Three friends are comparing their weekly paychecks. Donald discovers that he earned one-third of Michael's paycheque, and $80 less than Jacob's paycheque. Together, the three friends earned $2920 in one week. How much did each friend earn?

Answer:

1. (0,2)

2. (-2,-1)

Step-by-step explanation:

1.

y = 2x + 2

y = x + 2

2x + 2 = x + 2

2x = x

x = 0

Now we put 0 back in for x and solve for y

y = 2(0) + 2

y = 2

So, our answer for Q1 is (0,2)

2.

y = 3x + 5

y = -x - 3

3x + 5 = -x - 3

4x + 5 = -3

4x = -8

x = -2

Now we put -2 back in for x and solve for y

y = 3(-2) + 5

y = -6 + 5

y = -1

So, our answer for Q2 is (-2,-1)

A. The equation of a tangent line to the circle through the point (- 6 , 8) is y = 0.75x + 12.50

B. The point of tangency of L with the circle is (9.81 , - 1.96).

The full question is in the attachment. The equation of a tangent line to the circle with radius r centered at the origin through the point (p , q)

px + qy = r²

- 6x + 8y = 10²

8y = 6x + 100

y = 6/8x + 100/8

y = 3/4x + 25/2

y = 0.75x + 12.50

The equation line y = mx + c has the slope or the gradient m. If two lines are parallel, the two lines have the same slope.

y = 5x + 7

The tangent line L to the circle with the gradient m and radius r

[tex]y \:=\: mx \pm r \: \sqrt{1 \:+\: m^2}[/tex]

[tex]y \:=\: 5x \pm 10 \: \sqrt{1 \:+\: 5^2}[/tex]

[tex]y \:=\: 5x \pm 10 \: \sqrt{1 \:+\: 25}[/tex]

[tex]y \:=\: 5x \pm 10 \: \sqrt{26}[/tex]

Because L has a negative y-intercept, it means when x = 0, y is negative. So the equation L

[tex]y \:=\: 5x \:+\: 10 \: \sqrt{26}[/tex]

The point x of tangency of L with the circle

x² + y² = r²

x² + (5x - 10 √26)² = 10²

x² + 25x² - 100√26 x + 2,600 = 100

26x² - 100√26 x + 2,500 = 0

[tex]x_{1.2} \:=\: \frac{-b \pm \sqrt{b^2 \:-\: 4ac}}{2a}[/tex]

[tex]x_{1.2} \:=\: \frac{100 \sqrt{26} \pm \sqrt{(- 100 \sqrt{26})^2 \:-\: (4 \times 26 \times 2,500)}}{2 \times 26}[/tex]

[tex]x_{1.2} \:=\: \frac{100 \sqrt{26} \pm \sqrt{260,000 \:-\: 260,000}}{52}[/tex]

[tex]x \:=\: \frac{100 \sqrt{26}}{52}[/tex]

[tex]x \:=\: \frac{50 \sqrt{26}}{26}[/tex]

x = 50/26 × √26

x = 9.81

The point y of tangency of L with the circle

[tex]y \:=\: 5x \:+\: 10 \: \sqrt{26}[/tex]

[tex]y \:=\: 5 \times \frac{50 \sqrt{26}}{26} \:+\: 10 \: \sqrt{26}[/tex]

[tex]y \:=\: \frac{250 \sqrt{26}}{26} \:+\:  \frac{260 \sqrt{26}}{26}[/tex]

[tex]y \:=\: \frac{- 10 \sqrt{26}}{26}}[/tex]

y = - 10/26 × √26

y = - 1.96

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Steps to find the equation of a line with 2 points mentioned below:

In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The ratio of y to x is known as the slope. A slope triangle should be drawn connecting any two spots you find along the line.

To determine a line's equation from two points following steps are there:

1. Determine the slope and used the slope formula.

Slope(m) = (y₂ - y₁) / (x₂ - x₁)

2. To determine the y-intercept, use the slope and one of the points(b).

The x and y in your equation y = mx + b may be replaced by one of your locations, and the m can be replaced by the slope you just computed. The only variable remaining is b in such case. To solve for b, use the same methods you would to solve for a variable.

3. Once you have the values for m and b, you can use them to solve for the line's equation in the slope-intercept form (y = mx + b).

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Algebra Formulas for Class 8

Some essential 8th-class formulas related to Algebra are:

Algebraic Identities For Class 8

(a + b)2 = a2 + 2ab + b2

(a − b)2 = a2 − 2ab + b2

(a + b) (a – b) = a2 – b2

(x + a) (x + b) = x2 + (a + b)x + ab

(x + a) (x – b) = x2 + (a – b)x – ab

(x – a) (x + b) = x2 + (b – a)x – ab

(x – a) (x – b) = x2 – (a + b)x + ab

(a + b)3 = a3 + b3 + 3ab (a + b)

(a – b)3 = a3 – b3 – 3ab (a – b)

I tried my best!

12

12 times ten is 120

Answer: 12 groups of ten makes it 120

Step-by-step explanation:

here one group consists of ten.

and to make 120 we will need 12 groups of ten.

To  write coordinates in quadratic forms,

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According to given data, we can prove that Statement 1 is increasing function, Statement 2 is Decreasing Function, and Statement 3 is Constant Function.

1. The linear function that describes the relationship between the input value (number of days) and the output value (total number of texts sent) is y = 60x, where y is the total number of texts sent and x is the number of days. The graph of this function is increasing because as the number of days increases, the total number of texts sent also increases at a constant rate of 60 texts per day.

2. The linear function that describes the relationship between the input value (number of days) and the output value (total number of texts remaining for the month) is y = 500 - 60x, where y is the total number of texts remaining for the month and x is the number of days. The graph of this function is decreasing because as the number of days increases, the total number of texts remaining for the month decreases at a constant rate of 60 texts per day.

3. The linear function that describes the relationship between the input value (number of days) and the output value (total cost of texting each month) is y = 50, where y is the total cost of texting each month and x is the number of days. The graph of this function is constant because the cost of texting is the same regardless of the number of days.

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Judy needs 1 5/8 yards area more of flannel to stitch the kirt.

To find how much more fabric Judy needs, we need to subtract the amount she already has from the amount she needs.

Judy needs 2/3 yard of flannel

Judy has 3/8 yard of flannel

To subtract these fractions, we first need to convert them to the same denominator.

2/3 yard = 4/6 yard

3/8 yard = 6/8 yard

4/6 yard - 6/8 yard = (24 - 24)/48 = 0/48

To simplify, 0/48 = 0

Therefore, Judy needs 0 yards more of flannel.

However, Judy needs 2/3 yard of flannel to stitch the kirt. Since she has 3/8 yard, we can subtract the two to find how much more fabric she needs.

2/3 yard - 3/8 yard = (16 - 12)/24 = 4/24

To simplify, 4/24 = 1/6

Therefore, Judy needs 1 1/6 yards area more of flannel to stitch the kirt.

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Answer:

Step-by-step explanation:

Seven more than the product of a number and 3 is 8.

7 + 3x = 8

3x = 8 - 7

3x = 1

x = 1/3

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

7 + 3 x 1/3 = 8                           (remember PEMDAS)

7 + 1 = 8

8 = 8

After spending $17 the amount of money left with Lisa is $165.

What is equation?

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

Lisa worked 26 hours last month.

For each hour she earns $7.

Total earnings of Lisa in last month is equated as -

Earning = 26 × 7

Earning = $182

She spent $17 dollars on earring.

The amount of money left with her is equated as -

Total Earning - Money spent

Money Left = 182 -17

Money Left = $165

Therefore, the money left with Lisa is $165.

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Answer:

8^4

Step-by-step explanation:

The equation have infinite solutions.

What does a math equation mean?

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

                    Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

We can proceed to solve this equation by collecting like terms and then dividing through to know the coefficient of x.

 12x + 1 = 3(4x + 1) - 2

   12x + 1 =  12x + 3 - 2

     12x + 1 =   12x + 1

The equation have infinite solutions.

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How many solutions exist for the given equation?

12x + 1 = 3(4x + 1) – 2

Answer:

your answer is D

Step-by-step explanation:

I literally just finished the quiz on edge

As we know that Trinomial means a polynomial with three terms.

Therefore, option (c) x²y -xy² +y² is correct.

Given polynomials are:

(а) -7z

(b) z² – 4y²

(c) x²y – xy² + y²

(d) 12a – 9ab + 5b – 3.

To Find :  Which one is Trinomial.

Monomial:

A monomial is defined as an expression with one non-zero term. It consists of various parts such as variables, coefficients and orders. A unary variable is the character it contains. A coefficient is a number that is multiplied by a monomial variable. The monomial degree is the sum of the exponents of all variables.

Binomial:

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-no question and each has a Boolean result of Success (probability p) or failure. A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a series of results is called a Bernoulli process. For one trial, d. H. n = 1, binomial distribution is Bernoulli distribution. The binomial distribution is the basis for the common binomial test of statistical significance.

Trinomial:

A ternary expression is an algebraic expression with three terms. An algebraic expression consists of variables and constants in one or more terms. These expressions use symbols or operations such as +, –, ×, and ÷ as separators. Trinomials fall into this algebraic expression, along with monomials, binomials, and polynomials.

In Short :

Monomial - A polynomial with single Term

Binomial - A polynomial with 2 terms

Trinomial  - A polynomial with  3  terms

Based on the information:

(а) -7z    only one term hence Monomial  

(b) z² – 4y²     Two terms Hence Binomial

(c) x²y – xy² + y²    Three terms hence Trinomial  

(d) 12a – 9ab + 5b – 3.   Four terms hence quadrinomial.

So correct option is c)  x²y – xy² + y²    

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If we expand the bracket, -20 -2 = -22.

So the equivalent expression would be -22.

The expression 5(-4) means to take the number -4 and multiply it by 5.

Since multiplication is distributive, this is the same as -4 * 5 which results in -20.

And -20 -2 is -22.

So the equivalent expression is -22.

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Answer: The y-intercept of the line perpendicular to the line y = -3/4x+5 that includes the point (-3,-3) is -21/4. Thus option D is correct.

Step-by-step explanation: The line is a general straight line y=mx+c where c is the y-intercept and m is the gradient or the slope.

In this equation, m= -3/4. Putting the value of m, y and x in the equation gives

-3=3/4(-3) + c

-3= 9/4 +c

solving for c we get,

c= -3-9/4

c = - 21/4

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Answer:

The y-intercept of an equation is the point where the line crosses the y-axis, i.e when x = 0.

In this case, the cost equation is C = 2x + 180, where C is the total cost and x is the number of board games produced.

So when x = 0, C = 2(0) + 180 = 180

Therefore, the y-intercept of the cost equation is (0,180)

So the y-intercept of the cost equation is 180.

Answer:

90

Step-by-step explanation:

The process for converting 2D data to 3D data involves a few steps. First, a 3D model needs to be created, which is typically done using a 3D modeling software such as Blender or 3DS Max.

Data in math is information that can be used to draw conclusions or make decisions. It is typically collected, analyzed, and presented in the form of numbers, graphs, or tables. Data can be used to compare and contrast different scenarios, identify trends and patterns, or make predictions about the future. Data can also be used to help researchers develop hypotheses and develop models to explain phenomena.

Once the model is created, the data needs to be imported into the software in a format that can be used by the software, such as an .obj or .3ds file. The data can then be manipulated within the software to create the 3D model. Finally, the 3D model can be exported in a variety of file formats, such as .stl, .fbx, or .dae, that can be used for 3D printing, virtual reality, and other applications.

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Answer:

the answer is C should be

Step-by-step explanation:

the answer is C should be, I'm in middle school btw

Answer:

A round-shaped figure with no corners or edges.

Step-by-step explanation:

Answer: A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.

Step-by-step explanation:

Substitution property is a property in algebra that helps in substituting the value of a quantity/variable into an algebraic expression to solve a given mathematical problem.

The substitution property is a notion in algebra that is used for substituting the value of a given variable or a quantity into an expression to find the value of the unknown.

In other words, we can express that the substitution property is utilised to replace the value of a quantity in an equation or an expression to solve a mathematical problem.

For example, Using the substitution property of equality, find the value of the algebraic expression g(x) = sin x + cos x if x = 45°.

We will replace x with 45° in the expression. So we have

g(45°) = sin 45° + cos 45°

= 1/√2 + 1/√2

= 2/√2

= √2

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It is possible to construct a triangle whose sides are 17 cm 15 cm and 8 cm because the sum of two sides are greater than third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 17 cm 15 cm and 8 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 17 and 15.

17 + 15 > 8

32 > 8

Now we add 17 and 8

17 + 8 > 15

25 > 15

Now we add 15 and 8

15 + 8 > 17

23 > 17

It is possible to construct a triangle whose sides are 17 cm 15 cm and 8 cm because the sum of two sides are greater than third sides.

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Change to base 5 can be done by dividing the decimal number by 5 and then taking the remainder of the division in reverse order.

The number base is the number that forms the basis for the formation of other numbers in a number system.

The number base that we use a lot every day is the decimal system, which consists of 10 numbers, from 0 to 9. This decimal system is usually called the base 10 number system. Apart from base 10, there are also other base systems, for example, base 2 (biner system), 8 (octal system), and 16 (hexadecimal system) which are usually used in computer / digital systems.

Change of base 10 numbers to other base numbers is done by:

For example, we want to change 214₁₀ to a base 5 number:

214 : 5 = 42 remainder 4

42 : 5 = 8 remainder 2

8 : 5 = 1 remainder 3

1 : 5 = 0 remainder 1

Thus 214₁₀ = 1324₅

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The final balance on the card is $15350.92, rounded to the nearest penny.

The correct option is D.

Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to a period of time.

Formula of continuous compound interest rate;

P(t) = P₀[tex]e^{rt}[/tex], where P₀ is the principal amount, r is the interest rate and t is the time period.

Given:

A customer uses a store credit card to purchase a boat for $10,500.

The store credit card offers an annual interest rate, compounded continuously, of 18.99% with no payments due for the first two years.

That means,

P₀ = $10500, r = 18.99 and t = 2.

So,

P(t) = P₀[tex]e^{rt}[/tex]

Substituting the values,

P(t) = (10500)[tex]e^{(0.1899)(2)}[/tex]

P(t) = (10500)(1.46199)

P(t) = 15350.917

P(t) = $15350.92

Therefore, the final amount is $15350.92.

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Answer:

$4.45

Step-by-step explanation:

First, we try to find the slope of the table. We can do this by doing the following-  [tex]\frac{Change \ in \ y }{Change \ in \ x}[/tex]

When we do this, we find that the slope (or the change in y / change in x) is equal to 5.27

Now we subtract this from the slope of the price of steak at Store B which is 9.72

[tex]9.72-5.27 = 4.45[/tex]

You get 4.45 which is $4.45 or 4 dollars and 45 cents.

Answer: Missing angle= 42°

Step-by-step explanation:

Since the whole angle is a right-angled triangle the angle will obviously be 90 degrees therefore subtract the given value in order to find the missing angle.

Missing angle= 90°- 48°

                      = 42°

The four transformations of a function are translation, reflection, stretching/shrinking, and rotation.

Function is a group of related statements that perform a specific task. It is a block of organized, reusable code which can be used to perform a single, related action. Functions help make code more reusable and efficient. It also reduces the complexity of a program by breaking it down into smaller and simpler parts.

Translation involves shifting the graph of a function along a given axis; reflection involves flipping the graph of a function about a given axis; stretching/shrinking involves changing the scale of a graph along a given axis; and rotation involves rotating the graph of a function about a given point. All of these transformations can be used to modify the graph of a function, allowing for a variety of different outputs.

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By solving the linear equation in x Abebi receives $37.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. Here, A is a coefficient, B is a constant, and x is a variable.

On identifying the information given in the problem we have:

Abebi, Bella, and Chuku share $112. Abebi receives $x. Bella receives $12 less than Abebi. Chuku receives twice as much as Bella.

On setting up an equation using the information given:

We know that the total amount shared is $112 and we want to find out how much Abebi receives, represented by x.

We know that:

Bella receives $12 less than Abebi =(x - 12)

Chuku receives twice as much as Bella =(2 * (x - 12))

So we can set up the equation as:

x + (x - 12) + (2 * (x - 12)) = 112

On simplifying the equation:

x + x - 12 + 2x - 24 = 112

Combining like terms:

4x - 36 = 112

On solving for x we get:

Add 36 to both sides:

4x = 148

Divide both sides by 4:

x = 37

On interpreting the solution we get:

By solving the linear equation in x Abebi receives $37.

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Answer:2095.23

Step-by-step explanation:

Answer:

Let the chocolate souffles be x and lemon meringue pies be y.

For yesterday, it will be 6x+6y=30

For the day before, 4x+8y=24

By solving the two equations, the answers will be obtained.

4 eggs is required for chocolate souffles and an egg for lemon pie.