Please help me understand

2

3x. + 63x + 9x + 189

Step-by-step explanation:

Use distributive law, in other words multiply the first bracket terms by the second bracket terms

Part (a)

Consecutive odd integers are integers that odd and they follow one right after another. If x is odd, then x+2 is the next odd integer

For example, if x = 7, then x+2 = 9 is right after.

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Part (b)

The consecutive odd integers we're dealing with are x and x+2.

Their squares are x^2 and (x+2)^2, and these squares add to 394.

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Part (c)

We'll solve the equation we just set up.

x^2 + (x+2)^2 = 394

x^2 + x^2 + 4x + 4 = 394

2x^2+4x+4-394 = 0

2x^2+4x-390 = 0

2(x^2 + 2x - 195) = 0

x^2 + 2x - 195 = 0

You could factor this, but the quadratic formula avoids trial and error.

Use a = 1, b = 2, c = -195 in the quadratic formula.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(1)(-195)}}{2(1)}\\\\x = \frac{-2\pm\sqrt{784}}{2}\\\\x = \frac{-2\pm28}{2}\\\\x = \frac{-2+28}{2} \ \text{ or } \ x = \frac{-2-28}{2}\\\\x = \frac{26}{2} \ \text{ or } \ x = \frac{-30}{2}\\\\x = 13 \ \text{ or } \ x = -15\\\\[/tex]

If x = 13, then x+2 = 13+2 = 15

Then note how x^2 + (x+2)^2 = 13^2 + 15^2 = 169 + 225 = 394

Or we could have x = -15 which leads to x+2 = -15+2 = -13

So, x^2 + (x+2)^2 = (-15)^2 + (-13)^2 = 225 + 169 = 394

We get the same thing either way.

Answer:

B

Step-by-step explanation:

It opens downwards, so the parabola is negative. This also means the vertex of the parabola is the highest point, therefore it is a maximum.

Answer:

B = (1, -4)

Step-by-step explanation:

the midpoint formula is ((x1 + x2) / 2 , ( y1 + y2) / 2)

M = (-6,1) and A = (-7,-3)

if we make A (x1, y1), we can plug in and solve for B (x2, y2)

-7 + x2 = -6

x2 = 1

1 + y2 = -3

y2 = -4

B = (1, -4)

Answer: y=80/5x+80

Step-by-step explanation:

At one point graph goes from (0,400) to (25,800). So the y intercept is 400 because that’s where the line was at x=0. 0 to 25 is 25. 400 to 800 is 400. So the equation would be y=400/25x+400. But you can divide all of it by 5 to get y=80/5x+80.

Answer:

Both Ava and Finn are correct

Step-by-step explanation:

There are 4 tables and 9 pencils at each table

4 ( 9) = 36

9 * 4 = 36

Both Ava and Finn are correct

Answer:

-5x = 26 is 5.2

x/2 = 4 is -8

3/2x=6 is 4

x/-7.2=4 is 28.8

Answer:

Step-by-step explanation:

o find the unit rate , divide the numerator and denominator of the given rate by the denominator of the given rate.

start with the rate of miles to gallons . then divide , write as a rate.

hope this helps.

where are the following vehicles name

Answer:

10 men

Step-by-step explanation:

This is because men are inversly proportionate to days.

The more the days the lesser the men and bise versa.

This means 180 men can do a painting in one day and 10 men can do the painting in 18 days.

In any artihmetic sequence, consecutive terms differ by a fixed constant c. So given the first term a, the second term is a + c, the third terms is a + 2c, and so on, up to the n-th term a + (n - 1)c.

If the 15th term is 40, then

40 = -12 + (15 - 1) c   ==>   c = 52/14 = 26/7

We can then write the n-th term as

-12 + (n - 1) 26/7 = (26n - 110)/7

The sum of the first 15 terms is then

[tex]\displaystyle \sum_{n=1}^{15}\frac{26n-110}7 = \frac{26}7\sum_{n=1}^{15}n - \frac{110}7\sum_{n=1}^{15}n = \boxed{210}[/tex]

Another way to compute the sum: let S denote the sum,

S = -12 - 58/7 - 32/7 + … + 228/7 + 254/7 + 40

Reverse the order of terms:

S* = 40 + 254/7 + 228/7 + … - 32/7 - 58/7 - 12

Notice that adding up terms in the same position gives the same result,

-12 + 40 = 28

-58/7 + 254/7 = 28

-32/7 + 228/7 = 28

so that

S + S* = 2S = 28 + 28 + 28 + … + 28 + 28 + 28

There are 15 terms in the sum, so

2S = 15×28   ==>   S = 15×28/2 = 210

The function written in the rational form is, C. F(x) = (x - 5)/3x

Rational numbers are subsets of real numbers which can be written in the form of p/q, where q ≠ 0. As at q = 0 it is undefined.

Similarly, A rational expression is also written in the form of p/q, where p and q are algebraic expressions and q ≠ 0.

From the given options, F(x) is written in the form p/q,

Where, p = x - 5 and q = 3x.

Therefore, The rational function is, F(x) = (x - 5)/3x, where x ≠ 0.

As at x = 0 the function is undefined.

learn more about rational functions here :

https://brainly.com/question/27914791

#SPJ7

Answer:

1 /64

Step-by-step explanation:

2^-6

We know that a^-b = 1/a^b

1 / 2^6

1/64

Answer:

Area of parallelogram = 21

Step-by-step explanation:

A = BH

Plug in

A = 7×3

Solve

A = 21

The answer will be 21.

Answer:

Sure:)! the answer is-487.5

Step-by-step explanation:

As said in the problem pie=3 as determined in the problem. Hence, the answer is 487.5

Hope this helps :)!

Step-by-step explanation:

[tex]volume = \frac{4}{3} \pi \: {r}^{3} \\ = here\pi = 3 \\ then \: v = \frac{4}{3} \times 3 \times {5}^{3} \\ = 4 \times 125 \\ = 500 {in}^{3} \\ thank \: you[/tex]

do what you want ok and choose

Answer:

12

Step-by-step explanation:

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Answer:

x=1/2

Step-by-step explanation:

Answer:

35% = .35

2/5 = 4/10 = .4

.4 >.35

Step-by-step explanation:

Answer:

-7t

Step-by-step explanation:

you are correct

Answer:

C: 119 square inches

Step-by-step explanation:

We are given;

Slant height; L = 5 in

Base area; B = 49 in²

Since it's a square pyramid, the base portion has a square shape.

Thus, area of base = x²

Where x is a side of the square.

Thus;

x² = 49

x = √49

x = 7

Perimeter of base = 7 × 4 = 28 in

Area of pyramid = ½PL + B

Plugging in the relevant values;

Area of pyramid = (½ × 28 × 5) + 49

Area of pyramid = 119 in²

Answer:

0*i+5j

Step-by-step explanation:

The vector is given by 0*i+5j

Coordinate of D: (2, -2)

Multiply x and y by 0.5

Answer: D = (1, -1)

Answer:

ax + b + y^2 + 2yx + x^2

Step-by-step explanation:

(y+x)^2

= (y+x)(y+x)

= y^2 + 2yx + x^2

y^2 + 2yx + x^2 + (ax+b)

= ax + b + y^2 + 2yx + x^2

Answer:

20 books

Step-by-step explanation:

35/1.75

20

hopefully this answer can help you to answer the next question.

Answer:

x + 3

Step-by-step explanation:

Image below

Answer:

A

Step-by-step explanation:

Given

- 2x² + 5x - 3 ← factor out - 1 from each term

= - 1(2x² - 5x + 3) ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 3 = 6 and sum = - 5

The factors are - 2 and - 3

Use these factors to split the x- term

2x² - 2x - 3x + 3 ( factor the first/second and third/fourth terms )

2x(x - 1) - 3(x - 1) ← factor out (x - 1) from each term

(2x - 3)(x - 1)

Then

- 2x² + 5x - 3 = - 1(2x - 3)(x - 1) → A

Answer:

8b(4a-1)

Step-by-step explanation:

32ab-8b

8b(4a-1)

Answer:

Did ur question get answered ??

Step-by-step explanation:

Answer:

203 ft.

Step-by-step explanation:

Since we are given the measurements of two sides, we can use trig to find the angle (or our reference angle, we'll call it x) the sides form.

SOH-CAH-TOA

We'll use cosine since the adjacent and hypotenuse were given for our reference angle.

Cos(x) = (adj/hyp)

Cos(x) = (396/445)

[Cos(x)]cos^-1 = (396/445)(cos^-1)

x ≈ 27.1409 (Nearest ten-thousandth)

And now we find the missing side using our now known angle.

SOH-CAH-TOA

Tan(x) = (opp/adj)

Tan(27.1409) = (opp/396)

0.5126 ≈ (opp/396)

(0.5126)(396) ≈ (opp/396)(396)

Opp = 203

Missing Side = 203 ft

Final Answer:

x = 20

Step-by-step explanation:

we'll be using the pythagorean theorem method, in this triangle the missing letter is a.

formula: [tex]a=\sqrt{c^2-b^2}[/tex]

a = x

b = 21

c = 29

a = [tex]\sqrt{29^2-21^2}[/tex]

a = [tex]\sqrt{841-441}[/tex]     (note: 29² = 29 × 29 = 841 and 21² = 21 × 21 = 441)

a = [tex]\sqrt{400}[/tex]

a = 20

x = 20

Answer:

= -8x^5 y^4

Step-by-step explanation:

Multiply the numbers: -2 . 4 = -8

-2x^3 yx^2 y^3

Simplify x^3 x^2 : x^5

= -8x^5yy^3

Simplify yy^3 : y^4

= -8x^5 y^4