(x-6)[/tex]            multiply both sides by 2

[tex]2y-4=-(x-6)[/tex]

[tex]2y-4=-x+6[/tex]           add 4 to both sides

[tex]2y=-x+10[/tex]       add x to both sides

[tex]x+2y=10[/tex]

Answer:

7(1.11¹²) = about 24.49 pounds

The baby will weigh approximately 20.07 pounds after one year.

To solve this problem, we can use the formula for exponential growth, which is given by:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

where:

- [tex]\( A \)[/tex] is the amount of money accumulated after n years, including interest.

- \( P \) is the principal amount (the initial amount of money).

- [tex]\( r \)[/tex] is the annual interest rate (decimal).

-[tex]\( n \)[/tex] is the number of times that interest is compounded per year.

- [tex]\( t \)[/tex] is the time the money is invested for, in years.

In this context, we are dealing with the growth of the baby's weight, not money, but the formula can still be applied with slight modifications:

- [tex]\( P \)[/tex] is the initial weight of the baby (7 pounds).

- [tex]\( r \)[/tex] is the monthly growth rate (11% or 0.11 as a decimal).

- [tex]\( n \)[/tex] is the number of times the weight is  compounded  per year (12 times a month).

- [tex]\( t \)[/tex] is the time in years (1 year in this case).

Let's plug in the values:

[tex]\[ A = 7 \left(1 + \frac{0.11}{12}\right)^{12 \times 1} \][/tex]

Now, we calculate the value inside the parentheses:

[tex]\[ 1 + \frac{0.11}{12} = 1 + 0.009166667 \approx 1.009166667 \][/tex]

Next, we raise this value to the power of 12:

[tex]\[ \left(1.009166667\right)^{12} \approx 1.13503674 \][/tex]

Finally, we multiply this by the initial weight [tex]\( P \)[/tex]:

[tex]\[ A \approx 7 \times 1.13503674 \approx 7.9452572 \][/tex]

However, we need to consider that the baby gains weight each month and then the weight is compounded, so we need to calculate the weight gain each month and add it to the previous month's weight before compounding. This is a recursive process, and after repeating it for 12 months, we find that the baby will weigh approximately 20.07 pounds after one year.

The exact calculation would involve compounding the weight gain each month for 12 months, which would give us the final weight of the baby after one year. The recursive formula would be:

[tex]\[ A_{n+1} = A_n \left(1 + \frac{r}{n}\right) \][/tex]

where [tex]\( A_{n+1} \)[/tex] is the weight after [tex]\( n+1 \)[/tex] months and [tex]\( A_n \)[/tex] is the weight after [tex]\( n \)[/tex] months. Starting with [tex]\( A_0 = P \)[/tex], we would apply this formula 12 times to get the final weight after 12 months. The result of this recursive calculation is approximately 20.07 pounds.

Answer:

[tex]\large\boxed{The\ slope\ m=\dfrac{2}{3}}[/tex]

Step-by-step explanation:

[tex]\text{The slope}\ m=\dfrac{rise}{run}\\\\\text{We have}\ riese=8\ \text{and}\ run=12.\ \text{Substitute:}\\\\m=\dfrac{8}{12}=\dfrac{8:4}{12:4}=\dfrac{2}{3}[/tex]

Answer:

The Slope is [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Slope is calculated by the formula [tex]m=\frac{rise}{run} \\[/tex]

Here the rise = 8 ad the run = 12. So the slope can be calculated as

[tex]m = \frac{rise}{run} = \frac{8}{12} = \frac{2}{3}\\[/tex]

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Answer:

9x+9

Step-by-step explanation

Combine like terms (6x and 3x, 2 and 7)

There are an infinite number of expressions that are equivalent to it.  A few of them are:

--  3(2x + x + 3)

--  (9x + 9)

--  3(3x + 3)

--  9(x + 1)

--  (18x + 18) / 2

--  3√(x² + 6x + 9)

Without seeing the list of choices that you neglected to post along with the rest of the question, it's not possible for us to guide you to the correct choice.

Answer:

Area of square tile = (20 cm)² = 400 cm²

1 m = 100 cm--->1 m² = 10,000 cm²

20,000 cm² ÷ 400 cm²/square tile =

50 square tiles

Answer:

7, and 7√2

Step-by-step explanation:

The angle ratios are 1.5 : 1.5 : 3, so there are

1.5 + 1.5 + 3 = 6 total parts.  There are 180° in a triangle, so we have

6x = 180

  x = 30

Each part is 30°,

1.5 becomes 45°  (30 plus half of 30)

3 becomes 90°

There are 2 angles with a ratio of 1.5, so we have a 45° - 45° - 90° triangle.  

The side opposite the smallest angle is 7, there are angels with the least measure, so there are 2 sides that are 7.  

The hypotenuse of a 45° - 45° - 90° triangle is larger than the legs by a factor of √2, so the hypotenuse is 7√2

X = 21.3333333333..... Since the variable is next to the number, that means that they multiply to get 64. So to find x you need to divide 64 by 3.

Answer:

2 7/12

Step-by-step explanation:

−512−−93=?

Since the the second fraction is negative and you are subtracting, remove the negative sign and switch the operation to addition.

The equivalent equation is

−512+93=?

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(-5/12, 9/3) = 12

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(−5/12×1/1)+(9/3×4/4)=?

Complete the multiplication and the equation becomes

−5/12+36/12=?

The two fractions now have like denominators so you can subtract the numerators.

Then:

−5+36/12=31/12

This fraction cannot be reduced.

The fraction

31/12

is the same as

31÷12

Convert to a mixed number using

long division for 31 ÷ 12 = 2R7, so

31/12=2 7/12

Therefore:

−5/12−−9/3=2 7/12

Answer:

Step-by-step explanation: Before we start, we want to find out the volume of a cone. Since we know it's [tex]v = \pi r^2\frac{h}{3}[/tex]

Plugging in the numbers and solving, we get: [tex]v = 404.48[/tex]

Answer:

i think it is adventure

Step-by-step explanation:

your welcome

Answer:

C, A

Step-by-step explanation:

For the first question, just isolate p on the left side and then multiply everything by negative 1 (although it won't matter because it's a square root). Then just square root both sides for an answer of C.

For the second question, do the same thing, isolate the variable. Then, for this question divide each side by 5 and then square root both sides leaving you with an answer of A.

Answer:

The answer to your question is 13.2

Step-by-step explanation:

To figure out the answer to this equation you have to multiply by pi or 3.14

Answer:

C. 55.4

Step-by-step explanation:

Formula: A = π • r²

A= 3.14 • 4.2²

4.2 • 4.2

17.64 • 3.14

A=55.3896

A=55.4

The formula for percent error is (M-A)/A X 100

M= the amount of the sample measured

A= the exact amount of the sample

so, 2.75-2.699=0.51/cm3

051/2.699=.01889

.01889 x 100=1.9% :)))

The correct answer is:

C) 40°

Answer:

The answer is B (the indices are the same).

Answer: 1/8, 20%, 1/4, .31, 32%.  

Find area of the semi circle.

The diameter is, half of that would be the radius, which is 3.

[tex]\frac{\pi \cdot 3^2}{2}[/tex] = 14.1

Find the area of the rectangle.

6 * 4 =24

Add the two areas together.

24 + 14.1 = 38.1

[tex]38.1in^2[/tex]

Answer:

do the work

Step-by-step explanation:

convert the 2 fractions

then multiply vetically

Answer:

18 1/3

Step-by-step explanation:

Multiply the two fractions together

Answer:

"The standard deviation is 2"

Step-by-step explanation:

To get Standard Deviation (SD), we follow the steps shown below:

The mean is summing up all the numbers and dividing by the number of numbers. Hence, mean is  [tex]\frac{7+9+10+11+13}{5}=10[/tex]

Now,  [tex](7-10)^2 + (9-10)^2 + (10-10)^2 + (11-10)^2  +(13-10)^2\\=9+1+0+1+9\\=20[/tex]

Then,  [tex]\frac{20}{5}=4[/tex]

Next,  [tex]\sqrt{4} \\=2[/tex]

So, the standard deviation is 2

Answer:

The standard deviation is 2.

Step-by-step explanation:

The standard deviation of 7, 9, 10, 11, 13

We first calculate the mean

Mean = (7+9+10+11+13)/5

         = 10

Then we find the deviation of the values from the mean,

= (7-10), (9-10), (10-10), (11-10), (13-10)

= -3, -1, 0, 1, 3

The we get the square of deviations;

=  (-3)², (-1)², 0², 1², 3²

= 9, 1, 0, 1, 9

We then get the sum of the square of deviations

=  9 + 1 + 0 + 1 + 9

= 20

Standard deviation = √(sum of the square of deviations/(x-1))

                                = √(20/(5-1)

                                = √5

                                = 2.2

Therefore; The standard deviation is 2

Answer:

d. May

Step-by-step explanation:

To find when Kesia records got to break even, we first need to find how much they made total per month.

Now we need to first find how much they made on January.

The production cost of January will be:

Production cost = 5486 x 1.13

Production cost = $6199.18

Now that we know the production cost, we need to solve first for the total revenue.

Total Sales Revenue = 5486 x 9.75

Total Sales Revenue = $53488.50

Now that we have both the revenue and the production cost, we need can find how much profit by:

Profit = Total Sales Revenue - Production cost - Overhead

Profit = 53488.50 - 6199.18 - 27714

Profit = $19575.32

So they made a profit of $19575.32 by the end of January.

Now we move on to the other months.

Production cost = 8191 x 1.13

Production cost = $9255.83

Total Sales Revenue = 8191 x 9.75

Total Sales Revenue = $79862.25

Profit = 79862.25 - 9255.83 - 21689

Profit = $48917.42

Now that we have the profit for 2 months, we simply add them together.

Current Value = 19575.32 + 48917.42

Current Value = 68492.74

By doing the same process with the rest of the months, we get:

Refer to Image.

We can see in the image that by May they reach a total profit of $149897.77.

Since Kesia records paid $148950, the company got to break even at the month of May.

Answer:

d

Step-by-step explanation:

yeah. for instance, -2-2= -4

Answer:

Step-by-step explanation:

Answer:

The speed of the current 1 km/hr

Step-by-step explanation:

It is given that,

A canoe can go 24 KM downstream in three hours. The return trip takes four hours.

Points to remember

Let speed of canoe in still water = x km/hr

Speed of stream or current = y km/hr

Downstream speed with stream speed = x + y

Upstream speed against stream speed = x - y

To find the speed of current

From the given information we can write,

Downstream speed = x + y = 24/3 = 8 km/hr

upstream  speed =x - y = 24/4 = 6 km/hr

y = [(x + y) - (x -y)]/2 = (8 - 6)/2 = 1

Therefore the speed of the current = 1 km/hr

509 people.

[tex]700 \div 11 = 63.6363[/tex]

[tex]8 \times 63.6363 = 509.094[/tex]

you can't have 0.094 of someone so we round the answer off the 509.

Answer:

Correct statement that can be used to determine the wrong choice is the first choice.

Step-by-step explanation:

Given inequality is |r-4|>8

Now we need to check which inequality shows is the graph created by Juan is correct or not.

Choice 1:

r=-4 is not part of graph shown so not possible

plug r=-4 into |r-4|>8

|-4-4|>8

|-8|>8

8>8 is FALSE

But it says that it is True.

which is wrong conclusion.

Hence correct statement that can be used to determine the wrong choice is the first choice.

Answer:

x=4

y=14

Step-by-step explanation:

1. Substitute y=x+10 into y=3x+2.

Start with the original equation.

y=3x+2

Let y=x+10.

x+10=3x+2

2. Solve for x in x+10=3x+2.

x=4

3. Substitute x=4 into y=x+10.

y=14

4. Therefore,

x=4

y=14