x + 4y = 1 3x + 5y = 10

The hypotenuse measures 3 cm in length. (Using the Pythagorean theorem: c2 = a2 + b2 where c is the hypotenuse and a and b are the other two sides.)

According to the Pythagorean theorem, the square of the length of the hypotenuse in a right triangle equals the sum of the squares of the lengths of the legs. This formula may be used to get the hypotenuse length of a right triangle with sides that are 4 and 5 cm long.

With the Pythagorean theorem in use, we have:

2 hypotenuse Equals 4 + 5

(2)Hypotenuse = (16 + 25)

Hypotenuse 2 equals 41

When we square the two sides, we obtain:

41 cm is the hypotenuse.

Hence, the right triangle's hypotenuse measures around 6.4 cm in length (rounded to one decimal place).

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The shaded region representing the possible combinations of ticket sales is given by the image presented at the end of the answer.

The region containing the possible combinations is obtained using a system of inequalities, for which the variables are given as follows:

The amounts cannot be negative, as they are countable amounts, hence:

Each member of the team must make a minimum of $300, hence:

60x + 20y ≥ 300.

They cannot sell more than 10 tickets, hence:

x + y ≤ 10.

The graph containing the region that respects these four constraints is given by the image presented at the end of the answer.

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Answer:

Jaclyn spent $37 less than 2 times what Tracy spent:

2x - 37Jaclyn spent $13:

13We can set these two expressions equal to each other to get an equation:2x - 37 = 13Now we can solve for x:2x = 50x = 25So Tracy spent $25.

Answer:

Tracy spent $25.

Step-by-step explanation:

Tracy spent x.

" Jaclyn spent ​$37 less than 2 times what Tracy spent."

Jaclyn spent 2x - 37

Jacklyn spent $13

2x - 37 = 13

Add 37 to both sides.

2x = 50

x = 25

Tracy spent $25.

By working out or simplifying the given statement we will get  a)  26 and the equation b)  8 2/3.

In mathematics, a fraction is used to denote a piece or component of the whole. It stands for the proportionate components of the whole. Numerator and denominator are the two components that make up a percentage. The numerator is the number at the top, and the remainder is the number at the bottom.

a) By converting the numbersr into improper fraction we will get

4 1/3 = (4 x 3 + 1) / 3 = 13 / 3

By multiplying the both of the fractions:

13 / 3 * 6 =[tex]\frac{78}{3}[/tex] = 26

= 4 1/3 * 6 simplifies to 26.

b) Now we will convert both of the mixed numbers to improper fractions and we will get :

[tex]\frac{23}{5}[/tex] = [tex]\frac{2*5+3}{5}[/tex] = [tex]\frac{13}{5}[/tex]

[tex]\frac{31}{3}[/tex] = [tex]\frac{3*3+1}{3\\}[/tex] = [tex]\frac{10}{3}[/tex]

By multiplying both of the  fractions:

[tex]\frac{13}{5} * \frac{10}{3\\}[/tex] = [tex]\frac{130}{5}[/tex]

We can simplify say that the fraction by dividing both of the numerator and denominator by their greatest common factor, which is 5:

[tex]\frac{130}{15}[/tex] =[tex]\frac{26}{3\\}[/tex]

Therefore, we come to a conclusion where

2 3/5 * 3 1/3 simplifies to 26/3 or 8 2/3.

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Answer:

h(t) = 40 cos(π/22.5 t) + 10.

Step-by-step explanation:

The function that models Amelia's height, h, at time t can be written as:

h(t) = r cos(ωt) + a

where:

r is the radius of the ferris wheel (40 m)

a is the initial height of the cart above the ground (10 m)

ω is the angular velocity of the ferris wheel, which is equal to 2π divided by the time for one complete rotation (T)

T is the time for one complete rotation, which is given as 45 seconds

To find ω, we can use the formula:

ω = 2π/T

ω = 2π/45

ω = π/22.5

Substituting the values into the function, we get:

h(t) = 40 cos(π/22.5 t) + 10

Therefore, the function that models Amelia's height, h, at time t since she got on the ride is h(t) = 40 cos(π/22.5 t) + 10.

The category which has the lowest marginal frequency is the marginal frequency of middle school students who chose to play sports.

What is meant by marginal frequency?

By dividing the sum or total of a row or the sum or total of a column by the total number of observations in a dataset, one can get the marginal relative frequency of a data set. This dataset is presented as a two-way table for ease of understanding. Although the percentage value is typically chosen, the marginal relative frequency can be stated as either a decimal or a percentage number.

Here,

The total number of middle school students = 21

Number of middle school students playing sports = 21 - 16 = 5

Number of high school students watching movies = 19-16 = 3

Total number of high school students = 11 + 3 = 14

Total number of students = 14 + 21 = 35

Now,

The marginal frequency of middle school students who chose to play sports = 5 / 35 = 0.143

The marginal frequency of high school students who decided to watch movies/TV = 3/35 = 0.0857

The marginal frequency of students in high school = 14/35 =0.4

The marginal frequency of students who chose to play sports = 15/35

                                                                                                     = 0.429

Therefore the category which has the lowest marginal frequency is the marginal frequency of middle school students who chose to play sports.

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Answer:

Step-by-step explanation:

∠ADB = ∠CDB = 90°  (equal angles on a straight line are complimentary)

BD=BD                          (common side)

AD = CD                         (D is midpoint of AC)

∴[tex]\triangle[/tex]ABD ≡ [tex]\triangle[/tex]CBD          (SAS)  

I hope this is useful.

Abbey's acceleration is 0 m/s². Acceleration is the rate of change of velocity with respect to time.

If Abbey is running down the field at a constant speed of 10 m/s, then her velocity is not changing. Therefore, her acceleration is 0 m/s².

Mathematically, we can represent acceleration using the equation:

a = (v₂ - v₁) / t

Where,

a = acceleration

v₁ = initial velocity

v₂ = final velocity

t = time

In Abbey's case, her initial velocity (v₁) and final velocity (v₂) are the same, since she has a constant speed. Therefore,

v₂ - v₁ = 10 m/s - 10 m/s = 0 m/s

And since there is no change in velocity, her acceleration is 0 m/s².

So, Abbey's acceleration is 0 m/s².

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We can conclude after answering the provided question that We can see from the diagram that the sides of triangle XYZ are of varying lengths. As a result, XYZ is a scalene triangle.

A triangle is a closed, double-symmetrical object made up of three line segments called sides that meet at three points called vertices. Triangles can be identified by their sides and angles. Based on their sides, triangles can be equilateral (equal factions), isosceles, or scalene. Triangles can be acute (all angles less than 90 degrees), okay (one angle equal to 90 degrees), or orbicular (all angles greater than 90 degrees) (all angles greater than 90 degrees). A triangle's region can be calculated using the formula A = (1/2)bh, where a represents the neighborhood, b represents the triangle's base, and h represents the triangle's height.

We can see from the diagram that the sides of triangle XYZ are of varying lengths. As a result, XYZ is a scalene triangle.

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Answer:

Step-by-step explanation:

[tex]we \ can \ show \\(a^{b})^{c}=a^{bc}\\,as,\\2^{-2}t^{6}\\a^{-b}=\frac{1}{a^{b}}\\2^{-2}t^{6}=\frac{1}{4}t^{6}[/tex]

Answer:

See below.

Step-by-step explanation:

We are asked to simplify the given expression.

Let's begin by identifying an important rule. Because there's a negative exponent and a negative exponent outside of the parentheses, we multiply the exponents and the product will be a positive exponent.

We also need to remember that the exponent outside of the parentheses acts on everything inside the parentheses.

Evaluate:

[tex](2t^{-3} )^{-2} = 2^{-2} \times t^{6}.[/tex]

Further Evaluate:

[tex]2^{-2} = \frac{1}{2^2} = \frac{1}{4}. \\t^{6} = t \times t \times t \times t \times t \times t.[/tex]

Multiply:

[tex]t^{6} \times \frac{1}{4} = \frac{t^{6} }{4} \ or \ \frac{1}{4} (t^6) .[/tex]

We can't simplify any further.

Therefore, our final answer is [tex]\frac{t^{6} }{4} \ or \ \frac{1}{4} (t^6).[/tex]

Answer:

Step-by-step explanation

ayo so basically this is a pythagorus theorum question

the formula is

c²= a² + b²

where c is the hypotenuse (the longest line , opposite of the right angle aka here 13ft !!)

a and b ,  where a  is the down line as a (4ft ) and b the unknown one

(just remember and lookout for the hypotenuse!)

so now put the numbers in formula

(13)²= (4)² +(b)²

169= 16 +(b)²

169-16=(b)²

153= (b)²

(put b first )

(b)² = 153

√(b)²= √153

(the square gets cut with the square root)

b= 12.36931688

b+12.4

Answer:

not possible since 3 + 4 < 8

In response to the query, we can state that If you can't afford a whole equation cupcake, you should purchase: - 8

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

For the family, 9 halves

six halves for my pals

So overall:

- For the two of them, 15 halves.

It means that you need 712 cupcakes in total.

If you can only afford a half-cupcake, you'll need to buy: 712

If you can't afford a whole cupcake, you should purchase:

- 8

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Answer:12.85

Step-by-step explanation:

speed=distance/time

Answer:

12.85

Step-by-step explanation:

90/7=12.85

speed=distance/time

Answer:

ln(28.1) ≈ 3.336

log(2/5) ≈ -0.398

Step-by-step explanation:

In this question, we are asked to find the natural log of 28.1 and the log base 10 of 2/5, rounded to the nearest thousandth.

The natural log of a number x is what power the constant e is raised to to get x.

For example,

ln(e²) = 2

We can approximate ln(28.1) by inputting it into a calculator.

ln(28.1) ≈ 3.33576957634

Then, we can round this to the nearest thousandth.

ln(28.1) ≈ 3.336

Notice how the 7 in the ten-thousandths place is greater than or equal to 5, so we round the thousandths place digit up to 6.

__

The log base 10 of a number x is what power the number 10 is raised to to get x. However, note that since log base 10 is the "common log" the base of 10 is not always specified.

log(2/5) ≈ -0.398

Notice how the output is negative, since 2/5 is less than 1 (and any number to the zeroth power is 1).

The area of the given figure is 94.29 [tex]in^{2}[/tex].

An object of area is how much space it takes up in 2-D. It is the measurement of object is unit squares than , completely cover the surface of a closed figure. The square unit, is frequently expressed as square inches, square feet,square meter,etc. is the accepted unit of area.

A shape is created by combining multiple  shapes is known as a composite figure. We add up all of outside sides of shape to find the perimeter. We  calculate the areas of each independently, and then add the resulting areas to determine the area.

First of all ,we will find the area of, the triangle.

The formula for area of a triangle =[tex]\frac{1}{2} *base* height[/tex].

According to question ,

base of triangle = 10 in.

Height of triangle =11 in.

value of base and height  substitute in formula than we get,

area of a triangle =[tex]\frac{1}{2} * 10 * 11[/tex]

area of a triangle= 1* 5*11

area of a triangle= 55 [tex]in^{2}[/tex].

Now,we will find the area of semi circle,

The formula for area of semi circle  =[tex]\frac{1}{2} \pi r^{2}[/tex]

According to question ,

[tex]r=\frac{10}{2} =5 in.[/tex] and use [tex]\pi =\frac{22}{7}[/tex]

area of semi circle=

[tex]=\frac{1}{2} *\frac{22}{7}*5^{2} \\\\=\frac{1}{2} *\frac{22}{7}*25\\\\=\frac{11}{7}*25}\\\\=1.57*25\\\\=39.29 in^{2}[/tex]

Now,area of given shape =

[tex]55 in^{2}+39.29 in^{2}\\\\=94.29 in^{2}[/tex]

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Answer:

8pi

Step-by-step explanation:

Since the triangle is a 30-60-90 triangle, the hypotenuse is 2 times the shortest side and the second longest side is sqrt3 times the shortest side. Since it is given that the second longest side is 4sqrt3, this means that the shortest side is 4, so the hypotenuse is 8.

Because of this, the diameter is 8, which means the radius is half of the diameter, which is 4.

The formula for circumference is 2*pi*r, and since r is 4, we can plug this in to get 2*pi*4, which is 8pi.

Step-by-step explanation:

we simply use the definitions in the main expression.

f(x) = -3x²

therefore,

f(x + h) = -3(x + h)² = -3(x² + 2hx + h²) = -3x² - 6hx - 3h²

so, we have

((-3x² - 6xh - 3h²) - -3x²)/h

(-3x² - 6xh - 3h² + 3x²)/h

(-6xh - 3h²)/h

this is then

-6x - 3h

and for the limit of h going to 0 this is -6x.

The year in which the approximate cost of a pizza was of $9 is given as follows:

2000.

The rule of 72 is a quick and simple mathematical formula that is used to estimate the number of years it takes for an investment or a debt to double, given a fixed annual interest rate. The rule states that if you divide 72 by the annual interest rate (expressed as a percentage), the result will give you an approximate number of years it takes for the investment or debt to double.

Hence the equation is given as follows:

Time to double = 72/Rate.

The rate for this problem is of 3.25%, hence the time to double is given as follows:

T = 72/3.25

T = 22 years.

Hence the pizza cost half of what it cost in 2022 in 22 years before, hence:

2022 - 22 = year of 2000.

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Answer:

6√3 cm.

Step-by-step explanation:

The angle between the length of a rectangle and its diagonal is 30°. If the length of the rectangle is 6cm, find the length of the diagonal.

Let's call the width of the rectangle "w" and the diagonal "d". We know that the angle between the length and diagonal is 30 degrees, which means that the angle between the width and diagonal is 90 - 30 = 60 degrees (since the angles in a triangle add up to 180 degrees).

Now, we can use trigonometry to find the length of the diagonal. Specifically, we can use the sine function, which relates the lengths of the sides of a right triangle to the angles opposite them:

sin(angle) = opposite/hypotenuse

In this case, the angle we're interested in is 60 degrees, the opposite side is the width "w", and the hypotenuse is the diagonal "d". So we can write:

sin(60) = w/d

Solving for "d", we get:

d = w/sin(60)

Now we just need to find the width of the rectangle. Since we know the length of the rectangle is 6cm, we can use the fact that the opposite sides of a rectangle are equal to each other to write:

w = length*sin(30) = 6sin(30)

We can simplify sin(30) to 1/2, so:

w = 6/2 = 3

Now we can substitute this value of "w" into our expression for "d" to get:

d = w/sin(60) = 3/sin(60)

We can simplify sin(60) to √3/2, so:

d = 3/(√3/2) = 6/√3 = 2√3 * 2

So the length of the diagonal is 2√3 times the length of the width, or approximately 3.46 times the length of the width. Therefore, the length of the diagonal is:

d = 2√3 * 3 = 6√3 cm.

Answer:

Let's use variables to represent the unknowns:

Let x be the number of psychology textbooks sold.

Then, the number of history textbooks sold is 2x (twice the number of psychology textbooks sold).

The problem tells us that the total number of textbooks sold is 237, so we can set up an equation:

x + 2x = 237

Simplifying and solving for x:

3x = 237

x = 79

Therefore, 79 psychology textbooks were sold and 2x = 158 history textbooks were sold.

Step-by-step explanation:

By CER methοd it can be cοncluded that ABCD is a parallelοgram.

CER stands fοr "Cοngruent, Equal, and Midpοint Rule". This methοd is based οn the prοperties οf parallelοgrams, where οppοsite sides are parallel and cοngruent, and οppοsite angles are equal. By using the CER methοd, we can prοve that a quadrilateral is a parallelοgram if it satisfies the cοnditiοns οf having οppοsite sides cοngruent, οppοsite angles equal, and diagοnals bisecting each οther at their midpοint.

Tο shοw that ABCD is a parallelοgram, we need tο demοnstrate that bοth pairs οf οppοsite sides are parallel.

Let's begin by finding the slοpe οf each side using the fοrmula:

slοpe = (change in y) / (change in x)

Slοpe οf AB = (3 - (-1)) / (1 - 2) = 4/-1 = -4

Slοpe οf BC = (5 - 3) / (6 - 1) = 2/5

Slοpe οf CD = (1 - 5) / (7 - 6) = -4

Slοpe οf DA = (-1 - 1) / (2 - 7) = -2/5

Nοw, we can use the fact that twο lines are parallel if and οnly if their slοpes are equal. Thus, we need tο check whether AB is parallel tο CD and whether BC is parallel tο DA.

AB is parallel tο CD if their slοpes are equal. Since the slοpe οf AB is -4 and the slοpe οf CD is alsο -4, we can cοnclude that AB is parallel tο CD.

BC is parallel tο DA if their slοpes are equal. Since the slοpe οf BC is 2/5 and the slοpe οf DA is alsο 2/5, we can cοnclude that BC is parallel tο DA.

Therefοre, since bοth pairs οf οppοsite sides are parallel, we can cοnclude that ABCD is a parallelοgram.

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The expression for Kanika's mother's age, given Kanika's age and her father's is 32 + x .

To find Kanika's mother's age, we need to first find Kanika's age in relation to her father's who is 35 years more than her age.

Her father's age is therefore:

= Kanika's age + 35

= x + 35

Kanika's mother is 3 years less than the father which makes it :

= x + 35 - 3

= x + 32

In conclusion, Kanika's mother's age when expressed in terms of Kanika's age, is x + 32 .

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The first part of the question is:

Let Kanika's present age be x years. Her father's age exceeds her age by 35 years

The angle pairs are:

1. E. same side interior angles

2. G. Corresponding angles

3. A. Vertical angles

4. I. Supplementary angles

Angle pairs are two angles that share a common side and a common vertex. Angle pairs are important in geometry because they allow us to study the relationships between angles and the properties of geometric figures.

There are several types of angle pairs, including:

By understanding the properties of these angle pairs, we can solve problems in geometry involving angles and their measures.

Therefore:

1. The angles are E. same side interior angles

2. Angles labelled 2 are: G. Corresponding angles

3. Angles labelled 3 are: A. Vertical angles

4. Angles labelled 4 are: I. Supplementary angles

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The y-intercept is (0, -20) and the x-intercept is (20, 0).

what is an algebraic expression?

An algebraic expression is a mathematical phrase consisting of variables, numbers, and mathematical operations. It can include variables (such as x, y, or z), constants (such as 2, 3, or 4), and operators (such as +, -, *, or /) that combine these elements.

For example, 2x + 3y - 4 is an algebraic expression that contains the variables x and y, the constants 2, 3, and 4, and the operators + and -. It does not contain an equal sign and does not represent an equation, but it can be simplified or evaluated for specific values of the variables. Algebraic expressions are commonly used in algebra and other branches of mathematics to represent mathematical relationships and solve problems.

The given equation is y = -32 + 12.

To find the y-intercept, we set x = 0 and solve for y:

y = -32 + 12

y = -20

So the y-intercept is (0, -20).To find the x-intercept, we set y = 0 and solve for x:

0 = -32 + 12

20 = x

So the x-intercept is (20, 0).

Therefore, the y-intercept is (0, -20) and the x-intercept is (20, 0).

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It will take the Stand family approximately 29.17 hours to reach Disneyland, including the breaks taken every two hours.

The total time taken can be calculated as:

Here, distance = 860 miles, speed = 60 mph, and breaks are taken every two hours, which means 430 miles of driving before each break.

So, the equation becomes:

Simplifying the equation, we get:

Therefore, it will take the Stand family approximately 29.17 hours to reach Disneyland, including the breaks taken every two hours.

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The brown cows produced more milk than the white cows in the given situation.

"Same amount" means that two or more quantities are equal to each other in terms of their numerical value or quantity.

To find out whether the brown cows produce more milk or the white cows, we can make a ratio of milk produced by both the herds in one day.

For this, let’s assume the amount of milk produced by a white cow in one day is “w” and the amount of milk produced by a brown cow in one day is “b”.

Then, The amount of milk produced by eight white cows in 1 day = 8w.

The amount of milk produced by six brown cows in 1 day = 6b.

The amount of milk produced by six white cows in 1 day = 6w.

The amount of milk produced by ten brown cows in 1 day = 10b.

According to the given condition, both herds produce the same amount of milk in one day.

Therefore, 8w × 10 = 6w × 86w × 5/3

                               = 10b5w/4 = 5b/2b

                               = (5w/4) × (2/5)

                               = w/2

We can say that a brown cow produces double the milk produced by a white cow. Hence, brown cows produced more milk than the white cows in the given situation.

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The average daily balance is calculated by taking the sum of all the daily balances during a billing period and dividing it by the number of days in that period. The interest to be paid on April 1 is $150 * 1.5% = $2.25.

a. The average daily balance for the billing period is calculated by taking the sum of all the daily balances during the billing period and dividing it by the number of days in that period. For example, if the daily balances for the billing period are $100, $150, and $200, then the average daily balance is ($100 + $150 + $200) / 3 = $150. This can be rounded to the nearest cent if necessary.

b. The interest to be paid on April 1 is calculated by multiplying the average daily balance by the monthly interest rate of 1.5%. For example, if the average daily balance is $150, then the interest to be paid on April 1 is $150 * 1.5% = $2.25. This can be rounded to the nearest cent if necessary.

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As a result, the answer to the following question, This implies that the ballet shoe range in the class vary significantly, with some students having significantly bigger or smaller feet than others.

The variable's range is calculated by taking its greatest observed value and subtracting its minimum observed value (minimum). Possible range or variational bounds: a variety of steel costs; a variety of styles; The scope or size of a method or action: perception. The maximum or anticipated range of a weapon's projectile. A list or set's range is the number between the lowest and maximum. Align all of the numbers before determining the region. Next, subtract (reduce) the lowest number from the greatest number. The solution includes the range of the list. The solution specifies the range of the list.

The range is 4.5, which implies that the difference between the data set's biggest and lowest values is 4.5. The range is 8 - 3.5 = 4.5 since the biggest number is 8 and the smallest value is 3.5. This implies that the ballet shoe sizes in the class vary significantly, with some students having significantly bigger or smaller feet than others.

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The statement is True. According to the Central Limit Theorem, in a sufficiently large random sample, the distribution of a random variable X, with mean μ and standard deviation σ, is a normal distribution with mean μ and standard deviation σ/sqrt(n).

1. The Central Limit Theorem states that the distribution of the sample means of a large sample size will approach a normal distribution, regardless of the original distribution of the population from which the sample is drawn.
2. For a sufficiently large sample size, the mean of the sample means will approach the population mean (μ) and the standard deviation of the sample means will approach the population standard deviation divided by the square root of the sample size (σ/sqrt(n)).
3. Therefore, in a sufficiently large random sample, the distribution of a random variable X, with mean μ and standard deviation σ, is a normal distribution with mean μ and standard deviation σ/sqrt(n).

This is the case because the Central Limit Theorem states that the distribution of sample means is approximately normal, regardless of the original distribution of the population from which the sample is drawn.

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