Solve the system by substitution.
-8x – 7y = -5
-x = y

Answer:

\(\textsf{1)}\quad y = \dfrac{4}{3}x-\dfrac{13}{3}\)

\(\textsf{2)} \quad y = \dfrac{3}{2}x-6\)

Step-by-step explanation:

To find the equation of a line parallel to the line joining (1, 2) and (-2, -2) and passing through (4, 1), we first need to find the slope of the line joining (1, 2) and (-2, -2).

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-2}{-2-1}=\dfrac{-4}{-3}=\dfrac{4}{3}\)

Parallel lines have the same slope, so the slope of the parallel line is m = 4/3.

Substitute the found slope and point (4, 1) into the point-slope formula:

\(\begin{aligned} y - y_1 &= m(x - x_1)\\\\y - 1 &= \dfrac{4}{3}(x - 4)\\\\y - 1 &= \dfrac{4}{3}x-\dfrac{16}{3}\\\\y &= \dfrac{4}{3}x-\dfrac{13}{3}\end{aligned}\)

Therefore, the equation of the line parallel to the line joining (1, 2) and (-2, -2) and passing through (4, 1) is:

\(\boxed{y = \dfrac{4}{3}x-\dfrac{13}{3}}\)

\(\hrulefill\)

To find the equation of a line perpendicular to the line joining (2, -3) and (-1, -1) and passing through (2, -3), we first need to find the slope of the line joining (2, -3) and (-1, -1).

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-(-3)}{-1-2}=\dfrac{2}{-3}=-\dfrac{2}{3}\)

The slopes of perpendicular lines are negative reciprocals, so the slope of the parallel line is m = 3/2.

Substitute the found slope and point (2, -3) into the point-slope formula:

\(\begin{aligned} y - y_1 &= m(x - x_1)\\\\y - (-3) &= \dfrac{3}{2}(x - 2)\\\\y+3&= \dfrac{3}{2}x-3\\\\y &= \dfrac{3}{2}x-6\end{aligned}\)

Therefore, the equation of the line perpendicular to the line joining (2, -3) and (-1, -1) and passing through (2, -3):

\(\boxed{y = \dfrac{3}{2}x-6}\)

Slope intercept form ;

Where,

m = 3, b = -10

m = -2, b = 8

m = 4, b = -6

*Note - Graphs are in this sequence:

Answer:

Given that,

Two balls are drawn in succession without replacement from a box containing 5 red balls and 7 black balls.

The possible outcomes and the values of the random variable X, where X is the number of red balls.

1) To find the probability distribution of the number of red balls.

Total possible outcome is

We get the X=0,1,2

If there is no red ball,

Then X=0, we get

P(X=0) is,

we get,

If there is 1 red ball then X=1

we get,

P(X=1) is

If there is 2 red balls then X=2

we get,

P(X=2) is

2)To find cumulative distribution function F(x)

when x=0

we get,

When x=1 we get

When x=2 we get,

The powers can be used in the following manner using multiplicative identity.

Powers are mathematical expressions of the kind where x is the base and n is the exponent. In powers, the exponent specifies how many times to multiply the base by itself whereas the base is the integer or variable that is continuously multiplied.

The quotient rule states that exponents should be subtracted when dividing powers by the same base. For instance, h(6-2) Equals h when h(6) is divided by h(2) (4). Subtracting the exponents is a quick and easy way to simplify the issue.

When separating similar words with exponents, using the Quotient of Powers Rule to minimize the number of terms. This rule states that when dividing words with the same base, the exponents should be removed in order to find the result. When separating similar words with exponents, using the Quotient of Powers Rule to minimize the number of terms. This rule states that when dividing words with the same base, the exponents should be removed in order to find the result. The trick is to eliminate only exponents with compatible bases.

Since the multiplicative identity, or one, is the simple outcome of no numbers at all, it follows that every integer raised to the power of zero equals one.

Thus, we came to the logical conclusions.

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Answer:

They are the same

Step-by-step explanation:

So, as you can see there are 4 empty tiles in the middle. Now imagine that the 4 tiles outside don't exist. the width and height of both squares is the same. It's only the 4 tiles that have been misplaced. Therefore, technically they have the same area. Hope this helps!!

The blue shape and the green shape have the same area.

To determine the area of a shape, count or calculate the coloured tiles that form said shape.

1. Finding the area of the blue shape.

We can tell that the height of this shape is 4 tiles, and the width is 4 tiles too and it's a square. Therefore, the total area of this shape if 4x4, which equals 16. This rule only applies for squares and rectangles.

2. Finding the area of the green shape.

This shape is similar to the blue square, except that it is missing 4 tiles in the middle. But if we count all the green tiles one by one we get to the conclusion that there are 16 tiles in total, same as the blue square. This means that the blue shape and the green shape have the same area.

Answer:

  A, C

Step-by-step explanation:

You want to know which answer choices are angles that are coterminal with 3π/2.

Angles are coterminal when their terminal rays lie in the same position. In general, any angle will be coterminal with angles that are an integer multiple of 2π added to the original.

That is, an angle is coterminal with all angles that have the same value modulo 2π.

For the given angle and each of the answer choices, the attachment calculates the coefficient of π modulo 2. The ones that match the given angle are ...

 A. 11π/2 mod 2π = 3π/2

  C. -7π/-2 mod 2π = 3π/2

__

Additional comment

Both -π/-2 and π/2 match the angle π/2, which is not the same as 3π/2.

Of course, the minus signs in numerator and denominator cancel, so -7π/-2 is the same as 7π/2.

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Answer:

The values of 4 behind the decimal is 4 tenths and ahead of the decimal is 4 hundred.

-NULL

Brainliest will be appreciated thank you!

Using the concept of simple interest and compound interest, the first equation is \(S = 200(1.1)^t\), while the second is S = 250 + 20t

c. It will take over 7 years for the accounts to be equal.

The similarities between simple interest and compound interest is that both deals with saving of money over certain period of time with a fixed rate. While the difference between both is that in compound interest, the interest are compounded while in simple interest it is not. This implies that compound interest is an exponential function while simple interest is a linear function.

Simple interest = P(1 + rt)

Compound interest = P(1 + r/n)ⁿˣ

To solve this, we can write equations;

For the first scenario;

\(S = 200(1.1)^t\)

For the second scenario;

S = 250 + 20t

NB: The first case is a compound interest while the second is a simple interest.

c. To determine when the two accounts will be equal;

\(250 + 20t = 200(1.1)^t\)

Solving for t;

t = 7.01 ≈ 7 years

Therefore, it will take over 7 years for the accounts to be equal

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You're answer is (A) The cosine law only

Law of cosines signifies the relation between the lengths of sides of a triangle with respect to the cosine of its angle.

Answer:  The correct answer is (#1) the cosine law only.

Step-by-step explanation:  Confirmed correct.

The difference between Tom and Alfie is  1 kg

Let's call the weight of Tom T, the weight of Harry H, the weight of Freddie F, and the weight of Alfie A. We are given that T = H + 5, H = F + 3, and F = A - 2.

Substituting the second and third equations into the first equation gives us:

T = (A - 2) + 3 + 5

T = A - 2 + 3 + 5

T = A + 1

So the difference between Tom and Alfie is T - A = A + 1 - A = 1 kg.

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Answer:

the answer is 50 but I don't know if

Answer:

no

Step-by-step explanation:

80-225*1/3=80-75=5

The surface area of the figure is approximately 997.5π cm².

We have,

The figure has two shapes:

Cone and a semicircle

Now,

The surface area of a cone:

= πr (r + l)

where r is the radius of the base and l is the slant height.

Given that

r = 15 cm and l = 19 cm, we can substitute these values into the formula:

= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)

The surface area of a semicircle:

= (πr²) / 2

Given that r = 15 cm, we can substitute this value into the formula:

= (π(15)²) / 2

= 112.5π cm² (rounded to one decimal place)

The surface area of the figure:

To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:

Now,

Total surface area

= 885π + 112.5π

= 997.5π cm² (rounded to one decimal place)

Therefore,

The surface area of the figure is approximately 997.5π cm².

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Answer:

-6 < -1 or -1 > -6

How do you know?

Well since the starting point of it is:

-6

And it goes to -1.

Which is also 5 digits away.

-1 is the closest to 0, How?

-1 is one digit away from 0.

-6 is six digits away form 0.

Therefore -6 being further.

Hope this helps and have a lovely day!

Answer:

25% is greater then -25.

Step-by-step explanation:

-25 is in the negiatives, and is to the left of 0. Anything to the left of 0 will be less then anything on the right of 0. :D

-25% will always be less than 25% because a negative number, being less than 0, will always be less than a positive number, being greater than 0.

Thus, -25% is less than 25% or 25% is greater than -25%

Answer: 7x + 1

Step-by-step explanation:

(6x-4)+(x+5)

Step 1: Remove Parentheses:

              6x-4+x+5

Step 2: Combine Like Terms:

             7x +1

Then it will take approximately 6.3 hours for the culture to grow to 80,000 bacteria

The given formula for the number of bacteria in a culture after t hours is:y = 5000(3)^tWe are required to find the number of hours it will take the culture to grow to 80,000.

This can be done by setting y equal to 80,000 and then solving for t.5000(3)^t = 80,000

Divide both sides by 5000:3^t = 16Now, we need to solve for t by taking the logarithm of both sides.

However, it is easier to use logarithmic properties to simplify the equation first.3^t = 2^4

Raise both sides to the power of (1/log3):log3(3^t) = log3(2^4)t = 4/log3(2)Using a calculator, log3(2) ≈ 0.631, so:t ≈ 4/0.631 ≈ 6.3.

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Answer:

To make the denominators the same we can: Multiply top and bottom of each fraction by the denominator of the other. Ex. we simplified the fraction 2032 to 1016 , then to 58 by dividing the top and bottom by 2 each time, and that is as simple as it can get!

The median of the distances is M = 6.5 kilometers

Given data ,

To find the median of a set of numbers, we arrange the numbers in ascending order and then locate the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

Arranging the given set of numbers in ascending order: {4, 5, 8, 11}

Since the set has an even number of values, the median is the average of the two middle numbers. In this case, the two middle numbers are 5 and 8. To find the average, we add these two numbers and divide by 2:

(5 + 8) / 2 = 13 / 2 = 6.5

Hence , the median of the given set {4, 5, 8, 11} is 6.5

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Answer:

B.6x+4=7

Step-by-step explanation:

x represents how many miles is around her school building which she did 6 times, 4 miles is for the amount she ran home and 7 miles is the combination of the 6 times the miles around her school, 6x and the miles she ran home 4

making the equation 6x+4=7

Answer:

44

Step-by-step explanation:

5x8=40+4=44

Answer:a

Step-by-step explanation:

Answer:

138 grams of zinc

Step-by-step explanation:

Zinc : copper = 3 : 19

Let amount of zinc = 138 grams

3 : 19 :: x : 874

Product of means  = product of extremes

19 * x = 3 * 874

      x = \(\frac{3*874}{19}\)

      x = 3 * 46

Zinc = 138 grams

\(\underline{\underline{\sf \bigstar \qquad Solution \qquad \: \bigstar}} \\ \)

Let weight of copper be 3x and weight of zinc be 19x.

☯ \(\underline{\boldsymbol{According\: to \:the\: Question\:now :}} \\\)

\(:\implies \textsf {Total weight = weight of copper + weight of zinc} \\ \\ \\ \)

\(:\implies \textsf {Total weight = 3x +19x} \\ \\ \\ \)

\(:\implies \underline{ \boxed{ \textsf {Total weight = 22x}}} \\ \\ \\ \)

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━

\(\dashrightarrow\:\:\textsf{ Weight of chemical = weight of zinc + weight of copper} \\ \\ \\ \)

\(\dashrightarrow \: \: \sf 22x = 3x + 19x \\ \\ \\ \)

\(\dashrightarrow \: \: \sf 22x = 3x + 874 \\ \\ \\ \)

\(\dashrightarrow \: \: \sf 22x - 3x = 874 \\ \\ \\ \)

\(\dashrightarrow \: \: \sf 19x = 874 \\ \\ \\ \)

\(\dashrightarrow \: \: \sf x = \dfrac{874}{19} \\ \\ \\ \)

\(\dashrightarrow \: \: \underline{\boxed{ \sf x = 46}} \\ \\ \\\)

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

\(\bigstar\:\underline{\frak{Finding \: the \: weight \: of \: the \: zinc \: in \: a \: chemical : }}\)

\(\longrightarrow\:\:\sf weight \: of \: zinc = 3x \\ \\ \\ \)

\(\longrightarrow\:\:\sf weight \: of \: zinc = 3 \times 46 \\ \\ \\ \)

\(\longrightarrow\:\: \underline{ \boxed{\sf weight \: of \: zinc =138 \: grams}} \\ \\ \\ \)

\(\therefore\:\underline{\textsf{The chemical contains \textbf{138 grams}} \textsf{ of zinc}}. \\ \)

To get the Prime factorization of 3000 we need to multiply by 5.

When the number is factored using prime numbers, or primes, the process is known as prime factorization. The easiest method to determine the prime factors of a given number is to keep dividing the given number by the prime factors until we will get 1.

For example, the Prime factorization of 45 is given below

=> 45/5 = 9, 9/3 = 3,  3/3 = 1

=> 45 = 5 × 3 × 3

Here we have

The prime factorization of 600 is 2 x 2 × 2 × 3 × 5 × 5

Let us assume that on multiplying with p,

we will get the factorization of 3000

=> 2 x 2 × 2 × 3 × 5 × 5 × p = 3000

=> p = \(\frac{3000}{2\times 2 \times 2 \times 3 \times 5 \times 5}\)  

Her 2 x 2 × 2 × 3 × 5 × 5 = 600

=> p = \(\frac{3000}{600}\)

=> p = 5  

Therefore,

To get the Prime factorization of 3000 we need to multiply by 5.

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Answer:

84

Step-by-step explanation:

First, there are 6 pages of work. then multiply 6 by the number of questions (14)

6x14=84

Answer:

Not a right triangle

Step-by-step explanation:

\( {6}^{2} + {6}^{2} = 36 + 36 = 72...(1) \\ \\ {8}^{2} = 64....(2) \\ \\ from \: equations \: (1) \: and \: (2) \\ \\ {6}^{2} + {6}^{2} \neq {8}^{2} \\ \\ \)

Hence, triangle with side lengths 6ft.,

6ft., 8ft. is not a right triangle.

Answer:

Inverse Property of Addition

Step-by-step explanation:

Answer:

2520

Step-by-step explanation:

There are 7 letters in MCHNLRN and they can be arranged into 7 ways:

7! = 5040 ways in total

However, the letter 'N' is repeated so we have to divide it by 2.

5040 ÷ 2 = 2520 ways

Answer:

2,520 ways

Step-by-step explanation:

MCHNLRN has 7 letters with one repetition.

therefore, =7!/2!

=2,520 ways