1) through: (2,0), slope = -4/5

Answer:

∠EGB= 68°

Step-by-step explanation:

∠EGB= ∠AGF ( vert. opp. ∠s)

∠EGB= 68°

If 2 straight lines intersect, then the angles facing opposite each other are equal. In this case, the 2 lines are AB and EF.

Answer:

depend on watching action movies

Step-by-step explanation:

because most watch action

Based on the given data, watching romantic movies and watching action movies are independent events, as the probability of both occurring matches the product of their individual probabilities.

We need to determine if the events of watching romantic movies and watching action movies are independent or dependent. The definition of independent events in probability is that the outcome of one event does not change the probability of the outcome of another event.

If watching romantic and action movies were independent events, we would expect the percentage of people who watch both to be the product of the individual probabilities. That would be 0.40 (the probability of watching romantic movies) times 0.60 (the probability of watching action movies), which equals 0.24 or 24%.

However, we are told that 24% of people watch both romantic and action movies. This matches our calculation exactly, so we can infer that the event of watching romantic movies is independent from the event of watching action movies. This means that watching a romantic movie does not affect the likelihood of watching an action movie, and vice versa.

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Answer: nonenot congruent

Step-by-step explanation:

Solution:

Given that equation is:

[tex]x^2 - kx + 28 = 0[/tex]

Roots are:

[tex]\alpha\\\\\alpha + 3[/tex]

To find: value of x

The general quadratic equation is:

[tex]ax^2 + bx + c = 0[/tex]

[tex]\text{ Product of roots } = \frac{c}{a}\\\\\text{ Sum of roots } = \frac{-b}{a}[/tex]

From given,

[tex]x^2 - kx + 28 = 0[/tex]

a = 1

b = -k

c = 28

Therefore,

[tex]Product\ of\ roots = \frac{28}{1} = 28[/tex]

[tex]Sum\ of\ roots = \frac{-k}{1} = -k[/tex]

Given roots are:

[tex]\alpha\\\\\alpha + 3[/tex]

Therefore,

The two roots are two numbers whose difference is 3 and whose product is 28

Those two roots are 4 and 7 or -4 and -7

Then, sum of roots are:

4 + 7 = 11

-4 - 7 = -11

Therefore, the possible values of k are -11 and 11

Answer:

19 hours

Step-by-step explanation: he needs to work 19 hours because if you divide the sum of money(162$) he got from working 9 hrs you get that he makes 18$ per hour then divide that by the sum of money that he needs(342$)

Matt earns $18 per hour and needs to work a total of 19 hours to afford a $342 video game system.

Matt earned $162 this week by working 9 hours. This means that Matt earns $18 per hour (since 162 ÷ 9 = 18). To find out how many total hours Matt needs to work to buy a new video game system that costs $342, we divide the total cost of the video game system by his hourly wage. So, $342 ÷ $18 = 19 hours. Therefore, Matt needs to work a total of 19 hours to afford the video game system.

The given sum is based on the concept of percentage.0.54 is 2.25[tex]\%[/tex] out of 24.

Percentage is a way of expressing a fraction or proportion out of 100. It is represented by the symbol "%". The word "percent" comes from the Latin phrase "per centum", which means "per hundred."

Percentages are commonly used to describe ratios, rates, or proportions in various fields such as mathematics, finance, statistics, and everyday life. They allow us to compare quantities or express relative changes easily.

To find 2.25[tex]\%[/tex] of 24, multiply 24 by 2.25[tex]\%[/tex] (or 0.0225):

2.25[tex]\%[/tex] [tex]\times[/tex] 24 = 0.0225 [tex]\times[/tex] 24

                   = 0.54.

Therefore, 2.25[tex]\%[/tex] of 24 is 0.54.

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-r + 8(-5r -2).

Multiply 8 by -5r - 2

- r - 40r - 16.

Combine -r and -40r

-41r - 16 is a simplified equivalent expression of -r + 8(-5r - 2)

Answer:

-41r - 16

Step-by-step explanation:

-r + 8 (-5r - 2)

-r - 8*5 r -8*2

-r - 40r - 16

-41r - 16

Answer:

81

Step-by-step explanation:

All you have to do is times 9*9=81

Answer:

A=40.5

Step-by-step explanation:

A=pq /2

A= 9x9/2

A=81/2

A=40.5

Answer:

$224.

Step-by-step explanation:

If the packages cost $4 each then 56 packages will cost 56 * 4 dollars.

56 * 4 = $224.

Answer:

9.45 (rounded)

Step-by-step explanation:

- The formula is to divide the centimeters by 2.54, and this will give you the amount of inches.

Answer:

9.45 inches

Step-by-step explanation:

2.54cm in 1 inch

Answer:

10.78moles

Step-by-step explanation:

Avogadro's hypothesis gives us a background understanding that 1mole of any substance contains 6.02x10^23 atoms.

Now, If 1 mole of K3PO4 contains 6.02x10^23 atoms,

Then Xmol of K3PO4 will contain = 6.49x10^24 atoms i.e

Xmol of K3PO4 = 6.49x10^24/6.02x10^23 = 10.78moles

To find the number of moles of K3PO4 in 6.49 x 10^24 formula units, divide the number of formula units by Avogadro's number, resulting in 10.78 moles of K3PO4.

To calculate the number of moles of K3PO4 in 6.49 x 1024 formula units, we use Avogadro's number, which is 6.022 x 1023 formula units per mole. This is the key conversion factor for converting between the number of formula units and the number of moles.

First, we have the given number of formula units of K3PO4:

To convert this to moles, we divide by Avogadro's number:

Number of moles = (6.49 x 1024 formula units) / (6.022 x 1023 formula units/mole)

= 10.78 moles of K3PO4

This calculation shows that there are 10.78 moles of K3PO4 in 6.49 x 1024 formula units of K3PO4.

Answer:

The answer is C) Unlikely.

Step-by-step explanation: This is because the likelihood of you rolling a 3 on a six-sided die is approximately 3/36.

It is unlikely to roll a 3.

Option C is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Possible outcomes of rolling a six-sided die.

= {1, 2, 3, 4, 5, 6}

We can say that,

If the probability of an event is 50% or above it is likely.

If the probability of an event is less than 50% it is unlikely.

If the probability of an event is 100% it is certain.

If the probability of an event is less than 0% it is impossible.

Now,

Probability of rolling a 3.

= 1/6 x 100

= 16.67%

This means,

Unlikely.

Thus,

It is unlikely to roll a 3.

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Answer:

374

Step-by-step explanation:

Answer:

Carpenters can install about 123 hinges.

Step-by-step explanation:

Since each hinge requires 3 screws. Divide 371 by 3.

= 123.666667

Answer:

123

Step-by-step explanation:

   [tex]\lim_{n \to \infty} a_n \pi \beta[/tex][tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \alpha \leq x^{2} \sqrt{x} x^{2}[/tex]that's how I got it

[tex]\lim_{n \to \neq \geq \leq x^{2} x^{2}[/tex]

Answer:

1.  y = -3/2 x +11

2.  y = -2 x -7

Step-by-step explanation:

Slope intercept form is y = mx+b

1. A (8, –1) and B (–4, 17)

First we need to find the slope

m = (y2-y1)/(x2-x1)

m = (17--1)/(-4-8)

   =(17+1)/(-4-8)

   =18/-12

Dividing top and bottom by 6

  =-3/2

Given the slope

y = -3/2 x+b

Using the point (8,1) we can find b

-1 = -3/2(8) +b

-1 =-12 +b

Add 12 to each side

-1+12 = -12+12 +b

11 =b

The equation is y = -3/2 x +11

2. C (–19, 31) and D (1, –9)

First we need to find the slope

m = (y2-y1)/(x2-x1)

m = (-9-31)/(1--19)

   =(-40)/(1+19)

   = -40/20

   =-2

Given the slope

y = -2 x+b

Using the point (1,-9) we can find b

-9 = -2(1) +b

-9 =-2 +b

Add 2 to each side

-9+2 = -2+2 +b

-7 =b

The equation is y = -2 x -7

Answer:

Step-by-step explanation:

1 day -------------- $12

cost = 2(1 day) + 10

2 days ------------ $14

cost = 2(2 days) +10

3 days -------------$16

cost = 2(3)+10

and so on

Answer:

7/20

Step-by-step explanation:

The probability is 7/20.

Probability is a branch of mathematics that deals with the occurrence of a random event.

The hazard that a given event will arise. The ratio of the variety of results in an exhaustive set of similarly probable results that produce a given occasion to the overall number of feasible results.

possibility = the number of methods of reaching achievement. the total number of possible outcomes.

explanation:

Tails up represents white ducks

and heads up represents black ducks

probability of two white ducks number tails from the table = 7

total sample = 20

Hence probability = 7/20

The possibility is the branch of mathematics regarding the incidence of a random event, and four major styles of opportunity exist: classical, empirical, subjective, and axiomatic. the possibility is synonymous with possibility, so you should say it is the possibility that a particular event will show up.

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Answer:

if a 5 liter jug is 7.5 kg, The 2 liter jug weighs 3 kg

Step-by-step explanation:

7.5 / 5  = 1.5

1.5 x 2 = 3

Answer:

3kg

Step-by-step explanation:

w/2 = 7.5/5

w = 7.5/5 * 2

w = 15/5

w = 3

Answer:

Mary's score on the fifth test was 79.

Step-by-step explanation:

Let's solve for x, this way:

Mary's average score for the five tests = (Mary's 1st score + Mary's 2nd score + Mary's 3rd score + Mary's 4th score + Mary's 5th score)/5

Replacing with the values given:

81 = (88 + 91 + 75 + 72 + x)/5

81 * 5 = 326 + x

405 = 326 + x

- x = 326 - 405

x = 79

Answer:

1,782 CM

Step-by-step explanation:

Answer:

[tex] x = 6 \\ y = 9[/tex]

Step-by-step explanation:

[tex]2x - y - (x - y) = 3 - ( - 3) \\ 2x - y - x + y = 6 \\ x = 6[/tex]

[tex]2x - y = 3 \\ 2 \times 6 - y = 3 \\ 12 - y = 3 \\ - y = 3 - 12 \\ - y = - 9 \\ y = 9[/tex]

[tex] x - y = - 3 \\ 6 - 9 = - 3 \\ - 3 = - 3[/tex]

hope this helps you,! have a nice day!!

The system of equations is solved by substituting the expression for y from the linear equation into the quadratic equation, factoring the resulting quadratic, and solving for the two values of x, which are then used to find the corresponding y values, yielding solutions (3, 6) and (-2, 1).

To solve the system of equations given by

x2 - y = 3

x - y = -3

we observe that the second equation can immediately give us a value for y in terms of x. We can add 3 to both sides to isolate y:

y = x + 3

Next, we can substitute this expression for y into the first equation:

x2 - (x + 3) = 3

This simplifies to: x2 - x - 6 = 0

We can then solve this quadratic equation for x. A possible method is factoring, which, if the quadratic factors neatly, is often quicker than using the quadratic formula. The factored form is:

(x - 3)(x + 2) = 0

Setting each factor equal to zero gives us two solutions for x:

x = 3 or x = -2

Substituting these back into the equation y = x + 3 gives us the corresponding y values:

For x = 3: y = 3 + 3 = 6

For x = -2: y = -2 + 3 = 1

Thus, we have two solutions for the system: (3, 6) and (-2, 1).

Answer:

u < 4

Step-by-step explanation:

Step 1:  Subtract 8 from both sides

8 - u - 8 > 4 - 8

-u > -4

Step 2:  Divide both sides by -1

-u / -1 > -4 / -1

Since you divide by a negative, you flip the sign.

u < 4

Answer:  u < 4

y/(5 + 3) = 5/y

y/8 = 5/y

y² = 40

y = 2√10

5/x = x/3

15 = x²

√15 = x

Answer:

  3.9

Step-by-step explanation:

The right triangles are all similar, so the ratio of short side to long side is the same for all:

  3/x = x/5

  15 = x^2 . . . . . . . . multiply by 5x

  x = √15 ≈ 3.9

Answer:

1 and 6

2 and 5

3 and 8

4 and 7

Step-by-step explanation:

vertical angles: each of the pairs of opposite angles made by two intersecting lines.

Answer:

x=5, 8, 9

Step-by-step explanation:

in a function, one x value must be paired with one and only one y value, this means there cannot be two points where x values are the same, however the y values can repeat.

if x = 5, 8, or 9, the relation is not a function because there are 2 same x values.

Answer:

u just take the sum of all numbers divide by the number of numbers (5)

Answer:

25

Step-by-step explanation:

When the equations intercect, the y-value is 25. (2,25)

Answer:

25

Step-by-step explanation:

Answer:

Draw a model ⇒ See the attached figure

Tennis balls to tennis rackets ⇒ 5 : 3

Tennis balls to total pieces of tennis equipment​ ⇒ 5 : 8

Step-by-step explanation:

Let the number of tennis balls ⇒ x

Let the number of tennis rackets ⇒ y

The general form represents the situation is ⇒ y = mx

Where m is the slope

Given: For every 5 tennis balls in the bin, there are 3 tennis rackets.

So, when x = 5 ⇒ y = 3

So, 3 = m * 5⇒ m = 3/5 = 0.6

∴ y = 0.6 x

See the attached figure which represents a model to show the ratio of tennis balls to tennis rackets.

Tennis balls to tennis rackets = 5 to 3 or  5 : 3

Total pieces of tennis equipment​ = 5 + 3 = 8

Tennis balls to total pieces of tennis equipment​ = 5 to 8 or 5 : 8

At the denominator you have

(x-5)×4=4x-20.

But:

2(x+4)/(4(x-5))=(x+4)/2/(x-5)

Answer:

see explanation

Step-by-step explanation:

Given

[tex]\frac{2(x+3)(x+4)}{(x+1)(x-5)}[/tex] × [tex]\frac{(x+1)}{4(x+3)}[/tex]

Cancel the common factors (x + 1), (x+3) on the numerator/ denominator

and cancel 2 and 4 on the numerator/ denominator by 2

= [tex]\frac{x+4}{2(x-5)}[/tex]

Answer:

rational

Step-by-step explanation:

hope this helps!