Solve the system below by substitution
6x-y=-23
2x+5y=-13

Answer:

18

Step-by-step explanation:

6-4=2

2x4=8

10+8=18

The number of acres owned for which the average intake is 2200 calories per day is 2 acres obtained by the algebraic expression that relates the acres of land and the calories per day.

It is given that, the number of calories consumed daily by a person owing x acres of land is given by the algebraic expression,

C(x) = 270 ln(x+1) + 1900

The average intake of calories consumed per day is given by C(x) = 2200

Here x is the number of acres of land. Then, the required number of acres of land is

C(x) = 270 ln(x+1) + 1900

⇒ 2200 = 270 ln(x+1) + 1900

⇒ 270 ln(x+1) = 2200 - 1900

⇒ 270 ln(x+1) = 300

⇒ ln(x+1) = 300/270 = 10/9

Applying base 'e' on both sides, we get

⇒ (x+1) = [tex]e^\frac{10}{9}[/tex]

⇒ x+1 = 3.0377

⇒ x = 3.0377 - 1 = 2.0377

When rounding the final answer to the nearest tenths, we get x = 2 acres.

When rounding the final answer to the nearest thousand, we get x = 2.038 acres.

Thus, for an average intake of 2200 calories per day, the number of acres of land owned is approximately 2 acres.

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Answer: $3.55

Step-by-step explanation:

Started at 2.50 increased 4.75 which means the stock is 7.25 then decreased 1.25 making it 6 then another decrease of 2.45 making it $3.55

The number of notebook is 36.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the notebook be n.

Let the t shirt be t.

The equation will be:

n + t = 60 ..... i

7n + 12t = 540 ..... ii

From I n = 60 - t ..... iii

Put equation III into ii

7n + + 12t = 540 .

7(60 - t) + 12t = 540

420 - 7t + 12t = 540

5t = 540 - 420

5t = 120

Divide

t = 120 / 5

t = 24

Notebook will be:

= 60 - 24

= 36

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The linear equation represented in the table is:

y = (1/2)*x - 2

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Remember that if a line goes through two points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we can use the first two points on the table (0, -2) and (2, -1), so we will get:

a = (-1 + 2)/(2 - 0) = 1/2

And because of the point (0, -2) we know that the y-intercept is -2, so we can write:

y = (1/2)*x - 2

The correct option is C.

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The total surface area of this triangular prism = 976

Surface area is the amount of space covering the outside of a three-dimensional shape.

A triangle would be divided in half, but since there are two, the ratio would remain the same.

 14 x 24 = 336

 10 x 25 = 250[ because there are two of them, multiply by 2.]

 10 x 14 = 140

The total surface area of this triangular prism = 336 + 250 + 140

                                                                            = 976

Therefore, the total surface area of this triangular prism = 976

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Answer: A woman has 8 skirts, 5 blouses, and 5 pairs of shoes. This means that she has a total of 8 * 5 * 5 = <<855=200>>200 different skirt-blouse-shoe outfits that she can wear.

Step-by-step explanation: To find the number of different skirt-blouse-shoe outfits that a woman can wear, we need to find the total number of combinations of skirts, blouses, and shoes that she has. To do this, we simply multiply the number of skirts that she has by the number of blouses that she has by the number of pairs of shoes that she has. In this case, the woman has 8 skirts, 5 blouses, and 5 pairs of shoes, so the total number of combinations is 8 * 5 * 5 = 200. This means that she can wear 200 different skirt-blouse-shoe outfits.

The diver was 450 feet deep in the water 10 minutes ago.

Let our D be the depth of the diver 10 minutes ago.

Since diver is pulled out at 25 ft/minute, the depth formula can be written as:

[tex]D - 25t = 200[/tex] where t is the time in minutes.

Substituting t = 10, we have:

[tex]D - 25(10) = 200\\D - 250 = 200\\D = 200 + 250\\D = 450 feet.[/tex]

Translated question "A deep-sea exploration vessel is pulling a diver out to rate of 25 feet per minute. The diver is 200 feet below sea level. How deep was the diver 10 minutes ago?"

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Note that given the speed at which he is being pulled out, the diver was 50 feet about 10 minutes ago.

The diver is being pulled out at the rate of 25 feet per minute.

This means that after 10 minutes, he would have been pulled by a total of

25 x 10 = 250 feet.

Since the diver was 200 feet below sea level,

200-250 = -50ft.

hence 10 minutes ago, he was 50 feet below sea level.

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Translation:

A deep-sea exploration vessel is pulling a diver out to rate of 25 feet per minute. The diver is 200 feet below sea level. how deep there was the diver 10 minutes ago?

Answer:

200.96

Step-by-step explanation:

3.14*r²

so 3.14*8²=200.96

Answer:

The probability of rain on both Monday and Tuesday is .08, or approximately 8%.

Step-by-step explanation:

The probability of an event occurring on two separate days (such as rain on Monday and Tuesday) is calculated by multiplying the probabilities of the two events occurring separately. In this case, the probability of rain on both Monday and Tuesday is given by:

Probability of rain on Monday * Probability of rain on Tuesday = .1 * .8 = .08

Therefore, the probability of rain on both Monday and Tuesday is .08, or approximately 8%.

It's important to note that this probability assumes that the likelihood of rain on each day is independent of the other day. In other words, the probability of rain on Tuesday does not depend on whether or not it rained on Monday. If this is not the case, the probability of rain on both days may be different.

The measure of one interior angle of the 45-sided polygon is (c) 172 degrees

From the question, we have the following parameters that can be used in our computation:

Shape = 45-sided polygon

Parameter to calculate = the measure of one interior angle

The sum of the interior angles is calculated using the following angle formula

The sum of the interior angles = ( n − 2 ) × 180 ∘ where is the number of sides

In this case

n = 45

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

The sum of the interior angles = (45 − 2) × 180∘

Evaluate

The sum of the interior angles = 7740∘

So, the internal angle is

Angle = 7740/45

Evaluate

Angle = 172

Hence, the angle is (c) 172 degrees

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The true statement is that 2 in 142 represents a greater value than 2 in 124 because 142 > 124.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol. The place values on the left ofthe decimal point start as ones, tens, hundreds, and so on.

The place value on the right of the decimal point starts from a point and goes to right as tenths, hundredths, and so on.

We are given that encore or points for an NBA Team are usually as whole numbers.

For example, 1, 2, 3, 4, e.t.c. points of an NBA Team are not in decimals or fractions.

The withiner of points awarded for an NBA match is called Discrete because that can be counted with a given amount of time.

Hence, 2 in 142 represents a greater value than 2 in 124 because 142 > 124.

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There are $20468.55 must you deposit now in order to have $25,000 in 4 years in an account getting 5% interest compounded daily.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

Given:

A = Final amount = $25000

P = Initial principle balance

r = interest rate = 5% = 0.05

t = Number of time of years

n = number of times interest applied per time period = 365

Since, the formula for compound interest,

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

Plug the values of A, r, n and t in the above formula

[tex]25000 = P(1 + \frac{0.05}{365})^3^6^5^*^4 \\25000 = P(1.0001369863)^1^4^6^0\\25000 = P(1.2213860258)\\P = 20,468.549231702[/tex]

P ≈ 20,468.55

Hence, there are $20468.55 must you deposit now in order to have $25,000 in 4 years in an account getting 5% interest compounded daily.

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The inequality expression p + 1.4 ≤ 0.5 is false for p = 0.1

From the question, we have the following parameters that can be used in our computation:

p + 1.4 ≤ 0.5;

p = 0.1

Substitute p = 0.1 in p+ 1.4 ≤ 0.5;

So, we have the following representation

0.1 + 1.4 ≤ 0.5;

Evaluate the like terms

This gives

1.5 ≤ 0.5;

The above inequality is false

This is because 1.5 is greater than 0.5

Hence, p + 1.4 ≤ 0.5; p = 0.1 is false

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Part a: P(A) = 1/2; P(B) =  2/3; P(C) = 1/12; P(A ∩ B ∩ C) = 1/36.

Part b: Part b: A, B, and C independent events.

Rolling a dice twice has 36 possible results, hence the following is the sample space:

S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

For the stated question-

Part a:  P(A), P(B),P(C), and P(A ∩ B ∩ C).

P(A) = 18/36 = 1/2

P(B) = 24/36 = 2/3

P(C) = 3/36 = 1/12

P(A ∩ B ∩ C) = 1/36

Part b: A, B, and C independent or not.

For the events to be independent,

P(A ∩ B ∩ C) = P(A).P(B).P(C)

P(A).P(B).P(C) = 1/2*2/3*1/12 = 1/36

As, P(A ∩ B ∩ C) = P(A).P(B).P(C).

Thus, the events are independent.

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The number of games that must be played for the cost to be the same at both places is 4.

Bowl o rama charges 2.50 a game plus 2 for shoe rental, and bowling pinz charges 2 a game plus 4 for shoe rental.

The number of games that must be played for the cost to be the same at both places is as follows:

Using system of equation,

let

x = number of games

Hence,

2.50x + 2 = 2x + 4

2.50x - 2x = 4 - 2

0.5x = 2

divide both sides by 0.5

x = 2 / 0.5

x = 4

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C. x + 3y = 27 lines are perpendicular to 3x – y = 10

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. In a two-dimensional plane, it is specified by two points. The term "collinear points" refers to two points that are on the same line.

As we know,

When two lines are perpendicular then the product of their slope is -1.

The slope is given by: y = mx+c

where, m is the slope.

Thus, the given equation:

3x – y = 10

y = 3x - 10

Comparing this equation with y = mx+c, we get

m₁ = 3

So, the slope of the given equation (m₁) = 3

Now find slope of others lines:

A) y = 3x + 5, Comparing this equation with y = mx+c, we get -

m₂ = 3

When two lines are perpendicular then the product of their slope is -1.

Here, product of the slope is:

= m₁ × m₂

= 3×3 (putting the values we get)

= 9 ≠ -1

So, this line is not perpendicular to given line.

B) y = –13x + 17, Comparing this equation with y = mx+c, we get -

m₃ = -13

When two lines are perpendicular then the product of their slope is -1.

Here, product of the slope is:

= m₁ × m₃

= 3× (-13) (putting the values we get)

= -39 ≠ -1

So, this line is not perpendicular to given line.

C) x + 3y = 27

3y = 27 - x

y = 9 - x/3, Comparing this equation with y = mx+c, we get -

m₄ = -1/3

When two lines are perpendicular then the product of their slope is -1.

Here, product of the slope is:

= m₁ × m₄

= 3× (-1/3) (putting the values we get)

= - 1

So, this line is perpendicular to given line.

D) y – 2 = 13(3x + 36)

y = 39x +470, Comparing this equation with y = mx+c, we get -

So, m₅ = 39

When two lines are perpendicular then the product of their slope is -1.

Here, product of the slope is:

= m₁ × m₅

= 3× (39) (putting the values we get)

= 117 ≠ -1

So, this line is not perpendicular to given line.

Therefore, option C is correct.

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12.6

Step-by-step explanation:

We need to find the hypotenuse

hyp² = opp² + adj²

hyp²= 2² + 3²

hyp²= 4 + 9

hyp²= 13

hyp=√13

hyp=3.6

sinθ=opp/hyp

sinθ=2/3.6

sinθ=5.6

cosθ=adj/hyp

cosθ=3/3.6

cosθ= 0.8

tan θ=sinθ/cosθ

tanθ= 5.6/0.8

tanθ=7

tan θ+sinθ

=7+5.6

=12.6

The simplified form in base 3 for ln(3) + ln(9) is 3ln(3)

logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if b^x = n, in which case one writes x = logb n.

In(9) can be written as ln3^2

which according law of logarithm is 2ln(3)

Expression becomes

ln(3) + 2ln(3) which is 3ln(3)

In conclusion, the simplified form of the expression in base 3 is 3ln(3)

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Answer:

x = -6

Step-by-step explanation:

-6/3-4= -6

Answer:

[tex] 4\frac{1}{5} [/tex]

Step-by-step explanation:

[tex] 4\frac{2}{3} \times \frac{9}{10} [/tex]

[tex] \frac{14}{3} \times \frac{9}{10} [/tex]

[tex] \frac{126}{30} [/tex]

[tex] \frac{21}{5} [/tex]

Answer: -3/2

yeah use rise over run

Answer:

-2/3

Step-by-step explanation:

slope = rise/run

First find the y-intercept (point of crossing on the y-axis (the vertical one)), then find the next point that intercepts a box PERFECTLY, this next point is (4, -2)

Looking at the y-intercept's coordinates (0,1), count how many blocks down it takes to get to to 4 (2 blocks which is the RISE) and now count how many blocks to the right it takes to get to -2 (3 blocks)

Therefore it is 2/3 but it is also negative because it is going DOWN from left to right which is a negative decine

The measure of angle A of the triangle is 50°.

How to find angles of the triangle?

Similar side interior angles therefore:

So, ∠C = ∠A

∠A = 50°

Hence, the measure of angle A of the triangle is 50°.

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The probability of the customer wants to take snack B is 144/320 as they have already taken snack A

and the probability of the customer who has not taken snack A before

wants to take snack A =108/252

It is the ratio of favorable outcome to total possible outcome of an event.

based on given data, we calculated the number of customers who has taken snack A before may want to take snack B. The customers have not taken snack A yet may want to snack A.

hence, probability to take snack B = 144/320

probability to take A =108/252

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a) The probability a person who has eaten snack A before is 59/143.

b) The probability a person who has eaten snack A before is 84/143

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Given that the total number of people that are taken for the event is 572.

The number of people who have eaten snack A before is 236.

The number of people who have not eaten snack A before is 336.

Probability = The number of outcomes of favorable event/ Total number of outcomes

The probability getting a person who has eaten snack A before is

= 236/ 572

= 59/143 [Divide denominator and numerator by 4]

The probability getting a person who has not eaten snack A before is

= 336/ 572

= 84/143 [Divide denominator and numerator by 4]

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The fraction of the album he recorded in June is 1/2

When all the fractions of the album will be  = 1

Bruno recorded 2/12 was recorded in August

2/12 to the lowest term = 1/6

And 1/3 was recorded in July

So,

The fraction of the rest of the album in June is unknown

Let fraction recorded in June will be = x

x =  1 - 1/6 - 1/3

x = 1/1 - 1/6 - 1/3

x = [tex]\frac{18 - 3 - 6}{18}[/tex]

x = [tex]\frac{9}{18}[/tex]

x = [tex]\frac{1}{2}[/tex] to lowest term

Therefore, he recorded 1/2 of his Album in June

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Answer:

A

Step-by-step explanation:

-2x + 9 < x - 9

-2x - x < -9 - 9

-3x < -18

x > -18/-3

x > 6

The amounts of each type of coin that they have is given as follows:

The amounts of each type of coin are obtained using a system of equations, in which the variables are given as follows:

Kevin and Randy Muise have a jar containing 83 coins, hence:

x + y = 83.

The value of a nickel is of $0.05, while the value of a quarter is of $0.25. The total value of the coins in the jar is $12.95, hence:

0.25x + 0.05y = 12.95.

From the first equation, we have that:

y = 83 - x.

Replacing on the second equation, the amount of quarters is given as follows:

0.25x + 0.05(83 - x) = 12.95

0.2x = 8.8

x = 8.8/0.2

x = 44.

Then the amount of nickels is given as follows:

y = 83 - x = 83 - 44 = 39.

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To represent an inequality on a number line, such as x>3, first draw a circle around the number. Fill in the circle if the sign also says equal to (or ).

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