Each graph below shows a relationship between x and y. For each graph, determine whether x and y are proportional. If x and y are proportional, fill in the blank with a number in simplest form.

TY!!!

Answer:

Step-by-step explanation:

I think 9. 10/50

10. 6/50

11. 44/50

See the attached picture:

The formula for lateral surface of a cylinder is:

SA = 2 *PI * r *h

Replace the letters with the given values:

400 = 2 * PI * r *40

Multiply the right side:

400 = r * 251.2

Divide both sides by 251.2:

r = 400 / 251.2

r = 1.59

The radius is 1.59 inches.

Answer: 1.59

Step-by-step explanation:

Answer:

y = x²/4 + x/2 + 21/4 ⇒ -9 ≤ x ≤ 7

Step-by-step explanation:

∵ x = 2t - 1

∴ 2t = x + 1 ⇒ t = (x + 1)/2

∵ y = t² + 5

∴ y = [(x + 1)/2]² + 5 = (x² + 2x + 1)/4 + 5

  y = x²/4 + x/2 + 1/4 + 5 = x²/4 + x/2 + 21/4

∵ -4 ≤ t ≤ 4

∴ -9 ≤ x ≤ 7

Answer:

Step-by-step explanation:

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]

We have:

[tex]b_1=12,\ b_2=5,\ h=5[/tex]

Substitute:

[tex]A=\dfrac{12+5}{2}\cdot5=\dfrac{17}{2}\cdot5=8.5\cdot5=42.5[/tex]

Answer:

B. 3/5

Step-by-step explanation

1/5 of icing = 1/3 of a cake

1/3 * 3/1 = 3/3 = 1 (a whole cake)

1/5 * 3/1 = 3/5

The answer to your question is B, 3/5.

5 and 6

because 5 squared is 25 and 6 squared is 36 so 29 is in between

If the dices have equal probability, that means each number has a 1/6 chance of getting picked because there are 6 sides to a dice with 6 different numbers.

There are a total of 36 combinations, because 6 * 6 is 36.

It would be impossible to have a sum of 1, as the lowest number on both dice is 1. 1 + 1 = 2. Therefore there is a 0/36 probability of getting a sum of 1.

The last option is not even a function, because it ambiguously defines the endpoints.

The first option doesn't define the endpoint, because they are always excluded.

So, the correct option is the second one, because it includes the left endpoint and excludes the right one.

The function d(x) is given by:

d(x)=  1 if   1≤x<4

         2 if  4≤x<6

        3.5 if  6≤x<11

and  5  if 11≤x<13

                    1 when 1≤x<4

( because the graph is a straight horizontal line i.e. y=1 and the line has a closed circle at x=1 and open circle at x=4 )

( because the graph is a straight horizontal line i.e. y=2 and the line has a closed circle at x=4 and open circle at x=6 )

( because the graph is a straight horizontal line i.e. y=3.5 and the line has a closed circle at x=6 and open circle at x=11 )

( because the graph is a straight horizontal line i.e. y=5 and the line has a closed circle at x=11 and open circle at x=13 )

ANSWER

[tex]f( - 1) = 0[/tex]

EXPLANATION

From the table the values of x, are on the left and the values of f(x) are on the right.

To find f(-1), we look for the value under f(x) that corresponds to x=-1.

This value is 0.

Therefore

[tex]f( - 1) = 0[/tex]

A function assigns the values. The correct option is C.

A function assigns the value of each element of one set to the other specific element of another set.

As per the given table the value of f(-1), or the value of f(x), when the value of x=-1, is 0. Thus, it can be written that the value of f(-1) is 0.

Hence, the correct option is C.

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Answer:

A, C

Step-by-step explanation:

I had answered this earlier, so you better look back at that question.

To reiterate, use the Pythagorean Theorem a^2+b^2=c^2.

If a^2+b^2=c^2, it is a right triangle.

*remember that squaring a square root results in just the number inside the square root.

Slower bike = X

Faster bike = X+9

They both ride for 2 hours, now you have 2x and 2(x+9)

The sum of the two cyclists is 66 miles:

2x +2(x+9) = 66

Use distributive property:

2x + 2x+18 = 66

Simplify:

4x +18 = 66

Subtract 18 from both sides:

4x = 48

Divide both sides by 4:

x = 48/4

x = 12

The slower bike was going 12 mi/h

The faster bike was 12+9 = 21 mi/h.

Answer:

28 in

Step-by-step explanation:

6+2= 8 so therefore the length is eight.

To find perimeter, add up all the sides of the rectangle so 6+6+8+8=28

Final answer:

The perimeter of the rectangle is calculated using its length and width. With a width of 6 inches and 2 inches added to determine the length, the perimeter is found to be 28 inches.

Explanation:

To determine the perimeter of the rectangle, we first have to calculate both the width and the length. The width is given as 6 inches. The problem states that the length is 2 inches more than its width, which means the length is 6 inches + 2 inches = 8 inches.

The formula to compute the perimeter (P) of a rectangle is P = 2 * (length + width). Substituting our values, we get P = 2 * (8 inches + 6 inches) = 2 * 14 inches = 28 inches. Therefore, the perimeter of the rectangle is 28 inches.

A power of 10 is the number 10 multiplied by itself by the number of times indicated by the exponent. Thus, shown in long form, a power of 10 is the number 1 followed by n zeros, where n is the exponent and is greater than 0; for example, 106 is written 1,000,000.

1/100,000,000 expressed as a power of 10 is 10-8, reflecting the movement of the decimal point 8 times to the left.

The question asks for the expression of 1/100,000,000 as a power of 10. To find the answer, we need to realize that this fraction is the same as moving the decimal point 8 places to the left from 1, making it 0.00000001. This operation is equivalent to the negative power of 10, because you're making the number smaller (or dividing). Remembering that the exponent represents how many times we move the decimal place, we can express 1/100,000,000 as 10-8.

Given a quadratic equation [tex]ax^2+bx+c=0[/tex]

The discriminant is defined as

[tex]\Delta=b^2-4ac[/tex]

In your case, the equation is defined by the coefficients

[tex]a=3,b=0,c=-10[/tex]

So, the discriminant is

[tex]\Delta=0^2-4\cdot 3\cdot (-10) = 120[/tex]

The discriminant is involved in the solving formula as follows:

[tex]x_{1,2} = \dfrac{-b\pm\sqrt{\Delta}}{2a}[/tex]

Which implies that:

In your case, since the discriminant is positive, you have two distinct solutions. Since 120 is not a perfect square, however, you will not get rid of the square root, so you will have two distinct irrational solutions.

The equation 3x² - 10 = 0 has a discriminant of 120, which is greater than zero. This means that there are two distinct real roots for this equation.

To describe the roots of the equation 3x² - 10 = 0 using the discriminant, we must first understand that the discriminant (d) of a quadratic equation of the form ax² + bx + c = 0 is given by b2 - 4ac. For our equation, a = 3, b = 0, and c = -10, so the discriminant
would be:
= (0)2 - 4(3)(-10) = 0 + 120 = 120

Since  > 0, this indicates that there are two distinct real roots. When the discriminant is greater than zero, the quadratic equation has two real solutions. Therefore, in this case, 3x2 - 10 = 0 has two real roots, corresponding to the x-values where the parabola intersects the x-axis.

Answer:

Ben had biked 8 miles

Step-by-step explanation:

You would need to take 12 and divide it by three . That would make 4. After that you would take 4 and multiply it by 2 since he rode 2/3 miles of 12.  Then you would end up with 8.

Final answer:

Ben has biked 8 miles of the 12 miles he wants to, as he has completed 2/3 of his intended distance.

Explanation:

To calculate the number of miles Ben has biked, we simply need to multiply the total distance he wants to bike by the fraction of the trip he has completed. Ben wants to bike 12 miles, and he has biked 2/3 of that distance. Multiplying these together gives us 2/3 * 12 = 8 miles. Therefore, Ben has biked 8 miles so far.

Y=1000(1+00.6) so divide y by 92 and get 1

Answer:

y=6x+100

Step-by-step explanation:

im not 100% sure if this is correct but i used an online graphing calculator!

Answer:

x= -2,-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the indicated product, multiply each element in the 2x2 matrix by 3:

3(-6)     3(-11)

3(-14)     3(-8)

which comes out to:

-18         -33

-42         -24

This corresponds to the 2nd answer choice.

Answer:

120

Step-by-step explanation:

Using the definition

n[tex]P_{r}[/tex] = n! / (n - r ) !

where n! = n(n - 1)(n - 2) ....... × 3 × 2 × 1

Hence

5[tex]P_{5}[/tex] = 5! / 0! = 5! ← 0! = 1

5[tex]P_{5}[/tex] = 5! = 5 × 4 × 3 × 2 × 1 = 120

In mathematics, the permutation '5P5' equals 1 because there is exactly one way to arrange 5 items in 5 spots.

The problem you are asked to solve involves understanding permutations, which in mathematics, is a way to calculate the number of possible arrangements of a set of items. Specifically, the permutation you are asked to evaluate is written as '5P5'.

In permutation notation, the expression 'nPn' always equals 1, because there are exactly 1 ways you can arrange 'n' items in 'n' spots.

Therefore, the solution to '5P5' is 1.

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     Step-by-step explanation

i had to turn  my laptop just to read that

                 My

Both rectangles have the same dimensions and shape. P'Q'R'S' is a translated image of PQRS, shifted 3 units right and 3 units up. They are congruent but not identical due to their position.

Step-by-step comparison of rectangles PQRS and P'Q'R'S':

1. Original coordinates:

Assume specific coordinates for the vertices of rectangle PQRS. For example, let P = (1, 2), Q = (5, 2), R = (5, 6), and S = (1, 6).

2. Translation:

A translation moves every point in the shape the same distance and in the same direction. Since Rashid translated rectangle 3 units up and 3 units to the right, add 3 to x-coordinate and 3 to y-coordinate of each point in PQRS to find corresponding points in P'Q'R'S'.

3. New coordinates:

P' = (1 + 3, 2 + 3) = (4, 5)

Q' = (5 + 3, 2 + 3) = (8, 5)

R' = (5 + 3, 6 + 3) = (8, 9)

S' = (1 + 3, 6 + 3) = (4, 9)

4. Comparison:

Shape:

Both rectangles PQRS and P'Q'R'S' are rectangles because a translation preserves the shape of the original figure.

Size:

They have the same dimensions (length and width) as the translation only shifts the position without altering the size.

Orientation:

They maintain the same orientation relative to the axes, meaning their sides remain parallel and perpendicular to the x and y axes.

Position:

The key difference lies in their position. P'Q'R'S' is located 3 units to the right and 3 units above PQRS.

5. Rectangles PQRS and P'Q'R'S' are congruent (same size and shape) but not identical (different positions).

P'Q'R'S' is a translated image of PQRS, moved 3 units to the right and 3 units up.

Answer:

[tex]\large\boxed{y=\dfrac{1}{4}x^2,\ y=-\dfrac{1}{2}x^2,\ y=\dfrac{3}{2}x^2}[/tex]

Step-by-step explanation:

The equation of a parabola: y = ax²

The larger the value of |a|, the narrower the parabola.

We have the following coefficients a:

[tex]\left|\dfrac{1}{4}\right|=\dfrac{1}{4},\ \left|-\dfrac{1}{2}\right|=\dfrac{1}{2},\ \left|\dfrac{3}{2}\right|=\dfrac{3}{2},[/tex]

We arrange the coefficients from the smallest to the largest:

[tex]\dfrac{1}{4}\ <\ \dfrac{1}{2}\ <\ \dfrac{3}{2}[/tex]

Therefore you have the answer:

[tex]y=\dfrac{1}{4}x^2,\ y=-\dfrac{1}{2}x^2,\ y=\dfrac{3}{2}x^2[/tex]

Answer:

The numbers are

14

and

7

.

Explanation:

Let the numbers be

x

and

y

.

x

+

y

=

21

x

−

y

=

7

y

=

21

−

x

x

−

(

21

−

x

)

=

7

x

−

21

+

x

=

7

2

x

=

28

x

=

14

∴

14

+

y

=

21

y

=

7

Answer:  The required numbers are 14 and 7.

Step-by-step explanation:  Given that the sum of two numbers is 21 and their difference is 7.

We are to find the numbers.

Let x and y represents the two numbers.

Then, according to the given information, we have

[tex]x+y=21~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-y=7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Adding equations (i) and (ii), we get

[tex](x+y)+(x-y)=21+7\\\\\Rightarrow 2x=28\\\\\Rightarrow x=\dfrac{28}{2}\\\\\Rightarrow x=14.[/tex]

From equation (i), we get

[tex]x+y=21\\\\\Rightarrow 14+y=21\\\\\Rightarrow y=21-14\\\\\Rightarrow y=7.[/tex]

Thus, the required numbers are 14 and 7.

The cost at which both video rental plans are the same is $48, which occurs when a customer borrows 20 DVDs in a month.

The student asked about the cost at which both video rental plans offered by a company would be equal in value. To find this, we need to establish an equation for each plan and set them equal to each other. The first plan includes a membership fee of $8 and charges $2 for every DVD borrowed, which can be represented as cost = $2 × number of DVDs + $8. The second plan is a flat rate of $48 per month for unlimited rentals.

Now we set the equations equal to each other: $2 × number of DVDs + $8 = $48. Solving for the number of DVDs would look like this:

Therefore, the break-even point where both plans cost the same amount is at 20 DVDs borrowed. At this point, the customer would pay $48 with either plan.

As the exercise says, the triangles are similar. So, we can set up proportions between correspondent sides.

In order to solve for x we can set up the proportion between the horizontal and vertical sides:

[tex]28\div 11.2 = 27+x \div x[/tex]

Solving this proportion for x implies [tex]x=18[/tex]

Now you can solve for m and p using the pythagorean theorem, because both triangles are right:

[tex]m = \sqrt{18^2+11.2^2} =21.2[/tex]

Then, we know that the hypothenuse of the big triangle is m+p, so we have

[tex]m+p=\sqrt{(18+27)^2+28^2} = 53[/tex]

which implies

[tex]p = 53-p = 53-21.2=31.8[/tex]

The ratio of the given to similar triangles is 0.4. value of the x, m, and p is 18, 21.2, and 31.8.

Similar triangles are triangles whose corresponding sides are in ratio, while the corresponding angles are of equal measure.

As the two sides of the triangles are already given, therefore, the ratio of these two triangles are,

[tex]\dfrac{11.2}{28} = \dfrac{2}{5}[/tex]

As we already know the ratio of the two triangles, therefore,

[tex]\dfrac{x}{27+x} = \dfrac{2}{5}\\\\5x = 54 + 2x\\\\5x-2x = 54\\\\3x = 54\\\\x = 18[/tex]

Hence, the value of x is 18.

As the given triangle is a right-angled triangle, therefore, we can use the Pythagorean theorem to find the value of m,

[tex](Hypotenuse)^2 = (Perpendicular)^2+(Base)^2\\\\m^2 = x^2 + (11.2)^2\\\\m^2 = 18^2 + 11.2^2\\\\m^2 = 324+125.44\\\\m^2 = 449.44\\\\m = 21.2[/tex]

Thus, the value of side m is 21.2 units.

The value of m and p can be found using the same ratio, we already have for similar triangles,

[tex]\dfrac{m}{m+p} = \dfrac{2}{5}\\\\\dfrac{21.2}{21.2+p} = \dfrac{2}{5}\\\\106= 42.4 + 2p\\\\p = 31.8[/tex]

Thus, the value of the x, m, and p is 18, 21.2, and 31.8.

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Answer:

24 x + 10 y >= 200

Step-by-step explanation:

as x represents centerpiece and y represent  bouquet and total number of roses should be atleast 200 which means we can use roses more than 200 but not less than 200,  the equation will be:

24 x + 10 y >= 200

Answer:

[tex]24x+10y\geq 200[/tex]

Step-by-step explanation:

Givens:

According to the problem, we can define the number of roses per a centerpiece: [tex]24x[/tex]

The number of roses per bouquet: [tex]10y[/tex]

So, the problem restricts the amount of roses, at least 200, that means, 200 or more than 200 roses. Therefore the expression that represent the amount of roses would be:

[tex]24x+10y\geq 200[/tex]

As you can observe, the inequality includes the 200 roses restriction, and the amount of roses per centerpieces and per bouquet.

Answer:

The point of intersection is

(7,-2)

Step-by-step explanation:

We can easily solve this equation by plotting each graph in a graphing tool or calculator.

If we do this, we can find the intersection between the three lines and prove that it exists.

We are solving the system of equations

x+y=5

2x–y=16

x+2y=3

Please see attached picture.

The point of intersection is

(7,-2)

Answer: its B

Step-by-step explanation:

Answer:

7*-5=-35

so your answer would be D

Answer: OPTION D

Step-by-step explanation:

THe quadratic formula is shown below:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

Given the quadratic equation shown in the image, you have that:

a=1

b=3

c=4

Therefore, when you susbtityte these values into the formula you obtain the following solution:

[tex]x=\frac{-3\±\sqrt{3^2-4(1)(4)}}{2*1}[/tex]

[tex]x=\frac{-3\±\sqrt{-7}}{2}[/tex]

Answer:

D.x = (-3±√-7) / 2

Step-by-step explanation:

We have given  a quadratic equation.

x²+3x+4  = 0

From above equation, a = 1, b = 3 and c = 4

We have to find the solution of given equation bu using quadratic formula.

x  = (-b±√b²-4ac) / 2a

Putting given values in above formula, we have

x = (-3±√(3)²-4(1)(4) ) / 2(1)

x = (-3±√9-16) / 2

x = (-3±√-7) / 2 which is the answer.