Henry has quarters, dimes, nickels and pennies in a coin jar. He says that the total amount of money is two dollars and forty-one cents. He also claims that there are exactly twenty-three pennies. Let q be the number of quarters, d be the number of dimes, and n be the number of nickels. Which equation represents the relationship expressed above?
a. q + d + n = 23
b.q + d + n + 23 = 241
c. 25q + 10d + 5n + 23 = 2.41
d.25q + 10d + 5n + 23 = 241

Answer:

Area of a trapezium = 1/2(a+b)×h

where a and b are parallel sides of the trapezium

h is the height

First question

We must first find the height of the trapezium using Pythagoras theorem

That's

h² = 8² -3²

h =√ 64 - 9

h = √ 55m

a = 7m

b = 10+3 = 13m

Area of the trapezoid = 1/2(7+13)×√55

= 1/2×20×√55

= 74.16

= 74m² to the nearest tenth

Second question

We use sine to find the height

sin30° = h/12

h = 12 sin 30°

h = 6 in

Let the other half of the parallel side be x

To find the other half of the parallel side we use Pythagoras theorem

That's

x² = 12²- 6²

x = √144-36

x = √108

x = 6√3 in

So for this trapezoid

a = 9 in

b = (9 + 6√3) in

h = 6 in

Area of the trapezoid = 1/2(9 + 9+6√3) × 6

= 1/2(18+6√3)×6

= 85.176 in²

= 85 in² to the nearest tenth

Hope this helps you

Answer:

The first (left) trapezoid's area is [tex]10\sqrt{55}[/tex]m or ≈ 74.2m²

The second (right) trapezoid's area is [tex]54 +18\sqrt{3}[/tex] or ≈ 85.2 in²

Step-by-step explanation:

First trapezoid (left):

Because the first trapezoid is a normal trapezoid, we can use the equation [tex]A = \frac{a+ b}{2} * h[/tex] Where a is equal to one base length and b is equal to the other base length and h is the height of the trapezoid.

a = 7

b = 13

h = [tex]\sqrt{55}[/tex]   ([tex]3^{2}+h^{2} = 8^{2}[/tex])

Plug into the equation:

[tex]A = \frac{7+13}{2} *\sqrt{55}[/tex]

A = [tex]10\sqrt{55}[/tex] or ≈74.2m²

Second trapezoid (right):

Not a normal trapezoid (split into a triangle and a square)

Let's solve for the triangle first:

using [tex]sin(30) = \frac{x}{12}[/tex] to find the right-hand side of the triangle we get x = 6

because this is a 30 60 triangle, the last side has to be [tex]6\sqrt{3}[/tex]

Now we can calculate the area of the figure:

Triangle is [tex]\frac{1}{2} * 6 * 6\sqrt{3} = 18\sqrt{3}[/tex]

Rectangle is 6 * 9 = 54

Area = [tex]54 +18\sqrt{3}[/tex] or ≈ 85.2 in²

Answer:

[tex]2\sqrt{5}[/tex]

Step-by-step explanation:

[tex]\sqrt5-\sqrt{20}+\sqrt{45}[/tex]

It is the same process as in the last problem.

[tex]\sqrt5-2\sqrt{5}+3\sqrt{5}[/tex]

[tex]2\sqrt{5}[/tex]

Answer:

Your correct answer is 2√5

Step-by-step explanation:

√5 − √20 + √45 = 2√5

Answer:

Step-by-step explanation:

Lets start by defining the numbers in the equation.

This  equation is in slope-intercept form meaning that it is y=mx+b or y = b+mx they are both the same

In slope-intercept form,

Th equation is y=400+32x so now we know

For the first question the change per minute is the rate so it is 32.

For the second question the starting amount is the same as the y-intercept so it is 400.

Answer:

-12

Step-by-step explanation:

6 ÷ -1/2

Copy dot flip

6 * -2/1

-12

Answer:

Step-by-step explanation:

Answer:

d) y=(x+pi/2)

Step-by-step explanation:

edge 2020 correct & 100%

Answer:

ab = 1/2.

Step-by-step explanation:

The sides of the large square have length √5 while the sides of the small one have sides of length 2.

Each corner has a right triangle with legs of length a and b and hypotenuse 2.

So we have the system

a + b = √5

a^2 + b^2 = 2^2 = 4

Using the identity   a^2 + b^2 =  (a + b)^2 - 2ab:

4 = (√5)^2 - 2ab

4 = 5 - 2ab

2ab = 5 - 4 = 1

ab = 1/2.

Answer:

D

Step-by-step explanation:

12x + 6y = 24

Subtract 6y on both sides.

12x = 24 - 6y

Divide 12 into both sides.

x = 24/12 - 6/12y

x = 2 - 1/2y

The solution for x in terms of y is x = 2 - (1/2)y

We have,

To solve the equation 12x + 6y = 24 for x, we can isolate x on one side of the equation.

Starting with 12x + 6y = 24, we can subtract 6y from both sides:

12x + 6y - 6y = 24 - 6y

This simplifies to:

12x = 24 - 6y

Next, we divide both sides of the equation by 12 to solve for x:

(12x)/12 = (24 - 6y)/12

This gives us:

x = (24 - 6y)/12

x = 24/12 - 6y/12

x = 2 - (1/2)y

Therefore,

The solution for x in terms of y is x = 2 - (1/2)y

Learn more about equations here:

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#SPJ2

Answer:

40 cm

Step-by-step explanation:

the 414cm2 is eso they

Answer: C

Step-by-step explanation:

This is the answer because you have to multiply (x-1) on both sides and that will cancel out the denominator on the right. Then, multiply by x on both sides and that will cancel the denominator on the left side. When you do this, C should be your answer. Hope this helps :)

Answer:

Step-by-step explanation:

                                        [tex]\dfrac{5x+2}x=\dfrac{-12}{x-1}\\\\{}\quad\ \cdot x\qquad\ \cdot x\\\\5x+2\ =\ \dfrac{-12x}{x-1}\\\\\cdot (x-1)\quad \cdot (x-1)\\\\(5x+2)(x-1)=-12x[/tex]        

Answer:

7, with shaded dot (I hope this helps you)

Explanation:

Answer: The answer is "experiment."

Step-by-step explanation:

This procedure is being used in order to validate a hypothesis, particularly in a research study. In the situation above, you have to validate whether a new reading program can increase reading comprehension or not.

The experiment consists of independent, dependent, and controlled variables. The independent variables are the ones being changed by the researcher, while the dependent variables tell whether the changes in the independent variable is significant. The controlled variables are the ones that are constant.

The dependent variable above is reading comprehension, while the new reading program is the independent variable. Examples of controlled variables are the ages of the participants. The age directly affects the reading comprehension, thus it has to be considered.

Answer:

I think the answer is 7.2%

Step-by-step explanation:

2400-1680=720

720/100=7.2

7.2 is the answer

Hope this helps!

Answer: 2.5%

Step-by-step explanation:

Hi, to answer this question we have to apply the compounded interest formula:  

A = P (1 + r/n) nt  

Where:  

A = Future value of investment (principal + interest)  

P = Principal Amount  

r = Nominal Interest Rate (decimal form, 10/100= 0.1)  

n= number of compounding periods in each year (365)  

Replacing with the values given  

A=250(1+0.1/1)^t/1

A=250(1.1)^t

For a interest compounded annually, n=1, compounded quarterly n= 4 (4quarters in a year )

Interest rate 0.1 /4 = 0.025= 2.5%

Answer:

9.6%

Step-by-step explanation:

yw

Answer:

5x + 10 = 10

Step-by-step explanation:

5x + 10 = 10

5x = 10 - 10

5x = 0

x = 0/5

x = 0

Only one solution.

Answer:

when you wrote question there will be pin sign then you will attach any image   easily

Step-by-step explanation:

Answer:

Its the triangle one

Step-by-step explanation:

Just count them and you will see there are only 7 not 8 :)    

Answer:

Answer should be x^9

Step-by-step explanation:

This equation looks really complicted, but it's actually much easier when you break it down! First, your going to multiply the fraction 3/2 by 6 - since one is a fraction, youre going to find the GCF, or Greatest Common Factor, and reduce it. The GCF in this equation is 2, so we eliminate the two from the fraction (making it just 3) and divide 6 by 2 (getting 3). Thus, we are left with (x^3)^3 -> 3 x 3 = 9. So we are left with x^9. I hope this helps!

Answer: y = -6x + 5

Step-by-step explanation:

equastion is y = dx + e

+) Because it perpendicular y = \dfrac{1}{6} x + 3

d \times \dfrac{1}{6} = -1

<=> d =  -1 : \dfrac{1}{6}

<=> d = -6

=> y = -6x + e;

+) Because it contains the point (-3; 23)

=> 23 = -6 \times (-3) + e

<=> e = 5

=> y = -6x + 5

Answer:

D. 9

Step-by-step explanation:

From the question, we are given the following information:

The number of tennis balls represented by P(n), in n layers of the square pyramid is given as

P(n) = P(n - 1) + n²

In other to solve for n, we would be taking some values for n

Step 1

Let's take the first layer,

n is represented by 1

n = 1

P(1) = P(1 - 1) + 1²

P(1) = 1 tennis ball.

Step 2

Let's take the second layer

n is represented by 2

P(2) = P(2 - 1) + 2²

P(2) = P(1) + 2²

Note that: P(1) above = 1

P(2) = 1 + 2²

P(2) = 5 tennis balls

Step 3

Let's take the third layer

n is represented by 3

P(3) = P(3 - 1) + 3²

P(3) = P(3 - 1) + 3²

P(3) = P(2) + 3²

Note that: P(2) above = 5

P(3) = 5 + 3²

P(3) = 14 tennis balls

Step 4

Let's take the fourth layer

n is represented by 4

P(4) = P(4 - 1) + 4²

P(3) = P(4 - 1) + 4²

P(3) = P(3) + 4²

Note that: P(3) above = 14

P(3) = 14 + 4²

P(3) = 30 tennis balls

We can continue this process, on and on

From the above solution for the number of the tennis balls in first four layers will be: 1, 5, 14, 30,

Hence, the number of tennis balls that Coach Kunal could not have is 9.

Answer:

B. SAS

Step-by-step explanation:

3/1= 2.25/075

The 2 sides are congruent and the angle between them is common

B. SAS is the answer

Answer:

C. Cheryl accelerated to 65 mph, drove at a constant speed for 5.5 minutes, and then decelerated to 45 mph.  

Step-by-step explanation:

Assume the graph of Cheryl's commute was like the one below.

We see that she started at 0 mph.  

One minute later, she was up to 65 mph, so she had accelerated (increased her speed).

At 6.5 min (5,5 min later) her speed was still 65 mph, so she was driving at a constant speed.

Over the next 2.5 min, her speed dropped to 45 mph, so she was decelerating.

Answer:

D

Step-by-step explanation:

on Edmentum

Answer:

a.) k = 10

b.) x = 20

Step-by-step explanation:

Step 1: Plug in variables and calculate for k

2 = k/5

10 = k

Step 2: Plug in variables and calculate for x

0.5 = 10/x

0.5x = 10

x = 20

Answer:

D

Step-by-step explanation:

the scale factor will be the square of the fraction

7/4 =49/16

Answer:

D

Step-by-step explanation:

Answer:

The sum of any rational number and any irrational number will always be an irrational number. This allows us to quickly conclude that ½+√2 is irrational.

Step-by-step explanation:

Answer:

Answer: Option A F(x)=

Explanation:

Quadratic function is the function which has degree two

Degree is the highest power of a polynomial

In option B we have |x| in which degree is one hence, discarded

In option C we have  in which degree is three hence, discarded

In option D we have x which is a linear function being of degree one. Hence, discarded.

Answer:

The answer is option A.

Step-by-step explanation:

-5x-10 <20

Group like terms

-5x < 20 + 10

-5x < 30

Divide both sides by -5

x > - 6

Hope this helps

Hope this helps

Answer:

Step-by-step explanation:

volume =πr²h=π×7²×17≈2616.9 cm³

The volume of a cylinder is 2616.95 cubic centimeters.

It is defined as a three-dimensional space enclosed by an object or thing.

We have:

The height of the cylinder h = 17 cm

Base radius of the cylinder r = 7 cm

We know the volume of a cylinder is given by:

[tex]\rm V = \pi r^2h[/tex]

[tex]\rm V = \pi\times 7^2\times17[/tex]

V = 833π cubic centimeters

V = 833×3.141592

V = 2616.94668 cubic centimeters or

V = 2616.95 cubic centimeters.

Thus, the volume of a cylinder is 2616.95 cubic centimeters.

Learn more about the volume here:

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Answer:

V = 251.3 cm³

Step-by-step explanation:

Diameter  8 cm

Radius = 4 cm

Height = 5 cm

Volume of Cat Food contained by the tin can = [tex]\pi r^2 h[/tex]

Where r = 4 cm, h = 5 cm

V = (3.14)(4)²(5)

V = (3.14)(16)(5)

V = 251.3 cm³

Answer:

251.3 cm³

Step-by-step explanation:

The diameter is 8 cm

So the radius is 8/2 = 4 cm

The height is 5 cm

Volume of tin can:

[tex]\pi r^2 h[/tex]

r = 4 & h = 5

[tex]V =\pi (4)^2 (5)\\V = \pi (16)(5)\\V = 251.3[/tex]

Answer: D. FL | GK

Step-by-step explanation:

Assuming that it's a cube made of up line segments, you know that line FL and line GK are parallel because they will never intersect or meet.