Find the values of p and g such that
4x² + 12x = 4(x + p)^2-q

Answer:

B and D.

Step-by-step explanation:

Hope this helps! :D

Answer:

It is A, I highly suggest you should read my explanation.

Step-by-step explanation:

(2x - 3)(x - 4)(x^2 + 3)

Exponent of 2x = 1

Exponent of x = 1

Exponent of x^2 = 2

Add them all together to get the degree. 1 + 1 + 2 = 4

Now we can tell that the polynomial can have 1,2,3,4, or no roots at all. The max number roots it can have is 4

To see the number of roots it has, we have to set each part equal to 0

2x - 3 = 0

Add 3 to both sides

2x - 3 + 3 = 0 + 3

2x = 3

Divide both sides by 2

2x/2 = 3/2

x = 3/2 or 1.5

Next,

x - 4 = 0

Add four to both sides

x - 4 + 4 = 0 + 4

x = 4

Then,

x^2 + 3 = 0

Subtract 3 from both sides

x^2 + 3 - 3 = 0 - 3

x^2 = -3

Find the square root of both sides

sqrt(x^2) = sqrt(-3)

x = i*sqrt(3), -i*sqrt(3)

Those are imaginary numbers, therefore there are not real.

The real roots are x = 3/2, 4

Harvey stated that this equation has four real roots. We can cross options B and C out since they stated he was correct.

It is not D because finding a square root of a number gives two answers; the positive and negative version, so it will have two solutions. There were only two real roots and the other two roots are complex roots.

That leaves us to option A, which states that there are 2 real and 2 complex roots. It is correct

Answer:

$4,537.55

Step-by-step explanation:

I did it on paper and you gotta calculate it, Hope this helps!

Answer:

First: 3 units Second: 7 units Third: 9 units

Step-by-step explanation:

19=x+(x+4)+3x

19=5x+4

15=5x

x=3

first side is 3 units

3+4=7

second side is 7 units

3*3=9

third side is 9 units

Answer:

there were a total of 55 people at the party.

Step-by-step explanation:

In order to create the equation representing this scenario we first need to represent each step in a formula. Since the total number of people is represented by x we can multiply 3/5 by x and subtract 9 from that. This would then be equal to 24 like so...

3/5x - 9 = 24

Now that we have the formula we can perform opposite operations to isolate x and solve for it.

3/5x - 9 = 24   ... add 9 on both sides

3/5x = 33   ... divide both sides by 3/5

x = 55

Finally, we can see that there were a total of 55 people at the party.

Answer:

y=-1/4x+2

Step-by-step explanation:

The equation would be y=-1/4x+2 because the rise is -1 and the run is 4 (you could also say the run is -4 and the rise is 1. It doesn't really matter). The line also crosses the y axis at 2, which means that 2 is the y-intercept. :)

Answer:

y = (-1/4)x +2

Step-by-step explanation:

Having the actual graph is an easy way to calculate the equation of the line. Since the format is y = mx +b we just need to plug in numbers.

b = y-intercept

m = slope

We can automatically see that the y-intercept is 2, so b = 2. To find the slope we just calculate rise over run. The line is decreasing 1 unit for every 4 units it is "running". Therefore, -1/4 is your slope.

b = 2

m = -1/4

Now, all we need to do is plug in numbers.

y = (-1/4)x +2

Answer:

You typically apply the same rules as you would for 'regular' fractions.

So you can multiply numerator and denominator by the same value if needed. If you want to add fractions you must make sure the denominators are the same, etc.

The value you multiply by can be an algebraic expression.

Answer:

last one (d)

Step-by-step explanation:

adding subtracting or dividing is not how you use a growth factor(what my school calls a percentage in a decimal form).

Answer:

Your question is

1

=

2

5

1=\frac{x}{25}

1=25x

Solve

1

Multiply all terms by the same value to eliminate fraction denominators

2

Simplify

Multiply the numbers

Cancel multiplied terms that are in the denominator

Move the variable to the left

=

2

5

Solution

=

2

5

Hi! So what you will need to know is pythagorean theorm.

What the theorm basically says is a^2 + b^2 = c^2.

-- The (a,b,c) are referring to the sides of the triangles (3 letters for 3 sides).

Take note that "c" is always the side opposite of the right angle.

The other known side could be "a" or "b"

Taking a look at problem 9, identify the "c" value. The "c" value would be 35.

Then indentify the value of "b" or "a". "a" would = 20.

Plug it into the equation:

20^2 + b^2 = 35^2

400 + b^2 = 1225

solve for b.

1. subtract 400 from both sides.

b^2 = 825

b = [tex]\sqrt{825}[/tex]

you could solve for the square root but it would give a decimal numbers but I'm not sure what the teacher is looking for.

Answer:-28

Step-by-step explanation:

Answer:

Folk religions are based in tradition

Folk religions are animistic

The major religions are christianity and islam

Correct statement regarding religion in Africa is that the major religions are Christianity and Islam.

At some point, Africans practiced traditional religions where they worshipped multiple gods and held deep reverence for their ancestors. This changed as Islam and Christianity took over the continent.

Islam was spread around Africa by:

Christianity came later when:

Therefore, We can say in conclusion that due to Muslim and European incursions in Africa, the major religions became Islam and Christianity.

Learn more about Africa here:

https://brainly.com/question/11402989

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Answer:

Numerical expression 1

[tex]\frac{4}{10000} * \frac{5}{1000} = \frac{20}{10000000} = \frac{1}{500000}[/tex]

Numerical expression 2

[tex]\frac{1}{50000} = 0.2 * 10^{-4} = 2 * 10^{-5}[/tex]

Numerical expression 3

[tex]1 : 50000[/tex]

Step-by-step explanation:

Numerical expression 1

[tex]\frac{4}{10000} * \frac{5}{1000} = \frac{20}{10000000} = \frac{1}{500000}[/tex]

Numerical expression 2

[tex]\frac{1}{50000} = 0.2 * 10^{-4} = 2 * 10^{-5}[/tex]

Numerical expression 3

[tex]1 : 50000[/tex]

Answer:

the new price is 25.9

Step-by-step explanation:

Answer:

1. -3x - 5= 16

-16-5=3x

x=-21/3=-7

Answer:

DF = 1213ft

Step-by-step explanation:

Answer:

5^10

Step-by-step explanation:

Hope I helped!

Answer:

6.83 pints

Step-by-step explanation:

The first step is to calculate the volume of the blue paint

= 9.1 × 1/4

= 2.275

Therefore the volume of the white paint can be calculated as follows

= 9.1 - 2.275

= 6.83

Hence the volume of white paint that Caroline used to paint her bedroom walls is 6.83 pints

Answer:

31

Step-by-step explanation:

25/0.80=31.25

(You cant have a quarter of a parking space.)

Answer:

15.12

Step-by-step explanation:

Cost of meal = $20

Discount (coupon) = 30%

Amount of discount = 30% of $20

= 30/100 * 20

= 0.3 * 20

= $6

Amount paid after discount= initial cost of meal - discount

= $20 -$6

= $14

Sales tax =8%

Amount of sales tax = 8% of $14

= 8/100 * 14

= 0.08 * 14

= $1.12

Total amount paid = Amount paid after discount + Amount of sales tax

= $14 + $1.12

= 15.12

Answer: option 4

Step-by-step explanation:

The transformation of the parent function is stretched by a factor of 2 and translated 8 units right and 5 units down

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) = ∛x

And , the given function is y = ∛ ( 8x - 64 ) - 5

On simplifying , we get

Taking 8 as the common factor , we get

y = ∛ 8 ( x - 8 ) - 5

Now , the cube root of 8 is 2

So , y = 2∛(x - 8 ) - 5

The transformed function is y = 2∛(x - 8 ) - 5

And , the transformation is a vertical stretching by a factor of 2

And , a horizontal right shift by 8 and a vertical down shift by 5

Hence , the transformation of function is stretching by a factor of 2 and translated 8 units right and 5 units down

To learn more about transformation of function click :

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Answer:

D

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Use the values of  a ,  b , and  c  to find the discriminant.

Answer:

y=650+15x

Step-by-step explanation:

y=mx+b, b is starting amount, m is the multiplier for the x

uwu

Answer:

Step-by-step explanation:

The common ratio is 3, so multiply the numbers of the pattern by 3. So 1x3 is 3, 3x3 is 9, 9x3 is 27, 27x3 is 81, 81x3 is 243, and just continue until you're on the 7th number; 1 was the first, 3 was the second and 9 was the third.

Answer:

78

Step-by-step explanation:

Answer: 76

Step-by-step explanation:

48 + 56 = 104

180 - 104 = 76

Answer:

2 units to the right

1 units up

Step-by-step explanation:

Answer:

120°

Step-by-step explanation:

construct a line parallel to the two parallel lines through x

x = 70 + 50 = 120

Answer:

[tex]x = \frac{2}{3}[/tex]

Step-by-step explanation:

Given

See attachment for triangles

Required

Find x

First, calculate tan A

From the first triangle:

[tex]tan\ A= \frac{x + 2}{x}[/tex]

Next, calculate tan B

From the second triangle:

[tex]tan\ B= \frac{4}{3x-1}[/tex]

[tex]tan\ A = tan\ B[/tex]

So, we have:

[tex]\frac{x + 2}{x}= \frac{4}{3x-1}[/tex]

Cross Multiply

[tex](x + 2)(3x - 1) = 4 * x[/tex]

Open brackets

[tex]3x^2 + 6x - x - 2 = 4x[/tex]

[tex]3x^2 + 5x - 2 = 4x[/tex]

Collect Like Terms

[tex]3x^2 + 5x - 4x- 2 =0[/tex]

[tex]3x^2 + x- 2 =0[/tex]

Expand

[tex]3x^2 + 3x - 2x- 2 =0[/tex]

Factorize:

[tex]3x(x + 1) - 2(x+ 1) =0[/tex]

Factor out x + 1

[tex](3x - 2)(x +1) = 0[/tex]

Split:

[tex]3x - 2 = 0\ or\ x + 1 = 0[/tex]

[tex]x = \frac{2}{3}\ or\ x = -1[/tex]

x can not be negative, so:

[tex]x = \frac{2}{3}[/tex]