The point P(12, 16) is on the terminal side of θ. Evaluate tan θ.

4 2/3 = 14/3

15 = 15/1

14/3 * 15/1 = 14*15=210, 3*1 = 3

210/3 = 70

answer is 70

The system of equations has exactly one solution, but it is located at (16,15), not (–8, 3), (–4, 3) or any other points. So, none of the provided options are true.

The task is to identify the statement that is correct about the system of equations –3x + 4y = 12 and x – y = 1. To discover this, we must solve the system which consists of these two linear equations. Adjust equation two to be in the same format as equation one by adding y to both sides which gives x = y + 1. Substitute it into the first equation: -3(y + 1) + 4y = 12, which simplifies to -3y - 3 + 4y = 12, giving y = 15. Substitute y = 15 to the second equation, it gives us x = 16. Hence, none of the provided solutions is correct, because the system has exactly one solution at (16,15).

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Answer:

F( x) = 0.35 x + 55

Answer:

Step-by-step explanation:

First, let's find the equation of the line.

The slope is defined by

[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

Where we are gonna use points (2,0) and (9,7).

[tex]m=\frac{7-0}{9-2}=\frac{7}{7}=1[/tex]

Then, we use the point-slope formula to find the equation.

[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-2)\\y=x-2[/tex]

So, if David's bill came to $66 after coupon, it means [tex]y=66[/tex].

Replacing this value in the equation, we have

[tex]y=x-2\\66=x-2\\x=66+2\\x=68[/tex]

Therefore, the price without coupon is $68.

Answer:

the value of x= 4.5

Step-by-step explanation:

If x varies directly with y and x = 3.5 when y = 14

x varies directly with y , so equation is x= ky

where k is the constant of proportionality

x = 3.5 when y = 14, use the given values and find out k

Plug in the given values in x=k y

3.5= k * 14

Divide by 14 on both sides

0.25= k

So the value of k = 0.25

Now find out x when y= 18

x= ky

x= 0.25 * 18= 4.5

Answer: 2.661

Step-by-step explanation:

A P E X

Answer :- Yes the two triangles are similar because there are two pairs of congruent corresponding angles.

Explanation:-

In Δ ABC

∠A=30° , ∠C=65 °

By angle sum property of triangle

∠A + ∠B + ∠C= 180°

⇒∠B= 180°-∠A-∠C=180°-30°-65°=85°

⇒∠B=85°

Now in ΔABC and ΔDEF

∠A=∠D=30° and ∠B=∠E=85°

⇒ there are two pairs of congruent corresponding angles.

So by AA-similarity criteria

ΔABC ≈ ΔDEF

Answer:

Yes, because there are two pairs of congruent corresponding angles.

Step-by-step explanation:

Two triangles ABC and DEF are given .

The measure of angles in triangle ABC are:

m<A=30°,m< C=65°,

m<B= 180-(30+65)=85°(measure of sum of angles in any triangle is 180°)

In triangle DEF the measure of the angles are :

m<D=30°,m<E=85°,m<F=180-(30+85)=65°(sum of angles in a triangle add to 180°)

In triangles ABC and DEF,

< A=<D=30°

<B=<E=85°

<C=<F=65°

The two triangles are similar by AAA property.

8 squared = 64

so

(x/4)*2 = 64

divide x/4 by 2 to get x/2=64

 now multiply both sides by 2 to get x=128

x = 128

Final answer:

The simplified expression of 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³ is -4m³ + 13p³ - 5p, which is option d).

Explanation:

To simplify the expression 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³, we need to combine like terms.

Like terms have the same variable raised to the same power.

In this case, terms with p raised to the third power can be combined, and terms with m raised to the third power can also be combined, as well as the terms with just p.

Now the expression is simplified to -4m³ + 13p³ - 5p, which corresponds to option d).

An equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0) is [tex]\bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]

The correct answer is option (A)

"The standard form of equation of ellipse with center (0, 0) is, [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]

"The vertices of the standard ellipse [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex] are [tex](\pm a,0)[/tex] "

"The foci of the standard ellipse [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex] are [tex](\pm c,0)[/tex], where [tex]c^{2} =a^{2}- b^{2}[/tex] "

For given question,

The center of the ellipse is at the origin.

Using the standard form of equation of the ellipse,

[tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]

A vertex at (13, 0)

⇒ (a, 0) = (13, 0)

⇒ a = 13

And a focus at (12, 0).

⇒ (c, 0) = (12, 0)

⇒ c = 12

We know, [tex]c^{2}= a^{2}- b^{2}[/tex]

Now, we find the value of b i.e., minor axis

[tex]\Rightarrow 12^{2} =13^{2}- b^{2}\\\\\Rightarrow b^2=169-144\\\\ \Rightarrow b^2=25\\\\\Rightarrow b=\pm 5[/tex]

Substituting these values in the standard form of equation of ellipse with center (0, 0),

[tex]\Rightarrow \frac{x^2}{a^2} +\frac{y^2}{b^2} =1\\\\\Rightarrow \bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]

Therefore, an equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0) is [tex]\bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]

The correct answer is option (A)

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The solution would be like this for this specific problem:

Given:

{0, 1, 2, 3, 4}
Success = 2, 3, and 4

Solution:

Success = 3 numbers
Sample = 5

= 3 / 5

= .6

= .6 * 100%

= 60%

So, the estimated probability of a success based from the randomly generated list of numbers being used to simulate an event is 60%.

To add, the measure of the likelihood that an event will occur is called probability and it is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty.

Answer:

56

Step-by-step explanation:

The statistic that the coach should study is mean or the average score of the two teams. If the coach wants to know if football players who warm up before a game will score more points than those who don't warm up. He will break the team up into two groups and make sure each player gets equal time on the field. He will then count how many points each player makes during the game. After counting them, add the scores of the group that he divided and then divided it by the number of player in that group to get an average score on teams that warm up or do not warm up before the game. 

Answer:

The answer has a positive 5 and 33.

Step-by-step explanation:

I used a calculator.

The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]

Simplify the expression, then we have

⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]

⇒ [(x + 4)(x + 5) - 7(x + 3)] / [7(x + 5)]

⇒ [x² + 9x + 20 - 7x - 21] / [7(x + 5)]

⇒ (x² + 2x - 1) / 7(x + 5)

The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.

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Her mistake is in the first step, she wrote the equation incorrectly.

A general quadratic equation:

ax^2 + bx + c = 0

has the solutions:

x = (-b ± √(b^2 - 4ac))/(2a)

In this case, the equation is:

y = x^2 - 8x + 7

And what Joyce writes in each step is:

Step 1:

x = (-8 ± √(8^2 - 4*1*7))/(2*1)

Then we can already see the mistake.

Notice that in the given equation, we have:

b = -8

And the general solution has:

x = (-b ± √(b^2 - 4ac))/(2a)

-b would be equal to 8, then what Joyce must have written here is:

x = (8 ± √((-8)^2 - 4*1*7))/(2*1)

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