Need help quickly please!!!

Need Help Quickly Please!!!

Answers

Answer 1

Answer:

8

Step-by-step explanation:

Answer 2
Th3 answer is 8 goodbye

Related Questions

Find the value of x. Enter a decimal rounded to the nearest tenth.

Answers

Answer:

x = 3.6

Step-by-step explanation:

The 2 chords intersect inside the circle, thus

The product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord, that is

5x = 6 × 3 = 18 ( divide both sides by 5 )

x = 3.6

calculate the length of the line segment. round your answer to the nearest tenth.

a) 4.6
b) 6.9
c) 8.6
d) 9.3

Answers

Answer:

c) 8.6

Step-by-step explanation:

Take the coordinates of the two points.

(0,8) and (7,3)

Formula:

√(x₁ - x₂)² + (y₁ - y₂)²

Substitute:

√(0 - 7)² + (8 - 3)²

√(-7)² + (5)²

√(49) + (25)

√(74) ≈ 8.6

Final answer:

The question appears to be incomplete as it doesn't provide the necessary coordinates for calculating the length of a line segment. The distance formula or Pythagorean theorem would generally be used to calculate this in Mathematics.

Explanation:

Given the format of the question, it seems that it's incomplete or missing the relevant coordinates we need to calculate the length of a line segment. Normally in mathematics, we would use the distance formula, or Pythagorean theorem, to compute the length of a line segment between two points in a plane. The formula is √[(x₂-x₁)² + (y₂-y₁)²], where (x₁,y₁) and (x₂, y₂) are the coordinates of the two points. In this scenario, without information about the coordinates, we can't compute the length of a line segment. However, if you provided me with the coordinates, I can guide you in computing the length of the line segment.

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Simplify 7x+4-2x+6 pls help

Answers

It would be 5x+10 or 9x+10

Answer:

5x+10

Step-by-step explanation:

you will add 7x_2x=5x

then 4+6=10

What is the answer to -8(-8x-6)=-6x-22

Answers

Answer:

THE ANSWER IS 1.2068965517

Step-by-step explanation:

WILL MARK BRAINLIEST AND THANK YOU!!! PLEASE HELP!!

Find the area of the shaded region.

540 sq km


113.1 sq km


426.9 sq km


320 sq km

Answers

Answer:

426.9 Km²

Step-by-step explanation:

The shaded area is the area of the triangle subtract the area of the circle.

Area of triangle = 0.5 bh ( b is the base and h the perpendicular height )

Here b = 40 and h = 27, thus

Area = 0.5 × 40 × 27 = 20 × 27 = 540 Km²

Area of circle = πr² ← r is the radius

Here the diameter is 12, thus radius = 12 ÷ 2 = 6

Area = π × 6² = 36π ≈ 113.1 Km²

Shaded area = 540 - 113.1 = 426.9 Km²

find the length of the orther leg when one leg is 20 and hypotenous is 25

Answers

Answer:

15

Step-by-step explanation:

Do 25 ^ 2 = 625

Do 20 ^ 2 = 400

Because you're finding something that's nor the hypotenuse you subtract

So you do 625 - 400 = 225

Then you do the square root of 225 to get the answer

Which is 15

Answer:

15

Step-by-step explanation:

Let 'l' be the length of the other leg

Using pythagoras theorem,

25² = 20² + l²

625 = 400 + l²

225 = l²

l = 15

Solve these word problems by graphing, substitution or elimination.

Answers

(1) The numbers are 8 and 16.

(2) John have 12 nickels and 6 dimes.

Solution:

(1) Let x and y be the two numbers.

Sum of two numbers = 24

⇒ x + y = 24 – – – – (1)

One number = Other number – 8

⇒ x = y – 8 – – – – (2)

Substitute equation (2) in equation (1), we get

⇒ y – 8 + y = 24

⇒ 2y – 8 = 24

Add 8 on both side of the equation, we get

⇒ 2y = 32

Divide by 2 on both sides.

y = 16

Substitute y = 16 in equation (2)

⇒ x = 16 – 8

x = 8

Hence the numbers are 8 and 16.

(2) Let n and d be the nickels and dimes respectively.

Nickels + Dimes = 18

⇒ n + d = 18 – – – – (1)

Nickles = Dimes + 6

⇒ n = d + 6 – – – – (2)

Substitute equation (2) in equation (1), we get

⇒ d + 6 + d = 18

⇒ 2d + 6 = 18

Subtract 6 from both side of the equation.

⇒ 2d = 12

Divide by 2 on both side of the equation, we get

d = 6

Substitute d = 6 in equation (1), we get

⇒ n = 6 + 6

n = 12

Hence John have 12 nickels and 6 dimes.

Justify each step in the solution of the equation 5(x+2)=24-2x

Answers

Final answer:

To solve the equation 5(x+2)=24-2x, distribute, combine like terms, solve for x, and check the solution. The solution x = 2 satisfies the equation, so it is valid.

Explanation:

To solve the equation 5(x+2)=24-2x, we can justify each step as follows:

Distribute the 5 to the terms inside the parentheses: 5x + 10 = 24 - 2x

Combine like terms on both sides of the equation: 5x + 2x = 24 - 10

Combine the x terms: 7x = 14

Divide both sides of the equation by 7 to solve for x: x = 2

Check the solution by substituting it back into the original equation: 5(2+2) = 24 - 2(2)

Simplify the left side: 5(4) = 24 - 4

Multiply: 20 = 20

The solution x = 2 satisfies the equation, so it is valid.

Write a quadratic equation and solve it by completing the square. Show your work.

Answers

Answer:

Let the quadratic equation be  [tex]2x^2 +12x+ 6[/tex]

Step 1: Take the coefficients of the [tex]x^2[/tex] term and divide the entire equation

Here the coefficient of [tex]x^2[/tex] is 2

So  dividing the entire equation by 2, we get

[tex]x^2 +6x+ 3[/tex]

Step 2:  Move the constant term to the right side of the equation

[tex]x^2 +6x = - 3[/tex]

Step 3: Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation

[tex](\frac{b}{2})^2[/tex] =  [tex](\frac{6}{2})^2[/tex] = [tex](3)^2[/tex]  =  9

[tex]x^2 +6x + 9 = - 3 +9[/tex]

[tex](x+3)^2 = 6[/tex]

Step 4: Take the square root on both sides of the equation

[tex](x+3) = \sqrt{6}[/tex]

[tex]x+3 = \pm 2.45[/tex]

Step 5 Subtract 3 from both sides:

[tex]x+3 - 3 = \pm 2.45 -3[/tex]

[tex]x = \pm 2.45 -3[/tex]

x =  2.45 - 3   or x = -2.45 - 3

x = - 0.55  or  x = -5.45

Martin has a 7/23 balloon mortgage on his $195,000 home. He has been

making payments of $965 each month and will have a balloon payment due

for the amount of $170,143. If he decides to make the balloon payment, what

will be the total financed price he paid for his home?

Answers

Answer: 251,203

Step-by-step explanation:

Martin pays 965 every month for seven years. Therefore,

965×12×7= 81,060

Then, he has a balloon payment of 170,143 to make. Therefore, totaal financed price he paid for his home is 81,060+170,143= 251,203.

Answer: 251,203

Step-by-step explanation:

Martin pays 965 every month for seven years. Therefore,

965×12×7= 81,060

Then, he has a balloon payment of 170,143 to make. Therefore, totaal financed price he paid for his home is 81,060+170,143= 251,203.

Compare and contrast the methods used by African and Asian nations to achieve independence.

Answers

Answer: Decolonization as a result of World War II.

Step-by-step explanation:

With the end of World War II, the process of decolonization of the African and Asian continents began. It is the result of the destruction brought with it by World War II, but also by the liberalization that took place in Europe after World War II. In this context, it isn't effortless to point out the particular methods used by nations on these two continents. Decolonization is, however, an independent will and intervention of European countries.Yet the colonization of nations was not entirely passive in terms of resistance to the European invaders. There were several uprisings against the colonists. However, what characterizes both fights for independence is the emergence of nationalism. This is the pattern that African and Asian countries have taken over from Europeans. The form of resistance also consisted in the fact that there was a specific political will on the part of certain domestic elites, as in the case of the West African National Congress or the South African National Congress.A particular form of struggle for independence existed in India. This Asian country led its effort by methods of civil disobedience, non-payment of taxes, and refusal to work. The creator of this form of struggle was the leader of the Indian independence movement Mahatma Gandhi. An example of diminishing "third country" influence was an international intervention. Such an example is evident in Korea, where the United States and the Soviet Union eliminated Japanese colonial pretensions by their impact.

48) Amily wrote the riddle below.
I am a quadrilateral.
All my sides are parallel.
I have 4 angles, but they are not all equal.
What shape could I be?
What shape does Amily's riddle best describe?
A) Pentagon B) Rectangle C) Rhombus D) Trapezoid

Answers

Answer:

C)Rhomus

Step-by-step explanation:

a rhombus is parallel

The correct answer is option C. The shape Amily's riddle best describes is Rhombus.

Let's analyze the riddle step by step to determine which shape Amily is describing.

1. Quadrilateral: The shape has four sides.

2. All sides are parallel: This indicates that opposite sides are parallel to each other, which means the shape is a type of parallelogram.

3. 4 angles, but they are not all equal: This means that although the shape has four angles, they are not all the same measure.

Given these clues, let's evaluate each option:

A) Pentagon: This is a five-sided shape, not a quadrilateral. So, this option is incorrect.

B) Rectangle: A rectangle has four sides and opposite sides are parallel. However, all the angles in a rectangle are equal (each angle is 90 degrees). So, this option is also incorrect.

C) Rhombus: A rhombus has four sides and opposite sides are parallel. Additionally, all sides are of equal length. However, a rhombus can have angles that are not all equal (typically, it has two pairs of equal angles). Given the description, this could be a potential answer, but let’s also consider the last option.

D) Trapezoid: A trapezoid has one pair of parallel sides. However, the riddle specifies that all sides are parallel, which does not match the definition of a trapezoid.

Given that the shape described has all sides parallel and the angles are not all equal, the best match is C) Rhombus.

A bakery sells 5 apple muffins for every 2 bran muffins.

Answers

Answer:

[tex]Apple\ muffin\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Bran\ muffin\\10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4\\15\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6\\20\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8\\35\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 14[/tex]

Step-by-step explanation:

[tex]For\ 5\ apple\ muffins, bran\ muffin=2\\\\Ratio\ of\ bran\ muffin\ to\ apple\ muffin=\frac{number\ of\ bran\ muffin}{number\ of\ apple\ muffin}\\\\Ratio\ of\ bran\ muffin\ to\ apple\ muffin=\frac{2}{5}\\\\Bran\ muffin=\frac{2}{5}\times apple\ muffin\\\\When\ apple\ muffin=10\\\\Bran\ muffin=\frac{2}{5}\times 10=4\\\\When\ apple\ muffin=15\\\\Bran\ muffin=\frac{2}{5}\times 15=6\\\\When\ apple\ muffin=20\\\\Bran\ muffin=\frac{2}{5}\times 20=8[/tex]

[tex]When\ apple\ muffin=35\\\\Bran\ muffin=\frac{2}{5}\times 35=14[/tex]

1. I think of a positive number, multiply it by 4, add six, and then divide the answer by
2, and square the result. Then I subtract 9, and divide the result by the number I first
thought of. My answer is 20. What number did I think of?

Answers

Answer: 2

Step-by-step explanation:

2 times 4 = 8

8 plus 6 = 14

14 divided by 2 = 7

7 squared = 49

49 minus 9 = 40

40 divided by 2 = 20

Final answer:

In this problem we convert the operations into an equation and solve it step by step until we get two possible answers. We pick the one that fits the conditions of the problem, which gives us 9 as the positive number the student had originally thought of.

Explanation:

Let's denote the number you are thinking of as x. Following your sequence of operations we can translate this into an equation:

(((4x + 6) / 2)² - 9) / x = 20

Solving this equation can be done step by step:

Multiply through by 2x to remove the denominator: ((4x + 6)² - 9x) = 40x.Expand the square on the left side: 16x² + 24x + 36 - 9x = 40x.Simplify by combining like terms: 16x² + 15x + 36 = 40x.Subtract 40x from both sides to form a quadratic equation: 16x² -25x + 36 = 0.This quadratic equation can be factored as (4x -1)(4x -36) = 0.Setting each set of parentheses equal to zero gives us two solutions for x: x = 0.25 or x = 9.

Since you mentioned that the number you thought of was positive, we disregard 0.25 (since the squared result after the first operations would be too small to subtract 9 and still divide by the original number to get 20). Therefore, the number you thought of was 9.

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Prove that the value of the expression: (5^18–25^8)(16^4–2^13–4^5) is divisible by 30 and 44.

Answers

Final answer:

The expression given is factored to identify common factors of 30 and 44. By identifying factors like 3, 5 (for 30) and 2, 11 (for 44), it's shown that the expression is indeed divisible by both 30 and 44.

Explanation:

The student asked to prove that the value of the expression: (518−258)(164−213−45) is divisible by 30 and 44. To approach this proof, we will simplify and factor the expression where possible to find common factors of 30 (2*3*5) and 44 (4 × 11).

First, let's factor each part of the expression:

518 = (52)9 = 259

258 = (52)8 = 516

164 = (24)4 = 216

213 remains the same

45 = (22)5 = 210

Now, we rewrite the original expression with these factors:

(259 − 516)(216 − 213 − 210)

Looking at the first parenthesis, we see that 259 and 516 have a common factor of 516, so we can factor it out:

516(25−1)(216−213−210)

Recognizing that 25−1 = 24, and that 24 is divisible by both 3 and 8 (and thus 4), we have a clear division by 30.

For the second parenthesis, we can see that 210 is a common factor:

210(26−23−1)

Again, noticing that 26−23−1 leaves us with numbers of the form 2n − 2n-k − 1, we can confirm divisibility by 2 and potentially by 4 depending on the value of n. Checking the values, 26 − 23 − 1 equals 57, which is also divisible by 3.

So the original expression has factors that include 2, 3, 5, and 11, thereby confirming that the expression is divisible by both 30 and 44.

f(x) = x + 2 g(x) = x – 4

(f g)(x) =

Answers

Answer:

x-2

Step-by-step explanation:

x-4+2 = x-2

Answer:

x^2 - 2x - 8

Step-by-step explanation:

Workers in an office of 60 staff were asked their favourite type of take-away.
The results are summarised in the table.

Take-away Frequency Angle
Pizza 7
a
Curry 19
b
Fish & chips 4
c
Kebab 5
d
Other 25
e
Work out the size of each angle to draw a pie chart.

Answers

Answer:

Angles: 42°, 114°, 24°, 30°, 150°.

Step-by-step explanation:

Pie Charts

They represent the comparative values of a given variable subject to study. The whole pie is cut in angular sections where all the angles must sum 360°. If the sum of all the values is S and one particular value is x, then the angle of its circular section is given by

[tex]\displaystyle angle=\frac{x}{S}\ 360^o[/tex]

We have the staff of an office is S=60. When asked about their favorite type of takeaway we get:

Pizza: 7. Its corresponding angle is

[tex]\displaystyle angle=\frac{7}{60}\ 360^o=42^o[/tex]

Curry 19.

[tex]\displaystyle angle=\frac{19}{60}\ 360^o=114^o[/tex]

Fish & chips 4

[tex]\displaystyle angle=\frac{4}{60}\ 360^o=24^o[/tex]

Kebab 5

[tex]\displaystyle angle=\frac{5}{60}\ 360^o=30^o[/tex]

Other 25

[tex]\displaystyle angle=\frac{25}{60}\ 360^o=150^o[/tex]

We can see the sum of all angles is 360°

The angles for the pie chart are as follows:

- Pizza: 42 degrees

- Curry: 114 degrees

- Fish & chips: 24 degrees

- Kebab: 30 degrees

- Other: 150 degrees

These angles can be used to create a pie chart that accurately represents the favorite take-away choices of the office staff.

To calculate the size of each angle for the pie chart representing the favorite take-away choices of the 60 office staff, we need to determine the percentage each category represents in the total.

First, add up the frequencies:

Pizza + Curry + Fish & chips + Kebab + Other = 7 + 19 + 4 + 5 + 25 = 60

Now, calculate the percentage for each category:

- Pizza: (7/60) * 100% = 11.67%

- Curry: (19/60) * 100% = 31.67%

- Fish & chips: (4/60) * 100% = 6.67%

- Kebab: (5/60) * 100% = 8.33%

- Other: (25/60) * 100% = 41.67%

Now that we have the percentages, we can calculate the corresponding angles for the pie chart.

Each percentage corresponds to a fraction of the total 360 degrees in a circle.

So, for example, Pizza would be (11.67/100) * 360 = 42 degrees, Curry would be (31.67/100) * 360 = 114 degrees, and so on.

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Tony was Challenged to a half-court shooting competition. For every half-court shot that he makes, he will earn 20 points. For each half-court shot he misses, he will lose 5 points. After 20 half- court shots, Tony has zero points. How many half-court shots he make? How many half-court shots did he miss?

Answers

Answer:

Tony make 4 half-court shots and misses 16 half-court shots.

Step-by-step explanation:

Given:

Points earned for every successful, half-court shots = [tex]20[/tex]

Points deducted for missing the shots = [tex]5[/tex] or [tex]-5[/tex]

Total number of shots in the game = [tex]20[/tex]

Final points earned by Tony = [tex]0[/tex]

According to the question:

Let the number of successful half-court shot be [tex]x[/tex]

And the number of shots missed be [tex]20-x[/tex]

So,

In terms of points we can re-write it as:

⇒ [tex]20(x)-5(20-x) =0[/tex]

⇒ [tex]20x-100+5x=0[/tex]

⇒ [tex]25x-100=0[/tex]

⇒ [tex]25x-100+100=100[/tex]

⇒ [tex]25x=100[/tex]

⇒ [tex]\frac{25x}{25} =\frac{100}{25}[/tex]

⇒ [tex]x=\frac{100}{25}[/tex]

⇒ [tex]x=4[/tex]

Tony make 'x' shots that is 4 and the number of shot he missed is (20-x) =(20-4)=16

please tell explain what the right answer is

Answers

Angle 3 and angle 4 are supplementary angles and when added together need to equal 180 degrees.

To find angle 4 subtract angle 3 from 180.

Angle 4 = 180 - 101 = 79 degrees.

Answer:

your answer is correct

Step-by-step explanation: because each angle equals the same thing

What is the slope intercept form of this equation? 8x +6y=12

Answers

Answer:

y=-4/3x+2

Step-by-step explanation:

PLEASE HELP ME :(
The base of a square pyramid has side lengths that are 14 inches. The distance from the top of the pyramid to the middle of the side of the base is 15 inches. What is the height of the pyramid? Round to the nearest tenth, if necessary.

Answers

Answer:

The height of the pyramid is 13.3 inches

Step-by-step explanation:

Let

h ----> the height of the pyramid

b ---> the base of the square pyramid

we know that

Applying the Pythagorean Theorem

[tex]15^2=h^2+(\frac{b}{2})^2[/tex]

see the attached figure to better understand the problem

we have

[tex]b=14\ in[/tex]

substitute

[tex]15^2=h^2+(\frac{14}{2})^2[/tex]

Solve for h

[tex]225=h^2+49\\h^2=225-49\\h^2=176\\h=\sqrt{176}\ in\\h=13.3\ in[/tex]

Each class at Greenville school has 22 children enrolled.the school has 24 classes how many children are enrolled at Greenville school?

Answers

Answer:

528

Step-by-step explanation:

because each class has 22 students and there are 24 classes you multiply them

Answer: 528 children

Step-by-step explanation: 22 children in each class. 24 total classes.

22•24=528

NEED HELP ASAP RIGHT NOW

John sells ice cream bars at the beach. In addition to a fixed salary, he earns a commission for each ice cream bar he sells. The table shows John's total earnings, y, from selling x bars of ice cream:


Ice Cream Sales and Earnings
Number of Bars Sold (x) Total Earnings (dollars) (y)
0 40

1 44

2 48

3 52



Which equation best shows the relationship between x and y?
y = x + 44
y = 4x + 44
y = x + 40
y = 4x + 40

Answers

Answer:

y=4x+40

Step-by-step explanation:

The equation  best shows the relationship between x and y is y = 4x + 40.

The equation is as follows:

Given that,

John's total earnings, y, from selling x bars of ice cream

So based on this, the following equation should be considered

y = 4x + 40

Therefore, the last option is correct.

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What term can you add to StartFraction 5 over 6 EndFraction x minus 4 to make it equivalent to One-half x minus 4?

Answers

Answer:

The term to add is

[tex]-\frac{1}{3} x[/tex]

Step-by-step explanation:

Let

b ----> the term to add

we have

[tex]\frac{5}{6}x-4+b=\frac{1}{2} x-4[/tex]

Solve for b

Adds 4 both sides

[tex]\frac{5}{6}x+b=\frac{1}{2} x[/tex]

subtract 5/6x both sides

[tex]b=\frac{1}{2} x-\frac{5}{6}x[/tex]

Remember that

[tex]\frac{1}{2}=\frac{3}{6}[/tex]

substitute

[tex]b=\frac{3}{6} x-\frac{5}{6}x[/tex]

[tex]b=-\frac{2}{6} x[/tex]

Simplify

[tex]b=-\frac{1}{3} x[/tex]

therefore

The term to add is

[tex]-\frac{1}{3} x[/tex]

Answer:

A

Step-by-step explanation:

A rectangle has an area of 100 square centimeters. The base of the rectangle is 25 centimeters.
What is the height of the rectangle?
O
4 cm
10 cm
76 cm
2400 cm
Next →

Answers

Answer:

The height of the rectangle is 4 cm.

Step-by-step explanation:

You find area by multiplying base and height.

The formula is  A=bh

so 100=25h

25 times 4 is 100

100=25*4

4cm is your answer

The height of the rectangle is 4 cm.

What are the coordinates of the image of vertex R after a reflection across the y-axis? (–4, 3) (4, –3) (–3, –4) (3, 4)

Answers

(–4, 3) (4, –3) (–3, –4) (3, 4)

this is a rather simple yet complex concept the easiest way to solve these is to do the exact opposite.

so in this instance it is refrcted across the y-axiss so we swap ONLY the x value NOT the Y ie (-4,3) would switch to (4,3)

same thing would apply if it reflected across x-axis ex (-4,-3)

If it reflect across orgin you change both signs. ex (4,-3)

ie.

(–4, 3) (4, –3) (–3, –4) (3, 4)

changes to

(4, 3) (-4, –3) (3, –4) (-3, 4)

hope it helps

The coordinates of the image of vertex R after a reflection across the y-axis is (3, 4).

What is reflection?

A reflection is an involution: when applied twice in succession, every point returns to its original location, and every geometrical object is restored to its original state.

Given is a point R = (-3, 4) we need to find the coordinates of the point R after it being reflected over y-axis,

So, we know that,

When dealing with reflection of a line or shape or a figure in the coordinate plane, especially if it is reflected across the y-axis, you just have to give the opposite of the given (original) x- coordinate in order to give a symmetric figure.

The rule of reflection over y-axis is =

(x, y) = (-x, y)

So,

R = (-3, 4), after it being reflected over y-axis =

R' = (3, 4)

Hence the coordinates of the image of vertex R after a reflection across the y-axis is (3, 4).

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Write an equation of the line in slope-intercept form that is perpendicular to this line and has a y-intercept of 9.

y=2x

Answers

Answer:

(0,9) for y-intercept

perp.: (-1/2)= m

y - 9 = (-1/2)x - 0

y = (-1/2)x + 9

Step-by-step explanation:

Simply 5(x-2)-3x+7. Please

Answers

5(x-2)-3x+7

5x-10-3x+7

2x-10+7

2x-3

Hope this step by step process helped

The length of a rectangle is five feet less than
its width. If the area of the rectangle is 84
square feet, find its dimensions.

Answers

Answer:

Length is w-5

Area  = length x width

84 = (w-5)w

84 = w^2 - 5w

0 = w^2 - 5w - 84

0 = (  w     -    12 )( w   +     7    )

w + 7 = 0 leads to negative measures.

w-12=0 ---> w = 12

width is 12, length is 5 less, or 7

The dimensions of the rectangle are 12 feet by 7 feet, determined by solving the quadratic equation derived from the relationship between the length and width and the given area of the rectangle.

To find the dimensions of a rectangle where the length is five feet less than its width and the area is 84 square feet, we can set up an equation. Let's define the width of the rectangle as w feet. Then, the length would be w - 5 feet. Since the area of a rectangle is defined as the product of its length and width, we get the following equation:

w times (w - 5) = 84

Expanding the left side gives us:

w^2 - 5w = 84

To solve this quadratic equation, move all terms to one side to set the equation to zero:

w^2 - 5w - 84 = 0

Factoring the quadratic equation, we look for two numbers that multiply to give -84 and add to give -5. These numbers are -12 and +7. So the equation factors as follows:

(w - 12)(w + 7) = 0

The solutions to the equation are w = 12 and w = -7. However, width cannot be negative in this context, so we discard w = -7. Thus, the width is 12 feet and the length is 12 - 5 = 7 feet.

Therefore, the dimensions of the rectangle are 12 feet by 7 feet.

sum of money is placed at simple interest for 3 years at 10% per annum and then the amount is invested for 2 years at the same rate at compound interest . If the total amount of 5 years became Rs. 471900, what was the sum?

Answers

Answer:

sum was 300000

Step-by-step explanation:

let sum of money is placed  is x rs

Term T = 3 years, rate R = 10%

Then simple interest for for 3 years is

[tex]SI= \frac{PTR}{100}\\ SI=\frac{x\times 3\times 10}{100} \\SI = 0.3x[/tex]

Sum of x will become x+0.3x = 1.3x after 3 years. now this 1.3x is kept for compound interest for two years. ie

[tex]A =P[1+R]^t\\471900=1.3x[1+\frac{10}{100} ]^2\\x=\frac{471900}{1.573} \\x=300000[/tex]

Sum was 300000

At the simple interest rate, the rate is applied only to the initial sum, while

at the compound interest, the rate is applied to the amount in the account.

The sum of money is approximately Rs 355,847.466

Reasons:

Let P represent the sum of money invested, we have;

[tex](P + P \cdot r \cdot t_1) \times (1 + r)^{t_2} = \mathbf{ 471900}[/tex]

Where;

P = The initial sum invested

r = The simple and compound interest rate applied = 10% = 0.1

t₁ = The number of years the money is placed at simple interest = 3 years

t₂ = The number of years the money is placed at compound interest = 2 years

Therefore;

[tex]\mathbf{(P + P \times 0.1 \times 3) \times (1 + 0.01)^{2}} = 471900[/tex]

Which gives;

[tex]P \cdot (1 + 0.3 ) \times (1 .01)^{2} = 471900[/tex]

[tex]\displaystyle P =\mathbf{\frac{471900}{(1 + 0.3 ) \times (1 .01)^{2} }} \approx 355,847.466[/tex]

The sum of money invested, P ≈ Rs 355,847.466

Learn more about simple and compound interest here:

https://brainly.com/question/24603629

https://brainly.com/question/3783619

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