B. The sum of the measuresof two complimentaryangles is 90°. Find themeasure of the anglelabeled x.
Answers
B)
Given that angles (3x -10) and x are complementary, then we can write the following equation:
(3x -10) + x = 90º Definition of Complementary angles
3x-10 +x = 90º Combine like terms
4x -10 = 90 Add 10 to both sides
4x=100 Divide both sides by 4
x=25º
2) So , Angle x = 25º and m angle 3x- 10 is 65º
Related Questions
Does a maximum value exist for y = 8x^2 + 80x + 72? Explain your answer.
Answers
Solution
Reason 1:
[tex]\begin{gathered} y=8x^2+80x+72 \\ \\ \Rightarrow\frac{dy}{dx}=16x+80 \\ \\ \frac{d^2y}{dx^2}=16>0(\text{ Minimum\rparen} \end{gathered}[/tex]Reason 2:
Since the coefficient of x is positive, the graph is going to be minimum.
Maximum value does not exist.
Given secant of theta is equal to the square root of 6 over 3 comma what is cos?
Answers
Given that
[tex]\sec \text{ }\theta\text{ = }\frac{\sqrt[]{6}}{3}[/tex]Required: cos
From the reciprocal of trigonometric function,
[tex]\sec \text{ }\theta\text{ = }\frac{1}{\cos \text{ }\theta}[/tex]Thus, we have
[tex]\frac{1}{\cos \text{ }\theta}\text{ = }\frac{\sqrt[]{6}}{3}[/tex]Cross-multiply, we have
[tex]\begin{gathered} \sqrt[]{6}\text{ }\times\text{ cos }\theta\text{ = 3}\times1 \\ \sqrt[]{6}\text{ cos }\theta\text{ =3} \end{gathered}[/tex]Divide both sides by the coefficient of cos θ.
[tex]\begin{gathered} \frac{\sqrt[]{6}\text{ cos }\theta}{\sqrt[]{6}}\text{ =}\frac{\text{3}}{\sqrt[]{6}} \\ \Rightarrow\cos \text{ }\theta\text{ = }\frac{\text{3}}{\sqrt[]{6}} \\ \end{gathered}[/tex]Rationalizing the resulting surd, we have
[tex]\begin{gathered} \text{ }\frac{3}{\sqrt[]{6}}\times\frac{\sqrt[]{6}}{\sqrt[]{6}} \\ =\frac{3\times\sqrt[]{6}}{\sqrt[]{6}\times\sqrt[]{6}}=\frac{3\sqrt[]{6}}{6} \\ =\frac{\sqrt[]{6}}{2} \\ \text{Thus,} \\ \cos \text{ }\theta\text{ = }\frac{\sqrt[]{6}}{2} \end{gathered}[/tex]Hence, cos θ is evaluated to be
[tex]\frac{\sqrt[]{6}}{2}[/tex]The second option is the correct answer.
Aparachutist's speed during a free fall reaches 55 meters per second. What is this speed in feet per second? At this speed, how many feet will the parachutistfall during 15 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers
Answers
Part A:
The parachutist's speed is 55 m/s.
This means he covers 55m distance in every second
To convert this 55m distance to feet,
[tex]\begin{gathered} 1m=3.3ft \\ 55m=55\times3.3 \\ =181.5ft \end{gathered}[/tex]The speed will be a distance of 181 feet covered every second.
Hence, the speed in feet per second is;
[tex]181.5ft\text{ per second}[/tex]Part B:
The distance covered by the parachutist during 15 seconds of free fall will be;
Given:
[tex]\begin{gathered} \text{speed, s = 181.5 ft per second} \\ t=15\text{seconds} \\ distance,d=\text{?} \\ \text{speed = }\frac{dis\tan ce}{\text{time}} \\ \text{distance = spe}ed\text{ }\times time \\ d=181.5\times15 \\ d=2722.5ft \end{gathered}[/tex]Therefore, the parachutist fell 2722.5 feet in 15seconds during free fall.
if a bus travels an average of 44 miles per hour how long will it take for the bus to make a 1320 mile trip
Answers
Given:
a.) A bus travels an average of 44 miles per hour.
Which of the statements is true about the data displayed in the scatter plot? Computer Cost vs. Speed 2.6 2.2 1.8 Cost (s in thousands) 1.4 1.0 2.2 Speed (GHz) А It shows a positive correlation. B It shows a negative correlation. С It shows no correlation. D As speed increases, cost decreases.
Answers
From the graph, we can see that the data displayed correspond to a positive correlation.
Positive correlation is a relationship between two variables in which both variables move in the same direction. In this case when the speed increases the cost also increases.
Therefore, the answer is A: its shows a positive correlation
Vertices A(a, -6, 2), B(4,b,-9), C(3,5,c) and D(-2,-5,11) form a parallelogram. Determine the values of a,b,c.
Answers
Let's do a quick draw to help us visualize the problem:
That's a generic parallelogram, to verify that it's a parallelogram we can see that
[tex]\begin{gathered} AB=CD \\ \\ BC=AD \end{gathered}[/tex]The opposite lengths are equal, then, let's do something similar here, let's say that
[tex]\vec{AB}=\vec{CD}[/tex]then
[tex]\begin{gathered} \vec{AB}=B-A=(4,b,-9)-(a,-6,2)=(4-a,b+6,-9-2) \\ \\ \vec{AB}=(4-a,b+6,-11) \end{gathered}[/tex]And the vector CD
[tex]\begin{gathered} \vec{CD}=D-C=(-2,-5,11)-(3,5,c)=(-2-3,-5-5,11-c) \\ \\ \vec{CD}=(-5,-10,11-c) \end{gathered}[/tex]Let's impose our condition
[tex]\begin{gathered} \begin{equation*} \vec{AB}=\vec{CD} \end{equation*} \\ \\ (4-a,b+6,-11)=(-5,-10,11-c) \\ \\ \end{gathered}[/tex]Then
[tex]\begin{gathered} 4-a=-5 \\ \\ b+6=-10 \\ \\ 11-c=-11 \end{gathered}[/tex]By solving that equations we get
[tex]\begin{gathered} a=9 \\ \\ b=-16 \\ \\ c=22 \end{gathered}[/tex]why might interpreting multiplication by a negative number as a 180 degrees rotation make sense?
Answers
If we think of all the numbers as being on a line and from the left come the negative numbers, there is the zero [Neutral element] and to the rigth we have the positive numbers, then understanding the product as a rotation of 180° makes complete sence, since the magnitude is going to change but will be "written" on the opposite side.
8. Determine whether the following sequence of trials would result in a binomial probability distribution. (a) Calling 500 people and ask if they voted for a particular candidate in a given election. (b) The National Health Institute checks 100 people who had a certain type of cancer in the year 2000 and records whether they are alive or not.
Answers
a) This results in a binomial distribution because:
There are only two possible outcomes (yes or no).
The trials are independent.
There are a fixed number of trials.
The probability of success remains the same for each call.
Answer a: this will result in a binomial distribution.
b) This does result in a binomial distribution:
There is a fixed number of trials.
It has only two outcomes.
The trials are independent.
The probability of success remains the same for each trial.
Answer b: this will result in a binomial distribution
What is the least common multiple of 9 and 2?
Answers
The muliples of 9 are: 9, 18, 27, 36, 45, ...
The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26,...
So, the common multiples are 18, 36, 54,...
Therefore, the least common multiple is 18
Answer: 18
Find the qualities indicated without using the Pythagorean theorem.(Round to the nearest degree is needed)
Answers
ANSWER
[tex]\begin{gathered} (a)A=45\degree \\ (b)c=14.1^{\prime} \end{gathered}[/tex]EXPLANATION
First, let us find the value of c using the Pythagoras theorem:
[tex]a^2+b^2=c^2[/tex]where a and b are the other two legs of the triangle, and c is the hypotenuse
Therefore, we have that:
[tex]\begin{gathered} 10^2+10^2=c^2 \\ \Rightarrow100+100=c^2 \\ 200=c^2 \\ \Rightarrow c=\sqrt[]{200} \\ c=14.1^{\prime} \end{gathered}[/tex]Next, we find the measure of A by using the trigonometric ratios, SOHCAHTOA, of right angles:
[tex]\tan A=\frac{opposite}{adjacent}[/tex]Therefore, we have:
[tex]\begin{gathered} \tan A=\frac{10}{10} \\ A=\tan ^{-1}(1) \\ A=45\degree \end{gathered}[/tex]That is the answer.
I need help with this problem, I need the hole, the horizontal asymptote , domain and x intercept
Answers
The function
[tex]f(x)=\frac{x^2+2x\text{ -3}}{x+3}[/tex]let f(x) = y
[tex]y\text{ =}\frac{x^2+2x\text{ - 3}}{x+3}[/tex]substitute x = 0
[tex]y=\frac{0+2(0)-3}{0+3}[/tex]
[tex]y\text{ = }\frac{-3}{3}[/tex][tex]y\text{ = -1}[/tex]
(x = 0 and y = -1)
Next, put y = 0 in the function and then solve for x
[tex]0=\frac{x^2+2x\text{ -3}}{x+3}[/tex][tex]0=\frac{x^2+3x-x-3}{x+3}[/tex][tex]0=\frac{x(x+3)-1(x+3)}{x+3}[/tex][tex]0=\frac{(x+3)(x-1)}{x+3}[/tex][tex]0=x-1[/tex][tex]x=1[/tex](x = 1 and y =0)
The domain is (0 and 1)
The x -intercept is (1, 0)
The hole is
x + 3 =0
x= -3 is the hole
To find the horizontal asymptote;
since the degree of the numerator is greater than the denominator, then it has no horiizontal asymptote
horizontal asymptote = none
if ∆ABC ~ ∆FED which of the following is correct:
Answers
We know that the triangles ∆ABC and ∆FED are congruent. As such, we know that all sides and inner angles are congruent. Moreover, if we have:
Then,
[tex]\begin{gathered} \measuredangle A\cong\measuredangle F \\ \measuredangle B\cong\measuredangle E \\ \measuredangle C\cong\measuredangle D \end{gathered}[/tex]And this means that ∡A≅∡F.
Assume that AB is parallel to EC, es press y in terms of x
Answers
Knowing that AB is parallel to EC, we can say that the proportion between DC and CB is equal to the proportion between DE and EA. Then:
[tex]\frac{DC}{CB}=\frac{DE}{EA}[/tex]Finally, we replace each value:
[tex]\begin{gathered} \frac{y}{8}=\frac{6}{x} \\ y=\frac{6\cdot8}{x} \\ \therefore y=\frac{48}{x} \end{gathered}[/tex]Answer: Option a
Use the Pythagorean theorem to determine the unknown length of the right triangle. 1. Determine the length of side c in each of the triangles below. A B 8 b. 0.8 B 0.6 A
Answers
Pythagorean teorem:
c^2 = a^2+b^2
Where c is the hypotenuse and a & b are the two other legs of the triangle.
a.
c^2 = 6^2+8^2
Solve for c:
c^2 = 36+64
c^2 = 100
c =√100
c= 10
b.
c^2 = 0.6^2+ 0.8^2
c^2 = 0.36+ 0.64
c^2 = 1
c = √1
c=1
A satellite sends signals from space to the regions that lie within the shaded portion of the Earth, as shown below. If the radius of the Earth is approximately 6000 kilometers, and the central angle the satellite creates measures 60° the part of Earth that receives signals from the satellite has an area of ____ square kilometers. Use 3.14 for T.
Answers
ANSWER
18840000 square kilometers
EXPLANATION
We want to find the area that will receive the signal, that is the area of the shaded sector.
To do this, we apply the formula for the area of a sector of a circle:
[tex]\begin{gathered} A=\frac{\theta}{360}\cdot\pi\cdot r^2 \\ \text{where} \\ \theta=\text{ central angle of sector} \\ r\text{ = radius of circle} \end{gathered}[/tex]We are given the central angle and the radius of the circle.
Therefore, the area of Earth that receives the signals is:
[tex]\begin{gathered} A=\frac{60}{360}\cdot3.14\cdot6000^2 \\ A=18840000\text{ square kilometers} \end{gathered}[/tex]That is the area of Earth that receives the signals.
groom lawn equipment pays Amy a $1130 monthly salary plus 10% commission on merchandise she sells each month. Assume Amy's sales were $37,200 for last monthamount of commissionamount of gross pay
Answers
The monthly salary = $1130 plus 10% commission from the sells
The sales of the last month = $37,200
so, the amount of commission = 10% of 37,200 =
[tex]\frac{10}{100}\cdot37,200=0.1\cdot37,200=3,720[/tex]So, the gross pay = 1,130 + 3,720 = $4,850
The radii of two spheres are in a ratio of 1:4.What is the ratio of their volumes?
Answers
Given:
The radii of the two spheres are in a ratio of 1:4
Find-:
The ratio of their volume
Explanation-:
Radii of two spheres are in a ratio is 1:4
[tex]\frac{r_1}{r_2}=\frac{1}{4}[/tex]The volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]So the ratio of volume is:
[tex]\begin{gathered} \frac{V_1}{V_2}=\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r^_2^3} \\ \\ \frac{V_1}{V_2}=(\frac{r_1}{r_2})^3 \\ \\ \frac{V_1}{V_2}=(\frac{1}{4})^3 \\ \\ \frac{V_1}{V_2}=\frac{1}{64} \\ \end{gathered}[/tex]So the ratio is 1:64
Thaddeus models the number of hours of daylight in his town asD(t) = 3sin(pi/6•t) + 12, where D is the number of daylight hours and t is thetime in months since January 1.What are the least and greatest numbers of daylight hours over the course ofa year?
Answers
Step 1
Find the height value of the amplitude
[tex]\text{The highest value of the amplitude is 3}[/tex]Step 2
Find the greatest number of daylight hours over the course of the year, D
[tex]D=\text{ 3 +12 = 15 hrs}[/tex]Step 3
Find the least value of the amplitude
[tex]\begin{gathered} \text{The least value of the amplitude = -3} \\ \end{gathered}[/tex]Step 4
Find the least number of daylight hours over the course of the year, D
[tex]D=\text{ -3+12=9 hours}[/tex]Hence, the greatest number of daylight hours over the course of the year = 15 hours
and
the least number of daylight hours over the course of the year = 9 hours
Hence option C is correct.
Clare knows that Priya has a bunch of nickels and dimes in her pocket and that the total amount is $1.25. Write an equation that describes the relationship between the number of dimes and the number of nickels in Priya's pocket.
Answers
Answer:
The equation that describes the relationship between the number of dimes and the number of nickels in Priya's pocket. is;
[tex]0.05n+0.10d=1.25[/tex]Explanation:
Let n and d represent the number of nickels and dimes in her pocket;
We know that;
1 nickel is 5 cents = 0.05 dollar
1 dime is 10 cents = 0.10 dollar
Also;
n nickels = n times 0.05 dollars
[tex]0.05n[/tex]d dimes = d times 0.10 dollar
[tex]0.10d[/tex]The total is given as;
the total amount is $1.25.
So, we have the equation as;
[tex]0.05n+0.10d=1.25[/tex]Therefore, the equation that describes the relationship between the number of dimes and the number of nickels in Priya's pocket. is;
[tex]0.05n+0.10d=1.25[/tex]the jonson are having 14 children at a birthday party. they have hired peggy to dress up as a clown and entertain the children from 2:30 until 6:30. the jonhson will pay her $2.00 for each child per hour. Peggys expenses for balloons and paint will be $10.00. how much profit (income minus expenses) will peggy make?
Answers
Given
Total children = 14
Total hours = 6.30 - 2.30 = 4 hours
pay $2.00 for each children per hour
peggys expenses = $10.00
Find
how much profit (income minus expenses) will peggy make?
Explanation
pay for one child in 4 hours = $ 2.00 * 4 = $8.00
for 14 children = 14 * 8 = $112
so , profit = $112 - $10 = $102
Final Answer
Therefore ,the profit peggy make = $ 102
Find the zeros of each function by factoring. F(x)=5x^2–11x+2
Answers
We need to factor the following expression:
[tex]f(x)=5x^2-11x+2[/tex]The factor the equation we need to find which numbers "d" and "e" when multiplied result in 10. And when added are equal to -11.
[tex]\begin{gathered} d=-10 \\ e=-1 \end{gathered}[/tex]We can represent the function by:
[tex]f(x)=(x-10)(x-1)[/tex]The zeros of the function are 10 and 1.
The area of the entire rectangle shown is 96 cm2. What is the area of the shaded region? i need help fast please
Answers
Given:
Area of the rectangle = 96 sq. cm
The rectangle is divided by 24 blocks
Required:
Area of the two shaded blocks
Solution:
Area of a block = Area of the rectangle / no. of blocks = 96 sq. cm / 24 blocks
Area of a block = 4 sq. cm. / block
Area of two blocks = 2 blocks ( 4 sq.cm/ block) = 8 sqcm
Answer:
8 sq.cm.
what is the correct classification for the following two linear equations?-2x + y =3y = -1/2 x-2A. Parallel Lines B. Perpendicular Lines
Answers
Solution
we are given the two linear equations
First Equation
[tex]\begin{gathered} -2x+y=3 \\ \\ y=2x+3 \end{gathered}[/tex]Second Equation
[tex]y=-\frac{1}{2}x-2[/tex]Let mA and mB denotes the gradient of the first and second equation respectively written as
[tex]m_A\text{ and }m_B[/tex]Using the slope - intercepty form, one can see that
[tex]\begin{gathered} m_A=2 \\ \\ m_B=-\frac{1}{2} \end{gathered}[/tex]Now,
[tex]\begin{gathered} m_A\times m_B=2\times-\frac{1}{2} \\ \\ m_A\times m_B=-1 \end{gathered}[/tex]Therefore, the lines are Perpendicular
Option B
#61 explain WHY the answer is correct, it confuses me
Answers
To answer this question we need to remember what the derivative and the second derivative tells us geometrically:
The derivative of a function tells us the slope of the tangent line to the function; which means that we can determine if a function is increasing or decreasing if we look at the sign of its derivative:
• If the derivative is positive then the function is increasing.
,• If the derivative is negative then the function is decreasing.
The second derivative of a function tells us the concativity of a function:
• If the second derivative is positive then the function is concave up.
,• If the second derivative is negative then the function is concave dowm.
Now that we know this we can sketch a function:
For the first interval we know that the derivative is negative and the second derivative is also negative which means that the function has to be decreasing and concave down.
For the second interval we know that the derivative is negative and the second derivative is positve which means that the function has to be decreasing and concave up.
Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-1,6) and parallel to x + 2y = 7.
Answers
the line equation we want is parallel to x+2y=7, which means they have the same slope. Rewritting this function in the slope form
[tex]x+2y=7\Leftrightarrow y=-\frac{x}{2}+\frac{7}{2}[/tex]The slope of our equation is (-1/2)!
Now, we just need to substitute the point to find the intercept.
[tex]\begin{gathered} y=-\frac{x}{2}+b \\ 6=-\frac{(-1)}{2}+b\Rightarrow b=\frac{11}{2} \end{gathered}[/tex]Now we have the slope and the intercept. Solving item (a) and writing this function in slope-intercept form gives us
[tex]y=-\frac{x}{2}+\frac{11}{2}[/tex]The standard form is:
[tex]Ax+By=C[/tex]Rewriting our function like this, we get:
[tex]x+2y=11[/tex]and this is the answer to item b.
I'm not sure what I suppose to being doing, I don't understand it. I know it has something to do with the rectangle box above the number lines, but I'm having problems tbhnm
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
Sample size: 12
Median: 66
Minimum: 60
Maximum: 70
First quartile: 63.5
Third quartile: 67.5
Interquartile Range: 4
Outliers: none
Find the zero of h(x) = 3/4x - 72
Answers
To find the zero of a function, you equal that function to 0
[tex]\frac{3}{4}x-72=0[/tex]Then, you solve the variable x:
1. Add 72 in both sides of the equation
[tex]\begin{gathered} \frac{3}{4}x-72+72=0+72 \\ \\ \frac{3}{4}x=72 \end{gathered}[/tex]2. Multiply both sides of the equation by 4
[tex]\begin{gathered} 4(\frac{3}{4}x)=72\cdot4 \\ \\ 3x=288 \end{gathered}[/tex]3. Divide both sides of the equation into 3
[tex]\begin{gathered} \frac{3}{3}x=\frac{288}{3} \\ \\ x=96 \end{gathered}[/tex]Then, the zero of the given function is in x=96. Coordinates (96,0)solve for x and yy=2/3x - 2y= -x + 3
Answers
Answer: x = 3 and y = 0
Given that
y = 2/3x - 2 ------------- equation 1
y = -x + 3 ---------------- equation 2
These system of linear equation can be solve simultaneously
equate equation 1 and 2 together
[tex]\begin{gathered} \frac{2x}{3}\text{ - 2 = -x + 3} \\ \text{The common denominator for RHS is 3} \\ \frac{3\frac{2x}{3}\text{ - 3}\frac{2}{1}}{3}\text{ = -x + 3} \\ \frac{2x\text{ - 6}}{3}=\text{ -x + 3} \\ \text{Cross multiply} \\ 2x\text{ - 6 = 3(-x + 3)} \\ \text{Open the parenthesis} \\ 2x\text{ - 6 = -3x + 9} \\ 2x\text{ - 6 = -3x + 9} \\ \text{Collect the like terms} \\ 2x\text{ + 3x = 9 + 6} \\ 5x\text{ }=\text{ 15} \\ \text{Divide both sides by 5} \\ \frac{5x}{5}\text{ = }\frac{15}{5} \\ x\text{ = 3} \\ To\text{ find y, put the value of x in equation 2} \\ y\text{ = -x + 3} \\ y\text{ = -3 + 3} \\ y\text{ = 0} \end{gathered}[/tex]Therefore, x = 3 and y = 0 --- (3, 0)
Solve the equation (the answer might be no solution or “all real numbers “)8c+7c+6=66
Answers
We have the equation:
8c + 7c + 6 = 66
We add the c terms, and add -6 to each side of the equation (to cancel the 6 on the left-hand side):
15c + 6 - 6 = 66 - 6
15c = 60
Now, we divide each side of the equation by 15:
15c/15 = 60/15
c = 4
So the value of the variable c is 4.
If the base of the triangle is 1, how is the height of thetriangle associated with the common difference of thesequence and the slope of the line?
Answers
1) Gathering the data
Triangle base = 1
Triangle height = 2
Common difference: 2
Slope: m
Considering the points (0,2) and (1,4)
m =4-2/1-0 m=2
2) Working with the picture:
Looking at those triangles, whose base is 1 and height is 2 we can say that the common difference (2) is the same as the slope (2) In other words,
The height of the triangle is equal to the slope. The sequence goes on and on but the height remains the same as the slope of the line. In this case, the slope is m=2