Expand and simplify
(4 + √2 }(6-√2)
Give your answer in the form b + c√2
​

Answer:

Remember that the Pythagorean's theorem says that:

For a triangle rectangle with hypotenuse H and catheti A and B:

H^2 = A^2 + B^2

Here we also need to remember that the area of a square of side length L is:

area = L^2

Now let's solve this.

First, we start with two squares, one of side length a and the other of side length b.

Such that the complete area in the first image is:

area = a^2 + b^2

Now we draw two triangle rectangles with catheti a and b, and with hypotenuse c.

in step 3, we rotate those triangles in order to make a larger square, with side length c, with an area equal to:

area = c^2

Notice that we never added more shapes, so the area of the image did not change in all this process, then the initial area must be equal to the final area:

a^2 + b^2 = area = c^2

a^2 + b^2 = c^2

And remember that a and b are the catheti of the triangles, and c is the hypotenuse, then this is the Pythagorean's theorem.

1: yes

2:C

3:D

Step-by-step explanation:

a number is missing in no.3

the ans in 3 is -1,0,5,1,5,6

Answer: C. 1,485 cubic feet

Step-by-step explanation:

Ur welcome :)

Answer:

I am assuming the storage shed is shaped like a rectanglular prism.

v=lwh

v=9*15*11

v=1485 cubic feet

Answer is C.

Answer:

The bill is $1837.5

Step-by-step explanation:

Given

[tex]B = Bills[/tex]

[tex]T = Temperature[/tex]

[tex]B\ \alpha\ \frac{1}{T}[/tex] --- The variation

T = 35; when B = 210

Required

Find B when T = 40

[tex]B\ \alpha\ \frac{1}{T}[/tex]

Express as an equation

[tex]B = \frac{k}{T}[/tex]

Make k the subject

[tex]k = BT[/tex]

T = 35; when B = 210

[tex]k = 35 * 210[/tex]

[tex]k = 7350[/tex]

When T = 40, we have:

[tex]k = BT[/tex]

[tex]7350 = B * 40[/tex]

Make B the subject

[tex]B = \frac{7350}{4}[/tex]

[tex]B = 1837.5[/tex]

Answer:

The answer can be 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, or 3.9.

Step-by-step explanation:

All of those work

Answer:

answer option number 4

Step-by-step explanation:

Answer:

p(2,-4) q(3,-1) r(4,-4)

Step-by-step explanation:  Reflecting across the y axis changes the x coordinates.

You're using Newton's method to find the roots to

f(x) = g(x)   →   x ⁶ = cos(x)

Recast this as finding the roots to

h(x) = f(x) - g(x) = x ⁶ - cos(x)

First, get the tangent line approximation L(x) to h(x) at an arbitrary starting point x = x₀ ; in a small neighborhood of x₀, we have

h(x) ≈ L(x) = h(x₀) + h'(x₀) (x - x₀)

Find the root to the tangent line function:

0 = h(x₀) + h'(x₀) (x - x₀)   →   x = x₁ = x₀ - h(x₀)/h'(x₀)

x₁ is the first approximation of a root to h(x). Repeat the process - that is, take the tangent line to h(x) at x₁ to find the next approximation x₂, and so on - until you meet the required condition.

For the smaller root, take x₀ = -π/2 :

x₀ ≈ -1.5708

x₁ = x₀ - h(x₀)/h'(x₀) ≈ -1.31348

x₂ = x₁ - h(x₁)/h'(x₁) ≈ -1.11366

x₃ = x₂ - h(x₂)/h'(x₂) ≈ -0.982446

x₄ = x₃ - h(x₃)/h'(x₃) ≈ -0.928013

x₅ = x₄ - h(x₄)/h'(x₄) ≈ -0.920039

x₆ = x₅ - h(x₅)/h'(x₅) ≈ -0.919887

Stop at x₆ because |x₆ - x₅| ≤ 0.001.

For the larger root, you can start the process over with a different seed for x₀, such as π/2. But since h(x) is an even function and symmetric about the y-axis, the larger root will just be the same root with positive sign, 0.919887.

Answer:

7

Step-by-step explanation:

to find the circumference of a circle the equation is C=πd where C is circumference, d is diameter, and using 3.14 for π

once we plug in the known information we are left with

22=(3.14)d

all that's left is to solve for d

22=(3.14)d

22/3.14=(3.14)/3.14 d

7=1d

7=d

Answer:

45 mushrooms

Step-by-step explanation:

Ella and Ola had 70 mushrooms altogether. 5/9 of Ella's mushrooms are brown and 2/17 of Ola's mushrooms are white. How many mushrooms did Ella have?

Let the amount of Ella's mushrooms be x

Let the amount of Ola's mushrooms be y

If Ella and Ola had 70 mushrooms altogether, then;

x + y = 70

5/9 x = brown

2/17 y = white

Substiute

x + 5/9 x = 70

14 x/9 = 70

14x = 9 * 70

x = 9* 5

x = 45

Hence Ella has 45 mushrooms

Answer:

c

Step-by-step explanation:

one of the sides of the square is equal to one of the sides of the triangle that is perpendicular to the horizontal side of the triangle.

in order to find x we need to use the pythagorean theorem

(6)²+(3)²=x²

36+9=x²

x²=45

x=3√5

which is c

Answer:

5 cups of flour

Step-by-step explanation:

if mandy wants a total of 10 dozen muffins, and 2.5 dozen of muffins require 1.25 cups, you'd first have to divide 10 by 2.5 to get the answer of 4. this means that per 2.5 dozen muffins she will need 4 times the amount of materials in order to get a total amount of 10 dozen muffins. therefore if 2.5 dozen muffins require 1.25 cups of flour, then you'd need to multiply 1.25 by 4 which is equivalent to 5 cups of flour.

written math;

10/2.5=4

1.25*4=5

answer=5 cups of flour

Answer:

D. 76

Step-by-step explanation:

because students that has 5 absences and less most likely to get higher than 75 marks. The student who has 8 absences studied at home, he's a genius

Answer:

Corson had a better performance at the skills competition.

Step-by-step explanation:

In order to determine which player had a better performance at the skills competition, we need to find the percentage performance of both the players.

Therefore,

Corson's percentage performance

[tex] =\frac{5}{7}\times 100= 71.43%[/tex]

Charleigh's percentage performance

[tex] =\frac{3}{5}\times 100= 60%[/tex]

[tex] \because [/tex] Corson's percentage performance > Charleigh's percentage performance

So, Corson had a better performance at the skills competition.

Answer:

0.211 = 21.1% probability that 2 flights of BlueSky Air arrive late

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either they arrive late, or they do not. The probability of a flight arriving late is independent of any other flight. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

BlueSky Air has the best on-time arrival rate with 80% of its flights arriving on time.

This means that 100 - 80 = 20% are late, which means that [tex]p = 0.2[/tex]

Randomly selecting 16 BlueSky Air flights

This means that [tex]n = 16[/tex]

What is the probability that 2 flights of BlueSky Air arrive late?

This is P(X = 2).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{16,2}.(0.2)^{2}.(0.8)^{14} = 0.211[/tex]

0.211 = 21.1% probability that 2 flights of BlueSky Air arrive late

Answer:

Speed of first plane is  350 miles per hour

Speed of second plane is 100 miles per hour

Step-by-step explanation:

Let the speed of the second plane be X

Then the speed of the first plane will be 3.5 X

Distance travelled by first plane is 9.5 *X

Distance travelled by second plane is 9.5 * 3.5 X

Difference of distance between the two plane is

[tex]9.5 * 3.5 X - 9.5 *X = 2375\\23.75 X = 2375\\X = 100[/tex]miles per hour

Speed of first plane is 3.5 *100 = 350 miles per hour

Speed of second plane is 100 miles per hour

Answer:

Future value using simple interest = $10,880

Future value using Compound interest = $11,240 (Approx.)

Step-by-step explanation:

Given:

Principal Amount = $8,000

Rate = 12% = 0.12

Number of year = 3

Find:

Future value

Computation:

Future value using simple interest

Future value = P + (P)(R)(T)

Future value = 8,000 + (8,000)(0.12)(3)

Future value = 8,000 + 2,880

Future value using simple interest = $10,880

Future value using Compound interest

Future value = P[1+r]ⁿ

Future value = 8,000[1+0.12]³

Future value = 8,000[1.12]³

Future value using Compound interest = $11,240 (Approx.)

Answer:

39.5

Step-by-step explanation:

it's how many times 0.08 goes into 3.16

Answer: 2.53

Step-by-step explanation:

you divide it 0.08÷3.16 and like it would give you a large answer but just multiply it by 100 so you will get 2.53 and if you divide that by 3.16 it would give you 0.08 so the answer is "2.53"

0.08 ÷ 3.16 =0.0253164557 x 100= 2.53

Answer:

C

Step-by-step explanation:

We can calculate the area of triangles ABD and DBC, and then add them together to get the area of the whole quadrilateral.

[tex]A = \frac{11 \times 3 + 7 \times 9}{2} = \frac{33 + 63}{2} = \frac{96}{2} = 48[/tex]

Answer:

Since the fraction of this is very obviously 24/30, here's how you can get a decimal out of that:

First, you simplify that fraction.

24/30 = 4/5, since 5x6 is 30 and 6x4 is 24

Now, it's pretty easy to convert 4/5 into a decimal.

This is how I like to do it. You re-convert the fraction one step higher, so it's 8/10, and you just turn it into 0.8, since it's all out of 10.

I hope I helped, and I'd appreciate a "Brainliest"! ☺

Answer: 45

Step-by-step explanation:

Sum is addition so it would be

28+17=45

Answer:

45

Step-by-step explanation:

there are 47 cows in total !

Answer: -(m/n) = (m/n)^-1 = 1 / (m/n)

Hence, a^-(m/n) = (1 / a^(m/n)) where m,n are rational numbers.

For example: let 1/2 be rational number and 4 be real number then, 4^-(1/2) = 0.5 = 1/(4^(1/2))

Answer: Don't put if this is't right. based on my calculatios I got B

Step-by-step explanation:

Answer:

24x^2+41x-35

Step-by-step explanation:

(3x+7)(8x-5)

24x^2+56x-15x-35

24x^2+41x-35

i would say the answer is 5/8

because c is 3/4

Step-by-step explanation:

The original function is f(m) = 5(1.07)^m, with the m as an exponent

part A) if the final length is 9.19, we can set f(m) = 9.19 and solve for m

plugging it into a calculator, I get m = ~8.99, so a bit less than 9. therefore, a reasonable domain might be all the m values 9 or below, or m ≤ 9

part B) the y-intercept of a function is the value of the independent variable when the dependent variable = 0. the two variables in your problem are height and number of months - which one do you think is the independent one, and which one is dependent? then re-interpret "value of the independent variable when the dependent variable = 0" in terms of the actual quantities that the variables represent

part C) average rate of change from m = 1 to m = 9

f(9)−f(1)9−1

evaluate, and think about what that represents in terms of height and number of months

Answer:

My name is lil uzi vert

Step-by-step explanation:

maybach maybach