17. The length of a rectangle is 12 in, and the perimeter is 56 in. Find the width of the rectangle.
Oo oo
O A. 16 in.
O B. 32 in.
O c. 22 in.
O D. 21 in.

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.

12oz of the drink contains 159oz of calories.

A new energy drink advertises 106 calories for 8oz.

Based on the given conditions, formulate: 12*(106/8)

=12*(13.25)=159

Calories are in 12oz of the drink is 159oz

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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 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

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:

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:

Part A) The vertex is the point (22,100) see the explanation

Part B) The x-intercepts are the points (12,0) and (32,0 see the explanation

Part C) The y-intercept is the point (0,-384) see the explanation

Step-by-step explanation:

Let

x ----> the number of cups of coffee sold

f(x) ---> the amount of profit

we have

[tex]f(x)=-x^{2} +44x-384[/tex]

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

Part A) Determine the vertex. What does this calculation mean in the context of the problem?

Convert the quadratic equation in vertex form

Factor -1

[tex]f(x)=-(x^{2}-44x)-384[/tex]

Complete the square

[tex]f(x)=-(x^{2}-44x+22^2)-384+22^2[/tex]

[tex]f(x)=-(x^{2}-44x+484)+100[/tex]

Rewrite as perfect squares

[tex]f(x)=-(x-22)^{2}+100[/tex]

The vertex is the point (22,100)

That means ----> The maximum profit of $100 is when the number of cups of coffee sold is 22  

Part B)  Determine the x-intercepts. What do these values mean in the context of the problem?  

we know that

The x-intercepts are the values of x when the value of the function is equal to zero

so

we have

[tex]f(x)=-(x-22)^{2}+100[/tex]

For f(x)=0

[tex]0=-(x-22)^{2}+100[/tex]

solve for x

[tex](x-22)^{2}=100[/tex]

take square root both sides

[tex](x-22)=\pm10[/tex]

[tex]x=22\pm10[/tex]

so

[tex]x=22+10=32[/tex]

[tex]x=22-10=12[/tex]

The x-intercepts are the points (12,0) and (32,0)

That means -----> When the number of cups of coffee sold is 12 or 32 the profit is equal to zero

Part C) Determine the y-intercept. What does this value mean in the context of the problem?

we know that

The y-intercept is the value of the function  when the value of x is equal to zero

so

For x=0

[tex]f(x)=-x^{2} +44x-384[/tex]

substitute the value of x

[tex]f(x)=-(0)^{2} +44(0)-384[/tex]

[tex]f(x)=-384[/tex]

The y-intercept is the point (0,-384)

That means ----> When the number of cups of coffee sold is zero the profit is negative -$384 (the cost is greater than the revenue)

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:

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:

(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:

50/50 chance

Step-by-step explanation:

Answer: Classical Probability (also know as priori or theoretical probability)

Step-by-step explanation:

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

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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Answer:

JKL and ABC

DEF and GHI

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding angles is proportional and its corresponding angles are congruent

so

In this problem

1) triangles JKL and ABC are similar

because

[tex]\frac{KL}{BC} =\frac{JL}{AC}[/tex]

substitute the given values

[tex]\frac{10}{20} =\frac{7}{14}[/tex]

Simplify

[tex]\frac{1}{2} =\frac{1}{2}[/tex]  ---> is true

therefore

The ratio of the corresponding sides is proportional

That means----> The triangles are similar

2) triangles DEF and GHI are similar

because

[tex]\frac{HI}{EF} =\frac{GI}{DF}[/tex]

substitute the given values

[tex]\frac{15}{10} =\frac{12}{8}[/tex]

Simplify

[tex]1.5=1.5[/tex]  ---> is true

therefore

The ratio of the corresponding sides is proportional

That means----> The triangles are similar

The pairs of triangles that are similar to each other are:

B. ΔDEF ~ ΔGHI

E. ΔJKL ~ ΔABC

Corresponding angles of two triangles that are similar are always congruent, however, their corresponding sides are proportional to each other. This means, their ratio is equal.

Thus, triangles KJL and ABC are similar triangles because:

BC/KL = AC/JL = 2

Also, triangles DEF and GHI are similar triangles because:

GI/DF = HI/EF = 1.5

Therefore, the pairs of triangles that are similar to each other are:

B. ΔDEF ~ ΔGHI

E. ΔJKL ~ ΔABC

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Function 1 has a greater y-intercept than function 2

Step-by-step explanation:

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:

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:

4

Step-by-step explanation:

3x = 5x - 8 is your equation. To solve for x, you want to get all the x's on the same side. You first subtract 5x from each side to get -2x = -8, and multiply both by 1- to get 2x = 8, and then divide both sides by 2 to find x = 4.

Answer:

Step-by-step explanation:

3x=5x -8​

3x - 5x = - 8

-2x = -8

x = -8/-2

x = 4

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

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:

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:

No.

Step-by-step explanation:

Because standard form is ax+by=c.

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.

Answer:

The amount to be pay for coat is $128.70.

Step-by-step explanation:

Given:

The sales tax rate is 7.25% in California.

The cost for a coat in Los angeles is $120.00.

Now, to find amount to be paid.

Sales tax = 7.25%.

Cost = $120.00.

So, amount to be paid = $120 + 7.25% of $120.00.

[tex]=120+\frac{7.25}{100} \times 120.[/tex]

[tex]=120+\frac{870}{100}.[/tex]

[tex]=120+8.70[/tex]

[tex]=\$128.70[/tex]

Therefore, the amount to be pay for coat is $128.70.

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

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:

No.

Step-by-step explanation:

Because standard form is ax+by=c.

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]

Answer:

4w+3

Step-by-step explanation:

2/3(7w+4)-1/3(2w-1)

14/3w+8/3-2/3w+1/3

14/3w-2/3w+8/3+1/3

12/3w+9/3

4w+3