Rosa is participating in a fun run to raise money for the West Side Children's Hospital. The run is held at Rosa's high school track. The more laps Rosa runs around the track, the more money she raises for the hospital.
There is a proportional relationship between the number of laps Rosa runs, x, and the amount of money she raises for the hospital (in dollars), y.
x (laps) y (dollars)
1 $5
2 $10
3 $15
4 $20
Write an equation for the relationship between x and y.
y=

Answer:

0.00995024875622

Step-by-step explanation:

Answer:

0.0099502487562189054726

Step-by-step explanation:

divide 50 by 5025

Answer:

x=-2/5

y=-1/5

Step-by-step explanation:

[tex]-2x-y=1\\y=3x-1[/tex]

Get the y variables onto 1 side

[tex]y+1=-2x\\y=3x-1[/tex]

Now shift the 1 over

[tex]y=-2x-1\\y=3x-1[/tex]

To solve for x, we can subtract the second equation from the first equation

[tex](y-y)=-2x-3x-1-1 = 0=-5x-2\\5x=-2\\x=-2/5[/tex]

Plug back into the first equation we found and solve for y

[tex]y=-2x-1\\y=-2(-2/5)-1\\y=4/5-1=-1/5[/tex]

Option C: [tex]f(x)=2^x[/tex] is the function rule.

Explanation:

The sequence is [tex]2,4,8,16, \dots \dots[/tex]

Let us find the common difference of this sequence.

Common ratio = [tex]\frac{4}{2} =2[/tex]

Hence, [tex]r=2[/tex]

Thus, the given sequence is a geometric progression.

To determine the function rule, let us substitute the values in the general formula of GP which is given by

[tex]f(x)=ar^{x-1}[/tex] where [tex]a=2, r=2[/tex]

Substituting we get,

[tex]f(x)=2(2)^{x-1}[/tex]

Simplifying, we get,

[tex]f(x)=2\times2^x\times2^{-1[/tex]

Adding the powers, we get,

[tex]f(x)=2^{1+x-1}[/tex]

Simplifying, we get,

[tex]f(x)=2^x[/tex]

Hence, the function rule is [tex]f(x)=2^x[/tex]

Thus, Option C is the correct answer.

Option C:

5, 1, 7

Solution:

Given equation:

y = |3x + 1|

In the chart, x values are given as –2, 0, 2.

To find the value of y for the corresponding x given.

Substitute x  = –2 in the equation of y.

y = |3(–2) + 1|

  = |–6 + 1|

  = |–5|   (Absolute value of a negative number is positive)

y = 5

Substitute x  = 0 in the equation of y.

y = |3(0) + 1|

  = |0 + 1|

  = |1|

y = 1

Substitute x  = 2 in the equation of y.

y = |3(2) + 1|

  = |6 + 1|

  = |7|   (Absolute value of a negative number is positive)

y = 7

Option C is the correct answer.

The values of y are 5, 1, 7.

The answer image of the table is attached below.

Answer:

7,1,7

Step-by-step explanation:

Answer:

[tex]a_{n} = 0.3(- 0.2)^{n - 1}[/tex]

Step-by-step explanation:

The given sequence is 0.3, - 0.06, 0.012, - 0.0024, 0.00048 ........ so on.

Now, this is a G.P. sequence with common ratio [tex]\frac{- 0.06}{0.3} = - 0.2[/tex].

Now, the explicit formula of the given series will be

[tex]a_{n} = 0.3(- 0.2)^{n - 1}[/tex] , where [tex]a_{n}[/tex] is the nth term of the G.P. sequence.

Now, for n = 1, [tex]a_{1} = 0.3(- 0.2)^{1 - 1} = 0.3[/tex].

For, n = 2, [tex]a_{2} = 0.3(- 0.2)^{2 - 1} = 0.3 \times (- 0.2) = - 0.06[/tex] and so on. (Answer)

Answer:

a n+0.3(-0.2)n-1

Step-by-step explanation:

Answer:

A bag of pop corn costs $8, and each Pretzel costs $4.25.

Step-by-step explanation:

Let [tex]b[/tex] be the price of popcorn, and [tex]p[/tex] the price of Pretzels. If the girl bought 2 bags of popcorn and 5 Pretzels and it cost her $37.25, we have the equation

[tex]2b+5p=37.25[/tex]  (this says that the cost of 2 popcorn bags plus 5 pretzels equals $37.25) .

And, since Zoe bought 8 popcorn bags and 9 Pretzels with a total price of $102.25, we get the equation

[tex]8b+9p=102.25[/tex] (this says that the cost of 8 popcorn bags plus 9 Pretzels equals $102.25).

Thus, we have two equations

1. [tex]2b+5p=37.25[/tex]

2. [tex]8b+9p=102.25[/tex]

and we solve them by first multiplying equation (1) by 4:

[tex]4(2b+5p=37.25 )\rightarrow (8b+20p=149)[/tex],

and then subtracting it from equation (2):

[tex]\:\:\:\:\: 8b+9p=102.25\\-(8b+20p=149)\\\line(1,0){3 cm}\\-11p=-46.75\\\\\boxed{p=\$4.25}[/tex]

Now we put this value of [tex]p[/tex] into equation (1) and get:

[tex]2b+5(4.25)=37.25[/tex]

and we solve for [tex]b[/tex] to get:

[tex]2b=37.25-21.5[/tex]

[tex]\boxed{ b=8}[/tex]

Therefore, a bag of popcorn costs $8, and each Pretzel costs $4.25.

Answer:

8 is your answer

Step-by-step explanation:

Answer:

12 centimeters

Step-by-step explanation:

An isosceles triangle has two congruent sides which are legs(2 sides having same length )If x is length of each leg, then we ca write the equation like this

equation: x+x+8=32

combine like terms

2x +8 = 32

minus 8 from each side

2x=32-8

2x=24

divide both sides by 2

2x/2 = 24/2

x=12 centimeters

Answer:

Therefor the probability of having two boys  =  [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

i) In randomly selected family with two children, excluding multiple births

 the children can be in the following combinations:

  a) one girl, one girl    :   GG

  b)  one girl, one boy  :   GB

 c)  one boy, one boy :   BB

The order does not matter for this problem.

Therefor the probability of having two boys  =  [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

"At least x" means "that value x or more"

"At least 2" means "2 or more"

So Billy's plants grow 2 inches or more a month. The smallest increase possible is 2 inches.

We plot a closed circle at 2 on the number line. The closed circle tells us "include this value in the solution set". In contrast, the open circle says "exclude the endpoint from the solution set"

Then we shade to the right indicating all of the possible outcomes (growing 3 inches, growing 4 inches, etc.). 

Answer:

64

Step-by-step explanation:

pemdas says parenthesis first

3+5=8

8(8)

8 times 8 equals 64

We can add the numbers inside the parenthenses: 8(3+5)=8(8)

Now just multiply and we get 64.

So 64 is the simplified answer

Hope this helped!

Answer:

The system of inequalities is given by

i) x + y ≥ 10

ii) 9x + 4y ≤ 100

Step-by-step explanation:

i) let x be the number of grams of fat in the non-carb brownie.

ii) let y be the number of grams of protein in the non-carb brownie.

iii) The brownie must weigh at least 10 grams

iv) therefore we can write x + y ≥ 10

v) The brownie must have no more than 100 calories

vi) therefore we can write 9x + 4y ≤ 100

Answer:

[tex]x=34,y=-27andz=-1[/tex]

Step-by-step explanation:

Given:

[tex]2x+2y+6z=8[/tex]  equation:1

[tex]5x+6y+5z=3[/tex]     equation:2

[tex]5x+6y+3z=5[/tex]     equation:3

We have to find the value of x,y and z

Eliminating two variables to find the value of third variable

Subtracting  equation:2 from equation:3

[tex]5x+6y+3z-(5x+6y+5z)=5-3[/tex]

[tex]5x+6y+3z-5x-6y-5z=2\\-2z=2\\z=-1[/tex]

Solving the equation:1 for 'x'

[tex]2x+2y+6z=8[/tex]

[tex]2x=8-2y-6z\\2x=8-2y-6(-1)\\2x=8-2y+6\\2x=14-2y\\x=7-y[/tex]

Putting x and z in equation 2

[tex]5(7-y)+6y+5(-1)=3\\35-5y+6y-5=3\\y+30=3\\y=3-30\\y=-27[/tex]

Putting the value of 'y' and 'z' in equation:2 to find the value of 'x'

[tex]5x+6(-27)+5(-1)=3\\5x-162-5=3\\5x-167=3\\5x=3+167\\5x=170\\x=\frac{170}{5}\\ x=34[/tex]

The values of x,y and z are

[tex]x=34,y=-27andz=-1[/tex]

Answer:

112 will have been paid for their trip

Step-by-step explanation:

You have to divide $3920 by $35 to get your answer

Answer:

4k+3

Step-by-step explanation:

Answer:

-3<x<=4

Step-by-step explanation:

By using the expression 8 ÷ (4 + (6 - 2)), we can follow the order of operations with the digits 2, 4, 6, and 8 to achieve a result of 2.

Tocreate an expression with a value of 2 using the digits 2, 4, 6, and 8, and following the order of operations, one possible solution involves basic arithmetic operations and a thoughtful approach to number manipulation. An example of such an expression is 8 ÷ (4 + (6 - 2)).

Here is the step-by-step explanation:

This method strictly adheres to the order of operations, ensuring that operations within parentheses are done first, followed by division, to achieve the desired result.

Final answer:

An expression using the digits 2, 4, 6, and 8 to equal the value 2 is 16 / 8, achieved by manipulating the operations and order of the digits according to precedence rules and simplifying.

Explanation:

The question requires us to use the digits 2, 4, 6, and 8, along with the correct order of operations, to create an expression that equals 2.

One way to do this is to take advantage of the properties of division and multiplication, which have the same precedence level but are performed from left to right. Using these operations, we can come up with an expression such as 8 / (4 * (6 - 2)), which equals 2. Here's the step-by-step breakdown of the expression:

Thus, the expression that uses the digits 2, 4, 6, and 8 to yield a value of 2 is 16 / 8, after simplification.

Answer:

Step-by-step explanation:

We are given two relations we can use to find "a" and "b":

  a = 3b

  a² + b² = 30²

Substituting for "a", we have ...

  (3b)² +b² = 900

  10b² = 900

  b² = 90

  b = √90 = 3√10 ≈ 9.5

Then "a" is ...

  a = 3b = 3(3√10) = 9√10 ≈ 28.5

The values of "a" and "b" are about 28.5 and 9.5, respectively.

Answer:

The sum of their ages now is 13

Step-by-step explanation:

Dally's age = x

Dilly's age = x - 7

In 4 years time Dilly will be half Dally’s age, therefore:

Dilly's age plus four equals to half of Dally’s age plus four,

replacing with the values and variables we know:

x - 7 + 4 = (x + 4) /2

x - 3 = (x + 4) /2

2x - 6 = x + 4 (Multiplying by 2 at both sides)

2x - x = 4 + 6 (Like terms)

x = 10 ⇒ x - 7 = 3

The sum of their ages now is 13 (10 + 3)

The sum of their ages now is 13 years

Let the age of Dilly be "x"

Let the age of Dally be "y"

If Dilly is 7 years younger than Dally, then;

x = y - 7 ....... 1

In 4 years time, their age will be:

Dilly = x+ 4

Dally = y + 4

If in 4 years' time she will be half Dally’s age, then;

x+4 = 1/2(y+4) ............... 2

Substitute equation 1 intp 2 to have:

y-7+4 = 1/2(y+4)

y - 3 = 1/2(y+4)

2y - 6 = y + 4

2y - y = 6 + 4

y = 10

Recall that x = y - 7

x = 10 - 7

x = 3

Sum of their ages will be x + y = 10 + 3 = 13 years

Hence the sum of their ages now is 13 years

Learn more here: https://brainly.com/question/13805464

Answer:

84.82 ft³

Step-by-step explanation:

Answer:

84.823

Step-by-step explanation:

The formula of the volume of cone is v= 1/3 (PI* r^2) h

We have that h= 9feet , and r= 3

So, v =1/3 (Pi * 3^2) 9

V=84.82300

Answer:

0.86(28) = 24.08

Step-by-step explanation:

Turn the percent to decimal and solve

Answer:

28$

Step-by-step explanation:

Answer:

a decimal 0.225

Step-by-step explanation:

Answer:

6.3 x 10°

Step-by-step explanation:

6.3 can be written as 6.3 x 1

recall that anything to the power of zero = 1

hence 10° = 1 substitute this back into the expression above to get:

6.3

= 6.3 x 1

= 6.3 x 10°

Answer:

Divide 11 by 10 . Place this digit in the quotient on top of the division symbol. Multiply the newest quotient digit (1) by the divisor 10 . Subtract 10 from 11 . :) Hope this helps!

It can be a fraction of 11/10 as a mixed number is 1 1/10.

To convert a fraction into a mixed number, you need to divide the numerator (top number) by the denominator (bottom number).

The whole number part of the result is the whole number of the mixed number, and the remainder becomes the numerator of the fractional part.

As per the question, we have the fraction 11/10.

Dividing 11 by 10 gives:

11 ÷ 10 = 1 remainder 1

So the whole number part is 1, and the fractional part is 1/10. We can express this as a mixed number by writing:

11/10 = 1 1/10

Therefore, 11/10 as a mixed number is 1 1/10.

Learn more about the fraction here:

brainly.com/question/10354322

#SPJ5

Answer:

no

Step-by-step explanation:

6 and 5 are the smaller sides but they only add to 11

the need to get to something higher than 12

no equal or less than

Final answer:

Segments 6, 5, and 12 cannot form a triangle because the length of one segment (12) is equal to the sum of the other two (6 + 5), which violates the Triangle Inequality Theorem.

Explanation:

The question involves determining whether three given segments can form a triangle. To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the Triangle Inequality Theorem. Given the segments 6, 5, and 12, we can test this theorem:

Since one of the conditions fails, the segments 6, 5, and 12 cannot form a triangle. Visually, it's also clear that one segment (12) is as long as the sum of the other two (6 + 5), which means they could only form a straight line, not a triangle.

Answer:

Its 7

Step-by-step explanation:

24÷8= 3

6×3=18

?×3=21

7×3=21

Awnser is 7

The simplest polynomial function with the given roots is

[tex]x^4-x^3-19x^2-11x+30[/tex].

Solution:

Given roots of the polynomial are:

–3, –2, 1 and 5

If a is the root of the polynomial then the factor is (x –a).

So that, the factors of the given roots are:

(x –(–3)) = x + 3

(x –(–2)) = x + 2

(x – 1) = x – 1

(x – 5) = x –5

Polynomial = Product of the factors

                    = (x + 3)(x + 2)(x – 1)(x – 5)

Multiply first two factors.

                     [tex]=(x^2+2x+3x+6)(x-1)(x-5)[/tex]

                     [tex]=(x^2+5x+6)(x-1)(x-5)[/tex]

Now, multiply the next two factors.

                     [tex]=(x^2+5x+6)(x^2-5x-x+5)[/tex]

                     [tex]=(x^2+5x+6)(x^2-6x+5)[/tex]

Now multiply these two factors.

                    [tex]=x^2(x^2-6x+5)+5x(x^2-6x+5)+6(x^2-6x+5)[/tex]

                     [tex]=x^4-6x^3+5x^2+5x^3-30x^2+25x+6x^2-36x+30[/tex]

                     [tex]=x^4-x^3-19x^2-11x+30[/tex]

The simplest polynomial function with the given roots is

[tex]x^4-x^3-19x^2-11x+30[/tex].

Answer:

1)  (4,6),(-4,6), (4,12),(-4,12)

2) (4,9) or (-4,9)

Step-by-step explanation:

Observe that the two vertices given, (0,6) and (0,12) are on the y-axis.

The distance between this points is |12-6|=6

We know area of a triangle is [tex]A=\frac{1}{2}bh[/tex]

We were given area as 12.

[tex]\frac{1}{2}*b*6=12[/tex]

[tex]3b=12[/tex]

b=4 units

We can find a point 4 units horizontally away from any of the vertex.

So (4,6),(-4,6), (4,12),(-4,12) are feasible vertices.

For the triangle to be isosceles, then the third vertex must be on the horizontal line through the midpoint of (0,6) and (0,12) and must be 4 units away from the line x=0.

Therefore if thr triangle is isosceles, then third vertex must be at (4,9) or (-4,9)

Answer:

Option B.

Step-by-step explanation:

Given information: ∠MHL=(3x+20), ∠KHN=(x+25), and ∠JHN=(x+20).

We need to find the measure of ∠JHN.

[tex]\angle MHL=\angle JHK[/tex]                         (Vertical opposite angles)

[tex]\angle MHL=\angle JHN+\angle KHN[/tex]

Substitute the given values.

[tex]3x+20=(x+20)+(x+25)[/tex]

[tex]3x+20=2x+45[/tex]

[tex]3x-2x=45-20[/tex]

[tex]x=25[/tex]

The value of x is 25. So, the measure of ∠JHN is

[tex]\angle JHN=x+20=25+20=45[/tex]

The measure of ∠JHN is 45°.

Therefore, the correct option is B.

Answer:

it's B

Step-by-step explanation: