Katie is twice as old as her sister Mara. The sum of their ages is 24. Write one variable equation to represent the situation

1. Andy's oldest daughter ate the most pizza. She ate the entire personal pizza, which is 10 inches in diameter

2. If the company offered an extra large pizza, you could find out how much of it a person ate if they cut their own piece with a central angle of M°

Andy's oldest daughter ate the most pizza. She ate the entire personal pizza, which is 10 inches in diameter. This means that she ate 100% of the pizza. Andy's wife ate 2/6 of the small pizza, which is 12 inches in diameter. This means that she ate 1/3 of the pizza. Andy's younger daughter ate 1/8 of the medium pizza, which is 14 inches in diameter.

This means that she ate 12.5% of the pizza. Andy cut himself a piece that had a central angle of 180° from the large pizza, which is 16 inches in diameter. This means that he ate 50% of the pizza.

The least amount of pizza was eaten by Andy's younger daughter. She only ate 1/8 of the medium pizza.

2. If the company offered an extra large pizza, you could find out how much of it a person ate if they cut their own piece with a central angle of M° by using the following formula:

Percentage of pizza eaten = (M° / 360°) * 100%

For example, if a person cut themselves a piece of an extra large pizza with a central angle of 180°, they would have eaten 50% of the pizza.

Percentage of pizza eaten = (180° / 360°) * 100% = 50%

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Answer:

42,500

Step-by-step explanation:

The number which is ten times greater than 4250 is 42, 500.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The number 4,250 is ten times smaller than what number.

let the number be x.

So, x/10 = 4250

Now, make x as subject formula

x = 4250(10)

x= 42500

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Answer:

$110.5

Step-by-step explanation:

48 + 25(2.5)

48 + 62.5

=110.2

Answer:

The answer is 110.5

Step-by-step explanation:

48+25(2.5)=110.5

Answer:

9/4 ÷ 3/4 = 3

Step-by-step explanation:

Answer:

\(\frac{1}{2}\)k-\(\frac{3}{5}\)

Step-by-step explanation:

The dimensions of the rectangular slab are 16 meters in length and 2 meters in width.

Let's assume the length of the rectangular slab of concrete is L meters. According to the given information, the width is 14 meters less than the length, so the width would be L - 14 meters.

The formula for the area of a rectangle is A = length × width. In this case, the area is given as 32 m², so we can set up the equation:

32 = L × (L - 14)

Expanding the equation, we get:

32 = L² - 14L

Rearranging the equation, we have:

L² - 14L - 32 = 0

To solve this quadratic equation, we can either factorize it or use the quadratic formula. In this case, it's easier to use the quadratic formula:

L = (-b ± √(b² - 4ac)) / (2a)

Here, a = 1, b = -14, and c = -32. Substituting these values into the formula, we get:

L = (14 ± √((-14)² - 4 × 1 × (-32))) / (2 × 1)

Simplifying further:

L = (14 ± √(196 + 128)) / 2

L = (14 ± √324) / 2

L = (14 ± 18) / 2

Therefore, we have two possible values for L:

L₁ = (14 + 18) / 2 = 16

L₂ = (14 - 18) / 2 = -2

Since the length of the slab cannot be negative, we discard the negative value.

Thus, the length of the rectangular slab is 16 meters. To find the width, we subtract 14 meters from the length:

Width = 16 - 14 = 2 meters

Therefore, the dimensions of the rectangle are 16 meters by 2 meters.

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Answer:

23,098; 23,208 ; 234,358

Step-by-step explanation:

Hope this helps

Answer:

what do you mean by land ?

The intensity of sound is proportional to the square of its amplitude.

Thus, if I9 and I8 are the intensities of sounds at 9 decibels and 8 decibels respectively, then:

I9/I8 = (10^(9/10))/(10^(8/10))

I9/I8 = 10^(0.1)

I9/I8 = 1.2589

Therefore, the relative intensity of 9 decibels is approximately 1.26 times higher than that of 8 decibels.

May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!

Answer:

(5,0)

Step-by-step explanation:

The x-intercept is where y=0.

The exact acreage of wheat expansion during the first 5 years of the 1940s would require access to historical data .Land prices increased significantly due to the high demand for wheat and the increased production.

The Great Plains region includes parts of the United States and Canada, specifically the central and western portions of North America. In the United States, it includes parts of Montana, North Dakota, South Dakota, Nebraska, Kansas, Oklahoma, Texas, Colorado, Wyoming, and New Mexico. In Canada, it includes parts of Alberta, Saskatchewan, and Manitoba.

During the 1940s, the Great Plains region of the United States, which includes states such as Kansas, Nebraska, Oklahoma, and parts of other surrounding states, experienced a significant expansion in wheat production. This period is often referred to as the "wheat boom" era.

During the early 1940s, there was a high demand for wheat due to World War II, as wheat was a staple crop used to feed soldiers and provide food aid to war-torn regions. This resulted in increased wheat production in the Great Plains region. However, the exact acreage of wheat expansion during the first 5 years of the 1940s would require access to historical data .

As for the prices of land being sold during that time, it is also difficult to provide precise information without specific data. Land prices can vary depending on various factors such as location, quality of land, demand, and economic conditions. However, it is generally known that during the wheat boom era of the 1940s, land prices in the Great Plains region increased significantly due to the high demand for wheat and the increased production. The exact percentage of increase would require access to historical data and research.

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The amount that would be in the account when Alana is 21  is $2890

We have to know the formula for simple interest.

This is expressed as;

S.I = PRT/100

Given that the parameters of the formula are enumerated as;

From the information given, substitute the values, we have;

SI = 1000 × 9 × 21/100

Multiply the values,

Then, divide by the denominator, we have;

SI = $1890

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The expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

Pascal's Triangle is a triangular array of numbers in which the value in each cell is the sum of the two numbers directly above it.

To expand the given expression (x²-3y)⁴ as per Pascal's triangle:

First, write down the fourth row of Pascal's Triangle as:

1 4 6 4 1

The above numbers represent the coefficients of the terms in the expansion of (a+b)⁴, where a is x² and b is -3y. Therefore, it can be written as,

1×(x²)⁴ + 4×(x²)³×(-3y) + 6×(x²)²×(-3y)² + 4×(x²)(-3y)³ + 1(-3y)⁴

Simplify each term,

x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸

Therefore, the expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

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Answer:
7)55.6
9) 11.25
11)238.18

Step-by-step explanation:

7) ;et x be the number

so the price is $139 but there is a discount of 40%. how much does she save?

so, $139=100%
      x=100%-40%( why we said like this? coz am trying to show how much she will pay, if there was 40% off then she will pay the 60% only of the price)

$139=100%
x=60%, criss cross

x=$139*60%/100%
x=83.4

then to find how much she saves, the original price - x
$139-83.4
=$55.6

9) let x be the number

the original price was $75 and there were a discount for the table for 15% off.
so,

$75=100% (why we make 100%?, coz it says the original price is 75, got it?)

x=100%-15%
x=85%

so ,  $75=100%
        $x=85%, criss cross

     100%x=85*75
       x=63.75, but the question says how much does she save?|

so the original price minus x
75-63.75 = 11.25

11) let x be the number

she got a rise of 32% per hour. so 100%+32 is 132%
$314.40 for a 40-hour week

$314.4=132%
      x=100%, criss cross

$314.4*100=132x
x=31440/132
x=238.18
and the 238.18 is what she used to earn for a 40-hour week before her rise.

Hope it helped:)

Answer:

A, 150

Step-by-step explanation:

A kite has 4 interior angles and the sum of these interior angles is 360°. In these angles, it has one pair of opposite angles that are obtuse angles and are equal.

Ok, so we have R=150 as an obtuse angle. Draw out your kite and label the angles. The angle across from R will also be 150. These together make 300 degrees. The two acute angles will be S=50, and 10 degrees, because we have to have 60 total more degrees from the previous 300. We don't know whether T is an acute angle or an obtuse angle, but because the 10 degree angle isn't an option, it must be the angle across from R, which is equal to 150 degrees.

Answer:

Answer:110

Step-by-step explanation:

Interior angles sum to 360

angle S = Angle U

AngleR + Angle S +Angle T= 150+50+50=250

360-250=110

The Direction Angle Of The Given Vector is θ = 59.086

Given :

The Direction Angle Of The Given Vector. V <-3,5) Give Your Answer In Degrees In The Interval [0°, 360°). round to the nearest hundredth (2 decimal places). give just the number without the degree symbol.

what is Direction angle of vector ?

The direction angle of a vector v is the angle from the positive x -axis to v .using the arc tangent of the ratio of the vertical component of the vector and the horizontal component of the vector.

tan θ = b / a

= 5 / -3

= -5 / 3

= 1.67

θ = tan^-1 ( 1.67 )

θ = 59.086

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Answer:

95% of house sizes lie between 955.7 and 1454.1 square feet.

Step-by-step explanation:

The empirical rule formula states that:

68% of data falls within 1 standard deviations from the mean - between μ – σ and μ + σ .

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ

In the above question,

Mean (μ)= 1204.9 square feet

Standard deviation (σ) = 124.6 square feet.

We are to determine the approximate percentage of house sizes that lie between 955.7 and 1454.1 square feet.

Step 1

We have to find the number of standard deviation from the mean

μ – xσ

1204.9 - 124.6x = 955.7

1204.9 - 955.7 = 124.6x

249.2 = 124.6x

x = 249.2/124.6

x = 2

μ + xσ

1204.9 + 124.6x = 1454.1

124.6x = 1454.1 - 1204.9

124.6x = 249.2

x = 249.2/124.6

x = 2

Therefore from the calculation above, it is 2 standard deviations from the mean, hence: from the empirical formula above,

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ

Answer:

0.5 inches per a month

Step-by-step explanation:

you turn them to a decimal to make them easier and then divide them to get the answer.

Answer:

30

Step-by-step explanation:

3:4=9:12-total students 21

3:4=12:16-total students 28

3:4=15:20-total students 35

Answer:

I think it's,1,7,7 that will not make a triangle

hope this help

The route to an ancient pyramid is 79 miles long; if 20 miles is travelled each day for 3 days, the distance travelled in the fourth day would be 19 miles.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let the distance travelled in the first day be 20 miles. If the same time was travelled for 3 days, hence:

3(20) + x = 79

x = 19 miles

The route to an ancient pyramid is 79 miles long; if 20 miles is travelled each day for 3 days, the distance travelled in the fourth day would be 19 miles.

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Answer:

1. (x-2)(x-1)

3. (x-2)(x+4)

Step-by-step explanation:

To factor these, you need two factors that multiply together to give you the third number and add together to give you the second number.

1. (x-2)(x-1)

3. (x-2)(x+4)

In a case whereby Richard is saving money for a down payment on a car He models his savings plan with the equation y = 200x + 500 based on his current monthly savings rate  y-intercept of linear model represent B. The starting amount in his savings account.

It should be noted that in a  linear equation the y intercept  can be seen as one that is starting point  whereby x is zero, which implkies that starting balance he had is 1000 in the bank.

Therefore, from the  equation y = 200x + 500, the  y-intercept of linear model serves as the starting amount in his savings account.

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Answer:

To find 40% of a number, you can multiply the number by 0.4 or divide it by 2.5.

Using this method, we get:

40% of 100 is 40 (100 x 0.4 or 100 ÷ 2.5)

40% of 110 is 44 (110 x 0.4 or 110 ÷ 2.5)

40% of 140 is 56 (140 x 0.4 or 140 ÷ 2.5)

40% of 120 is 48 (120 x 0.4 or 120 ÷ 2.5)

Therefore, 40% of 100 is 40, 40% of 110 is 44, 40% of 140 is 56, and 40% of 120 is 48.

The distance between X(-9,2) and Y(5,-4) is 15.23 units.

The distance formula states that if there are 2 points A(x1, y1) and B(x2, y2), then the distance between the two points is given by the formula-

\(\sqrt{(x1-x2)^{2} + (y1-y2)^{2} }\)

Here, we are given that there are 2 points- X(-9, 2) and Y(5, -4)

So here we can say that,

x1 = -9, y1 = 2

and x2 = 5, y2 = -4

Now, plugging in the values given above in the distance formula we will find XY as follows-

XY = \(\sqrt{(-9-5)^{2} + (5+4)^{2} }\)

XY = \(\sqrt{(-14)^{2} + (9)^{2} }\)

XY = \(\sqrt{196+ 81 }\)

XY = \(\sqrt{277 }\)

The square root of 277 is approximately 15.23.

Thus, XY = 15.23

Therefore the value of XY to the nearest hundredth is 15.23 units.

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Answer: f(3) = g(6)

Step-by-step explanation: if you plug them in we see that f of 3 on the y axis intercept g of x so we then go up and see that g of 6 intercepts f of 3 so therefore that is the answer

Answer:

3/8

Step-by-step explanation:

3/4 x 1/2 = 3/8

3/8 x 1/1 = 3/8

Hope that helps!

It takes 10 minutes for the number of bacteria in the population to double.

To determine the time it takes for the number of bacteria in a population to double, we need to find the value of t when the function f(t) equals twice the initial number of bacteria.

The given function is f(t) = 60,000 * 2^(t/10).

To find the time it takes for the number of bacteria to double, we set f(t) equal to twice the initial number of bacteria, which is 2 * 60,000 = 120,000:

120,000 = 60,000 * 2^(t/10).

Next, we can simplify the equation by dividing both sides by 60,000:

2 = 2^(t/10).

Since both sides of the equation have the same base (2), we can equate the exponents:

t/10 = 1.

To solve for t, we multiply both sides by 10:

t = 10.

Therefore, it takes 10 minutes for the number of bacteria in the population to double.

This result is obtained by setting the growth rate of the bacteria population in the given function. The exponent t/10 determines the rate of growth, and when t is equal to 10, the exponent becomes 1, resulting in a doubling of the initial number of bacteria.

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Answer:The answer is 12 7/12.

Hope that helps.

Step-by-step explanation:        

Step 1: See Steps Below  

5  1/3  + 7  1/4

= 16/3  +  7  1/4

= 16/3  +  29/4

= 151/12

= 12  7/12

Explanation in words:        

- The first step is to add whole numbers which are 5 + 7: 12

- The second step is to combine the fractions 1/3 + 1/4: 7/12  

- The third step is to solve the fraction. So it will result as 12 + 7/12  

- The answer is 12  7/12  

Easy Steps: See Attachment

Answer:    

12 7/12  

(Decimal: 12.583333)

Hope this helps.

Answer:

Answer is given below.

Step-by-step explanation:

let us solve the numerator first

=4x²-14x+6

=2(2x²)+2(-7x)+2(3)

= GCF of the terms of the numerator is 2.

denominator

x³-7x²+12x

x(x²)+x(-7x)+x(12)

GCF of the terms of the denominator is x.

factorise the numerator

4x²-14x+6

4x²-2x-12x + 6  (by splitting the middle term; the numbers should produce the product  4*6 and when the no.s are added they should give -14)

(4x²-2x) + (-12x+6)

2x(2x-1) -6(2x-1)

(2x-6)(2x-1)

factors are

(2x-6), (2x-1)

denominator

this can also be done by splitting the middle term

x³-7x²+12x

x³-3x²-4x²+12x

(x³-3x²) + (-4x²+12x)

x²(x-3) -4x(x-3)

(x²-4x)(x-3)

factors are

(x²-4x), (x-3)