What is the solution of the system of equations below?
x + 3y = 7
2x - y = 7

The area of the quadrilateral ABCD is 105 square units

From the question, the vertices are given as

A = (4, 2)

B = (-2, -10)

C = (14, -y)

D = (14, y)

By the equation of perpendicular slopes, we have

(-10 - 2)/(-2 - 4) = -(14 - 4)/(-y - 2)

When evaluated, we have

2 = -10/(-y - 2)

So, we have

-y - 2 = -5

This gives

y = 3

So, we have

A = (4, 2)

B = (-2, -10)

C = (14, -3)

D = (14, 3)

The area is then calculated as

Area = 1/2 * |(x1 - x3)(y2 - y4) - (x2 - x4)(y1 - y3)|

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * |(4 - 14)(-10 - 3) - (-2 - 14)(2 + 3)|

Evaluate

Area = 105

Hence, the area is 105 square units

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Answer:

0.2

Step-by-step explanation:

Answer:

175

Step-by-step explanation:

500*.35

Answer:

60students

Step-by-step explanation: 4 x 15=60

This is because each bottle can make 4 slimes and if there are 15 bottles you multiply 4 by 15. Now you will receive 60.

Answer:

y= -7

Step-by-step explanation:

There's no need to include x as the y-value will always be -7, but if your question requires it then you could say something like y=(x-x)-7

Answer:

SOLUTION??? And btw thanks for free pts...

Step-by-step explanation:

Answer:

c. base area + lateral area

this is the best describe the surface area of a solid figure.

Answer: d. $264 hope this helps :)

Step-by-step explanation:12x22=264

Answer:

For the problems presented, the following are the answers:

1. No graph is provided, sorry.

2. 2, 1/2

3. 12m

4. 30

5. 1.1, 9.1

6. 10.35, 1.35

22. -6, 2

Step-by-step explanation:

Please mark me brainliest if my answer is correct thank you and have a nice day

We have to toss two dice. Let A be the event that the first die rolls 1, 2, or 3. Let B be the event that the first die rolls 3, 4, or 5. Let C be the event that the sum of the dice is 9.

P(A) = Probability of the first die rolling 1, 2, or 3.

P(B) = Probability of the first die rolling 3, 4, or 5.

P(C) = Probability of the sum of the dice is 9.

P(A ∩ B) = Probability of the first die rolling 3.

P(A ∩ C) = Probability of the first die rolling 1 and the sum of the dice being 9.

P(B ∩ C) = Probability of the first die rolling 4 and the sum of the dice being 9.

P(A ∩ B ∩ C) = Probability of the first die rolling 3, the second die rolling 6, and the sum of the dice being 9.

P(A)P(B) = Probability of the first die rolling 1, 2, or 3 and 3, 4, or 5 = P(A ∩ B).P(A)P(C) = Probability of the first die rolling 1, 2, or 3 and the sum of the dice being 9 = P(A ∩ C).P(B)P(C) = Probability of the first die rolling 3, 4, or 5 and the sum of the dice being 9 = P(B ∩ C).

Therefore, P(A ∩ B ∩ C) = P(A)P(B)P(C), but P(A) and P(B), P(A) and P(C), and P(B) and P(C) are not independent because the occurrence of one event does affect the probability of the other event occurring.

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The test statistic is given by Z = (p1 - p2) / SE = [(690 / 700) - (472 / 700)] / 0.027 ≈ 7.62For α = 0.07, the critical value of Z for a two-tailed test is Zα/2 = 1.81 Rejection region: |Z| > Zα/2 = 1.81. Since the calculated value of Z (7.62) is greater than the critical value of Z (1.81), we reject the null hypothesis.

In this question, we have to perform hypothesis testing for two independent binomial populations using the two-sample z-test. We need to test the hypothesis H0: (p1 - p2) = 0 against Ha: (p1 - p2) ≠ 0 using α = 0.07. We can perform the two-sample z-test for the difference between two proportions when the sample sizes are large. The test statistic for the two-sample z-test is given by Z = (p1 - p2) / SE, where SE is the standard error of the difference between two sample proportions. The critical value of Z for a two-tailed test at α = 0.07 is Zα/2 = 1.81.

If the calculated value of Z is greater than the critical value of Z, we reject the null hypothesis. If the calculated value of Z is less than the critical value of Z, we fail to reject the null hypothesis. In this question, the calculated value of Z is 7.62, which is greater than the critical value of Z (1.81). Hence we reject the null hypothesis and conclude that there is a significant difference between the population proportions of two independent binomial populations at α = 0.07.

Since the calculated value of Z (7.62) is greater than the critical value of Z (1.81), we reject the null hypothesis. We have enough evidence to support the claim that there is a significant difference between the population proportions of two independent binomial populations at α = 0.07.

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Answer:

198

Step-by-step explanation:

hope this helps

Option A will be the correct option for the given origami folding question by doing it or using logical concept.

If we do it physically and take a piece of paper make a dot over it then fold it in the direction as shown there then we can see that that dot will come downward then they have asked in second step to flip it over backside so turn it as the arrow shows. Then we will see that the dot again arises at the top as shown then we have to make the part of eyes and a mouth and already at the top in second step there is a dot so whole paper will look as shown in option A .

By logical method we can see that step 1 remains the same and then we can add step 2 and step 3 pictures then ultimately we get option A as required answer.

So Paper folding method can be used for observing and visualizing the patter.

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The correct option is D. By using the pattern of cutting and folding we will get D figure.

A repeated arrangement of numbers, shapes, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, that arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a sequence. A pattern in mathematics is a series of recurring figures, shapes, or numbers. Any kind of event or thing can be connected to a pattern. A pattern has a rule that identifies the objects that are part of the pattern and those that are not.

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To find the derivative of the function A(x) = 17 - 2x, we need to apply the power rule of differentiation. The derivative of the function A(x) = 17 - 2x is A'(x) = -2.

The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1). Using this rule, we can find the derivative of A(x) as follows:

A'(x) = d/dx (17 - 2x)
      = 0 - 2 d/dx(x)
      = -2

Therefore, the derivative of A(x) is -2.

As for the second part of the question, we are given another function 3(7 - 3x) and we need to find its derivative. Using the power rule again, we can find the derivative as follows:

d/dx [3(7 - 3x)]
= 3 d/dx (7 - 3x)   (by the constant multiple rule)
= 3 (-3)             (since the derivative of 7 - 3x is -3)
= -9

Therefore, the derivative of 3(7 - 3x) is -9.

To find the derivative of the given function A(x) = 17 - 2x, follow these steps:

Step 1: Identify the function
A(x) = 17 - 2x

Step 2: Apply the power rule for differentiation
The power rule states that if f(x) = x^n, then f'(x) = n * x^(n-1). Here, we have two terms: a constant (17) and a linear term (-2x).

Step 3: Differentiate each term
The derivative of a constant (17) is 0.
The derivative of -2x is -2, as per the power rule (n=1).

Step 4: Combine the derivatives
A'(x) = 0 - 2
A'(x) = -2

The derivative of the function A(x) = 17 - 2x is A'(x) = -2.

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Answer:

$46.27

Step-by-step explanation:

210.29×.78=164.02

210.29-164.02=46.27

There are several examples of relation which is symmetric but neither reflexive nor transitive.

Let A={5,6,7}

Define a relation R on A as R= {(5,6),(6,5)}

Relation R is not reflexive as (5,5),(6,6),(7,7) ∉ R.

Now, as (5,6) ∈R and also (6,5) ∈R, R is symmetric.

⇒(5,6),(6,5)∈R, but (5,5)∉R, Hence R is not transitive.

Hence, relation R is symmetric but not reflexive or transitive.

The relationship between perpendicularity in the set of all straight lines in a plane is one such example. Because;

(1) Since no line may cross itself, the relationship is not reflexive

(2) It follows that M is perpendicular to line L if line L is perpendicular to line M. Thus relationship is thus symmetrical.

(3) If line L is parallel to line M and M is parallel to line N, then L is not parallel to N but || to N, proving that the connection is not transitive.

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Answer:

x=1/4

Step-by-step explanation:

1.distribute the 7 and 3 into parentheses

2. combine like terms

3. add 9 on both sides

4. divide both sides by 4

x=1/4

hope this helped!

Answer:

x = \(\frac{1}{4}\)

Step-by-step explanation:

7(x-3)+3(4-x)= -8

Expand 7(x-3) and 3(4-x)

i.e. 7x-21+12-3x= -8

4x-9=-8

Collect like terms

4x= -8+9

4x= 1

x = \(\frac{1}{4}\)

Hope this helps!!!

Answer:

a

Step-by-step explanation:

Answer: 7/24

Step-by-step explanation:

Answer:

16%

Step-by-step explanation:

Find the total number of throws

3 + 5 + 8+ 11 + 14 + 16 + 15 + 12 + 9 + 5 + 1

When you add these together, you get 100

Find the number of 7s that were thrown

The number of 7s thrown was 16

Find the probability that a 7 was thrown.

P(7) = 16/100 = 0.16

Find the %.

0.16 * 100 = 16%

Answer:

x=45

Step-by-step explanation:

weights and routes

weights and routes

weights and routes

VvvvVV

The amount of snow on the ground when the storm started is the y- intercept of graph which is 5 inches.

The y- intercept of a graph gives the value y when the value of x = 0.

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Answer:

slope m = - 8

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y + 3 = - 8(x - 4) ← is in point- slope form

with slope m = - 8

The slope is :

Solution:

Given: \(\bf{y+3=-8(x-4)}\)

To determine the slope, it's important to know the form of the equation first.

There are 3 forms that you should be familiar with.

The three forms of equations of a straight line are:

This equation matches point slope perfectly.

The question becomes, how do you work with point slope to find slope?

In point slope, m is the slope and (x₁, y₁) is a point on the line.

Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.

Answer:

3.3%

Step-by-step explanation:

compound interest: A = Pe^(rt)

A = 534.46

P = 450

t = 5

534.46/450 = e^(5r)

e^(5r) = 1.18

lne^(5r) = ln 1.18

(5r)lne = ln1.18

ln1.18 = 5r

5r = 0.165

r = 0.033

or 3.3%

The difference between the two high altitudes is therefore 300 feet.

Let 't' denote the time in minutes when both birds are at the same height. If both of these fowls are traveling, one descending and the latter ascending, then we obtain a formulaic value for t using the equations below.

Therefore, if we solve: 75t - 25t = 400, it follows that 50t = 400 and t = 8 minutes.

Given this information, after 8 minutes, the two birds reach the same height.

Consequently, before the 8-minute interval, bird A is situated at a higher level than bird B since the prior's rate of descent is less than the current bird's ascent.

Once they have reached the shared altitude, bird B is above bird A given its continuous upward elevation, contrasting against bird A's descending course.

Their heights after only 1 minute has elapsed; the Height of bird A after 1 minute is calculated to be 425 feet - (500 - 75(1)) and for bird B it is 125 feet - (100 + 25(1)).

The difference between the two high altitudes is therefore 300 feet.

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The balance in the account 10 years after Jakie stopped her monthly payments, with the interest compounding quarterly at a rate of 6.9% per year, is approximately R373,185.53.

To calculate the balance in the account 10 years after Jakie stopped her monthly payments, we need to consider two periods: the period when she was making monthly payments and the period after she stopped making payments.

During the period when she was making monthly payments, the interest was compounded monthly at a rate of 6.9% per year. We can use the formula for compound interest to calculate the future value of the monthly payments. Using the formula:

Future Value = Payment * [(1 + interest rate/compounding periods)^(compounding periods * number of years) - 1] / (interest rate/compounding periods)

Plugging in the values: Payment = R4,500 , Interest rate = 6.9% = 0.069, Compounding periods = 12 (monthly)

Future Value = R4,500 * [(1 + 0.069/12)^(12 * 4) - 1] / (0.069/12)

Future Value = R280,192.52

Now, we need to calculate the balance after 10 years when the compounding periods change to quarterly. We can use the same formula for compound interest, but with a different compounding period.

Future Value = Previous Balance * (1 + interest rate/compounding periods)^(compounding periods * number of years)

Plugging in the values: Previous Balance = R280,192.52, Interest rate = 6.9% = 0.069, Compounding periods = 4 (quarterly), Number of years = 10

Future Value = R280,192.52 * (1 + 0.069/4)^(4 * 10)

Future Value = R526,618.01. Therefore, the balance in the account 10 years after Jakie stopped her monthly payments is A. R373 185,53.

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9514 1404 393

Answer:

  Dan obviously didn't measure the remainder, which is (C) 3 11/12 ft.

Step-by-step explanation:

After the cut, Dan has ...

  8 3/4 - 4 5/6 = 8 9/12 - 4 10/12

  = (8 -4) +(9/12 -10/12) = 4 -1/12 = 3 11/12 . . . ft

Answer:

A: 12 B: 80

Step-by-step explanation:

92 - 80 = 12

80 students

12 Chaperones

Answer:

12 chaperones and 80 students

Step-by-step explanation:

Start by multiplying the numbers seperatly and then add. Keep doing this till you get to 92.

  20(2)=40. 3(2)=6 46

  20(3)=60. 3(3)=9 69

  20(4)=80. 3(4)=12 92

Now you know there are 12 chaperones and 80 students. There are other ways to answer this problem like using systems of equations but it still gives the correct answer and is less advanced.

       Hope this helps:)

Answer:

36/5 as a decimal is 7.2

Step-by-step explanation:

In the fraction 36/5, 36 is the numerator and 5 is the denominator, the fraction bar means "divided by". Therefore, the fraction 36/5 is same as "36 divided by 5" or "36 ÷ 5".

When we calculated 36 divided by 5, we found that 36/5 in decimal form is:

36 ÷ 5 = 7.2

Therefore, the decimal form of 36/5 is 7.2