Sketch a right triangle corresponding to the trigonometric function of the acute angle 8. Then find the exact values of the other five trigonometric functions of
Solution:
Given:
[tex]cot(\theta)=2[/tex]Using the trig ratio of cot;
[tex]\begin{gathered} cot\theta=\frac{1}{tan\theta} \\ tan\theta=\frac{opposite}{adjacent} \\ Hence, \\ cot\theta=\frac{adjacent}{opposite} \\ cot\theta=\frac{2}{1} \\ adjacent=2 \\ opposite=1 \end{gathered}[/tex]The hypotenuse is gotten using the Pythagoras theorem;
[tex]\begin{gathered} h^2=2^2+1^2 \\ h^2=4+1 \\ h^2=5 \\ h=\sqrt{5} \end{gathered}[/tex]Thus, the sketch of the right triangle is;
[tex]\begin{gathered} Thus, \\ opposite=1 \\ adjacent=2 \\ hypotenuse=\sqrt{5} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} sin\theta=\frac{opposite}{hypotenuse} \\ sin\theta=\frac{1}{\sqrt{5}} \\ sin\theta=\frac{1}{\sqrt{5}}\times\frac{\sqrt{5}}{\sqrt{5}}=\frac{\sqrt{5}}{5} \\ sin\theta=\frac{\sqrt{5}}{5} \end{gathered}[/tex][tex]\begin{gathered} cos\theta=\frac{adjacent}{hypotenuse} \\ cos\theta=\frac{2}{\sqrt{5}} \\ cos\theta=\frac{2\sqrt{5}}{5} \end{gathered}[/tex][tex]\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ tan\theta=\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} csc\theta=\frac{1}{sin\theta} \\ csc\theta=\frac{1}{\frac{\sqrt{5}}{5}} \\ csc\theta=\sqrt{5} \end{gathered}[/tex][tex]\begin{gathered} sec\theta=\frac{1}{cos\theta} \\ sec\theta=\frac{1}{\frac{2\sqrt{5}}{5}} \\ sec\theta=\frac{\sqrt{5}}{2} \end{gathered}[/tex]Fill in the blank so that the resulting statement is true.To divide x³+4x²-3x+6 by x-2 using synthetic division, the first step is to write
Answer:
Explanation:
Given the polynomial:
[tex]x^3+4x^2-3x+6[/tex]To divide the polynomial by the linear function x-2 using synthetic division, first, set the linear function equal to 0 and solve for x:
[tex]x-2=0\implies x=2[/tex]The result is written outside the line as shown below:
Next, write the coefficients of the polynomial inside as shown above:
help please thank you
Problem
Express the number 0.00005348 in terms of a power of 10
Solution
For this case we just need to count the number of zeros before the first number different from 0 and if we do this we have 5 numbers before 5 so we can write the number like this:
5.348 x10^-5
[tex]5.348x10^{-5}[/tex]Consider the quadratic equation below. 412 - 5= 3 + 4 Determine the correct set-up for solving the equation using the quadratic formula.
Given:
[tex]4x^2-5=3x+4[/tex]To find:
The correct setup for solving the equation using the quadratic formula.
Explanation:
It can be simplified as,
[tex]\begin{gathered} 4x^2-5-3x-4=0 \\ 4x^2-3x-9=0 \end{gathered}[/tex]Here,
[tex]\begin{gathered} a=4 \\ b=-3 \\ c=-9 \end{gathered}[/tex]Using the quadratic formula,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Plugging in the values, we get
[tex]x=\frac{-(-3)\pm\sqrt{(-3)^2-4(4)(-9)}}{2(4)}[/tex]Final answer:
The correct choice is D.
x y w z is a quadrilateral with verticals W 1 - -4 - x - -4
Midpoint formula
We are given the points
X=(-4,2)
Y=(1,-1)
Z=(-2,-3)
W=(1,-4)
They define the quadrilateral XYWZ
To find the intersection of the diagonals, we can use the Midpoint Formula
This formula gives us the midpoint of a segment defined by points (x1,y1) (x2,y2) as follows:
[tex]xm=\frac{x1+x2}{2},\text{ ym=}\frac{y1+y2}{2}[/tex]We must identify the opposite points of the quadrilateral and calculate the midpoint between them
Segment XY:
Midpoint of XY:
[tex]x_m=\frac{-4+1}{2}=-\frac{3}{2}[/tex][tex]y_m=\frac{2-1}{2}=\frac{1}{2}[/tex]Midpoint of ZW:
[tex]x_m=\frac{1-2}{2}=-\frac{1}{2}[/tex][tex]y_m=\frac{-3-4}{2}=-\frac{7}{2}[/tex]Finally, find the midpoint of the opposite sides' midpoints:
[tex]x_c=\frac{-\frac{3}{2}-\frac{1}{2}}{2}=-1[/tex][tex]y_c=\frac{\frac{1}{2}-\frac{7}{2}}{2}=-\frac{3}{2}[/tex]The intersection of the diagonals is the point (-1,-3/2)
The table represents a quadratic function. Write an equation of the function in standard form.
x -3 -1 1 3
y 0 -12 -16 -12
y =
The standard form of the quadratic equation is given as follows:
y = x² - 2x - 15.
What is a quadratic equation?A quadratic equation is modeled according to the following rule:
y = ax² + bx + c.
From the given table, when x = -3, y = 0, hence the first equation is given by:
(-3)²a + (-3)b + c = 0
9a - 3b + c = 0.
When x = -1, y = -12, hence the second equation is given by:
-12 = a(-1)² + b(-1) + c
a - b + c = -12.
When x = 1, y = -16, hence the third equation is given by:
-16 = a(1)² + b(1) + c
a + b + c = -16.
Then the system of equations to find the coefficients is given as follows:
9a - 3b + c = 0.a - b + c = -12.a + b + c = -16.Using a calculator, the solution to the system is:
a = 1, b = -2, c = -15.
Hence the equation is given by:
y = x² - 2x - 15.
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A nurse is given instructions to give a nitroglycerin drip at 10 mcg/minute. The nitroglycerin is mixed at 50 mg per 500 mL. The flow rate needs to be in mL/hr. Complete parts a through c.
a) What is the dosage in milligrams per minute (mg/min)?
b) What is the dosage in milligrams per hour, mg/hr?
c) How many milliliters per hour, ml/hr, should be administered?
The Dosage in milligrams per min, mg/min : 0.01mg / min
The Dosage in milligrams per hour, mg/hr : 0.6mg/hr
The dosage available in milliliters per hour, ml/hr: 6ml/hr
What is Dosage ?
A dosage is a predetermined amount of a drug, food, or pathogen that is administered as a single unit. The dose increases with the amount administered. In medicine, doses are most frequently calculated for substances.
Given,
Dose(mcg) = 10mcg/min
Dose available = 50mg
Volume of dose available = 500ml
a) The dosage in milligram per minute will be:
= 10mcg / 1000mcg
= 0.01mg / min
b) The dosage in milligrams per hour, mg/hr :
= 10mcg x 60min / 1000mcg
= 0.6mg/hr
c) By dosage formula we can write:
= OxV / A
Where,
O = Dose ordered
V = Volume of dose available
A = Dose available
So that we know,
Dose ordered (mg) = 0.6 mg
Volume of dose available (mL) = 500 mL
Dose available (mg) = 50 mg
= 0.6 x 500 / 50
= 6ml/hr
Hence,
The Dosage in milligrams per min, mg/min : 0.01mg / min
The dosage in milligrams per hour, mg/hr : 0.6mg/hr
The dosage available in milliliters per hour, ml/hr: 6ml/hr
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A line that passes through (3, 1) and (0, -3) A line that passes through (-1,-5) and (2, 4)
The equation of a line is given by
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x1,y1) is a point on the line.
The slope is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Fisrt line:
In this case the slope is
[tex]\begin{gathered} m=\frac{-3-1}{0-3} \\ =\frac{-4}{-3} \\ =\frac{4}{3} \end{gathered}[/tex]The the equation is
[tex]y-1=\frac{4}{3}(x-3)[/tex]Second line:
In this case the slope is
[tex]\begin{gathered} m=\frac{4-(-5)}{2-(-1)} \\ =\frac{4+5}{2+1} \\ =\frac{9}{3} \\ =3 \end{gathered}[/tex]Then the equation is
[tex]\begin{gathered} y-(-5)=9(x-(-1)) \\ y+5=9(x+1) \end{gathered}[/tex](1)/(3)(12+x)=-8(6-x)
In the diagram below, assume that all points are given in polar coordinates. Determine the rectangular coordinates for each point. Visually check your answers to ensure they make sense.(r,θ)=(6.9,0.7) corresponds to (x,y)=(r,θ)=(7.2,1.5) corresponds to (x,y)=(r,θ)=(8,3.4) corresponds to (x,y)= (r,θ)=(4.7,3π/2) corresponds to (x,y)=
"What happens if the slope is equal to zero? Provide an example of two points that would be on a line with a zero slope."
The line which is parallel to X-axis or which is drawn horizontally in the cartesian plane has its slope equal to zero.
As per the question statement, we are supposed to tell the significance of a zero sloped line. Before solving it, we need to know the formula for calculating the slope i.e., m = tanθ, where θ is the inclination angle of the line wrt X-axis.
Slope zero means m = 0 i.e., tanθ = 0 i.e., θ = 0 degrees
Hence a line having NO inclination or in simple words, is parallel to X-axis is known as a zero sloped line.
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What is 7/9 ÷ 2/3 please help
Solution:
Given;
[tex]\frac{7}{9}\div\frac{2}{3}[/tex]Change the division sign to multiplication and reciprocate the other side;
[tex]\frac{7}{9}\times\frac{3}{2}=\frac{7}{6}[/tex]ANSWER:
[tex]\frac{7}{6}=1\frac{1}{6}[/tex]Ty ordered a storage pod in the shape of a rectangular prism to store some extra things at his house. The storage pod has a length of 16 feet and a height of 8 feet. If the volume of the storage pod is 896 cubic feet, what is the width of the storage pod?
Answer:
7 cubic feet
Step-by-step explanation:
so first you do length times height in this case it would be 16 times 8
you get 128 now you divide 896 by 128 and you get an answer of 7.
One way to check is you do length times width times height.
So 16 × 7 × 8 =896
Answer: 7 feet cubed
what is the value of x in the equation negative x equals 2 - 3x + 6
Given the equation
-x = 2 -3x + 6
To solve this:
Step 1: collect like terms
-x + 3x = 2 + 6
2x = 8
Step 2: Divide both sides by 2
[tex]\begin{gathered} \frac{2x}{2}\text{ =}\frac{8}{2} \\ \\ x=\text{ 4} \end{gathered}[/tex]The value of x = 4
The volume of a spherical balloon with radius 2.6 cm is about 74 cm3. Estimate the volume of a similar balloon with radius 10,4 cm,
To find the volume of a similar ballon with radius 10.4 cm, we will simply take the proportion
Let v be the volume of the similar ballon;
[tex]\frac{74}{v}=\frac{2.6}{10.4}[/tex]Cross -multiply
[tex]2.6v\text{ = 769.6}[/tex]Divide both-side by 2.6
[tex]v=296\operatorname{cm}^3[/tex]5.8. The lifetime in hours of an electronic tube is a random variable having a probability density function given by
f(x)= xe^-x. x>-0
The lifetime in hours of an electronic tube will be of 2 hours.
A probability density function, also known as the density of a continuous random variable, is a function used in probability theory whose value at any given sample (or point) in the sample space can be interpreted as giving a relative likelihood that the random variable's value would be close to that sample. While the absolute likelihood of a continuous random variable taking on any given value is 0, probability density (PDF) at two different samples can be used to infer, in any given draw of the random variable, how much more likely it would be that the random variable would be close to one sample compared to the other sample.
We have,
f(x) = xe^(-x) x>0
= 0 o.w.
Consider,
[tex]E(X) = \int\limits^a_0 {xf} (x)\, dx \\\\E(X) = \int\limits^a_0 {xxe}^{-x} \, dx \\\\E(X) = \int\limits^a_0 {x}^{2}e^{-x} \, dx \\\\E(X) = \int\limits^a_0 {x}^{b-1}e^{-mx} \, dx = \frac{n}{m^{n} } \\\\= 2! = 2[/tex]
Therefore, a tube of this type should last for 2 hours.
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I'll give you brainliest if it's right =D
Which equation shows a proportional relationship between x and y?
A) y = 12x + 1
B) y = 3.5x
C) y = 2
D) y=−4x−6
Answer:
C.
Step-by-step explanation:
The relationship is proportion if y/x is constant.
So it is C because 12/4 = 15/5 = 18/6 = 3.
use the equation 1/4+s=18/20 pls help
The value of (s) that satisfy the given equation → 1/4+s=18/20 is 0.65.
What is equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. There are different types of equation such as - Linear Equations, Radical Equations, Exponential Equations, Rational Equations etc.
Given is the following equation written in variable (s)
1/4 + s = 18/20
We have -
1/4 + s = 18/20
We will solve the given expression using the transpose method -
1/4 + s = 18/20
Shifting (s) to the left hand side and constant numbers to right hand side, and then solving for (s), we get -
s = 18/20 - 1/4
s = 9/10 - 1/4
s = 0.9 - 0.25
s = 0.65
The value of s will be 0.65
Therefore, the value of (s) that satisfy the given equation → 1/4+s=18/20 is 0.65.
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The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one.Is f one-to-one?
A function is called being one-to-one if, for every value of x, there is only one value of y and vice-versa.
If the graph of the function is given, a practical rule to determine if the function is one-to-one is to use the horizontal-line test.
This test is as follows: Imagine you have a horizontal line (maybe a ruler) and you can move it up and down the grid.
If your line touches the graph only once at every vertical position, then your function is one-to-one.
Now if we test our function drawn in blue, we can touch it only once as we move our line up and down, thus:
Is f one-to-one?
Yes
Sarah used the Quadratic Formula to solve the equation x² - 4x - 16 = 0. What should her solutions be?
Answer
x = (2 + 2√5)
OR
x = (2 - 2√5)
Explanation
In order to use the quadratic formula for the general quadratic equation,
ax² + bx + c = 0 is given as
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]For x² - 4x - 16 = 0,
a = 1
b = -4
c = -16
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1\times-16)}}{2(1)} \\ x=\frac{4\pm\sqrt[]{16+64}}{2} \\ x=\frac{4\pm\sqrt[]{80}}{2} \\ \sqrt[]{80}=\sqrt[]{16\times5}=\sqrt[]{16}\times\sqrt[]{5}=4\sqrt[]{5} \\ x=\frac{4\pm\sqrt[]{80}}{2} \\ x=\frac{4\pm4\sqrt[]{5}}{2} \\ x=2\pm2\sqrt[]{5} \\ x=2+2\sqrt[]{5} \\ OR \\ x=2-2\sqrt[]{5} \end{gathered}[/tex]Hope this Helps!!!
Given the sequence -7, -3, 1, 5,What is the explicit formula to represent this sequence?A. a^n= 4n-7B. a^n= -7n+4C. a^n= 5-7nD. a^n= 4n-11
The given sequence is
[tex]-7,-3,1,5[/tex]To find the explicit formula, first, we have to find the difference by subtracting two consecutive terms.
[tex]-3-(-7)=-3+7=4[/tex]As you can observe, the difference is 4.
[tex]d=4[/tex]From the sequence, we observe that the first term is -7.
[tex]a_1=-7[/tex]The formula for arithmetic sequences is
[tex]a_n=a_1+(n-1)d[/tex]Now, let's replace the values we've got.
[tex]a_n=-7+(n-1)\cdot4[/tex]Then, we simplify.
[tex]\begin{gathered} a_n=-7+4n-4 \\ a_n=4n-11 \end{gathered}[/tex]Therefore, the right answer is D.4. Jason can travél 24 miles in hour. What is his average speed in miles per hour?
Answer:
24 miles in 1 hour
speed = distance/time
so 24/1
24 mph (miles per hour) is the speed
hope it helps, mark as brainliest :D
Rewrite the expression as an equivalent exponential expression with a positive exponent.
you can do this I know you can !!!!!
find the value or measure. Assume all lines that appear to be tangent are tangent.m(angle) TUV=
Answer:
Angle TUV = 46 degrees.
Explanation:
In the diagram, angle TUV is the external angle.
The external angle is always half the difference of the internal angles.
Therefore:
[tex]\angle\text{TUV}=\frac{1}{2}(145^0-53^0)[/tex]We simplify to obtain our result.
[tex]\begin{gathered} \angle\text{TUV}=\frac{1}{2}\times92^0 \\ =46^0 \end{gathered}[/tex]The measure of angle TUV is 46 degrees.
What is the sign of -2 to the power of 49
Answer:
negative
Step-by-step explanation:
-2 to the power of odd numbers is negative
to the power of even numbers is positive
Given m∥n, find the value of x
Answer:
x=55
Step-by-step explanation:
2x+6+x+9=180
3x=165
x=55
:]
Answer: x=55
Step-by-step explanation:
Since the lines are parallel, the two angles on the line are supplementary angles.
It means they would add to 180.
1) Set up the equation
(2x+6)+(x+9)=180
2) Combine like terms
3x+15 = 180
3) Move the 15 to the other side to leave x
3x = 180 - 15
3x = 165
4) Set x by itself
x = 165/3
x=55
4) At a farm the ratio of cows to horses was 7: 1. If there were 49 cows at the farm, how
many horses were there?
can you show me step by step on how to answer this problem 11/5 + 23/10 = ?
Answer: 45/10
Explanation:
We want to add
11/5 + 23/10
The first step is to find the lowest common multiple, LCM of the denominators. The LCM of 5 and 10 is 10. We would divide the LCM by each denominator and multiply each numerator by the results. The common denominator of the final fraction would be the LCM. We have
For the first fraction,
10/5 = 2
2 x 11 = 22
For the second fraction,
10/10 = 1
1 x 23 = 23
Thus, the final fraction would be
(22 + 23)/10
= 45/10
Question 10(Multiple Choice Worth 1 points)
(08.01 LC)
Susan wants to conduct a survey to find how much time the students of her school spent eating in a local cafeteria. Which of the following is an appropriate statistical question for this survey?
Who eats at the cafeteria on weekends?
How many students eat in the cafeteria on Mondays?
How many students eat in the cafeteria once a week?
How many hours during the week do you eat in the cafeteria?
Answer:
How many hours during the week do you eat in the cafeteria?
Step-by-step explanation:
since susan wants to find out how much time they are spending, the appropriate question would be the one asking about how many hours (time) they spend in the cafeteria
Batman’s age is 12 less than triple Robin’s age. When you add Batman’s age to Robin’s age, you get 68. How old is Batman and how old is Robin? Show work. Handwritten. Complete Sentence.
Answer: Mr. Bond is gonna be mad at youuuuuuuuuuu.
Step-by-step explanation: But I think Batman is like 40 and robin's like 18. I had problems with this too and I can't rlly give u proof rn. Good luck with the unit testtt.