Solve the system of equations.
y=x+57
y=8x+15

The given series is a geometric series. The sum of this series can be calculated using the formula for the sum of a geometric series, Sn = a(Rn-1)/(R-1). By substituting the given values into the formula, the sum of the series is found to be 242.

The series given is a geometric series. A geometric series is a series of numbers where each term after the first is found by multiplying the previous term by a constant.

The series is 2+6+18+54+162, where each successive term is 3 times the previous term. Hence, the common ratio (R) is 3.

The sum of the first 'n' terms (Sn) of a geometric series can be found using the formula: Sn = a(Rn-1)/(R-1), where a is the first term, R is the common ratio and n is the number of terms.

Here, 'a' = 2 and 'R' = 3. The total number of terms (n) is 5 in this case. Substituting these values into the formula gives: S5=2(35-1)/(3-1)= 2*(243-1)/2= 242

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Answer:

y = 2x + 11

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 7, - 3) and (x₂, y₂ ) = (- 3, 5)

m = [tex]\frac{5+3}{-3+7}[/tex] = [tex]\frac{8}{4}[/tex] = 2, thus

y = 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation.

Using (- 3, 5 ), then

5 = - 6 + c ⇒ c = 5 + 6 = 11

y = 2x + 11 ← equation of line

To write an equation of a line that passes through two points, use the slope-intercept form. Find the slope using the formula and substitute the values into the equation.

To write an equation of a line that passes through two points, we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

Given the points (-7, -3) and (-3, 5), we can find the slope by using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the values, we get m = (5 - (-3)) / (-3 - (-7)) = 8 / 4 = 2.

Now that we have the slope, we can choose either point and substitute the values into the equation. Let's use the first point (-7, -3): -3 = 2(-7) + b. Solving for b, we get b = -3 - 2(-7) = -3 + 14 = 11.

Therefore, the equation of the line that passes through the points (-7, -3) and (-3, 5) is y = 2x + 11.

Answer:

11/12

Step-by-step explanation:

Simple addition.

1/4 + 2/3

=

3/12 + 8/12 =

11/12

Answer:

11/12

Step-by-step explanation:

All you have to do is simply add 1/4 and 2/3 leaving you with

3/12 + 8/12  then add them to get the answer 11/12

Hopefully this helps.

Btw Can i get my heart?

We know that the volume of a prism is defined by:

[tex]V=lwh \\ \\ \\ Where: \\ \\ l:length \\ \\ w:width \\ \\ h:height \\ \\ \\ l=\frac{d-2}{3d-9} \\ \\ w=\frac{4}{d-4} \\ \\ h=\frac{2d-6}{2d-4}[/tex]

Substituting values:

[tex]V=\left(\frac{d-2}{3d-9}\right)\left(\frac{4}{d-4}\right)\left(\frac{2d-6}{2d-4}\right) \\ \\ \\ Simplifying: \\ \\ V=\frac{d-2}{3d-9}\cdot \frac{4}{d-4}\cdot \frac{d-3}{d-2} \\ \\ V=\frac{\left(d-2\right)\cdot \:4\left(d-3\right)}{\left(3d-9\right)\left(d-4\right)\left(d-2\right)} \\ \\ V=\frac{4\left(d-3\right)}{\left(3d-9\right)\left(d-4\right)} \\ \\ V=\frac{4\left(d-3\right)}{3\left(d-3\right)\left(d-4\right)}[/tex]

[tex]Finally: \\ \\ \boxed{V=\frac{4}{3\left(d-4\right)}}[/tex]

The volume of the given prism in simplified form is [tex]V = \frac{4}{3(d - 4)}[/tex].

To find the volume of the prism, we use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

Given the dimensions of the prism:

l = \frac{d - 2}{3d - 9}

[tex]l = \frac{d - 2}{3d - 9}\\\\w = \frac{4}{d - 4}\\\\h = \frac{2d - 6}{2d - 4}[/tex]

We substitute these into the formula:

[tex]V = \left(\frac{d - 2}{3d - 9}\right) \left(\frac{4}{d - 4}\right) \left(\frac{2d - 6}{2d - 4}\right)[/tex]

Now we simplify this expression step-by-step:

Simplify the height term:

[tex]\frac{2d - 6}{2d - 4} = \frac{2(d - 3)}{2(d - 2)} = \frac{d - 3}{d - 2}[/tex]

Substitute the simplified height term:

[tex]V = \left(\frac{d - 2}{3(d - 3)}\right) \left(\frac{4}{d - 4}\right) \left(\frac{d - 3}{d - 2}\right)[/tex]

Combine and cancel common terms:

[tex]V = \frac{4}{3(d - 4)}[/tex]

This gives us the volume of the prism in its simplest form.

Complete question:

Using V = lwh, what is an expression for the volume of the following prism? The dimensions of a prism are shown.

The height is (2 d - 6) / (2 d - 4).

The width is 4 / (d - 4 ).

The length is StartFraction (d - 2) / (3 d - 9 ).

Answer:

6x-3=3x+12

    +3 .    +3

6x=3x+15

-3x=-3x  

3x=15

X=5

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

6x - 3 = 3x + 12

Combine like terms

6x - 3x = 3 + 12

3x = 15

Divide both sides by 3

3x/3 = 15/3

x = 5

Answer:

9 years

Step-by-step explanation:

Its right

Using the exponential growth formula, it will take approximately 8 years for a population of 20,000 growing at 2.5% per year to reach 24,700.

To determine how long it will take for a town with a population of 20,000 to grow to 24,700 with an annual growth rate of 2.5%, we can use the formula for exponential growth: P = P0ert, where P is the future population, P0 is the initial population, r is the growth rate, and t is time in years.

First, we convert the growth rate to a decimal, so 2.5% becomes 0.025. Our equation will look like this: 24,700 = 20,000e(0.025t). Taking the natural logarithm of both sides gives us ln(24,700/20,000) = 0.025t.

We can use a calculator to find that ln(24,700/20,000) ≈ 0.2112, and so 0.2112 = 0.025t. Dividing both sides by 0.025 gives us t ≈ 8.448. We round this to the nearest whole number to find that it will take approximately 8 years for the population to reach 24,700.

Answer:

Rs. 4,444

Step-by-step explanation:

Let her pocket money be represented as A

She spent 25% of A on her clothes and 11% on shoes and then saved Rs. 1600

Total percentage spent = 25 + 11 = 36%

So, she spent 36% of A and was left with Rs. 1600

This can be represented by the equation below

36% of A = 1600

36/100 x A = 1600

0.36 x A = 1600

Divide both sides by 0.36

0.36/0.36 A = 1600/0.36

A = 4444.44

A = Rs. 4,444

Her pocket money was approximately Rs. 4,444

Suvita's total pocket money is calculated by representing her total pocket money as variable x, relating it to the known percentages and the saved amount, and solving for x, which is found to be Rs. 2500.

Suvita spent a certain percentage of her pocket money on clothes and shoes, and saved a specific amount. Given that she spent 25% on clothes, 11% on shoes, and saved Rs. 1600, we want to find her total pocket money. To do this, we can represent the total pocket money as x. The amount spent on clothes is 0.25x, and on shoes is 0.11x. The saved amount is known, which is Rs. 1600.

We know that the total pocket money is the sum of money spent on clothes, shoes, and savings. Therefore, x = 0.25x + 0.11x + 1600. Simplifying, we combine like terms to find the total percentage spent: 0.25 + 0.11 = 0.36. So, x = 0.36x + 1600. Subtract 0.36x from both sides to get 0.64x = 1600. To find x, we divide both sides by 0.64, which gives us x = 1600 / 0.64.

After calculating the division, we discover that Suvita's total pocket money is Rs. 2500. Therefore, she had Rs. 2500, out of which she spent 25% on clothes, 11% on shoes, and saved Rs. 1600.

Answer:

Step-by-step explanation:they are even

More friends like berry than vanilla now because 3 friends chose berry and there is no mention of any friends choosing vanilla.

To determine whether more friends like berry or vanilla now, let's break down the information provided. Hara asked 5 friends, out of whom 3 chose berry and 2 chose lime. The key here is to note that there is no mention of any friends choosing vanilla. Therefore, based on the new information:

Since 3 friends chose berry, and no friends chose vanilla, more friends like berry than vanilla now. This comparison clearly shows that berry is the favorite among the provided options.

Answer

a)

[tex]{(2b - 5)}^{2} - 36 =( 2b - 11)(2b + 1)[/tex]

b)

[tex]9 - {(7 + 3a)}^{2} = (3a - 4)(3a + 11)[/tex]

c)

[tex]( {4 - 11m)}^{2} - 1 =( 3 - 11m )( 5 - 11m )[/tex]

Explanation

a) The given expresion is

[tex] {(2b - 5)}^{2} - 36[/tex]

We rewrite as difference of two squares

[tex]{(2b - 5)}^{2} - 36 = {(2b - 5)}^{2} - {6}^{2} [/tex]

Recall that:

[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]

This implies that:

[tex]{(2b - 5)}^{2} - 36 =( {(2b - 5)} -6)(2b - 5 )+ 6)[/tex]

Or

[tex]{(2b - 5)}^{2} - 36 =( 2b - 5-6)(2b - 5 + 6)[/tex]

This simplifies to give:

[tex]{(2b - 5)}^{2} - 36 =( 2b - 11)(2b + 1)[/tex]

b) The second expression is

[tex]9 - {(7 + 3a)}^{2} [/tex]

We rewrite as perfect squares yo get:

[tex]9 - {(7 + 3a)}^{2} = {3}^{2} - {(7 + 3a)}^{2} [/tex]

This gives:

[tex]9 - {(7 + 3a)}^{2} = ({3} - {(7 + 3a)})({3} + {(7 + 3a)})[/tex]

This implies that

[tex]9 - {(7 + 3a)}^{2} = ({3} - 7 + 3a)({3} + 7 + 3a)[/tex]

We simplify to get:

[tex]9 - {(7 + 3a)}^{2} = (3a - 4)(3a + 11)[/tex]

c) The third expression is:

[tex]( {4 - 11m)}^{2} - 1[/tex]

We obtain the difference of two squares as:

[tex]( {4 - 11m)}^{2} - 1 =( ( {4 - 11m)} - 1 )( ( {4 - 11m)} + 1 )[/tex]

We simplify within the parenthesis to get:

[tex]( {4 - 11m)}^{2} - 1 =( 4 - 11m - 1 )( 4 - 11m+ 1 )[/tex]

We simplify further to get;

[tex]( {4 - 11m)}^{2} - 1 =( 3 - 11m )( 5 - 11m )[/tex]

Answer:

The ordered pairs (-1, -4) an (-1, 2) have the same first coordinate i.e. -1 is occurring twice. Therefore, the given relation is not a function.

Step-by-step explanation:

Considering the relation

{(3, −2), (1, 2), (−1, −4), (−1, 2)}

No! the following relation is not a function.

Here is the reason:

Check the table

x                  y                occurrence of x

3                 -2                          1                        

1                   2                          1

-1                 -4                          1

-1                  2                          2

From the above table, it is clear that the value of input x is occurring more than once (twice here), so the set of ordered pairs is not a function.

Because a set of ordered pairs will be a function only if the ordered pairs do not have the same first coordinate with different second coordinates.

But the ordered pairs (-1, -4) an (-1, 2) have the same first coordinate i.e. -1 is occurring twice. Therefore, the given relation is not a function.                          

Answer:

no i have this on flvs who else does

Step-by-step explanation:

The solution to the system of equations y = -4x and y = 2x + 12 is found by setting the two equations equal to each other, solving for x, and then finding y. The ordered pair solution is (-2, 8).

To find the ordered pair solution to the system of equations y = -4x and y = 2x + 12, we need to set the two equations equal to each other since they both describe y in terms of x. This gives us:

-4x = 2x + 12

Now, we will solve for x by combining like terms:

-4x - 2x = 12

-6x = 12

To get x by itself, divide both sides by -6:

x = -2

Next, we substitute x = -2 back into one of the original equations to find y. For example:

y = 2(-2) + 12

y = -4 + 12

y = 8

Therefore, the solution to the system of equations is the ordered pair (-2, 8).

Answer:

To distribute 4 ones into 5 groups, you have a few options. Here are three possible ways to distribute the 4 ones evenly among the 5 groups:

Option 1:

- Give each group 1 one: 1 1 1 1 0

Option 2:

- Give three groups 1 one, and leave two groups with 0 ones: 1 1 1 0 0

Option 3:

- Give one group 2 ones, and the other four groups 1 one each: 2 1 1 1 1

These are just a few examples, and there may be other ways to distribute the 4 ones into 5 groups. The important thing is to ensure that each group receives the same number of ones, if possible, or as close to equal as possible.

Answer: 3

Step-by-step explanation: Plug in x = -7

Answer:C

Step-by-step explanation:

The best deal can be calculated by dividing the cost of the nail by the total amount of nails present in the pack.

A = $6.50/75 = $0.076

B = $15.50/200 = $0.0775

C = $36.00/500 = $0.072

D = $72.00/1000 = $0.078

From the above, the best deal is C (500 nails for $36.00) and the worst deal is D (1000 nails for $72.00).

Answer:

It´s A not C

Step-by-step explanation:

Answer:

B.     Ray

Step-by-step explanation:

When they ask what does AB represent because they put the A first this means that the line is going from A to B and because there is an arrow and the end of B this means its a ray.

A ray is a half-infinite line. AB represents a ray.

A ray is a half-infinite line (sometimes called a half-line) in which one of the two points A and B is assumed to be at infinity.

As we can see that AB has a point on one side while the other side of the line has an arrow, therefore, AB represents a ray.

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Answer:

Rs 927.

Step-by-step explanation:

For simple interest we have:

I = PRT/100    where I = interest, P = amount invested, R = the rate and T = the time.

900 = P*6* 2 / 100

P = 900*100/ 12

P = Rs 7500

The formula for the amount  after t years when investing P amount at a rate of r%  is:

A = P(1 + r/100)^t  

A = 7500(1 + 6/100)^2

= Rs 8427.

So the compound interest is 8427 - 7500

= Rs 927.

Answer:

192 gymnasts

Step-by-step explanation:

16*12=192

Answer:

12 x 16 = 192 gymnasts

Answer:

3 = x, 2 = y

Step-by-step explanation:

Opposite sides in a parallelogram are always congruent, so 2y+3=y+5 and 4y+1=4x-3

The first equation, when solved, shows that y = 2

When you plug that into the second equation, you get 4(2) + 1 = 4x - 3

This means that 12 = 4x, so 3 = x

Answer: x = 3

Step-by-step explanation:

-5 -x = -8

-× = -8 + 5

-x = -3

x = 3

Answer:

Step-by-step explanation:

6:10 ratio

6x8=48 10x8=80

About 151. That seems pretty close. If it is incorrect, sorry.

Answer:

424 yards²

Step-by-step explanation:

Diameter 22, radius 11

Outer circle: radius = 11+5 = 16

Area of the path:

Pi× (16²-11²)

= 135pi yards²

Or, 424 yards² (3 sf)

Answer:

135pi

Step-by-step explanation:

(I'm guessing you want to know the ring's area)

Diameter = 22 yards, meaning Radius = 11 yards

[tex](11+5)^{2}\pi[/tex] = 256pi = Outer Ring + Pool

[tex](11)^{2}\pi[/tex] = 121pi = Pool

Outer Ring = 256pi - 121pi = 135pi

Answer:

12 ounces

Step-by-step explanation:

3

Final answer:

To find out how many ounces Juanita has from 3 1/4 pounds of sugar, we convert the 1/4 pound into ounces and add it to the full pounds after converting them into ounces. The calculation shows that she has 52 ounces of sugar in total.

Explanation:

To answer how many ounces of sugar Juanita has from 3 1/4 pounds, we must first understand the relationship between pounds and ounces. There are 16 ounces in 1 pound. Since Juanita has 3 1/4 pounds, we will first convert the 1/4 pound to ounces and then add that to 3 times 16 ounces.

Here's the calculation step by step:

Convert 1/4 pound to ounces: 1/4 pound = 0.25 × 16 ounces = 4 ounces.

Multiply the whole number of pounds (3) by 16 to get ounces: 3 × 16 = 48 ounces.

Add the ounces from the fractional pound to the ounces from the whole pounds: 48 ounces + 4 ounces = 52 ounces.

Hence, Juanita has 52 ounces of sugar.

The required value of a + b = -14.

The quadratic equation is defined as a function containing the highest power of a variable is two.

The standard quadratic function is given by as f(x) = ax² + b x + c.

The roots of the quadratic equation z² + az + b = 0 are -7 + 2i and -7 - 2i,

As we know that the sum of roots is -b/a for the standard quadratic function.

So the sum of these roots, -7 + 2i + (-7 - 2i) = -14, is equal to -a/2.

Hence, a = -28, and the sum of the coefficients, a + b = -28 + b = -14.

So, a + b = -14.

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Final answer:

The sum of the coefficients a and b from the quadratic equation with roots -7 + 2i and -7 - 2i is 67.

Explanation:

The roots of the quadratic equation z2 + az + b = 0 given are -7 + 2i and -7 - 2i. These roots are complex conjugates of each other. According to the properties of quadratics, the sum of the roots (given by -a) is equal to -7 + 2i + (-7 - 2i), which simplifies to -14. Therefore, the coefficient a is 14. To find b, we use the fact that the product of the roots is b. Thus, b equals (-7 + 2i) x (-7 - 2i), which expands to 49 + 4, giving us b = 53. The question asks us for the sum of a and b, which is 14 + 53 = 67.

6 hours

Hope this helped

Answer:

6 hours

Step-by-step explanation:

She can make 15 necklaces in 2 hours. Which means, in another 2 hours, she's going to make another 15 necklaces. So in 2+2 hours, she would be making 15+15 necklaces.

That is, in 4 hours, she would be making 30 necklaces.

And in another 2 hours, another 15 necklaces would be made.

In 4+2 hours, she would have made a total of 30+15 necklaces. Which means, in 6 hours, she would make 45 necklaces.

Another way to get this is:

If she makes 15 necklaces in 2 hours.

Then 45/15 gives 3.

Multiply the 3 to 2 gives 6 hours.

Answer:

3

Step-by-step explanation:

Answer:

n = 3

Step-by-step explanation:

-1(n2 + 3) if n = -3.

from the question

-1(n2 + 3)

we are then asked to find n if its equals to -3

solution

-1(n2 + 3) .................. we are going to open the bracket with-1 according to BODMAS rule

we have,

-n²-3

when the value of n = -3

we have,

= (-3)² - 3

= 9 - 3

= 3

therefore  when n = -3 in the expression -1(n2 + 3)  the value of n = 3

to check if your answer is correct you will put the value of n which is 3 into the -1(n2 + 3)  then you will see that the right handside = lefthandside

which is

3=3...........proved.

Answer:

48

Step-by-step explanation:

[tex] \frac{10}{25} [/tex]

athletes are female. Now, we need to find what

[tex] \frac{x}{120} [/tex]

athletes are female.

10 ÷ 25 = 0.4

0.4 × 100 = 40 so

[tex] \frac{10}{25} = 40\%[/tex]

40% is the experimental probability for the number of female athletes in the sample. 40% of 120 should be about the number of female athletes in the whole school.

120 × 0.4 (or 40%) = 48.

You can infer that 48 athletes in the school are female.

Answer:

Step-by-step explanation:48

Solution:

Given that,

Dan, Angad & David share some money in the ratio 1 : 1 : 3

Let the share of Dan be 1x

Let the share of Angad be 1x

Let the share of David be 3x

In total, Dan and David receive £52

Therefore,

1x + 3x = 52

4x = 52

x = 13

Therefore,

share of angad = 1x = 13

Thus share of Angad is £ 13