Geometry: fill in the blanks, ASAP! It’s urgent

hodyreva [135]

Similarities: They both are polynomials of degree 2, both of their graphs is a parabola, both have either 2 or 0 real solutions, they are both continuous functions over R
(DOS= difference of two squares, PST=perfect square trinomial
Differences: PST has three terms, whereas the difference of squares has 2. PST's factors are both the same, whereas DOS's elements are conjugates of each other. DOS can always be factored into two distinct polynomials with rational coefficients, whereas PST has two same polynomial factors.

7 0

3 years ago

If a = 7 and b = 11, what is the measure of ∠B? (round to the nearest tenth of a degree)

Naddik [55]

Answer:

57.5 degrees

Step-by-step explanation:

Assuming this is a triangle

a is adjacent is ∠B

b is opposite of ∠B

Use the inverse tangent equation: $tan^{-1} (11/7)$

This equals to 57.52880771

3 0

3 years ago

What is the fourth term in the binomial expansion (a+b)^6)

Dafna11 [192]

Answer:

$20a^3b^3$

Step-by-step explanation:

Binomial Series

$(a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n$

Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Example: 4! = 4 × 3 × 2 × 1

Therefore, the fourth term in the binomial expansion (a + b)⁶ is:

$\implies \dfrac{n!}{3!(n-3)!}a^{n-3}b^3$

$\implies \dfrac{6!}{3!(6-3)!}a^{6-3}b^3$

$\implies \dfrac{6!}{3!3!}a^{3}b^3$

$\implies \left(\dfrac{6 \times 5 \times 4 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}{3 \times 2 \times 1 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}\right)a^{3}b^3$

$\implies \left(\dfrac{120}{6}\right)a^{3}b^3$

$\implies 20a^3b^3$

7 0

2 years ago

Bella and Heather put some money into their money boxes every week. The amount of money (y), in dollars, in their money boxes af

Hatshy [7]

Answer:

$\boxed{ \text{B. 10 weeks, \$310 }}\\$

Step-by-step explanation:

We have two conditions:

$\begin{array}{lrcll}(1) & y & = & 25x + 60 & \\(2) & y & = & 30x + 10 & \\ & 25x + 60 & = & 30 x + 10 & \text {Set (1) = (2)} \\ & 50 & = & 5x & \text{Subtracted 25x from each side} \\& x & = & 10 &\text{Divided each side by 5} \\\end{array}\\$ $\\\boxed{ \textbf{The number of weeks is }x = 10}\\$

Bella: y = 25x + 60 = 25(10) + 60 = 250 + 60 = 310

Heather: y = 30x + 10 = 30(10) + 10 = 300 + 10 = 310

7 0

3 years ago

James has a certain amount of money. If he buys $3$ pens and $2$ pencils, he will have $\$2$ left over. If he buys $2$ pens and

labwork [276]

The cost of pen and pencils are related to the number that can be bought

with a given amount of money.

$\underline{The \ ordered \ pair \ (a, \, b) \ is \ (6, \, 2)}$

Reasons:

The given parameters are;

If the number number of pens and pencils James buys = 3 pens and 2 pencils, the amount James will have left = $2

If the number of pens and pencils James buys = 2 pens and 3 pencils, the amount James will have left = $6

The amount of money Judith has = The amount of money with James

The number of pens and pencil James and Judith can buy = 6 pens and 6 pencils

The cost of one pen = a

The cost of one pencil = b

Required:

To find the ordered pair (a, b)

Solution:

Let X represent the initial amount of money James has, we get;

X - (3·a + 2·b) = 2...(1)

X - (2·a + 3·b) = 6...(2)

2·X = 6·a + 6·b...(3)

Therefore;

X = (6·a + 6·b) ÷ 2 = 3·a + 3·b

Which from equation (1) gives;

3·a + 3·b - (3·a + 2·b) = 2

3·a + 3·b - 3·a - 2·b = 2

3·b - 2·b = 2

b = 2

Subtracting equation (1) from equation (2) gives;

(X - (2·a + 3·b)) - (X - (3·a + 2·b)) = 6 - 2 = 4

-2·a - 3·b + 3·a + 2·b = 4

a - b = 4

a = 4 + b

∴ a = 4 + 2 = 6

a = 6

$\underline{The \ ordered \ pair \ (a, \, b) \ is \ (6, \, 2)}$

Learn more about word problems and simultaneous equations here:

brainly.com/question/14294864

8 0

2 years ago