30 treadmills to 36 elliptical machines the ratio in simplest form

Answer:

Step-by-step explanation:

7x + 95+2x + x+25 + 90 = 360

10x + 210 = 360

10x = 360 -210

10x = 150

x = 150/10

x = 15

Function 1 has a greater y-intercept than function 2

Step-by-step explanation:

Answers:

1220 dollars invested at 5% interest rate.

2120 dollars invested at 10% interest rate.

===============================================

Explanation:

Label the two accounts A and B.

Account A earns 5% interest

Account B earns 10% interest

Brian invests x dollars in account A and x+900 dollars in account B.

Using the formula, i = P*r*t, we can compute the simple interest for both accounts

----------

Start with account A over the course of t = 1 year.

i = P*r*t

i = x*0.05*1

i = 0.05x

then compute the interest for account B (use t = 1 also).

i = P*r*t

i = (x+900)*0.10*1

i = 0.10x + 90

---------

Over the course of 1 year, Brian earns 0.05x dollars in interest with account A and also 0.10x+90 dollars in interest with account B.

In total he earns 0.05x+0.10x+90 = 0.15x+90 dollars in interest.

We're told this amount of interest he earns is $273, so,

0.15x+90 = 273

0.15x+90-90 = 273-90

0.15x = 183

0.15x/0.15 = 183/0.15

x = 1220

This means $1220 was invested at 5% interest.

x+900 = 1220+900 = 2120

and $2120 was invested at 10% interest.

---------

Check:

If you invested $1220 in account A, then you earn

i = P*r*t

i = 1220*0.05*1

i = 61 dollars in interest

If you invest $2120 in account B, then you earn

i = P*r*t

i = 2120*0.10*1

i = 212 dollars in interest

So you get a total of 61+212 = 273 dollars in interest from both accounts. This confirms the two answers.

Final answer:

The question involves setting up a system of equations to find out how much Brian has invested in each of his savings accounts — one with a 5% interest rate and the other with a 10% rate, given that the total interest earned is $273 and the difference in the amount in each account is $900.

Explanation:

Brian has money in two different savings accounts, one with a 5% interest rate and the other with a 10% interest rate. He has $900 more in the account with the higher interest rate, and the total interest earned from both accounts is $273. To solve the problem, we need to set up a system of equations.

Let x be the amount in the 5% account, therefore x + $900 will be the amount in the 10% account. Using the formula Interest = Principal × Rate × Time, and assuming the time is 1 year, we get two equations:

The sum of these two interests is $273, so we have:

Solving the equation, we find that x = $1,220 and x + $900 = $2,120. Therefore, Brian has $1,220 in the account with a 5% interest rate and $2,120 in the account with a 10% interest rate.

Answer:

The area of the shaded region is 37.70 cm2

Step-by-step explanation:  

hoped this helped ;3

Answer:

Area of smaller circle is a = pi times  2^{2}  = 4 pi

Area of larger circle is A = pi times {4}^{2}  = 16 pi

The area of the shaded region is: 16 pi - 4 pi = 12 pi

and 12 times pi= 37.70 cm2

Answer:

4.0

Step-by-step explanation:

AB / AC = AE / AD

1 / 4.5 = AE / 18

4.5 AE = 18

AE = 4.0

Since BE and CD are parallel, triangles ABE and ACD are similar, meaning their side lengths are proportional.

AC = AB + BC = 1 + 3.5 = 4.5

The proportion of AB to AC (corresponding sides of two similar triangles) is 1 / 4.5

Let x be the variable that represents the unknown length of AE

The proportion of AE to AD (another set of corresponding sides of two similar triangles) is x / 18

Since the triangles are similar, these two proportions must be equal.

1 / 4.5 = x / 18

Cross multiply

4.5x = 18

Divide both side by 4.5

x = 4

The length of AE is 4, no need to round since the answer is already a whole number.

Let me know if you need any clarifications, thanks!

Answer:

C. 6

Step-by-step explanation:

Since the number is greater than one million and less than ten million, the number is seven digit which ranges from two million to nine million

Therefore, Alex will use 6 as the exponent

Answer:

x² + y² - 3x - 13y + 18 = 0

Step-by-step explanation:

Recall that the general equation of a circle looks something like this:

x² + y² + Ax + By + C = 0

substituting each of the points into the equation we get:

for (-1,2)

(-1)² + (2)² + A(-1) + B(2) + C = 0

1 + 4 -A+2B + C = 0

-A + 2B + C + 5 = 0 ------------ eq 1

for (4,2)

(4)² + (2)² + A(4) + B(2) + C = 0

16 + 4 + 4A + 2B + C = 0

4A + 2B + C + 20 = 0 ------------- eq 2

for (-3,4)

(-3)² + (4)² + A(-3) + B(4) + C = 0

9 + 16 -3A + 4B + C = 0

-3A + 4B + C + 25= 0 ----- eq 3

Now we have a system of equations with 3 equations and 3 unknowns.

Solving for A, B and C, we eventually get:

A = -3, B = -13, C = 18

Substituting these into the general equation:

x² + y² + Ax + By + C = 0

x² + y² - 3x - 13y + 18 = 0

Well, when your rounding by ones, if the ones place is lower than 5,  round lower. Like for example, 4 is lower than 5. So if you have 5,784, you have to round that 4 down to a 0. So it would be 5,780.

if it's higher that 5, like 7, you round up. Like for example, 507, you round it to 10, so 510.

Rounding up numbers involves looking at the digit to be dropped: if it's 5 or above, round up the last retained digit. Several examples like 31.57 up to 32 and 8.1649 down to 8.16 illustrate this process.

Rounding up a number involves several steps. Let's take a few examples:

(a) The number 31.57 rounds up to 32. Here, the dropped digit is 5, and the digit we keep or retain is even. Since our dropped digit is 5 or higher, we add one to the retained digit, thus getting 32.

(b) The number 8.1649 rounds down to 8.16. The dropped digit is 4, which is less than 5, so we do not add any to our retained number, getting 8.16.

These examples demonstrate that we are rounding to the nearest whole number or to certain decimal places depending on the precision needed in the problem. When the digit we are dropping is 5 or above, we round up the previous digit. If it is less than 5, we leave the previous digit as it is.

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Answer:

(5-1)/-11-(-6) = -4/5

Step-by-step explanation:

since the lines are parallel they have same slope/gradient

Answer:

-4/5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(1-5)/(-6-(-11))

m=-4/(-6+11)

m=-4/5

Answer:

The solution is the point (0.5,-3)

Step-by-step explanation:

we have

[tex]y=4x-5[/tex] ----> equation A

[tex]y=-3[/tex] ----> equation B

Solve the system by substitution

Substitute equation B in equation A

[tex]-3=4x-5[/tex]

Solve for x

Adds 5 both sides

[tex]-3+5=4x[/tex]

[tex]2=4x[/tex]

Divide by 4 both sides

[tex]x=0.5[/tex]

therefore

The solution is the point (0.5,-3)

Verify your  answer using the graph

using a graphing tool

Remember that the solution of the system of equations is the intersection point both graphs

The intersection point is (0.5,-3)

therefore

The solution is the point (0.5,-3)

see the attached figure

Answer:

Since y= -3, just put that in the equation.

-3 = 4x - 5

+5         +5

2 = 4x

/4    /4

x=1/2

Answer:

-3

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-13-(-1))/(1-(-3))

m=(-13+1)/(1+3)

m=-12/4

m=-3

Answer:

The 10th term from the end of the AP is 39 th term

[tex]\therefore a_{39} =114[/tex]

Step-by-step explanation:

Given:

Arithmetic Sequence as

7 , 10 , 13........154,157

∴ First term = a₁ = 7

Second term = a₂ = 10

∴ Common Difference = d = a₂ - a₁ = 10 - 7 = 3

∴ d = 3

[tex]a_{n} = 157[/tex]

To Find:

[tex]a_{10} = ?[/tex]

Solution:

An equation for the nth term of the arithmetic sequence is given by

[tex]a_{n} =a_{1} + (n-1)\times d[/tex]

Substituting  a₁  and d  and we get

[tex]157=7+(n-1)\times 3\\150=3n-3\\\\3n=147\\n=\frac{147}{3}\\\\n=49\\[/tex]

There are 49 terms in given AP

Therefore the 10th term from the end will be 39th term

[tex]a_{39} =a_{1} + (39-1)\times 3=7+38\times 3=114[/tex]

[tex]\therefore a_{39} =114[/tex]

The value of w is 10

Solution:

Given equation is:

[tex]8.25 + \frac{1}{4}w = 10.75[/tex]

We have to solve above given equation for "w"

[tex]8.25 + \frac{1}{4}w = 10.75[/tex]

We know that 1 divided by 4 gives 0.25

8.25 + 0.25w = 10.75

Moving 8.25 from L.H.S to R.H.S

0.25w = 10.75 - 8.25

0.25w = 2.5

[tex]w = \frac{2.5}{0.25}[/tex]

w = 10

Thus value of w is 10

Answer:

2(x-8) < -20

Step-by-step explanation:

Answer:

x = a number

2(x - 8) < -20

Answer:

With the first term is 2 and common difference is 13 then the series is 2,15,28,...

Step-by-step explanation:

Given first term is 2 and common difference is 13.

Arithmetic progression:

[tex]a_{1}=2[/tex] and d=2  [given]

Therefore we can find arithmetic series  [tex]a_{1},a_{2},a_{3},...[/tex] with [tex]a_{1}=2[/tex] and d=2

d can be written as  [tex]d=a_{2}-a_{1}[/tex]. Therefore we can write [tex]a_{2}[/tex] as below:

[tex]a_{2}=a_{1}+d[/tex]

Now substitute the values [tex]a_{1}=2[/tex] and d=2

[tex]a_{2}=2+13[/tex]

[tex]a_{2}=15[/tex]

Similarly we can find [tex]a_{3}[/tex]

d can be written as  [tex]d=a_{3}-a_{2}[/tex]. Therefore we can write [tex]a_{3}[/tex] as below:

[tex]a_{3}=a_{2}+d[/tex]

[tex]a_{3}=15+13[/tex]

[tex]a_{3}=28[/tex]

and so on.

Therefore the series is 2,15,28,...

Answer:

No.

Step-by-step explanation:

Because standard form is ax+by=c.

367.5, there are 367.5 8's in 2,940.

Hope this helps, if not, comment below please!!!!

Answer:

365.7

Step by step solving:

Answer:

The larger angle is 70°

And The smaller angle is 20°  .

Step-by-step explanation:

Given as :

The ratio of two complementary angles = 7 : 2

Let The larger angle = 7 x

And The smaller angle = 2 x

Now, According to question

Complementary angle is define as when two angles were added to make right angle i.e 90° are complementary to each other .

So, here

7 x + 2 x =  90°

Or, 9 x =  90°

∴  x = [tex]\dfrac{90^{\circ}}{9}[/tex]

i.e x = 10°

Now, putting the value of x

So, The larger angle = 7 × 10° = 70°

And The smaller angle = 2 × 10° = 20°

Hence, The larger angle is 70°

And The smaller angle is 20°  . Answer

Final answer:

The larger angle in a pair of complementary angles with a ratio of 7:2 measures 70 degrees, found by figuring the common ratio as 10 and multiplying it by 7.

Explanation:

To find the measure of the larger angle when two angles are complementary and their ratio is 7:2, we first need to understand that complementary angles add up to 90 degrees. If the ratio of the angles is 7 to 2, we can express this as 7x and 2x for some number x. By adding these two expressions, 7x + 2x, we get the total amount of degrees in complementary angles, which is 90 degrees. Therefore, we have the equation 9x = 90, which we can solve for x by dividing both sides by 9 to get x = 10.

The larger angle, which is 7 parts of the ratio, will be 7x which is 7 times 10, so it is 70 degrees.

Answer:

The sum of any two supplementary angles is 180⁰. If you have been given a task to that one angle measures 120⁰ and have to find its supplement, you will compute as ⇒ 180⁰ - 120⁰ = 60⁰. So, the missing will be 60⁰.

Step-by-step explanation:

Let us consider the m∠MON = 45⁰, as shown in figure a. As straight line measure 180⁰, and the sum of any two supplementary angles is 180⁰. So, 180⁰ - 45⁰ = 135⁰ ⇒ m∠MOL = 135⁰.

So, the supplement of m∠MON = 45⁰ is m∠MOL = 135⁰.

Keywords: supplementary angle, angle measure

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t = 5 + 3m is the required expression that represents weight of Tony fish

Let "t" represent the weight of Tony’s fish, and let "m" represent the weight of Mary’s fish

To find: expression that represents the weight of Tony's fish

According to given information,

Tony’s fish weighs five pounds more than three times the weight of Mary’s fish

Here the word "times" represents multiplication and "more than" represents addition

Weight of Tony fish = 5 + three times the weight of Mary’s fish

Weight of Tony fish = 5 + 3(m)

t = 5 + 3m

Thus the required expression is found out

Answer:

B

Step-by-step explanation:

If you add 6 to both sides, you get -3x-8+6=19+6 which is then -3x-2=25

Answer:

OPTION A

Step-by-step explanation:

Roots of a function can be determined from the graph by the point which cuts the x - axis.

Here, (-4, 0) and (2, 0) are the points that cut the x - axis.

That means, the roots should have been x = -4, 2.

So, from the options, we see that OPTION A has roots f(x) = (x + 4)(x - 2)².

Since, it is a parabola, we have (x - 2)².

Note that f(-4) = 0 and

f(2) = 0.

Hence, OPTION A is the answer.

The unit rate of speed is 52.5 miles per hour

Solution:

Given that On a trip to visit relatives you drive 1,115.625 miles over the course of 21  hours and 15 minutes

We know that, 1 hour = 60 minutes

21  hours and 15 minutes = 21 hours + (15/60) hours = 21 + 0.25 = 21.25 hours

So they drive 1115.625 miles in 21.25 hours

To find the unit rate of speed of your vehicle in miles per hour, divide the total miles by time taken

unit rate of speed means miles driven in 1 hour

[tex]\rightarrow \frac{1115.625}{21.25} = 52.5[/tex]

So the unit rate of speed is 52.5 miles per hour

Answer:

1 year

Step-by-step explanation:

Create two equations to represent each tree. Linear equations are written in the form y = mx + b. "m" is the slope or rate. "b" is the constant or starting value.

In this problem, "m" is the rate of growth in inches per year.

"b" is the starting height.

let "x" be the number of years

let "y" be the height in inches

Tree A: y = 8x + 3

Tree B: y = 9x + 2

Solve the system of equations. Since both are equal to "y", you can equate them to each other and solve for "x". Isolate by doing reverse operations.

8x + 3 = 9x + 2

8x + 3 - 3 = 9x + 2 - 3      Subtract 3 from both sides

8x = 9x - 1

8x - 9x = 9x - 9x - 1     Subract 9x form both sides

-x = -1       Divide both sides by -1 to isolate

x = 1         Number of years for the trees to be the same height

Therefore it will take 1 year for the trees to be the same height.

If you wanted to know how tall the trees will be at the same height, find y. You can substitute x=1 in one of the equations.

y = 8x + 3

y = 8(1) + 3

y = 11     Number of inches when trees are the same height

Answer: 37

Step-by-step explanation:

if n=24

n+13 becomes 24+13

24+13 = 37

The value of the expression is 37.

An expression in mathematics is a set of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

Given the expression n+13

Substitute the value of n the given expression.

24+13 = 37

Hence the value is 37.

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Answer:

I think its 500 each or its Love seat=500. Sofa=1000

Step-by-step explanation:

For 500 you would do 1500/3 because sofa is double+love seat. So each would cost 500 if you divide it by 3. So the sofa would be 1000. The love seat would be 500. 1000+500=1500.

Hope this helps!!

Final answer:

To determine the cost of the sofa and love seat, we create an equation from the given information. Solving for x, we find that the love seat costs $500 and the sofa, costing double, is $1000.

Explanation:

To solve the problem in question, let's call the cost of the love seat x. According to the information given, the sofa costs double the love seat, so the sofa's cost will be 2x. Together, the sofa and love seat cost $1500, which gives us the equation:

x + 2x = $1500

Combining like terms, we get:

3x = $1500

To find the value of x, we divide both sides of the equation by 3:

x = $1500 / 3

x = $500

This means the love seat costs $500. To find the cost of the sofa, we multiply the cost of the love seat by 2:

2x = 2 * $500

2x = $1000

Therefore, the sofa costs $1000, and the love seat costs $500.

Answer:

No.

Step-by-step explanation:

Because standard form is ax+by=c.

Answer:

The maximum value of C is 14

Step-by-step explanation:

we have the following constraints

[tex]x\geq 0[/tex] ----> constraint A

[tex]y\geq 0[/tex] ---> constraint B

[tex]2x+2y\leq 10[/tex] ---> constraint C        

[tex]3x+y\leq 9[/tex] ---> constraint D

Determine the area of the feasible region using a graphing tool

see the attached figure

The vertices of the feasible region are

[tex](0,0),(0,5),(2,3),(3,0)[/tex]

To find out the maximum value of the objective function C, substitute the value of x and the value of y of each vertices in the objective function an then compare the results

we have

[tex]C=4x+2y[/tex]

For (0,0) ----> [tex]C=4(0)+2(0)=0[/tex]

For (0,5) ----> [tex]C=4(0)+2(5)=10[/tex]

For (2,3) ----> [tex]C=4(2)+2(3)=14[/tex]

For (3,0) ----> [tex]C=4(3)+2(0)=12[/tex]

therefore

The maximum value of C is 14

Answer:

12.87%

Step-by-step explanation:

To identify the % of their monthly income is spent on entertainment we use following formula

Total Budget of Entertainment / Total Net Income

$399/$3,100*100

12.87%

We know that we can use y for "how much the job pays" and x for "hours of work."

Let's find how much the job pays in 1 hour by dividing.

25 / 2 = $12.5 per hour

We can mulitply x to 12.5 because this shows how much he earned.

An equation will look like 12.5x = y

Best of Luck!

The job pays $12.50 per hour. The equation to represent the pay, y, for x hours of work is 'y = 12.5x', which depicts direct proportionality.

To solve this question, you must first understand that the job pays $25 for every 2 hours worked. Therefore, to find out how much the job pays for x hours of work, you'd simply multiply the rate per hour ($12.50, since $25 divided by 2 is $12.50) by x hours.

The equation that represents how much the job pays, y, for x hours of work is: y = 12.5x.

Here, 'y' denotes the total payment received and 'x' is the number of hours worked. This format is commonly used in equations representing direct proportionality, where one variable (in this case, pay) changes directly as the other (hours worked).

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