Express cos -30 as a function of the reference angle.Question 13 options:-cos30cos210cos150cos30
Answers
The reference angle is the angle between the terminal side of the angle and the x axis. It is always positive
We know that cos ( -30) has a reference angle of 30 degrees
The cos is the x direction so cos (30) and cos (-30) will have the same value
cos (-30) = cos (30)
Answer: cos(30)
Related Questions
i need to graph h(x) =4|x+4| +3 using 2 movible points on my graph my graph is only 7 integers long.
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The graph of the function:
h(x) = 4|x + 4| + 3 is shown below
We have the following points (-4.75, 6), (-4, 3), (0, 19), (0.25, 20), (0.75, 22)
Given u=<-3.0,-9.5> and z=<-5.3,5.8>, what is the value of u times s
Answers
u.z = <-15.9, -55.1>
Explanation:Given
u = <-3.0, -9.5> and
z = <-5.3, 5.8>
u.z = <-3.0 * -5.3, -9.5 * 5.8>
= <-15.9, -55.1>
Select the response that best represents the x - intercept
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The points that best represents the x-intercept is E.
This comes from the fact that the x-intercept is the point where the graph cuts the x-axis.
Solve for x.2x - 4x=0OA0,-4OB.0,-2Ос.0,2OD. 2,4PLEASE HELP????
Answers
Given the equation
[tex]2x^2-4x=0[/tex]To get x,
Step 1: Simplify by expanding
[tex]2x(x-2)=0[/tex]Step 2: Find the zeros of the expression
[tex]2x=0\text{ and (x-2)=0}[/tex]so that
[tex]\begin{gathered} 2x=0 \\ x=\frac{0}{2}=0 \\ x=0 \\ \end{gathered}[/tex]and
[tex]\begin{gathered} x-2=0 \\ x=0+2 \\ x=2 \end{gathered}[/tex]Therefore the values of x = 0, 2
Thus, option C is correct
Find the circumference and area of a circle with diameter 6 inches
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Given a circle with d = 6 in.
Circunference:
C = π × d
C = π × 6 in
C = 18.85 in
Area:
A = π × r²
A = π × 3²
A = 28.27 in²
ANSWER
circumference = 18.85 in
area = 28.27 in²
Debra takes classes at both Westside Community College and Pinewood Community College. At Westside,class fees are $98 per credit hour,and at Pinewood, class fees are $115 per credit hour. Debra is taking a combined total of 15 credit hours at the two schools. suppose that she is taking a credit hours at Westside. write an expression for the combined total dollar amount she paid for her class fees.
Answers
Solution
For this case we can create the following notation:
x= number of hours at westside
And we can create the following expression for the total amount of money that she paid like this:
A = 98 x+ 115 (15-x)
A= 98 x + 1725 -115x
A= 1725 - 17 x
After watching some fish 55 feet below the surface of the water, a scuba diver went up 20 feet to explore a coral reef. Use a number line to help you create an equation that shows the location of the coral reef in relation to the water's surface? interpret the sum in the context of the problem
Answers
Option A
The diver was 55feet below the water surface, this is translated to -55 feet since he is below the water surface. Movement down away from the sea surface will be negative but since he moves up to inspect a coral reefm moving up is positive. so it is +20feet in translation
on the numberline = -55+20= -35 feet
so the coral reef is -35 feet above the water surface
A
You see imaginary number I to rewrite the expression below as a complex member simplify all radicals
Answers
Given the below;
[tex]-\sqrt[]{-25}[/tex]We can break this up as shown below;
[tex]\begin{gathered} -\sqrt[]{(-1)\ast(25)} \\ =-(\sqrt[]{-1}\ast\sqrt[]{25}) \end{gathered}[/tex]Remember, that the square root of -1 is i. So let's go ahead and substitute i into our expression;
[tex]\begin{gathered} =-(i\sqrt[]{25)} \\ =-(5i) \\ =-5i \end{gathered}[/tex]Therefore our answer is -5i.
What is the vertex of for the parabola y = x2 - 2kx + 6? k is a constant that is not zero. Write your answer as an ordered pair in terms of k.
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Okay, remember that the x-coordinate of a parabola is given by x = -b/2a. After we find x, we are going to substitute it into the equation and solve for the y-coordinate. Let's do it:
x=-(-2k)/2(1)=2k/2=1k=k
Replacing x=1 in the equation:
y=(k)²-2k(k)+6=k²-2k²+6=-k²+6
Finally we obtain the following ordered pair: (k, -k²+6)
The graph of fAx) = 4^x was shifted S unitsdown to form the graph of b What is theequation of
Answers
Correct option is C, i.e. 4^x-5.
Given:
A graph of f(x) = 4^x is given.
Find:
We have to find the function whose graph is given by shifting the original graph by 5 units,
Explanation:
we can make the graph of all the functions as given in options and find the function whose graph is matched with the transformed graph.
So,correct option is C.
Completely stuck on this question
Answers
Answer:
I am not certain I think it's 223
can you use both the quotient and product rule to find this derivative? if you can, show it please
Answers
You should apply both properties of derivative, quotient and product. Remember that:
Anya is wrapping gift boxes in paper. Each gift box is a rectangular prism. The larger box has a length, width, and height twice as large as the smaller box. Which statement shows the relationship between the surface areas of the gift boxes?A. The larger gift box has a surface area 2 times as large as the smaller gift box.B. The larger gift box has a surface area 4 times as large as the smaller gift box.C. The larger gift box has a surface area 6 times as large as the smaller gift box.D. The larger gift box has a surface area 8 times as large as the smaller gift box.thank you ! :)
Answers
The surface area of a rectangular prism is calculated using the formula:
[tex]\begin{gathered} SA=2LW+2LH+2WH \\ or \\ SA=2(LW+LH+WH) \end{gathered}[/tex]Let us assume that this is the surface area of the smaller box.
Now, let's represent the surface area of the bigger box by doubling the dimensions of the smaller box.
[tex]SA_{big}=2(2L\cdot2W+2L\cdot2H+2W\cdot2H)[/tex]Let's simplify this by factoring out the common factors.
[tex]\begin{gathered} SA_{b\imaginaryI g}=2(2L\cdot2W+2L\cdot2H+2W\cdot2H) \\ \\ SA_{b\imaginaryI g}=2\cdot2\cdot2(L\cdot W+L\cdot H+W\cdot H) \\ \\ SA_{big}=4\cdot2(LW+LH+WH) \\ \\ SA_{big}=4SA \end{gathered}[/tex]So the answer is option B (The larger gift box has a surface area 4 times as large as the smaller gift box).
Complete the table for the properties of each quadrilateral
Answers
Step 1
State properties of each diagram by construction.
Find the value of 3y-4 given that 2y-6=8Simplify your answer as much as possible
Answers
Given:
[tex]2y-6=8[/tex]is given expression
Required:
We need to find the value of
[tex]3y-4[/tex]Explanation:
First simplify the given expression
[tex]\begin{gathered} 2y-6=8 \\ 2y=14 \\ y=7 \end{gathered}[/tex]now put the value of y in reauired
[tex]3y-4=2*7-4=21-4=17[/tex]Final answer:
Required value is 17
Find the x- and y- intercepts of the equationH(x)=2x-1Enter answer as points (a,b)
Answers
Given the function
[tex]H(x)=2x-1[/tex]To find the x-intercept, set H(x)=0 and solve for x, as shown below
[tex]\begin{gathered} H(x)=0 \\ \Rightarrow2x-1=0 \\ \Rightarrow2x=1 \\ \Rightarrow x=\frac{1}{2} \\ \Rightarrow(\frac{1}{2},0)\to\text{ x-intercept} \end{gathered}[/tex]As for the y-intercept, set x=0 and find H(0)
[tex]\begin{gathered} H(0)=2(0)-1=-1 \\ \Rightarrow(0,-1)\to\text{ y-intercept} \end{gathered}[/tex]The answers are (1/2,0)->x intercept and (0,-1)-> y-intercept
Solve the system by substitution. -10x + 4y = -18 x — у Submit Answer
Answers
You have the following system of equations:
-10x - 4y = -18
x = y
In order to solve the previous equation, replace x = y into the first equation, and solve for y, just as follow:
.10(y) - 4y = -18
-10y - 4y = -18 simplify left side
-14y = -18 divide by -14 both sides
y = 18/14
consider x = y:
x = y = 18/14
Solve the following system of linear equations using elimination. 5x+3y=30 3x+3y=18
Answers
Given the following System of equations:
[tex]\begin{cases}5x+3y=30 \\ 3x+3y=18\end{cases}[/tex]You can solve it using the Elimination Method. The steps are shown below:
1. You can multiply the first equation by -1
2. Add both equations.
3. Then solve for the variable "x".
Then:
[tex]\begin{gathered} \begin{cases}-5x-3y=-30 \\ 3x+3y=18\end{cases} \\ ----------- \\ -2x=-12 \\ \\ x=\frac{-12}{-2} \\ \\ x=6 \end{gathered}[/tex]4. Substitute the value of "x" into any original equation:
[tex]\begin{gathered} 3x+3y=18 \\ 3(6)+3y=18 \end{gathered}[/tex]5. Finally, solve for the variable "y". This is:
[tex]\begin{gathered} 18+3y=18 \\ 3y=18-18 \\ 3y=0 \\ y=0 \end{gathered}[/tex]The solution is:
[tex]\begin{gathered} x=6 \\ y=0 \end{gathered}[/tex]Find the value of X. Then find the measure of each labeled angle.X=20;the labeled angles are 80 and 100 degrees X=20; both labeled angles are 90 degreesX=30; both labeled angles are 120 degreesX=30;both labeled angles are 150 degrees
Answers
Notice that the two given angles are generated by a transversal crossing a pair of parallel lines; therefore, those two angles are consecutive interior angles, and they are supplementary. Thus,
[tex]\begin{gathered} 5x+4x=180\degree \\ \Rightarrow9x=180\degree \\ \Rightarrow x=20\degree \\ Therefore \\ \Rightarrow4x=80\degree \\ and \\ 5x=100\degree \end{gathered}[/tex]Hence, the answer is x=20°, the labeled angles are 80°, and 100°, the first option.
19. For the simple interest loan whose terms are given below, find the principal required to reach the given future value at the end of the specified time. Future value: $9000 Interest rate: 3.2% Time: 5 years Principal: $
Answers
We will use the following formula:
[tex]PV=\frac{FV}{(1+i/12)^{12n}}[/tex][tex]undefined[/tex]Question 9: Identify the co-vertices. *A. (-3, 4) and (-3, -2)B. (0, 1) and (-6, 1)C. (1, 1) and (-7, 1)D. (4, -3) and (-2, -3)
Answers
The general equation for a hyperbola is
[tex]\frac{(y-h)^2}{b^2}\text{ + }\frac{(x-k)^2}{a^2}\text{ = 1}[/tex]The equation we are considering is a hyperbola with the following parameters:
[tex]\begin{gathered} (k,\text{ h) = (-3 , 1)} \\ a^2\text{ = 9 } \\ \text{a = 3} \\ b^2\text{ = 16} \\ b\text{ = 4} \end{gathered}[/tex]The co-vertices can be obtained by locating the vertices along the x-axis
[tex]\begin{gathered} (-3\text{ + 3, 1) and (-3 -3 , 1)} \\ (0,\text{ 1) and (-6 , 1)} \end{gathered}[/tex]This corresponds to option B
a ball is thrown from an initial 5 feet with an initial upward 29 ft per second in the balls height H in feet after T seconds is given by the followingh=5+29t-16t^2find all the values of t for which the balls height is 17 ft round all your answers tk the nearest hundredth.
Answers
Answer:
t=0.64s and t=1.17s
Explanation:
The function that models the height of the ball is given below:
[tex]h(t)=5+29t-16t^2[/tex]When the ball's height is 17 feet, we have:
[tex]\begin{gathered} 17=5+29t-16t^2 \\ 0=-17+5+29t-16t^2 \\ -16t^2+29t-12=0 \end{gathered}[/tex]We solve the quadratic equation derived above for the values of t.
We use the quadratic formula.
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]In our own equation: a=-16, b=29, c=-12
[tex]\begin{gathered} t=\dfrac{-29\pm\sqrt[]{29^2-4(-16)(-12)}}{2(-16)} \\ =\dfrac{-29\pm\sqrt[]{841-768}}{-32} \\ =\dfrac{-29\pm\sqrt[]{73}}{-32} \end{gathered}[/tex]Therefore, we have:
[tex]\begin{gathered} t=\dfrac{-29+\sqrt[]{73}}{-32}\text{ or }t=\dfrac{-29-\sqrt[]{73}}{-32} \\ t=0.6392\text{ or t=1}.1733 \\ t=0.64\text{ or t=1}.17\text{ (to the nearest hundredth)} \end{gathered}[/tex]The values of t for which the ball's height is 17 ft are 0.64 seconds and 1.17 seconds.
The ratio of red jelly beans to blue jelly beans is 5 to 7. If there are 49 bluejelly beans, how many red jelly beans are there? *
Answers
Solution
Part a
For this case we can create the following ratio:
[tex]\frac{5red}{7blue}=\frac{x}{49blue}[/tex]And then we can solve for x and we got:
[tex]x=49\cdot\frac{5}{7}=35\text{red}[/tex]Part b
For this case we can do the following:
[tex]\frac{2\text{inches}}{100mi}=\frac{3.5inches}{x}[/tex]Solving for x we got:
[tex]x=\frac{3.5\cdot100}{2}=175mi[/tex]What is the accumulated value of the money is compounded monthly?
Answers
Given: An investment of $20000 for 6 years at 5.5%.
Required: To determine the accumulated value of the money is compounded monthly.
Explanation: The formula for compound interest is-
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where n is the number of times, interest is compounded in a year. Here we have-
[tex]\begin{gathered} P=20000 \\ n=12 \\ t=6 \\ r=0.055 \end{gathered}[/tex]Substituting the values into the formula as-
[tex]A=20000(1+\frac{0.055}{12})^{12\times6}[/tex]Further solving-
[tex]A=\text{\$}27,798.40[/tex]Final Answer: The accumulated value of the money is $27,798.40
A 8. B 3 y B' 10 N X C 8 C' E E! 9 6 D' Find the value of x. O . Not enough information. 2 O 63 O 5 Previous
Answers
Given:
The two similar polygons are given, whose sides are proportional.
[tex]\frac{E^{\prime}D^{\prime}}{ED}=\frac{A^{\prime}E^{\prime}}{AE}=\frac{A^{\prime}B^{\prime}}{AB}=\frac{B^{\prime}C^{\prime}}{BC}=\frac{C^{\prime}D^{\prime}}{CD}[/tex]To find the value of x.
consider,
[tex]\begin{gathered} \frac{E^{\prime}D^{\prime}}{ED}=\frac{A^{\prime}E^{\prime}}{AE} \\ \frac{6}{9}=\frac{x}{10} \\ x=\frac{6\times10}{9} \\ x=\frac{20}{3} \\ x=6\frac{2}{3} \end{gathered}[/tex]Answer: option c)
I need help especially on section C . I want to see the graph please explain.
Answers
Plot the following points for the table,
x = 0, 1, 4, 8, 12, 16
[tex]\begin{gathered} f(x)=4-x^{\frac{3}{2}} \\ \\ f(0)=4-0^{\frac{3}{2}} \\ f(0)=4 \\ \text{First point }(0,4) \\ \\ f(1)=4-1^{\frac{3}{2}} \\ f(1)=4-1 \\ f(1)=3 \\ \text{Second point }(1,3) \\ \\ f(4)=4-4^{\frac{3}{2}} \\ f(4)=4-\sqrt[]{4^3} \\ f(4)=4-\sqrt[]{64} \\ f(4)=4-8 \\ f(4)=-4 \\ \text{Third point }(4,-4)_{} \\ \\ f(8)=4-8^{\frac{3}{2}} \\ f(8)=4-\sqrt[]{8^3} \\ f(8)\approx-18.62 \\ \text{Fourth point }(8,-18.63) \\ \\ f(12)=4-12^{\frac{3}{2}} \\ f(12)=4-\sqrt[]{12^3} \\ f(12)\approx-37.57 \\ \text{Fifth point }(12,-37.57) \\ \\ f(16)=4-16^{\frac{3}{2}} \\ f(16)=4-\sqrt[]{16^3} \\ f(16)=-60 \\ \text{Sixth point }(16,-60) \end{gathered}[/tex]The table therefore is
The graph f(x) is
How can I find the equation of a circle with the coordinates (4,6)Center = (4,6), Diameter = 3 ft
Answers
a) We have to find the equation of a circle with center c = (4,6) and diameter D = 3 ft.
We can express a circle with center (a,b) and radius r as:
[tex](x-a)^2+(y-b)^2=r^2[/tex]Then, in this case, r = D/2 = 1.5, so we can write the equation as:
[tex]\begin{gathered} (x-4)^2+(y-6)^2=1.5^2 \\ x-4)^2+(y-6)^2=2.25 \end{gathered}[/tex]b) We now have to place another circle with its center 7 ft to the right and 2 ft up from the previous sprinkle.
Its radius, due to the increase in the preasure, will be two times the radius of the previous cicrle. Then, for this circle, r = 1.5*2 = 3 ft.
We can calculate the new center as:
[tex]\begin{gathered} x_c=4+7=11 \\ y_c=6+2=8 \end{gathered}[/tex]With a center of (11, 8) and radius r = 3, the circle can be expressed as:
[tex]\begin{gathered} (x-11)^2+(y-8)^2=3^2 \\ (x-11)^2+(y-8)^2=9 \end{gathered}[/tex]We can graph both circles as:
Answer:
a) (x - 4)² + (y - 6)² = 2.25
b) (x - 11)² + (y - 8)² = 9
what is the value of log e10? round to three decimal places
Answers
2.303 (option C)
Explanation:[tex]\log _{e_{}}10[/tex][tex]\log _{e_{}}\text{ is the same as ln}[/tex][tex]\begin{gathered} \log _{e_{}}=\text{ln }=\text{ natural logarithm} \\ \log _{e_{}}10\text{ = ln 10} \\ we\text{ would use a calculator to find the answer} \\ \end{gathered}[/tex][tex]\log _{e_{}}10\text{ = ln 10 = }2.3026[/tex]To 3 decimal place, the answer = 2.303 (option C)
Show steps on finding x,y int and end behaviors of a polynomial.
Answers
To find the y-intercept we have to evaluate the given function at x=0:
[tex]\begin{gathered} f(0)=(0-1)^3(0+3)^2(0-4)(0+2),^{} \\ f(0)=(-1)^3(3^{})^2(-4)(2), \\ f(0)=72. \end{gathered}[/tex]Therefore, the coordinates of the y-intercept are (0,72).
To find the x-intercepts we set f(x)=0 and solve for x:
[tex]\begin{gathered} (x-1)^3(x+3)^2(x-4)(x+2)=0. \\ \Leftrightarrow x=1\text{ or x=-3 or x=4 or x=-2.} \end{gathered}[/tex]The x-intercepts have coordinates (1,0), (-3,0), (4,0), (-2,0).
Finally, the end behaviours are:
[tex]\begin{gathered} \lim _{x\rightarrow+\infty}f(x)=\lim _{x\rightarrow+\infty}(x-1)^3(x+3)^2(x-4)(x+2)=+\infty, \\ \lim _{x\rightarrow-\infty}f(x)=\lim _{x\rightarrow-\infty}(x-1)^3(x+3)^2(x-4)(x+2)=-\infty. \end{gathered}[/tex]Answer:
Antonio is purchasing jerseys for his soccer team. He will pay $8.75 per jersey, and one time processing fee for $30.25. Which equation can be used to find y, the total cost to purchase x jerseys?
Answers
Given Data:
Total cost of a jersey= $8.75 per piece
The one time proccess fee is: $30.25
The total number of jerseys purchased is: x
The expression to calculate the total cost 'y' is,
[tex]undefined[/tex]