When a trinomial is factored as (x + p)(x + q), what is the sum of p and q? A.The constant term of the trinomial B.The coefficient of the x-term of the trinomial C.The coefficient of the x2-term of the trinomial D.The degree of the trinomial

Answers

Answer 1

Answer: It is B, the coefficient of the x-term. When you multiply this out, you get x*x+x*q+x*p+p*q, or x^2+x(p+q)+p*q
Notice how the x term is multiplied by p+q.

Hope this helps!

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NEED HELP NOW!!!!!!!a 5 inch bamboo shoot doubles in height every 3 days. if the equation y=ab^x , where x is the number of doubling periods , represents the height of the bamboo shoot, what are the values of a and b?

Answers

Answer a = 5 and b = 2.

Procedure

Initially means x = 0, then

5 = a*b^0 = a*1 = a, then a = 5

When x = 1, the height is the double of 5, i.e 10 and

10 = a.b^1 = a.b ⇒ b = 10/a = 10/5 = 2

The a = 5 and b = 2, so the equation is y =5(2)^x

Figure WXYZ is a rectangle with a semicircle added to its base.What is the perimeter of figure WXYZ? Use 3.14 to approximate pi.

Answers

Figure WXYZ is a rectangle that has a semicircle added to its base. The rectangle has a length of sixteen inches and a width of seven inches. The semicircle has a diameter equal to the length of the rectangle.

Given:
Rectangle: Length = 16 inches ; width = 7 inches
Semicirle added to its base, the length of the rectangle. Only one length.

We need to get the circumference of the semi circle and add the length and 2 widths of the rectangle.

Circumference of a circle = 2πr ⇒ 2 * 3.14 * 8 inches = 50.24
Circumference of a semicircle = 50.24/2 = 25.12 inches
Widths of the rectangle = 2 * 7 inches = 14 inches

Perimeter of the figure = 25.12 in + 14 in + 16 in = 55.12 inches.

what is the exact value of sin 22.5 degrees using the sum, difference, half, or double angle formulas and the exact value chart in the solution.

Answers

$cos 2x=1-2sin^2x \n cos 45^0=1-2sin^2(22,5)^0 \n ( √(2) )/(2) =1-2sin^2(22,5)^0 \to sin(22,5)^0= \frac{ \sqrt{2- √(2) } }{2}$

Moria solves a problem on the board. What error did Moria make and how can she correct it? 12x + 10 = 54- 10x

Answers

Answer:

12x + 10 = 54 - 10x

12x + 10x = 54 - 10

22x = 44

divide both side by 22

22x= 44

22 22

x = 2

At Joe's Pizzeria, small pizzas cost $7.50, and large pizzas cost$11.00. One day between 3:00 PM and 9:00 PM, Joe sold 100 pizzas
and took in $848. How many more small pizzas than large pizzas did
Joe sell during that 6-hour period?
(A) 28
(B) 44
(C) 56
(D) 72

Answers

Answer:

Option B. 44 is the correct answer

Step-by-step explanation:

Let l be the number of large pizzas and s be the number of small pizzas

Then according to the given statement the equations will be:

$l+s = 100\ \ \ Eqn\ 1\n11l+7.5s = 848\ \ \ Eqn\ 2$

From equation 1

$l = 100-s$

Putting in equation 2

$11(100-s)+7.5s = 848\n1100-11s+7.5s = 848\n-3.5s+1100 = 848\n-3.5s = 848-1100\n-3.5s = -252\n(-3.5s)/(-3.5) = (-252)/(-3.5)\ns = 72$

Putting s=72 in equation 1

$l+72 = 100\nl = 100-72\nl = 28$

How many more small pizzas means we have to find s-l

So,

s-l = 72-28 = 44

Hence,

Option B. 44 is the correct answer

The area of the sector formed by the 110 degree central angle is 50 units squared. What is the radius of this circle??

Answers

Answer:

Area of the sector(A) is given by:

$A = \pi r^2 \cdot (\theta)/(360^(\circ))$

where,

r is the radius of the circle and $\theta$ is the central angle in degree.

As per the statement:

The area of the sector formed by the 110 degree central angle is 50 units squared.

⇒A = 50 units squared and $\theta = 110^(\circ)$

Substitute these in [1] and use 3.14 for pi we have;

$50 = 3.14 \cdot r^2 \cdot (110)/(360)$

⇒ $50 = 0.959444446r^2$

Divide both sides by 0.959444446 we get;

$r^2 = 52.1134915$

⇒ $r = √(52.1134915)$

Simplify:

r ≈ 7.22 units

Therefore, the radius of this circle is, 7.22 units

Hello,
Let make a rule of three.

For 360° area of the circle is π R²
For 1° ............of the sector .. πR²/360
For 110° ............................... πR²*110/360 =50(units squared)

R²=50*360/(110π)
==>R=6*√(50/(11π))≈7,217137....(units)

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