All together Maria and Nick had $12. After Maria spent 30% of her money and Nick spent 50 % of his money, Maria and Nick were left with the same amount. How much money did Nick have to begin with?

Answer:

It would be 4.

Step-by-step explanation:

Alright, this is a 30-60-90 special triangle. With special triangles, there is a formula that you can use to find unknown side lengths of a triangle if you know the angles of it.

With a 30-60-90 triangle, the sides opposite of these angles are:

30 degrees : x

60 degrees: x√3

90 degrees: 2x

With this, we can see that opposite of the 60 degrees is the length 2√3. From this, it can be found that the opposite of the 30 degrees would be 2, given the formula of the special triangle. Lastly, the unknown value would be 4, since it is two times this amount.

Answer:

x = 4

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2\sqrt{3} }{x}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

[tex]\sqrt{3}[/tex] x = 4[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )

x = 4

Answer:

Grey Hairs? Try some of our free Pi-Lights

Step-by-step explanation:

Answer:

We are finding hypotenuse:

6^2 + 8^2

36 + 64 = 100

Now we need to find a number that should be squared to equal 100.

10^2 = 100!

10 is your answer.

Answer:

[tex]130cm^{2}[/tex]

Step-by-step explanation:

1) Calculate the entire rectangle and subtract the right triangle area

15 x 10 = 150 Entire rectangle area

(5 x 8) ÷ 2 = 20 Triangle area

150 - 20 = 130 Area of shaded region

Answer: 28 i think or 12

Step-by-step explanation:

Step-by-step explanation:

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Answer:

<2= 65°

<3= 65°

<4= 115°

<5= 115°

<6= 65°

<7=65°

<8=115°

Answer: A and D are the correct answers.

Step-by-step explanation:

Answer:

5/6

Step-by-step explanation:

So to do this, lets convert all of these fractions into decimals by dividing:

5/6 --> 0.833...

7/12 --> 0.583...

4/7 --> 0.571...

2/3 --> 0.66...

From this, it can be see that it is 5/6, since it is a larger decimal compared to the other choices.

Answer:

B. y > 14

y which is students age is greater than 14

Answer:

28.58 pounds, about 29 pounds

Step-by-step explanation:

Poultry meat with bones ; divide number to be served by 2.5

Meat with little or no bone ; divide number to be served by 3.5

If number of guests to be served = 100

Meat served = 100

The number of pounds of chicken required :

Number of guests to be served / meat served

Hence,

100 / 3.5

= 28.58 ; which is about 29 pounds

Answer:

43

Step-by-step explanation:

Answer:

Hello There!!

Step-by-step explanation:

342 + x = 782 -342

x=440

hope this helps,have a great day!!

~Pinky~

Answer:

b

Step-by-step explanation:

you can take the rectagel and you x the rectagel

Answer:

Step-by-step explanation:

I need help

Answer: 1306.5 m^3

Step-by-step explanation:

1. The formula for the volume of a cylinder is: V=[tex]\pi[/tex]r^2h

2. If you substitute the values into the equation, you get

V = pi * 5.7^2 * 12.8 = 1306.5

3. 1306.5 is already to the nearest tenth, so that is the answer.

Answer:

60 :)

Step-by-step explanation:

The middle two numbers are 59 and 61 so you add them together and divide by 2.

Answer:

The percentage is 1/2 * 2/5 = 1/5 = 20%.

Answer:

The correct answer is 20%

Step-by-step explanation:

If you were to pick two marbles from the pile, there would be 30 different possible combinations. Out of the 30 possible combinations, 6 of them meet the requirement of green marble on the first pick and red marble on the second pick. The fraction that represents the situation would be [tex]\frac{6}{30}[/tex] or [tex]\frac{1}{5}[/tex], which would be equal to 20%, so that is the correct answer.

from blank one five

from blank two is right

The cost of a t-shirt is £3 and the cost of a hat is £2.

What is a linear equation?

When an equation contains one or more variables with exponents as 1 then such equations are linear equations.

For example, 3x+2y=9 and 4y=6. The first equation is a linear equation with two variables and the second equation is with the linear equation in one variable.

Let the cost of a t-shirt is £m and the cost of a hat is £n.

Formulate two linear equations using the given statements in the question.

[tex]2m+3n=12\,\,\, ...(1)\\5m+4n=23\,\,\, ...(2)[/tex]

Obtain the value of m from equation (1).

[tex]2m=12-3n\\m=\frac{12-3n}{2}[/tex]

Substitute the obtained value of m into equation (1) and find n.

[tex]5 \times(\frac{12-3n}{2})+4n=23\\ 60-15n+8n=46\\14=7n\\n=2[/tex]

Substitute the value of n into [tex]m=\frac{12-3n}{2}[/tex]and obtain the value of m.

[tex]m=\frac{12-3(2)}{2}\\=\frac{12-6}{2}\\ =\frac{6}{2}\\ =3[/tex]

Thus, the cost of a t-shirt is £3 and the cost of a hat is £2.

Learn more about linear equations at https://brainly.com/question/11897796

#SPJ2

Answer:

144

Step-by-step explanation:

Answer:

Equal volumes

Step-by-step explanation:

Given

[tex]h \to[/tex] height of cone

[tex]d \to[/tex] diameter of cone

[tex]H \to[/tex] height of cylinder

[tex]D \to[/tex] diameter of cylinder

Such that:

[tex]d = 2D[/tex]

[tex]h =\frac{3}{4}H[/tex]

Required

The relationship between the volumes

The volume of a cylinder is:

[tex]V_1 = \pi R^2H[/tex]

Where

[tex]R = 0.5D[/tex]

So:

[tex]V_1 = \pi (0.5D)^2H[/tex]

[tex]V_1 = \pi *0.25*D^2H[/tex]

[tex]V_1 = 0.25\pi D^2H[/tex]

The volume of the cone is:

[tex]V_2 = \frac{1}{3}\pi r^2h[/tex]

Where

[tex]r =0.5d[/tex]

[tex]r = 0.5 * 2D[/tex]

[tex]r = D[/tex]

and

[tex]h =\frac{3}{4}H[/tex]

So, we have:

[tex]V_2 = \frac{1}{3}\pi * D^2 * \frac{3}{4}H[/tex]

[tex]V_2 = \frac{1}{4}\pi * D^2H[/tex]

[tex]V_2 = 0.25\pi * D^2H[/tex]

[tex]V_2 = 0.25\pi D^2H[/tex]

So, we have:

[tex]V_1 = 0.25\pi D^2H[/tex]

[tex]V_2 = 0.25\pi * D^2H[/tex]

[tex]V_1 = V_2[/tex]

Answer: : When a cone and cylinder have the same height and radius the cone will fit inside the cylinder. The volume of the cone will be one-third that of the cylinder. If the radius or height are different, then there is no relationship between them.

Step-by-step explanation:

Answer:

1=  0.109

2= 3.46

3 = -(minus)1.24

Step-by-step explanation:

Answer:

See answers below.

Step-by-step explanation:

All of these use the same idea: multiply numerator and denominator by the conjugate radical (an identical expression but with the sign between terms changed).

[tex]\frac{1}{13-\sqrt{15}}\cdot\frac{13+\sqrt{15}}{13+\sqrt{15}}=\frac{13+\sqrt{15}}{169-15}}\\\\=\frac{13+\sqrt{15}}{154}[/tex]

[tex]\frac{1}{\sqrt{13}-\sqrt{11}} \cdot \frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}+\sqrt{11}}=\frac{\sqrt{13}+\sqrt{11}}{13-11}\\\\=\frac{\sqrt{13}+\sqrt{11}}{2}[/tex]

[tex]\frac{1}{\sqrt{21}+\sqrt{29}}\cdot\frac{\sqrt{21}+\sqrt{29}}{\sqrt{21}+\sqrt{29}}=\frac{\sqrt{21}+\sqrt{29}}{21-29}\\\\=\frac{\sqrt{21}+\sqrt{29}}{-8}[/tex]

Note:  Here's an example of what happens when you multiply conjugate radicals.

[tex](\sqrt{13}-\sqrt{11}})(\sqrt{13}+\sqrt{11})=13-\sqrt{11}\sqrt{13}+\sqrt{13}\sqrt{11}-11=13-11[/tex]

When you FOIL those binomials, the square roots go away!

The answer is 493 if you don't add the decimal.

If you do it's 493.5.

You're Welcome :)

Answer:

a⁸=112 is the answer.

Step-by-step explanation:

a⁸=32(1/2)⁷

a⁸=32(7/2)

a⁸=112

Answer:

x=9

Step-by-step explanation:

You would change it to x^2 = 81 which is 9.

Answer:

a b c and f

Step-by-step explanation:

rectangle parallelogram square and rhombus