If Jon has 26 apples and ate four how many does he have

Please help me! Given (x+a)(x+b) = x^2+x-12, what is the value of a^2+b^2

Sonja [21]

(x + 4) (x - 3)
a = 4
b = -3

a^2 + b^2 = ...
= 4^2 + (-3)^2
= 16 + 9
= 25

4 0

3 years ago

A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythag

Sveta_85 [38]

Answer:

$\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

$\displaystyle A_{\text{surface}}=B+\dfrac{1}{2}\times P \times s$

where B stands for Base area

and P for Base Parimeter

so

$\sf\displaystyle \: 144=(8 \times 8)+\dfrac{1}{2}\times (8 \times 4) \times s$

now we need our algebraic skills to figure out s

simplify parentheses:

$\sf\displaystyle \: 64+\dfrac{1}{2}\times32\times s = 144$

reduce fraction:

$\sf\displaystyle \: 64+\dfrac{1}{ \cancel{ \: 2}}\times \cancel{32} \: ^{16} \times s = 144 \\ 64 + 16 \times s = 144$

simplify multiplication:

$\displaystyle \: 16s + 64 = 144$

cancel 64 from both sides;

$\displaystyle \: 16s = 80$

divide both sides by 16:

$\displaystyle \: \therefore \: s = 5$

now we'll use Pythagoras theorem to figure out height

according to the theorem

$\displaystyle \: {h}^{2} + (\frac{l}{2} {)}^{2} = {s}^{2}$

substitute the value of l and s:

$\displaystyle \: {h}^{2} + (\frac{8}{2} {)}^{2} = {5}^{2}$

simplify parentheses:

$\displaystyle \: {h}^{2} + (4 {)}^{2} = {5}^{2}$

simplify squares:

$\displaystyle \: {h}^{2} + 16 = 25$

cancel 16 from both sides:

$\displaystyle \: {h}^{2} = 9$

square root both sides:

$\displaystyle \: \therefore \: {h}^{} = 3$

recall the formula of a square pyramid

$\displaystyle V_{pyramid}=\dfrac{1}{3}\times A\times h$

where A stands for Base area (l²)

substitute the value of h and l:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times \{8 \times 8 \}\times 3$

simplify multiplication:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times 64\times 3$

reduce fraction:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{ \cancel{ 3 \: }}\times 64\times \cancel{ \: 3}$

hence,

$\sf\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

8 0

2 years ago

Answer it answer it answer it

Usimov [2.4K]

Answer:

The correct option is;

C. 52.2 × 4.4 × 2 + 47.8 × 4.4 × 2

Step-by-step explanation:

The area of the square frame is the area of the inner square subtracted from the area of the outer square

Which gives;

52.2² - 47.8² = 440

Therefore;

Option A. 52.2² - 47.8² is a correct way of finding the area of the square frame

Option B. 2 × ((52.2×2.2) + (47.8×2.2)) = 440, is a correct way of finding the area of the square frame

Option C. 52.2 × 4.4 × 2 + 47.8 × 4.4 × 2 = 880, is not a correct way of finding the area of the square frame

The error is the thickness is 2.2 not 4.4

Option D. 100×(52.2 - 47.8) = (52.2 + 47.8) × (52.2 - 47.8) = 52.2² - 47.8² = 440, is a correct way of finding the area of the square frame

5 0

2 years ago

Triangle ABC has vertices A(–2, –3), B(–5, –3), and C(–4, –2). The triangle is rotated 90° counterclockwise around the origin.

Ulleksa [173]

The rule for this rotation is (x, y) converted into (-y, x). So, to find the answer you would make the y negative and switch the values in the ordered pair. A would be (3, -2), B would be (3, -5), and C would be (2, -4). So, your answer would be B. Hope this helps!

4 0

2 years ago

Read 2 more answers

Write as an expression and simplify:<br> The square of the difference of x and 8y

lukranit [14]

Answer:

x² - 16xy + 64y²

Step-by-step explanation:

The difference of x and 8y is x - 8y

The square of the difference is (x - 8y)² = (x - 8y)(x - 8y)

Expand by multiplying each term in the second factor by each term in the first factor, that is

x(x - 8y) - 8y(x - 8y) ← distribute both parenthesis

= x² - 8xy - 8xy + 64y² ← collect like terms

= x² - 16xy + 64y²

6 0

3 years ago