Mathematics High School

If tan theta = -4/3 in quadrant II, what is cos theta?

A. -4/5

B. 3/5

C. 4/5

D. -3/5

Answers

Answer 1
[tex]\bf tan(\theta)=\cfrac{opposite}{adjacent}\qquad \qquad cos(\theta)=\cfrac{adjacent}{hypotenuse}\\\\ -------------------------------\\\\ tan(\theta )=-\cfrac{4}{3}\cfrac{\leftarrow opposite}{\leftarrow adjacent}[/tex]

notice, the tangent has a negative sign, for that to happen, either the numerator or denominator must be negative, who may that be? well, we know the angle is in the II quadrant, on the II quadrant, the cosine or x-coordinate (adjacent side) is negative, so, is the adjacent.

that means, the opposite side is 4 and the adjacent one is -3

well, let's find the hypotenuse

[tex]\bf \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{(-3)^2+4^2}\implies c=\sqrt{25}\implies \boxed{c=5}\\\\ -------------------------------\\\\ cos(\theta)=\cfrac{adjacent}{hypotenuse}\qquad \qquad cos(\theta )=\cfrac{-3}{5}[/tex]

bear in mind that, the square root will give use +/- roots, however, in the case of the hypotenuse, is just the radius unit, thus is never negative.
Answer 2

Answer:


The answer is:

D. -3/5

Related Questions

If 9<15mx-8<27, where m is a positive constant, what is the possible range of values of 8/3 -5mx?

Answers

9<15mx-8<27
Divide the all by 3
3<5mx-8/3<9
After that times all by -1
-3<8/3-5mx<-9
Answer:

The possible range of [tex]\dfrac{8}{3}-5mx[/tex] is:

                   (-9,-3) i.e. [tex]-9<\dfrac{8}{3}-5mx<-3[/tex]

Step-by-step explanation:

We are given a set of inequalities of the form:

[tex]9<15mx-8<27[/tex]

Now when we divide all of the inequality by 3 we get that:

[tex]\dfrac{9}{3}<\dfrac{15mx}{3}-\dfrac{8}{3}<\dfrac{27}{3}\\\\i.e.\\\\3<5mx-\dfrac{8}{3}<9[/tex]

Now when we multiply the inequality by -1 then the sign of the inequality gets interchanged.

i.e.

[tex]-3>-(5mx-\dfrac{8}{3})>-9\\\\i.e.\\\\-3>\dfrac{8}{3}-5mx>-9[/tex]

i.e.

[tex]-9<\dfrac{8}{3}-5mx<-3[/tex]

Hence, the possible range of [tex]\dfrac{8}{3}-5mx[/tex] is:

    (-9,-3) i.e. between -9 and -3 with -9 and -3 excluded from the range.

what is the area of a triangle that has a base of 8 yd and height of 3 yd

Answers

area = 1/2 x b x h

1/2 x 8 x 3 = 12

area is 12 square yards

Choose the equation of the horizontal line that passes through the point (-5,9).

Y= -5

Y= 9

X= -5

X= 9

Answers

b because y = 9 is true and in order to be horizontal the equation must have a y in it

Answer: Y=9 Just because the guy above me said so.

What are the constants in the expression below? 12x -3.7 -8y +1/3

Answers

Anything without a variable in front.

In other words, the constants are -3.7 and 1/3 

A sandwich shop offers ham, turkey, tuna, chicken salad, and roast beef. It has Swiss, American, and provolone cheese. You can order a sandwich on white, wheat, or rye bread. If a person orders a sandwich and chooses a meat, cheese, and bread at random, how many sandwich choices are there?

Answers

5 different meats

3 different cheeses

3 different breads

5x3x3 = 15*3 = 45

 there are 45 choices

Final answer:

The sandwich shop offers a total of 45 different sandwich combinations based on the given options of meats, cheeses, and breads. Each sandwich consists of one type of each category.

Explanation:

The question asked is related to the concept of combinations in mathematics. It gives a variety of choices for making a sandwich - 5 types of meats, 3 types of cheeses, and 3 types of breads. Assuming that each sandwich will have one meat, one cheese, and one type of bread, we can calculate the total combinations by multiplying the number of options in each category together. Combinations are used when the order of selection does not matter.

So, the total number of sandwich combinations would be 5 (meats) * 3 (cheeses) * 3 (breads) = 45 different sandwich choices.

Learn more about Sandwich Combinations here:

https://brainly.com/question/29295486

#SPJ12

In a certain? country, the true probability of a baby being a girlgirl is 0.4640.464. among the next fivefive randomly selected births in the? country, what is the probability that at least one of them is a boyboy??

Answers

This is a binomial probability:

ⁿCₓ(p)ˣ(q)ⁿ⁻ˣ

P(girls) = 0.464 ; P(NO girls) = 1-0.464 = 0.536
Then:
p(girls) = 0.464
q(NO girls) = 0.536
n = 5
Probability(NO GIRLS) = ⁵C₀(0.464)⁰(0.536)⁵⁻⁰
⁵C₀ = 1; (0.464)⁰ = 1

Probability(NO GIRLS) = (0.536)⁵
Probability(NO GIRLS) = 0.04424

Probability(at LEAST one boy) = 1 - 0.04424 = 0.955

Final answer:

Calculate the probability of at least one boy being born among the next five randomly selected births in a country where the true probability of a baby being a girl is known.

Explanation:

The probability of at least one boy being born among the next five randomly selected births can be calculated by finding the probability of all girls being born and subtracting it from 1. This is known as the complement rule in probability.

Step-by-step calculation:

Find the probability of all births being girls: 0.4645 = 0.00532Subtract this from 1 to get the probability of at least one boy: 1 - 0.00532 = 0.99468

Therefore, the probability of at least one of the next five births being a boy in this country is approximately 0.99468 or 99.468%.

Can someone factor this problem for me?

Answers

your factored answer will be

(3x-4y) (x-5y)

hope this helps
3x² - 19xy + 20y² = 
3x² - 4xy - 15xy + 20y² = 
x(3x-4y) - 5y(3x-4y) = 
(3x-4y)(x-5y)

What are the solutions of the equation 9x^4 – 2x^2 – 7 = 0? Use u substitution to solve.

Answers

[tex]9x^4 - 2x^2 - 7 = 0 \\ \text{substitution: } x^2=t, \ \ t\ \textgreater \ 0\\ 9t^2-2t-7\ \textgreater \ 0 \\ D=b^2-4ac=(-2)^2-4*9*(-7)=4+252 = 256 \\ t_{1,2}= \frac{-bб \sqrt{D} }{2a}= \frac{2б 16 }{18} \\ t_1=- \frac{14}{18} \ \ \ \ \O \\ \boxed{t_2=1} \\ \\x^2=1\\x=б \sqrt{1} \\ x=б1 [/tex]

Answer: x=-1, x=1

An amusement park charges $9.00 for admission $4.00 per ride. Write an equation that gives the cost in dollars as a function of number of rides

Answers

a $9 fee plus $4 oper ride

let T = total cost

X= number of rides

T=9.00+4.00X

With y = the total cost, and x = # of rides, we get the equation y=4x+9 where 9 is the fixed cost of the admission, the 4 is the cost per ride.

I'm not sure what this is exactly?

Answers

[tex]_nC_k=_nC_{n-k}[/tex]

so
[tex]_{100}C_{98}=_{100}C_{100-98}=_{100}C_2=4,950[/tex]
[tex]\bf _nC_r=\cfrac{n!}{r!(n-r)!}\\\\\\ _{100}C_2=\cfrac{100!}{2!(100-2)!}\qquad\qquad _{100}C_{98}=\cfrac{100!}{98!(100-98)!}[/tex]

(a)at davidson's bike rentals, it costs $14 to rent a bike for 3 hours. how many dollars does it cost per hour of bike use?

Answers

It costs about $4.66

What is the slope of the line that is perpendicular to the line whose equation is 2x + y = 4.

Answers

peprendicular lines have slopes that multiply to get -1

y=mx+b
m=slope

2x+y=4
minus 2x
y=-2x+4
slope is -2

-2 times what=-1
what=-1/-2
what=1/2

the slope is 1/2

Answer:

The slope of the line that is perpendicular to the line whose equation is 2x + y = 4 is   [tex]\frac{1}{2}[/tex].

Step-by-step explanation:

Given : Equation is 2x + y = 4.

To find : What is the slope of the line that is perpendicular to the line.

Formula used : equation of line y =  m[tex]m_{1}[/tex] x + c.

Solution : We have 2x + y = 4.

Rearranging the equation :  y = - 2x + 4.

On comparing   m[tex]m_{1}[/tex] = - 2.

Condition for  slope of the line that is perpendicular to the line :

      m[tex]m_{1}[/tex] × m[tex]m_{2}[/tex] = -1 .

So,       -2 × m[tex]m_{2}[/tex] = -1 .

On dividing by 2 both we get ,

  m[tex]m_{2}[/tex] = [tex]\frac{1}{2}[/tex].

Therefore, The slope of the line that is perpendicular to the line whose equation is 2x + y = 4 is   [tex]\frac{1}{2}[/tex].

Use the graph below to answer the following question:

graph of parabola going through negative 4, 4, negative 1, 5, and 1, negative 1

What is the average rate of change from x = –4 to x = 1?

–3
–1
0
1

Answers

Average change = (final y - start y ) / (final x - start x ) = (-1-4)/(1-(-4) ) = -5/5=-1!

Second one!

Your answer should be

-1


Don't forget to MARK BRAINLIEST!! <3 :)

Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a). x^2 – 3x + 6 and x-9

Part 1. Show all work using long division to divide your polynomial by the binomial.

Part 2. Show all work to evaluate f(a) using the function you created.
x – 9 = 0
x = 9
First take the original expression. x^2 - 3x + 6
Fill in the blanks.
9^2-3(9)+6
81-27+6
81-21
60

Answers

Part 1. In the long division, you find the greatest factor that could divide the dividend. You do this one at a time per term. Then, you find the product of the factor and the divisor, then subtract it from the dividend. The cycle goes on until all the terms are divided:
               x  +  6
            ----------------------------
    x - 9 |  x² - 3x + 6
             - x² - 9x
             -------------------
                       6x + 6
                     - 6x - 54
                     --------------
                           60

There quotient is (x+6) with a quotient of 60.

Part 2. The steps shown are from the concept of Factor and Remainder Theorem. When you substitute x=a to the function, the answer could determine if x=a is a factor or not. If the answer is zero, then x=a is a factor. If not, the answer represents the remainder.

Therefore, x = 9 is not a factor of the given function. It yields a remainder of 60 which coincides with Part 1.

If the value of 2x3 is 2, then what is the value of x?

Answers

If the expression is 2*x*3, x must be 1/3 in order to cancel out the 3 which would leave the 2.
x = 1, -1 .
____________________________
  Given:  2x³ = 2 ;  Divide each side of the equation by "2" ;

               [2x³] / 2 = 2 / 2 ; 

    to get:   x³ = 1 ;  

Now, take the "cube root" of EACH SIDE of the equation; to isolate "x" on ONE SIDE of the equation; and to solve for "x" ;

   ∛(x³)  = ∛1  ;

      x = 1, -1 .
____________________________________________

A skier is trying to decide whether whether or not to buy a season ski pass. A daily pass cost 67. A season ski pass costs 350. The skier would have to rent skis with either pass for 25 per day. How many days would the skier have to go skiing in order to make the season pass cost the same as the daily pass option.

Write an expression using words to represent the cost of a daily pass. Write the algebraic expression. Write an expression using words to represent the cost of a season pass. Write the algebraic expression
How can you compare the cost of a daily pass with the cost of a season pass algebraically?

Answers

The total cost of using daily passes is the number of days the skier goes skiing times 67.
The algebraic expression for this is 67n (n=the number of days).

 The cost of a season pass is 350. If the number of days the skier skis times 67 equals 350 then the cost for both options is the same.
67n=350
n=350/67

 n=5.22

If the skier goes skiing 5 times or fewer using daily passes costs less. If the skier goes skiing 6 times or more a season pass costs less.

Can someone please explain me this

Answers

sure for a 4*2 is 8 so 3*2 = x aka x=6
u r dealing with proportions...

x/8 = 3/4
cross multiply...multiply denominator of one, by numerator of the other and vice-versa
(4)(x) = (3)(8)
4x = 24
x = 24/4
x = 6

sub it back into the proportion
6/8 = 3/4.....notice that if u reduce 6/8, it equals 3/4. Proportions are nothing but equivalent fractions.
====================
2/5 = x/40
cross multiply
(5)(x) = (40)(2)
5x = 80
x = 80/5
x = 16

check..
2/5 = 16/40... u can aslo cross multiply to check
(2)(40) = (5)(16)
80 = 80...correct
===================
1/8 = x/12
cross multiply
(8)(x) = (1)(12)
8x = 12
x = 12/8
x = 3/2

check...
1/8 = (3/2) / 12
cross multiply
(8)(3/2) = (12)(1)
24/2 = 12
12 = 12 (correct)
=================
I am gonna leave u with the last one....u can do this :)




What is the projection of (4 4) onto (-7 3) open study?

Answers

Write the two vectors as
[tex]\vec{a} =4\vec{i} + 4\vec{j}[/tex]
[tex]\vec{b} = -7\vec{i}+3\vec{j}[/tex]

By definition, the projection of [tex]\vec{a}[/tex] onto [tex]\vec{b}[/tex] is
[tex]a_{b} = \vec{a} . \frac{\vec{b}}{|b|} [/tex]

[tex]\hat{b} = \frac{\vec{b}}{|b|} = \frac{1}{\sqrt{49+9}} (-7\vec{i}+3\vec{j})=(-7\vec{i}+3\vec{j})/\sqrt{58}[/tex]

Therefore
[tex]\vec{a} . \vec{b} = -28+12=-16[/tex]
[tex]a_{b} = -16/\sqrt{58} = -2.1[/tex]

Answer:
The projection of (4 4) onto (-7 3) is -2.1.

If EFGH is a parallelogram, then ___________________.

Answers

B. It might be, as a square and a rectangle might be as well.

Answer:  The correct option is (B) It might be a rhombus.

Step-by-step explanation:  Given that EFGH is a parallelogram. We are to select the correct statement for EFGH.

A PARALLELOGRAM is a quadrilateral whose opposite sides are parallel and equal, opposite angles are equal, the sum of the interior angles is 360 degree.

A RHOMBUS is a particular type of parallelogram, where all the sides are equal and diagonals bisect each other perpendicularly.

Therefore, we can say that every rhombus is a parallelogram, but every parallelogram is not a rhombus.

Therefore, the parallelogram EFGH might be a rhombus.

So, option (B) is correct.

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -5 - 5 cos θ

Answers

It is symmetric about the x-axis

Answer:

The graph of polar equation is symmetric about the x-axis.

Step-by-step explanation:

The given polar equation is

[tex]r=-5-5\cos \theta[/tex]

If [tex](r,\theta)[/tex] and [tex](r,-\theta)[/tex] lie on the graph then the graph of polar equation is symmetric about the x-axis.

Substitute [tex]\theta=-\theta[/tex] in the given equation.

[tex]r=-5-5\cos (-\theta)[/tex]

Cosine is an even function.

[tex]r=-5-5\cos \theta[/tex]                   [tex][\cos (-\theta)=\cos (\theta)][/tex]

Point [tex](r,-\theta)[/tex] lies on the graph, therefore the graph of polar equation is symmetric about the x-axis.

A gumball machine contains 230 gumballs of 5 different colors: 64 red, 22 blue, 32 orange, 26 green, and the rest white. The machine dispenser randomly selects one gumball. What is the probability that the gumball dispensed is white?
72/115 ≈ 63%
32/115 ≈ 28%
43/115 ≈ 37%
86/100 = 86%

Answers

The probability is the statistics of your chances of an event occurring which signifies a part of a whole. You express the probability in either fraction form or in percentage. The numerator would be number of all possibilities, while the denominator is the number of all events. In this case, the numerator is the number of white gumballs, while the denominator is the number of all gumballs available.

To solve for the number of white gumballs, you subtract all the other balls to the total. 

Number of white balls = 230 - 64 red - 22 blue - 32 orange - 26 green
Number of white balls = 86

Thus,
Probability of white ball = 86/230 = 43/115 or 37%

Answer:

43/115 or 37%

Step-by-step explanation:

If you have 5 distinct positive integers and the median is 17 and the mean is 12, what are the 5 numbers? How do you know for sure? Can you find 5 distinct positive integers with a median of 17 and a mean of 10? What whole-number means will work for 5 distinct positive integers with a median of 17? What medians will work for 5 distinct positive integers with a mean of 12?

Answers

1) Part 1: 5 distinctive positive integers with median 17 and mean 12

If the median is  17, that means that one number is 17, two numbers are greater than 17 and two numbers are less than 17.

Remember that the five numbers are distint positive integers.

If the mean is 12, that means that the sum of the five numbers is 12 * 5 = 60

The minimum values could be 1 and 2, with which the partil sum of the three first terms would be 1 + 2 + 17 = 20.

So, the partial sum of the two greater terms is 60 - 20 = 40.

That leads to these possibilities:

1, 2, 17, 18, 22
1, 2, 17, 19, 21

If the two smaller terms are 1 and 3, the possibilities are:

1, 3, 17, 18, 21
1, 3, 17, 19, 20.

If the two smaller terms are 2 and 3, the only possibility is:

2, 3, 17, 18, 20

If the smaller terms are 1 and 4, the only possibility is

1, 4, 17, 18, 20

Other options are:

1, 5, 17, 18, 19

2, 4, 17, 18, 19

You can realize that you cannot use other set of numbers.

2) Part 2: five distinctive numbers with median 17 and mean 10.

sum of the five numbers = 5 * 10 = 50

Given that 17 + 18 + 19 = 54, it is not possible to find those five distinctive numbers.

3) Part 3: What whole-number means will work for 5 distinctive integers with a median of 17.

=>the minimum whole-number means that will work is the whole number equal or greater than [1+2+17+18+19] / 5 = 11.4 => 12.

So, the whole-number means that will work are 12 or more.

4) Part 4. What medians will work for 5 distinctive positive integers with a mean of 12:

total sum = 5*12 = 60.

The smallest median would be 3, because the smaller values would be 1 and 2. The highest median would be.

Also, 1 + 2 = 3 => the median + the two greatest values = 60 - 3 = 57.

=> 18, 19, 20

=> 1, 2,18, 19, 20

So the median has to be between 3 and 18, inclusive.

a group of college students are volunteering for help the homeless during spring break. They are putting the finishing touches on a house they built. Working alone, irina can paint a certain room in 4 hours. Paulo can paint the same room in 3 hours. write an equation that can be used to find how long it will take them working together to paint the room. how many hours will it take them to paint the room?
A.12 hours
B.1.71 hours
C.0.14 hours
D.3.5 hours

Answers

Let us say that x is the total amount of time it will take if they work together.

From the given statement above, we know that the rate of Irina working alone is 1 job / 4 hours. While that of Paulo is 1 job / 3 hours. Where 1 job indicates to the job of completely painting the room. So adding the two rates would result in 1 job / x hours. Therefore:

1 / 4 + 1 / 3 = 1 / x

Multiplying both sides with 12 x:

(1 / 4 + 1 / 3 = 1 / x) 12 x

3 x + 4 x = 12

7 x = 12

x = 1.71 hours

So working together, they can paint the room for 1.71 hours.

 

Answer:

B

Compulsive hand washing often increases in frequency because it relieves feelings of anxiety. This best illustrates the impact of

Answers

reinforcement on compulsive behaviors

in order to use a normal distribution to calculate confidence intervals for p, what conditions on np and nq need to be satisfied? Select one: a. n and q must be integers b. n must be positive c. np>10 and nq<0 d. np and nq must be > 5

Answers

Final answer:

To use normal distribution for calculating confidence intervals for proportion p, both np and nq must be greater than or equal to 5.

Explanation:

In order to use a normal distribution to calculate confidence intervals for a population proportion p, the conditions on np and nq need to be such that both np ≥ 5 and nq ≥ 5. These conditions are necessary because they ensure that the shape of the binomial distribution is similar to that of a normal distribution, which allows for the approximation of the binomial distribution by the normal distribution. When performing a hypothesis test of a single population proportion, it is imperative that the sample data meet these conditions to ensure a valid test. Therefore, the correct answer to the question is d. np and nq must be > 5.

How smart are you? A lady walk in the store and steals $100 bill from the register without the owners knowledge. She comes back 5 mins later and buys $70 worth of goods with the $100 bill. The owner gives her $30 in change. How much did the owner lose?

Answers

-100-70+100-30=-100

I included the value of the merchandise that she "purchased", so the owner lost $100 in total value.
The owner lost $100 ($ 30 cash and $70 worth of goods)

think about it...she stole $ 100.....but then the $ 100 was given back to the store....so she basically exchanged the $ 100 for $ 70 worth of goods and $ 30 cash.

How do you factor the quadratic equation 36^2= 25

Answers

This calculates to 1,296 = 25 which it is NOT.
Do you have the question typed correctly?

In a certain set of numbers, 12.5 is 1.5 units of standard deviation above the mean, and 8.9 is 0.5 units of standard deviation below the mean. what is the mean of the set?

Answers

Standard deviation is a statistical tool that is used to measure the spread or variation of a certain set of data. It is the square root is the variance. It determines the difference of each data relative to the mean. To calculate the mean, we do as follows:

12.5 is 1.5 units of standard deviation
So the value for the upper standard deviation would be:
12.5 - 1.5 = 11

8.9 is 0.5 units of standard deviation
So the value for the lower standard deviation would be:
8.9 + 0.5 =  9.4

So, the range of the standard deviation would be about 11 - 9.4 = 1.6 units. The mean would be located at the center of this range which is 0.8 from each of the values. Therefore, the mean would be 11-0.8 = 10.2.

What is the sum of the first five terms of a geometric series with a1 = 10 and r = 1/5?

Answers

a₁ = 10
r = 1/5

Sum of GP = a₁(1-rⁿ)/(1-r), where a₁ = 1st term; n= rank and r = common ratio

Sum = 10[1-(1/5)⁵] /(1-1/5)
Sum = 10(1-1/3250)/(4/5)
Sum = 1562/125

Answer: 12.496

Step-by-step explanation:

The formula to find the sum of geometric progression is given by :-

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

Given : The first term : [tex]a_1=10[/tex]

Common ratio = [tex]r=\dfrac{1}{5}=0.2[/tex]

Then , the sum of first five terms of a geometric series is given by :-

[tex]S_5=\dfrac{10(1-(0.2)^5)}{1-0.2}=12.496[/tex]

Hence, the sum of the first five terms of given geometric series =12.496

The variable Z is directly proportional to X, and inversely proportional to Y. When X is 10 and Y is 4, Z has the value 47.5.

What is the value of Z when X = 13, and Y = 10

Answers

Because Z is directly proportional to X and inversely proportional to Y, therefore
[tex]Z=k( \frac{X}{Y}),\\k=constant [/tex]

When X=10 and Y=4, Z=47.5.
Therefore
k(10/4) = 47.5
   2.5k = 47.5
        k = 19.

That is,
[tex]Z= \frac{19X}{Y} [/tex]

When X=13 and Y=10, obtain
Z = (19*13)/10 = 24.7

Answer: 24.7
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