How many solutions does the linear equation 3x 11y 10 have?.

The total time Karen spent riding her bike and swimming in the race is 135 minutes.

What is algebra ?

Algebra is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics.

To find the total time Karen spent riding her bike and swimming in the race, you need to add the time she spent riding her bike and the time she spent swimming.

Karen rode her bike for 1 1/2 hours, which is equivalent to 1.5 * 60 = 90 minutes.

She also swam for 45 minutes.

90 + 45 = 135,

The total time Karen spent riding her bike and swimming in the race is 135 minutes.

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Karen spent 135 minutes riding her bike and swimming in the race.

Algebra is a common thread that runs through practically all of mathematics. It involves the study of variables and the rules for manipulating them in formulas.

You must add the time Karen spent swimming and riding her bike to get the total amount of time she spent doing both during the race.

First, we need to convert Karen's bike riding time to minutes:

1 1/2 hours = 1 1/2 * 60 minutes = 90 minutes

Now we can add up Karen's bike riding time and swimming time:

90 minutes + 45 minutes = 135 minutes

So Karen spent 135 minutes riding her bike and swimming in the race.

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The functions for the total cost per month for data use are linear in each of the given options.

Correct responses;

1. A(1) = 60,   B(1) = 35

2. A(7.5) = 60,   B(7.5) = 100

3. The monthly charge for Option A fixed. The monthly charge for Option B includes a fixed monthly fee and $10 per gigabyte used.

4. Please find attached the combined graph of Option A and Option B. Option B is more affordable when the (extra) data usage is less than 3.5 gigabytes each month.

The amount of gigabytes of data the student would have for $50 is 2.5 gigabytes.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given parameters are;

Both plans data allowance per month = 2 gigabytes

The monthly cost for each option is;

Option A: A(x) = 60 = Constant

Option B: B(x) = 10·x + 25

Solution:

1. The values of A(1) and B(1) are;

A(1) = 60

B(1) = 10 × 1 + 25 = 35

Therefore;

A(1) = $60

B(1) = $35

2. The values of A(7.5), and B(7.5) are;

A(7.5) = 60

B(7.5) = 10 × 7.5 + 25 = 100

A(7.5) = $60

B(7.5) = $100

3. The description of each data plan are;

Option A

The data plan of option A has a fixed charge of $60

Option B

The charges on the data plan on option B consist of a fixed monthly charge of $25, and $10 per gigabyte of data used.

4. Please find attached the graph of the functions of Option A and Option B. From the graph, the most affordable plan to use based on the data usage is;

Option B; If the data used a month, x < 3.5 gigabytes

Option A; If the data used a month, x > 3.5 gigabytes

Either Option A or Option B if the data usage per month is exactly 3.5 gigabytes

The amount the student budgets per month = is $50

By using Option B, we have;

B(x) = 10·x + 25 = 50

10·x = 50 - 25 = 25

x = 25 / 10 = 2.5

At $50, the amount of gigabytes the student can get is x = 2.5 gigabytes

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The values of the credit utilization are

He should pay highest interest debt first

a. His Visa?

Here, we are given that

$2000 limit and a balance of $450

So, we have

Ozzie's credit utilization on his Visa is

Utilization = (450/2000) * 100 = 22.5%

b. His store credit card?

Here, we are given that

$500 limit and a $200 balance

So, we have

Ozzie's credit utilization on his store credit card is

Utilization = (200/500) * 100 = 40%

c. The joint card with his mom?

Using the same formula, we have

Ozzie's credit utilization on the joint card with his mom is (700/5000) * 100 = 14%

Overall credit utilization

This is calculated as:

Ozzie's overall credit utilization is the sum of his balances divided by the sum of his credit limits

So, we have

Utilization = (450 + 200 + 700) / (2000 + 500 + 5000) = 13.5%.

The debt with the highest interest rate first. This is because high-interest debt will cost more in the long run, so paying it off sooner will save money on interest charges.

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Tan 30 degrees has a value of 1/√3. 30° is represented by the radian symbol tan /6.

Trigonometric functions are crucial for much research, including those involving wave motion, light motion, the velocity of harmonic oscillators, and other topics.

Tan 30° has a value of 1/√3 in fractional form and 0.577 in decimal form.

Using trigonometric functions, the value of tan 30° is represented as follows:

Tan 30° is equal to (sec 2 30°-1)

Tan = 1/cot = 30°

=1/√3

There are several ways to calculate tan 30 degrees, including using the trigonometric ratio formula since we already know that tan x = Perpendicular / Base.

ABC with angle A being 30° in a right-angled triangle.

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Answer:

96/x

Step-by-step explanation:

When two variables x and y vary inversely, their product is a constant. Therefore, the function that models the inverse variation between x and y is:

x*y = k

where k is the constant of proportionality.

We can use the given information to find the value of k:

x = 12 when y = 8

so, k = xy = 128 = 96

Now we can use this value of k to write the function that models the inverse variation:

x*y = 96

To find the inverse variation, we divide both sides by y,

x = 96/y

Alternatively, we can write y = 96/x

So, the function that models the inverse variation between x and y is either x = 96/y or y = 96/x

The associative property of rational numbers shows that addition and multiplication are associative with rational numbers. For x,y,z,p,r,q∈Q

The associative property of rational numbers is defined as on adding or multiplying any three rational numbers leaves the same result no matter how the numbers are grouped. But if the order of the numbers in subtraction or division changes, the result will also change.

For addition : A, B, C belong to rational numbers (A + B) + C = A + (B + C). For example, (1/3 + 1/3) + 1/2 = 1/3 + (1/3 + 1/2)

= 7/6. Addition is said to be associative for rational numbers.

For multiplication: Multiplication is expressed as (A × B) × C = A × (B × C). For example: (1/3 × 1/4) × 1/2 = 1/4 × (1/3 × 1/2)

= 1/24 = 1/24. It turns out that multiplication is associative for rational numbers. However, division and subtraction operations do not follow the associative properties of rational numbers.

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An exponential function F(y)=g^y (g power y).

The log function is one of the functions and  We know that the inverse of a log function is an exponential. So, we know that the inverse of f(x) = log subb(x) is f^-1(y) = b^y. If the base is e and we are dealing with the natural log, then the inverse of f(x) = ln(x) is f^-1(y) = e^y.Rewriting these relationships substituting f(x) with y and f^-1(y) with x, we see that the inverse of y = log subb(x) is x = b^y and the inverse of y = ln(x) is x = e^y. Both the inverse and the original function state the same relationship,

so now,

f(x)=log base g x.

g^f(x)=x

g^y=f(y).

f(y)=g^y.

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Answer:

$6750.50

Step-by-step explanation:

F = Pe^(rt)

8327.94 = P × e^(0.0175 × 12)

P = 8327.94/e^0.21

P = 8327.94/1.23376806

P = 6750.5

The vertex form of the quadratic function is f(x) = x² + 8x + 3 is (x + 4)² = y +13.

The term Vertex form of a quadratic equation refers as

=> (x - h)² = 4a (y - k) form or in another written as,

=>  (y - k)² = 4a (x - h) form depending on whether the square is on x-term or y-term respectively.

Here we have given quadratic function is that is written f(x) = x² + 8x + 3

And in the given equation square term is for x.

As we all know that equation must be reduced to (x - h)² = 4a (y - k) form.

Then here we know that we have

=> y = f(x) = x² + 8x + 3

Now we have to completing the square,

=> y = (x² + 8x +16) -16 + 3

Then it can be written by using the factorize the expression

=> y = (x + 4)² -13

Now we have to rewrite the expression, then we get,

=> y + 13 = (x + 4)²

Then resulting vertex form of the expression as,

=> (x + 4)² = y +13

Complete Question:

What is the vertex form of f(x) = x² + 8x + 3?

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Answer:

the compass was used to locate all 6 vertices

The easiest way to find a specific term in a binomial expansion is to use the binomial theorem.

The binomial theorem is a fundamental theorem in mathematics that is used to expand expressions which involve two terms, known as binomials, raised to a power.

The binomial theorem states that for any non-negative integer n, the expansion of (x+y)ⁿ is given by the sum of all terms of the form (xⁿ-k)(y^k)/k! where k ranges from 0 to n. This theorem can be used to calculate any term of a binomial expansion.

For example, to calculate the third term of (x+y)⁵, set k = 2 and substitute the appropriate values into the expression (x⁵-2)(y²)/2! which gives 5x³y². This is the third term of (x+y)⁵. The binomial theorem is a powerful tool that can be used to simplify, expand and simplify expressions involving binomials.

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The equation of the line containing midsegment XZ in the standard form is:

y = 2x +0

What is the Equation of line?

The equation of a line is a mathematical representation of the relationship between the variables x and y on a coordinate plane. It is typically written in the form "y = mx + b", where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

The equation of the line containing the midsegment of a triangle can be found by taking the average of the coordinates of the midpoints of the two line segments that make up the midsegment.

First, we need to find the midpoint of AB:

Midpoint of AB = ((-4+8)/2, (1+-1)/2) = (2,0)

Then, we need to find the midpoint of BC:

Midpoint of BC = ((8+-2)/2, (-1+9)/2) = (3,4)

The equation of line XZ can be found by taking the average of the coordinates of X and Z, and solving for y:

y = (0+4)/2 = 2

x = (2+3)/2 = 2.5

Hence, the equation of the line containing midsegment XZ in the standard form is:

y = 2x +0

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Angela practiced piano during the weekend for 6 hours.

According to the question,

Amount Angela spent on Saturday  = [tex]2\frac{1}{3}[/tex]

Amount Angela spent on Sunday = [tex]3\frac{2}{3}[/tex]

To find out the total amount spent on both days of the weekend =

The amount that Angela spent on Saturday + the amount that Angela spent on Sunday

= [tex]2\frac{1}{3}[/tex] (otherwise expressed as 7/3) + [tex]3\frac{2}{3}[/tex] (otherwise expressed as 11/3)

[tex]= \frac{7}{3} + \frac{11}{3}[/tex]

[tex]= \frac{7 + 11}{3}[/tex]   ( using addition)

= [tex]\frac{18}{3}[/tex] = 6 hours

Noted, Friday’s value was not added because it didn’t fall on the weekend.

The denominators of both fractions are the alike (3), thereby it was used to factor out the numerators (7) and (11), and subsequently arrive at the final answer which is 6 hours.

So, Angela practiced for 6 hours.

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Yes, 1 is a square number.

Now, According to the question:

Square numbers are those numbers that are produced by multiplying an integer to itself. If n is an integer, then [tex]n^2[/tex] is the square of n.

What are the examples of square numbers?

The examples for square numbers are:

[tex]6^2[/tex] = 36

[tex]10^2[/tex] = 10 x 10 = 100

[tex]15^2[/tex] = 15 x 15 = 225

[tex]12^2[/tex] = 12 x 12 = 144

When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers.

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A unique type of right triangle known as a Pythagorean triple has lengths on all three sides that are whole numbers.

The 3-4-5 triangle, with a hypotenuse of 5 and sides 3 and 4, is the most well-known and smallest of the Pythagorean triples.

The 3 : 4 : In arithmetic progression, the only right triangles with edges are the five triangles. Pythagorean triple-based triangles are Heronian, with an integer area and integer sides.

A right triangle with side lengths that are 3:4:5 is called a 3-4-5 right triangle. To put it another way, Pythagorean Triples are the sides-to-side ratios of a 3-4-5 triangle. This ratio can be stated as follows: Side 1: Side 2: 3n = hypotenuse: 4n: 5n = 3: 4: 5.

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The total number of people at the stadium is 11000.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

At a football stadium, 2% of the fans in attendance were teenagers.

If there were 220 teenagers at the football stadium.

the total number of people at the stadium= 220*100/2

                                                                     =1100

Hence, the total number of people at the stadium is 11000.

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Answer:

Step-by-step explanation:

You need to save 399.99 - 15.28 = £384.71

384.71 / 7 = 54.95

So, you will get the required amount 54 weeks on a Friday, starting from the Friday you start saving,

Answer:

See pictures:

Answer:

I think its 8

Step-by-step explanation:

Because from 2010 to 2015 population grew by 8•/• that mean 8 people per 100

Answer:

7+3

Step-by-step explanation:

6+4 = 10 and 7+3 = 10