Ethan sold exactly eight TVs this quarter. Frank sold exactly twice as many TVs as Gina. Gabriel sold more TVs than Ethan. Gina sold exactly three more TVs than Gabriel and Ethan combined. Which statement must be true? Gabriel and Gina combined sold more TVs than Frank. Frank sold more than 40 TVs. Gina sold more than twice as many TVs as Ethan. Gina sold exactly twice as many TVs as Gabriel. Ethan, Gabriel, Gina, and Frank combined sold more than 80 TVs.​

Answer:

x = √52

Step-by-step explanation:

Triangle PLM and JLK are connected together at L, which means that they share the same vertex L and therefore, the angle at L is the same for both triangles.

Since PLM and JLK are both triangles, we know that the sum of the angles in each triangle is always 180 degrees.

Let's call the angle at L as a. So we have:

a + (180-a) = 180

We know that PL = 6 and PM = 12, so we can use the Law of Cosines to find the value of the angle a:

c^2 = a^2 + b^2 - 2ab*cos(C)

where c is the hypotenuse, a and b are the other two sides and C is the angle opposite to c.

c = PL = 6

a = PM = 12

b = JL = 4

c^2 = 12^2 + 4^2 - 2124cos(a)

36 = 144 - 48cos(a)

cos(a) = (144 - 36)/48 = (108/48) = 9/4

a = arccos(9/4)

Now we know the measure of angle a and we can use it in the equation of the sum of angles in a triangle.

a + (180-a) = 180

We also know that JL = 4 and JK = x and we can use the Law of Cosines again to find the value of x.

x^2 = 4^2 + 6^2 - 246cos(a)

x^2 = 16 + 36 - 24(9/4)

x^2 = 52

x = √52

Answer:

Step-by-step explanation:

Using the Law of Cosines, we can calculate the three angles of the triangle.

A = cos⁻¹((17² + 30² - 20²) / (2 x 17 x 30))

A = cos⁻¹(7 / 510)

A = cos⁻¹(0.0137254901960784)

A = 84.2°

P = cos⁻¹((20² + 30² - 17²) / (2 x 20 x 30))

P = cos⁻¹(11 / 600)

P = cos⁻¹(0.0183333333333333)

P = 70.0°

K = 180° - (84.2° + 70.0°)

K = 25.8°

Therefore, the angles of △HPK are:

Angle H = 84.2°

Angle P = 70.0°

Angle K = 25.8°

Round your final answer to the nearest tenth:

Angle H = 84.2°

Angle P = 70.0°

Angle K = 25.8°

Answer:

3/10

This is to reach the character limit

Answer:

3/10

Step-by-step explanation:

0.3 =

3/10  ==> since there is a non-zero number before the decimal, the

number is being divided by 10. If there was an extra 0, add a 0 to 10 and divide the number by 100. (0.3 = 3/10. 0.03 = 3/100)

Add another 0 to make 0.003, which is 3/1000 (add an extra 0 to 100 to make 1000, 10->100->1000).

Both lines are parallel to each other, so it has no any intersection point.

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;

The system of equation is,

⇒ 8x +10y =14   .. (i)

⇒ 4x + 5y = 4   .. (ii)

Now, By multiply by 2 in equation (ii), we get;

⇒ 2 (4x + 5y) = 4 × 2

⇒ 8x + 10y = 8  .. (iii)

Hence, By equation (i) and (iii), we get;

The both equations are parallel to each other and it has no solution.

Hence, It can never intersect each other at any point.

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Answer:

Below  

Step-by-step explanation:

Vertex at 8,1      and includes point 9,-1    <=====given

Vertex form :

y = a (x-8)^2 + 1

Plug in the point (9,-1)  to find 'a'

  -1 = a ( 9-8) + 1

    a = -2

                   Parabola equation is then  y = -2(x-8)^2 + 1

Answer:

14

Step-by-step explanation:

Basically, x is substituted by 10.

So if you plug that into the function, you would get

[tex]f(10)=2(10)-6[/tex]

Simplify it and you get

[tex]f(10)=14[/tex]

Answer:

B.The operating space of the blue car is closed because the driver's line of sight is restricted.

Step-by-step explanation:

it is not the best lane because lanes depend on which direction you are going so neither a nor c were correct and the driver's straight-ahead vision is not at this angle for there is a car roof and the driver can't see it like this as if you were above the cars this perspective is from above and also not a central vision

Answer:

1. Distribute the 9

2. Add 9 to both sides

3. Divide both sides by 27

4. Write the fraction in lowest terms

Step-by-step explanation:

Generally for these problems we would first distribute the 9 and that is indeed going to be the first step in this equation, although one thing to note is it's really not necessary, since you could divide both sides by 9, and 0/9 is still 0, so it kind of simplifies the problem.

From that first step we would get:

[tex]27x-9=0[/tex]

From here we want to isolate the "x" variable, which we want to achieve by removing any constants on it's side, in this case -9, and then remove any coefficients in this case 27. We usually first start by removing any constants on the variables side which we can achieve by subtracting or adding a value, depending on the sign. The important thing to note is we want to do the inverse operation, essentially what cancels it out. So to cancel out minus 9 we simply add 9 to both sides to cancel out the minus 9 and to maintain equality.

[tex]27x=9[/tex]

Now from here we want to remove coefficients which we do by dividing, since the coefficient is simply multiplying, so the inverse is division. In this case we want to divide by 27, to cancel out the multiplication of 27.

[tex]x=\frac{9}{27}[/tex]

From here we can divide both the numerator and denominator by 9 to simplify the fraction.

[tex]x=\frac{1}{3}[/tex]

The correct statement regarding the addition of the fractions is given as follows:

A. (3x² + 14x + 196)/[(x + 14)(x - 14)], x ≠ -14, x ≠ 14.

The addition of fractions for this problem is given as follows:

[tex]\frac{2x}{x + 14} + \frac{x + 14}{x - 14}[/tex]

They have different denominators, hence the least common factor of the denominator is used.

The terms at the denominator have no common factor, hence the least common factor is the multiplication of them.

Dividing the least common factor by the denominator and multiplying at the numerator, the addition of the fractions is given as follows:

[2x(x - 14) + (x + 14)(x + 14)]/[(x + 14)(x - 14)]

Expanding the numerator, we have that:

2x² - 14x + x² + 28x + 196.

Combining the like terms, the added fraction is given as follows:

(3x² + 14x + 196)/[(x + 14)(x - 14)]

The denominator cannot be zero, hence the restrictions are given as follows:

x ≠ -14, x ≠ 14.

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Answer:

x = arccos(3/4) + 2πn where n = 0,1,2,3,4, ....

Step-by-step explanation:

We can solve the equation 4cos(x) + 3 = 6 by isolating the cos(x) term on one side of the equation.

4cos(x) + 3 - 3 = 6 - 3

4cos(x) = 3

cos(x) = 3/4

Now we can find the solutions of the equation by finding the values of x that make cos(x) equal to 3/4. Since -π < x < π, we can find the solutions in the range of -π < x < π.

x = cos^-1(3/4) + 2πn, where n is an integer

x = cos^-1(3/4) + 2πn, where n = 0, 1, 2, ...

The solutions are x= cos^-1(3/4) and x = cos^-1(3/4) + 2π, x = cos^-1(3/4) + 4π

Keep in mind that cos^-1(3/4) is the inverse cosine function or arccos(3/4) so the final solution is x = arccos(3/4) + 2πn where n = 0,1,2,3,4, ....

Answer:

Step-by-step explanation:

A line of reflection can be represented by a line of dashes that is used to reflect a geometric shape or figure over it.

A line of reflection can be represented by a line of dashes, which is the mirror line. When a shape is reflected over it, the shape is flipped over the line in a 180-degree angle, creating a mirror image of the original shape.

For example:

(Picture attached)

In this example, the horizontal line represented by the dashes is the line of reflection. If a shape is reflected over this line, it would create a mirror image of the original shape.

Please note that this representation is only for visualization purposes and it's not a mathematical representation.

Answer: -5

Step-by-step explanation:

y2 - y1/x2 - x1

3 + 2/3 - 4

5/-1

-5

The value from the subtraction of the polynomials is -5x³ - 6xy -17y²

The degree is 3

An algebraic expression is defined as an expression that consists of terms, coefficients, variables, constants and factors.

They are also made up of mathematical expressions, such as;

Also, polynomials are algebraic expressions that are made up of coefficients and indeterminants.

These polynomials have degree of the variable, x, greater than one.

From the information given, we have that;

x³ + 4xy -8y² - (6x³ + 10xy - 9y²)

expand the bracket

x³ + 4xy - 8y² - 6x³ - 10xy - 9y²

Now, collect like terms

x³ - 6x³ + 4xy - 10xy - 8y² - 9y²

Add or subtract like terms

-5x³ - 6xy -17y²

Hence, the value is 3

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Answer: To the nearest dollar,  you should invest $84,639

Step-by-step explanation:

First, we need to calculate the number of compounding periods in a year.

For the first 18 months, the compounding period is monthly, so there are 18 x 12 = 216 compounding periods

For the next 6 months, the compounding period is quarterly, so there are 6 x 4 = 24 compounding periods

For the last 12 months, the compounding period is semi-annual, so there are 12 x 2 = 24 compounding periods

The total number of compounding periods is 216 + 24 + 24 = 264

Next, we need to calculate the effective annual interest rate for the entire 3-year period.

The effective annual interest rate is (1 + (8%/216))^216 x (1 + (1.5%/24))^24 x (1 + (2%/24))^24 - 1

Now we can calculate the principal amount (P) required to achieve the desired maturity value (F) using the formula:

P = F / (1 + r)^n

where F is the maturity value, r is the effective annual interest rate and n is the number of compounding periods

P = 100,000 / (1 + r)^264

Explanation: To receive $100,000 on the maturity date, the principal amount has to be invested such that it earns the effective annual interest rate for the entire 3-year period. The principal amount was calculated using the formula for future value of an investment, where the maturity value, effective annual interest rate and the number of compounding periods are known.

The algebraic rule for the reflection of FG is solved to be

Transformation is a term used in mathematics to refer to the movements made by objects.

Reflection is one of the movements in transformation that involve creation of mirror image

Transformation rule for reflection over x-axis at origin (0, 0)) is

(x, y) → (x, -y)

Transformation rule for reflection over line y-axis at origin (0, 0)) is

(x, y) → (-x, y)

The reflection of line FG is done across the x axis hence the transformation rule to be used is (x, y) → (x, -y)

This is equal to the last option

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In actuality, modern electronic calculators with advanced features are specialised computers with a specific function.

The two numbers can be rounded to the closest ten to get an estimate for the calculation 348 + 598.

Rounding 348 to the nearest 10, we get 350.

600 is the result when 598 is rounded up to ten.

Consequently, 350 + 600 = 950 is what we estimate the sum of 348 and 598 to be.

The correct calculation is 348 + 598 = 946 when using a calculator.

In comparison to the actual answer of 946, our guess of 950 is 4 higher. This indicates that we slightly overestimated the result in our estimation. Since the figures are rounded to the closest 10, there isn't much of a change, and this is reasonable.

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40cm as a fraction of 2.4m is 1/6

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. In a proper fraction, the numerator is less than the denominator. e.g . 2/7, 4/5, 3/10 e.t.c

An improper fraction had it's numerator higher than it's denominator .Example is 5/2 , 7/3 e.tc.

By expressing 40 cm as a fraction of 2.4m. The first thing we have to do is making both of thesame unit. therefore ;

2.4m = 2.4×100 = 240cm

40 as a fraction of 240 = 40/240

divide through by 40

= 1/6

therefore the fraction of 40 in 240 is 1/6 i.e 240×1/6 = 40

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Answer:

2900000cm

Step-by-step explanation:

1km=10=100000cm

29km=

29×100000/1= 2900000cm

A counterexample to show that the statement is false is -1<x<0 or >1

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

EXPLANATION;

Rearrange unknown terms to the left side of the equation: x^3-x>0

Factor the expression:x(x+1)(x-1)>0

Convert inequality to equation:x(x+1)(x-1)=0

Apply Zero Product Property: x=0 or x+1=0 or x-1=0

Rearrange unknown terms to the left side of the equation:x=-1

Rearrange unknown terms to the left side of the equation:x=1

Combine the results: :x=0 or :x=1  or- :x=1

Order x-intercepts from smallest to greatest: x1=-1or x2=0  or x3=1

EXPLANATION;

Rearrange unknown terms to the left side of the equation:

Factor the expression:

Convert inequality to equation:

Apply Zero Product Property: or  or

Rearrange unknown terms to the left side of the equation:

Rearrange unknown terms to the left side of the equation:

Combine the results: or  or

Order x-intercepts from smallest to greatest: or  or

Plot: As shown in figure

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Answer:

Step-by-step explanation:

Two opposite numbers are 16 units away from each other. What are the numbers?

16 : 2 = 8

-8 and 8, the distance is 16

The equivalent equations are 2 + x = 5,  x + 1 = 4 , Negative 5 + x = negative 2. Option A, B and E

An algebraic expression can be defined as a mathematical expression made up of terms, coefficients, constants, factors and variables.

Algebraic expression are also known to consist arithmetic operations, which includes;

From the information given, we have the equations;

1.  2 + x = 5

collect like terms

x = 3

2. x + 1 = 4

collect like terms

x = 3

3. 9 + x = 6

collect like terms

x = 15

4.  x + (negative 4) = 7

x - 4 = 7

collect like terms

x = 11

5. Negative 5 + x = negative 2

-5 + x = -2

collect like terms

x = 3

Hence, the options are A, B, E

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Answer:

x < -16.714... or x > 2.428...

Step-by-step explanation:

|0.7x + 5| > 6.7

=> 0.7x + 5 = -6.7 or 0.7x + 5 = 6.7

=> 0.7x = -6.7 - 5 or 0.7x = 6.7 - 5

=> x = -11.7/0.7 or x = 1.7/0.7

=> x = -16.714... or x = 2.428...

note: if |u| > a, a > 0 then u < -a or u > a

Answer:

y = -1/2

Step-by-step explanation:

We are given the equation -10 - 8y = 2y - 5.

We want to solve this equation for y.

To do that, we need to isolate y on one side of the equation.

To start, add 10 to both sides.

-10 - 8y = 2y - 5

+10               +10

________________

-8y = 2y + 5

Subtract 2y from both sides.

-10y = 5

Divide both sides by -10.

y = -5/10

-5/10 can be simplified to -1/2.

Hence, y = -1/2.

The expected value of playing a single game is given as follows:

-$0.499.

As the expected value is negative, it is not a wise investment to play the NC pick 3 in the long run.

The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.

You have to pick three digits in correct order. Considering that for each digit there are 10 possible outcomes, the probability of winning is given as follows:

1/10 x (1/10) x (1/10) = 1/1000 = 0.001.

The probability of losing is given as follows:

1 - 1/1000 = 1000/1000 - 1/1000 = 999/1000 = 0.999.

Considering that you get $500 winning, while you lose $1 losing, the distribution is given as follows:

Hence the expected value of the distribution is given as follows:

E(X) = 500 x 0.001 - 1 x 0.999

E(X) = -$0.499.

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Answer:

Step-by-step explanation:

Solving by factoring is a strategy used to solve quadratic equations, which are polynomials of the form ax^2 + bx + c = 0. The goal of this strategy is to factor the quadratic expression on one side of the equation and set each factor equal to zero to find the solutions of the equation.For example, consider the equation x^2 - 6x + 8 = 0. To solve this equation by factoring, we can first find the factors of the constant term (8) which are 1 and 8. And the factors of the leading coefficient (1) and the constant term (8) which are (1,-8) and (1,8). We can then use the distributive property to rewrite the equation as (x - 4)(x - 2) = 0.Once we have factored the quadratic expression, we set each factor equal to zero and solve for x. In this case, x - 4 = 0 and x - 2 = 0. Solving for x, we get x = 4 and x = 2. These are the solutions to the equation.We can check our solutions by plugging them back into the original equation to see if they make the equation true.x = 4 and x = 2 are the solutions of the equation x^2 - 6x + 8 = 0.It's important to note that factoring can also be used to solve equations that are not in the standard form, like x^2 - 6x + 8 = 12 by subtracting 12 from both sides of the equation, and then factor the left side.In summary, factoring is a strategy used to solve quadratic equations by factoring the quadratic expression on one side of the equation, setting each factor equal to zero, and solving for x. The solutions of the equation are the values of x that make the equation true.

Answer:

22.75

Step-by-step explanation:

2a + 4c = 43.5

5a + 3c = 65

10a + 20c = 217.5

subtract

10a +6c = 130

= 14c = 87.5

c = 6.25

2a + 25 = 43.5

2a = 18.5

a = 16.5

16.5 + 6.25 = 22.75

Answer:

One adult ticket costs £9.25, and one child ticket costs £6.25.

Step-by-step explanation:

Let a = price of 1 adult ticket.

Let c = price of 1 child ticket.

"A family of two adults and four children pay £43.50. for entry."

2a + 4c = 43.5

"Another family of five adults and three children pay £65."

5a + 3c = 65

We have a system of simultaneous equation in two unknowns.

2a + 4c = 43.5

5a + 3c = 65

Let's solve the system by the method of elimination. We need to add multiples of the two equations in a way that one variable will be eliminated (add to zero).

Let's eliminate the variable a. Multiply both sides of the first equation by -5  Multiply both sides of the second equation by 2. Then add them.

      -10a - 20c = -217.5

+     10a +   6c = 130

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

                -14c = -87.5

                     c = 6.25

Now substitute 6.25 for c in the first original equation and solve for a.

2a + 4c = 43.5

2a + 4(6.25) = 43.5

2a + 25 = 43.5

2a = 18.5

a = 9.25

Answer: One adult ticket costs £9.25, and one child ticket costs £6.25.

Answer:

Step-by-step explanation:

The company will need to hire approximately 200 freelancers in order to complete the remaining 40,000 hours of work. This is because each freelancer works 200 hours per month, so in order to complete the 40,000 hours of work in the last 4 months, the company will need to hire 200 freelancers.

Answer:2√5

Step-by-step explanation:

5. If OR is perpendicular to PQ and O its the center of the cincunference it means that RP has the same size of QR, then all you have to do its a Pythagorean theorem

H^2=C^2+C^2

OP^2=(2√3)^2+(2√2)^2

(=)OP^2= 12+8

(=)OP^2=20

(=)OP=±√20 ∧ OP>0

(=)OP=2√5

I'm Sorry for the bad english

Answer:

62.5%

Step-by-step explanation:

(mass of solute/mass of solution) x 100 = 62.5%

The minimum and maximum values, over the interval x ≥ 3, for the function f(x) = -|x - 1| + 1 graphed are -36 and 64 respectively.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Here Relative minimum are the minimum values  in the interval

Looking at the graph, we find the lowest point in the interval

Relative minimum : (-3, -36) and (3,-36)  

y value -36

Looking at the graph, we can find the highest point in the interval

Relative maximum : (0,64)  

y value 64

The minimum and maximum values, over the interval x ≥ 3, are -36 and 64 respectively.

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