If the interest earned on an account after 7 years at 6% is $1785 ,what is the initial value

Answer:

c ≈ 4.2 ft

Step-by-step explanation:

Using the cosine rule with a = 7, b = 8 and C = 32°, then

c² = 7² + 8² - (2 × 7 × 8 × cos32°)

   = 49 + 64 - (112 × cos32°)

   = 113 - 94.98

c = [tex]\sqrt{113-94.98}[/tex] ≈ 4.2 ft ( to the nearest tenth )

Answer:

x=√67 or x=−√67

Step-by-step explanation:

Step 1: Add 7 to both sides.

x2−7+7=60+7

x2=67

Step 2: Take square root.

x=±√67

x=√67 or x=−√67

Answer:

The slope intercept is y=mx+b

y=-1x (you go down one over one from your y-intercept)

y=-1x-1 (It would be minus one because that is where it crosses the y-axis)

Step-by-step explanation:

Answer:

The co-ordinates of Q' is (5,2).

Step-by-step explanation:

Given:

Pre-image point

Q(-7,-6)

To find Image point Q' after following translation.

[tex](x,y)\rightarrow (x+12,y+8)[/tex]

Solution:

Translation rules:

Horizontal shift:

[tex](x,y)\rightarrow (x+k,y)[/tex]

when [tex]K>0[/tex] the point is translated [tex]k[/tex] units to the right.

when [tex]K<0[/tex] the point is translated [tex]k[/tex] units to the left.

Vertical shift:

[tex](x,y)\rightarrow (x,y+k)[/tex]

when [tex]K>0[/tex] the point is translated [tex]k[/tex] units up.

when [tex]K<0[/tex] the point is translated [tex]k[/tex] units down.

Given translation [tex](x,y)\rightarrow (x+12,y+8)[/tex] shows the point is shifted 12 units to the right and 8 units up.

The point Q' can be given as:

Q'=[tex](-7+12,-6+8)=(5,2)[/tex]

So, the co-ordinates of Q' is (5,2). (Answer)

Answer:

Step-by-step explanation:

y=mx+b

Answer:

y=-1/3x+2/7

Step-by-step explanation:

y=-3x+6/7

x=-3y+6/7

-3y=x-6/7

y=-1/3x+(6/7)/3

y=-1/3x+(6/7)(1/3)

y=-1/3x+6/21

y=-1/3x+2/7

Answer:

2 y for every 1 x

Step-by-step explanation:

2 and 1 is the answer

Answer:

infinately many solutions

Step-by-step explanation:

Let's note the information.

This is what we know:

Every buttons came in packages of 30 per student.

Every bookmark came in packages of 50 per person.

Know, we need to do some multiplying.

30 x 400 & 50 x 400

Now solve.

30 X 400 = 12000.

So we now know that they have an estimated 12000 buttons total.

Now, we find x for bookmarks.

50 x 400 = 20000

That means total that estimated that 20000 bookmarks will be given.

Answer:

15 packages of buttons

9 packages of bookmarks

Step-by-step explanation:

We need to find the least common multiple (LCM) of 30 and 50.

30 = 2×3×5

50 = 2×5²

LCM = 2×3×5²

LCM = 150

Now we need to find a multiple of LCM that is greater than 400.

3LCM = 450

The committee needs at least 450 of each, which means they need at least 15 packages of buttons and 9 packages of bookmarks.

Answer:

53

Step-by-step explanation:

f(n) = 7n - 3

f(8) = 7*8 - 3 = 56 - 3 = 53

Final answer:

To find the 8th term of the arithmetic sequence given by f(n) = 7n - 3, substitute n with 8 and calculate the result to get 53.

Explanation:

The question is about finding the 8th term of an arithmetic sequence. The function for the sequence is given as f(n) = 7n - 3. To find the 8th term, we substitute n with 8 in the function. So, f(8) = 7(8) - 3. Calculating the value, we get f(8) = 56 - 3 = 53.

So, the 8th term of the sequence is 53. This result is obtained by applying the formula for the general term of an arithmetic sequence, where f(n) represents the term at position n. In this sequence, each term is obtained by adding 7 to the previous term.

The constant difference between successive terms (7 in this case) is a characteristic feature of an arithmetic sequence. Therefore, the 8th term of the sequence is 53.

Answer:

The solution is y> -1

Step-by-step explanation:

y- 6 > -7

y> -7+6 (add 6 on both sides)

y> -1

The graph should the the first option from the right, with the dot above -1.

Since y is greater than -1, the dot should be on -1 and the arrow should be pointing towards the right. It shouldn't be a coloured dot because the sign is 'greater than' (>) not 'greater or equal to' (≥)

Answer:

a. y = 0.012x²

b. 4.80 m

c. 25 m/s

Step-by-step explanation:

a. First, we need to determine what kind of function this is (linear, quadratic, etc.).

Logically, the function must pass through the origin, so we can compare the ratios between points.

Let's look at (5.00, 0.30) and (10.00, 1.20).  When we double the speed, the depth quadruples.  That tells us this must be a quadratic equation.

y = kx²

Plug in a point to find k:

0.30 = k (5.00)²

k = 0.012

Therefore, the equation is:

y = 0.012x²

We can check our answer by plugging in more points.

1.20 = 0.012 (10.00)²

2.70 = 0.012 (15.00)²

b. Find y when x = 20.00.

y = 0.012 (20.00)²

y = 4.80

c. Find x when y = 7.50.

7.50 = 0.012 x²

x = 25

Answer:

$ 140.55 ≤ $ 7.59x + 0.89$ y

$ 140.55 ≤ $ 9.37x   where 0≤ x ≤ 15.

Step-by-step explanation:

$ 140.55 ≤ $ 7.59x + 0.89$ y

Let x be the number of sweatshirts and y be the number of bags where y= 2x

and 0≤ x ≤ 15.

$ 140.55 ≤ $ 7.59x + 0.89$ (2x)   Putting y= 2x

$ 140.55 ≤ $ 7.59x + $ 1.78x

$ 140.55 ≤ $ 9.37x  where 0≤ x ≤ 15.

Answer:

$ 140.55 ≤ $ 7.59x + 0.89$ y

$ 140.55 ≤ $ 9.37x   where 0≤ x ≤ 15.

Step-by-step explanation:

$ 140.55 ≤ $ 7.59x + 0.89$ y

Let x be the number of sweatshirts and y be the number of bags where y= 2x

and 0≤ x ≤ 15.

$ 140.55 ≤ $ 7.59x + 0.89$ (2x)   Putting y= 2x

$ 140.55 ≤ $ 7.59x + $ 1.78x

$ 140.55 ≤ $ 9.37x  where 0≤ x ≤ 15.

Step-by-step explanation:

Answer:

B)12

Step-by-step explanation:

6/x = 4/8

6/x = 1/2

6 * 2 = 1 * x

12 = x

x = 12

Answer:

25%

Step-by-step explanation:

Draw a Venn diagram.  One circle is 95%, and the other circle is 30%.  Let's say x is the overlap.  The total is 100%.  If you add the 95 and 30 together, you'll be counting the overlap twice, so subtract one x.

95 + 30 − x = 100

x = 25

Complete Question:

As you missed to add the area and length value. So, after a little research I was able to find the complete question. I will answer the question based on this complete question I am mentioning, but hopefully it would clear your concept anyways. So, here is the complete question.

The Area of a rectangular patio is 5 5/8 square yards, and it's length is 1 1/2 yards.What is the patio's width,in yards?

Answer:

The width of patios is [tex]w = \frac{15}{4} yards[/tex].

Step-by-step explanation:

As the area of a rectangular patio is [tex]A = 5\frac{5}{8}[/tex] square yards.

⇒ [tex]A = 5\frac{5}{8}[/tex]

⇒ [tex]A = 5\frac{5}{8}[/tex] can be written as : [tex]A = \frac{45}{8}[/tex]

The length of a rectangular patio is [tex]l = 1\frac{1}{2}[/tex] square yards.

⇒[tex]l = 1\frac{1}{2}[/tex]

⇒[tex]l = 1\frac{1}{2}[/tex]  can be written as : [tex]l = \frac{3}{2}[/tex]

As the area of rectangular patio can be computed by multiplying the length and width. So, width [tex](w)[/tex] can be computed by dividing the Area by length.

[tex]A = lw[/tex]

[tex]w = \frac{A}{l}[/tex]

So, [tex]w = \frac{\frac{45}{8}}{\frac{3}{2} }[/tex]

[tex]w = (\frac{45}{8}) (\frac{2}{3} )[/tex]

[tex]w = \frac{90}{24}[/tex]

[tex]w = \frac{15}{4}[/tex] or [tex]w = 3\frac{3}{4}[/tex]

Hence, the width of patios is [tex]w = \frac{15}{4} yards[/tex].

Keywords: area of rectangle, width, length

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Answer:

the answer is 3

Step-by-step explanation:

Final answer:

The multiplication property of equality states that multiplying or dividing both sides of an equation by the same number does not change the equality. The reciprocal of 1/3 is 3/1 or 3. So, if you multiply or divide both sides of an equation by 3/1 (the reciprocal of 1/3), you will maintain the equality.

Explanation:

The multiplication property of equality states that multiplying or dividing both sides of an equation by the same number does not change the equality. In this case, we have the fraction 1/3. The reciprocal of 1/3 is 3/1 or 3. Multiplying both sides of an equation by 3 is equivalent to dividing both sides by 1/3. So, if you multiply or divide both sides by 3/1 (the reciprocal of 1/3), you will maintain the equality.

Answer:

D

Step-by-step explanation:

You can see, MN consists of the three lines in the picture. So you just need to sum them tougher in an equation with it's original value 81.

5 + 3x - 8 + 4x = 81

7x = 81 + 3

7x = 84 / : 7

x = 12

The value x from the given line segment is 12 units. Therefore, option D is the correct answer.

A line segment is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon.

Given that, MN=81.

Here, MN=5+3x-8+4x

MN=7x-3

7x-3=81

7x=81+3

7x=84

x=84/7

x=12

Therefore, option D is the correct answer.

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Answer:

The total payment Janie have to make is $5466 .

Step-by-step explanation:

Given as :

The loan principal = $4850

The rate of interest applied = 13.8% compounded monthly

Let The time period of loan = t years

The monthly payment she make = $455.50 each month

I.e She make payment for t years = $455.50 × n

where n is the number of terms

From Compound Interest

Amount = Principal × [tex](1+\dfrac{\textrm rate}{12\times 100})^{12\times time}[/tex]

Or,  $455.50 × n  = $4850 × [tex](1+\dfrac{\textrm 13.8}{12\times 100})^{12\times time}[/tex]

Or, [tex]\dfrac{455.50}{4850}[/tex] × n  = [tex](1.0115)^{12\times 1}[/tex]

Or, 0.0939 × n  = [tex](1.0115)^{12}[/tex]

Or, 0.0939 × n = 1.14707

∴ n = [tex]\dfrac{1.14707}{0.0939}[/tex]

I.e n = 12.21 ≈ 12

So, The number of terms Janie she will pay = 12

So, The total payment she have to make = $455.50 × 12 = $5466

Hence The total payment Janie have to make is $5466 . Answer

Answer:

She will have to make 12 payments

Step-by-step explanation:

To calculate the area of a carpet square with sides of 9 inches, you multiply the side length by itself, resulting in an area of 81 square inches.

The question is asking for the area of a carpet square whose sides are 9 inches long. To find the area of a square, you multiply the length of one side by itself, because the formula for the area of a square is Area = side × side. In this case, each side of the carpet square is 9 inches long.

So, the area of the carpet square would be calculated as follows:

Therefore, the area of the carpet square is 81 square inches.

Answer:

22.18 = x

Step-by-step explanation:

a^2 + (b)^2 = (x/2)^2

a = sqrt(74)

b = 7

x/2 = ?

(74)[^1/2]^2 = 74            

b^2 = 7^2 = 49

74 + 49 = (x/2)^2       Substitute into a^2 + b^2 = c^2

123 = (x/2)^2              Combine like terms

(123^0.5) = x/2           Take the square root of both sides.

11.09 = x/2                  Multiply both sides by 2

11.09*2 = x

22.18 = x                     The full length of the base of the triangle is 22.18

Answer:

10

Step-by-step explanation:

Trust me

Answer:

2!

Step-by-step explanation:

To find out what fraction of 2 1/2 is 4/5, convert 2 1/2 to a fraction (5/2), then multiply 4/5 by the reciprocal of 5/2 which gives 8/25. So, 4/5 is 8/25 of 2 1/2.

The question is asking about what fraction of 2 1/2 is 4/5. In order to solve this, we should firstly convert the mixed number 2 1/2 to a fraction, which is 5/2. Then we have to divide 4/5 by 5/2 to find out the fraction. To divide fractions, we multiply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor).

So, the problem becomes 4/5 * 2/5, and the solution is 8/25. Therefore, 4/5 is 8/25 of 2 1/2.

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Answer:

The closed linear form of the given sequence is [tex]a_{n}=0.75n-0.45[/tex]

Step-by-step explanation:

Given that the first term [tex]a_{1}=0.3[/tex] and [tex]a_{n+1}=a_{n}+0.75[/tex]

To find the closed linear form for the given sequence

The formula for arithmetic sequence is

[tex]a_{n}=a_{1}+(n - 1)d[/tex]  (where d is the common difference)

The above equation is of the given form  [tex]a_{n+1}=a_{n}+0.75[/tex]

Comparing this we get d=0.75

With [tex]a_{1}=0.3[/tex] and d=0.75

We can substitute these values in [tex]a_{n}=a_{1}+(n - 1)d[/tex]

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

[tex]=0.3+(n-1)(0.75)[/tex]

[tex]=0.3+0.75n-0.75[/tex]

[tex]=-0.45+0.75n[/tex]

Rewritting as below

[tex]=0.75n-0.45[/tex]

Therefore [tex]a_{n}=0.75n-0.45[/tex]

Therefore the closed linear form of the given sequence is [tex]a_{n}=0.75n-0.45[/tex]

Answer:

The first step in evaluating {[(−)]}÷ is operating the brackets

Step-by-step explanation:

To find the first step in evaluating {[(−)]}÷ :

In general we may use BODMAS operation to evaluate the expression and is stands for

BODMAS- B for Brackets in the expression

                 O for operations in brackets for the expression

                 D for  doing division operation in the  expression

                M for doing multiplication operation in the expression

                 A for  doing addition operation in the expression

                 S for doing subtraction operation in the expression

Applying all the operations and finally weget the evaluated expression or values.

Therefore the first step in evaluating {[(−)]}÷ is operating the brackets

Answer:

$5.75

Step-by-step explanation:

3.45 divided by 3 is 1.15. 1.15 times 5 is 5.75.

The cost of 5 pounds of oranges at a unit rate of 1.15 dollars is 5.75 dollars.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Mrs. Alveres purchased 3 pounds of oranges for $3.45.

∴ The cost of 1 pound of orange is (3.45/3) dollars.

= 1.15 dollars.

If the cost of 1 pound of orange is 1.15 dollars,

∴ The cost of 5 pounds of oranges is,

= (5×1.15) dollars.

= 5.75 dollars.

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Answer:

1 11/20m

Step-by-step explanation:

4 times 5 is 20

3/4(5) 4/5(4) =

15/20m + 16/20m =

31/20m = 1 11/20m

Answer:

[tex]3n^3(2-n^2)[/tex]

Step-by-step explanation:

Given expression:

[tex]6n^3-3n^5[/tex]

To factor out the expression completely.

Solution:

In order to factor out the expression, we will find the greatest common factor of each term.

To find the G.C.F. of the two terms, we will list down their factors and then find the common ones.

The factors of the terms can be given as:

[tex]6n^3=2\times 3\times n\times n\times n[/tex]

[tex]3n^5=3\times n\times n\times n \times n\times n[/tex]

The G.C.F. = [tex]3\times n\times n\times n=3n^3[/tex]

So, we factor out the G.C.F. and write the remaining factors inside the parenthesis.

The expression will be given using distributive property as:

⇒ [tex]3n^3(2-n^2)[/tex] (Answer)

Final answer:

To factor out [tex]6n^3 - 3n^5,[/tex] find the greatest common factor and simplify the expression.

Explanation:

A factor, in mathematics, refers to a number or algebraic expression that divides another number or expression evenly, meaning without leaving a remainder. When we say that one number is a factor of another, it means that when you divide the larger number by the factor, the result is an integer. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because each of these numbers divides 12 without leaving a remainder.

Factoring out [tex]6n^3 - 3n^5[/tex] involves finding the greatest common factor of the terms.

Step 1: Factor out [tex]n^3[/tex] from both terms to get [tex]n^3(6 - 3n^2).[/tex]

Step 2: Further simplify to [tex]n^3(2)(3 - n^2[/tex]) for the final factored form.

Answer:All the answers were correct but her calculating was wrong.

Step-by-step explanation: Jordana could not find the scale factor she was looking in the wrong place but the answer was correct and when she calculated she it wrong but the answer was correct.

Answer:

C

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

87/29=3

3$ for each pound.

20*3= 60.

answer is 60.

The perimeter of the triangle is: 13x+6

Step-by-step explanation:

The perimeter is the length of the outer boundary of any closed geometrical shape.

So,

Given

[tex]Side\ 1 = s_1 = 5x+3\\Side\ 2 = s_2 = 5x+5\\Side\ 3 = s_3 = 3x-2[/tex]

The perimeter will be:

[tex]P = s_1+s_2+s_3\\= (5x+3)+(5x+5)+(3x-2)\\=5x+5x+3x+3+5-2\\=13x+6[/tex]

The perimeter of the triangle is: 13x+6

Keywords: Perimeter, geometry

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