Christopher is the oldest of three siblings whose ages are consecutive odd integers. If the sum of their ages is 6363, find Christopher's age.

Answer:

number is - 4

Step-by-step explanation:

let the number be n then 4 times the sum of the number and 2 is 4(n + 2)

4(n + 2) = 2n

4n + 8 = 2n ( subtract 2n from both sides )

2n + 8 = 0 ( subtract 8 from both sides )

2n = - 8 ( divide both sides by 2 )

n = - 4

the number is - 4

[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]

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

[tex]\textsf{Let the number be t.}[/tex]

[tex]\textsf{The Sum means adding two numbers together.}[/tex]

[tex]\textsf{Then,}[/tex]

[tex]\textsf{4 times the sum of a number and 2 = 4 times t+2 = 4(t+2).}[/tex]

[tex]\textsf{Remember to write the parentheses when you're multiplying something times}\\\textsf{a sum or a difference.}[/tex]

[tex]\textsf{You know how to write "is equal to", don't you? It's =}[/tex]

[tex]\therefore\\\textsf{4(t+2)=}[/tex]

[tex]\textsf{Next, twice the number is written as 2t.}[/tex]

[tex]\textsf{\textbf{Our expression looks like this:}}[/tex]

[tex]\Large\boldsymbol{\rm{4(t+2)=2t}}[/tex]

[tex]\textsf{Now let's find the number: }[/tex]

[tex]\Large\begin{gathered} \sf{4(t+2)=2t}\\\sf{4t+8=2t}\\\sf{4t-2t=-8}\\\sf{2t=-8}\\\sf{t=-4} \end{gathered}[/tex]

[tex]\ddot\smile[/tex]

[tex]\Large\overbrace{\underbrace{\boldsymbol{\rm{Reflection - RoSe}}}}^\star_\star[/tex]

The graph at:

x=-6,-4→intersects directly

x=0→passes through

x=1→tangent

At different x-intercepts, graphs exhibit varying behaviours. On occasions, the graph will intercept the x-axis and cross it. On occasions, the graph will contact the x-axis and then deviate from it. The graphs contact or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities. Higher even powers, such as 4, 6, and 8, will still cause the graph to contact and deviate from the x-axis, but as even power increases, the graph will appear flatter as it does so.The graph will still cross through the x-axis for higher odd powers like 5, 7, and 9, but for each rising odd power, the graph as it approaches and departs the x-axis, it seems flatter.

∴x=-6,-4→intersects directly

x=0→passes through

x=1→tangent

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The value of x using the change of base formula of logarithm is 25.

What are the various properties of the logarithm?

Out of several properties of logarithms, some of the main properties are given below:

Product Rule

log (ab) = log a + log b

Change of base

log ₇ x = log x / log 7

Power Rule

log a² = 2 log a

Quotient Rule

log (a / b) = log a - log b

Solving the given equation by using the change of base formula

We are given a logarithmic expression: log ₉ x = log ₃ 5

Using properties of the logarithm, we have

log x / log 9 = log 5 / log 3

log x = (log 5 × log 9) / log 3

= (log 5 × 2 log 3) / log 3

= 2 × log 5

= log 5²

log x = log 5²

Applying exponent both sides, we get,

x = 25

Hence, the value of x is 25.

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Answer: 2 laps four minutes

explanation:

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Remember that we're using absolute values. A negative number plus a positive number is the same as a positive number subtracted by another positive number.

Answer:

Find out the number of video games that Jasmine can buy with her savings .

To proof

Let us assume that the number of video games Jasmine can buy  be x .

As given

Jasmine wants to use her savings of $1128 to buy video games and music CDs.

The total price of the music CDs she bought was $72. The video games cost $43 each.

Than the equation becomes

72 + 43× x = 1128

simplify

72 + 43x = 1128

43x = 1128 - 72

43x = 1056

x = 24.6 (approx)

Take

x = 24

Therefore the maximum number of video games that Jasmine can buy with her savings be 24 .

Step-by-step explanation:

The maximum number of video games that Jasmine can buy with her savings is... 24 ✅

Allow me to explain...

First, subtract $72 from $1,128

1,128 - 72 = 1,056

       ⬆️         ⬆️

Then, divide $1,056 by $43

1,056 ÷ 43 = 24.5581...

        ⬆️            ⬆️

Coming to the conclusion that Jasmine only has enough money for a maximum of 24 video games. ✅

I hope this was helpful! (✿◠‿◠)

Answer: 3c^2  +4 -5c

Step-by-step explanation:

-2c^2 -c +1 -(-5c^2 -3 +4c)

3c^2  +4 -5c

Firstly we will convert the percent R into a decimal value r. For that, we will divide with a hundred,

r = R/100

r = 6/100

r = 0.06 rate per year,

Then solve the equation for A

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

A = 500.00(1 + 0.06/12) ^ (12 x 10)

A = 500.00(1 + 0.005)^ 120

A = $909.70

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $500.00 at a rate of 6% per year compounded 12 times per year over ten years, is $909.70.

I = A - P = $2,000.00

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 4%/100 = 0.04 per year.

Solving our equation:

A = 5000(1 + (0.04 × 10)) = 7000

A = $7,000.00

The total amount accrued, principal plus interest, from simple interest on a principal of $5,000.00 at a rate of 4% per year for ten years is $7,000.00.

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The equation of the parabola in vertex form is y = - (1 / 4) · x².

In this problem we find a parabola whose axis of symmetry is on the y-axis and the directrix is above the parabola, which means that the least distance between the vertex and the directrix is negative. The equation of the parabola in vertex form is described below:

4 · p · (y - k) = (x - h)²

Where:

If we know that p = - 1 and (h, k) = (0, 0), then the equation of this parabola is:

4 · (- 1) · y = x²

- 4 · y = x²

y = - (1 / 4) · x²

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The extraneous solution is √2 and -√2

Extraneous solutions refer to the ones which when found the roots appear to be right, but are not exactly valid roots.

We have to check, whether the given solution is an extraneous one or not. We have to solve this equation,

√x+1 + √2 x = √5 x+3

or, √x + √2 x - √5 x = 3 - 1

or, - √2 x = 2Now, we have to square both sides,

∴ 2x² = 4

or, x² = 4/2

or, x² = 2

or, x = + √2 and - √2

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The inequality for the load in truck is 300r + 425p ≤ 6300.

11 refrigerators and 8 pianos will overload the truck.

Given,

The carrying capacity of truck = 6300 lbs

The truck is used to transport refrigerators and pianos.

The weight of 1 refrigerator = 300 lb

The weight of 1 piano = 425 lb

We have to find an inequality which shows the number of refrigerators and pianos could the truck carry.

Let's take the number of refrigerators as r and number of pianos as p.

We can equate by using their weights:

That is,

300r + 425p ≤ 6300

Next, we need to determine that, will 11 refrigerators and 8 pianos overload the truck:

We have to multiply the given number with their weights:

That is,

(300 × 11) + (425 × 8) = 3300 + 3400 = 6700

6700 is greater than 6300.

So, we can conclude that 11 refrigerators and 8 pianos will overload the truck.

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Answer:

A) [tex]y = \frac74x[/tex]

Step-by-step explanation:

Since the equation's graph passes through the origin, its [tex]c[/tex] value is equal to 0, and, therefore, you will only need to find the slope as the equation is of the template [tex]y = mx[/tex] where [tex]m[/tex] is the slope.

To find the slope, you can substitute the coordinates of the given points into the formula for a line's slope: [tex]y = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]y = \frac{7 - 0}{4 - 0} \to \frac74[/tex]

Therefore, the line's equation is [tex]y = \frac74x[/tex]

Answer:

It got colder by 9 degrees

Step-by-step explanation:

Answer:

the answer is 90⁰ ok that

Answer: 4r + 4s - 16s

Step-by-step explanation:

r +3r = 4r

-10s -6s =16s

2t + 2t =4t

key when you see the word perimeter than think of addition

Answer:

NOT GREATER!!!

Step-by-step explanation:

0.6667 is NOT greater than 0.6667 which also means that 2/3 is NOT greater than 4/6.

Answer:

the harvester costs 1200 a day.

54 hectares / 12 per day = 4.5 days.

Step-by-step explanation:

if she can rent the harvester for half a day, it will cost her 4.5 * 1200 = 5400.

if she can only rent the harvest for full days, it will cost her 5 * 1200 = 6000.

Answer:

100 and 10

Step-by-step explanation:

Answer:

[tex] \sf{x=−12}[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

90+x+67+35=180

Step 1: Simplify both sides of the equation.

90+x+67+35=180

(x)+(90+67+35)=180(Combine Like Terms)

x+192=180

x+192=180

Step 2: Subtract 192 from both sides.

x+192−192=180−192

x=−12

Step-by-step explanation:

You could use a calculator to make it simple

(0.067 × 42.1) ÷ (17.4 - 4.19). to 1s.f

=(2.8207) ÷ (13.21)

= 0.213527 to 1s.f

= 0.2

*you could also check using your own calculator

*let me know if you want me to expand it if you don't have a calculator

Answer: 40 hours

Step-by-step explanation:

As stated in the question the total amount spent in the month of august is $35.

First of all you have to subtract 15 out of the entire amount spent so that you can start calculating how many hours did Julie use the pool.

(35-15) = 20 (divide the answer with 0.50)

(20/0.50) = 40 (We have to divide to get the amount of hours she spent in pool)

Answer:

[tex] \sf \large \: x = -1[/tex]

Step-by-step explanation:

4x + 7 = 3

Substract 7 from both sides

4x + 7 - 7 = 3 - 7

4x = -4

Divide both sides by the coefficient of x

4x/4 = -4/4

calculate

x = -1

Answer:

x=6.28 0r 0.72

Step-by-step explanation:

The explanation is in the image

Answer:

[tex]\sf \bf h^{21}[/tex]

Step-by-step explanation:

  We have to multiply the powers.

[tex]\sf \boxed{\bf (a^m)^n=a^{m*n}}[/tex]

       [tex]\sf (h^3)^7=h^{3*7}[/tex]

                [tex]\sf = h^{21}[/tex]

The absolute value will always be a positive number while solving an equation that does not involve an absolute value could be any number.

The absolute value of a number n, written |n|, can be described

geometrically as the distance of n from 0 on the number line.

For instance, |42| = 42 and |–42| = 42. Both 42 and –42 are 42 units

from zero.

Algebraically, the absolute value of a number can be defined

piecewise as follows.

|x| = {

 x, for x ≥ 0

–x, for x < 0

Examine the definition carefully. Because –x is the opposite of x,

–x is positive when x is negative. For instance, |–7.4| = –(–7.4) = 7.4.

Thus |x| are |–x| are never negative, and, in fact, |x| = |–x|.

On many graphing utilities, spreadsheets, and CAS, the absolute–

the value function is denoted abs. For example, abs(x–3) = |x–3|.

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The value of x would be 28 and the measure of angle M will be 90 degrees.

That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.

A rectangle is always a parallelogram and a quadrilateral but reverse statement may or may not be true.

WE have been given the Quadrilateral MNOP is a rectangle, and ∠M = 3x + 6.

WE know that interior angle of the rectangle are 90 degrees each.

Therefore,

∠M = 3x + 6 = 90

3x + 6 = 90

3x = 90 - 6

3x = 84

x = 84/3

x = 28

Hence, the value of x would be 28 and the measure of angle M will be 90 degrees.

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There are two types of exponential functions. For x or y increases as the value of y increases, the value of y decreases, approaching zero. For

approaching zero as the value of {x} increases, the value of y increases.

Which two forms of exponential functions are there?

What does Y mean in the exponential growth equation?

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Answer: 2 6/7

Step-by-step explanation:

Answer:

Answer is 75/32

Step-by-step explanation:

Convert the mixed number to an improper fraction so 7 1/2 changes to 15/2 divided by 2x5/8 but then you change the 2 to 1/2 so 15/2 x 1/2 x 5/8

then you multiply the fractions then you get 75/32

Based on the constant average rates of change. , the missing value in the table is 16

Linear relationships are relationships that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The table of values is given as

x    y

1     4

2     7

3     10

4     13

5

The constant average rates of change of linear relationships imply that:

As the x values constantly change by a value, the y values constantly change by another value (could be the same value)

On the given table, we can see the trend to be;

As x increase by 1, y increase by 3

So, the missing y value is

y = 13 + 3

Evaluate the sum

y = 16

Hence, the missing value in the table is 16

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