5(2c + 7) - 3c = 7(c + 5)

The principal amount is 85227.27 and the interest is 64772.73.

Solution:

Given:

Amount (A)= 150000

Number of years (n)= 8

Rate of interest (r)= [tex]9\frac{1}{2}\%=\frac{19}{2}\%[/tex]

To find: The principal (P)

We know that the principal is the sum of amount and interest. That is, [tex]\bold{P+I=A}[/tex]

This can be written as [tex]\bold{I=A-P \rightarrow(1)}[/tex]

The formula of simple interest is [tex]\bold{I=\frac{Pnr}{100} \rightarrow(2)}[/tex]

On equating (1) and (2) we get,

[tex]\Rightarrow\bold{A-P=\frac{Pnr}{100}}[/tex]

On substituting the values we get,

[tex]\Rightarrow\bold{150000-P=\frac{P\times8\times19}{100\times2}}[/tex]

On solving we get,

[tex]\bold{\Rightarrow 150000-P=0.76P}[/tex]

On grouping the like terms together we get,

[tex]\bold{\Rightarrow 150000=0.76P+P}[/tex]

[tex]\bold{\Rightarrow 150000=1.76P}[/tex]

[tex]\bold{\Rightarrow P=\frac{150000}{1.76}}[/tex]

[tex]\bold{\Rightarrow P=85227.2727\approx85227.27}[/tex]

If principal is 85227.27, then the interest will be [tex]\bold{I=150000-85227.27\rightarrow64772.73}[/tex]

Answer:

5

Step-by-step explanation:

Answer:

10 5

Step-by-step explanation:

10 ÷ 2 = 5 and 5 + 10 = 15

Answer:

5 and 10

Step-by-step explanation:

X×Y=15

X=15-Y

X=Y/2

Y/2=15-Y

Add Y to both sides

3Y/2=15

3Y=30

Y=10

X=5

The correct option that is not a characteristic of all parallelograms is C, 'diagonals are angle bisectors,' as it does not apply to every parallelogram, unlike the other options listed.

The question is related to the properties of parallelograms, and specifically, it asks which option is not a characteristic of all parallelograms. To answer this, we must review the properties of parallelograms:

Option A (Diagonals bisect each other) and Option B (Opposite angles are congruent) are indeed true characteristics of parallelograms. However, diagonals being angle bisectors is not a general characteristic of all parallelograms, making it incorrect for Option C. Finally, Option D (The sides are congruent) describes a property specific to a rectangle or a rhombus rather than all parallelograms. Thus the correct answer is C, diagonals are angle bisectors, as it is not a defining feature for all parallelograms. Parallelograms have diverse shapes like rectangles, squares, and rhombi, and this property doesn't apply universally.

Answer:

The Three expressions that have a sum or difference of 3 /4 .

B . 11/12 − 1/6

C. 3/5 + 3/20

E . 2/3 + 1/12

Step-by-step explanation:

The Three expressions that have a sum or difference of 3 /4 .

are

B . 11/12 − 1/6

[tex]\dfrac{11}{12}-\dfrac{1}{6}=\dfrac{11}{12}-\dfrac{1\times 2}{6\times 2}\\\\\dfrac{11}{12}-\dfrac{1}{6}=\dfrac{11}{12}-\dfrac{2}{12}=\dfrac{11-2}{12}=\dfrac{9}{12}=\dfrac{3}{4}[/tex]

Therefore,

[tex]\dfrac{11}{12}-\dfrac{1}{6}=\dfrac{3}{4}[/tex]

C. 3/5 + 3/20

[tex]\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{3\times 4}{5\times 4}+\dfrac{3}{20}\\\\\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{12}{20}+\dfrac{3}{20}=\dfrac{15}{20}=\dfrac{3}{4}[/tex]

Therefore,

[tex]\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{3}{4}[/tex]

E . 2/3 + 1/12

[tex]\dfrac{2}{3}+\dfrac{1}{12}=\dfrac{2\times 4}{3\times 4}+\dfrac{1}{12}\\\\\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{8+1}{12}=\dfrac{9}{12}=\dfrac{3}{4}[/tex]

Therefore,

[tex]\dfrac{2}{3}+\dfrac{1}{12}=\dfrac{3}{4}[/tex]

Expressions B (11/12 − 1/6), C (3/5 + 3/20), and E (2/3 + 1/12) each simplify to a sum or difference of 3/4 after finding a common denominator and simplifying the fractions.

To find 3 expressions that have a sum or difference of 3/4, let's evaluate each option given:

Therefore, the three expressions that have a sum or difference of 3/4 are B, C, and E.

[tex]\frac{-1}{18}[/tex]

Solution:

Given expression is [tex]\frac{y}{3}=-6[/tex]

To find the inverse of y.

⇒ [tex]\frac{y}{3}=-6[/tex]

Do cross multiplication.

⇒ y = –6 × 3

⇒ y = –18

Inverse of y means reverse the function.

We know that inverse of y is [tex]\frac{1}{y}[/tex].

⇒ [tex]\frac{1}{y}= \frac{-1}{18}[/tex]

Hence, inverse of y is [tex]\frac{-1}{18}.[/tex]

Answer:

Step-by-step explanation:

there's your graphed line
credits to desmos graphing calculator

Answer:

x = 2,  y = 3

Step-by-step explanation:

i) It is given that 5x - 3y =1

ii) It is also given that x = 2y - 4

iii) we can substitute the value of x from ii) in the equation in i) and we will get 5(2y - 4) - 3y = 1   ⇒ 10y - 20 -3y =  1   ⇒  7y = 21  ∴ y = 3

iv) substituting the value of y obtained in ii) we get x = (2 × 3) - 4 = 6 - 4 = 2.

v) Therefore x = 2.

Answer:

a, e

Step-by-step explanation:

a. function A has a slope of -2/3. the negative means it goes down. function B is going down on the graph so both functions have neg. rates of change.

b. function A's slope is -2/3. function b has a slope of -1.

c. since both functions slopes aren't the same they are not parallel.

d. 2/3 is a lesser rate of change than 1.

e. looking at the graph, function b is linear. A is linear since the "x" is not squared, cubed, etc.

Answer:

0.0025

Step-by-step explanation:

:)

1/4 of 1%, when expressed as a decimal, is equal to 0.0025

A percentage is a ratio with the second part always equal to 100. It represents parts per hundred.

We have been given 1%.

We replace percentage in fraction, and then fraction to decimal.

1% = 1/100 = 0.01

Now, we need to calculate 1/4th of this value, that is, 0.25 multiplied by the above value,

= 0.25 * 0.01 = 0.0025

So, our answer is 0.0025.

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Answer: -41

Step-by-step explanation:

-7 × 5 = -35

-35 - 6 = -41

Answer:

-41

Step-by-step explanation:

If 24 people have the flue out of 360 people then out of 900, 60 people would have flue if solved through percentage.

It is a ratio expressed as a fraction of 100. it's expressed using the sign %.

The percentage of individuals gets affected from flue out of 360 is 24*100/360

=2400/360

=6.67%

Then per 6.67% out of 900 approx 60 (900*6.67%) people would be affected from flue.

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Answer:

$8

Step-by-step explanation:

Given: Television advertising= $38 out of every $100 spent on advertising.

           Radio advertising= 21% as much as was spent on television ads.

As given there are $38 spent on television ads on every $100 of advertising.

∴ Amount spent on television ads= [tex]\frac{38}{100}[/tex]

Now, finding amount spent on radio advertising on every $100 spent on advertising.

We know, The amount spent on radio advertising was about 21% as much as was spent on television advertising.

∴ Amount spent on radio advertising= [tex]\frac{38}{100} \times \frac{21}{100}[/tex]

⇒ Amount spent on radio advertising= [tex]\$ 0.0798[/tex]

To know the amount spent on radio advertising on every $100 spending on advertising.

Amount spent on Radio advertising on every $100 spending= [tex]0.0798\times 100= \$ 7.98 \approx \$ 8[/tex]

Hence, $8 spent on radio advertising on every $100 spending.

About $7.98 out of every $100 spent on advertising was allocated to radio advertising, based on the information that $38 out of every $100 was used for television advertising and radio advertising accounted for 21% of the television advertising amount.

In 2004, about $38 out of every $100 spent on advertising was spent on television advertising. To find out how much of every $100 was spent on radio advertising, which was about 21% as much as was spent on television advertising, we apply the following calculation:

Amount spent on radio advertising = Television advertising amount × (Radio advertising percentage / 100)

Amount spent on radio advertising = $38 × (21 / 100)

Amount spent on radio advertising = $7.98

Therefore, $7.98 out of every $100 spent on advertising was spent on radio advertising.

Answer:

[tex]\large\boxed{u^2+5u-6=0,\ where\ u=(x+2)}[/tex]

Step-by-step explanation:

[tex](x+2)^2+5(x+2)-6=0\\\\\text{Substitute}\ (x+2)=u:\\\\\underbrace{(x+2)}_{u}^{}^2+5\underbrace{(x+2)}_{u}-6=0\\\\u^2+5u-6=0[/tex]

Answer:

The answer is C

Step-by-step explanation:

Use the distance formula Sqrt ( (x2-x1)^2 +(y2-y1)^2)

Distance = sqrt ( (-8 - -2)^2 +(4- -4)^2)

Distance = sqrt(-6^2 + 8^2)

Distance = sqrt ( 36 + 64)

Distance = sqrt(100)

Distance = 10

The length is 10

Answer: 10 units

Step-by-step explanation: took test hope this helps

Answer:

-60

Step-by-step explanation:

9+x/9=7/3

x/9=7/3-9

x/9=7/3-27/3

x/9=-20/3

x=(-20/3)(9)

x=-180/3

x=-60

The area of the part of the tablecloth that hangs over the table is 285 square inches

Step-by-step explanation:

In order to find the area of table cloth that hangs over the table, we have to find the area of table and the total area of table cloth.

Given

Area of table = [tex]A_t = 2116\ in^2[/tex]

To find the side of the square

[tex]A_t = s^2\\s^2 = 2116[/tex]

Taking Square root on both sides

[tex]\sqrt{s^2} = \sqrt{2116}\\s = 46\ inches[/tex]

When the table cloth is hanged, 3 inches are left to hang over this means that the side will now be: 46+3 = 49 inches

The area of table cloth = [tex]A_c = 49*49 = 2401\ in^2[/tex]

The area of table cloth that will be hung over the table is:

[tex]A_c-A_t\\= 2401-2116\\= 285\ in^2[/tex]

Hence,

The area of the part of the tablecloth that hangs over the table is 285 square inches

Keywords: Square, side

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Answer:

44

Step-by-step explanation:

10 + 12 + 4 + 4 + 6 + 8 = 44

The perimeter of the figure is 26 inches.

The perimeter of the figure is the total length of all the sides. To calculate the perimeter, we simply add up the lengths of all the sides:

Perimeter = 6in + 4in + 4in + 12in

Perimeter = 26in

Therefore, the perimeter of the figure is 26 inches.

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Answer:

the given statement is true.

Step-by-step explanation:

i) It is given that the base angles of an isosceles triangle each measure 37°.

ii) Adding the values of the base angles is = 37° + 37° = 74°

iii) from the property of triangles we know that the sum of all the angles in a triangle is equal to 180°

iv) let the vertex angle be = y°

v) Therefore we can say from ii), iii) and iv) above that

      74° + y° = 180°

vi) therefore the vertex angle y = 180° - 74° = 106°

Hence the given statement is true.

Answer:

there would be 100 flowers in basket a

Step-by-step explanation:

for the second part of the ratio to be 40 you have to multiply the 2 by 20. to find out how many would be in basket a you do the same thing to the other side of the ratio and multiply 5 by 20 which gives you 100

Hello there i hope you are having a good day :) Your question : The sum of twice a number and half the number is 10.

Answer would be : 2x + x/2 = 10

Hopefully that helps you ❤

Answer:

2x+x/2 = 10

Step-by-step explanation:

x is the unknown value.

2x would be used to represent the unknown value of twice that number.

/2 would be used to represent half the number.

Hope this helps you!

Answer:x=-11

Step-by-step explanation:

Answer:

The square root of 64 is 8.   8*8=64

Hope this helps,  

:)

Answer: [tex]\theta\approx1.78\ rad[/tex]

Step-by-step explanation:

By definition, the Arc lenght can be calculated with the following formula:

[tex]s=r\theta[/tex]

Where "s" is the Arc lenght, "r" is the radius and [tex]\theta[/tex] is the central angle measured in radians.

From that equation you can solve for [tex]\theta[/tex] dividing both sides of the equation by the radius "r", then:

[tex]\frac{s}{r}=\frac{r\theta}{r}\\\\\theta=\frac{s}{r}[/tex]

According to the information given in the exercise:

[tex]s=21.3\ in[/tex]

And you can identify in the figure that the radius of the circle is:

[tex]r=12\ in[/tex]

Therefore, you can substitute values into the equation:

[tex]\theta=\frac{21.3\ in}{12\ in}[/tex]

Finally, evaluating, you get the following result:

[tex]\theta=1.775\ rad[/tex]

Rounded to the nearest hundredth of a radian:

[tex]\theta\approx1.78\ rad[/tex]

Answer:

please show the figure

Step-by-step explanation:

Which figure lol looool

The company should sell each widget for $28.25, to the nearest cent.

To maximize profit, we need to find the vertex of the parabola represented by the profit equation y = -2x^2 + 113x - 497. Since the coefficient of x^2 is negative, the parabola opens downwards, and the vertex represents the maximum point. The x-coordinate of the vertex of a parabola in the form of y = ax^2 + bx + c can be found using the formula -b/2a.

For the equation y = -2x^2 + 113x - 497, a = -2 and b = 113. Plugging these values into the formula gives us: x = -113 / (2 × -2) = -113 / -4 = 28.25. Therefore, to maximize profit, the company should sell each widget for $28.25, to the nearest cent.

Amanda must spend more than 8 minutes on Routine #1 to burn more calories than Routine #2.

Step-by-step explanation:

Routine # 1;

Calories burned in running = 15.5 per minute

Let,

t be the minutes spent running.

T = total calories burned

T = 15.5t

Routine # 2;

Calories burned while walking = 22 calories

Calories burned while running = 12.75 per minute

T = 12.75t + 22

For burning more calories in Routine 1;

Routine 1 > Routine 2

[tex]15.5t>12.75t+22\\15.5t-12.75t>22\\2.75t>22\\[/tex]

Dividing both sides by 2.75

[tex]\frac{2.75t}{2.75}>\frac{22}{2.75}\\t>8[/tex]

Amanda must spend more than 8 minutes on Routine #1 to burn more calories than Routine #2.

Keywords: linear inequality, division

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Answer:

The 2nd deal is better

Step-by-step explanation:

First you divide the chicken nuggets by the price and then find how much one chicken nugget costs. In this case $10 divided by 8 is $1.25 while $7.50 divided by 5 is $1.50. The first deal costs more for one chicken nugget so deal 2 is better

Answer:

deal 2 is better the chicken nuggets are cheaper and you could have more chicken nuggets even though it cost more then deal 1, 1 chicken nugget is cheaper in deal 2 than it is in deal 1 so I think you should go for deal 2 Hope I Helped :)

Step-by-step explanation: