What are mutually exclusive events?
Events in which event#1 must happen before event #2
Events in which event#1 and event#2 must happen at the same time
Events in which event#1 must happen after event#2
Events in which neither event is dependent upon the other

Answer:

C. The system has no solution.

C. The system has no solution.

A system of linear equations has no answer whilst the graphs are parallel. A coordinate plane. The x- and y-axes both scale by way of one-1/2. A graph of a line is going through the factors 0, one and a half of and three, two.

No solution would suggest that there's no answer to the equation. it's miles not possible for the equation to be proper regardless of what price we assign to the variable. infinite answers would suggest that any value for the variable would make the equation authentic.

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There are 52,920 ways to select 5 appetizers, 4 main courses, and 5 desserts for the banquet.

To solve this problem, we can use the concept of combinations, as we're selecting items without considering the order.

For appetizers:

We need to choose 5 appetizers out of 6 available. This can be calculated using the combination formula: nCr = n! / [r! * (n-r)!], where n is the total number of items, and r is the number of items to be chosen.

So, for appetizers, it's [tex]6C_5 = 6! / [5! * (6-5)!] = 6 ways[/tex].

For main courses:

Similarly, we need to choose 4 main courses out of 7 available. So, it's

[tex]7C_4 = 7! / [4! * (7-4)!] = 35 ways[/tex].

For desserts:

We need to choose 5 desserts out of 10 available. So, it's

[tex]10C_5 = 10! / [5! * (10-5)!] = 252 ways[/tex].

To find the total number of ways:

We multiply the number of ways for each category since these choices are independent.

Total ways = (6 ways for appetizers) * (35 ways for main courses) * (252 ways for desserts) = 52920 ways.

Thus, there are 52,920 ways to select 5 appetizers, 4 main courses, and 5 desserts for the banquet.

Complete Question:

A catering service offers 6 appetizers, 7 main courses, and 10  desserts. A customer is to select 5 appetizers, 4 main courses, and 5 desserts for a banquet. In how many ways can this be done?

Answer:

A = 14 units ^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 b h  where b is the base and h is the height

b = the length of EF  which is 7 units

h = D to the line EF which is 4 units

A = 1/2 (7*4)

A = 14 units ^2

Answer:

Lol you answered your own question but yes it is -4 thanks!

Step-by-step explanation:

Answer:

x-intercept (-3,0)

y-intercept  (0,-9)

Step-by-step explanation:

The x-intercepts can be found by setting y to 0 and solving for x.

y=-3x-9

0=-3x-9

Add 9 on both sides:

9=-3x

Divide both sides by -3:

9/-3=x

-3=x

The x-intercept is (-3,0).

The y-intercepts can be found by setting x to 0 and solving for y.

y=-3x-9

y=-3(0)-9

y=0-9

y=-9

The y-intercept is (0,-9).

Answer:

Step-by-step explanation:

x-intercept is for y = 0.

y-intercept is for x = 0.

y = -3x - 9

x-intercept (put y = 0):

0 = -3x - 9            add 9 to both sides

9 = -3x          divide both sides by (-3)

-3 = x → x = -3

y-intercept (put x = 0):

y = -3(0) - 9

y = 0 - 9

y = -9

Answer:

0.88 feet

Step-by-step explanation:

The tire covers 0.88 feet in 1 rotation.

1 rotation means the whole tire moves, which is basically its circumference. So, the distance it covers in moving 1 rotation IS ITS CIRCUMFERENCE.

Hence, 0.88 feet is the circle's circumference.

Answer:

The top tag price you could pay for the shorts = $32.71....

Step-by-step explanation:

Total amount = $ 60.00

Cost of jacket = $25.50

Sales tax = 7% = .07

First of all find the total price of the jacket including sales tax.

25.50* .07 = 1.79( this is the sales tax)

Now add this sales tax into the original price.

25.5 + 1.79 = 27.29

Total price of a jacket = $27.29

Now subtract the total amount by the amount of the jacket.

$60.00 - $27.29 = $32.71

Thus the top tag price you could pay for the shorts = $32.71....

Answer:

-17

Step-by-step explanation:

Plug in -2 as your x value for the g(x) equation and simplify.

[tex]g(-2)=\sqrt{-2+6} \\g(-2)=\sqrt{4} \\g(-2)=2[/tex]

Next, plug in your g(x) value (2) to the f(x) equation for x and simplify.

[tex]f(2)=-7(2)-3\\f(2)=-14-3\\f(2)=-17[/tex]

Answer:

(4/3, 4  5/9) and (-32, -53)

Step-by-step explanation:

When a curve is given as a set of parametric equations, as this one is, then the slope of the tangent line to the curve is

              dy/dt

dy/dx = ------------

               dx/dt

which here is

              dy/dt        8 - 20t

dy/dx = ----------- = --------------

               dx/dt         12t^2

If the slope at a certain point on this curve is 1, then we conclude that:

8 - 20t = 12t^2, or

12t^2 + 20t - 8 = 0, or

3t^2 + 5t - 2 = 0

We have to solve this equation for the parameter, t:

Here a = 3, b = 5 and c = -2, and so the discriminant is

b^2 - 4ac = 25 - 4(3)(-2), or 49, and the square root of that is 7.

Thus, the roots are:

     -5 ± 7

t =  --------- = 1/3 and t = -2

        2(3)

Evaluate x and y twice, once each for each t value.

Case 1:  t = 1/3

x = 4(1/3) and y = 3 + 8(1/3) - 10(1/3)^2, or

x = 4/3 and y = 3 + 8/3 - 10/9:  (4/3, 4  5/9)

Case 2:  t = -2

x = 4(-2)^3 and y = 3 + 8(-2) - 10(-2)^2, or y = 3 - 16 - 40, or y = -53.

This gives us the point (-32, -53)

To find the points where the tangent line has a slope of 1 on the given curve, we derive expressions for dx/dt and dy/dt, set dy/dx equal to 1, and solve for t.

The given equation defines a parametric curve with x = 4t3 and y = 3 + 8t − 10t2. To find the points on this curve where the tangent line has a slope of 1, we'll first need to find expressions for dx/dt and dy/dt, which represent the rates of change of x and y with respect to the parameter t.

By differentiating x = 4t3 with respect to t, we find dx/dt = 12t2. Similarly, by differentiating y = 3 + 8t − 10t2 with respect to t, we find dy/dt = 8 - 20t.

The slope of the tangent line at a particular point on the curve corresponds to dy/dx, which we can find by dividing dy/dt by dx/dt, yielding (8 - 20t) / (12t2). We can set this equal to 1 (since we want a slope of 1) and solve for t to find the points on the curve where the tangent line has slope 1.

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Check the picture below.

so, the vertex at N, is noticeably not a right angle is an acute angle, so is less than 90°, so we don't need to check that one.

now, is the angle at L 90°?

well, if that's true LM and LN are perpendicular, and if they're indeed perpendicular, their slopes are negative reciprocal, meaning the slope of one is the same as the other but negative and upside down, well, let's check.

[tex]\bf L(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad M(\stackrel{x_2}{2}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-0}{2-0}\implies \cfrac{2}{2}\implies 1 \\\\[-0.35em] ~\dotfill\\\\ L(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad N(\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-0}{2-0}\implies \cfrac{-1}{2}\implies -\cfrac{1}{2}[/tex]

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope~of~LM}{1\implies \cfrac{1}{\underline{1}}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{\underline{1}}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{\underline{1}}{1}\implies -1}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{slope of LM}}{1}\qquad \stackrel{\textit{negative reciprocal of LM}}{-1}\qquad \stackrel{\textit{slope of LN}}{-\cfrac{1}{2}}~\hfill -1\ne -\cfrac{1}{2}[/tex]

so that means Lydia put too much espresso on her last cup.

Answer:

Angles congruent to angle 2 is first. Angles congruent to angle 6 is second. Angles congruent to angle 1 is third. Angles congruent to angle 7 is last.

Step-by-step explanation:

Opposite angles are always equal. Alterbate interior/exterior angles are always equal.

Answer:

The right answer us "is always" as its all angles are 60 degree.

Answer:

yes

Step-by-step explanation:

this is right i think

The correct answer is line HJ .

1. **Line AB**: The slope of line AB is not the negative reciprocal of 1/2, so it is not perpendicular.

2. **Line CD**: The slope of line CD is not the negative reciprocal of 1/2, so it is not perpendicular.

3. **Line FG**: The slope of line FG is not the negative reciprocal of 1/2, so it is not perpendicular.

4. **Line HJ**: The slope of line HJ is the negative reciprocal of 1/2, which makes it perpendicular.

A line with a slope of **-3/5** can be represented by the equation:

[tex]\[ y = -\frac{3}{5}x + b \][/tex]

where \(b\) is the y-intercept. To find points on this line, we need to consider different values of \(x\) and calculate the corresponding \(y\).

Let's explore some potential points:

1. **Point A (x, y)**:

  - Assume \(x = 0\):

  [tex]\[ y = -\frac{3}{5} \cdot 0 + b = b \] - So, point A is \((0, b)\).[/tex]

2. **Point B (x, y)**:

  - Assume \(x = 5\):

  [tex]\[ y = -\frac{3}{5} \cdot 5 + b = -3 + b \] - So, point B is \((5, -3 + b)\).[/tex]

3. **Point C (x, y)**:

  - Assume \(x = 10\):

  [tex]\[ y = -\frac{3}{5} \cdot 10 + b = -6 + b \] - So, point C is \((10, -6 + b)\).[/tex]

These are just a few examples. You can find more points by choosing different values of \(x\). Remember that any point on the line will satisfy the equation [tex]\(y = -\frac{3}{5}x + b\).[/tex]

Now, let's explore the concept of parallel lines. Two lines are parallel if they have the **same slope**. If we have another line with a slope of 1/2, we can find points on that line as well.

Answer:

y = 3(x + 2) + 2 and y = -3(x + 2) + 2

Step-by-step explanation:

* Lets revise the equation of the hyperbola with center (h , k) and

 transverse axis parallel to the y-axis is (y - k)²/a² - (x - h)²/b² = 1

- The coordinates of the vertices are  (h , k ± a)

- The coordinates of the co-vertices are (h ± b , k)  

- The coordinates of the foci are (h , k ± c) where c² = a² + b²

- The equations of the asymptotes are  ± a/b (x - h) + k  

* Lets solve the problem

∵ The equation of the hyperbola is (y - 2)²/9 - (x + 2)² = 1

∵ The form of the equation is (y - k)²/a² - (x - h)²/b² = 1

∴ h = -2 , k = 2  

∴ a² = 9

∴ a = √9 = 3

∴ b² = 1

∴ b = √1 = 1

∵ The equations of the asymptotes are y = ± a/b (x - h) + k  

∴ The equations of the asymptotes are  y = ± 3/1 (x - -2) + 2

∴ The equations of the asymptotes are  y = ± 3 (x + 2) + 2    

* The equations of the asymptotes of the hyperbola are

  y = 3(x + 2) + 2 and y = -3(x + 2) + 2

Answer: I just did this quiz in Plato the correct answer is in the pic I did this question 3 times because I listened to the other people and finally got the answer which is the correct one, Hope this helps :)

Step-by-step explanation:

Answer:

x≤ 60 - (3÷1/15)

Step-by-step explanation:

Number of blankets to be made = 3

Darcie crochets 1/15 blanket per day

To crochet one carpet she needs = 15 days

To crochet three carpets she needs = 15*3 = 45 days

Number of days she had = 60 days

She can skip days = 60-45 = 15 days

Let x be the number of days to complete her work.

Thus the equation becomes x≤ 60 - (3÷1/15)

You can solve for x to determine the number of days, Darcie can skip crocheting, you will get the answer 15....

The answer explains how to set up and solve an inequality to determine the number of days Darcie can skip crocheting while still meeting her goal of donating blankets.

To determine the number of days Darcie can skip crocheting and still meet her goal, we need to set up an inequality based on the information given.

First, calculate the total number of blankets Darcie needs to crochet: 3 blankets.

Set up the inequality: 1/15 * (60 - x) ≥ 3, where x represents the number of days she can skip crocheting.

Solve the inequality: 60 - x ≥ 45, x ≤ 15.

Therefore, Darcie can skip crocheting for up to 15 days and still meet her goal of donating 3 blankets.

Answer:

5

Step-by-step explanation:

Given

Original Measurement = 11*9 inches

Measurement after enlargement = 55 * 45 inches

In order to find the scale factor, we can choose one side of the figure or the whole area and find the ratio between the measurement before enlargement and after enlargement.

In case of a side the answer will be the scale factor while in case of finding scale factor using areas the answer will be the square of scale factor.

So,

[tex]Scale\ factor =s^2= \frac{55*45}{11*9} \\s^2 = \frac{2475}{99} \\s^2=25[/tex]

As we know that this is the square of scale factor.

Hence the scale factor will be:

[tex]\sqrt{s^2}=\sqrt{25}  \\s=5[/tex]

So, the scale factor is 5 ..

Answer:

D. 66.

Step-by-step explanation:

There has to be 3 even multiples in the 5 numbers so we try:

22+33+44+55+66

= 220.

Answer:

Option D. 66

Step-by-step explanation:

A multiple is an exact number of times to another number.

The five consecutive multiples of 11 are:

22 -> 11/22 = 2 times, no remainder

33 -> 33/11 = 3 times, without remainder

44 -> 44/11 = 4 times, without remainder

55 -> 55/11 = 5 times, without remainder

66 -> 66/11 = 6 times, without remainder

Of those five multiples of 11 (22, 33, 44, 55, 66), the greatest is 66.

Answer:

  2√3

Step-by-step explanation:

You recognize this as a 30°-60°-90° triangle, so you know the hypotenuse (R) is twice the length of the shortest side (√3).

The magnitude of R is 2√3.

_____

In case you haven't memorized the ratios for a 30°-60°-90° triangle, you can use trigonometry and the fact that ...

  Sin = Opposite/Hypotenuse

  sin(30°) = √3/R

  R = √3/sin(30°) = √3/(1/2) = 2√3

Of course, doing this on your calculator will give a numerical answer, which you may not want.

Answer:

b ≈ 17

Step-by-step explanation:

Using trigonometric ratio, sine we can find side b.

sine x = opposite/hypotenuse

sin 45 = 12/b

b ≈ 17

Answer:

b = 12[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex]

From the triangle

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{12}{b}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]

Cross- multiply

b = 12[tex]\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

It all depends upon what the terms are.  If each term of the 3 all have a variable you can factor out, then you'd do that first.  For example, if your trinomial looks like this:

[tex]x^3+3x^2+4x[/tex]

you would begin by factoring out the common x, reducing the third degree polynomial to a quadratic which can then be factored many ways.

[tex]x^3+3x^2+4x=x(x^2+3x+4)[/tex]

If that is not the case, then you are factoring higher degree polynomials, and the way I always recommend to my students is the Rational Root Theorem and then synthetic division.

Answer:

47.88 in^2 of paper.

Step-by-step explanation:

The amount of paper needed for the base = 4.2^2 = 17.64 in^2.

There are 4 triangular faces.

The area of each triangular face = 1/2* base * height

= 1/2 * 4.2 * 3.6

=  7.56 in^2

That is a total of 4 * 7.56 = 30.24 in^2.

So the total amount of paper need to cover the entire pyramid

= 17,64 + 30.24

= 47.88 in^2.

Answer:

37°

Step-by-step explanation:

By definition all internal angles of a triangle add up to 180°

Hence,

98° + 45° + x = 180°

x = 180° - 98° - 45° = 37°

Answer:

Step-by-step explanation:

If you observe the image, you deduct that the polygon ABCD was increased in size, that means the scale factor applied dilated the figure. In other words, there was applied a factor of dilation.

To find the exact factor of dilation, we just have to divide each prime coordinate by the original ones.

For example, you can observe that coordinates [tex]A(3,0)[/tex] was changed to [tex]A'(6,0)[/tex], [tex]B(1,0)[/tex] was changed to [tex]B'(2,0)[/tex], [tex]C(1,2)[/tex] was changed to [tex]C'(2,2)[/tex] and [tex]D(3,2)[/tex] was changed to [tex]D'(6.2)[/tex].

Now, observe that the dilation was horizontal, that is, the scale factor was only applied to x-coordinates, and this factor is 2, beacuse each x-coordinate was increase by a factor of 2.

Therefore, this transformation is a horizonta dilation by a factor of 2.

Answer: x=-3

Step-by-step explanation:

F(x)=9x^2-54x-19

F(x)=(x-57)(x+3)

X=57 X=-3

Answer:

5.2 Km/Min

Step-by-step explanation:

Speed/Rate= Distance/Time

Speed/Rate = 114.4/22

Speed/Rate = 5.2 KM/min

Answer:

5.3 km/min

Step-by-step explanation:

Distance = 114.4 kilometers

Time = 22 minutes

Rate = 114.4 km /22 min

Rate = 5.2 km/min

f(x)=(x-5)(x-4)(x-2)

x-5=0

x-5+5=0+5

x=5

x-4=0

x-4+4=0+4

x=4

x-2=0

x-2+2=0+2

x=2

Answer: 5,4,2 -C

The zeros of the function f(x) = (x-5)(x-4)(x-2) are 5, 4, 2

Option C is correct

Note that:

The zeros of a function f(x) are the values of x that makes f(x) to be equal to zero

If f(x)  =  (x - a)(x - b)(x - c), then the zeros of the function f(x) are:

x  = a,  x  =  b,  x  =  c

Therefore, the zeros of f(x)=(x-5)(x-4)(x-2) are found by equating f(x) to zero

(x - 5)(x - 4)(x - 2)  =  0

Equate each of the terms to zero

x  -  5  =  0

x  =   5

x  -  4  =  0

x   =  4

x  -  2  =  0

x   =  2

The zeros of the function f(x) = (x-5)(x-4)(x-2) are 5, 4, 2

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Answer:

  $1.45

Step-by-step explanation:

To answer the question, we would like to have an equation that has the cost of a game as its only variable. That is, we would like to eliminate the cost of a ride from the system of equations we must write.

Let g and r represents the costs of a game and a ride, respectively. Then the expenses of the two carnival-goers can be described by ...

  5g +6r = 11.75

  7g +8r = 16.15

We note that the ratio of coefficients in the variable (r) that we want to eliminate is 3:4. So we can subtract 4 times the first equation from 3 times the second to eliminate that variable.

  3(7g +8r) -4(5g +6r) = 3(16.15) -4(11.75)

  g = 1.45 . . . . . . simplify

The cost to play one game was $1.45.

Answer:

$1.45

Step-by-step explanation:

Answer:

x = 11.79

? = 6.25

Step-by-step explanation:

Using the law of sines

[tex]\frac{10}{sin58}[/tex] = [tex]\frac{x}{sin90}[/tex]

x = sin 90° x [tex]\frac{10}{sin58}[/tex] = 11.79

by Pythagorean theorem,

?² + 10² = x²

? = √  (x²- 10²)

? = √  (11.79²- 10²) = 6.25

Answer:

m = 3, n = 4

Step-by-step explanation:

Solve using the substitution process. First, start with the second equation:

2m + 2n = 14

Simplify. Divide 2 from all terms within the equation. What you do to one side, you do to the other:

(2m + 2n)/2 = (14)/2

m + n = 7

Isolate the variable m. Subtract n from both sides:

m + n (-n) = 7 (-n)

m = 7 - n

Plug in 7 - n for m in the first equation:

-5m + 9n = 21

-5(7 - n) + 9n = 21

Solve. First, distribute -5 to all terms within the parenthesis:

(-35 + 5n) + 9n = 21

Simplify. Combine like terms:

-35 + (5n + 9n) = 21

-35 + 14n = 21

Isolate the variable, n. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, add 35 to both sides:

14n - 35 (+35) = 21 (+35)

14n = 21 + 35

14n = 56

Isolate the variable n. Divide 14 from both sides:

(14n)/14 = (56)/14

n = 56/14

n = 4

Plug in 4 to n in one of the equations, and solve for m.

2m + 2n = 14

2m + 2(4) = 14

2m + 8 = 14

Isolate the variable, m. Do the opposite of PEMDAS. First, subtract 8 from both sides:

2m + 8 (-8) = 14 (-8)

2m = 14 - 8

2m = 6

Divide 2 from both sides:

(2m)/2 = (6)/2

m = 6/2

m = 3

Your answers: m = 3, n = 4

~

Answer:

(3, 4)

Step-by-step explanation:

Please include the instructions.  I'm assuming that you want to solve this system of linear equations.

If that's the case, let's use elimination by addition and subtraction.

Multiply the first equation, -5m + 9n = 21, by 2:  -10m + 18n = 42, and

multiply the second equation, 2m + 2n = 14, by 5:  10m + 10n = 70

Next, combine these two "new" equations:

-10m + 18n = 42

10m + 10n = 70

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

          28n = 112.  Dividing both sides by 28, we get  n = 4.

Subbing 4 for n in the second equation, we get 2m + 2(4) = 14, or

2m = 6.  Then m = 3, and the solution is thus

(3, 4).

Answer:

Shaded to the left

Step-by-step explanation:

I cannot see the illustration, but I know for a fact that after using the zero-interval test [plug 0 in for BOTH y and x], you get 0 < 4, which is a genuine statement, so it gets shaded on the left hand side, otherwise shaded on the right of it were false statement.

I am joyous to assist you anytime.