Mr. Rockwell's class is holding a canned food drive for charity. Kim collected 10 more cans than Stephanie. Natasha collected twice as many cans as Kim. If they collected 130 cans altogether, how many cans did Kim collect?

Given:

The figure of a right triangle.

To find:

The value of x.

Solution:

In a right angle triangle,

[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

In the given right triangle,

Hypotenuse = 15

Perpendicular = 12.5

Now,

[tex]\sin x^\circ=\dfrac{12.5}{15}[/tex]

[tex]\sin x^\circ=0.83333[/tex]

[tex]x^\circ=\sin^{-1}0.83333[/tex]

[tex]x^\circ =56.442345^\circ[/tex]

[tex]x\approx 56[/tex]

Therefore, the equation used to find x is [tex]\sin x^\circ=\dfrac{12.5}{15}[/tex] and the value of x is 56.

Answer:

26

Step-by-step explanation:

Answer:

Distribute

Subtract   two from both sides of the equation

Simplify

and that's your solution

which should be t=4

Step-by-step explanation:

Answer:Hence, x = 5, y = 0 is the required solution.

Step-by-step explanation:

Answer:

There is only one solution

Step-by-step explanation:

Answer:

Explicit : [tex]a_n=3(2)^{n-1}[/tex]

Recursive: a₁ = 1

                  [tex]a_n=a_{n-1}(2)[/tex]

Step-by-step explanation:

We have to write the recursive formula for the geometric sequence with second term 2 and third term 12.

Geometric sequence will be in the form of,

a, ar, ar², ar³,...........

Here, r = common ratio

a = first term of the sequence

Here, ar = 6 ------(1)

And ar² = 12 ------(2)

By dividing equation (2) by (1),

[tex]\frac{ar^2}{ar}=\frac{12}{6}[/tex]

r = 2

From equation (1),

a(2) = 6

a = 3

Recursive formula of a geometric sequence is given by,

a₁ = a

[tex]a_n=a_{n-1}(r)[/tex]

Therefore, for the given sequence,

a₁ = 1

[tex]a_n=a_{n-1}(2)[/tex]

Similarly, explicit formula of the geometric sequence is given by,

[tex]a_n=a_1(r)^{n-1}[/tex]

[tex]a_n=3(2)^{n-1}[/tex]

Answer:

11 feet

Step-by-step explanation:

3 yards equals 9 feet because there are 2 feet in one yard. 2*3=9

9+2= 11

Answer:

-3 and 0 are like terms because both of them are numbers

Answer:

a is the answer for this question

Answer:

72.3

Step-by-step explanation:

So, to find the average you need to add all the numbers together and divide it by the amount of numbers there are, if that makes sense.

so in your question: 100 + 90 + 80 + 89 + 75 + 0= 434

and there are 6 numbers that you had to add together, so you divide 434 by 6, which is 72.3 so that's the answer! It's quite easy once you understand how to do it :)

Answer:

Q = (9, 4 )

Step-by-step explanation:

Use the midpoint formula and equate to the coordinates of the midpoint.

M = ([tex]\frac{x_{1}+x_{2} }{2}[/tex] ) , ([tex]\frac{y_{1}+y_{2} }{2}[/tex] )

let the coordinates of Q = (x, y ) , R = (- 7, 0 ) , then

[tex]\frac{x-7}{2}[/tex] = 1 ( multiply both sides by 2 )

x - 7 = 2 ( add 7 to both sides )

x = 9

and

[tex]\frac{y+0}{2}[/tex] = 2 ( multiply both sides by 2 )

y = 4

Thus Q = (9, 4 )

c is the answer

Answer:

Step-by-step explanation:

Answer:

10 makes this equation true

Step-by-step explanation:

2x -4 = 16 /+4

2x= 20 /÷2

x= 10

Test

2(10) - 4 = 16

20 - 4 = 16 Correct

Answer:

64 square units

Step-by-step explanation:

if you spilt up the polygon you can find the area of the square and triangle making up the square.

length * width = Area;   6 * 8 = 48 sq units for the square part

1/2 * base * height = Area;   1/2 * 4 * 8 = 16 sq units for the triangle part

then add the two areas together for the area of the entire polygon:

48 + 16 = 64 sq units

Answer:

It is already in an increasing order

1. 4x - 8 Highest

2. 3x - 2

3. 2x + 1

4. 1x - 0 Lowest

Step-by-step explanation:

1. 56

2. 25

3. 9

4. 1

Answer:

The sides of the equilateral triangle are 11.7 m.

Step-by-step explanation:

Let's find the area of the isosceles triangle:

[tex] A_{i} = \frac{bh}{2} [/tex]

Where:

b: is the base = 12 m

h: is the height

We can find the height by using Pitagoras:

[tex] x^{2} = \frac{b^{2}}{2} + h^{2} [/tex]    

Where:

x is the hypotenuse = side of the triangle = 10 m

[tex] h = \sqrt{x^{2} - \frac{b^{2}}{2}} = \sqrt{(10)^{2} - 6^{2}} = 8 m [/tex]

Then, the area is:

[tex] A_{i} = \frac{12*8}{2} = 48 m^{2} [/tex]

Now, since the area of the isosceles triangle is equal to the area of the equilateral triangle:

[tex] A_{e} = A_{i} = 48 m^{2} [/tex]

[tex] A_{e} = \frac{bh}{2} [/tex]

The height of the equilateral triangle is given by:

[tex] b^{2} = \frac{b^{2}}{2} + h^{2} [/tex]    

[tex] h = \sqrt{b^{2} - \frac{b^{2}}{2}} = \frac{b}{\sqrt{2}} [/tex]

Hence, the sides are:

[tex] A_{e} = \frac{1}{2}b\frac{b}{\sqrt{2}} = \frac{b^{2}}{2\sqrt{2}} [/tex]            

[tex] b = \sqrt{A*2\sqrt{2}} = \sqrt{48*2\sqrt{2}} = 11.7 m [/tex]      

Therefore, the sides of the equilateral triangle are 11.7 m.

I hope it helps you!      

Answer:

The sides must be  around     10.53 m

Step-by-step explanation:

You can calculate the area of isosceles  dividing into 2 equal right triangles

Once you know that the area of the isosceles is 48 m²,solve for the side of the equilateral triangle

Formula for the Area:    (A= area    a = side)

A = (√3* a² ) / 4

48= (√3* a² ) / 4

Multiply both sides by 4

192 =√3* a²

Divide both sides by√3               (   √3 = 1.732050....)

110.851303 =   a²

Square root on both sides

10 .5385...( 10.53 )  = a

Answer:

4.8%

Step-by-step explanation:

Answer:4.8

Step-by-step explanation:

Trust

Answer:

The answer is 0.0085 So I'm guessing less than one.

Answer:

The probability that none of the balls selected is red ²⁴/₉₁

Step-by-step explanation:

Given;

number of red balls, R = 5

number of white balls, W = 4

number of blue balls, B = 6

Total number of balls, = 5 + 4 + 6 = 15

Probability of selecting 3 none red balls = P(WWW) or  P(BBB) or P(WWB) or  P(WBW) or P(BWW) or P(BBW) or P(BWB) or P(WBB)

[tex]P = (\frac{4}{15} \times \frac{3}{14} \times \frac{2}{13} ) + (\frac{6}{15} \times \frac{5}{14} \times \frac{4}{13} ) + (\frac{4}{15} \times \frac{3}{14} \times \frac{6}{13} ) + (\frac{4}{15} \times \frac{6}{14} \times \frac{3}{13} ) + \\\\(\frac{6}{15} \times \frac{4}{14} \times \frac{3}{13} ) + (\frac{6}{15} \times \frac{5}{14} \times \frac{4}{13} ) + (\frac{6}{15} \times \frac{4}{14} \times \frac{5}{13} ) + (\frac{4}{15} \times \frac{6}{14} \times \frac{5}{13} )[/tex]

[tex]P = \frac{24}{2730} + \frac{120}{2730} + \frac{72}{2730} +\frac{72}{2730} + \frac{72}{2730} + \frac{120}{2730} + \frac{120}{2730} + \frac{120}{2730} \\\\P = \frac{720}{2730} \\\\P = \frac{24}{91} \\\\[/tex]

Therefore, the probability that none of the balls selected is red ²⁴/₉₁

Answer:

72km/h

Step-by-step explanation:

the formula of changing metres per second to km/h is 18/5 and kilometre per hour into metres per second is 5/8 in hope it helps.

Answer:

Step-by-step explanation:

From what I understand, you are trying to solve for a.

So,

d=g+2ac

d-g=2ac

(d-g)/2c=a

So,

a = (d-g) / 2c

Answer:

They donated 6%.

Step-by-step explanation:

The total sales were $9800.

The amount donated is $588.

We want to know what percent of 9800 is 588.

Let's make an equation.

what percent of 9800 is 588

x/100 • 9800 = 588

Divide by 9800.

x/100 = 0.06

Multiply by 100.

x = 6

They donated 6%.

Hope this helps!

Answer:

i think its second pythagreom therom

Step-by-step explanation:

because

Answer:f(x)=-16(x-1)^2+22

Step-by-step explanation:

The equation for the trajectory of ball in the air is h(t) = -16t² + 32t + 6.

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) =  lim h --> 0 (f(x + h) - f(x)) /(x + h - x).

It can also be said as the slope of the tangent for the  function at a given point.

Given that,

The maximum height reached by the ball  after 1 sec is 22 ft above ground.

And, the height at which it is thrown is 6 ft above the ground.

Which implies at 0 sec the height is 6 ft.

The quadratic function for the height can be written as,

h(t) = at² + bt + c

Substitute t = 0 to gat,

f(0) = a × 0² + b × 0 + c

=> c = 6

Now, for maximum height,

h'(t) = 0

=> 2at + b = 0

At maximum height t = 1

Then, the above expression becomes,

2a × 1 + b = 0

=> a = -b/2

Substitute t = 1 in h(t) = at² + bt + c to get,

22 = a + b + c

=> 22 = -b/2 + b + 6

=> b/2 = 16

=> b = 32

Then, a = -b/2

            = -32/2

            =-16

Thus substituting the corresponding values the equation can be written as h(t) = -16t² + 32t + 6.

Hence, the required equation for the path of the ball in the air is  h(t) = -16t² + 32t + 6.

To know more about differentiation click on,

https://brainly.com/question/24898810

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Answer:

top 8, middle 7, 16, bottom 13

Answer:

Area is A≈282.8 cm  

Step-by-step explanation:

Answer:

A=2(1+ √2)a2

482.84271

Step-by-step explanation:

:))

Answer:

1,344

Step-by-step explanation: So first I multiplied 1,200 by .03 because in order to multiply by a percent you need to move it decimal back two times. After you multiply 1200 x .03 = 36. Next you would do 36 x 4 for the 4 years and it would = 144. Then you would add 144 to the original because it's interest and you would end up with Colin having 1,344.

Step-by-step explanation:

12a-9a>-12+6

3a>-6/:3

a>-2

Answer: B

Step-by-step explanation:

Because they are on opposite sides and they are outside the parallel lines