If cos A = 3/√13 and angle A is not in quadrant I, determine the exact value of sin A.

Answers

Answer 1

To determine the exact value of sin A we get -2/√13

What is determinant?

the determinant is a scalar of value that is a function of to the entries of a square matrix. It is allows characterizing of some properties of to the matrix and the linear map of represented by the matrix.

It is a scalar value which is associated with the square matrix.

Sol-Cos A =3/√13

angle A is not in quadrant I

So angle A is in quadrant IV

Thus,

Sin A =-√(√13)^2-3^2/√13

=-√13-9/√13

=-√4/√13

=-2/√13

Thus the answer is -2/√13.

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Related Questions

15 = a/3 - 2
what is a?

Answers

Answer: a is 51

Step-by-step explanation:

Hope this help.

Answer:

a==51

Step-by-step explanation:

15=a/3-2

a/3-2+2=15+2

a/3=17

a=17*3

a=51

To find the area of a shape region:Find the area of the entire region:Fimd the area of the unshaded region(s)Subtract the area of the unshape region from the area of the entire region

Answers

IN order to find the area of the shaded region, proceed as follow:

calculate the area of the right triangle:

A = b·h/2

A = (21 yd)(34 yd)/2 = 357 yd²

next, calculate the area of the circle:

A' = π r²

A' = (3.1415)(7 yd)² = 153.93 yd²

next, subtract the area of the circle to the area of the rectangle:

AT = A - A' = 357 yd² - 153.93 yd²

AT = 203.07 yd²

Hence, the area of the shaded region is 203.07 yd²

1) K thinks of a number, then doubles the number ,and then multiplies the result by 3 . If her final number is 65 more than her original number, then what was her original number?

Answers

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The original number is 13.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 2x = 4 is an equation.

We have,

Let the number be K.

K thinks of a number, then doubles the number, and then multiplies the result by 3.

This can be written as:

(2 x k) = 2k ____(1)

3 x (2k) = 6k ____(2)

If her final number is 65 more than her original number can be written as:

6k = 65 + k _____(3)

From (3) we get,

6k = 65 + k

Subtract k on both sides.

6k - k = 65 + k - k

5k = 65

Divide both sides by 5.

5k / 5 = 65 / 5

k = 13

Thus,

The original number is 13.

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5. How would you solve the system of equations y = 5x + 1 and -2x + 3y =-10 ? What is the solution? *

Answers

SOLUTION:

Step 1:

In this question, we are given the following:

Solve the system of equations y = 5x + 1 and -2x + 3y =-10 ?

What is the solution?

Step 2:

The solution to the systems of equations:

[tex]\begin{gathered} y\text{ = 5x + 1 -- equation 1} \\ -2x\text{ + 3y = -10 -- equation 2} \end{gathered}[/tex]

check:

Given y = -4 , x = -1

Let us put the values into the equation:

y = 5x + 1 and -2x + 3y = -10

[tex]\begin{gathered} y\text{ = 5x + 1} \\ -4=5(-1)\text{ + 1} \\ -4=-5+1 \\ -4\text{ = - 4 (COR}\R ECT) \end{gathered}[/tex][tex]\begin{gathered} -2x+3y\text{ = -10} \\ -2(-1)+3(-4)_{}_{} \\ 2-12=-10\text{ (COR}\R ECT) \end{gathered}[/tex]

CONCLUSION:

The solution to the system of equations are:

[tex]\begin{gathered} \text{x = -1} \\ y=-4 \end{gathered}[/tex]

Brandon's car used 10 gallons to travel 310 miles. At what rate does the car use gas, in miles per gallon?On the double number line below, fill in the given values, then use multiplication or division to find the missing value.

Answers

Given:

At 10 gallons, the car is able to cover 310 miles.

Find: At 1 gallon, the car can travel ____ miles.

Solution:

First, let's fill in the number line with the given values.

To solve for the question mark at 1 gallon, simply divide 310 by 10.

[tex]310\div10=31[/tex]

Hence, the car uses gas at 31 miles per gallon.

Help pleas Which statement best completes the diagram.

Answers

The statement which best completes the cause and effect diagram is that: A. British leaders limit the ability of colonists to expand westward.

What is a cause and effect graphic organizer?

A cause and effect graphic organizer is also referred to as cause and effect diagram and it can be defined as a type of chart which highlights and shows the relationship between two things, phenomenon, or events in which an occurrence of one (cause) typically leads to the occurrence of another (effect).

During the late 18th to mid 19th centuries, the United States of America began to grow westward and this led to the emigration of Native American tribes who had in this geographical region for thousands of years before the arrival of European colonists.

Consequently, conflict developed between them which was known as "The French and Indian War" and this caused British leaders to limit the ability of many European colonists to continue expanding westward.

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Complete Question:

Which statement best completes the diagram?

A. British leaders limit the ability of colonists to expand westward.

B. British merchants refuse to buy raw materials from the colonies.

C. British military forces are ordered to leave North America.

D. British leaders end policies that strictly controlled the colonies.

a line with a slope of 1/3 and containing the point (-4,7)

Answers

An equation of line with a slope of 1/3 and containing the point (-4,7) is

y = 1/3 x + 25/7

In this question, we have been given

slope (m) = 1/3

and a point (-4, 7)

We need to find an equation of a line with a slope of 1/3 and containing the point (-4,7)

Using the formula for the slope-point form of equation of line,

y - y1 = m(x - x1)

y - 7 = 1/3(x + 4)

y - 7 = (1/3)x + 4/3

y = (1/3)x + 4/3 + 7

y = 1/3 x + 25/7

Therefore, an equation of line with a slope of 1/3 and containing the point (-4,7) is y = 1/3 x + 25/7

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divide and Simplify 7/5 ÷7/9

Answers

What we have is a fractional division, this is following expression

[tex]\frac{(\frac{7}{5})}{(\frac{7}{9})}[/tex]

For this procedure, it says to multiply the top and bottom ends to get the numerator, and the middle numbers to get the denominator

[tex]\frac{7\cdot9}{7\cdot5}=\frac{9}{5}[/tex]

In conclusion after splitting and simplifying this, the answer is 9/5

1a. 100 foot-long rope is cut into 3 pieces.The first piece of rope is 3 times as long asthe second piece of rope. The third piece istwice as long as the first piece of rope.What is the length of the longest piece ofrope?

Answers

To solve the exercise, it is easier to make a drawing, like this

So, you have

[tex]\begin{gathered} z=3y \\ y=y \\ x=2z \\ z+y+x=100 \end{gathered}[/tex]

Now solving

[tex]\begin{gathered} x=2z \\ x=2(3y) \\ x=6y \end{gathered}[/tex][tex]\begin{gathered} z+y+x=100 \\ 3y+y+6y=100 \\ 10y=100 \\ \frac{10y}{10}=\frac{100}{10} \\ y=10\text{ ft} \end{gathered}[/tex][tex]\begin{gathered} x=6y \\ x=6(10) \\ x=60\text{ ft} \end{gathered}[/tex][tex]\begin{gathered} z=3y \\ z=3(10) \\ z=30\text{ ft} \end{gathered}[/tex]

Therefore, the length of the longest piece is 60ft.

Triangle Inequality TheoremDetermine if a triangle can be formed with the given lengths. If so, classify the triangle by its angle.YESorNO

Answers

Given:-

[tex]7,20,12[/tex]

To find:-

Wheather the given sides form a valid triangle.

So now let,

[tex]A=7,B=20,C=12[/tex]

To check we use the condition,

[tex]A+B>C,B+C>A,C+A>B[/tex]

Substituting the values we get,

[tex]7+20>12,20+12>7,12+7>20[/tex]

In the above condition 12+7>20 is wrong.

So the condition fails and the given sides doesnt form a triangle.

Enter your solution as an ordered pair, with no spaces and with parentheses. OR the answer could be: Infinitely many OR No Solution

Answers

Given the equation system:

[tex]\begin{gathered} 1)y=4x \\ 2)3x+2y=55 \end{gathered}[/tex]

The first step is to replace the first equation in the second equation

[tex]3x+2(4x)=55[/tex]

With this, we have a one unknown equation. Now we can calculate the value of x:

[tex]\begin{gathered} 3x+8x=55 \\ 11x=55 \\ \frac{11x}{11}=\frac{55}{11} \\ x=5 \end{gathered}[/tex]

Now that we know the value of x, we can determine the value of y, by replacing x=5 in the first equation

[tex]\begin{gathered} y=4x \\ y=4\cdot5 \\ y=20 \end{gathered}[/tex]

This system has only one solution and that is (5,20)

J is the midpoint of CT if CJ=5x-3 and JT=2x+21 find CT

Answers

Since J is the midpoint of the CT segment, then:

[tex]\begin{gathered} CJ=JT \\ 5x-3=2x+21 \end{gathered}[/tex]

Now, you can solve the equation for x:

[tex]\begin{gathered} 5x-3=2x+21 \\ \text{ Add 3 from both sides of the equation} \\ 5x-3+3=2x+21+3 \\ 5x=2x+24 \\ \text{ Subtract 2x from both sides of the equation} \\ 5x-2x=2x+24-2x \\ 3x=24 \\ \text{ Divide by 3 from both sides of the equation} \\ \frac{3x}{3}=\frac{24}{3} \\ x=8 \end{gathered}[/tex]

Replace the value of x into the equation for segment CJ or segment JT to find out what its measure is. For example in the equation of the segment CJ:

[tex]\begin{gathered} CJ=5x-3 \\ x=8 \\ CJ=5(8)-3 \\ CJ=40-3 \\ CJ=37 \end{gathered}[/tex]

Finally, you have

[tex]\begin{gathered} CJ=37 \\ CJ=JT \\ 37=JT \\ \text{ Then} \\ CT=CJ+JT \\ CT=37+37 \\ CT=74 \end{gathered}[/tex]

Therefore, the measure of the segment CT is 74.

PLEASE HELP ASAP! What is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola?

Answers

A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.

What is hyperbola?A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set. A hyperbola is made up of two mirror images of one another that resemble two infinite bows.These two sections are known as connected components or branches. A series of points in a plane that are equally spaced out from a directrix or focus is known as parabolas. The difference in distances between a group of points that are situated in a plane and two fixed points—which is a positive constant—is what is referred to as the hyperbola.

Therefore, a hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.

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Please help me don't understand

Answers

Answer:

x=13

Step-by-step explanation:

50+3x=89

89-50=3x

39=3x

13=x

1+——>1/12 write. Fraction to make each number sentence true, answer I got is 1/1

Answers

c) Set x to be the number we need to find; therefore, the inequality to be solved is

[tex]\begin{gathered} 1+x>1\frac{1}{2}=1+\frac{1}{2}=\frac{3}{2} \\ \Rightarrow1+x>\frac{3}{2} \\ \Rightarrow-1+1+x>-1+\frac{3}{2} \\ \Rightarrow x>\frac{1}{2} \end{gathered}[/tex]

Therefore, any number greater than 1/2 (greater, not equal to) satisfies the inequality; particularly 1/1=1>1/2. Thus, 1/1 is a possible answer

Martin and Isabelle go bowling. Each game costs $10, and they split that cost. Martin has his own bowling shoes, but Isabelle pays $3 to rent shoes.Which graph shows a proportional relationship? Explain why.

Answers

We have the following:

Martin's graph is good and correct, although it is not totally straight, but the relationship that it keeps is totally proportional.

On the other hand, Isabelle's graph, although it is totally straight, is wrong, because she must start from 3, which is the rental value of the shoes, and her graph starts at 0, therefore it is wrong, despite of which shows a proportional relationship.

Therefore the correct answer is Martin's graph.

Answer:

Step-by-step explanation:

A genetic experiment with
peas resulted in one sample of offspring that consisted of 447 green peas and 169 yellow peas.
a. Construct a 90% confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
a. Construct a 90% confidence interval. Express the percentages in decimal form.
L s p< (Round to three decimal places as needed.)
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
O
No, the confidence interval includes 0.25, so the true percentage could easily equal 25%
L
O Yes, the confidence interval does not include 0.25, SO the true percentage could not equal 25%

Answers

Using the z-distribution, it is found that:

a. The 90% confidence interval to estimate of the percentage of yellow peas is: (34.04%, 41.58%).

b. The correct option is: Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%.

What is a confidence interval of proportions?

The bounds of a confidence interval of proportions is given according to the equation presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the parameters are described as follows:

[tex]\pi[/tex] is the sample proportion.z is the critical value of the distribution.n is the sample size, from which the estimate was built

The confidence level is of 90%, hence the critical value is z = 1.645, using a z-distribution calculator.

The values of the sample size and of the estimate are given as follows:

[tex]n = 447, \pi = \frac{169}{447} = 0.3781[/tex]

Hence the lower bound of the interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3781 - 1.645\sqrt{\frac{0.3781(0.6219)}{447}} = 0.3404[/tex]

The upper bound is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3781 + 1.645\sqrt{\frac{0.3781(0.6219)}{447}} = 0.4158[/tex]

As a percentage, the interval is given as follows: (34.04%, 41.58%).

The confidence interval does not contain 0.25, hence the true percentage would not be equal to 25%, contradicting the expectation.

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ratio problems that I am struggling with

Answers

7 out of every 500 Americans are aged 13-17 years generation are vegetarian

Thus the ratio of the vegetarian is 7 : 500

In a group of 350,

Let x be the number of people who are vegetarian

So, the ratio out of 350 who are vegetarian are : x : 350

SInce the ratio is same so:

[tex]\begin{gathered} 7\text{ : 500=x:250} \\ \frac{7}{500}=\frac{x}{250} \\ \text{ Simplify for x,} \\ x=\frac{7}{500}\times250 \\ x=\frac{7}{2} \\ x=3.5 \\ x\approx4 \end{gathered}[/tex]

So, the number of people who are vegetarian out of 350 people is 4 people

A box contains 6 red pens, 4 blue pens, 8 green pens, and some black pens. Leslie picks a pen and returns it to the box each time. the outcomes are: number of times a red pen is picked: 8number of times a blue pen is picked: 5 number of times a green pen is picked: 14number of times a black pen is picked: 3Question: if the theoretical probability of drawing a black pen is 1/10, how many black pens are in the box?

Answers

We have:

x = total pens

n = number of black pens

so:

[tex]x=6+4+8+n=18+n[/tex]

and for black pen:

[tex]\begin{gathered} \frac{1}{10\text{ }}=0.1\text{ (probability)} \\ \text{then} \\ \frac{n}{18+n}=0.1 \\ n=0.1(18+n) \\ n=1.8+0.1n \\ n-0.1n=1.8+0.1n-0.1n \\ 0.9n=1.8 \\ \frac{0.9n}{0.9}=\frac{1.8}{0.9} \\ n=2 \end{gathered}[/tex]

answer: 2 black pens

Please help with this question

Answers

The average velocities of the stone are: i) 12.96 m / s, ii) 13.20 m / s, iii) 13.20 m / s, iv) 13 m / s. The instantaneous velocity is approximately equal to 13 meters per second.

How to find the average velocity and the instantaneous velocity of a stone

The average velocity (u), in meters per second, is the change in the height (h), in meters, divided by the change in time (t), in seconds. And the instantaneous velocity (v), in meters per second, is equal to the average velocity when the change in time tends to zero.

a) Then, the average velocities are determined below:

Case i)

u = [f(1.05) - f(1)] / (1.05 - 1)

u = (18.748 - 18.1) / 0.05

u = 12.96 m / s

Case ii)

u = [f(1.01) - f(1)] / (1.01 - 1)

u = (18.232 - 18.1) / 0.01

u = 13.20 m / s

Case iii)

u = [f(1.005) - f(1)] / (1.005 - 1)

u = (18.166 - 18.1) / 0.005

u = 13.20 m / s

Case iv)

u = [f(1.001) - f(1)] / (1.001 - 1)

u = (18.113 - 18.1) / 0.001

u = 13 m / s

The fourth option offers the best estimation for the instantaneous velocity at t = 1 s. Then, the instantaneous velocity is approximately equal to 13 meters per second.

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helpppppppppppppppppppppppppppppppppppppp

Answers

Answer:

[tex]\large \text{$f^{-1}(x) = 3x -6$}[/tex]

Graphs attached

Step-by-step explanation:

Your inverse function is correct. So not sure what additional information you need

I am not familiar with the graphing tool you have been provided with. My graph is attached. I used a free online graphing tool

A 35-foot wire is secured from the top of a flagpole to a stake in the ground. If the stake is 1 feet from the base of the flagpole, how tall is the flagpole?

Answers

The figure for the height of flagpole, wire and ground is,

Determine height of the pole by using the pythagoras theorem in triangle.

[tex]\begin{gathered} l^2=b^2+h^2 \\ (35)^2=(14)^2+h^2 \\ 1225-196=h^2 \\ h=\sqrt[]{1029} \\ =32.078 \\ \approx32.08 \end{gathered}[/tex]

Thus, height of the flagpole is 32.08 feet.

Attached is a photo of my written question, thank you.

Answers

Given:

The function is,

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

Explanation:

Determine the function for f(x + h).

[tex]\begin{gathered} f(x+h)=-2(x+h)^2-(x+h)+3 \\ =-2(x^2+h^2+2xh)-x-h+3 \\ =-2x^2-2h^2-4xh-x-h+3 \end{gathered}[/tex]

Determine the value of expression.

[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-2x^2-2h^2-4xh-x-h+3-(-2x^2-x+3)}{h} \\ =\frac{-2h^2-4xh-h}{h} \\ =-2h-4x-1 \end{gathered}[/tex]

So exprression after simplification is,

-2h - 4x - 1

why are whole numbers rational numbers?

Answers

Answer:

Step-by-step explanation:

A whole number can be written as a fraction that has a denominator of 1. So, the whole numbers 18, 3, and 234 can be written as the rational numbers 18/1, 3/1, and 234/1.

So, all whole numbers are rational numbers, but not all rational numbers are whole numbers.

Please can I have the answer for number 12?Thanks a lot

Answers

Given:

length of the piece of string = 3/4 inches

length of the piece that we need = 1/8 inches

The number of smaller piece that we can get from the original piece of string can be calculated using the formula:

[tex]\text{Number }of\text{ smaller piece = }\frac{length\text{ of original piece}}{length\text{ of smaller piece}}[/tex]

Applying this formula:

[tex]\begin{gathered} \text{Number of smaller piece = }\frac{3}{4}\div\text{ }\frac{1}{8} \\ \end{gathered}[/tex]

If the number of pieces is represented as n:

[tex]n\text{ = }\frac{3}{4}\div\text{ }\frac{1}{8}[/tex]

Answer:

find the area of the circle with a circumference of 30π. write your solution in terms of π

Answers

we know that

the circumference of a circle is giving by

[tex]C=2\pi r[/tex]

we have

C=30pi

substitute

[tex]\begin{gathered} 30\pi=2\pi r \\ \text{simplify} \\ r=\frac{30}{2} \\ r=15\text{ units} \end{gathered}[/tex]

Find the area of the circle

[tex]A=\pi r^2[/tex]

substitute the value of r

[tex]\begin{gathered} A=\pi(15^2) \\ A=225\pi\text{ unit\textasciicircum{}2} \end{gathered}[/tex]the area is 225π square units

the sum of interior angle measures of a polygon with n sides is 2340 degrees. find n15

Answers

the measure of each angle will be 2340/n then if n=15 the measure of each one of the angles will be 2340/15=156 degrees

6. Line 1 passes through the points (1,4) and (-2,5). Line 2 passes through the points (1,0) and (0,3). What is true about Line 1 and Line 2? (2 points) (A) (B) They are perpendicular. They are parallel. They both decrease. They both increase. (C) (D)

Answers

First, calculate the slope (m) of both lines.

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Line 1:

Point 1 = (x1,y1) = (1,4)

Point 2 = (x2,y2) = (-2,5)

Replacing:

[tex]m=\frac{5-4}{-2-1}=\frac{1}{-3}=-\frac{1}{3}[/tex]

Line 2:

Point 1 = (x1,y1) = (1,0)

Point 2 = (x2,y2) = (0,3)

[tex]m=\frac{3-0}{0-1}=\frac{3}{-1}=-3[/tex]

Lines to be parallel must have the same slope, and to be perpendicular, they must have negative reciprocal slope.

None of the slopes are equal or negative reciprocal. SO, A and B are false-

Now, for the increase/ decrease

We can see that both lines have a negative slope, so they both decrease.

Correct option: C

Find a function of the form y = A; A * sin(kx) + C or y = A * cos(kx) + C whose graph matches this one:I don’t understand how my answer is wrong

Answers

Recall that the graph of the cosine function is:

Now, notice that the given graph is the above graph but with a midline

[tex]y=1,[/tex]

and amplitude equal to 4. The frequency is also different.

Therefore, the equation of the function given in the graph is:

[tex]y=4cos(\frac{\pi}{5}x)+1.[/tex]Answer: [tex]y=4cos(\frac{\pi x}{5})+1.[/tex]

Solve the inequality and write the solution using:
Inequality Notation:

Answers

The solution for the given inequality is x >7.

Inequality

It is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).

The solutions for inequalities can be given by: a graph in a number line or numbers.

For solving this exercise, it is necessary to find a number and a graph solution for the given inequality.

The given inequality is [tex]1-\frac{6}{7}x < -5[/tex] . Then,

Move the number 1 for the other side of inequality and simplify.

[tex]-\frac{6}{7}x < -5 -1\\ \\ -\frac{6}{7}x < -6[/tex]

Multiply both sides by -1 (reverse the inequality )

[tex]-\frac{6}{7}x < -6 *(-1)\\ \\ \frac{6}{7}x > 6[/tex]

Solve the inequality for x

[tex]\frac{6}{7}x > 6\\ \\ 6x > 42\\ \\ x > \frac{42}{6} \\ \\ x > 7[/tex]

You should also show the results t > 7 in a number line. Thus, plot the number line. See the attached image.