which of the following ordered pairs are a solution to the equation y = 6x -3

(4,61)

(0,-3)

(-4,-27)

(1,3)

It will take 14.87 years for $100 to reach $500 when it grows at 10 percent per year.

To find out how long it will take, we can use the formula for compound interest:

A = P(1 + r)^t

Where A is the final amount, P is the principal amount, r is the interest rate, and t is the number of years.

In this case, we want to find out how long it will take for $100 to reach $500 when it grows at 10 percent per year. So we can plug in the values and solve for t:

500 = 100(1 + 0.10)^t

5 = (1.10)^t

Taking the natural logarithm of both sides:

ln(5) = t ln(1.10)

t = ln(5) / ln(1.10)

t = 14.87 years

So it will take 14.87 years for $100 to reach $500 when it grows at 10 percent per year.

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Answer:

22 dollars

Step-by-step explanation:

Answer: The revenue of last year = 33,345

Step-by-step explanation:

35% = .35 Percentage to decimal

51,3000 x .35 = 17,955 Find the increase

51,300 - 17,955 = 33,345 Subtract it from this year to find last year

Check: 33,345+ (51,300 * .35) = 51,300 Do the reverse to check.

Brainliest please?

Answer:

  x ∈ {6, 7, 8, 9, 10}

Step-by-step explanation:

You want possible values of whole number x such that ...

  4 ≤ √3 +√x < 5

We can solve this inequality by first subtracting √3 from all sides:

  4 -√3 < √x < 5 -√3

Squaring these positive numbers does not change their order:

  19 -8√3 < x < 28 -10√3

  5.14 < x < 10.67

The value of x may be any whole number in the range 6–10, inclusive.

The equivalence of the remainder following the division of 17 and 30 by N indicates that the largest value N can have is 30

The remainder term in a division of one value by a second value is the value which is less than the divisor, remaining after the divisor divides the dividend by a number of times indicated by the quotient.

The remainder following the division of 17 and 30 by the number N are the same.

Let R represent the remainder following the division of the integers 17 and 30 and let b represent the number of times N divides 30 than 17. Using the long division formula, we get;

17/N = Q + R/17

30/N = b·Q + R/17

30/N - 17/N = 13/N

The substitution property indicates that we get the following equation;

30/N - 17/N = b·Q + R/17 - (Q + R/17) = b·Q - Q

30/N - 17/N = b·Q - Q

13/N = b·Q - Q = (b - 1)·Q

13/N = (b - 1)·Q

The fraction 13/N which is equivalent to the product of (b - 1) and Q indicates that N is a factor of 13

13 is a prime number, therefore, the factors of 13 are 13 and N

Therefore, the possible values of N are 13 and 1

The largest value N can have is therefore, 13

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Answer:

sdd

Step-by-step explanation:

seds

Answer:

C. 600

Step-by-step explanation:

There are 25 different choices for the first scoop.

There are 24 scoops for the second scoop

25*24

600 different ways

Answer:

(5v)²-(2)²

(5v-2)(5v+2)

Hence the factors are 2/5 and -2/5

Answer:

7.85 x 10^-4

Step-by-step explanation:

the first value must be between 1 and 9, inclusive

in this case it would be 7.85

we had to move the decimal point 4 places to the left to make 7.85

when you move the decimal to the left then the exponent is a negative

We can fill in the given blanks as follows:

x1 =6, x2 = 7 , y1 = -1,  y2 =3. The slope is 4.

What is meant by the slope of a line?

We have seen lines drawn on the coordinate plane in geometry. The best approach to determine without using any geometrical tools if the lines are parallel, perpendicular, or at any angle is to measure the slope. A line's steepness can be determined by looking at its slope. A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinates. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

Given,

(x1, y1)  = (6, −1)

(x2, y2) = (7, 3)

The slope of the line = \(\frac{y_2-y_1}{x_2-x_1}\) = 3 -(-1) / 7-6 = 4/1 = 4

Therefore we can fill in the given blanks as follows:

x1 =6, x2 = 7, y1 = -1,  y2 =3. The slope is 4.

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The value of  x of chord = 5

By definition of circle,

The chord of a circle is defined as the line segment connecting any two locations on the circle's perimeter; nevertheless, the diameter is the longest chord of a circle that goes through the centre of the circle.

The chord is one of the several line segments that may be made in a circle, and its endpoints are on the circumference.

⇒ 6 (6 + x) = 7 (7 + 11)

Solve for x;

⇒ 36 + 6x = 7 × 18

⇒ 36 + 6x = 126

⇒ 6x = 126 - 36

⇒ 6x = 90

⇒ x = 15

Thus, The value of x = 5

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The number of miles that Mr.Cruz drive in February is 40  miles .

In the question ,

it is given that ,

Mr.Cruz drove 70 miles in March .

let the number of miles that Mr.Cruz drive in January is "x" miles .

He drive 4 times as many miles in February as he did in January ,

So , the number of miles driven in February is = 4x .

he also drive 7 times as many miles in march as he did in January .

So , the number of miles driven in March is = 7x

According to the question ,

7x = 70

x = 10

So , miles driven in February is = 4(10)

= 40 miles .

Therefore , the number of miles driven is February is 40 miles .

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Answer:

10

Step-by-step explanation:

10

Answer:

10

Step-by-step explanation:

1) -9 on both sides

2) m/5=2

3) multiply both sides by 5

4) m=10

A hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. The statement that is true is, a hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. A hypothesis is a suggested explanation of a phenomenon or observed data that is testable.

Hypotheses are more detailed, and are written to explain precisely what you think is going to occur in your research and the reason for that prediction. A hypothesis will be rejected if it does not fit the data, whereas a theory will be modified to fit the data.

A hypothesis is more like a forecast, and a theory is more like a law that explains how certain events operate. Thus, we can conclude that a hypothesis is a specific prediction arising from the theory.

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Answer:

6/35

Step-by-step explanation:

After an earthquake, $$ 3 /7​ of all claims were paid within a month.

Let the total number of claims be represented by 1

Therefore, the amount of claims that were not paid within the month is calculated as:

1 - 3/7 = 4/7

Hence, 4/7 claims were not yet paid.

Of the remaining claims that had not yet been paid, $$ 2/5​ of them were paid within the second month. What fraction of all claims were paid in the second month?

This is calculated as:

2/5 of the claims that were not yet paid

= 2/5 of 4/7

= 2/5 × 4/7

= 6/35

Answer: Slope = 6.000/2.000 = 3.000

 x-intercept = 51/-3 = 17/-1 = -17.00000

 y-intercept = 51/1 = 51.00000

Step-by-step explanation: "y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  y-3x-51  = 0 and calculate its properties

Notice that when x = 0 the value of y is 51/1 so this line "cuts" the y axis at y=51.00000

 y-intercept = 51/1  = 51.00000

When y = 0 the value of x is 17/-1 Our line therefore "cuts" the x axis at x=-17.00000

 x-intercept = 51/-3 = 17/-1  = -17.00000

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 51.000 and for x=2.000, the value of y is 57.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 57.000 - 51.000 = 6.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  6.000/2.000 =  3.000  

Slope = 6.000/2.000 = 3.000

 x-intercept = 51/-3 = 17/-1 = -17.00000

 y-intercept = 51/1 = 51.00000

The dual linear program is as follows:

y1 + 4y2 - w1 = 1

2y1 + 3y2 + w2 = -2

-y1 + 4y2 + 2y3 >= 1

y1 - 2y3 <= 0

y2, y3 >= 0

The primal linear program is:

x1 + 2x2 - x3 + x4 >= 0

4x1 + 3x2 + 4x3 - 2x4 <= 3

-x1 - x2 + 2x3 + x4 = 1

x2, x3 >= 0

To find the dual, we introduce dual variables y1, y2, and y3 for the primal's three constraints, and w1 and w2 for the primal's two non-negativity constraints on x2 and x3, respectively.

The dual linear program is:

maximize 0y1 + 3y2 + y3

subject to:

y1 + 4y2 - w1 = 1

2y1 + 3y2 + w2 = -2

-y1 + 4y2 + 2y3 >= 1

y1 - 2y3 <= 0

y2, y3 >= 0

The objective function of the dual is the sum of the products of the primal's objective coefficients and the dual variables, which gives 0y1 + 3y2 + y3. The new objective is to maximize this expression subject to the dual constraints.

Note that the dual program is also written in standard form, with all inequality constraints replaced by equality constraints and non-negativity constraints.

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Answer:

x = 7

Step-by-step explanation:

You want to subtract 11 from 18 so you get the x alone.

18-11=7

So if you plug it back into the equation it would be

x = 7

Answer:

Line I and II are perpendicular

Step-by-step explanation:

Parallel is when the slope is the same

Perpendicular is when the slope is the opposite (positive and negative)

Hope this helps!

Answer:

B. x+4y=16

Step-by-step explanation:

y=-1/4 x +4

4y=-x+16

x+4y=16

Answer: Thought I’d return the favor and help u with this question! But anyways, the axis of symmetry is at x = -3.

Explanatio: This can be found by looking at the basic form of vertex form:

y = (x - h)^2 + k

In this basic form the vertex is (h, k). By looking at what is plugged into the equation, it is clear that h = -3 and k = -4. This means the vertex is at (-3, -4).

It is a fact that the axis of symmetry is a vertical line of x = (vertex value of x). So we can determine that the axis of symmetry is at x = -3

i hope this helps u

Using trigonometric identities, it is found that the sine and the tangent of the angle are given as follows:

We use the following identity:

\(\sin^{2}{\theta} + \cos^{2}{\theta} = 1\)

In this problem, the cosine is:

\(\cos{\theta} = -\frac{\sqrt{3}}{2}\)

Hence the sine is found as follows:

\(\sin^{2}{\theta} + \left(-\frac{\sqrt{3}}{2}\right)^2 = 1\)

\(\sin^{2}{\theta} + \frac{3}{4} = 1\)

\(\sin^{2}{\theta} = \frac{1}{4}\)

\(\sin{\theta} = \pm \sqrt{\frac{1}{4}}\)

Second quadrant, so the sine is positive, hence:

\(\sin{\theta} = \frac{1}{2}\)

The tangent is given by the sine divided by the cosine, hence:

\(\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}\)

Hence:

\(\tan{\theta} = \frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2}}\)

\(\tan{\theta} = -\frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\)

\(\tan{\theta} = -\frac{\sqrt{3}}{3}\)

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Answer: 18 pieces

Step-by-step explanation:

If she took 10 pieces and then each child received 2 pieces and she has four children then

10+2+2+2+2=

10+8=

18

Answer:

C. She used GF = 2BG, but the correct statement is BG = 2GF.

Step-by-step explanation:

credits to the other person!

Answer:

C.

Step-by-step explanation:

Edge 2021

Answer:

I think its A to the third plus 12 to the third power

Answer:

\(T=s^3+12\)

Step-by-step explanation:

The total volume will simply be the sum of each storage space.

We can see that the storage space on the right as a total volume of 12 cubic feet.

The storage space on the left will have a volume of:

\(V=s^3\)

(This is the volume formula for a cube).

Therefore, the total storage space will be:

\(T=s^3+12\)

Our answer is the bottom-right choice.

And we're done!

The correct statement that establishes the identity is C. cot²x + csc²x = cot²x + (1 - cot²x) = 1 + 2cot²x. This statement demonstrates the correct simplification of the left-hand side to match the right-hand side, thus establishing the identity.

To verify the identity cot²x + csc²x = 1 + 2cot²x, we can simplify both sides of the equation and see if they are equal.

Starting with the left-hand side (LHS):

cot²x + csc²x

Using the reciprocal identities, we can rewrite csc²x as (1 + cot²x):

cot²x + (1 + cot²x)

Combining like terms, we get:

2cot²x + 1

Now, comparing this with the right-hand side (RHS), which is 1 + 2cot²x, we see that both sides are equal.

Therefore, the correct statement that establishes the identity is:

C. cot²x + csc²x = cot²x + (1 - cot²x) = 1 + 2cot²x

This statement demonstrates the correct simplification of the left-hand side to match the right-hand side, thus establishing the identity.

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For the given data, the cutoff point using the upper fence is 791.25 minutes.

To find the cutoff point using the upper fence, we need to first calculate the lower and upper fences.

The lower fence is given by the formula:

Lower fence = Q1 - 1.5 x IQR

where Q1 is the first quartile and IQR is the interquartile range.

The upper fence is given by the formula:

Upper fence = Q3 + 1.5 x IQR

where Q3 is the third quartile and IQR is the interquartile range.

To find these values, we first need to order the data:

307 311 322 321 354 363 377 406 410 425

435 461 464 474 499 505 513 534 548

The first quartile (Q1) is the median of the lower half of the data:

Q1 = (354 + 363) / 2 = 358.5

The third quartile (Q3) is the median of the upper half of the data:

Q3 = (513 + 534) / 2 = 523.5

The interquartile range (IQR) is the difference between the third and first quartiles:

IQR = Q3 - Q1 = 523.5 - 358.5 = 165

Now we can calculate the lower and upper fences:

Lower fence = Q1 - 1.5 x IQR = 358.5 - 1.5 x 165 = 91

Upper fence = Q3 + 1.5 x IQR = 523.5 + 1.5 x 165 = 791.25

Therefore, the cutoff point using the upper fence is 791.25 minutes. Any customer who uses more than 791.25 minutes in a month should be contacted by the phone company as part of the fraud prevention program.

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The corresponding sides have equal ratios, so the triangles are similar triangles.

From the question, we have:

In triangle ABC, AB = 3, BC = 5 and AC = 4

In triangle EDC, ED = 9, DC = 15 and EC = 12

For the triangles to be similar, then the corresponding sides must have an equivalent ratio.

This is calculated as:

\(\mathbf{Ratio = \frac{ED}{AB} = \frac{DC}{BC} = \frac{EC}{AC}}\)

So, we have:

\(\mathbf{Ratio = \frac{9}{3} = \frac{15}{5} = \frac{12}{4}}\)

\(\mathbf{Ratio =3 = 3 = 3}\)

\(\mathbf{Ratio =3}\)

Because the corresponding sides have equal ratios, then the triangles are similar.

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