What quadrant does the terminal side of this angle lie in?
A) Quadrant III
B) Quadrant II
OC) Quadrant IV
OD) Quadrant I

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Equation of straight line in point - slope form :

[tex]\qquad❖ \: \sf \:y - y1 = m(x - x1)[/tex]

( m = slope = 4, point (5 , 17) )

[tex] \qquad◈ \: \: \sf \: y - 17 = 4(x - 5)[/tex]

[tex] \qquad◈ \: \: \sf \: y - 17= 4x - 20[/tex]

[tex] \qquad◈ \: \: \sf \: y = 4x - 20 + 17[/tex]

[tex] \qquad◈ \: \: \sf \: y = 4x - 3[/tex]

Now, it's the form of line in slope - intercept form, ( slope = coefficient of x = 4 and y - intercept = -3 )

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex] \qquad◈ \: \: \sf \: y \: \: int = - 3[/tex]

Answer:

- 4/7 , -1/9, 7/4

Step-by-step explanation:

You know that 7/4 is the largest number because it is the only positive number.  To compare the two negative numbers you need common denominators.  The common denominator would be 133 (19 x 7).  Now make equivalent fractions.-4/7 = x/133  133 divided by 7 is 19.  Multiple the -4 by 19 to get -76/133.  Next, make an equivalent fraction for -1/19.  The new denominator will be 133.  If I divide 133 by 19, I will get 7, so I multiple -1x7 and get -7 and the new fraction -7/133.

I have two fractions to compare -7/133 and -76/133.  -76/133 if farthest from 0 so it has the least value.

Part 1

Angles in a triangle add to 180 degrees, so

[tex]m\angle E=180^{\circ}-82^{\circ}-43^{\circ}=55^{\circ}[/tex]

Part 2

By the Law of Sines,

[tex]\frac{EF}{\sin 43^{\circ}}=\frac{15}{\sin 55^{\circ}}\\\\EF=\frac{15 \sin 43^{\circ}}{\sin 55^{\circ}}\\\\EF \approx 12.49[/tex]

Answer:

What is the measure of angle E?

m∠E =

✔ 55

°

What is the length of EF rounded to the nearest hundredth?

EF ≈

✔ 12.49

Step-by-step explanation:

Answer:

Horizontal reflection

Step-by-step explanation:

a math chart that was labeled had these pattern examples with the the translation and transformation.

I'm guessing the equation should read something like

[tex]7(x^2+y^2) \,dx + 5xy \, dy = 0[/tex]

or possibly with minus signs in place of +.

Multiply both sides by [tex]\frac1{x^2}[/tex] to get

[tex]7\left(1 + \dfrac{y^2}{x^2}\right) \, dx + \dfrac{5y}x \, dy = 0[/tex]

Now substitute

[tex]v = \dfrac yx \implies y = xv \implies dy = x\,dv + v\,dx[/tex]

to transform the equation to

[tex]7(1+v^2) \, dx + 5v (x\,dv + v\,dx) = 0[/tex]

which simplifies to

[tex](7 + 12v^2) \, dx + 5xv\,dv = 0[/tex]

The ODE is now separable.

[tex]\dfrac{5v}{7+12v^2} \, dv = -\dfrac{dx}x[/tex]

Integrate both sides. On the left, substitute

[tex]w = 7+12v^2 \implies dw = 24v\, dv[/tex]

[tex]\displaystyle \int \frac{5v}{7+12v^2} \, dv = -\int \frac{dx}x[/tex]

[tex]\displaystyle \dfrac5{24} \int \frac{dw}w = -\int \frac{dx}x[/tex]

[tex]\dfrac5{24} \ln|w| = -\ln|x| + C[/tex]

Solve for [tex]w[/tex].

[tex]\ln\left|w^{5/24}\right| = \ln\left|\dfrac1x\right| + C[/tex]

[tex]\exp\left(\ln\left|w^{5/24}\right|\right) = \exp\left(\ln\left|\dfrac1x\right| + C\right)[/tex]

[tex]w^{5/24} = \dfrac Cx[/tex]

Put this back in terms of [tex]v[/tex].

[tex](7+12v^2)^{5/24} = \dfrac Cx[/tex]

Put this back in terms of [tex]y[/tex].

[tex]\left(7+12\dfrac{y^2}{x^2}\right)^{5/24} = \dfrac Cx[/tex]

Solve for [tex]y[/tex].

[tex]7+12\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}}[/tex]

[tex]\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}} - \dfrac7{12}[/tex]

[tex]y^2= \dfrac C{x^{14/5}} - \dfrac{7x^2}{12}[/tex]

[tex]y = \pm \sqrt{\dfrac C{x^{14/5}} - \dfrac{7x^2}{12}}[/tex]

Answer:

  a₄₅ = 13

Step-by-step explanation:

The n-th term of an arithmetic sequence with first term a₁ and common difference d is given by the formula ...

  aₙ = a₁ +d(n -1)

You want the 45th term where a₁ = 2 and d = 1/4. Putting these values into the formula gives ...

  a₄₅ = a₁ +d(n -1) = 2 +(1/4)(45 -1)

Evaluating this expression, we have ...

  a₄₅ = 2 +44/4 = 2 +11

  a₄₅ = 13

The 45th term of the sequence is 13.

The forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]

How to find the nth term of the Arithmetic series?

The nth term of the arithmetic series is find by [tex]Tn = a+(n-1)d[/tex] where Tn is the nth term of the series a is called the initial number and is the common difference between two number. n is the number of term of that arithmetic series.

In the given series initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex]

We have the find the forty-fifth term of the given series.

= [tex]Tn=a+(n-1)d[/tex]

= [tex]Tn = 2+(45-1)\frac{1}{4}[/tex]

= [tex]Tn=2+44\cdot\frac{1}{4}[/tex]

= [tex]Tn = 2+11[/tex]

= [tex]Tn = 13[/tex]

So, the forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]

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Answer:

the principal amount is 10000 is the rate of interest is 10 and the number of years is 10 you can calculate the simple interest a is equal to 10000 1 + 0 is equal to 1.6 is equal to 16000 interest is equal to a - b is equal to 6000 - 1000

Answer:

$1,760

Step-by-step explanation:

So I'm assuming the interest is simple interest rate which means that the interest applied each year is 12% of the original amount.

So this means that we can find the interest rate from one year by finding 12% of 800, and to do this we convert 12% to a decimal by dividing by 100 to get 0.12 and then use this decimal value to multiply by 800 to get: 0.12 * 800 = 96.

This means annually $96 will be charged in interest. To find how much interest there is after 100 years, simply multiply by 10, to get $96 * 10 = $960.

This is only the interest rate, it's like a fee, you still have to pay back the original amount, so all together you pay: $ borrowed + interest

So we add the interest rate 960 to the amount borrowed 800 to get: 960 + 800 = 1,760

The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the equation:

x/3 - 3/4 = 5/12

Hence:

x/3 = 5/12 + 3/4

x/3 = 7/6

x = 7/2

The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2

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Answer:

It is the first graph

Step-by-step explanation:

The line under the > and < sign means that it must include the 3 and the 0.  The closed circle is showing that the 3 and 0 or included.

Probability that a card selected at random is purple = 7/25

Number of red cards, N(red) = 12

Number of blue cards, N(blue) = 17

Number of purple cards, N(purple) = 14

Number of yellow cards, N(yellow) = 7

Total number of cards, N(total) = 12 + 17 + 14 + 7

N(total) = 50

Probability that a card selected at random will be purple

P(purple) = N(purple) / N(total)

P(purple) = 14/50

Reduce to the lowest fraction

P(purple) = 7/25

Therefore, probability that a card selected at random is purple = 7/25

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Complete Question

There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat. If a card is selected at random, what is the probability that the card is purple

Rotation is a transformation where an object is rotated about a fixed point.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation, reflection and rotation are rigid transformations because they preserve the shape and size of the figure.

Rotation is a transformation where an object is rotated about a fixed point.

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The system of equations best represents the number of apples a and the number of garonia bars g be a+b=60, 0.75x+0.15y=21.

Given that cost of 1 apple is $0.75, cost of 1 gargonia bars be $0.15 ,total things are 60 and total money paid be $21.

Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be a linear equation,quadratic equation, cubic equation.

Because we have been told that there are 60 total things and a represents the number of apples and g represents number of garonia represents the number of garonia bars.

a+b=60--------1

Money paid by consumers is cost per units*number of units

So,

0.75a+0.15b=21

Hence the system of equations best represent the number of apples and the  number of garonua bars g are a+b=60, 0.75a+0.15b=21.

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Answer:60g

Step-by-step explanation:

Hope this the answer

The expression θ = - 50° ± i · 360°, [tex]i \in \mathbb{N}_{O}[/tex] represents the family of all angles coterminal with - 50° angle.

Two angles are coterminal if and only if their end have the same direction. Two consecutive coterminal angles have a difference of 360°. Then, we can derive an expression representing the family of all angles coterminal to - 50° angle.

θ = - 50° ± i · 360°, [tex]i \in \mathbb{N}_{O}[/tex]

The expression θ = - 50° ± i · 360°, [tex]i \in \mathbb{N}_{O}[/tex] represents the family of all angles coterminal with - 50° angle.

The statement is incomplete and complete form cannot be reconstructed. Thus, we modify the statement to determine the family of angles coterminal to - 50° angle.

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Answer:

6

Step-by-step explanation:

If you divide 78 by all of the numbers, only one, 6, is a whole number, making it the only factor. You can check this by multiplying 6 by 13, (you get 13 from the division) and you get 78.

I hope this helps!

Answer:

9

(Correct On Edgen)

The probability solved by binomial distribution that all will survive is 0.8154.

When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution. The likelihood of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.

Computation of probability of all survived people from heart attack;

A heart attack patient has a 0.04 percent chance of dying from the attack (i.e., 4 of 100 die of the attack).

What is the likelihood that each of the five patients who experience a heart attack will survive?

We'll refer to a victory in this scenario as a heart attack (p = 0.04). In other words, we are interested in the likelihood that none of our n=5 patients will die (0 successes).

Each attack has a chance of being fatal or not, with a probability of 4 percent for all patients, and each patient's result is independent.

Assume for the purposes of this example that the five individuals being examined are unrelated, of the same age, and free of any concomitant disorders.

By binomial distribution,

[tex]\begin{gathered}P(0 \text { successes })=\frac{5 !}{0 !(5-0) !} 0.04^{0}(1-0.04)^{5-0} \\P(0 \text { successes })=\frac{5 !}{5 !}(1)(0.96)^{5}=(1)(1)(0.8154)=0.8154\end{gathered}[/tex]

Therefore, with a 4 % chance that anyone will die, there is an 81.54% chance that every patient will survive the onslaught. The outcomes in this example could be 0, 1, 2, 3, 4 or 5 successes (fatalities).

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we conclude that the system of inequalities has more solutions than the system of equations.

We have the system of equations:

y = (-1/2)*x + 1

y = x - 5

And the system of inequalities:

y > (-1/2)*x + 1

y < x - 5

First, if you look at the first system you can see that we have two non-parallel lines, so that system has only one solution.

Now let's look at the system of inequalities, we can get solutions like:

x = 10

y = 1

1 > (-1/2)*10 + 1 = -4

1 < 10 - 5 = 5

So both inequalities are true, which means that the point (10, 1) is a solution.

And also is the point (11, 1), and (12, 1), and infinite other points.

Then we conclude that the system of inequalities has more solutions than the system of equations.

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The first equation is 5x² - 20x + 27 and the second equation will be y = 3x² + 6x + 15.

It should be noted that an equation simply means a formula that's used to express the equality of two expressions that are given in Mathematics.

It should be noted that before solving the equations, it's important to expand the functions that are squared and then solve accordingly. This will be illustrated below.

The first equation that's given is:

y = 5(x - 2)² + 7

= 5(x - 2)(x - 2) + 7

= 5(x² - 2x - 2x + 4) + 7

= 5(x² - 4x + 4) + 7

= 5x² - 20x + 20 + 7

= 5x² - 20x + 27

The second equation given is illustrated as:

y = 3(x + 1)² + 12

y = 3(x + 1)(x + 1) + 12

y = 3(x² + 2x + 1) + 12

y = 3x² + 6x + 3 + 12

y = 3x² + 6x + 15

In conclusion, writing the equations in form of y = ax² + bx + c will be y = 5x² - 20x + 27 and y = 3x² + 6x + 15.

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Sine rule:

30/sin(17) = x/sin(90)

x sin(90)

30 x sin(90) / sin(17) = x

x = 102.6091086

So, x = 102.6 to the nearest tenth.

Hope this helps!

Answer: B

[tex]x + 2y \leq 4 \textrm{ and } 3x + y \leq 4[/tex]

Step-by-step explanation:

Insert the values of x and y for any point in the heavily shaded region and see if it satisfies both inequalities

We can see that the origin (0,0) is inside the shaded region so use these values because they are the easiest to compute

Plug in x = 0 and y = 0 into the first inequality
0 + 2.0 = 0 which is greater than 5.

So we can eliminate both A and D since they both contain incorrect inequalities

Now, test the second inequality with x = 0 and y = 0

For B we get

3.0 + 0 = 0 which is indeed less than 4

C is not applicable since 0 is not greater-than-equal to 4

Hence B is the correct solution

This can be verified using a graphing tool (see image)

The mean of the scores to the nearest 10th digit will be 74.9.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean.

Then the mean is given as,

Mean = (Total score) / (total student)

The total score will be

Total score = 65 x 8 + 70 x 7 + 75 x 3 + 80 x 8 + 85 x 3 + 90 x 2 + 95 x 2

Total score = 520 + 490 + 225 + 640 + 225 + 180 + 190

Total score = 2470

The total number of students will be

Total student = 8 + 7 + 3 + 8 + 3 + 2 + 2

Total student = 33

Then the mean will be

Mean = 2470 / 33

Mean = 74.85 ≈ 74.9

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The probability of catching a bass in the lake is given by:

Probability = probability 1 × probability 2

Since the forest ranger caught a fish from his prior fishing experience, we can infer that he has a probability of catching a bass in a lake:

Probability 1 = Number of fish caught/Number of tries

By using a special type of bait, he should calculate the probability of catching a fish as follows:

Probability 2 = Number of fish caught/Number of tries

Therefore, the probability of catching a bass in the lake is given by:

Probability = probability 1 × probability 2

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The angles ∠1 ≅ ∠4 since the line BD bisects ∠ABC, AD║ BC, and AB ║ CD. This is obtained by using the angle bisector theorem, alternate interior angles, and the transitive property of congruence.

Transitive property:

If ∠a and ∠b are congruent and ∠b and ∠c are congruent, then ∠a and ∠c are also congruent.

I.e., If ∠a ≅ ∠b and ∠b ≅ ∠c, then ∠a ≅ ∠c.

The angles bisector theorem states that the ray or line which bisects the angle divides the angle into two equal parts.

I.e., If line BD bisects the angle ∠ABC, then ∠B = ∠B1 + ∠B2

(where ∠B1 = ∠B2)

The line BD bisects ∠ABC, AD║BC, and AB║CD

The line BD bisects ∠ABC. So,

∠B = ∠3 + ∠4

According to the angle bisector theorem, ∠3 ≅ ∠4.

Since AD║BC and AB║CD, the alternate angle are congruent.

I.e., ∠3 ≅ ∠1

Thus, by the transitive property of congruence,

∠1 ≅ ∠4

Hence proved.

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Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

The factored expression of the polynomial is (4 - x)(5 + x)

The polynomial expression is given as;

20 - x - x^2

Expand the expression

20 - 5x + 4x - x^2

Factorize the expression

5(4 - x) + x(4 - x)

Factor out 4 - x

(4 - x)(5 + x)

Hence, the factored expression of the polynomial is (4 - x)(5 + x)

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Answer:

blue dot have value of -6 in y inverse axis