1 point
If x = -2, what is the value of y in the equation 3x – 2y = 2
=

A a gang of 17 bandits stole a chest of gold coins, using Chinese Remainder Theorem the smallest possible number of coins in the chest is given as 7.

The Chinese Remainder Theorem in Mathematics states that, assuming that n and the divisors are pairwise coprime, one may utilise the remainders of n's division by the product of these other numbers to get the unique remainder of n's division by n. (no two divisors share a common factor other than 1).

Apply Chinese Remainder Theorem we get,

x≡3(mod17),

So, (x-3) is divided by 17

so, x = 20

x≡10(mod16),

(x-10) is divided by 16

x = 26

x≡4(mod11)

(x-4) is divided by 11

So, x = 15

x≡0(mod7)

(x-0) is divided by 7.

So, x=7

So smallest possible coin is 7.

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Answer:

46

Step-by-step explanation:

Just by common sense you can see there's difference of 4 in every value so you just add 4, four times in it to make 10 months.

Answer:

50

Step-by-step explanation:

There is a interval of Rs 4 in each ..

Mary's Tuesday distance is 1/8 times her Monday distance

On Monday Mary ran 1 3/5 miles

= 8/5

On Tuesday Mary ran 1/5 miles

Therefore the number of times her Tuesday distance was her Monday distance can be calculated as follows

1/5 ÷ 8/5

= 1/5 ×5/8

= 1/8

Hence her Tuesday distance was 1/8 times her Monday distance

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Answer:

60 degrees

Step-by-step explanation:

Vertical angles are angles opposite of each other created by intersecting lines.

Vertical angles are always congruent ( equal ) to each other.

So if an angle has a measure of 60 degrees then its vertical angle would also have a measure of 60 degrees

Answer:

60°

Step-by-step explanation:

Vertical angles are angles of the same measure.

One of the vertical angles is 60°. Therefore, the other angle must be 60°.

Hope this helps!!!

Please give me brainliest!!!

I only need one more brainliest for Virturoso so please give me brainliest

Answers in bold:

S9 = 2

i = 20

R = -2

=====================================================

Explanation:

\(S_0 = 20\) is the initial term because your teacher mentioned \(A_0 = I\) as the initial term.

Then R = -2 is the common difference because we subtract 2 from each term to get the next term. In other words, we add -2 to each term to get the next term.

Here is the scratch work for computing terms S1 through S4.

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{1} = S_{1-1} - 2 & S_{2} = S_{2-1} - 2\\S_{1} = S_{0} - 2 & S_{2} = S_{1} - 2\\S_{1} = 20 - 2 & S_{2} = 18 - 2\\S_{1} = 18 & S_{2} = 16\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{3} = S_{3-1} - 2 & S_{4} = S_{4-1} - 2\\S_{3} = S_{2} - 2 & S_{4} = S_{3} - 2\\S_{3} = 16 - 2 & S_{4} = 14 - 2\\S_{3} = 14 & S_{4} = 12\\\cline{1-2}\end{array}\)

Then here is S5 though S8

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{5} = S_{5-1} - 2 & S_{6} = S_{6-1} - 2\\S_{5} = S_{4} - 2 & S_{6} = S_{5} - 2\\S_{5} = 12 - 2 & S_{6} = 10 - 2\\S_{5} = 10 & S_{6} = 8\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{7} = S_{7-1} - 2 & S_{8} = S_{8-1} - 2\\S_{7} = S_{6} - 2 & S_{8} = S_{7} - 2\\S_{7} = 8 - 2 & S_{8} = 6 - 2\\S_{7} = 6 & S_{8} = 4\\\cline{1-2}\end{array}\)

And finally we arrive at S9.

\(S_{n} = S_{n-1} - 2\\\\S_{9} = S_{9-1} - 2\\\\S_{9} = S_{8} - 2\\\\S_{9} = 4 - 2\\\\S_{9} = 2\\\\\)

--------------------

Because we have an arithmetic sequence, there is a shortcut.

\(a_n\) represents the nth term

S9 refers to the 10th term because we started at index 0. So we plug n = 10 into the arithmetic sequence formula below.

\(a_n = a_1 + d(n-1)\\\\a_n = 20 + (-2)(n-1)\\\\a_n = 20 - 2(n-1)\\\\a_{10} = 20 - 2(10-1)\\\\a_{10} = 20 - 2(9)\\\\a_{10} = 20 - 18\\\\a_{10} = 2\\\\\)

In other words, we start with 20 and subtract off 9 copies of 2 to arrive at 20-2*9 = 20-18 = 2, which helps see a faster way why \(S_9 = 2\)

You're at a shooting range. Your brother shoots x3+y3+z3=k your sister shoots x3+y3+z3=k, 2x³ + 2y³+ 2z³= 2k much did you and your sister shoot combined. This can be solved using the concept of equation solving

Equations are mathematical statements that show the equivalence or balance of two expressions. The equal sign (=) signifies that it contains variables, integers, and mathematical operations. Equations are used to represent connections between different quantities and can be solved to get unknown values. For example, to find x in the equation 2x + 3 = 7, take the third term away from both sides, giving 2x = 4, and then divide both sides by two, giving x = 2.

Given that,

brother shoots x³+y³+z³=k

your sister shoots x³+y³+z³=k

now, shoot combined = 2x³ + 2y³+ 2z³= 2k

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The scale factor was used for each dilation are-

A transformation that changes the size of a figure is called a dilatation. This indicates that the preimage as well as image are similar and have been scaled up or down, respectively.

A dilatation that results in a reduction (imagine shrinking) or an enlargement (think stretching) produces a smaller or larger image, respectively.

Part a: For ΔABC

Length AB = 2 units

Length A'B' = 4 units

A'B' = 2 *AB

Thus,  For ΔABC - scale factor = 2

Part b: For ΔDEF -

Length DF = 2 units

Length D'F' = 1  units

D'F' = 1/2 DF

Thus, For ΔDEF - scale factor = 1/2

Part c: For ΔGHJ -

Length GH = 3 units

Length G'H' = 1  units

G'H' = 1/3 GH

Thus,  For ΔGHJ - scale factor = 1/3

Part d: For ΔKML -

Length KM = 2 units

Length K'M' = 6  units

K'M' = 3*KM

Thus, For ΔKML - scale factor = 3

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Answer:

No, they are co-planar.

Step-by-step explanation:

Points Q, R, X, and W are all in the plane QRXW. Planes do not have to be at ninety-degree angles (that is, straight up and down or straight to the left and right). However, the points Q, S, U, and X would not be coplanar as a plane must be a flat surface.

Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

Step-by-step explanation:

Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=2x f - 1 ( x ) = 2 x is the inverse of f(x)=12x f ( x ) = 1 2 x .

Replace f(x)f(x) with yy.

y=12xy=12x

Interchange the variables.

x=12yx=12y

Solve for yy.

Rewrite the equation as 12y=x12y=x.

12y=x12y=x

Multiply both sides of the equation by 22.

2⋅12⋅y=2⋅x2⋅12⋅y=2⋅x

Simplify 2⋅12⋅y2⋅12⋅y.

Cancel the common factor of 22.

Cancel the common factor.

2⋅12⋅y=2⋅x2⋅12⋅y=2⋅x

Rewrite the expression.

1⋅y=2⋅x1⋅y=2⋅x

Multiply yy by 11.

y=2⋅xy=2⋅x

Solve for yy and replace with f−1(x)f-1(x).

Replace the yy with f−1(x)f-1(x) to show the final answer.

f−1(x)=2xf-1(x)=2x

Set up the composite result function.

g(f(x))

Answer:

m=3

Step-by-step explanation:

subtract the e from both sides so you now have 15=5m divide each by 5 and you get 3=m

Answer:

m = 3

Step-by-step explanation:

-5m + 18 = 3

-5m = 3 - 18

-5m / -15 = 3

Answer: m = 3

Hope this helped

Brainliest is aprreciated.

The required sample size for the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 is 68.

Given that the number of hours spent studying by students on large campus in the week before final exams follows a normal distribution with a standard deviation of 8.4 hours.

we want to find the size of the sample which is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05.

Here, the margin of error is E=2 and the level of significance is α=0.05

The critical value is Zα/2=Z₀.₀₂₅

or the critical value is 1.96

Now, we will find the sample size

n=((Zα/2)×σ/E)²

n=(1.96×8.4/2)²

n=67.76

n≈68

Hence, the size of sample which is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 is 68.

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The answer is that the value of x such that ex > 1,000,000,000 is x > 14.876 (rounded to three decimal places) and the exponential function f(x) = Cbx whose graph is given is f(x) = 25000e0.03x.

a) To estimate the value of x such that ex > 1,000,000,000, we can use a graph of the exponential function ex. On the graph, we can locate the point (x, ex) = (14.876, 1,000,000,000), which means that when x = 14.876, ex > 1,000,000,000. Therefore, the value of x such that ex > 1,000,000,000 is x > 14.876 (rounded to three decimal places).

b) The exponential function f(x) = Cbx whose graph is given is f(x) = 25000e0.03x.

The answer is that the value of x such that ex > 1,000,000,000 is x > 14.876 (rounded to three decimal places) and the exponential function f(x) = Cbx whose graph is given is f(x) = 25000e0.03x.

The complete question is :

Use a graph to estimate the values of x such that ex > 1,000,000,000. (round your answer to three decimal places.) a) Use a graph to estimate the values of x such that ex > 100,000. (Round your answer to three decimal places.) x >b) Find the exponential function f(x) = Cbx whose graph is given. f(x) = 25000e0.03x.

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Answer:

c us the correct answer for this question

The length of side b, rounding off it to the nearest tenth is 24.0.

To find the length of side b in triangle ABC, we can use the Law of Sines, which states:

a/sin(A) = b/sin(B) = c/sin(C)

Given the following information:

A = 43°

B = 55°

c = 28.0

We are interested in finding the length of side b.

We can set up the equation using the Law of Sines:

b/sin(B) = c/sin(C)

Substituting the known values:

b/sin(55°) = 28.0/sin(C)

To find sin(C), we can use the fact that the sum of the angles in a triangle is 180°:

C = 180° - A - B

C = 180° - 43° - 55°

C = 82°

Substituting sin(55°) and sin(82°) into the equation:

b/sin(55°) = 28.0/sin(82°)

Now, we can rearrange the equation to solve for b:

b = (28.0 * sin(55°)) / sin(82°)

Using a calculator, we can evaluate sin(55°) and sin(82°) and substitute the values:

b = (28.0 * 0.819152) / 0.978148

b ≈ 23.504 / 0.978148

b ≈ 24.035

Rounding to the nearest tenth, the length of side b is approximately 24.0.

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The correct inequality according to the given situation of the teacher would be (A) $385.41 ≤ m ≤ $539.58.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

When resolving an inequality, you can do one of the following: • Add the same amount to each side; Subtract the same amount from each side; Multiply or divide each side by the same positive amount.

We must flip the inequality sign if you multiply or divide each side by a negative number.

So, we know that teacher earns:

$1,541.65

25% of $1,541.65:

1,541.65/100 * 25

$385.4125

35% of $1,541.65:

1,541.65/100 * 35

$539.5775

Inequality: $385.4125 < x < $539.5775

Rounding off: $385.41 ≤ m ≤ $539.58

Therefore, the correct inequality according to the given situation of the teacher would be (A) $385.41 ≤ m ≤ $539.58.

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Correct question:
A high school teacher earns an average bi-weekly net pay of $1,541.65. which compound inequality correctly shows the amount of money, m, the teacher can spend if the monthly budget for housing is between 25% and 35%.

a. $385.41 ≤ m ≤ $539.58

b. $668.05 ≤ m ≤ $1,002.07

c. $770.83 ≤ m ≤ $1,079.16

d. $835.06 ≤ m ≤ $1,169.08

After solving the equation for x , we get the solution as  x = 1 \(+\) √47 and x = 1 - √47 .

In the question ,

it is given that ,

the equation in words is written as "2 x squared plus 3 x minus 7 \(=\) x squared plus 5 x plus 39 " .

So , the equation in number can be written as

2x² \(+\) 3x - 7 = x² \(+\) 5x + 39

Making Like terms together ,

we get ,

2x² - x² \(+\) 3x - 5x - 7 - 39 \(=\) 0

(2 - 1)x² \(+\) (3 - 5)x - 46 \(=\) 0

x² - 2x - 46 \(=\) 0

Applying quadratic formula in the above quadratic Equation ,

we get ,

x = -b ± √(b² - 4ac)/2a

From the given quadratic equation , we get that a = 1 , b = -2 and c = -46 .

So ,

x = -(-2) ± √((-2)² - 4(1)(-46))/2(1)

= 2 ± √(4 \(+\) 4(46))/2

= 2 ± √4(1 \(+\) 46)/2

= 2 ± 2√47/2

= 2(1 ± √47)/2

= 1 ±√47

x = 1 + √47 and 1 - √47 .

Therefore , After solving the equation for x , we get the solution as  x = 1 + √47 and x = 1 - √47 .

The given question is incomplete , the complete question is

Solve for x in the equation , "2 x squared plus 3 x minus 7 = x squared plus 5 x plus 39 " .

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Answer:

23

Step-by-step explanation:

Explanation:

The common ratio is calculated by dividing each term by its previous one.

The nth term formula for this particular geometric sequence is:

\(a_n = a*r^{n-1}\\\\a_n = 7*4^{n-1}\\\\\)

The last step is to plug n = 8 into that formula.

\(a_n = a*r^{n-1}\\\\a_n = 7*4^{n-1}\\\\a_8 = 7*4^{8-1}\\\\a_8 = 7*4^{7}\\\\a_8 = 7*16384\\\\a_8 = 114688\\\\\)

The 8th term is 114688

Avoid using commas to separate out the digits. This is because commas are used to separate each term of the geometric sequence.

8th term of this geometric sequence is 114,688.

In a geometric sequence, each term is found by multiplying the previous term by a common ratio. To find the 8th term, we need to know the common ratio and the first term. Given that the first term is 7 and the second term is 28, we can find the common ratio as follows:

r = 28/7 = 4

Now that we know the common ratio, we can find the 8th term by multiplying the first term by the common ratio raised to the power of 7:

a_8 = 7 * r^(8-1) = 7 * 4^7 = 7 * 16,384 = 114,688

Therefore, the 8th term of the sequence is 114,688.

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Here we can use given cost function C(x) = 30,000 + 10x + 50,000/x. By calculating the difference in total cost when x increases by h units and dividing it by h, we can determine average rate of change of total cost.

The given cost function is C(x) = 30,000 + 10x + 50,000/x, where x represents the production level. To find the average cost we can calculate the difference in total cost when x increases by h units and divide it by h.

For h = 10, the average rate of change of the total cost would be (C(x+h) - C(x))/h. Plugging in the values, we get (C(x+10) - C(x))/10 = [30,000 + 10(x+10) + 50,000/(x+10) - (30,000 + 10x + 50,000/x)]/10.

For h = 1, we can similarly calculate (C(x+1) - C(x))/1 = [30,000 + 10(x+1) + 50,000/(x+1) - (30,000 + 10x + 50,000/x)]/1.

To estimate the instantaneous rate of change of the total cost at a specific production level, such as x = 100, we can take the derivative of the cost function C(x) with respect to x. . For example, to find C'(100), we would differentiate C(x) = 30,000 + 10x + 50,000/x with respect to x and evaluate it at x = 100.

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a) The scale factor from shape A to B is 4/3.

b) Using the scale factor, the value for w is obtained as 5.25.

What is scale factor?

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

The diagram have two quadrilaterals which are similar.

To find the scale factor apply the proportion formula -

A : B = 4 : 3

So, the scale factor is -

A/B = 4/3

Therefore, the scale factor value is 4/3.

To find the value for length w use the scale factor.

The proportion expression is -

A : B = 7 : w

Substitute the values into the equation -

4 : 3 = 7 : w

Solve to get the value for w.

4/3 = 7/w

4w = 21

w = 21/4

w = 5.25

Therefore, the value for w is obtained as 5.25.

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Answer:

true

Step-by-step explanation:

Answer:

I think this is a pretty good question of law of indices

Step-by-step explanation:

Given that

\((9^p)(27^q)=3^n\\\)

a) express n in terms of p and q ,

b) hence if p = 1 and q = 2 find the value of n

Solution to part a)

\((9^p)(27^q)=3^n\\\\\)

Simplify the equation and how do we do that? As we can see that 9 can also be written as 3^2 and 27 can be written as 3^3 we can rewrite the following equation like this,

\((3^2)^p(3^3)^q=3^n\\\)

now we multiply p with 2 and

multiply q with 3 respectively,

\((3^{2p})(3^{3q})=3^n\\\)

now since the bases are same and are multiplying the exponents will add themselves like this, in this equation the number 3 is the base

\(3^{2p+3q}=3^n\\\)

now since the bases on the left hand side and on the right hand side are equal the exponents will also be equal so now,

\(2p+3q=n\\\)

hence n is expressed in terms of p and q

Solution to part b)

if p = 1 and q = 2 we plug in these values in the above equation we found for n

n = 2p + 3q

n = 2(1) + 3(2)

n = 2 + 6

n = 7

sin(x) is a mathematical function that calculates the sine of angle x, where x is in radians.

In mathematics, angles are measured in radians or degrees. The symbol π represents the mathematical constant pi, which is approximately equal to 3.14159.

When we say π/2, it means half of the circumference of a circle, which corresponds to 90 degrees.

The inequality "π/2 < 0" suggests that π/2 is less than zero, implying that the angle of 90 degrees is negative. However, this is incorrect.

In the standard coordinate system, angles are measured counterclockwise from the positive x-axis.

Thus, π/2 or 90 degrees lies in the positive direction. The correct relationship should be "π/2 > 0" to indicate that the angle is greater than zero.

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Therefore, in about 15 years and 2 months, the senior class will have about 100 students.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

Let P be the initial population of the senior class in the high school, and r be the rate of decrease in population per year (in decimal form).

Then, we can write the following equation to represent the situation:

P\((1-r)^{n}\) = 100

We know that the current population of the senior class is 320, so we can substitute these values into the equation:

320\((1-0.07)^{n}\) = 100

Simplifying the equation, we get:

\(0.93^{n}\) = 0.3125

Taking the natural logarithm of both sides, we get:

n ln (0.93) = ln (0.3125)

Dividing both sides by ln (0.93), we get:

n = ln (0.3125) / ln (0.93)

Using a calculator, we find that n is approximately equal to 15.21 years.

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Answer:

use long divison  ike this

      16

  -------

8 | 132

    8

  -----

    52

    48

  -----

     4

Step-by-step explanation:

Answer:

Step-by-step explanation:

                                         132/8 = 16 with 4 leftover

                                             32 divided by 8 is 4, 96 divided by 8 is 12, the                                                                  

                                                  extra 4 left over

The option that describes the graph of the inequality is:

"number line with open circle on point negative 5 and arrow shaded to the left"

Here we have the following inequality:

2.5 < -0.5*x

First, need to isolate the variable which is x, to do that we divide both sides by -0.5

Remember that because we divide by a negative number, we need to change the direction of the inequality.

2.5/-0.5 > -0.5*x/-0.5

-5 > x

The graph of this inequality will be a number line with an open circle at x = -5, and a line that extends to the left of it, because x is smaller than -5.

Thus the correct option is:

"number line with open circle on point negative 5 and arrow shaded to the left"

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Answer: B.

Step-by-step explanation: It's B, -5 with the arrow pointing to the left.