As part of a competition Diego must spin around in a circle six times and then run to a tree. The time he spends on each spin is represented by s and the time he spends running is r. He gets to the tree 21 seconds after he starts spinning. Write an equation showing the relationship between s and r.

Answer:

B. Prices increase.

Step-by-step explanation:

When demand for a product is greater than the product's supply, that increases the value of said product, and thus they bring the price up.

When demand exceeds supply, it's referred to as a shortage or excess demand, and generally leads to an increase in prices. Sellers are able to charge more because more consumers are vying for a limited number of goods.

When demand exceeds supply in economic terms, it leads to a situation called excess demand or shortage. In this scenario, more people want a product than the amount of the product available. As a result of this excess demand, prices generally increase. This increase happens due to the basic law of demand and supply. Since more consumers are chasing a limited number of goods, sellers can charge higher prices. This increase in prices can help reduce the demand and bring the market back into equilibrium.

For instance, consider a situation where new smartphones are released, and the demand outstrips the supply. The prices will likely increase because people are willing to pay a higher price to secure one of the limited handsets.

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Answer:

$12

Step-by-step explanation:

30% is 0.3

So 0.3 × 40 = 12

Answer:

solve for y

Step-by-step explanation:

[tex]5x-2y=-10[/tex]

subtract 5x from both sides

[tex]5x-5x-2y=-10-5x[/tex]

[tex]-2y=-10-5x[/tex]

Divide each term in the equation by -2

[tex]\frac{-2y}{-2}=\frac{-10}{-2} -\frac{-5x}{-2}\\\\y=\frac{-10}{-2} +\frac{-5x}{-2} \\\\y=5+\frac{5x}{2}[/tex]

(negative+negative=positive)

re-write in slope-intercept form [tex]y=mx+b[/tex] , where m is the slope and b is the y-intercept

[tex]y=\frac{5}{2}x+5[/tex]

Now you know that the slope is [tex]\frac{5}{2}x[/tex] and the y-intercept is [tex]5[/tex].

Now, to graph, you just need to choose random values for x (like 0,1,2,3 or any other number) and insert into the equation [tex]y=\frac{5}{2}x+5[/tex] to find the points, or you can just use the slope. To find the x-intercept, do the following:

make y equal to 0

[tex]0=\frac{5}{2}x+5[/tex]

Solve for x:

simplify [tex]\frac{5}{2}x[/tex]

[tex]0=\frac{5x}{2} +5[/tex]

Subtract 5 from both sides

[tex]0-5=\frac{5x}{2}+5-5\\ \\-5=\frac{5x}{2}[/tex]

Multiply both sides by 2

[tex]2(-5)=2(\frac{5x}{2})\\\\-10=5x[/tex]

Divide both sides by 5

[tex]\frac{-10}{5}= \frac{5x}{5}\\\\-2=x[/tex]

Flip

[tex]x=-2[/tex]

The x-intercept is -2.

To draw an integer chips model for the subtraction problem, first draw nine positive chips to represent the grapes Mary took, then draw four negative chips for the grapes she gave back. Subtract the negative from the positive chips to get the final answer.

In this integer subtraction problem, you would first draw 9 positive chips, symbolizing the 9 grapes Mary initially received from Rohin. Positive chips can be represented by circles or squares. You could use different colors, such as blue for positive (or grapes Mary has).

Next, to represent the 4 grapes that Mary returned to Rohin, you would draw 4 negative chips. Negative chips (or the grapes Mary gave back) could be represented by a different color, such as red.

Subtracting 4 from 9, we then remove 4 positive chips from the model, leaving five positive chips, representing the 5 grapes Mary has left after she returned 4 to Rohin.

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Answer:

14 hits in 28 games

Step-by-step explanation:

every 2 games there is 1 hit

Answer:

615.75216....

Step-by-step explanation:

The formula is A = π * (ø/ 2)^2

A = Circle area

π = Pi = 3.14

ø = Circle diameter

A= 3.14  (28/2)^2

Answer:

Area = 615.44 inches

Step-by-step explanation:

Diameter = 2 * radius

28 = 2 * radius

Divide both sides of the equation by 2

14 = radius

Find area

A = π r²

A = 3.14 (14)²

A = 3.14 (196)

A = 615.44

Hope this helps :)

Answer:

42ft

Step-by-step explanation:

Area of a triangle = 1/2 * base * height

So that little triangle section:

 1/2 * 2 * 3 = 1/2 * 6 = 3

Now we do the rectangle Section:

Area of a rectangle = length * width

So that rectangle is 3 * 7 = 21

If you eliminate those two shapes, you are left with a trapezoid.

Area of a trapezoid is 1/2 * (base 1 + base 2) * height

Base 1 is 3 which is the width of the rectangle.

Base 2 is the 6.

The height is the given 11 feet subtracted by the 7 feet from the length of the rectangle which is 4.

Plug all this in to the formula you get 1/2 * (6 + 3) * 4 = 1/2 * 9 * 4 = 1/2 * 36 = 18.

Now add all of your areas together;

21 + 3 + 18 = 24 + 18 = 42

Answer:

Area=42 ft.²

Step-by-step explanation:

This is an area problem. But since there are multiple shapes (2 triangles and a rectangle) we have to split the shapes and work each one separately. First we will start on the far right, with the small triangle. This one is the easiest one since the line is already drawn to separate it from the rest of the shape.

    Area of a triangle=1/2 bh

                               A=1/2(2x3)

                               A=1/2(6)

                               A=3

The next shape is the the rectangle in the middle.  Looking at the first image, I've drawn a line across the bottom, we need to find the area of that new image, the width is 3 ft and the length is 11 ft.

    Area of a rectangle=lw

                                  A=(11x3)

                                  A=33

Finally, we need to find the area of the last triangle. Looking at the second image, I've add the correct base and height, 4 and 3. So now we need to use the triangle formula and solve

    Area of a triangle=1/2bh

                               A=1/2(4x3)

                               A=1/2(12)

                               A=6

Now we can add the three areas together and get the total area:

  3+33+6=42 ft

I hope this helps:)

Answer:

a. 4/21

b. 4/7

Step-by-step explanation:

Please kindly check the attached files for explanation.

Answer:

A) 3/12

B)7/12

Step-by-step explanation:

I used a tree diagram to go through this with my daughter, bear in mind the second question asks for the probability of exactly one red counter to be taken from the bag.

Answer:

B.350

Step-by-step explanation:

let's hope it helps

Answer: 0.34

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Answer:

B is the correct answer

Step-by-step explanation:

Answer:

The simplified expression is -4x and the value is -516

Step-by-step explanation:

−12x+14x−6x

Combine like terms

2x-6x

-4x

Let x =129

-4*129

-516

Answer:

f(x) = y

y = 7.50x

To find the inverse, swap x and y

x = 7.50y

Now solve for y

y = x/7.50

f-1(x) = x/7.50

Answer:

3 min 12 seconds

Step-by-step explanation:

Using the conversion

1 minute = 60 seconds, then

2 min 6 seconds = (2 × 60) + 6 = 120 + 6 = 126 seconds

Divide 126 by 525 then multiply by 800, that is

time = [tex]\frac{126}{525}[/tex] × 800 = 192 seconds = 3 min 12 seconds

Final answer:

After calculating Tomos's average speed from the 525 m ski race, we use that speed to determine that it should take him approximately 3 minutes and 12 seconds to complete an 800 m race.

Explanation:

To determine how long Tomos should take to complete an 800 m race given his average speed, we start by calculating his speed during the 525 m race. Tomos completed the 525 m ski race in 2 minutes and 6 seconds, which is a total of 126 seconds.

Firstly, we calculate Tomos's average speed:

Average speed (v) = Total distance (d) / Total time (t)

v = 525 m / 126 s

v = 4.1667 m/s (approximately)

Now, to find out how long it will take Tomos to ski 800 m at the same speed, we use the formula:

Time (t) = Distance (d) / Speed (v)

t = 800 m / 4.1667 m/s

t = 192 seconds (approximately)

Finally, we convert the time from seconds to minutes and seconds:

There are 60 seconds in a minute, so:

Time = 192 s = 3 minutes and 12 seconds

Therefore, it should take Tomos approximately 3 minutes and 12 seconds to complete an 800 m race at his average speed.

1. y = 2/3x - 5

2. 4x - 6y = 30

Divide 2. by 2

3. 2x - 3y = 15

Substitute 1. into 3.

4. 2x - 3(2/3x - 5) = 15

5. 2x - 2x + 15 = 15

6. 15 = 15

False. There are an infinite number of solutions.

Answer:2nd one

Step-by-step explanation:

Answer:

1/2 and 1/3

Step-by-step explanation:

1/2 can have a denominator of 6 by multiplying by 3

[tex]\frac{1}{2} *\frac{3}{3} =\frac{3}{6}[/tex]

1/3 can have a denominator of 6 by multiplying by 2

[tex]\frac{1}{3} *\frac{2}{2} =\frac{2}{6}[/tex]

[tex]p - \sqrt{q} = 1 \\ q + p = 7[/tex]

[tex]p = 7 - q[/tex]

[tex]7 - q - \sqrt{q} = 1 \\ - q - \sqrt{q } = - 6 \\ q + \sqrt{q } = 6 \\ q = 4[/tex]

[tex]p = 7 - 4 = 3[/tex]

Answer:

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Step-by-step explanation:

Graph (-5,-3) and use the slope, -2, to find another point. -2 can also be written as [tex]-\frac{2}{1}[/tex]

[tex]\frac{rise}{run} =\frac{-2}{1}[/tex] and  [tex]\frac{rise}{run} =\frac{2}{-1}[/tex] **

Use both. This works because either way, they will lie on the same line with the same slope. So, starting at (-5,-3), go down two points (-)* and to the left 1 (+)*, then, starting at (-5,-3) again, go up two points (+)* then to the right 1 point (-)*.

* If the number is negative, you either go down or to the right. If the number is positive, you go up and to the left.

**Rise over run refers to the change in the y-axis and the change in the x-axis: [tex]\frac{rise}{run} =\frac{y-axis}{x-axis}[/tex]. Only one number is negative because, if both were negative, that would make a positive number, but the slope is -2, not 2.

Another way you could do this is by finding points first. All you need to do is turn the slope into a "point". Remember, 2 is the y and 1 is the x:

[tex]-2=-\frac{2}{1} = (1,-2)[/tex] and [tex](-1,2)[/tex]

Then, using (-5,-3) and your new points, add them separately:

[tex](-5,-3)+(1,-2)\\(-5+1,-3+(-2))\\(-5+1,-3-2)\\(-4,-5)[/tex]

(-4,-5) is one point

[tex](-5,-3)+(-1,2)\\(-5+(-1),-3+2)\\(-5-1,-3+2)\\(-6,-1)[/tex]

(-6,-1) is another point. Connect the three points. You can check your work on the graph:

Density = Mass / Volume

The volume is length * width * height, which equals 25 * 10 * 15, making it 3750 cm^3.

Mass / Volume = 3000 g / 3750 cm^3 = 0.8 g/cm^3

Answer:

Density = Mass / Volume

The volume is length * width * height, which equals 25 * 10 * 15, making it 3750 cm^3.

Mass / Volume = 3000 g / 3750 cm^3 = 0.8 g/cm^3

Step-by-step explanation:

The value of c from the given equation is 34.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The given equation is x²+19x+c=0

Vieta's Theorem is If f(x) = ax² + bx + c is a quadratic equation with roots α and β then,

Sum of roots = α + β = -b/a

(x + a) (x + b) = x² + (a + b) x + ab

a + b = 19

a - b = 15

a = 17

b = 2

c = ab = 34

Therefore, the value of c from the given equation is 34.

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Using Vieta's Theorem, the difference of the roots was used to set up two equations. Solving them simultaneously gave us the individual roots, which were then multiplied to find the required product, c, which is 34.

To solve for c in the quadratic equation x^2 + 19x + c = 0 using Vieta's Theorem, we need to find the two roots of the equation and their relationship to the coefficients.

According to Vieta's formulas, for a quadratic equation of the form ax^2 + bx + c = 0, the sum of the roots -b/a and the product of the roots c/a. Since the coefficient a is 1 in our equation (x^2 + 19x + c = 0), the sum of the roots is -19, and the product is c.

We are told the difference of the two roots is 15. Let's denote the larger root as r1 and the smaller one as r2. Thus, r1 - r2 = 15. But we also know that r1 + r2 = -19 (the negative coefficient of x).

We can now set up two equations:

By solving these two equations simultaneously, we add them together to eliminate r2:

2r1 = -4

r1 = -2

Substitute r1 back into one of the original equations to find r2:

r1 + r2 = -19

-2 + r2 = -19

r2 = -17

Now, we use the product of the roots to find c:

c = r1 * r2

c = -2 * -17

c = 34

Therefore, the value of c in the quadratic equation is 34.

To find the missing constant term, we want to think about what two numbers would add up to 2. Of the numbers we've thought of, we want to find the numbers that are the same. In this case, that would be 1 and 1. If we multiply, or square, 1 and 1 together, we get 1. So, the missing constant term in the perfect square given here would be 1.

Hope this helps!! :)

The graph of both functions are positive, thus the graph is increasing in the upward direction.

The graph of a quadratic equation.

The graph of a quadratic equation is a parabolic curve or a U-shaped curve. From the given function, the parent function is f(x) = x² and the g(x)  is the transformed function of the original function.

The function of g(x) = 5x² - 2 is vertically stretch by 5 units and  it is shifted vertically downward by 2 units.

Thus, we can say that the graph of g(x) = 5x² - 2 is related to  f(x) = x² because of the vertical stretch and the vertical shift. Also, since both functions are positive, the graph is increasing in the upward direction.

Answer:

14:20 :)

Step-by-step explanation:

Answer:

1 1/2

Step-by-step explanation:

60/40 = (60 ÷ 20)/(40 ÷ 20) = 3/2; 3 > 2 => improper fraction Rewrite: 3 ÷ 2 = 1 and remainder = 1 => 3/2 = (1 × 2 + 1)/2 = 1 + 1/2 = = 1 1/2, mixed number (mixed fraction)

Hope this helped!

Answer:

1 1/2

Step-by-step explanation:

40 can go into 60 1 time

simplify the rest

Answer:

9 months.

Step-by-step explanation:

225 / 25 = 9

Feel free to let me know if you need more help! :)

Answer:

9

Step-by-step explanation:

225/25 is 9

Answer:

d) 10

Step-by-step explanation:

Answer:

The answer is 10

Step-by-step explanation:

Answer:

The two expressions of an equation are separated by an equal sign. When the statement is given in words, the equal sign is indicated by the word “is” or the words “the same as.”

Step-by-step explanation:

Two expressions of the equation by properly interpreting the words into appropriate signs and digits.

An equation is a mathematical statement that two expressions are equal. The solution of an equation is the value that when substituted for the variable makes the equation a true statement. To achieve our goal, we use two principles of equality, the addition principle and the multiplication principle.

A binomial expression is an algebraic expression which is having two terms, which are unlike. Examples of binomial include 5xy + 8, xyz + x3, etc.

Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression.

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Answer:

Yes, there s a vertical shift to the right by 1

Step-by-step explanation:

If you distribute the 2 among the (x+2) you get:

              2x+4-5

Combine like terms:

              2x+1

There fore the line shifts right by one.

Answer:

Yes, the equation shifts down by five.

Step-by-step explanation:

In equations, vertical shifts happen when the ENTIRE equation, or y, is added or subtracted a number.

Horizontal shifts happen when JUST the x value is added or subtracted a number, but this is a little different.

The formula for the equation you gave us is

m(x - h) + k

Since "h" is already negative, we have to flip the sign of the +2, so the horizontal shift would be LEFT two units.

As far as the vertical shift goes, we just have to look at the "+k."

Since k = -5, the equation shifts down five units.

Answer:

all work is pictured and shown