Solve by factorisation.
3x² + 10x - 8 = 0

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:

see explanation

Step-by-step explanation:

Given

AB + BC = 31

AB - BC = 17

Add the 2 equations

2AB = 48 ( divide both sides by 2 )

AB = 24

Substitute AB = 24 into the first equation

24 + BC = 31 ( subtract 24 from both sides )

BC = 7

Using Pythagoras' identity to find the hypotenuse AC

AC² = AB² + BC² = 24² + 7² = 576 + 49 = 625 ( take square root of both sides )

AC = [tex]\sqrt{625}[/tex] = 25

Then

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{7}{25}[/tex]

cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{24}{25}[/tex]

sinC = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{24}{25}[/tex]

cosC = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{7}{25}[/tex]

Answer:

they are in order cross x with the y across from it

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

n is the number of litres.

if you substitute 1 for 'n' then you will get :

C = 8 + 1.5(1)

C = $9.5

$9.50 for every litre

Answer:

C is correct

Step-by-step explanation:

The $8 charge is only once regardless of how many liters are ordered, so only answer C works.

Answer:

D

Step-by-step explanation:

It is the law of cos

C^2= A^2+B^2-2*A*B*cosL where L is the angle between A and B

so C = 32^2 + 35^2 - 2(32)(35)cos120°

Answer:

[tex] {(x - y)}^{2} \\ = (x - y)(x - y)[/tex]

open the brackets:

[tex] = ( {x}^{2} - xy - xy + {y}^{2} ) \\ = {x}^{2} - 2xy + {y}^{2} [/tex]

Answer:

h = 504, k = 65, t = -1

Step-by-step explanation:

56 = h/9

h = 56 x 9

h = 504

k/5 - 10 = 3

k/5 = 3 + 10

k/5 = 13

k = 13 x 5

k = 65

3t + 5 = 2

3t = 2 - 5

3t = -3

t = -3/3

t = -1

[tex]\\ \sf\longmapsto q+12-2(q-22)>0[/tex]

[tex]\\ \sf\longmapsto q+12-2q+44>0[/tex]

[tex]\\ \sf\longmapsto q-2q+12+44>0[/tex]

[tex]\\ \sf\longmapsto -q+56>0[/tex]

[tex]\\ \sf\longmapsto -q>-56[/tex]

[tex]\\ \sf\longmapsto q<56[/tex]

Answer:

162

Step-by-step explanation:

because this is a parallelogram :

m<2 = m<4 so

4x - 22 = 3x - 12

4x - 3x = 22 - 12

x = 10 replace x with 10 in the equation for m<4

3x - 12 is 30 - 12 = 18

m<4 and m<1 are supplementary and their sum is equal to 180

m<4 + m<1 = 180

m<1 = 180 - 18

m<1 = 162

Answer:

3

Step-by-step explanation:

7-4

Answer:

DE = 11

Step-by-step explanation:

DF = DF +EF

4x+2 = x+7 + 7

Combine like terms

4x+2 = x+14

Subtract x from each side

4x+2-x = x+14-x

3x+2 = 14

Subtract 2 from each side

3x+2-2 =14-2

3x=12

Divide by 3

3x/3 = 12/3

x = 4

DE = x+7 = 4+7 =11

Answer:

DE is 11

Step-by-step explanation:

[tex]DE = DF - EF \\ DE = (4x + 2) - 7 \\DE = 4x - 5 [/tex]

But for x:

[tex]4x + 2 = (x + 7) + 7 \\ 4x + 2 = x + 14 \\ 3x = 12 \\ x = 4[/tex]

Therefore:

[tex]DE = (4 \times 4) - 5 \\ = 16 - 5 \\ = 11[/tex]

Answer:

A

Step-by-step explanation:

lm‎ao this problem is b‎u‎l‎ls‎h‎‎‎i‎t because the actual answer would be [2, 2] U (7, infty) but thats literally not there, so ig the closest one would be [2, infty) which is A

if it was asking for the domain on the other hand, then it would be B lm‎ao

but I would go with A

Answer:

-3(2x-4) or -6x+12

Step-by-step explanation:

Area is H*W

theres no value for x so that would be it, unless there is then all you do is plug that into the answer I put.

Answer:

y = -x + 4

Step-by-step explanation:

(x₁,y₁)= (5, - 1)    & (x₂,y₂)= (2 , 2)

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

         [tex]\frac{2-[-1]}{2-5}\\\\=\frac{2+1}{-3}\\\\=\frac{3}{-3}\\\\= -1[/tex]

m = -1

Equation of the line y - y₁ = m(x - x₁)

y  - [-1] = (-1)*(x - 5)

y + 1 = -x + 5      {-1 is distributed}

y = -x + 5 - 1

y = -x + 4

Step-by-step explanation:

3(6+b)+2b+1

18+3b+2b+1

5b+19

Answer:

Domain: [tex](-\infty,\infty)[/tex]

Range: [tex]f(x) \ge 0[/tex]

Step-by-step explanation:

Given

[tex]f(x) = |x + 6|[/tex]

Required

The domain and the range

First, we calculate the domain

[tex]f(x) = |x + 6|[/tex]

The above function does not have roots or fraction, where x is the denominator. This means that the domain is all real numbers, i.e. [tex](-\infty,\infty)[/tex]

The range

The function is an absolute function; So, the minimum value is 0.

Hence, the range is:

[tex]f(x) \ge 0[/tex]

Answer:

A

Step-by-step explanation:

on edge

Answer:n=6

Step-by-step explanation:

Answer:

Hello

Step-by-step explanation:

[tex]y=2x^2-12x+19\\=2(x^2-6x)+19\\=2(x^2-2*3*x+9)+19-18\\=2(x-3)^2+1\\\\Vertex\ is\ (3,1)\\\\Axis\ of\ symmetry\ is\ x=3\\\\y-intercept\ is \\\\y=2(0-3)^2+1=19\\[/tex]

Answer:

-5x - 7y

Step-by-step explanation:

Answer:

there is a 25% decrease in books being read

Use the formula given. R is half the diameter

R = 14/2 = 7 inches.

Area = 3.14 x 7^2

Area = 153.86 inches^2

Answer:

Does the answer help you?

Answer:

Step-by-step explanation:

Let the regular price is x, then:

Answer:

-8x^3 + 64x^2 - 24x

Step-by-step explanation:

To distribute, we must multiple -8x to each term:

-8x(x^2) - 8x(-8x) - 8x(3)

-8x^3 + 64x^2 - 24x

Step-by-step explanation:

[tex] - 8x( {x}^{2} - 8x + 3) \\ = ( - 8x \times {x}^{2}) - ( - 8x \times 8x) + ( - 8x \times 3) \\ = - 8 {x}^{3} + 64 {x}^{2} - 24x[/tex]

distribute -8x to each term in the perenthesis i.e. multiply each term by -8x

Answer:

All of them except 12:25 simply to 2:5. So 12:25 is the odd one out.

Answer:

-3/4

Step-by-step explanation:

First, let's convert the mixed numbers into improper fractions in an effort to make this problem easier to solve.

-2 1/2 as a mixed number is -5/2 and -1 3/4 as a mixed number is -7/4.

Our problem is now -5/2 - (-7/4).

We still can't solve this because the two fractions do not share a common denominator. 4 can serve as one, so -5/2 with a denominator of 4 would be -10/4.

The problem is now -10/4 - (-7/4).

Two negatives make a positive so the problem can be rewritten as -10/4 + 7/4. The final answer is -3/4.

Answer:

Step-by-step explanation:

I can't believe I'm doing this for 5 points, but ok!

For the first 3, we are going to multiply to find the value of that 3 x 3 matrix by picking up the first 2 columns and plopping them down at the end and then multiplying through using the rules for multiplying matrices:

[tex]\left[\begin{array}{ccccc}7&4&6&7&4\\-4&8&9&-4&8\\1&8&7&1&8\end{array}\right][/tex]  and from there find the sum of the products of the main axes minus the sum of the products of the minor axes, as follows (I'm not going to state the process in the next 2 problems, so make sure you follow it here. This is called the determinate. The determinate is what you get when you evaluate or find the value of a matrix. Just so you know):

[tex](7*8*7)+(4*9*1)+(6*-4*8)-[(1*8*6)+(8*9*7)+(7*-4*4)][/tex] which gives us:

392 + 36 - 192 - [48 + 504 - 112] which simplifies to

236 - 440 which is -204

On to the second one:

[tex]\left[\begin{array}{ccccc}-8&-4&-1&-8&-4\\1&7&-3&1&7\\8&9&9&8&9\end{array}\right][/tex] and multiplying gives us

[tex](-8*7*9)+(-4*-3*8)+(-1*1*9)-[(8*7*-1)+(9*-3*-8)+(9*1*-4)][/tex] which gives us:

-504 + 96 - 9 - [-56 + 216 - 36] which simplifies to

-417 - 124 which is -541, choice c.

Now for the third one:

[tex]\left[\begin{array}{ccccc}-2&-2&-5&-2&-2\\2&7&-3&2&7\\8&9&9&8&9\end{array}\right][/tex] and multiplying gives us

[tex](-2*7*9)+(-2*-3*8)+(-5*2*9)-[(8*7*-5)+(9*-3*-2)+(9*2*-2)][/tex] which gives us:

[tex]-126+48-90-[-280+54-36][/tex] which simplifies to

-168 - (-262) which is 94, choice c again.

Now for the last one. I'll show you the set up for the matrix equation; I solved it using the inverse matrix. So I'll also show you the inverse and how I found it.

[tex]\left[\begin{array}{cc}-4&-5&\\-6&-8\\\end{array}\right][/tex] [tex]\left[\begin{array}{c}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{c}-5\\-2\\\end{array}\right][/tex] and I found the inverse of the 2 x 2 matrix on the left.

Find the inverse by:

* finding the determinate

* putting the determinate under a 1

* multiply that by the "mixed up matrix (you'll see...)

First things first, the determinate:

|A| = (-4*-8) - (-6*-5) which simplifies to

|A| = 32 - 30 so

|A| = 2; now put that under a 1 and multiply it by the mixed up matrix. The mixed up matrix is shown in the next step:

[tex]\frac{1}{2}\left[\begin{array}{cc}-8&5\\6&-4\end{array}\right][/tex]  (to get the mixed up matrix, swap the positions of the numbers on the main axis and then change the signs of the numbers on the minor axis). Now we multiply in the 1/2 to get the inverse:

[tex]\left[\begin{array}{cc}-4&\frac{5}{2}\\3&-2\\\end{array}\right][/tex] Multiply that inverse by both sides of the equation. This inverse "undoes" the matrix that's already there (like dividing the matrix that's already there by itself) which leaves us with just the matrix of x and y. Multiply the inverse matrix by the solution matrix:

[tex]\left[\begin{array}{c}x&y\end{array}\right] =\left[\begin{array}{cc}-4&\frac{5}{2} \\3&-2\end{array}\right] *\left[\begin{array}{c}-5&-2\\\end{array}\right][/tex] and that right side multiplies out to

x = 20 - 5 which is

x = 15 and

y = -15 + 4 which is

y = -11

(It works, I checked it)