What is the first step in solving a quadratic equation of the form given below?

(ax + b)^2 = c

A. Divide both sides by c

B. Take the square root of both sides

C. Use the zero product rule

D. Factor out a common factor

Step-by-step explanation:

Using BODMAS rule

[3x+12+x] = [4(3+x)]

[4x+12] = [12+4x]

Parentheses 1 = Parentheses 2

LHS = RHS

HENCE PROVED

[tex]y < \frac{1}{2} x - 2 \\ [/tex]

Answer:

3 and 4

Step-by-step explanation:

30/8=3.75

3.75 lies between 3 and 4

Hey there!

30/8

= 30 ÷ 2 / 8 ÷ 2

= 15 / 4

≈ 3 3/4

≈ 3.75

It falls in between three (3) and four (4). But, fun fact it rounds to up to four (4)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

B. 100 units

Step-by-step explanation:

What I did was I couunted the lines at the bottum and since it was 10 then I counted up  and that was 10 so you would do 10x10 get 100 units.

Answer:

Area of a triangle is 1/2 x base x height.

area of triangle = 1/2 x 20 x 17 = 170 square feet.

the image shows 4 triangles, total area = 170 x 4 = 680 square feet.

the answer is A. 680 sq. ft.

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Answer:

832.5²

Step-by-step explanation:

Base x height ÷ 2 is the formula to find a triangles area.

45 x 37= 1665 then 1665 ÷ 2 = 832.5 dont forget to add the ²

Answer:

832.5²

Step-by-step explanation:

[tex]x=\frac{1+4f-\sqrt{16f^{2}+8f+25 } }{2}[/tex]

Answer:

1620

Step-by-step explanation:

(-18)×(-10)×9= 1620

since there are 36 inches in 1 yard, 12 yards will have 12(36) = 432 inches.

The polynomial of least possible degree having the graph as given is; f(x) = x³-8x²+x +42.

It follows from the graph that the roots of the polynomial are; -2, 3 and 7.

On this note, the factors of such polynomial are;

Hence; (x+2)(x-3)(x-7) = f(x)

Read more on polynomials;

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Answer:

72

Step-by-step explanation:

84/7 = 12

12 × 6 = 72

84 to 72

Answer:

72

Step-by-step explanation:

divide 84 by 7, and then multiply 12(what you got from the division) by 6 and you get 72

Answer:

56

Step-by-step explanation:

two of the angles are the same meaning the bottom two are 62. angles in a triangle add up to 180° so you just do 62 + 62 and then take the answer away from 180

62+62=124

180-124=56

Answer:

Option C, [tex]36x^2 + 60x + 25[/tex]

Step-by-step explanation:

Step 1:  Determine the perfect square

According to online, "When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b)"

The only one that seems to work is Option C so lets factor it.

[tex]36x^2 + 60x + 25[/tex]

[tex](6x + 5)(6x + 5)[/tex]

[tex](6x + 5)^2[/tex]

Yup!  We can see that Option C would give us a perfect square

Answer:  Option C, [tex]36x^2 + 60x + 25[/tex]

best answer of this equation is 10.772

Answer: 10.772

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

exact form:

x= 10 4/3

--------- (its a fraction)

2

decimal form: 10.77217345....

after that round to the nearest thousandth.

Answer:

It's a function because when you simplify it becomes y=-x-3. the only reason it wouldn't be a function would be if the equation were to be x = a random number that is not a variable. The equation would not pass the vertical line test which is the requirement to see if an equation is a function.

Simply put, it's a function.

Probability helps us to know the chances of an event occurring. The probability of a family owning a cat or a dog is 0.22.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

As it is given that the probability of a family owning a cat is 0.10, the probability of owning a dog is 0.20, and the probability of owning a cat and a dog is 0.08. Therefore, the probability of a family owning a cat or a dog can be written as,

Probability (family owning a cat or a dog)

= Probability (Cat) + Probability (Dog) - Probability (Cat And Dog)

[tex]\text{Probability (family owning a cat or a dog)} = 0.10+0.20-0.08 = 0.22[/tex]

Hence, the probability of a family owning a cat or a dog is 0.22.

Learn more about Probability:

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Answer:

b

Step-by-step explanation:

2/3 * 2/3 = 4/9

2/3 * 3/2 = 1

2/3 * 3/4 = 1/2

2/3 * 4/4 = 2/3

Answer:

[tex]\tt 1)\: \boxed{\tt 4y+10}[/tex]

[tex]\tt 2)\:\boxed{\tt 0.5x^4+10.5}[/tex]

Step-by-step explanation:

1) y + 4 + 3(y + 2)

Expand:-

[tex]\tt y+4+3y+6[/tex]

Combine like terms:-

[tex]\tt y+3y+4+6[/tex]

[tex]\boxed{\tt 4y+10}[/tex]

__

2) 0.5(x⁴ - 3) + 12

Expand:-

[tex]\tt 0.5x^4-1.5+12[/tex]

Add/Subtract Numbers:-

[tex]\boxed{\tt 0.5x^4+10.5}[/tex]

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Answer:

3x - 5 fits the equation perfectly

Step-by-step explanation:

if we put the following value in X we get,

x processing y

3. 3*3 - 5. 4

5. 3*5 - 5. 10

7. 3*7 -5. 16

9. 3*9 - 5. 22

11. 3*11 - 5. 28

Answer:

F = ma

m = F/a

m = 88/4

m = 22 kg

Step-by-step explanation:

To calculate hydronium concentration from pH, type on you calculator

10 to the power of negative pH value

10^-5.5 = 3•10^6 mol/L

Since there are 3 hydrogens in every hydronium molecule,

There are 9 • 10^6 hydrogens in that liter of acid.

Answer:

See below.

Step-by-step explanation:

A(1, 4)

B(3, 0)

C(-3, -2)

We find the coordinates of he midpoints using the midpioint formula.

D([1 + 3]/2, [4 + 0]/2) = D(2, 2)

E([1 + (-3)]/2, [4 + (-2)]/2) = E(-1, 1)

We find the slopes using the slope formula.

slope of BC:

m_BC = (-2 - 0)/(-3 - 3) = -2/(-6) = 1/3

slope of DE:

m_DE = (1 - 2)/(-1 - 2) = -1/(-3) = 1/3

Since the slopes of BC and DE are equal, the lines are parallel.

Answer:

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]

Given equation: [tex]kx^2+2x+(1-k)=0[/tex]

[tex]\implies a=k,\:b=2,\:c=(1-k)[/tex]

[tex]\begin{aligned}\implies b^2-4ac & =(2)^2-4(k)(1-k)\\ & =4-4k(1-k)\\ & =4-4k+4k^2\\ & = 4k^2-4k+4 \end{aligned}[/tex]

Complete the square:

[tex]\begin{aligned}\implies 4k^2-4k+4 & =4(k^2-k+1)\\ & = 4\left[k^2-k+\left(\dfrac{-1}{2}\right)^2+1-\left(\dfrac{-1}{2}\right)^2\right]\\ & = 4\left[\left(k-\dfrac12\right)^2+\dfrac34\right]\\ & = 4\left(k-\dfrac12\right)^2+3\end{aligned}[/tex]

[tex]\textsf{As }\left(k-\dfrac12 \right)^2 \geq 0 \implies 4\left(k-\dfrac12 \right)^2+3\geq 3[/tex]

Therefore, the roots are always real.

Answer:

  a. exception: C; obtuse angle with a different measure

  b. corresponding angles are congruent; corresponding sides are proportional

  c. corresponding angles are congruent among the similar triangles; they are not congruent when the triangles are not similar

  d. corresponding sides are porportional; they are not proportional when the triangles are not similar

Step-by-step explanation:

As you know, similar triangles have congruent corresponding angles, and proportional corresponding sides. This gives them the same shape, but they may be of differenent sizes.

__

Figure C appears to have a larger smallest angle and a smaller largest angle than the rest of the figures. Its long side relative to its second-longest side appears to be shorter, consistent with a smaller largest angle.

__

The similar triangles have congruent corresponding angles and proportional corresponding sides.

__

See (b) regarding similar triangles. Non-similar triangles have different angles.

__

See (b) regarding similar triangles. Non-similar triangles have different side proportions.

Answer

91.67inch^3

Step-by-step explanation:

The volume of a cone can be calculated using below formula

V= 1/3 π.r^2h

Where h= height of the cone

r= radius of the cone

V= volume of the cone

Given :

height= 11 inches

radius= 5 inches

π= 3.14

Then substitute into the formula we have

V= 1/3 × 3.14× 5^2 ×11

V= 91.67inch^3

Therefore volume of the cone is 91.67inch^3

Answer:

The origin is at (0,0) its where the x and y coordinate intersect.

Step-by-step explanation:

what was the question here?

Answer:

1. x=4

2. x=14

3. x=3

Step-by-step explanation:

x is just a symbol they use as a temporary symbol to tell the person reading the problem that there is number that you do not know yet. if the x in the problem is next to a number then it needs to be multiplied with the number it's next to. in this case we know that 4 times 3=12 and if you take two away from 12 you get 10 so because 3 works in the equation it's the answer for 4x-2=10. this applies to every problem like this another way to solve it is if you add 2 to the left side it cancels out but you need to add 2 to the other side which would look like 4x=10+2 which equals 4x=12 and 4 times three equals 12. it doesn't matter how the equation changes as long as you find out whatx equals then that is the answer.

Answer:

1. x = 2

2. x = 14

3. x = 3

Step-by-step explanation:

1. 12 + 2x = 16

First, I did 16 - 12 which is 4. I did this because you want to know how much 2x is supposed to be fully, and you always want to do the opposite. like in this case it was addition so the opposite is subtracting. Next, the 2x is supposed to equal 4, and when you see 2x that means you have to multiply. So, 2 x 2 = 4. You can also do 4 divided by 2 equal 4. Finally, the answer for x is 2.

________________________________________________________

2. 12 + x = 26

So, you have to do 26 - 12 which is 14. I turned the addition problem to a subtraction problem because you always want to do the opposite. and you should already know that x will equal 14. you can double check if you want and change it back to addition which will be 12 + 14 = what ? 26 . so 14 is the answer for x !

________________________________________________________

3. 4x - 2 = 10

First, you want to do 10 + 2 which is 12. You should know by now if you read above for the other equations that you have to do the opposite. Next, 4x is going to have to be equal to 12. So, 4 x 3 = 12 or you can do 12 divided by 4 which will still equal 3. Finally the answer for x is 3.

________________________________________________________

Hope this helps !

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