Ben went to the farmer’s market with $14.00, bought 2 pounds of cherries and still had enough money left to buy 3 pounds of apples. Tom went to the farmer’s market and bought 6 pounds of apples and 4 pounds of cherries for $28.00.

14 – 2y = 3x, 6x + 4y = 28

The boys solved the equations to find the price per pound that they paid for cherries and found the solution 14 = 14. How should they interpret this result?



A: The price of 4 pounds of cherries is $14.00.

B: The price of 2 pounds of cherries is $14.00.

C: They made a math error when solving the equations, and should try a different solution method to find the price of the cherries.

D: The two equations describe the same line, so there is not enough information to determine the price per pound of cherries.

Answer:

[tex]x^{2/3}[/tex]

Step-by-step explanation:

When you have a power then a root like that, you have to divide the power by the root.

So, in this case, you have q square (x²) and a cubic root (³√).

So, you take your square (2) and divide it by the cube (3), to get a new power of 2/3.

Let's verify it with x = 2

[tex]\sqrt[3]{2^{2} } = \sqrt[3]{4} = 1.59\\\\\\2^{2/3} = 1.59[/tex]

So, both expressions equal the same thing, it means they're equivalent.

Answer:

6.4 m

Step-by-step explanation:

We have 2 expressions here.  The first one is the fact that r = y.  That's one of 2 equations.  The second one involves whats' left after cutting off certain lengths of each color string.  We cut 2.5 m from red, we cut 3.8 m from yellow.  We know that what's left of red is 1.5 times the length of what's left of yellow.  What's left of red is r - 2.5; what's left of yellow is y - 3.8.  We know that r = 1.5y, so filling that in with our corresponding expressions gives us

r - 2.5 = 1.5(y - 3.8)

Distribute to get

r - 25 = 1.5y - 3.2

Now from the first expression, r = y, so fill in y for r to get an equation in one variable:

y - 2.5 = 1.5y - 3.2

Combine like terms:

-.5y = -3.2 and divide to get

y = 6.4

Check it to make sure it works.  What's left of red should be 1.5 times the length of what's left of yellow and y = 6.4:

What's left of red: 6.4 - 2.5 = 3.9

What's left of yellow: 6.4 - 3.8 = 2.6

1.5 x 2.6 = 3.9, just like it should!

Answer:  the answer is a

Answer:

a

Step-by-step explanation:

The Answer is 7.7

Add all the Shoe size From the second Table

7+7+10+6+9+6+8+7.5+8.5+8=77

77 divide by the number of Shoe size

There are 10 shoe size So,

77/10=7.7

Hope this Help:)

Answer:

7.7

Step-by-step explanation:

The mean (or average) is the sum of the data points divided by the number of data points.

μ = (7 + 7 + 10 + 6 + 9 + 6 +8 + 7.5 + 8.5 + 8) / 10

μ = 77/10

μ = 7.7

Answer:

0

Because -2/3x-1=2-2/3x

-2/3x+2/3x=2+1

0=3

and that's wrong, so there is no solution.

ANSWER

A. 0

EXPLANATION

The first equation is

2x + 3y = 6

The second equation is

y=-2/3x-1

Let us rewrite the first equation in slope-intercept form.

3y =-2x+ 6

[tex]y = - \frac{2}{3} x + 2[/tex]

We can see that both equations has the same slope,

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

but different y-intercepts.

This implies that the two lines do not intersect because they are parallel.

Therefore the system has no solution.

Answer:

6.125 minutes per song

Step-by-step explanation:

Unit rates are based on a single unit of something.  Like price per 1 gallon of gas; price for 1 pound of bananas; miles driven per 1 gallon of gas, etc.  What we are looking for in minutes per song.

Use a proportion to solve this with minutes on top and number of songs on the bottom.  We know that 49 minutes = 8 songs, and we want to know how many minutes (x) per 1 song:

[tex]\frac{min}{song}:\frac{49}{8}= \frac{x}{1}[/tex]

Cross multiply to get

8x = 49 so

x = 6.125 minutes per song

The question asked was about finding the average length of songs on a CD. We calculated this by dividing the total length of the CD (49 minutes) by the total number of songs (8), which gives us an average song length of 6.125 minutes.

The subject of the question is average, a fundamental concept in mathematics. In this particular question, we need to find out the average length of the songs on Randall's CD. We know that the total length of his CD is 49 minutes, and he has recorded 8 songs on it. Finding the average involves dividing the total by the number of units.

The steps to find the average length per song are as follows:

Upon carrying out this calculation, we discover that the average length of each song is approximately 6.125 minutes.

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Answer:

x = -0.04166666667

Step-by-step explanation:

2x + 8 * 96 = 0

2x * 96 = -8

x/2 * 96 = -8/2

x * 96 = -4

x = -4/96

x = -0.04166666667

Answer:

198

Explanation:

The way to solve this equation is by using the "X=96" from moving it to the x in the equation witch makes it "2(96) + 6" When the variable is after the letter like 2x it always means multiplying. So when you multiply 2(96) together you get 192, then you would add 6+192 which would equal 198. I hope I helped! :D

Answer:

-7+6i

Step-by-step explanation:

On the Cartesian x-y plane, a point is located by giving the ordered pair of its coordinates. A point in this position on the x-y plane would have coordinates (-7, 6). That is, it is located 7 units to the left of the vertical axis, and 6 units above the horizontal axis.

The complex plane is similar in many ways, but each point represents a single number (not a pair of numbers). That single number has two parts: a real part and an imaginary part. The real part is measured by the real axis, a horizontal axis that looks very much like the x-axis of a Cartesian plane. The imaginary part is measured against the imaginary axis, a vertical axis that looks very much like the y-axis of a Cartesian plane.

Just as an ordered pair locates a point on the Cartesian plane, a complex number with a real part and an imaginary part locates a point on the complex plane. The imaginary part is identified by the "i" multiplier. (In some fields of study, notably Electrical Engineering, "j" is used instead of "i", because "i" has a different meaning.)

Here, your point is 7 units left of the imaginary axis, so has a real part of -7. It is 6 units above the real axis, so has an imaginary part of 6. When both parts are written together, the number is written -7+6i.

Comparing this form to a+bi, we find a=-7, b=6.

Answer:

first name the triangles

triangle 1=triangleABC

triangle2=trianglePQR

therefore,SSS:sideAB of ABC=sidePQ of PQR

Choice D), since Katie went way over the decimals, and Amaya went slightly under to the closest number

Answer:

Amaya's estimate is the closer one.

D. Katie’s estimate will be greater than the actual product, and Amaya’s estimate will be less than the actual product

Step-by-step explanation:

The original expression is 89.1 x 9.3. Katie changed the 89.1 to 99 (difference of 9.9) and the 9.3 to 10 (difference of 0.7). On the other hand, Amaya changed the 89.1 to 89 (0.1 difference) and the 9.3 to 9 (0.3 difference).

Therefore the best comparison would be Amaya's estimate since her numbers are closer to the original expression.

Katie's estimate will be greater than the actual product because she rounded up the numbers and Amaya's estimate will be less than the actual product because she rounded down the numbers.

Answer:

[tex]5.x=5x\\x^{2} =4, x=2\\x=2[/tex]

Step-by-step explanation:

hope its right

Answer:

162π ft²

Step-by-step explanation:

The surface area (SA) of a sphere is

SA = 4πr² ← r is the radius

Calculate r from the volume, that is

V = [tex]\frac{4}{3}[/tex]πr³ = 972π

Multiply both sides by 3

4πr³ = 2916π ( divide both sides by 4π )

r³ = [tex]\frac{2916\pi }{4\pi }[/tex] = 729

Take the cube root of both sides

r = [tex]\sqrt[3]{729}[/tex] = 9, hence

SA = 4π × 9² = 4π × 81 = 324π

Answer:

The center is at 2

Step-by-step explanation:

The spread is only from 0 to 5.

There are two clusters (one at 0-2 and one at 4-5)

The peak is at 5 not at 8

Answer:

oh i did this one the answer is B.

Answer:

a. [tex]A\geq B[/tex]

Step-by-step explanation:

[tex]sin\frac{\pi }{2} =1[/tex]

and

[tex]cos(-\pi )=-1[/tex]

Answer:

Sin (pi/2) > Cos (-pi)

Step-by-step explanation:

Sin (pi/2) = 1

Cos (-pi)  -1

The following integers from least to greatest are as follows:

0, -2, -4, -5, -6

Answer:

-6, -5, -4, -2, 0

Step-by-step explanation:

Find them on the number line and read them from left to right.

__

You can also enter the numbers into a spreadsheet and use the 'sort' function.

_____

The key understanding here seems to be that negative numbers with a larger magnitude are smaller or less than negative numbers with a smaller magnitude:

-6 is less than -5

And all negative numbers are less than zero or any positive numbers.

Answer:

189°

Step-by-step explanation:

∠UPR = ∠UOP + ∠POQ + ∠QOR = 81° + 56° + 52° = 189°

Answer:

Step-by-step explanation:

Here y = -x^2 + 36.

We can choose x values pretty much at random and then calculate the associated y values:

x    y = -x^2 + 36

----  --------------------

0                      36

2                 -2^2 + 36 =  32

-2                  -4 + 36 = 32

3                  -9 + 36 = 27

You did not share the equation of the slanted line.  Let's assume that the equation of this line is y = mx + b.  The first two points in the table above are (0, 36) and (2, 32).  We could find the equation of this line as follows:

Slope:  as we move from (0, 36) to (2, 32), x increases by 2 and y decreases by 4.  Thus, the slope is m = rise / run = -4/2, or -2.  Using info from the point (0, 36), we find the y-intercept of this straight line:

y = mx + b becomes 36 = m(0) + b, so b = 36, and the line is y = -2x + 36.

We need to find the points of intersection of y = -2x + 36 and y = -x^2 + 36.  We can equate these equations to eliminate y:  -2x + 36 = -x^2 + 36, or

-2x = -x^2.  Equivalently, 2x - x^2 = 0, or (x)(2 - x) = 0.  Then x = 0 and x = 2.

This says that the line and the parabola intersect in at least two places:

(0, 36) and (2, 32).

Answer:

3. 415926535

Step-by-step explanation:

The range of the given data is $48.50, i.e. option D.

The range is defined as a relation between a set of inputs having one output each.

We have,

The prices of the 10 most popular truck tires,

i.e.

$249.99, $239.99, $236.99, 223.99, 221.99, $219.99, $219.99, $212.49, $207.49, $201.49.

Now,

Arrange the given data in the ascending form,

i.e.

$201.49, $207.49, $212.49, $219.99, $219.99, $221.99, $223.99, $236.99, $239.99, $249.99.

Now,

We have,

The Greatest and the smallest number,

i.e.

Greatest number = $249.99

Smallest number = $201.49

So,

The range = Greatest number - Smallest number

i.e.

The range = $249.99 - $201.49 = $ 48.50

So,

The range of the given data is $48.50.

Hence, we can say that the range of the given data is $48.50, i.e. option D.

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Answer:

 The line x=6.

Step-by-step explanation:

The usual translations between polar and rectangular coordinates are ...

If we multiply the given equation by cos(θ), we get ...

  r·cos(θ) = 6

Using the above translation, this becomes ...

 x = 6

Answer:

I think it is 25.

Step-by-step explanation:

Answer with explanation:

Population Mean = 25

Standard Deviation =2.5

[tex]Z_ {Score} =\frac{5}{100}\\\\Z_ {Score} =0.05\\\\Z_{0.05}=0.5199[/tex]

Let ,Margin of error= m

 And, Sample Population = n  

[tex]m=Z_{0.05} \times \frac{\sigma}{\sqrt{n}}\\\\ m=0.5199 \times \frac{2.5}{\sqrt{25}}\\\\m=0.5199 \times 0.5\\\\m=0.25995[/tex]

m= 0.2599 × 100%

m=25.99%=26%

Option A: 25=Margin of error

Ask: Which two numbers add up to -12 and multiply to 32?

-8 and -4

Rewrite the expression using the above

= (y - 4)(y - 8)

Answer:

The correct answer is option B.

Step-by-step explanation:

Given quadratic equation : [tex]y^2-12y+32[/tex]

Using middle term splitting theorem:

=[tex]y^2-12y+32[/tex]

=[tex]y^2-8y-4y+32[/tex]

=[tex]y(y-8)-4(y-8)[/tex]

=[tex](y-8)(y-4)[/tex]

y = 8, 4

The factors of given quadratic equation is (y-8)(y-4).

Answer:

  27

Step-by-step explanation:

If the slope of f(x) is no less than 3, then the value of f(9) can be no less than 27.

  f(x) ≈ f(4) +f'(x)·(x-4)

  f(9) = 12 +3(9 -4) = 27 . . . . . for f'(x) = 3.

For larger numbers of f'(x), f(9) will be larger.

We want to find the minimum possible value of f(9) given that:

We will see that the smallest value that f(9) can take is 27.

We know that the derivate of f(x) gives the slope to the tangent line to the graph of f(x) in a given point where it is evaluated.

If this slope is positive, the function is increasing. So if we want to find the minimum value for f(9), then we need to take the smallest slope possible (knowing that it is positive).

Then we must use f'(x) = 3

Now, we can integrate this to get:

f(x) = 3*x + b

Where b is a constant of integration, to find the value of b, we can use the fact that f(4) = 12, then:

12 = f(4) = 3*4 + b

12 = 12 + b

12 - 12 = 0  = b

Thus the equation is just:

f(x) = 3*x

Now we can evaluate this in x = 9 to get:

f(9) = 3*9 = 27

The smallest value that f(9) can take is 27.

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Answer:

if she drove away she would have to drive 14 hours, or if it were i the same direction she would have to drive 2 1/2 hours

Step-by-step explanation:

8 1/4 + 5 3/4 = 14

8 1/4 - 5 3/4 = 2 1/2

Lisa has to drive an extra 2 1/2 hours to get to her aunt's house compared to her uncle's house. This is determined by converting the mixed numbers to improper fractions, subtracting the smaller fraction from the larger one, and simplifying the result.

The subject of this question falls under Mathematics, specifically subtraction of fractions. In this question, Lisa takes 8 1/4 hours to get to her aunt's house and 5 3/4 hours to get to her uncle's house. The time difference is the extra distance she must travel to reach her aunt's house compared to her uncle's house.

So, Lisa has to drive for an extra 2 1/2 hours to get to her aunt's house as compared to her uncle's house.

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A function is a relation where each input is related to exactly one output. In mapping diagrams, if an 'x' value is associated with multiple 'y' values, the relation is not a function. Make sure to check the mapping to determine this.

In mathematics, specifically in the area of functions and relations, a function is a type of relation where each input (or 'x' value) is related to exactly one output (or 'y' value). If a relation has an 'x' value that is associated with more than one 'y' value, we say that this relation is not a function. When examining mapping diagrams, you can tell if it's a function or not by checking this rule.

For example, if you have a mapping diagram where the number 1 (the 'x' value) is mapped to both 2 and 3 (the 'y' values), this would not be a function because one input is associated with more than one output. On the other hand, if you have a mapping where every 'x' value is mapped to one 'y' value, such as 1 to 2, 2 to 3 and 3 to 4, this is a function.

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Answer: 17 in.

Step-by-step explanation:

The sides of an equilateral triangle measure 16 inches. The midpoints of the sides of the triangle are joined to form another equilateral triangle with sides that are half the length of the outer triangle. This process is continued until three triangles are inscribed in the first triangle. The sum of the perimeters of all four triangles is 17 in.

Answer with explanation:

⇒Side of largest equilateral triangle in which three equilateral triangles are inscribed = 16 inches

Perimeter of a triangle = Sum of three sides of triangle

Perimeter of equilateral triangle having side length 16 inches = 16 +16+16=48 inches

⇒→Second equilateral triangle which is inscribed in this equilateral triangle having side length half of that equilateral triangle in which it is inscribed

 [tex]=\frac{16}{2}\\\\=8[/tex] inches

Perimeter of equilateral triangle having side length 8 inches = 8 +8+8=24 inches

⇒→Third equilateral triangle which is inscribed in this equilateral triangle having side length half of that equilateral triangle in which it is inscribed

 [tex]=\frac{8}{2}\\\\=4[/tex] inches

Perimeter of equilateral triangle having side length 4 inches =4+4+4=12 inches

⇒→Fourth equilateral triangle which is inscribed in this equilateral triangle having side length half of that equilateral triangle in which it is inscribed

 [tex]=\frac{4}{2}\\\\=2[/tex] inches

Perimeter of equilateral triangle having side length 2 inches =2+2+2=6 inches

→≡Total Perimeter of all four Equilateral Triangle

  =48 +24+12+6

= 90 inches

Answer:

  22.6°

Step-by-step explanation:

Since all three sides of the right triangle are given, you can use any of the trig ratios to find the angle. I choose to use the tangent.

  tan(A) = BC/AC = 5/12

Then the inverse trig function tells you ...

  A = arctan(5/12) = 22.6°

Check the picture below.

make sure your calculator is in Degree mode.

The purple area is the sum of the circle sector and the triangle:

[tex]A = A_s+A_t[/tex]

Let's compute them one at the time:

The sector is identified by an angle of 260°, because it is the remainder of a 100° angle.

We can build this simple proportion

[tex]\text{total area}\div\text{total angle}=\text{sector area}\div\text{sector angle}[/tex]

The area of the circle is [tex]\pi r^2[/tex], so we have

[tex]\pi 8.35^2\div 360= A_s\div 260[/tex]

Solving for the sector area, we have

[tex]A_s = \dfrac{\pi\cdot8.35^2\cdot260}{360} = \dfrac{8.35^2\cdot 13\pi}{18}[/tex]

The triangle is an isosceles triangle, because two of the sides are radii. This means that the height is also a bisector, so we can cut the triangle in two 90-50-40 triangles.

Using the law of sines, we can deduce that the height is

[tex]8.35\sin(40)[/tex]

And half the base is

[tex]8.35\sin(50)[/tex]

So, the area of the triangle is

[tex]A_t = 8.35^2\sin(40)\sin(50)[/tex]

So, the purple area is

[tex]A = A_s+A_t =\\\dfrac{8.35^2\cdot 13\pi}{18}+8.35^2\sin(40)\sin(50) = 8.35^2\left(\dfrac{13}{18}\pi+\sin(40)\sin(50)\right)\approx 192.5[/tex]

Answer:

4 yards. The radius is half the diameter of the circle and the length of one point of the circle to the center of the circle.

Step-by-step explanation:

Final answer:

The diameter of a prize wheel with a radius of 2 yards is calculated by multiplying the radius by 2, resulting in a diameter of 4 yards.

Explanation:

Akash, a contestant on a game show, gets to spin a prize wheel with a radius of 2 yards. The diameter of a circle is twice the length of its radius. Therefore, to find the prize wheel's diameter, we simply need to multiply the radius by 2.

Calculating Diameter:

Diameter = 2 × Radius
Diameter = 2 × 2 yards
Diameter = 4 yards

The prize wheel's diameter is 4 yards.

I believe it is section 3 because it is the closest to 0.