After 10 months the simple interest earned annually on an investment of $6000 was $769. Find the interest rate to the nearest tenth of a percent.

Let’s first know what y=mx+b is.

M= slope

B=y-intercept

Since the problem gives us the slope, we can add it in already, which helps us a lot.

y=4x+b

This problem gives us a coordinate. We can substitute the numbers with the values.

3=4(1)+b

3=4+b

-b=4-3

-b=1

b=-1

Now that we have the y-intercept, we now have the hard parts done and now all we do is put it together.

Answer: y=4x-1

To see if it is correct, we can substitute numbers in (like the coordinate) to see if it was right.

3=4-1

3=3

There is your answer!

The formula for arc length is:

s= r∅

Given that ∅= 7π/4

and r= 5

Therefore, arc length s= 7π/4 *5 = 35π/4

Answer:  The required arc length will be 27.5 units.

Step-by-step explanation:  We are given to find the arc length with the following information :

[tex]\theta=\dfrac{7\pi}{4},~~~\textup{radius},~r=5.[/tex]

We know that the length of an arc with angle subtended at the center α and radius of the circle r units is given by

[tex]\ell=r\alpha.[/tex]

Therefore, the required arc length will be

[tex]\ell=r\theta=5\times\dfrac{7\pi}{4}=\dfrac{35}{4}\times \dfrac{22}{7}=\dfrac{5\times 11}{2}=\dfrac{55}{2}=27.5.[/tex]

Thus, the required arc length will be 27.5 units.

The interval you use when finding the rate of change of a proportional relationship does matter because the behavior of the relationship could vary within different intervals. To illustrate this, consider a proportional relationship where y is directly proportional to x. If we calculate the rate of change for different intervals, we might get different results. Therefore, it is important to specify the interval when finding the rate of change to accurately represent the behavior of the relationship within that interval.

The interval you use when finding the rate of change of a proportional relationship does matter. The rate of change represents how a quantity changes with respect to another quantity. If you use different intervals, you may get different rates of change because the behavior of the relationship could vary within different intervals. Let me provide an example to illustrate this:

Suppose we have a proportional relationship where y is directly proportional to x:

y = kx

If we calculate the rate of change for different intervals, we might get different results. For example, if we consider the interval from x = 1 to x = 5, the rate of change would be (y2 - y1) / (x2 - x1) = (5k - k) / (5 - 1) = 4k / 4 = k. However, if we consider the interval from x = 3 to x = 7, the rate of change would be (y2 - y1) / (x2 - x1) = (7k - 3k) / (7 - 3) = 4k / 4 = k. In both cases, the rate of change is the same within each interval, but it may differ between intervals.

Therefore, it is important to specify the interval when finding the rate of change of a proportional relationship to accurately represent the behavior of the relationship within that interval.

Lets put Monday as 'm'

Monday: m

Tuesday: 2m

Wednesday 2m-6

The Three Days: 5m-6

Final Answer: 5m-6=19

Since 18 people withdrew 100 dollars each, that would be 18 multiply by 100 which is 1800

100 + 10m = 15m

5m = 100

m=20 movies

20 is the amount of movies to make it cost the same.

To find the number of movies at which the cost of both movie clubs would be the same, you set the cost equations for both clubs equal to each other and solve for the number of movies, m. The result is m=20.

The subject here is essentially figuring out where the total cost of each movie club is equal. In this case, we can define two equations representing the total costs of each movie club. For the first club, which charges a $100 membership fee and $10 per movie, that equation is C1 = 100 + 10m . For the second club, which charges no membership fee but $15 per movie, the equation is C2 = 15m. Setting these two equations equal to each other gives us 100 + 10m = 15m. Solving for m (the number of movies) we subtract 10m from both sides to get 100 = 5m, then divide both sides by 5, to find that m = 20.

Therefore, if you plan to buy 20 or more movies in a year, the first club would be more cost effective. If you plan to buy less than 20 movies, the second club would be the better option.

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the answer is -16 sooooo brainliest plzz

In mathematics, the absolute value of a number represents its distance from zero on the number line. If X is a rational number and Y is the opposite of X, their absolute values are the same because they are the same distance from zero, regardless of direction.

In the realm of mathematics, rational numbers have a property called absolute value. The absolute value of a number is its distance from zero on the number line, regardless of direction. So, if X is a rational number, Y being its opposite means it is the same distance from zero, but in the other direction.

For example, if X = 3 (a rational number), then Y = -3 (the opposite of X). Despite X and Y being opposites, their absolute values are the same: |3| = |-3| = 3, as both are 3 units away from zero.

Hence, no matter what values X and Y may have, if Y is the opposite of X (either positive or negative), their absolute values will always be equal because they are the same distance from zero.

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Lines L and M are parallel

m<2 = 38° (corresponding angles are equal)

We know:

[tex]LCM(a,\ b)=\dfrac{ab}{GCF(a,\ b)}[/tex]

We have

[tex]GCF(a,\ b)=2,\ LCM(a,\ b)=20,\ a\leq12,\ b\leq12[/tex]

Substitute:

[tex]20=\dfrac{ab}{2}\qquad|\cdot2\\\\ab=40[/tex]

[tex]40=1\cdot40=2\cdot20=4\cdot10=5\cdot8[/tex]

Only 4 and 10 meet the requirements of the question.

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40 and 1 NOT, because 40 > 12

20 and 2 NOT, because 20 > 12

5 and 8 NOT because GCF(5, 8) = 1

The numbers are 4 and 10 or 5 and 8.

The relation is given as,

                 [tex]LCM*GCF=m*n[/tex]

Where m and n are two numbers.

Given that,  [tex]GCF=2,LCM=20[/tex]

Substitute values in above relation.

              [tex]m*n=2*20=40[/tex]

Since, both numbers less than or equal to 12.

We observed that,

              [tex]4*10=40\\\\5*8=40\\[/tex]

The numbers are 4 and 10 or 5 and 8.

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An equivalent ratio of 64:60 is 16:15.

To get an equivalent ratio, you are going to simplify it like you would a fraction. An equivalent ratio would be 32:30. Then, just keep dividing both sides by the same number until both sides can't be divided by the same number. i.e. 9:6 -> 3:2 Both sides were divided by three.

I'm not quite sure what it's asking for you to do but...

_________

Yes, 15 includes 3 and 5, 5 and 3 multiplied is a way to get 15.

The multiple of 15 is 30, 45 and 60.

Yes, 15 is a multiple of each of its factors.

The factors of 15 include 3, and 5. Which is excluding 1 and itself, 15. So, if you ask if 15 is a multiple of its factors, the answer is yes. If you multiply 3 by 5, you get 15. If you multiply 5 by 3, you get 15.

Therefore, we can conclude that 15 is a multiple of its factors.

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Answer:

The possible digits 0, 1, 2 , 3 or 4 .

Step-by-step explanation:

The possible digits that could go in the thousands place to make  13_,644 ≈ 130,000   this statement correct are: 0 1, 2,3 or 4.

For example:  132,644 may rounded off to 130,000

Round the number to the nearest thousand make the numbers whose last three digit through 644 into the next lower numbers that ends in 000.

Using number line for this possibility as shown in the below diagram:

4x + 5y = 2(x + 3y)

4x + 5y = 2x + 6y   distributed 2 on the right side

2x + 5y = 6y           subtracted 2x from both sides

2x = y                      subtracted 5y from both sides

         if y = 2x

then 17(y) = 17(2x)

          17y = 34x

Answer: 34x

Answer:

Amplitude

Step-by-step explanation:

I just had this question and got it right

$12 per ticket divide 48 and 4 then if u want multipy 4x12=48

We are required to find the cost of 5 movie tickets

The Cost of 5 movie tickets is $60

Given:

Cost of 4 movie tickets = $48

Cost of each movie tickets = Cost of 4 movie tickets ÷ 4

= $48 ÷ 4

= $12

So,

Cost of 5 movie tickets = Cost of each movie tickets × 5

= $12 × 5

= $60

Therefore, the Cost of 5 movie tickets is $60

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[tex]f(x)=\dfrac{x}{2}-3,\ g(x)=3x^2+x-6\\\\(f+g)(x)=f(x)+g(x)=\left(\dfrac{x}{2}-3\right)+(3x^2+x-6)=\dfrac{1}{2}x-3+3x^2+x-6\\\\=3x^2+1\dfrac{1}{2}x-9[/tex]

[tex]Answer:\ \boxed{B.\ 3x^2+\dfrac{3}{2}x-9}}[/tex]

The perimeter of the rectangular pattern, formed by arranging 16 squares with an area of 16 square units in a 4x4 layout, is 16 units.

To determine the perimeter of a rectangular pattern formed by arranging 16 squares, each with an area of 16 square units, in a 4x4 layout, we can follow these steps.

First, we know the area of each square is 16 square units, which means the side length of each square is the square root of 16, which is 4 units.

Now, when these squares are arranged in a 4x4 pattern, you have 4 squares along the length and 4 squares along the width. The length and width, in terms of these squares, are both 4 squares.

The perimeter of a rectangular shape is calculated using the formula: Perimeter = 2 × (Length + Width).

Plugging in the values:

Perimeter = 2 × (4 + 4) = 2 × 8 = 16 units.

So, the perimeter of the resulting figure is 16 units. This means, when you trace the outline of this 4x4 arrangement of squares, the total distance around the shape is 16 units. Each side contributes 4 units, and there are four sides, giving us a total perimeter of 16 units. This calculation follows the basic principles of perimeter for rectangular shapes and applies them to the given arrangement.

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Answer:

ΔSTR is similar to ΔRTQ

Step-by-step explanation:

Given QRS is a right angled triangle. we have to find the similarity statement ΔSTR ~ Δ__

Let ∠S=x

In ΔSTR, by angle sum property

∠S+∠STR+∠SRT=180°

⇒ ∠SRT=90°-x

In ΔSRQ, by angle sum property

∠S+∠R+∠Q=180°

⇒ ∠Q=90°-x

In ΔSTR and ΔRTQ

∠SRT=∠Q=90°-x     (proved above)

∠STR=∠RTQ           (each 90°)

RT=RT                      (common)

Hence, by AAS rule ΔSTR≅ΔRTQ

∴ ΔSTR is similar to ΔRTQ

Option 4 is correct.

Answer:

RTQ

Step-by-step explanation:

Let ∠S=a, In ΔSTR, using angle sum property, we have

∠S+∠STR+∠SRT=180°

⇒ ∠SRT=90°-a

Again In ΔSRQ, using angle sum property, we have

∠S+∠R+∠Q=180°

⇒ ∠Q=90°-a

Now, In ΔSTR and ΔRTQ

∠SRT=∠Q=90°-a    (proved above)

∠STR=∠RTQ              (each 90°)

 RT=RT                      (common)

Hence, by AAS rule,

ΔSTR≅ΔRTQ

Thus,  ΔSTR is similar to ΔRTQ

Option 4 is correct.

Divide $62.50 by 5, and your answer will be $12.50 per ticket.

She should buy 5 boxes because if she bought 4 then she would have 8 without a box

d=discount tickets

f=full price tickets

d=f+180  (180 more full price tickets than discount tickets)

f+d=240

Answer:

b is the answer

Step-by-step explanation:

f + d = 240

f - d = 180

Answer: [tex]a=\frac{k}{9b+4}[/tex]

Step-by-step explanation:

↓↓↓↓↓↓↓↓↓↓↓↓↓↓

First, flip the equation.

[tex]9ab+4a=k[/tex]

Next, factor out variable a.

[tex]a(9b+4)=k[/tex]

Then, divide by 9b+4 from both sides.

[tex]\frac{a(9b+4)}{9b+4}=\frac{k}{9b+4}[/tex]

[tex]=a\frac{k}{9b+4}[/tex]

Hope this helps!

Thank you for posting your question at here on brainly.

-Charlie

Answer:

The value of a is [tex]a=\frac{K}{4+9b}[/tex].

Step-by-step explanation:

The given equation is

[tex]K=4a+9ab[/tex]

We have to solve the above equation  for a. So, we need to isolate the variable a.

Taking out a from the left side.

[tex]K=a(4+9b)[/tex]

Divide both sides by 4+9b to get the value of a.

[tex]\frac{K}{4+9b}=\frac{a(4+9b)}{4+9b}[/tex]

Cancel out the common factors from numerator and denominator.

[tex]\frac{K}{4+9b}=a[/tex]

Therefore the value of a is [tex]a=\frac{K}{4+9b}[/tex].

first simplify the inequalities:

3x+2>2  --> x>0   that corresponds to an open circle at 0 and shading to the right

3x <= 6 --> x<=2  that is a closed circle at 2 and shading to the left

together they have shading between open@0 and closed @2 so the

Answer (D) is correct

Let f(n) represent the number of bottles in the store on n-th week.

When n=0, f(n)=250.

Then  40% of the bottles were sold, this means that were sold 250·0.4=f(n)·0.4. The amount of bottles left is 250-250·0.4=f(n)-f(n)·0.4=f(n)·0.6.

If 48 new bottles arrived in shipments, then the amount of bottles became

f(n)·0.6+48=f(n+1).

Since n>0, then

f(n)=f(n-1)·0.6+48.

Answer: correct choice is A.

Option: A is the correct answer.

         A:    f(n) = f(n − 1) ⋅ 0.6 + 48, n > 0    

It is given that:

A store had 250 bottles of water.

Each week, 40% of the bottles were sold and 48 new bottles arrived in shipments.

This means that the number of bottles that will be present in the store after 40% of the bottles will be sold at a particular week= 100%-40%=60% plus 48 new arrival

This means that each time the number of bottles in the store will be 60% of the bottles that were sold previous week plus 48.

        Hence, if f(n-1) represent the number of bottle in the (n-1)th week then the number of bottles in the nth week will be represented by:

                     [tex]f(n)=60\%\ of\ f(n-1)+48\\\\i.e.\\\\f(n)=0.6\cdot f(n-1)+48[/tex]

f is increasing over the interval 0 < x < 2.

f(2) = 3.

f is decreasing over the interval 2 < x < 5.

In Mathematics and Geometry, a function f(x) is considered as an even function if the following condition holds for all x-values (both positive x-values and negative x-values) in the domain of function f(x):

f(x) = f(-x)  ⇒ symmetrical with y-axis.

This ultimately implies that, a function that is symmetric with respect to the y-axis is an even function.

In this context, we can logically deduce the opposite of this graph would be defined over the interval x ≥ 0. Therefore, we can reasonably infer and logically deduce the following true statements;

f is increasing over the interval 0 < x < 2.

f(2) = 3.

f is decreasing over the interval 2 < x < 5.

Answer:

Sample Response: You need to show that two sides of one triangle are proportional to two corresponding sides of another triangle, with the included corresponding angles being congruent.

Step-by-step explanation:

Different similarity theorems require different information.

The SAS similarity theorem requires two congruent sides and a congruent angle, between the corresponding sides.

The SAS similarity theorem stands for: Side-Angle-Side

This means that:

Hence, the SAS similarity theorem requires two congruent sides and a congruent angle, between the corresponding sides.

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12.2 jlasjajlsajlajlzwljdazdazwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww

Answer:

12.2

Step-by-step explanation:i did the work and got 12.2

Note the equal sign. What you do to one side, you do to the other.

First, combine like terms

-7x + -7x = -14x

-14x = 84

Isolate the x. Divide -14 from both sides

(-14x)/-14 = (84)/-14

x = 84/-14

Divide

x = -6

-6 is your answer for x

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