Solve the equation
−3(x + 8) − x = 2(2x − 7)

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:

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

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:

2 3/6 feet of cookie dough

Step-by-step explanation:

Final answer:

To make 15 cookies, 2.5 feet of cookie dough is needed.

Explanation:

To find how many feet of cookie dough is needed to make 15 cookies, we can set up a proportion using the given information. The ratio 1/6 represents the amount of cookie dough needed to make 1 cookie. We can set up the proportion:

1/6 = x/15

To solve for x, we can cross multiply:

15 * 1 = 6 * x

Simplifying the equation gives:

15 = 6x

To isolate x, we can divide both sides of the equation by 6:

x = 15/6 = 2.5 feet of cookie dough

Therefore, 2.5 feet of cookie dough is needed to make 15 cookies.

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.

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:

d

Step-by-step explanation:

bjkbj

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:

GCF is [tex]9x^2y[/tex]

Step-by-step explanation:

When the GCF or the greatest common factor of the expression is required to be found, then take the common terms, and write the expression in the factor form first.

Now, here we have to find the factor of the expression:

[tex]6x^4y^3\cdot 21x^2y^2-9x^2y\\[/tex]

which can be re-written as:

[tex]6x^4y^3\cdot 21x^2y^2-9x^2y\\=126x^6y^5-9x^2y[/tex]

Now, this is further written as:

[tex]126x^6y^5-9x^2y\\=14\cdot \:9x^2x^4yy^4-9x^2y\\[/tex]

Here taking the term [tex]9x^2y[/tex] common, we will get:

[tex]14\cdot \:9x^2x^4yy^4-9x^2y\\=9x^2y\left(14x^4y^4-1\right)\\[/tex]

So we have the expression:

[tex]6x^4y^3\cdot 21x^2y^2-9x^2y= 9x^2y\left(14x^4y^4-1\right)\\[/tex]

So the GCF or the greatest common factor is  

[tex]9x^2y[/tex]

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.

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.

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.

Answer: -8 -7 -6 -5

Step-by-step explanation:

The four consecutive integers just greater than -9 are -8 -7 -6 -5

Answer:

-8, -7, -6, -5

Step-by-step explanation:

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?

Answer: 16 Rows

Step-by-step explanation: 48*10= 480, meaning there is 480 people that will be attending. If each row has 30 chairs you divide 480/30 which equals 16. If you multiply 16 times 30 you will get 480 (to check your answer)

Answer:

16 rows

Step-by-step explanation:

There are 48 members in the choir .

Each member expects to have 10 people in the audience.

That’s

48 x 10 = 480 people

There will be 480 people in the audience.

If each row has 30 chairs in it

Number of rows to accommodate 480 people will be 480 divided by the number of seats in one row

That’s

= 480/30

= 16 rows

16 rows of chair will need to be set up

The coordinates of U, the endpoint of the segment, can be found by using the midpoint formula. The x-coordinate of U is (-7 + 5) / 2 = -1, and the y-coordinate is (2 + (-8)) / 2 = -3. Thus, the coordinates of U are (-1, -3).

The coordinates of the midpoint O are given as (5, -8). To find the coordinates of the endpoint U, we can use the midpoint formula. The x-coordinate of the midpoint can be found by taking the average of the x-coordinates of the endpoints, and the y-coordinate can be found by taking the average of the y-coordinates. So, the x-coordinate of U is (-7 + 5) / 2 = -1, and the y-coordinate is (2 + (-8)) / 2 = -3. Therefore, the coordinates of U are (-1, -3).

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Answer:

Step-by-step explanation:

6:10 ratio

6x8=48 10x8=80

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:-22

Step-by-step explanation:

5 times -3 equals -15, and the combine it with -7 to get -22

Answer:

y = -22

Step-by-step explanation:

y=5x-7

Let x=-3 and substitute it into the equation

y = 5(-3) -7

Multiply

y = -15-7

y = -22

Answer:

Step-by-step explanation:

"The equation of the cross-sectional parabola of the dome is [tex]\( y = -\frac{1}{800}x^2 + 50 \).[/tex]

To find the equation of the cross-sectional parabola of the dome, we can use the standard form of a parabola, which is[tex]\( y = ax^2 + bx + c \).[/tex]Since the parabola is symmetric and the vertex is at the origin (0,50), the equation simplifies to [tex]\( y = ax^2 + c \),[/tex]where determines the width of the parabola and \is the maximum height of the dome.

Given that the maximum height of the dome is 50 feet, we have[tex]\( c = 50 \)[/tex]. The diameter of the dome is 2002 feet, so the radius is half of that, which is 1001 feet. The radius corresponds to the x-coordinate at the base of the dome where the height \ is 0.

Using the point (1001, 0) and the vertex (0, 50), we can set up the equation [tex]\( 0 = a(1001)^2 + 50 \).[/tex] Solving for [tex]\( a \)[/tex]gives us:

[tex]\[ 0 = a(1001)^2 + 50 \] \[ -50 = a(1001)^2 \] \[ a = -\frac{50}{(1001)^2} \] \[ a = -\frac{50}{1002001} \] \[ a \approx -\frac{1}{20040} \][/tex]

For simplicity, we can round [tex]\( a \) to \( -\frac{1}{2000} \)[/tex]or even more simply to [tex]\( -\frac{1}{800} \)[/tex] to make the calculations easier without significantly changing the shape of the parabola for practical purposes.

Thus, the equation of the cross-sectional parabola of the dome is:

[tex]\[ y = -\frac{1}{800}x^2 + 50 \]"[/tex]

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.

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

Answer:

192 gymnasts

Step-by-step explanation:

16*12=192

Answer:

12 x 16 = 192 gymnasts

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

Answer: 60 feet

Step-by-step explanation:

50+10=60

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:

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:

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.