what is the x-coordinate of the solution​

The algebraic representation of the given statement is:

[tex]n^2 + (n + 1)^2 = 85[/tex]

Expanding and simplifying:

[tex]n^2 + (n^2 + 2n + 1) = 85[/tex]

[tex]2n^2 + 2n + 1 = 85[/tex]

[tex]2n^2 + 2n + 1 - 85 = 0[/tex]

[tex]2n^2 + 2n - 84 = 0[/tex]

Dividing the equation by 2 to simplify:

[tex]n^2 + n - 42 = 0[/tex]

Now, we can solve this quadratic equation using the quadratic formula:

[tex]n = [-b ± √(b^2 - 4ac)] / (2a)[/tex]

Where a = 1, b = 1, and c = -42:

n = [-(1) ± √((1)^2 - 4(1)(-42))] / (2(1))

n = [-1 ± √(1 + 168)] / 2

n = [-1 ± √169] / 2

n = [-1 ± 13] / 2

This yields two possible values for n:

n₁ = (-1 + 13) / 2 = 12 / 2 = 6

n₂ = (-1 - 13) / 2 = -14 / 2 = -7

Since n represents the smaller of the two consecutive integers, we discard the negative value.

Therefore, the smaller integer (n) is 6.

To solve this problem algebraically, we first translate the given statement into an equation. We know that the sum of the squares of two consecutive integers can be represented as[tex]n^2 + (n + 1)^2, v[/tex]where n is the smaller integer. Setting this expression equal to 85, we get the equation [tex]n^2 + (n + 1)^2 = 85.[/tex]

We then expand and simplify this equation to get a quadratic equation in standard form: [tex]2n^2 + 2n - 84 = 0.[/tex]

Next, we use the quadratic formula to solve for n, which gives us two possible values. Since we are looking for the smaller of the two consecutive integers, we discard the negative solution.

Thus, the smaller integer is n = 6.

Complete question:

The sum of the squares of two consecutive integers is 85. Using n to represent the smaller of the two consecutive integers, express this statement in algebraic form

Answer:

5

Step-by-step explanation:

Answer:

The correct answer option is -7.

Step-by-step explanation:

We are asked to determine the minimum value of y on the graph of [tex]y = sin x - 6 [/tex].

[tex]y' = cos(x) = 0[/tex]

[tex]x = arccos(0) = \pm\frac{\pi }{2} +2k\pi[/tex] where 'k' is any integer.

So, [tex] y = sin ( \frac { \pi} { 2 } ) - 6 = 1 - 6 = -5 [/tex] (it is the absolute minimum value)

and [tex]y=sin(\frac{-\pi}{2}+2\pi )-6 = sin(\frac{3\pi}{2})-6 [/tex] = -7 (absolute minimum y value)

Answer:

The correct answer option is -7.

We are asked to determine the minimum value of y on the graph of . where 'k' is any integer.

So,  (it is the absolute minimum value)and  = -7 (absolute minimum y value)

Answer:

[tex]\large\boxed{x=\log_\frac{5}{3}5}[/tex]

Step-by-step explanation:

[tex]3^x=5^{x-1}\qquad\text{use}\ a^{n-m}=\dfrac{a^n}{a^m}\\\\3^x=\dfrac{5^x}{5^1}\qquad\text{multiply both sides by 5}\\\\5\cdot3^x=5^x\qquad\text{divide both sides by}\ 3^x\\\\5=\dfrac{5^x}{3^x}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\5=\left(\dfrac{5}{3}\right)^x\qquad\text{logarithm both sides}\ \log_\frac{5}{3}\\\\\log_\frac{5}{3}5=\log_\frac{5}{3}\left(\dfrac{5}{3}\right)^x\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log_\frac{5}{3}5=x\log_\frac{5}{3}\dfrac{5}{3}\qquad\text{use}\ \log_aa=1\\\\\log_\frac{5}{3}5=x[/tex]

0.53 is 69.96 divided by132

Answer:

The answer is 0.53

The answer is B. I just answered this question earlier!

Answer:

i need the ansrew too

Step-by-step explanation:

hehe

For this case we have the following functions:

[tex]g (x) = 9 + 4x\\h (x) = \frac {x + 21} {5}[/tex]

We must find [tex](h * g) (x)[/tex]. By definition of composite functions we have to:

[tex](h * g) (x) = h (x) * g (x)[/tex]

So:

[tex](h * g) (x) = 9 + 4x * \frac {x + 21} {5}[/tex]

We apply distributive property:

[tex](h * g) (x) = \frac {9x + 9 * 21 + 4x ^ 2 + 4x * 21} {5}\\(h * g) (x) = \frac {9x + 189 + 4x ^ 2 + 84x} {5}\\(h * g) (x) = \frac {4x ^ 2 + 93x + 189} {5}\\[/tex]

Answer:

[tex](h * g) (x) = \frac {4x ^ 2 + 93x + 189} {5}[/tex]

What exactly does the question consist of

6(b+5) would be the factorization

Answer:

The value of x is [tex]4\ cm[/tex]

Step-by-step explanation:

step 1

Find the radius of the sphere

The surface area of the sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

we have

[tex]SA=784\pi\ cm^{2}[/tex]

substitute and solve for r

[tex]784\pi=4\pi r^{2}[/tex]

Simplify

[tex]r^{2}=196[/tex]

square root both sides

[tex]r=14\ cm[/tex]

step 2

Find the diameter

Remember that

The diameter is two times the radius

so

[tex]D=2(14)=28\ cm[/tex]

step 3

Find the value of x

we have

[tex]D=28\ cm[/tex]

[tex]D=4(x+3)\ cm[/tex]

equate the equations

[tex]4(x+3)=28[/tex]

[tex](x+3)=7[/tex]

[tex]x=7-3=4\ cm[/tex]

Answer:

The equation is in standard form. You will have to convert it to slope intercept form, which is -0.125x + 3.75 = y

Step-by-step explanation:

s = x and a = y, therefore 0.5x + 4y = 15

0.5x + 4y = 15

0.5x + 4y = 15  first subtract  0.5x

4y = -0.5x + 15   then divide all by 4

y = -0.125x + 3.75  slope intercept form

3.25 • p = t

Or

p = t/3.25

Hope this helps!

The time it takes to print a number of photos can be shown as a proportionality relationship p = (78/24) * t, with p being the number of photos printed and t being time in seconds.

The relationship between the time (t) needed to print pictures and the number of pictures (p) printed by a photo printer can be represented by a simple proportionality relationship. This means that we can express this relationship as a rate. In this case, the printer prints 78 pictures in 24 seconds, so we can write the relationship as:

p / t =78/24

Or in other words:

p = (78/24) * t

This equation suggests that for any given unit of time t, you simply multiply t by the rate (78/24) to find the number of pictures p that can be printed in that time.

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Answer: view image. its a proof (in red)

Step-by-step explanation:

Answer:

(a) [tex]x ^ 2 + y ^ 2 = 6 ^ 2[/tex]    circle centered on the point (0,0) and with a constant radius [tex]r = 6[/tex].

(b) [tex](x-1) ^ 2 + y ^ 2 = 1[/tex]  circle centered on the point (1, 0) and with radio [tex]r=1[/tex]

Step-by-step explanation:

Remember that to convert from polar to rectangular coordinates you must use the relationship:

[tex]x = rcos(\theta)[/tex]

[tex]y = rsin(\theta)[/tex]

[tex]x ^ 2 + y ^ 2 = r ^ 2[/tex]

In this case we have the following equations in polar coordinates.

(a) [tex]r = 6[/tex].

Note that in this equation the radius is constant, it does not  depend on [tex]\theta[/tex].

As

[tex]r ^ 2 = x ^ 2 + y ^ 2[/tex]

Then we replace the value of the radius in the equation and we have to::

[tex]x ^ 2 + y ^ 2 = 6 ^ 2[/tex]

Then [tex]r = 6[/tex] in rectangular coordinates is a circle centered on the point (0,0) and with a constant radius [tex]r = 6[/tex].

(b) [tex]r = 2cos(\theta)[/tex]

The radius is not constant, the radius depends on [tex]\theta[/tex].

To convert this equation to rectangular coordinates we write

[tex]r = 2cos(\theta)[/tex]     Multiply both sides of the equality by r.

[tex]r ^ 2 = 2 *rcos(\theta)[/tex]     remember that [tex]x = rcos(\theta)[/tex], then:

[tex]r ^ 2 = 2x[/tex]        remember that [tex]x ^ 2 + y ^ 2 = r ^ 2[/tex], then:

[tex]x ^ 2 + y ^ 2 = 2x[/tex]         Simplify the expression.

[tex]x ^ 2 -2x + y ^ 2 = 0[/tex]     Complete the square.

[tex]x ^ 2 -2x + 1 + y ^ 2 = 1[/tex]

[tex](x-1) ^ 2 + y ^ 2 = 1[/tex]  It is a circle centered on the point (1, 0) and with radio [tex]r=1[/tex]

hence x is1

hope it helps you!!!!!!

Answer:

x = 3

Step-by-step explanation:

Combine the 3 fractions on the left side.

[ note x ≠ - 1, 0, + 1 as this would make the fractions undefined ]

Multiply the numerators/ denominators by the lowest common multiple of

x - 1, x + 1, x , that is x(x - 1)(x + 1), that is

[tex]\frac{x(x+1)}{x(x-1)(x+1)}[/tex] + [tex]\frac{2x(x-1)}{x(x-1)(x+1)}[/tex] - [tex]\frac{3(x-1)(x+1)}{x(x-1)(x+1)}[/tex] = 0

distribute and simplify the numerators

[tex]\frac{x^2+x+2x^2-2x-3(x^2-1)}{x(x-1)(x+1)}[/tex] = 0

[tex]\frac{x^2+x+2x^2-2x-3x^2+3}{x(x-1)(x+1)}[/tex] = 0

[tex]\frac{3-x}{x(x-1)(x+1)}[/tex] = 0

The denominator cannot equal zero only the numerator, hence

3 - x = 0 ⇒ x = 3

Answer:

Length=8     Width=4

Step-by-step explanation:

Step 1- make an equation. The equation for perimeter is usually 2l+2w=P, but since the length is twice as long, we'll 2l x 2 =4l. So our equation is

4l + 2w = 24. note that 8+16 = 24

Step 2- Since 16 is 8 x 2, we know that the length is 16 and width is 8. We divide both those numbers because there is 2 lengths and 2 widths.

Answer:

Do you need work shown?

Step-by-step explanation:

(I don't know where to comment here)

Answer:

5/48

Step-by-step explanation:

Answer:

5/48

Step-by-step explanation:

[tex]\( 44 - 11 \)[/tex] factors to [tex]\( 33 \)[/tex] when using the greatest common factor method.

To factor the expression [tex]\( 44 - 11 \)[/tex] using the greatest common factor (GCF), we first need to find the GCF of the two numbers.

The numbers 44 and 11 have a common factor of 11.

Now, we can factor out 11 from both terms:

[tex]\( 44 - 11 = 11 \times (4 - 1) \)[/tex]

This simplifies to:

[tex]\( 44 - 11 = 11 \times 3 \)[/tex]

Finally, we calculate the product: [tex]\( 11 \times 3 = 33 \)[/tex]

So, the factored expression for [tex]\( 44 - 11 \)[/tex] using the GCF is [tex]\( 33 \)[/tex].

To summarize:

[tex]\( 44 - 11 = 11 \times (4 - 1) \)[/tex]

[tex]\( 44 - 11 = 11 \times 3 \)[/tex]

[tex]\( 44 - 11 = 33 \)[/tex]

Therefore, [tex]\( 44 - 11 \)[/tex] factors to [tex]\( 33 \)[/tex] when using the greatest common factor method.

Complete Question:

Factor the expression using the GCF. 44 - 11 = _____

The correct answer is D.[tex](5x^4-9x^3+7x-1)[/tex].

To simplify the given polynomial expression, one would typically look for like terms that can be combined. However, in the expression provided, there are no like terms. Each term in the expression [tex](5x^4, -9x^3, 7x, and -1)[/tex]has a different power of x or is a constant with no x term at all.

Since there are no common terms to combine, the expression is already in its simplest form. Therefore, the simplified expression remains as it was originally given:

[tex]\[ 5x^4 - 9x^3 + 7x - 1 \][/tex]

Answer:

[tex]\large\boxed{B.\ (x,\ y)\to(x-4,\ y-2)}[/tex]

Step-by-step explanation:

[tex](-5;\ 4)\xrightarrow{(+4,-2)}(-1;\ 2)\\\\-5+4=-1\to(x+4)\\4-2=2\to(y-2)[/tex]

Perimeter = 24m

Cost of half metre(1/2m) = €1.20

Cost of one metre = €2.40

Cost of fencing = 24 × 2.40 = €57.60

HOPE THIS WILL HELP YOU

Answer:

£57.6

Step-by-step explanation:

Given :The pen must have a perimeter of 24 m

Every half meter of fencing costs him £1.20

To Find : Work out the cost of the fence used to make the sheep pen.

Solution :

Cost of fencing 0.5 m = £1.20

Cost of fencing 1 m = [tex]\frac{1.20}{0.5}=2.4[/tex]

The pen must have a perimeter of 24 m

So, cost of fencing 24 m = [tex]2.4 \times 24 = 57.6[/tex]

Hence the cost of the fence used to make the sheep pen is £57.6

ANSWER

The train is moving 82.5mi/hr

EXPLANATION

How fast the train is going is the same as the speed of the train:

The speed of the train is calculated using the formula,

[tex]Speed = \frac{distance}{time} [/tex]

[tex]Speed = \frac{330}{4} [/tex]

[tex]Speed = 82.5[/tex]

Therefore the train is moving 82.5mi/hr

Simplify 6x/9 to 2x/3

2x/3(x + y)

Simplify

= 2x(x + y)/3

Answer:

Expression for Base Area is 16y²  and height of the prism is y² + y + 3.

Step-by-step explanation:

Given: Expression for volume of a prism = [tex]16y^4+16y^3+48y^2\:cubic\:units[/tex]

To find: Expression for the Base area and Height of the Prism.

We know that

Volume of a prism = Base Area × height

So we need to factorize given expression of volume into two factors in which 1st is for Base area and 2nd is for Height of the prism.

[tex]Volume=16y^4+16y^3+48y^2[/tex]

Take 16y² common from each terms, we get

[tex]Volume=16y^2(y^2+y+3)[/tex]

It is factorized in two factors,

So,

Base Area = 16y²

Height = y² + y + 3

Therefore, Expression for Base Area is 16y²  and height of the prism is y² + y + 3.

Answer:

d is the answr

Step-by-step explanation:

Answer:

Step-by-step explanation:

First step: calculate the difference:

[tex]\$246.95-\$199.95=\$47.00[/tex]

Second step: calculate the ratio of the difference and the original price:

[tex]\dfrac{\$47.00}{\$246.95}\approx0.1903219[/tex]

Third step: Convert to the percent:

[tex]0.190319\cdot100\%=19.0319\%\approx19\%[/tex]

The percent of change if the original price is $246.95 and the new price is $199.95 is 19.0%.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

The original price is $246.95 and the new price is $199.95.

Change in price = 246.95-199.95

= $47

The percentage of each value to the overall value when there are two or more values that sum up to 100 is the actual number.

The percent of change = (Original price-New price)/Original price ×100

= 47/246.95 ×100

= 4700/246.95

= 19.03

= 19.0%

Therefore, the percent of change with the given original price and the new price is 19.0%.

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Answer: $32.45

Step-by-step explanation:

Because....

55%  × 59 = $32.45

You could also write 55% as 0.55.

So it will look like this :

0.55 × 59 = 32.45.

It will still give you the same answer :)

* Hopefully tis helps:) Mark me the brainliest:)!!

Answer:

120 square centimeters

Step-by-step explanation:

The question says the formula already.

Area = bh

b = base length   b = 10

h = height length   h = 12

Area = 10 · 12

Area = 120 square centimeters

Answer: B. 120 square centimeters

Step-by-step explanation:

Given : The area of a parallelogram is found using the formula [tex]bh[/tex], where b represents the length of the base and h represents the length of the height.

Then , the area of a parallelogram that has a base of 10 centimeters and a height of 12 centimeters will be:-

[tex]\text{Area}=10\times12\\\\\Rightarrow\text{Area}=120\text{ square centimeters}[/tex]

Therefore , the area of the parallelogram = 120 square centimeters

Answer:

The last option (62 degrees)

Step-by-step explanation:

Angle F is the same measure as angle E, just like angle D is the same measure as G.

The measure of angle ∠E will be 62°. Then the correct option is D.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.

DEFG is an isosceles trapezoid.

Then the angle ∠E and ∠F will be congruent.

∠E = ∠F

∠E = 62°

Then the correct option is D.

More about the trapezium link is given below.

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first off let's convert the mixed fraction to improper fraction, and then do the division, since it was divided among all 6, he and 5 friends.

[tex]\bf \stackrel{mixed}{4\frac{4}{5}}\implies \cfrac{4\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{24}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{24}{5}\div 6\implies \cfrac{24}{5}\div \cfrac{6}{1}\implies \cfrac{24}{5}\cdot \cfrac{1}{6}\implies \cfrac{24}{6}\cdot \cfrac{1}{5}\implies \cfrac{4}{1}\cdot \cfrac{1}{5}\implies \cfrac{4}{5}[/tex]

Answer:

0.8 or 4/5

Step-by-step explanation:

4/5=.8 4.8/6=.8

Answer:

1320

Step-by-step explanation:

This is a simple permutation.

Since you start with 12 people and there are 3 winners, after every winner the number pf people available to win decrease.

First, there are 12 people, then after the first win there are 11 people, and after the 2nd win, for the third win the there are 10 people.

Thus, to find the total number of combinations, you multiply:

12*11*10=1320

Thus, there are 1320 possible combinations