What is the formula of a parabola with the vertex at 2/3 and focus at 0 3 )?.

The linear equation for this scenario is y = 2x + 10 and $20 was charged for 5 ATM transactions

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Let y represent the total cost for x monthly transactions.

$10 is charged monthly plus $2 per transaction, hence:

m = 2, b = 10

y = 2x + 10

For 5 ATM transactions:

y = 2(5) + 10 = $20

The linear equation for this scenario is y = 2x + 10

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Yes, 35 and 36 are co-prime numbers. The factors of 35 are 1,,5, and 7 while for 36 it is 1,3,4,6,9, and 12. They share only 1 as factor hence they are coprime

The only two numbers that have 1 in common are known as co-prime numbers. From 1 to 100, some of these Co-Prime Numbers include: There are numerous pairs of Co-Primes from 1 to 100 that adhere to the aforementioned characteristics. The following are a few of them: (1, 99), (14, 15), (28, 57), (29, 31), (23, 1), (59, 97), etc. Sets of numbers that are coprime with one another are referred to as coprime numbers. Each and every prime number is a co-prime: One and the number itself are the only two factors that each prime number has, so the only factor that two prime numbers will have in common is 1. Two prime numbers are, for instance, 11 and 17.

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The F-14 Tomcat was created as a long-range naval interceptor and air superiority fighter, allowing it to perform the roles of an escort attack aircraft when equipped with Sparrow missiles and a fleet air defense loitering interceptor when equipped with Phoenix missiles.

The F-14 was equipped with the capacity to shoot down ANY enemy aircraft, anywhere in the globe. No other Cold War aircraft could dispatch two nuggets on a "normal" mission from the CV and capture two Aces a few hours later. Incredible combat capabilities were made possible by the AIM-54 and the AWG-9.

During the war, the F-14 was credited with one air-to-air victory. On February 6, 1991, a VF-1 F-14A employing an AIM-9 Sidewinder brought down an Iraqi Mil Mi-8 helicopter. Budget cuts that came into effect in 1991, after the conclusion of both the Cold War and the Persian Gulf War, forced the early retirement of the Tomcat.

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In this situation, it is true that the population who go to the movie theater, and the sample is the first 150 people of the theater.

In statistics and related fields, the population can be considered as the whole or the complete group that is being studied. On the other hand, the sample is a fraction taken from the whole population.

The purpose of a sample is to make the process of studying the population easier as studying every individual of the population is too complicated.

Based on this, the population are all customers going to the theater but the sample are the 150 people.

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The y-intercept of y =- 2/3x + 7 is 7.

The equation, y = mx + b, is the slope-intercept form of a straight line.

Here, x and y are the coordinates of the points, m is the gradient, and b is the intercept of the y-axis.

y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept.

The value of b is equal to y when x = 0, and m shows how steep the line is. The slope of the line is also called the gradient.

Thus, The y-intercept of y =- 2/3x + 7 is 7.

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Find the x and y-intercepts of the line. Let y and solve for x. Let x and solve for y. Find a third solution to the equation. Plot these three coordinates and check that they line up. Draw the line.

Let the equation be y = Px + Qz. P and Q are constants, and x and z are 2 variables.

Firstly, make one variable 0, z = 0. This implies that you are dealing with only two variables, so you can make a graph(1) on X and Y axis. A simple line passes through the origin. Now take z = 1, and plot on the same plane, i.e., Plot y = Px + Q (this will be graph 2). Similarly, for all z. You will get a set of parallel lines separated by B.

Then you realize that only Graph(1) belongs to the z = 0 plane. and Graph(2) belongs to z = 1 plane and so on for z = 2, 3, 4….

So all you get is a Plane with slope P with respect to the x-axis and slope Q with respect to slope Q.

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The equivalent fractions of 3/4 are 6/8, 9/12, 12/16, and 15/20.

Equivalent fractions are fractions that represent the same value, even though they look different. For example, if you have a cake, cut it into two equal pieces, and eat one of them, you will have eaten half the cake. If you cut a cake into eight equal pieces and eat four of them, you will still have eaten half the cake. These are equivalent fractions.

To find the equivalent fractions for any given fraction, multiply the numerator and the denominator by the same number. For example, to find an equivalent fraction of 3/4, multiply the numerator 3 and the denominator 4 by the same number, say, 2. Thus, 6/8 is an equivalent fraction of 3/4. We can find some other equivalent fractions by multiplying the numerator and the denominator of the given fraction by the same number.

3/4= 3×3/4×3

=9/12.

3/4=

3/4= 3×4/4×4

=12/16

3/4= 3×5/4×5

=15/20

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The second step required to solve the given system of equations using elimination method is to add or subtract the modified system of equations.

As given in the question,

Steps required to solve the given system of equations by elimination method :

Let us consider two system of equations are :

2x + 3y = 1  __(1)

3x + 2y = 1  __(2)

1. Multiply 3 to (1) and 2 to (2)  to eliminate the x-term.

6x + 9y = 3  __(3)

6x + 4y = 2   __(4)

2. Now in second step subtract (4) from (3) to get the value of y.

6x + 9y = 3  

6x + 4y = 2

0x + 5y = 1

⇒ y = 1/5

3.  Multiply 2 to (1) and 3 to (2)  to eliminate the x-term

4x + 6y = 2 __(5)

9x + 6y = 3  __(6)

4. Now in subtract (5) from (6) to get the value of x.

9x + 6y = 3

4x + 6y = 2

5x = 1

⇒ x = 1/5

Therefore, the second step in the given system of equation using elimination method is add or subtract the modified equations.

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A 20 degree angle called an acute angle.

Any angle which is less than 90 degree but greater than 0 degree is called an acute angle. For example - 20, 30, 40 , 50 etc are acute angles.

Polygons with at least one acute angle include triangles, parallelograms, trapezoids, and so on.The acute angle that are present in the triangle they are known as acute angle triangle.

Properties of acute angle triangles:

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The equation that represents the situation in terms of x is 4x = 50 -13.5,

and there will be 9 whole pieces of wire of 4 feet.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator)

Given the total length of wire = 50 feet

length used = 13.5 feet

length of wire left = 50 - 13.5

A. wire is cut into 4 feet pieces

let there are x pieces,

expression for the pieces is

4x = 50 -13.5

B. 4x = 50 - 13.5

4x = 36.5

x = 36.5/4

x = 9.125

the whole number is 9

so there will be 9 pieces in a whole.

Hence the expression is 4x = 50 -  13.5,

and there will be 9 pieces of wire.

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Answer:

8:00

Step-by-step explanation:

This is probably extremely late

distance between their ends greater at 8.00

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The number of small boxes it is carrying is 60 and the number of large boxes it is carrying is 50.

The first step is to form a system of equations using the information in the question:

l + s = 110 equation 1

60l + 30l = 4800 equation 2

Where:

l = number of large boxes

s = number of small boxes

The elimination method would be used to solve these equations.

Multiply equation 1 by 60

60l + 60s = 6,600 equation 3

Subtract equation 2 from equation 3:

30s = 1800

Divide both sides of the equation by 30

s = 1800 / 30

s = 60

Substitute for s in equation 1

l + 60 = 110

l = 110 - 60

l = 50

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The function y whose graph is a horizontal shrink of f(x) = 5x + 8 by a factor of 1/5 is given as follows:

y = 25x + 8.

The function for this problem is defined as follows:

f(x) = 5x + 8.

For the horizontal shrink by a factor of a, the function is defined as follows:

f(x/a).

The parameter a for this problem is given as follows:

a = 1/5.

Hence the shrunk function is defined as follows:

y = f(x/(1/5)) = f(5x) = 5(5x) + 8 = 25x + 8.

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Part A: percent of 70 is 10.

x% of 70 = 10

70x / 100 = 10

x = 1000 / 70

x = 14.28 %.

Part B: percent of 2.8 is 20.

x% of 2.8 = 20

2.8x/ 100 = 20

x = 2000/ 2.8

x = 714.28%

Part C: percent of 90 is 18.

x% of 90 = 18

90x/100 = 18

x = 1800 / 90

x = 2 %

Part D: percent of 10 is 55.

x% of 10 = 55

10x / 100 = 55

x = 5500/ 10

x = 550%.

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A 45-45-90 triangle is an isosceles right triangle, meaning that it has two congruent sides and one right angle. To find the area and perimeter of a 45-45-90 triangle, use the following formulas:

Area:

(1/2) * (side length)^2

Perimeter:

2 * (side length) + (side length) * √2

Note that the perimeter of a 45-45-90 triangle is equal to twice the length of one of its sides plus the length of the hypotenuse.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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A 3x4 matrix is ​​a matrix with 3 rows and 4 columns is a rectangular matrix. The number of solutions in a matrix depends on the context in which it is used.

When the matrix is ​​used to represent a system of linear equations, the number of solutions to the system depends on the rank of the matrix, which is the number of linearly independent rows or columns.

A 3x4 matrix has no solutions because it is not a square matrix and does not have a well-defined inverse. A square matrix has the same number of rows and columns and can be inverted if and only if its determinant is nonzero. A non-square matrix, on the other hand, has no inverse and cannot be inverted.

It should be noted that in the case of the rectangular matrix, the solution depends on the context of the problem and by using other techniques, such as the linear least squares method.

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The quadratic formula, factoring, using the square roots, and completing the square are the four methods for solving a quadratic equation.

The quadratic formula x = [-b(b2 - 4ac)] / (2a) provides the solutions of the quadratic equation ax2 + bx + c = 0. Therefore, to use the quadratic formula to solve a quadratic equation, simply transform the equation into its standard form, ax2 + bx + c = 0, and then apply the quadratic formula.

A quadratic equation is a second-order equation written as ax2 + bx + c = 0, where a is a real number and b and c are real number coefficients.

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Her gross pay is $850.

Commission, also known as sales commission, is a payment given to employees based on the sales they make. Create invoices for free with SumUp Invoices. Commission is often calculated as a percentage of the value of a sale.

Gross salary is the amount received by an employee without any tax deductions. Net salary is the amount that an individual receives after all deductions have been taken out.

Salary of Carly = $720

Commission of Carly = 4%

Amount of products sold by Carly = $3250

Commission of Carly on the goods sold = 4% of $3250 = $130

Hence gross pay of Carly = $720 + $130 = $850

Carly hence gets $850 at the end of the week.

Her gross pay is her salary plus her commission.

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Answer: f(2) = g(2)

Step-by-step explanation:

Well, this is kind of a comparison so you can do this by putting "2" as x value for both functions.

If you do that for both functions:

[tex]f(x) = 4x^{5}\\f(2) = 128 = (2^{7}) \\----------\\g(x) = 8.4^{x} = 2^{2x + 3}\\g(2) = 128[/tex]

So, this shows that f(2) = g(2).

We can demonstrate the solution set in a number of different ways. Number line, interval notation, and set notation are all options for accomplishing this.

Depending on the question, these methods may or may not be used.

There are two ways to write the interval notation solution set.

The closed interval is the first. The solution is enclosed by square brackets and includes the endpoints in a closed interval.

The form [a, b] is used to indicate this. The set notation, on the other hand, is x a x b. This indicates that the solution set runs from a to b, with the second interval being open. The endpoints are not included in the solution when an open interval is enclosed by round brackets ().

The format used for this is (a, b). The set notation, on the other hand, is x a x b. The solution set is therefore situated between a and b.

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Your monthly payment for this house will be $1689.5 if your mortgage payment is $1345, your annual insurance premium is $678, and your real estate taxes are $3456.

Describe the mortgage payments in brief?

Principal and interest payments make up your monthly mortgage payments. You must purchase private mortgage insurance if your down payment is less than 20%, which raises your monthly payment. Real estate or property taxes are also included in some payments. Early on in the mortgage, the borrower pays more interest, whereas the principle balance is favored in the latter stages. A greater down payment will directly increase your home's equity.

To find the total monthly payment for the home, we need to divide the annual costs by 12.

Total monthly payment = Mortgage payment + (Annual insurance premium / 12) + (Annual real estate taxes / 12)

= $1345 + ($678 / 12) + ($3456 / 12)

= $1345 + $56.5 + $288

= $1689.5

So the total monthly payment for the home is $1689.5

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Your monthly payment for this house will be $1689.5 if your mortgage payment is $1345, your annual insurance premium is $678, and your real estate taxes are $3456.

Principal and interest payments make up your monthly mortgage payments. You must purchase private mortgage insurance if your down payment is less than 20%, which raises your monthly payment. Real estate or property taxes are also included in some payments. Early on in the mortgage, the borrower pays more interest, whereas the principle balance is favored in the latter stages. A greater down payment will directly increase your home's equity.

To find the total monthly payment for the home, we need to divide the annual costs by 12.

Total monthly payment = Mortgage payment + (Annual insurance premium / 12) + (Annual real estate taxes / 12)

= $1345 + ($678 / 12) + ($3456 / 12)

= $1345 + $56.5 + $288

= $1689.5

So the total monthly payment for the home is $1689.5

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Due to its peculiar ratio of 1:2:3  , the  30-60-90 triangle is referred to as a special right triangle. Any triangle with a ° angle is considered to be a right triangle in this context.

A unique type of right triangle known as  30-60-90 a  triangle always has angles of

30-60 and -90 ,

The length of the hypotenuse is twice the length of the shortest side and the length of the other side is √ times the length of the shortest side in a  30-60-90  Triangle.

The above theorem can be written mathematically as the 30-60-90  Triangle Formula as

√  which is the ratio of the three sides of the  30-60-90 Triangle.

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Radical 3, also known as the cube root of 3, is a number that when multiplied by itself three times equals 3. It is denoted as ∛3. To find the value of radical 3, one way is to use a calculator with a cube root function.

Another way to find the value of radical 3 is to use a process called prime factorization. It involves breaking the number down into its prime factors and then taking the cube root of the result. In the case of ∛3, we have:

∛3 = ∛(3)

Since 3 is a prime number, we don't need to factor it further, and thus the cube root of 3 is just 3^(1/3) = 3^(1/3) = ∛3.

It's important to note that cube roots can be negative or positive and in this case, ∛3 is positive.

∛3 is an irrational number, which means that it cannot be expressed as a ratio of two integers, and its decimal representation is non-repeating and non-terminating. But it can be approximated to some decimal values.

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Answer:

Step-by-step explanation:

(a) 1.653 x 10^12 / 87 * 10^6

= (1.653 / 87) x (10^12 / 10^6)

= 0.019 x 10^6

= 1.9 x 10^4

or 19,000 days.

(b) 6 billion / 87 million

= 6,000,000,000 / 87,000,000

= 6000/87

= 69 days.

Answer:

If you're looking for the equivalent of m then it is -390

Step-by-step explanation:

-30 = m divided by 13 is the same as -30 times 13 = m

Finally m is equal to -390

Answer:

m = -390

Step-by-step explanation:

Given statement,

→ -30 = m divided by 13.

Forming the equation,

→ -30 = m/13

Now the value of m will be,

→ -30 = m/13

→ m/13 = -30

→ m = -30 × 13

→ [ m = -390 ]

Hence, value of m is -390.

Jackson's company $1.2 more than Micaela's.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Micaela charges a $3.50 pickup fee and $1.30 per mile.

And, The table represents what Jackson's company charges.

Now, Micaela charges a $3.50 pickup fee and $1.30 per mile.

Hence, The equation that represents Mathew's charges is given as,

⇒ y = 1.30x + 3.50  .. (i)

And, From table,

The equation that represents Jackson's charges is given as:

Take two points (x, y) = (10, 30.50) and (30, 88.50)

Hence, The equation is,

⇒ y - 88.50 = (88.50 - 30.50)/(30 - 10)  (x - 10)

⇒ y - 88.50 = 50/20 (x - 10)

⇒ y - 88.50 = 2.5 (x - 10)

⇒ y - 88.50 = 2.5x - 25

⇒ y = 2.5x + 88.50 - 25

⇒ y = 2.5x + 63.50  .. (ii)

We know that;

A linear equation is represented as:

⇒ y = mx + b

Where: m represents the slope/rate.

Hence, Jackson's company $1.2 more than Micaela's.

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Answer:

13.5 blocks

12 blocks

Step-by-step explanation:

Each division on the number line represents half a block.

From inspection of the number line:

Therefore, the distance between John's house and Liam's house is:

From inspection of the number line:

Therefore, the distance between Katie's house and Trina's house is:

Answer:

4 hours

Step-by-step explanation:

We know

Mr. Bagnulo charges $60 per hour for the labor, and you must pay $100 for the part. Let C represent the cost and x represent the number of hours; we have the equation

C = 60x + 100

Now put 340 in for C and solve

340 = 60x + 100

240 = 60x

x = 4 hours

So, Mr. Bagnuoto take 4 hours to fix your car,

Step-by-step explanation:

22 pounds for $11.

we could now calculate how many pounds we can buy for $1.

that would be 22/11 = 2 pounds.

or we can calculate as requested how much (how many $) he needed to pay for 1 pound.

that would be 11/22 = 1/2 = $0.50

and as you can see, both answers work prefectly together. they are just different views of the same basic problem.

we have to pay $0.50 per pound, and so we can buy 2 pounds with $1.

  The mathematical function known as a logarithm expresses the degree to which a base number must be raised in order to obtain a specific value. The symbol logb(x), where b is the logarithm's base and x is the value being evaluated, stands for the logarithm of a number. The natural logarithm, which has a base of e, is the most widely used logarithm (approximately 2.71828). The inverse function of exponentiation is the logarithm, according to this definition. The exponent to which we must raise b in order to obtain a number x is its logarithm to base b.

       It reads log2(3x + 8) = 5.

logb(a^n) = n * logb(a) where b is the base of the logarithm, is a property of logarithms that can be used to rewrite expressions. Since the base in this instance is 2, we obtain log2(3x + 8) = 5.

 corresponding to 2^5 = 3x + 8

Now that x is on one side of the equation, we can solve for it.

32 = 3x + 8

After deducting 8 from both sides, we arrive at 24 = 3x, which we then multiply both sides by to get 8

 Thus, x = 8 is the corresponding equation.

and the solution is 8.

     Therefore, the x=8 is the solution of this problem .

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Answer:

1. a 2. 8

Step-by-step explanation: