Last year Amber went to gymnastics classes 21 days every month. This year she only went 19 days a month. How many more days did she go to gymnastics class last year than this year?

Using Algebraic equations, The diagram might also show other values or quantities related to the equation, depending on the specific context or purpose of the diagram.

Algebraic equations are mathematical statements that involve one or more variables, as well as constants and mathematical operations such as addition, subtraction, multiplication, and division. An algebraic equation usually has an equals sign (=) that separates the two sides of the equation. The goal of an algebraic equation is to find the value of the variable that makes the equation true.

For example, the equation x + 3 = 7 is an algebraic equation that involves the variable x. The goal is to find the value of x that makes the equation true. In this case, we can solve the equation by subtracting 3 from both sides, which gives us x = 4.

Algebraic equations can be used to model a wide variety of real-world situations, such as the relationship between the price and quantity of goods sold, the growth rate of a population, or the amount of interest earned on an investment. They are a fundamental tool in many branches of mathematics, science, engineering, and economics, and they are also used extensively in computer programming and data analysis.

Without a specific diagram to refer to, it's difficult to provide a specific answer. However, I can provide a general explanation of how a diagram might show that x + 4 has the same value as 17 and how it might indicate the quantity x.

One way a diagram might represent this equation is through the use of a balance or scale. For example, the diagram might show a balance with a weight of 17 on one side and a weight of x + 4 on the other side. If the balance is level, it indicates that the weight of x + 4 is equal to the weight of 17, which means that x + 4 has the same value as 17.

To indicate the quantity x, the diagram might show a box or symbol on the side of the balance representing x + 4. This box might have a label or caption indicating that it represents x + 4. By subtracting 4 from both sides of the equation, we can determine that x is equal to 13, which would be the value of x that the diagram is representing. The diagram might also show other values or quantities related to the equation, depending on the specific context or purpose of the diagram.

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The area of the image of the triangle under T is 5/9.

What is Triangle?

In geometry, a triangle is a closed two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is characterized by its three vertices (points where two sides intersect) and three sides (line segments that connect the vertices). The sum of the interior angles of a triangle is always 180 degrees, and the length of each side is less than the sum of the lengths of the other two sides.

To show that T maps the given triangle to the domain D, we need to find the image of the three vertices of the triangle under T and then show that the image lies inside D.

Let's first consider the vertex (0,0) of the triangle. Applying T, we get T(0,0) = (0,0). So the image of the vertex (0,0) is the origin, which clearly lies inside D.

Now let's consider the vertex (1,1) of the triangle. Applying T, we get T(1,1) = (0,2), which lies on the y-axis and satisfies y²=4-4x, so it lies inside D.

Finally, let's consider the vertex (u,0) of the triangle, where 0≤u≤1. Applying T, we get T(u,0) = (u²,0). This lies on the x-axis and satisfies y²=4-4x only when x=1, which is outside D. Therefore, the image of this vertex is not inside D.

Hence, we can conclude that T maps the triangle to the domain D, except for the line segment {(u,0):0≤u≤1}.

To evaluate the area of the image, we can use the fact that the area of the image of a region under a transformation is equal to the absolute value of the determinant of the Jacobian matrix of the transformation, multiplied by the area of the original region.

The Jacobian matrix of T is given by

J(T) = [2u -2v]

[2v 2u]

The absolute value of the determinant of this matrix is 4u² + 4v², so the area of the image of the triangle is

∫∫R 4u²+4v² dA,

where R is the region in the uv-plane corresponding to the triangle.

Integrating over R, we get

∫0 ∫v 4u²+4v² dudv

= ∫0 (4/3) (1-v³+3v²) dv

= (4/3) (1/4 - 1/16 + 1/3 - 1/12)

= 5/9.

Therefore, the area of the image of the triangle under T is 5/9.

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Answer:

Aisha, Arsenio

Step-by-step explanation:

Because it adds up to a total of 180 degrees

The area of the larger triangle is 72cm²

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle. Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.

The large triangular figure below is composed of triangles with a base and height of 4 cm.

The area of small triangle is 1/2 base × height = 1/2 × 4 × 4 = 8cm²

There are 9 small triangles in the large one so the area will be 9 × 8 =72cm²

Hence the area of the larger triangle is 72cm².

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Answer:

26

Step-by-step explanation:

[tex] \sqrt{ {24}^{2} + {10}^{2} } = 26[/tex]

Answer:

----------------------------

Given is the right triangle with legs of 24 and 10.

Find the hypotenuse using Pythagorean theorem:

There are 3.79 litres in 4 quarts.

Unit conversion is the conversion between different units and measurements of the same quantity through a process of multiplication or division. In mathematics, conversion is the process of changing values ​​in one form to another form like Inches to millimeters or liters to gallons.

Given in the table

1 quart = 0.9464 liter

4 quarts = 4 × 0.9464 litre

4 quarts = 3.7856 litres

hundredths means 2 digit right to the decimal point

3.7856 litres rounded to nearest hundredths

= 3.79 litres

Hence, 3.79 litres are there in 4 quarts.

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The required real diameter of the tin is 250 mm.

Diameter is the length of a straight line drawn through the center of a circular object, such as a circle or sphere. It is the distance between two locations on the object's edge that are furthest apart and pass through the object's center.

Here,

If the diameter of the tin in the picture is 10 cm, then the actual diameter of the tin can be calculated as:

To convert the actual diameter to millimeters (mm), we can multiply by 10:

Therefore, the real diameter of the tin is 250 mm.

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Full Question:
See the attached.

As a result, the usual professional basketball player makes 125000 times more than the typical American worker.

Mathematicians use the unitary method to tackle proportionality-related issues. Finding the value of one unit of a quantity and then using that value to determine the value of another quantity is what this process entails. The unitary technique, for instance, can be used to calculate how far a car will travel on 5 gallons of gas if it travels 40 miles on 2 gallons. We start by determining the price of one unit of gasoline: 2 gallons of fuel equals 20 miles per gallon, while 1 gallon of gasoline travels 40 miles. The distance the car will drive on 5 gallons of gasoline can then be calculated using this value:

given

The query does not include information on the typical wage of a professional basketball player. Let's say the average wage for a professional basketball player in the NBA is $5x106 per year.

We divide the salary of the basketball player by the salary of the worker to determine how many times higher the typical professional basketball player's salary is than the average American worker's salary:

$5x10^6 / $4x10^4 = $125000 / $1 = 125000

As a result, the usual professional basketball player makes 125000 times more than the typical American worker.

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Answer:

10

Step-by-step explanation:

(-9,5) (-9,-5)

[tex]x_{1} = -9\\y_{1} =5\\x_{2} =-9\\y_{2} =-5[/tex]

[tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2} -y_{1} )^{2} }[/tex]

[tex]\sqrt{(-9-(-9)^{2} +(-5-5)^{2} }[/tex]

[tex]\sqrt{(-9+9)^{2}+(-5-5)^{2} }[/tex]

[tex]\sqrt{(0)^{2}+(-10)^{2} }[/tex]

[tex]\sqrt{0+100}[/tex]

[tex]\sqrt{100} =[/tex] 10

Solution is in the attachment!! :)

The domain and range and the type of relation should be determined as follows;

In Mathematics, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).

Based on relations 3 and 4, we can logically deduce that they do not represent a function because their independent value (domain) has more than one dependent value (range).

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Answer: To find the equation of a line parallel to 12x + 8y = -40, we need to first rearrange the equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

12x + 8y = -40

8y = -12x - 40

y = -1.5x - 5

So, the slope of the line is -1.5.

Since the line we want is parallel to this line, it will have the same slope, which is -1.5. Now we can use the point-slope form of a line to find the equation:

y - y1 = m(x - x1)

where (x1, y1) is the point through which the line passes, and m is the slope.

Substituting (6,-3) and -1.5 for x1, y1, and m respectively, we get:

y - (-3) = -1.5(x - 6)

y + 3 = -1.5x + 9

y = -1.5x + 6

So the equation of the line parallel to 12x + 8y = -40 through the point (6,-3) is y = -1.5x + 6.

Step-by-step explanation:

The required population of Algeland 16 years from now will be approximately 524937236.

In essence, percentages are fractions with a 100 as the remainder. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on an examination (75/100).

To find the population of Algeland after 16 years, we can use the formula:

[tex]$P = P_0 \times (1 + r)^n$[/tex]

where P is the population after 16 years, [tex]$P_0$[/tex]is the initial population, r is the annual growth rate, and n is the number of years.

Given that the population of Algeland increases by 33% each year, we can express the annual growth rater as:

[tex]$r = 33% = 0.33$[/tex]% = 0.33

We are also given that the current population [tex]$P_0$[/tex] is 5,476,223.

Thus, the population of Algeland after 16 years can be calculated as:

[tex]$P = 5,476,223 \times (1 + 0.33)^{16}$[/tex]

Simplifying this expression, we get:

P = 524937236

Therefore, the population of Algeland 16 years from now will be approximately 524937236.

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Answer:

Step-by-step explanation:

I don’t understand this app how do I use it

Answer:

Base = 5inches

Step-by-step explanation:

2(x+2) + x
2x+4+x
3x+4=19
3x=15
x=5

Answer:x5

Step-by-step explanation:

The coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin are;

M = (1, 2)

N = (2, 4)

P = (4, 5)

Q = (3, 3)

The coordinates of the quadrilateral RSTU is

R = (1, -2)

S =(2, -4)

T = (4, -5)

U = (3, -3)

When the quadrilateral RSTU is rotated 90 degrees about the origin, it forms the quadrilateral MNPQ which has the coordinates

M = (1, 2)

N = (2, 4)

P = (4, 5)

Q = (3, 3)

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Answer:

Step-by-step explanation:

We can use the Pythagorean theorem to find the distance from second base to home plate, which is the diagonal of a right triangle with legs of 60 feet each:

d = sqrt(60^2 + 60^2) = sqrt(7200) ≈ 84.85 feet

So the total distance that you ran is:

60 + 60 + 84.85 ≈ 204.9 feet

Rounded to the nearest tenth, the answer is:

204.9 feet ≈ 204.9 feet

The population of 2 guppy fishes that grows at a rate of 1700% per month indicates;

A population growth formula is a formula of the form; A = P·(1 + r)^t, where, A is the amount after a period of t months, (or days or years), at a growth rate of r.

Number of guppy fish bought = 2

Rate at which guppy populations grow = 1700% per month

The formula that models the population of guppies can be obtained as follows;

The population growth equation is an exponential formula that can be modeled using the following equation;

Where;

A = The number after the number of months

P = The initial population of the guppy fish = 2

r = The percentage growth rate = 1700%

t = The time of growth in months = 4

Therefore, after 4 months the population of guppy fish will be;

A = 2 × (1 + 17)^4 = 209952

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Determing how many x intercepts the graph has, as those are the points when y = 0.

The answer of the question based on monthly installment is Anver's monthly installment is R6 253.27.

What is Formula?

In mathematics,  formula is  set of symbols or expressions representing mathematical relationship or the rule. Formulas are often used to describe and solve the problems in mathematics, science, engineering, and other fields.

To determine the amount of the loan, we can calculate 85% of the price of the van, which is the amount that Anver would have to borrow after paying the 15% deposit:

Amount of loan = 85% of R392 900

= 0.85 x R392 900

= R333 965

To determine the monthly installment, we need to use the formula for the present value of an annuity:

PV = PMT x (1 - (1 + r/n)^(-nt)) / (r/n)

We can calculate the annual interest rate by adding 1% to the prime rate. According to the South African Reserve Bank, the prime rate in September 2013 was 9%.

Annual interest rate = prime rate + 1%

= 9% + 1%

= 10%

Therefore, we can substitute the given values into the formula:

PV = R333 965

r = 10% / 12 = 0.8333%

n = 12

t = 72 / 12 = 6

Rearranging the formula to solve for PMT, we get:

PMT = PV x (r/n) / (1 - (1 + r/n)^(-nt))

Substituting the values, we get:

PMT = R6 253.27 (rounded to two decimal places)

Therefore, Anver's monthly installment is R6 253.27.

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The inequality which represents the least number of days that Kelli needs to run to reach her goal is

2 1/4 + 1/3d ≥ 4.

The least number of days after Monday that Kelli needs to run to reach her goal is 5.25 days

Monday= 2 1/4 miles

Other days of the week = 1/3 miles

Her goal =™4 miles

Number of days = d

2 1/4 + 1/3d ≥ 4

subtract 2 1/4 from both sides

1/3d = 4 - 2 1/4

1/3d = 4 - 9/4

1/3d = 16-9 /4

1/3d = 7/4

divide both sides by 1/3

d = 7/4 ÷ 1/3

d = 7/4 × 3/1

= 21/4

d = 5.25 days

Hence, Kelli will reach her goal in at least 5.25 days.

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Answer: 94%

Step-by-step explanation: there are 16 .4's in 6.4 and if he missed by .4 then he got 15/16 which equals 94%

Answer:

2 = 5

Step-by-step explanation:

4 + (-2) = 5

After opening the parenthesis, the + will turn into a -

4 - 2 = 5

Not sure if there was any other part to this question, so I just answered what was given

Julie used direct proof because each statement is deduced from a previous statement. Samuel used indirect proof because the final statement contradicts the assumption.

What are direct and indirect proofs?

The complete question is given below.

Both Julie and Samuel are asked to prove m∠CBD  = 65°.

Let us look at Julie's proof.

She used the known facts which are given and finally proved that m∠CBD  = 65°. So Julie used direct proof.

Now let us observe Samuel's proof.

He started contradicting the statement when he wrote

 m∠CBD  + 65° ≠ 90°

So the last statement goes against what he was asked to prove.

Samuel used indirect proof.

Therefore Julie used direct proof because each statement is deduced from a previous statement. Samuel used indirect proof because the final statement contradicts the assumption.

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To model with mathematics is to test ideas using math and computer programs to simulate an object or action.

In order to understand a real-life problem, modelling entails developing a set of mathematical equations that accurately reflects a situation.

The model frequently needs to be modified because it does not adequately capture the situation.

By knowing how the system functions, which variables are significant in the system, and how they relate to one another, one can utilise a mathematical model to better understand a real-life situation. Moreover, models can be used to forecast and predict what a system will do in the future or for various parameter values. Finally, a model can be used to estimate variables that are challenging to precisely evaluate.

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The correct sample space is given in option C.

What exactly is a sample space?

In probability theory, a sample space is the set of all possible outcomes or results of an experiment or random phenomenon. It is denoted by the symbol "S". For example, when rolling a fair six-sided die, the sample space would be {1, 2, 3, 4, 5, 6} because those are the only possible outcomes. The sample space can be finite, countably infinite, or uncountably infinite, depending on the experiment being considered. The concept of a sample space is fundamental to probability theory, as all probabilities of events are defined in terms of the sample space.

Now,

To determine the sample space for spinning the spinner two times, we need to consider all possible outcomes for each spin and then combine them.

For one spin of the spinner, there are three possible outcomes: blue, orange, and red.

For two spins of the spinner, we need to consider all possible combinations of outcomes from the first and second spin. This can be done by creating a table

            1st spin      2nd spin

1       blue                  blue

2       blue                  orange

3            blue                  red

4       orange               blue

5       orange          orange

6      orange           red

7      red                   blue

8      red                   orange

9      red                   red

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(Total saplings- Saplings with a height greater than 27 1/4 inches) = Number of saplings with a height of 27 1/4 inches or less.

To find the height of an object in mathematics, you must first identify the shape of the object. Then, use the relevant formula for the shape to calculate the height. For example, if the object is a right triangle, the height can be found by using the Pythagorean Theorem. Additionally, if the object is a rectangle, you can use the formula for the area of a rectangle to calculate the height. Finally, if the object is a circle, you can use the formula for the circumference of a circle to find the height.

To solve this question, we will use the numerical approach. First, we need to subtract the number of saplings with a height greater than 27 1/4 inches from the total number of saplings. Then, we subtract the result from the total number of saplings. The result will be the number of saplings with a height of 27 1/4 inches or less.

Therefore, the equation is (Total saplings- Saplings with a height greater than 27 1/4 inches) = Number of saplings with a height of 27 1/4 inches or less.

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The inverse of the given functions are f⁻¹(x) = 3/4(x + 7) and f⁻¹(x) = x^2 + 10x + 25

The inverse of a function is a new function that undoes the effects of the original function.

In other words, if we have a function f(x) that maps x to y, then the inverse of f(x), denoted by f^-1(y), maps y back to x.

Given that:

f(x) = 4/3x - 7

Write as an equation

y = 4/3x - 7

Interchange the variables

x = 4/3y - 7

Solve for y

y = 3/4(x + 7)

Replace y with f⁻¹(x) to show the final answer.

f⁻¹(x) = 3/4(x + 7)

Also, the inverse of the function f(x) = √x -5 is computed as follows:

Interchange the variables and solve for y;

x = √y -5

y = x^2 + 10x +25

Replace y with f⁻¹(x) to show the final answer.

f⁻¹(x) = x^2 + 10x + 25

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We will be able to put out $36598.19. The solution has been obtained by using the concept of present value of annuity.

The present value of an annuity is the current value of its anticipated future payments at a given rate of return, or discount rate. With higher discount rates, the annuity's present value falls.

We are given that $400,000 are saved for retirement. The account earns  6% interest.

Using present value of annuity,

⇒Present value of annuity due = P + P [tex][\frac{1-(1+r)^{-(n-1)} }{r}][/tex]

⇒400,000 = P + P [tex][\frac{1-(1+0.06)^{-(15-1)} }{0.06}][/tex]

⇒400,000 = P [1 + 9.295]

⇒P = 400,000/10.9295

⇒P = $36598.19 (approx.)

Hence, we will be able to put out $36598.19.

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Answer:

B) 15 days

Step-by-step explanation:

Total Work = (Number of men) x (Hours worked per day) x (Number of days)

Using this formula, we can find the total amount of work to be done in the scenario given in the question:

Total Work = (20 men) x (6 hours per day) x (10 days) = 1200 hours

(a) To find out how many hours a day the remaining 16 men should work to finish the work in 10 days, we need to subtract the work that was not done due to the absence of the 4 men:

Remaining Work = Total Work - Work not done by 4 men

Remaining Work = 1200 - (4 men) x (6 hours per day) x (10 days)

Remaining Work = 840 hours

To finish the remaining work in 10 days, the 16 men would need to work:

Hours per day = Remaining Work / (Number of men) x (Number of days)

Hours per day = 840 / (16 men) x (10 days)

Hours per day = 5.25 hours

Therefore, the 16 men would need to work 5.25 hours per day to finish the work in 10 days.

(b) To find out how many hours a day the remaining 16 men should work to finish the work in 15 days, we need to calculate the total amount of work that needs to be done each day:

Daily Work = Total Work / Number of days

Daily Work = 1200 / 15

Daily Work = 80 hours

To finish the daily work of 80 hours, the 16 men would need to work:

Hours per day = Daily Work / Number of men

Hours per day = 80 / 16

Hours per day = 5 hours

Therefore, the 16 men would need to work 5 hours per day to finish the work in 15 days.

Step-by-step explanation:

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