A post it note has an area of A square inches. The width of the post it note is 4 inches.which equation represents X the length of the post it note in inches A X=4/A. B. X=A+2(4) C. X=A/4. D. X=A-2(4)

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.

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]

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

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:

Answer:

length=8+w........1

area=84square feet........2

area of rectangle =length x width

area=(8+w)x W

area=8w+w^2

84=8w+w^2

w^2+8w+(4^2)=84+(4^2)

(w+4)^2=84+16

(w+4)^2=100

√(w+4)^2=√100

w+4=±100

w+4=100 or w+4=-100

w=96 or w=-104

the answer is 96

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

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

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.

for such more questions on angles

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Answer:

THE ANSWER IS 1.2068965517

Step-by-step explanation:

Answer:

5x+10

Step-by-step explanation:

you will add 7x_2x=5x

then 4+6=10

Yo sup??

we know that the sum of all the angles of a triangle is 180

therefore

11x+7x+90=180

18x=90

x=5

exterior angle formed on the ground=180-11x

=180-55

=125

Hope this helps

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.

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

Answer:

y=4x+40

Step-by-step explanation:

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

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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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

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.

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:

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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5(x-2)-3x+7

5x-10-3x+7

2x-10+7

2x-3

Hope this step by step process helped

(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.

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

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

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.

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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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.

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

Answer:

Ricky hits 1202 base

Pedro hits = 1485 base

Step-by-step explanation:

Pedro + Ricky = 2687 hits

Let Ricky hits = x

So the Pedro hits will be = x + 283

( x + 283 ) + x = 2687

2 x + 283 = 2687

2 x = 2687 - 283

2 x = 2404

x = 1202

So the Ricky hits 1202 base

Pedro hits (1202 + 283) = 1485 base

Final answer:

To determine the number of hits Ricky and Pedro had, a system of equations was set up and solved. Ricky had 1202 hits, while Pedro had 1485 hits last season.

Explanation:

To solve the problem involving teammates Pedro and Ricky's base hits, we need to set up a system of equations based on the information given:

Pedro and Ricky's hits together total 2687.

Pedro had 283 more hits than Ricky.

Let's denote Ricky's hits as R and Pedro's hits as P. The two equations representing the situation are:

R + P = 2687

P = R + 283

To find the number of hits Ricky had, we can substitute the second equation into the first:

R + (R + 283) = 2687

2R + 283 = 2687

2R = 2687 - 283

2R = 2404

R = 2404 / 2

R = 1202

Now that we have Ricky's hits, we can find Pedro's hits by adding 283 to Ricky's total:

P = R + 283

P = 1202 + 283

P = 1485

Therefore, Ricky had 1202 hits, and Pedro had 1485 hits last season.

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:

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.

Reasons:

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

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

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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]

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

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

Answer: Decolonization as a result of World War II.

Step-by-step explanation:

Answer:

Step-by-step explanation:

A i think sorry if it is wrong

The only ordered pair that can be added to make the relation a function, without repeating an x-value, is option B. (-1,-1).

The question is asking which ordered pair (x,y) makes the given set of ordered pairs a function. A function is defined as a relation where every x-value (input) is associated with exactly one y-value (output). We already have the points (2,3), (–2,5), (4,4), and (-4,5) in our set. To maintain the definition of a function, the x-value of the ordered pair we are going to add cannot be the same as any x-value already present in the set. Looking at our options:

Therefore, the only ordered pair that makes the relation a function is option B. (-1,-1).

Answer:

x-2

Step-by-step explanation:

x-4+2 = x-2

Answer:

x^2 - 2x - 8

Step-by-step explanation: