This is an equation puzzle.
Fill in the blanks so that each row and column makes a true equation. (first puzzle)
This is an equation puzzle.
Click on each blank to change the sign so that each row and column makes a true equation. (second puzzle)

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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The linear equation 3x + 11y = 10 has one solution.

The given linear equation is 3x + 11y = 10. To find the number of solutions for this equation, we can use the following method:

1. Rewrite the equation in the form of y = mx + c, where m is the coefficient of x and c is the constant term.

   3x + 11y = 10

   -3x/11 = y -10/11

   y = -3/11x +10/11

2. Check the slope and the y-intercept, if the slope is infinite, it means the equation is a vertical line and it has no solutions, if the y-intercept is infinite, it means the equation is a horizontal line and it has infinitely many solutions.

In this case, the slope is -3/11 which is a finite value, also the y-intercept is (0,10/11) which is a finite value, so the equation is not a vertical or horizontal line, it is a standard form of a linear equation, and it has a unique solution.

Therefore, the linear equation 3x + 11y = 10 has one solution.

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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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Answer:

I think its 8

Step-by-step explanation:

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

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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Answer:

the compass was used to locate all 6 vertices

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,

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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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

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:

7+3

Step-by-step explanation:

6+4 = 10 and 7+3 = 10

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 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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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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