The sum of John and Sally’s ages is 24. John is 6 years older than Sally. Which system of equations below represents this relationship and what are their ages? ASAP

Answer:

49152

Step-by-step explanation:

To find the 15th term of the geometric sequence 3, -6, 12, ..., we identify the common ratio as -2 and use the formula for the nth term of a geometric sequence. By calculating 3 * (-2)^14, we find that the 15th term is 49152.

To find the 15th term of the geometric sequence 3, -6, 12, ... we first need to determine the common ratio. By dividing the second term by the first term, we find that the common ratio is -2.

Formula for the nth term of a geometric sequence:

an = a1 × r(n-1), where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.

Finding the 15th term:

Plugging in the values, we get: a15 = 3 × (-2)(15-1) = 3 × (-2)14. Since (-2)14 is positive (because any even power of a negative number is positive), the 15th term will be positive. Calculating the value, a15 = 3 × 16384 = 49152.

Therefore, the 15th term of the geometric sequence is 49152.

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Answer:

16 packages

Step-by-step explanation:

240 / 15 = 16 packs

Answer:

Exterior angles are the ones on the outside and same side means they sit on the same side of the bisector so your answer is 1 and 8

Step-by-step explanation:

∠1 and ∠8  are same side exterior angles

If a transversal line intersect 2 parallel lines, then same sides exterior angles

are supplementary.

This means same side exterior angles sum up to 180 degrees. Therefore,

∠1 and ∠8 are same side exterior angles.

This means ∠1 and ∠8  are supplementary angles . They sum up to 180 degrees.

∠1 + ∠8 = 180°

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Answer:

Explanation:

This question requires that you find the value of    [tex]a[/tex]    given that:

That is you have to solve the equation for a.

1. Rewrite the equation in form of fractions, convert the mixed number into an improper fraction, and convert the decimal number into fraction too.

[tex]2\frac{1}{7}:(15a)=(5/14)/(0.8)\\ \\ \frac{2+\frac{1}{7} }{15a} =\frac{5/14}{8/10}\\ \\\frac{(14+1)/7}{15a} =\frac{5\times 10}{8\times 14}\\ \\ \frac{15}{7\times 15a} =\frac{50}{112}[/tex]

2. Cross multiply to leave a alone:

[tex]a=15\times 112/(7\times 15\times 50)\\ \\a=1680/5250\\ \\a=0.32[/tex]

Answer:The numbers are already in standard form

Step-by-step explanation:

Answer:

m=29/14

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(9-(-20))/(9-(-5))

m=(9+20)/(9+5)

m=29/14

The required slope is [tex]\dfrac{29}{14}[/tex].

Given:

The two points are [tex](-5,-20)[/tex] and [tex](9,9)[/tex].

To find:

The slope of the line.

Explanation:

Slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Using the slope formula, we get

[tex]m=\dfrac{9-(-20)}{9-(-5)}[/tex]

[tex]m=\dfrac{9+20}{9+5}[/tex]

[tex]m=\dfrac{29}{14}[/tex]

Therefore, the slope of the line is [tex]\dfrac{29}{14}[/tex].

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To find the coordinates of point P along the directed line segment AB so that AP to PB is in the ratio 3 to 1, we use the section formula. Substituting the values into the formula, we find that the coordinates of point P are (-1, -2).

To find the coordinates of point P along the directed line segment AB so that AP to PB is in the ratio 3 to 1, we can use the concept of section formula.

The section formula states that if we have two points A(x1, y1) and B(x2, y2), and we want to find a point P along the line segment AB such that AP to PB is in the ratio m to n, then the coordinates of P can be found using the following formulas:

x = (mx2 + nx1) / (m + n)

y = (my2 + ny1) / (m + n)

In this case, A(-4, -8) and B(0, 0).

Let's substitute the values into the formula:

x = (3 * 0 + 1 * -4) / (3 + 1) = -4/4 = -1

y = (3 * 0 + 1 * -8) / (3 + 1) = -8/4 = -2

Therefore, the coordinates of point P are (-1, -2).

Final answer:

To find point P on line segment AB where AP:PB = 3:1, we use section formula to get P's coordinates as (-1,-2). This method applies interpolation of the endpoints' coordinates, A(-4,-8) and B(0,0), by their respective weights in the given ratio.

Explanation:

To find the coordinates of point P on the directed line segment AB such that the ratio of AP to PB is 3 to 1, we can use the section formula which combines the x and y coordinates of A and B weighted by the given ratio, since P divides AB internally in the ratio 3:1.

The coordinates of A are (-4, -8) and the coordinates of B are (0, 0). Using the section formula, we can find the coordinates of P as follows:

Let x and y be the coordinates of P.

The x-coordinate of P is given by ((3 * 0) + (1 * (-4))) / (3 + 1) = -1.

The y-coordinate of P is given by ((3 * 0) + (1 * (-8))) / (3 + 1) = -2.

Therefore, the coordinates of P are (-1, -2).

This process involves interpolation of the given points in the specific ratio to find the required coordinates.

the solution is y = 7

Step-by-step explanation:

Given equation is

[tex]8+5y=(8y-6)-7[/tex]

The equation has to be solved for y

So,

Opening brackets first

[tex]8+5y=8y-6-7\\8+5y=8y-13[/tex]

Subtracting 8 from both sides

[tex]8+5y-8=8y-13-8\\5y=8y-21[/tex]

subtracting 8y from both sides

[tex]5y-8y = 8y-21-8y\\-3y=-21y[/tex]

Dividing both sides by -3

[tex]\frac{-3y}{-3} = \frac{-21}{-3}\\y = 7[/tex]

so,

the solution is y = 7

Keywords: Linear equation, variables

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Answer:

4 over 3 or 4 : 3.

Step-by-step explanation:

See the diagram attached.

Now, The ratio of X's to O's is 12 : 9.

Now, we have to determine another ration for X's to O's.

The image will help us to do that.

There are 12 numbers of X and that can be broken into 3 sets of X with 4 X in each set. Hence, 12 = 3 × 4

Again, there are 9 numbers of O and that can be broken into 3 sets of O with 3 O in each set. Hence, 9 = 3 × 3

Therefore, the ratio of X's to O's is 12 : 9 ≡ (3 × 4) : (3 × 3) ≡ 4 : 3

{Cancelling 3 from each term} (Answer)

Answer:

The answer is 4 over 3.

Step-by-step explanation:

if you look at the image all you have to do is count the X's on the top, and that's the top of your fraction, then count the bottom number, that's the bottom of your fraction.

4 on the top three on the bottom so your fraction/ratio is 4 over 3!

hope this helped!!!

Answer:

The value of Mode is 2.43

Step-by-step explanation:

Answer:

The table B represent an inverse variation  

The constant of variation k is 30

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

Verify table A

For x=3, y=8 ----> [tex]k=y*x[/tex] ----> [tex]k=8*3=24[/tex]

For x=4, y=6 ----> [tex]k=y*x[/tex] ----> [tex]k=6*4=24[/tex]

For x=5, y=4.8 ----> [tex]k=y*x[/tex] ----> [tex]k=4.8*5=24[/tex]

For x=5.5, y=4 ----> [tex]k=y*x[/tex] ----> [tex]k=5.5*4=22[/tex]

The values of k are different

therefore

The table A not represent an inverse variation  

Verify table B

For x=0.1, y=300 ----> [tex]k=y*x[/tex] ----> [tex]k=300*0.1=30[/tex]

For x=0.5, y=60 ----> [tex]k=y*x[/tex] ----> [tex]k=60*0.5=30[/tex]

For x=75, y=0.4 ----> [tex]k=y*x[/tex] ----> [tex]k=75*0.4=30[/tex]

For x=100, y=0.3 ----> [tex]k=y*x[/tex] ----> [tex]k=100*0.30=30[/tex]

All the values of k are the same

therefore

The table B represent an inverse variation  

The equation is equal to

[tex]y*x=30[/tex]

Answer: Only (A)

If you go RSM this the Answer.

Answer:

12

Step-by-step explanation:

120 divide by 10

Answer:

12

Step-by-step explanation:

120/10

Multiply the number of gallons by the price per gallon:

12.25 gallons x 3.75 per gallon = $45.94 total.

The fraction 27/22, when converted into a decimal and rounded to the nearest tenth, is approximately 1.2.

To convert a fraction to a decimal, divide the numerator by the denominator. In this case, divide 27 by 22.

The question asks to convert the fraction 27/22 into a decimal, rounded to the nearest tenth. First off, we calculate the division of 27 by 22, which gives us approximately 1.227. However, we need to round this figure to the nearest tenth, which results in the value of 1.2. Be sure to understand that when we say 'rounded to the nearest tenth', we refer to the first digit after the decimal point.

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The equation [tex]A=5000(1.000958333)^{108}[/tex] will determine how much money Bevo will have in his account after 9 years

Step-by-step explanation:

The formula for compound interest, including principal sum is

[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where:

Bevo has $5000 to invest. Bank A offers a savings account that has an APR of 1.15% and compounds monthly

We need to find Which equation will determine how much money Bevo will have in his account after 9 years

Because there is no choices we will write the equation

∵ Bevo has $5000 to invest

∴ P = 5000

∵ Bank A offers a savings account that has an APR of 1.15%

   and compounds monthly

∴ r = 1.15% = 1.15 ÷ 100 = 0.0115

∴ n = 12 ⇒ compounds monthly

∵ t = 9

- Substitute all of theses values in the formula below

∵ [tex]A=P(1+\frac{r}{n})^{nt}[/tex]

∴ [tex]A=5000(1+\frac{0.0115}{12})^{(12)(9)}[/tex]

∴ [tex]A=5000(1.000958333)^{108}[/tex]

The equation [tex]A=5000(1.000958333)^{108}[/tex] will determine how much money Bevo will have in his account after 9 years

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The equation to find out how much Bevo will have in his account after 9 years by investing $5000 in a saving account at Bank A which offers an APR of 1.15% compounding monthly is given by the future value formula of compound interest: FV = P(1 + r/n)^(nt). By plugging the values into this formula, Bevo can determine his future balance.

The subject of this question is about understanding compound interest. Specifically, it is about interpreting how Bevo's financial investment would grow over a certain period at a specific rate of interest in a savings account. The equation to calculate the future value (FV) of Bevo's investment, compounded monthly, is given by the compound interest formula:

FV = P(1 + r/n)^(nt)

Where:

This gives a better understanding of how savings accounts and compounded interest work.

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Answer:

The number of roots for  equation [tex]5x^4 + 12x^3 – x^2 + 3x + 5 = 0[/tex] is 4 .

Step-by-step explanation:

Here, the given function polynomial is :

[tex]P(x) : 5x^4 + 12x^3 – x^2 + 3x + 5 = 0[/tex]

The Fundamental Theorem of Algebra says that a polynomial of degree n will have exactly n roots (counting multiplicity).

Now here, the degree if the polynomial is 4 (highest power of variable x).

So, according to the Fundamental Theorem, the given polynomial can have AT MOST 4 roots, counting Multiplicity.

Hence,  the number of roots for  equation [tex]5x^4 + 12x^3 – x^2 + 3x + 5 = 0[/tex] is 4 .

Answer:

[tex]cos(\theta)=\frac{\sqrt{21}}{5}[/tex]

Step-by-step explanation:

we have that

The angle [tex]\theta[/tex] belong the the First Quadrant (see the figure)

so

[tex]cos(\theta)\ and\ sin(\theta)[/tex] are positive values

we know that

[tex]sin^2(\theta)+cos^2(\theta)=1[/tex] ----> trigonometric identity

we have

[tex]sin(\theta)=\frac{2}{5}[/tex]

substitute in the identity

[tex](\frac{2}{5})^2+cos^2(\theta)=1[/tex]

[tex]cos^2(\theta)=1-\frac{4}{25}[/tex]

[tex]cos^2(\theta)=\frac{21}{25}[/tex]

square root both sides

[tex]cos(\theta)=\frac{\sqrt{21}}{5}[/tex]

Answer:

this answer is. _48 am I right

the factored form of the expression [tex]\(3x^2 + 7x - 6\) is \((3x - 2)(x + 3)\).[/tex]

To factor the expression [tex]\(3x^2 + 7x - 6\),[/tex] we need to find two numbers that multiply to give [tex]\(3 \times (-6) = -18\)[/tex] and add to give the middle coefficient, (7)

The two numbers that meet these criteria are [tex]\(9\) and \(-2\).[/tex]

Now, we can rewrite the middle term \(7x\) as the sum of these two terms:

[tex]\[3x^2 + 9x - 2x - 6\][/tex]

Next, we group the terms and factor by grouping:

[tex]\[3x(x + 3) - 2(x + 3)\][/tex]

Now, we can factor out the common factor [tex]\(x + 3\):[/tex]

[tex]\[(3x - 2)(x + 3)\][/tex]

So, the factored form of the expression [tex]\(3x^2 + 7x - 6\) is \((3x - 2)(x + 3)\).[/tex]

Answer:

-71-10n

Step-by-step explanation:

-4(11+4n)-3(-2n+9)

-44-16n+6n-27

-44-27-10n

-71-10n

Answer:

5/6

Step-by-step explanation:

5 is the amount of cheese pizzas Mrs. Jones ordered out of the 6 pizzas in total. 5 is a prime number, so the fraction cannot be simplified.

good evening ,

Answer:

let D represent the line

D : y = (-1/2)x + 4.5

Step-by-step explanation:

The equation for the line D is y=mx+p

now let’s find m and p

m is the slope then m= (-1/2)

A(5,2)∈D ⇌ 2=(-1/2)×5+p ⇌ p=9/2=4.5.

that’s it.

Look at the photo below for more info.

:)

It's [tex]g(x)=f(-x)=f(x)[/tex].

Reflection over y-axis is the same as original function.

Hope this helps.

Answer:

$ 12.09

Step-by-step explanation:

formula Y = KX

Where; y = $ 24.18

            x = 2 books

            k = constant of proportionality

Step 1. Do the equation based on the formula

Y = kx

$24.18 = k2

Step 2.  Divide by 2

$24.18/2 = k2/2

k = $12.09 (answer)

Answer:

2.25 cups of flour

1 teaspoon of baking soda

1 teaspoon of salt

1 cup of butter

0.75 cups of granulated sugar

1 teaspoon of vanilla extract

2 large eggs

2 cups of Semi-Sweet Chocolate Morsels

Step-by-step explanation:

The ingredients should be 4 times less than the original ones because 240:4=60

The simplified expression of 3z + (3/4) - 2z is z + (3/4).

The expression 3z + (3/4) - 2z can be simplified by combining like terms. Like terms have the same variable and exponent. In this case, the like terms are the 3z and the -2z. When you combine them, you get z. So the simplified expression is z + (3/4).

Answer:

8

Step-by-step explanation:

Im guessing that the x means multiplication

so PEMDAS

so 2 times 1 is 2 so basically it is now

2+2+2+2= 8

Answer:

Your answer is 8 :)

Step-by-step explanation:

2+2 is 4

4+2 is 6

6+2 is 8

Then 8 times 1 is 8, because anything times 1 is that number!

Hope it helps!!

Answer:

Step-by-step explanation:

The last one

The equation 7 - x = 3 is best modeled by the situation where the original price of a book at $7 is lowered by an amount of $4 to reach the final price of $3.

The given equation 7 - x = 3 can be used to model a situation where the price of a book, originally $7, is reduced by some amount to $3. After solving the equation by subtracting 7 from both sides and then multiplying by -1, we get x = 4. This means the amount reduced from the original price is $4, which is consistent with a price reduction scenario: the book's original price was $7, and it was reduced by $4, bringing the final price to $3.

Answer:

the first answer posted is wrong

Step-by-step explanation:i put it in my exam and it was wrong  and  i think the right answermight be

AKLM = AONM because m23 =mZ6 and mZ1=m24

Answer:

c, d

Step-by-step explanation:

If f(x) = x, then f(x) - 5 = x - 5.

The two functions in slope-intercept form (y = mx+ b) are:

[1] y = x     and     [2] y = x - 5

In equation [1], the slope is 1 and the y-intercept is 0.

In equation [2], the slope is 1 and the y-intercept is -5.

a. The y-intercepts are not the same. 0 ≠ -5

b. The rates of change, or the slopes, are the same, neither are greater than the other. 1 = 1

c. They are parallel lines. Lines are parallel when they have the same slope.        1 = 1.

d. The (-5) indicates that the new function is translated down (-) by 5 units (5) from the parent function f(x) = x.

c and d are correct.

Answer:

3 km per minute

Step-by-step explanation:

12/4=3 laps

3 km per minute