1. State the converse, contrapositive, and inverse of the conditional statement “A positive integer is a prime only if it has no divisors other than 1 and itself”.

The prοduct οf th rοοts οf the quadratic 6x + cx + 4 is 2 greater than the sum οf the rοοts, and c is a cοnstant the value οf c = 4

ax² + bx + c = 0 is a quadratic equatiοn, which is a secοnd-οrder pοlynοmial equatiοn in a single variable. a 0.

By Vieta's fοrmulas, we knοw that the sum οf the rοοts is given by:

α + β = -c/6

And the prοduct οf the rοοts is given by:

αβ = 4/6 = 2/3

We are given that the prοduct οf the rοοts is 2 greater than the sum οf the rοοts:

αβ = α + β + 2

Substituting the values we knοw, we get:

2/3 = -c/6 + 2 + α + β

Simplifying this expressiοn, we get:

2/3 = -c/6 + 2 - c/6

Multiplying bοth sides by 6, we get:

4 = -c + 12 - c

Simplifying, we get:

2c = 8

c = 4

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Answer:

145°

Step-by-step explanation:

∠1 + ∠2 = ∠3

5x + (4x + 10) = 10x - 5

9x + 10 = 10x - 5

10x - 9x = 10 + 5

x = 15

∠3 = 10x - 5 = 10(15) - 5 = 150 - 5 = 145

The equation that Sharon can use to find c is

                               300(c-0.20)= 180

The average amount the cable company charges per channel was $0.8.

An equation is a mathematical statement which can be constructed by two expressions connected by an sign which is called equal '=' sign to find out the value of unknown variable.

For example, 3x – 11 = 16 is an equation. Solving this equation, we get the value of x as x = 9.

Sharon wants to switch from cable to satellite TV. She calls Great Vista Satellite to get a quote. After looking at her cable bill, the salesperson explains that they can provide the same 300 channels Sharon has for $0.20 less per channel. If she switches, her monthly satellite bill will come to $180.

Let us take in previous case the bill was $c for one channel.

so for 300 channels it will be $300c.

If Sharon has for $0.20 less per channel

Then price per channel will be $(c-0.20)

For 300 channels it will be $300(c-0.20)

It equals to $180

so equating both values we get the  equation and the equation will be,

          300(c-0.20)= 180

The equation that Sharon can use to find c is

                               300(c-0.20)= 180

To find the average amount we will solve c from the equation.

                                  300(c-0.20)= 180

                                ⇒ c-0.20 = 180/300 [ dividing both sides by 300 we get]

                                 ⇒ c- 0.20 =0.6

                                  ⇒ c= 0.8 [ Adding both sides 0.20 we get]

 Hence, The average amount the cable company charges per channel was $0.8.  

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Answer:

  3 times the second equation, plus the first

Step-by-step explanation:

You want a strategy for eliminating x-terms in the system of equations ...

You can eliminate x-terms by making their coefficients opposites. We observe that the coefficient of x in the first equation is -3 times the coefficient of x in the second equation.

Multiplying the second equation by 3 will make the x-coefficient -9, the opposite of that in the first equation. Doing that makes the system ...

Adding these two equations together will eliminate the x-terms:

  (9x -7y) +(-9x +15y) = (-3) +(27)

  8y = 24 . . . . . . . simplify; x-terms are gone

You can eliminate x-terms by multiplying the second equation by 3, then adding the two equations together.

y= 2x+1 y = -3x-4

2x-y+1 = 0. 3x+y+4 = 0

a1 + b1 + c1 = 0 a2+ b2 + c2 = 0

x,y = b1c2- b2c1/ a1b2-a2b1 , a2c1-a1c2/a1b2-a2b1

x,y = -1×4 - 1×1 /2×1 - 3×-1 , 3×1-2×4 / 2×1 -3×-1

x,y = -5/-1 , -5/2

x,y= 5, 5/2

The value of log(27) is 1.431.

What is logarithm?

The power to which a number must be raised in order to obtain other numbers is referred to as a logarithm. The easiest method to express large numbers is this way. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms can also be expressed as multiplication and division of logarithms.

We can use the property of logarithms that states that log a (b^c) = c log a (b) to evaluate log 27 using the given approximations:

log 27 = log (3³) = 3 log 3 ≈ 3(0.477) ≈ 1.431

Therefore, log 27 ≈ 1.431.

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The bearing from A to F is 38

Answer:

k=0 or k=1/27

Step-by-step explanation:

3k-81k^2=0

3k(1-27k) =0

3k=0 or 1-27k=0

k=0 or -27k= -1

k= 1/27

A model to find a fraction equivalent to 1/4 is found to be 0.25.

The intervals among two integers are illustrated by the display of fractions on a number line, which also reveals the basic idea behind the generation of fractional numbers.

Now, for the given fraction 1/4.

To get the model of 1/4, draw number line and mark number starting from

0 to 4.

Divide in 4 equal part.

The first part shows the fraction 1/4 = 0.25.

Thus, a model to find a fraction equivalent to 1/4 is found to be 0.25.

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There is no logarithm base provided in the expression "log 5 + 2". Therefore, we assume that the base is 10, which is the default base for logarithms when no base is specified.

Using the logarithmic identity that states

"log a + log b = log(ab)",

we can combine the terms as follows:

log 5 + 2 = log(5) + log(10^2) [Note that 10^2 = 100]

Now, using the same identity, we can simplify this further:

log(5) + log(100) = log(5 * 100) = log(500)

Therefore, the expression "log 5 + 2" can be simplified as a single logarithm of "log 500" with base 10.

Answer:

16

Step-by-step explanation:

Find an equivalent fraction which is 6/16.

Proof of Quadrilateral WXYZ as a Parallelogram using SSS Criterion for Congruence.

What is the proof that Quadrilateral WXYZ is a parallelogram using SSS criterion for congruence?

Since WY and XZ bisect each other at point A, we have AW = AY and AZ = AX.

Now, consider the triangles AWX and AYZ. By the Side-Side-Side (SSS) criterion for congruence, we have:

AW = AY (given)

AZ = AX (given)

WY = XZ (as WY and XZ bisect each other)

Therefore, by the SSS criterion for congruence, we have AWX ≅ AYZ.

By the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem, we have WX = YZ.

Since opposite sides are congruent, we have WX || YZ.

Similarly, we can show that WZ || XY.

Therefore, since both pairs of opposite sides are parallel, we can conclude that quadrilateral WXYZ is a parallelogram.

Missing statement: "By the SSS criterion for congruence, we have AWX ≅ AYZ."

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Each of the value of x in the diagram above are as follows

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines.

Next, we would determine each of the missing angles denoted by x as follows with respect to the START BOX;

x = 141° (alternate interior angles theorem).

x = 39° (corresponding angles).

x + 169 = 180

x = 180 - 169 = 21°.

x = 88° (vertically opposite angles).

x = 180°- 82°

x = 98°

x + 41 = 180

x = 180 - 41 = 139°.

x + 117 = 180

x = 180 - 117 = 139°.

x = 102° (vertically opposite angles)

x + 130 = 180

x = 180 - 130 = 50°.

x + 14 = 180

x = 180 - 14 = 166°.

x + 18 = 180

x = 180 - 18 = 162°.

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The value of x using Pythagoras theorem to solve the diagram is 1.25 m.

Pythagoras theorem states that the square of the hypotenus in a right angled triangle is equal to the sum of the of the two other sides.

To solve for x we use pythagoras theorem in the diagram below.

Formula:

From the diagram,

Substitute these values into equation 1 and solve for x

Hence, x is 1.25 m.

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(a) The probability of the questions being history, literature, and science, in that order, is 4.28%.

(b) The probability of all three cards being literature questions is 2.4%.

(c) 5%.

Probability can be used to estimate the chances of drawing a certain card and can help players to decide which moves to make when playing card games.

(a) The probability of the questions being history, literature, and science, in that order, is 5/18 x 6/17 x 7/16 = 0.0428 or 4.28%.

To calculate this probability, we use the formula

P(A and B and C) = P(A) x P(B|A) x P(C|B and A).

The probability of the first card being a history card is 5/18, since there are five history cards out of 18 total cards.

The probability of the second card being a literature card, given that the first card is a history card, is 6/17, since there are six literature cards out of the remaining 17 cards.

The probability of the third card being a science card, given that the first two cards are history and literature, is 7/16, since there are seven science cards out of the remaining 16 cards.

(b) The probability of all three cards being literature questions is 6/18 x 5/17 x 4/16 = 0.024 or 2.4%.

To calculate this probability, we use the formula P(A and B and C) = P(A) x P(B|A) x P(C|B and A).

The probability of the first card being a literature card is 6/18, since there are six literature cards out of 18 total cards.

The probability of the second card being a literature card, given that the first card is a literature card, is 5/17, since there are five literature cards out of the remaining 17 cards.

The probability of the third card being a literature card, given that the first two cards are literature cards, is 4/16, since there are four literature cards out of the remaining 16 cards.

(c) The probability of the first card being a science card, the second being a history card, and the third being a science card is 7/18 x 5/17 x 7/16 = 0.05 or 5%.

To calculate this probability, we use the formula P(A and B and C) = P(A) x P(B|A) x P(C|B and A).

The probability of the first card being a science card is 7/18, since there are seven science cards out of 18 total cards.

The probability of the second card being a history card, given that the first card is a science card, is 5/17, since there are five history cards out of the remaining 17 cards.

The probability of the third card being a science card, given that the first two cards are science and history, is 7/16, since there are seven science cards out of the remaining 16 cards.

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there are 1,008 different computer systems possible, given the constraints provided.

what is constraints?

Constraints are limitations or conditions that must be satisfied in order to solve a problem or make a decision. In other words, constraints are rules or restrictions that define the boundaries within which a solution or decision must be made.

In the given question,

To determine the number of different computer systems possible, we need to multiply the number of choices for each component. This is based on the multiplication principle of counting, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things together.

So, for this problem, we have:

8 different choices for computers

7 different choices for monitors

9 different choices for printers

2 different choices for scanners

Using the multiplication principle, the total number of different computer systems possible is:

8 x 7 x 9 x 2 = 1,008

Therefore, there are 1,008 different computer systems possible, given the constraints provided.

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Answer:

a. lines intersecting at a single point

b. one solution

Step-by-step explanation:

a. The equations can be rewritten as:

y = -5x+23 and y = -1/6x+1

Comparing the equations with standard equation: y=mx+c, where m is the gradient of the line formed by the linear equation.

Since the gradient of the lines are different then the lines cannot be parallel and will intersent at one point.

b. The equation will have one solution as below.

The equations can be rewritten as:

5x+y=23

5x+30y=30

Subtracting both equation will result in,

29y=7

=> y=7/29

Hence x= 660/29

Answer:

the y intercept is 1 so put a point there then move up 1 and to the right 3 and put a point then draw a line through the 2 points

The correct answer is option 2: if Lamont's sales are $2708.33, he earns $2290.63 with Plan B.

To determine which pay structure is better for Lamont, we need to compare the total amount of money he earns under each plan for different levels of sales. We can set up a system of equations to represent the two plans:

Plan A:

Total Pay = 1775 + 0.19S

where S is Lamont's total monthly sales

Plan B:

Total Pay = 2100 + 0.07S

To find the point at which the two plans yield the same result, we can set the two equations equal to each other and solve for S:

1775 + 0.19S = 2100 + 0.07S

0.12S = 325

S = 2708.33

If Lamont's monthly sales are exactly $2,708.33, then he earns the same amount of money under both plans - this is the break-even point.

However, for sales above this amount, Plan A becomes the better option as the commission rate is higher. Option 1 is incorrect because it assumes that Plan A is always better, whereas we know from the calculations that this is not the case. Option 3 is correct for sales above $2,708.33, but not for sales below this amount. Option 4 is also incorrect as we know that Plan B yields a slightly higher payout for sales exactly equal to the break-even point.

Therefore, option 2 is the correct answer as it accounts for the break-even point and accurately reflects the difference in total pay between Plan A and Plan B for Lamont's sales of $2,708.33.

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The graph of x²-x-2=y crosses the x-axis at the points (-1,0) and (2,0).

What is graph?

A graph is a data structure consisting of a set of vertices (also called nodes or points) connected by edges (also called arcs or lines). It is used to represent relationships between objects or entities in a system or network. Graphs are commonly used in computer science, mathematics, and other fields where complex data structures need to be analyzed and visualized.

In a graph, each vertex may be connected to one or more other vertices by edges. The edges may be directed (pointing from one vertex to another) or undirected (connecting vertices without a specific direction). A graph can be represented mathematically as a set of vertices and a set of edges that connect them.

To find where the graph of the equation x²-x-2=y crosses the x-axis, we need to find the values of x when y=0.

So, let's set y=0 and solve for x, x²-x-2=0

We can factor this quadratic equation as (x-2)(x+1) = 0

So, the solutions are

x-2=0 or x+1=0

which give:

x=2 or x=-1

Therefore, the graph of x²-x-2=y crosses the x-axis at the points (-1,0) and (2,0).

So the answer is option D: (-1,0) and (2,0).

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The two-column proofs of the line segments are shown below

Given that

HI = 13

IJ = 13

IJ ≅ JH

The proof is as follows

Statement                                                Reason

HI = 13, IJ = 13, IJ ≅ JH                            Given

HI ≅ IJ                                                      Substitution property

HI ≅ JH                                                    Substitution property (proved)

Given that

AL = SK

The proof is as follows

Statement                                                Reason

AL = SK                                                    Given

AL + LS = AS                                            Point–line–plane postulate

LS + SK = LK                                            Point–line–plane postulate

LS + AL = LK                                            Substitution property

AS = LK                                                    Point–line–plane postulate

                                                                (proved)

Given that

DG = 11

GF = 11

GF ≅ EF

The proof is as follows

Statement                                                Reason

DG = 11, GF = 11, GF ≅ EF                        Given

DG ≅ GF                                                   Substitution property

DG ≅ EF                                                    Substitution property (proved)

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The first statement given is not a random sample because athletes leaving practice are not representative of all athletes.

A random sample is a sample in which every member of the population being studied has an equal chance of being selected. In the given statement, the sample is not random because the athletes leaving practice are not representative of all athletes, as they may have different preferences or levels of skill in their favorite sport.

Additionally, the sample is not chosen through a random selection process, but rather through a convenience sampling method, in which participants are chosen based on their availability and willingness to participate.

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Answer:

To find the slope of a line parallel to 5x - 2y = 2, we need to first rearrange the equation in slope-intercept form, y = mx + b, where m is the slope of the line. 5x - 2y = 2 -2y = -5x + 2 y = (5/2)x - 1 The slope of the line is 5/2. Since we are looking for a line parallel to this line, the slope of the parallel line will be the same as the slope of the original line, which is 5/2. Therefore, the slope of a line parallel to 5x - 2y = 2 is 5/2.

When the slope is an integer the best answer would be a. the rise number is one.

Any number, including zero, positive numbers, and negative numbers, is an integer. An integer can never be a fraction, a decimal, or a percent, it should be observed. Integers include things like 1, 3, 4, 8, 99, 108, -43, -556, etc.

When the slope is an integer, it means that the rise over run is also an integer, and the rise and run are relatively prime. Therefore, the best answer would be:

Therefore, the correct answer is a. the rise number is one.

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Answer:

The solid formed by rotating the two-dimensional shape (which appears to be a right-angled triangle) about the line is a cone.

Answer:

identy the solid formed by

Answer:

Yes, the data is an example of numerical data.

1. This is about data, which means information that we can measure and count.

2. There are two types of numerical data: continuous and discrete.

3. Continuous numbers CAN have fractions, like 3.5, 4.2, or 5.0. 4. like show sizes

4. Discrete data CANNOT have fraction. only whole numbers, like 0, 1, 2, 3, and so on. like number of students in a class

7. "range" formula used to find the difference between discrete & continuous numerical data

8.  "range" formula is largest value minus smallest value

Step-by-step explanation:

chatgpt

Answer: yes because it records the shoe sizes and you can calculate average, median, mode and range from this

Step-by-step explanation:

a. You would need to invest approximately $3,436.76 each year, starting now, to reach your goal of $100,000

b. The present value of $100,000 when your child is born is $100,000.

Compound interest is interest that is calculated on the initial principal and also on the accumulated interest of previous periods. This results in exponential growth of the investment over time.

a. To calculate the amount that needs to be invested each year, we can use the formula for the future value of an annuity:

[tex]FV = PMT*((1 + r)^n - 1)/r[/tex]

where FV is the future value, PMT is the annual payment, r is the interest rate per period (which is 5% in this case), and n is the number of periods (which is 18 years).

Plugging in the values, we get:

$100,000 = PMT*((1 + 0.05)^18 - 1)/0.05

Solving for PMT, we get:

PMT = $3,436.76

Therefore, you would need to invest approximately $3,436.76 each year, starting now, to reach your goal of $100,000 for your child's college education in 18 years, assuming continuous compounding at a 5% annual interest rate.

b. To calculate the present value of $100,000 when your child is born, we need to discount it back to the present time using the formula:[tex]PV = FV/(1 + r)^n[/tex]

where PV is the present value, FV is the future value ($100,000), r is the interest rate per period (which is 5%), and n is the number of periods (which is 0 since the money is being received now).

Plugging in the values, we get:

PV = $100,000/(1 + 0.05)^0

Solving for PV, we get:

PV = $100,000

Therefore, the present value of $100,000 when your child is born is $100,000.

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