The picture below shows a box sliding down a ramp:A right triangle ABC has measure of angle ABC equal to 90 degrees and measure of angle ACB equal to 65 degrees. The length of AB is 12 feet.What is the distance, in feet, that the box has to travel to move from point A to point C? 12 divided by sec 65 degrees 12 cosec 65° 12 sin 65° 12 divided by cot 65 degrees
Answers
The length of the hypotenuse of the triangle is the solution to the question.
The length of the hypotenuse can be found using the Sine Trigonometric Ratio given to be:
[tex]\sin\theta=\frac{opp}{hyp}[/tex]From the image, we have the following parameters:
[tex]\begin{gathered} \theta=65\degree \\ opp=12 \\ hyp=AC \end{gathered}[/tex]Therefore, we have:
[tex]\sin65=\frac{12}{AC}[/tex]To solve for AC, we can cross-multiply:
[tex]AC=\frac{12}{\sin65}[/tex]Recall the identity:
[tex]\cosec x=\frac{1}{\sin x}[/tex]Therefore, the equation will be:
[tex]AC=12\cosec65[/tex]The SECOND OPTION is correct.
The distance that the box has to travel to move from point A to point C is equal to the length of side AC of the right triangle ABC. Since angle ACB is 62 degrees and side AB is opposite this angle, we can use the definition of sine to find the length of side AC. The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. So, we have:
$$\sin(62°)=\frac{AC}{AB}$$
Substituting the known values, we get:
$$\sin(62°)=\frac{AC}{10}$$
Solving for AC, we get:
$$AC=10\sin(62°)$$
So, the distance that the box has to travel to move from point A to point C is **10 sin 62°** feet.
Related Questions
Translate each phrase into a mathematical expression using x as the variable, and simplify.See Example 4.> 99. Five times a number, added to the sum of the number and three100. Six times a number, added to the sum of the number and six101. A number multiplied by - 7, subtracted from the sum of 13 and six times the number102. A number multiplied by 5, subtracted from the sum of 14 and eight times the number103. Six times a number added to -4, subtracted from twice the sum of three times the num-ber and 4 (Hint: Twice means two times.)104. Nine times a number added to 6, subtracted from triple the sum of 12 and 8 times thenumber (Hint: Triple means three times.)
Answers
#103 (on request of kassy247):
six times a number is:
6x
added to -4, it becomes:
6x + (-4) = 6x - 4
THIS WHOLE THING is subtracted from TWICE the SUM OF 3 times number and 4
Breaking it apart,
sum of 3 times number and 4 means: 3x + 4
Twice of this would be: 2(3x+4)
Now, look above, the bold-underlined part. That is subtracted from what we got now, so we have:
[tex]2(3x+4)-(6x-4)[/tex]This is the expression.
On the third example (where we added a garage on the end), we came up with the function an 4n + 4, where n represents the number of houses built. If we build 50 houses with just the one garage on the end, how many fence panels will we need?
Answers
The expression is for the fence pannels is
4n+4
n represents the number of houses.
You have to replace n with the given value of houses:
4*50+4=204
For 50 houses you need to use 204 fence pannels.
*-*
an=4n+4
an= number of fence pannels
You have to calculate the number of houses, n, you can build with 84 fence pannels, you have to clear the expression for n:
an= 4n+4
an-4=4n
n=(an-4)/4
n=(84-4)/4
n=20
You can biuld 20 houses with 84 fence pannels.
between what 2 consecutive integers, √65 lies? a, 4 and 5b, 5 and 6c, 7 and 8d, 8 and 9
Answers
Given:
The integer is,
[tex]\sqrt[]{65}[/tex]First find the value of given square root,
[tex]\sqrt[]{65}=8.062\text{ (approxi}mately)[/tex]So, the value of given integer will lie in,
[tex]8<8.062<9[/tex]Answer: Option d) 8 and 9.
a pilot took 1/2 hour to complete 1/3 of hjis trip. How much longer will it take him to complete his trip
Answers
It took the pilot half an hour to complete one-third of the trip, to determine how much it will take him to complete the trip, you can use cross multiplication to determine it.
1/3 of the trip → 1/2 hour
Whole trip → x hours
Let "1" represent the whole trip, that is, all three parts of it. Both relationships are at the same ratio so that:
[tex]\begin{gathered} \frac{\frac{1}{2}}{\frac{1}{3}}=\frac{x}{1} \\ \frac{\frac{1}{2}}{\frac{1}{3}}=x \end{gathered}[/tex]When you divide by a fraction, is the same as multiplying the dividend by the reciprocal fraction of the divisor, you can write the expression as follows:
[tex]\begin{gathered} \frac{1}{2}\cdot\frac{3}{1}=x \\ \frac{1}{2}\cdot3=x \\ x=\frac{3}{2}=1.5 \end{gathered}[/tex]It will take him one and a half hours to complete the trip.
5. ). A cosmetic company has developed a new after-shave lotion. If the company goesinto small-scale production its annual fixed costs will be $200,000 and it can produce theproduct for a variable cost of $3 per unit. If the company goes into large-scale production itsannual fixed costs will be $400,000 and it can produce the product for a variable cost of$1.25 per unit.Assume that the selling price is $7 per unit.a) Determine the break-even points for small scale and large scale production.b) If the expected sales are for 500,000 units, which production process is more profitablesmall-scale or large-scale?c) Determine profits for both cases,d) Find the number of units for which one would be indifferent between small-scale andlarge-scale production
Answers
This is a simple question to solve.
First, we need to understand what is a break-even point.
Well, a break-even point is a point in sales where your company know it has covered all money they spent on fixed and variable costs but still don't have a profit. It means --> no loss but also no profit.
Letter A) To calculate a break-even point we can use the following equation:
[tex]BEP=\frac{C_{fixed}}{S_{price}-C_{variable}}[/tex]Where:
BEP = Break-even point;
Cfixed = Fixed Cost;
Sprice = Selling price; and
Cvariable = Variable cost.
So, for small-scale we have:
[tex]\begin{gathered} BEP=\frac{C_{fixed}}{S_{price}-C_{variable}} \\ BEP=\frac{200000_{}}{7_{}-3_{}} \\ BEP=50000 \end{gathered}[/tex]And, for large-scale:
[tex]\begin{gathered} BEP=\frac{C_{fixed}}{S_{price}-C_{variable}} \\ BEP=\frac{400000_{}}{7_{}-1.25_{}} \\ BEP\cong69565.217 \end{gathered}[/tex]Letter B:
We can see above the break-even point for small-scale(50000) is lower than large-scale(69565.217). That means for small-scale we need to sell fewer units to cover all our cost and start profit after that point, so if the expected sales are for 500000 units, the small production is more profitable.
Letter C:
The profits for small-scale starts after 50000 units sold and for large-scale starts after 69565 units sold approximately.
Letter D:
As we understand what is a break-even point, we know the number of units for each one would be indifferent between small-scale and large-scale is 50000 units and approximately 69565 respectively because at these points for both (small and large scale) we have neither a profit nor a loss.
Consider the right triangle shown below that has an interior angle measure of θ radians.Use the slider in the applet above to show a circle centered at the left-most vertex of the triangle.Consider the terminal point P.What is the measure of the terminal point's vertical distance above the center of the circle in units of the radius of the circle? What is the value of sin(θ)?sin(θ)=Consider the terminal point P.What is the measure of the terminal point's horizontal distance to the right of the center of the circle in units of the radius of the circle? What is the value of cos(theta)?cos(θ)=
Answers
Given
Graph
Procedure
b.
i)
[tex]\frac{1.93}{2.5}=0.772[/tex]ii)
[tex]\begin{gathered} \sin \theta=\frac{1.93}{2.5} \\ \sin \theta=0.772 \end{gathered}[/tex]c.
i)
[tex]\frac{1.59}{2.5}=0.636[/tex]ii)
[tex]\begin{gathered} \cos \theta=\frac{1.59}{2.5} \\ \cos \theta=0.636 \end{gathered}[/tex]10. A bacteria culture is started with 200 bacteria. After 4 hours, the population has grown to 769 bacteria. If the population grows exponentially according to the formula Pt=P0(1+r)t (a) Find the growth rate. Round your answer to the nearest tenth of a percent.r = %(b) If this trend continues, how many bacteria will there be in one day? bacteria(c) How long will it take for this culture to triple in size? Round your answer to the nearest tenth of an hour. hours
Answers
Given:
A bacteria culture is started with 200 bacteria.
After 4 hours, the population has grown to 769 bacteria.
the population grows exponentially according to the formula:
[tex]P(t)=P_0(1+r)^t[/tex](a) Find the growth rate.
so, when:
[tex]\begin{gathered} P_0=200,t=4,P(t)=769 \\ 769=200(1+r)^4 \end{gathered}[/tex]Solve for r:
[tex]\begin{gathered} \frac{769}{200}=(1+r)^4 \\ 3.845=(1+r)^4 \\ \sqrt[4]{3.845}=1+r \\ 1+r=1.4 \\ r=1.4-1=0.4 \end{gathered}[/tex]So, the value of r = 0.4 = 40%
The growth rate = r = 40%
(b) If this trend continues, how many bacteria will there be in one day?
For one day, t = 24 hours
so,
[tex]\begin{gathered} P_t=200\cdot(1+0.4)^{24} \\ P_t=200\cdot1.4^{24}=642,840 \end{gathered}[/tex]Bacteria = 642,840
(c) How long will it take for this culture to triple in size?
So,
[tex]\begin{gathered} P_t=3\cdot200=600 \\ 600=200\cdot(1+0.4)^t \end{gathered}[/tex]Solve for t:
[tex]\begin{gathered} \frac{600}{200}=1.4^t \\ 3=1.4^t \\ \ln 3=t\cdot\ln 1.4 \\ t=\frac{\ln 3}{\ln 1.4}\approx3.265 \end{gathered}[/tex]Round your answer to the nearest tenth of an hour.
So, t = 3.3 hours
AnglesX 1.1.28If mZQOS = 52, mZPOR = 63, and mZPOQ = 26, what is mZROS?mZROS = I1(Type an integer or a decimal. Do not include the degree symbol in your answer.)
Answers
m angleROS=15
Given the following picture with those angles:
m ROQ = 63-26 =37
So, m angle ROQ = 37
m ROS= 52-37=15
So m ROS = 15
A ball has a radius of 18 cmWhat is the approximate volume of the ball? Use 3.14 to approximate pi. Round to the nearest hundredth if necessary.
Answers
The volume of the ball can be estimated using the volume of a sphere.
The volume of a sphere is:
[tex]V=\frac{4}{3}\pi *r^3[/tex]Where:
V = volume
r = radius
Knowing that r = 18 cm and using π = 3.14, let's substitute the values in the formula and find the volume:
[tex]\begin{gathered} V=\frac{4}{3}*3.14*18^3 \\ V=\frac{4}{3}*3.14*5832 \\ V=24416.64cm^3 \end{gathered}[/tex]Answer: The volume of the ball is 24416.64 cm³.
The median for the given set of six ordered data values is 30.5.5,12,23, ___ ,41, 50What is the missing value?
Answers
Given data is,
[tex]5,12,23,-_{},41,50_{}[/tex]Given the median of the given data is 30.
Let the unknown value be x.
Since there are two middle terms in the given data. The median of the given data containg the two middle term is given by,
[tex]\begin{gathered} \frac{23+x}{2}=30.5 \\ \end{gathered}[/tex]By simplify the above equation the x value can be found,
[tex]\begin{gathered} \frac{23+x}{2}=30.5 \\ 23+x=30.5\times2 \\ 23+x=61 \\ x=61-23 \\ x=28 \end{gathered}[/tex]The required value of the missing term is 28.
-5+n÷2=-17 the answer I have is 24, when I check it, the calculator says 7 instead. what am I doing wrong?
Answers
We are given the following equation:
[tex]-5+\frac{n}{2}=-17[/tex]To solve for "n" we will first add 5 to both sides:
[tex]\begin{gathered} \frac{n}{2}=-17+5 \\ \frac{n}{2}=-12 \end{gathered}[/tex]Now we multiply both sides by 2:
[tex]\begin{gathered} n=2(-12) \\ n=-24 \end{gathered}[/tex]Therefore, the value of "n" is -24.
BRAINLIST BRAINLIST PLEASE URGENTLY NEED HELP. Need help graphing and filling in the table
Answers
Graph the quadratic function f(x) = 2(x - 3)2 - 2 and select all of the following which are true.maximum at (-3,-2)minimum at (3,-2)x-intercept at (2,0)x-intercept at (4,0)y-intercept at (0, -16)
Answers
Graph:
By looking at the graph we can see that:
It opens upwards, so it has a minimum at (3,-2)
I crosses the x axis at x=2 and x=4
x- intercepts at (2,0) and (4,0)
It doesn't cross the y axis
Honor spent 3 1/4 hours on homework yesterday sequoia spent 2 5/6 hours on homework. how much more time did honon spend on homework than sequoia?
Answers
Given:
[tex]\begin{gathered} \text{Time Honor spent = 3}\frac{1}{4}\text{ hours} \\ \\ \text{Time Sequoia spent = 2}\frac{5}{6}\text{ hours} \end{gathered}[/tex]To find how much more time Honor spent than Sequoia, subtract the amount of time Sequoia spent from that of Honor.
Therefore, we have:
First convert to simple fraction:
[tex]\begin{gathered} 3\frac{1}{4}\text{ hours = }\frac{13}{4}\text{ hours} \\ \\ 2\frac{5}{6}\text{ hours = }\frac{17}{6}\text{ hours} \end{gathered}[/tex]Now, let's subtract:
[tex]\begin{gathered} \frac{13}{4}-\frac{17}{6} \\ =\frac{39-34}{12} \\ \\ =\text{ }\frac{5}{12}\text{ hours} \end{gathered}[/tex]Therefore, Honor spent 5/12 more hours on homework than Sequoia.
ANSWER:
[tex]\frac{5}{12}\text{ hours}[/tex]Answer: 5/12
Step-by-step explanation:
Hello! I am having a little trouble understanding this question? May I have any help?
Answers
Given
Answer
Matrices are equal if their corresponding elements are equal
3x - x =4
2x = 4 ;
x =4/2 ;
x= 2
Also , -(4y+8)= 7y + 14
-4y -8 =7y +14;
-4y - 7y =14 + 8;
-11y = 22 ;
y = -22/11
y=-2
Find the equation of the line passing through the points (0,5) and (7,4).Input equation. Pls see picture
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
where
y2 and y1 are the y coordinates of the initial points on the line.
x2 and x1 are the x coordinates of the initial points on the line.
From the information given, the line passes through the points (0,5) and (7,4). This means that
x1 = 0, y1 = 5
x2 = 7, y2 = 4
By substituting these values into the slope formula,
m = (4 - 5)/(7 - 0) = - 1/7
We would find the y intercept, c by substituting x = 0, y = 5 and m = - 1/7 into the slope intercept equation. We have
5 = - 1/7 * 0 + c
5 = 0 + c
c = 5
By substituting m = - 1/7 and c = 5 into the slope intercept equation, the equation of the line is
y = - x/7 + 5
Evaluate. (Round your answer to two decimal places.)(5pi - 9e) / (7pi + 3e)
Answers
ANSWER
-0.29
EXPLANATION
We want to evaluate the value of the fraction given to two decimal places.
To do this, we have to know the value of pi and e:
[tex]\begin{gathered} \pi\text{ = 3.1416} \\ e\text{ = 2.7183} \end{gathered}[/tex]Therefore, to simplify the fraction:
[tex]\begin{gathered} \frac{5(3.1416)\text{ - 9(2.7183)}}{7(3.1416)\text{ + 3(2.7183)}} \\ \Rightarrow\text{ }\frac{15.708\text{ - 24.4647}}{21.9912\text{ + 8.1549}} \\ \Rightarrow\text{ }\frac{-8.7567}{30.1461} \\ =>\text{ -0.2905 }\cong-0.29 \end{gathered}[/tex]That is the answer.
When McDonald's opened their shakes cost $0.20, today they cost $2.19. What is the percent of change?
Answers
ANSWER
995%
EXPLANATION
When they opened their shakes cost $0.20 and now they cost $2.19.
To find the percent of change, we have to first find the difference in the initial cost and the current (or final) cost and then divide that by the initial cost, then multiply by 100 (per cent).
Initial Cost = $0.20
Final Cost = $2.19
Difference = Final - Initial = 2.19 - 0.20
Difference = $1.99
The percent of change is:
[tex]\begin{gathered} \text{ \% change = }\frac{1.99}{0.20}\cdot\text{ 100} \\ \text{ \% change = 995\%} \end{gathered}[/tex]8. The table below shows college textbook sales in the U.S. from 2000 to 2005. Year Textbook Sales (millions of dollars) 2000 4265 2001 4571 2002 4899 2003 5086 2004 5479 2005 5703 (a) Use a graphing calculator or spreadsheet program to find a quadratic model that best fits this data. Let t represent the year, with t = 0 in 2000. Round each coefficient to two decimal places. P t = (b) Based on this model, how much would you expect to be spent on college textbooks in 2015? Round your answer to the nearest whole number. million dollars (c) When would you expect textbook sales to first reach $7 billion (7000 million dollars)? Give your answer as a calendar year (ex: 1997). During the year
Answers
We have been given a table that indicates Textbook sales (millions of dollars) from the year 2000 to 2005.
Method: Since we have been told to model the equation that best fits the data.
To do this, we have been told to let t represent the years.
We can also represent the textbook sales as Pt
Using a graphing calculator
Question A
Thus, the quadratic model that best fits this data is:
[tex]P_t=-2.68t^2_{1^{^{^{}}\text{ }}}+301.99t_1+4270.07[/tex]Question B
We are told to predict the Textbook sales in 2015
In 2015, the value of t1 will be
[tex]\begin{gathered} t_1=2015-2000=15 \\ t_1=15 \end{gathered}[/tex]We can now proceed to substitute
[tex]t_1=15[/tex]Into the equation
[tex]\begin{gathered} P_t=-2.68\times15^2+301.99\times15+4270.07 \\ P_t=8196.92 \end{gathered}[/tex]in 2015, we would expect
[tex]P_t\approx8197\text{ million dollars}[/tex]Thus, approximately 8197 million dollars is expected to be spent on college textbook
Question C
To predict when the total sales will be approximately $7billion,
We will take our value for
[tex]P_t=7000[/tex]This means that
[tex]7000=-2.68t^2_{1^{^{^{}}\text{ }}}+301.99t_1+4270.07[/tex]Thus, we will have to find the value of t1
Again, using the graph to predict when Pt = $7000
We can see from the graph that this value is about 9.952 years
So we will try when
[tex]\begin{gathered} t_1=9\text{years} \\ \text{and when} \\ t_1=10\text{years} \end{gathered}[/tex]Using the model
[tex]P_t=-2.68t^2_{1^{^{^{}}\text{ }}}+301.99t_1+4270.07[/tex]When
[tex]\begin{gathered} t_1=9\text{ years} \\ P_t=\text{ \$}6770.9 \end{gathered}[/tex]When
[tex]\begin{gathered} t_1=10 \\ P_t=\text{ \$7021}.97 \end{gathered}[/tex]Therefore, we can say that in approximately 10 years from 2000.
This means that in the year 2010, we would expect textbook sales to first reach $7 billion
name the point of intersection –2x = −2y - 4 -6 = 3у – бх
Answers
–2x = −2y - 4
-6 = 3у – бх
Solve the first equation for x:
x = (-2y-4) /-2
x= y + 2
Replace x in the second equation and solve for y
-6= 3y - 6 (y+2)
-6= 3y -6y - 12
-6= -3y -12
-6+12= -3y
6=-3y
6/-3= y
y= -2
Replace y on any equation and solve for x
x= y + 2
x= -2+2 = 0
Point of intersection = (0,-2)
Graph triangle ABC with vertices A(0,5) B(4,3) and C(2,-1) and it’s image after a reflection in the line y=2I starting by graphing triangle ABC just so you know!
Answers
Given the triangle ABC, you can identify that the coordinates of its vertices are:
[tex]\begin{gathered} A\mleft(0,5\mright) \\ B\mleft(4,3\mright) \\ C\mleft(2,-1\mright) \end{gathered}[/tex]You know that it is reflected over the following line:
[tex]y=2[/tex]Notice that it has the form of a horizontal line. It intersects the y-axis at this point:
[tex](0,2)[/tex]Knowing that you can graph the line. See the picture below:
By definition, when a figure is reflected over a line, the points of the Image (the figure obtained after the transformation) and the points of the Pre-Image (the original figure), have the same distance from the line of reflection.
Notice that:
- Point A is 3 units away from the line of reflection.
- Point B is 1 unit away from the line.
- Point C is 3 units away from the line.
See the picture attached:T
Therefore, the points of the Image will have this distance from the line of reflection:
- Point A' will be 3 units away from the line of reflection.
- Point B' will be 1 unit away from the line.
- Point C' will be 3 units away from the line.
The sum of the angle measures of a polygon with n sides is 1440 . Find n.
Answers
We have that the sum of the angles measures of a polygon with n sides is 1440
The formula to find this is
[tex]\mleft(n-2\mright)\mleft(180\mright)=1440[/tex]we need to clear x
[tex]\begin{gathered} (n-2)=\frac{1440}{180} \\ n-2=8 \\ n=8+2 \\ n=10 \end{gathered}[/tex]the value of n =10
the polygon has 10 sides
The sequence is arithmetic or geometric and the common difference or ratio is 5.
Answers
1. Arithmetic
2. common difference
1) Examining that sequence we can see that:
[tex]\begin{gathered} -6,-1,4,9 \\ -6+5=-1 \\ -1+5=4 \\ 4+5=9 \end{gathered}[/tex]So as we can see this sequence is an Arithmetic one, whose common difference is 5
2) That is the answer.
I need to solve this to get zero can you help?
Answers
EXPLANATION
We can see in the picture that it's a right triangle, so, the sum of angles should be equal to 180°.
90°+29°+ left angle = 180°
Isolating left angle = 180 - 90 - 29 = 61°
By the Law of Sines:
[tex]\frac{x}{Sin29}=\frac{16}{Sin61}[/tex]Multiplying both sides by Sin 29°:
[tex]x=Sin29\cdot\frac{16}{Sin61}[/tex]Multiplying:
[tex]x=8.87[/tex]The answer is x= 8.87.
A biology class has a total of 47 students. The number of males is 11 more than the number of females. How many males and how many females are in the class?
Answers
As per given by the question,
There are given that ,
The total number of student is 47.
Now,
The number of male is 11 more than numbers of females.
So,
Suppose, the number of students is x.
Then,
The female is x, then
The number of males is,
[tex]11+x[/tex]Beacuse 11 more than females.
Then,
According to the question,
There are total student is 47.
Now,
[tex]\begin{gathered} x+11+x=47 \\ 11+2x=47 \\ 2x=47-11 \\ 2x=36 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 2x=36 \\ x=\frac{36}{2} \\ x=18 \end{gathered}[/tex]The numbers of female student is 18.
Then,
The numbers of male student is,
[tex]\begin{gathered} x+11=18+11 \\ =29 \end{gathered}[/tex]Hence, the number of males student is 29 and the numbers of female student is 18.
Solve. Write the solution set in interval notation.-2x > -8 and - 3x < 24
Answers
Solve. Write the solution set in interval notation.
-2x > -8 and - 3x < 24
-2x > -8
divide both sides by -2
x < 4
And -3x < 24
divide both sides by -3
So, x > -8
So, x < 4 and x > -8
it can be written -8 < x < 4
So, the interval of solution is ( -8 , 4 )
and can be represented on the line of numbers as shown at the following figure :
Which choice is equivalent to the product below when x> 0? 3x xli 3x ОАА O A. ОВ. Ос. C. Ž O D. D. x 2.
Answers
We can use the following properties of radicals:
[tex]\begin{gathered} \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\Rightarrow\text{ Product property} \\ \sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}\Rightarrow\text{ Quotient property} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} \text{ Apply the product property} \\ \sqrt[]{\frac{3x}{2}}\cdot\sqrt[]{\frac{x}{6}}=\sqrt[]{\frac{3x\cdot x}{2\cdot6}} \\ \sqrt[]{\frac{3x}{2}}\cdot\sqrt[]{\frac{x}{6}}=\sqrt[]{\frac{3x^2}{12}} \\ \text{ Simplify the expression inside the radical} \\ \sqrt[]{\frac{3x}{2}}\cdot\sqrt[]{\frac{x}{6}}=\sqrt[]{\frac{3x^2}{3\cdot4}} \\ \sqrt[]{\frac{3x}{2}}\cdot\sqrt[]{\frac{x}{6}}=\sqrt[]{\frac{x^2}{4}} \\ \text{ Apply the quotient property} \\ \sqrt[]{\frac{3x}{2}}\cdot\sqrt[]{\frac{x}{6}}=\frac{\sqrt[]{x^2}}{\sqrt[]{4}} \\ \sqrt[]{\frac{3x}{2}}\cdot\sqrt[]{\frac{x}{6}}=\frac{x}{2} \end{gathered}[/tex]Therefore, the choice that is equivalent to the given product when x > 0 is:
[tex]\frac{x}{2}[/tex]The functions f(x) and g(x) are shown on the graph.f(x)=x²What is g(x)?A. g(x)= -x^2-2B. g(x) = -x²+2C. g(x) = (-x)²-2D. g(x) = (-x)² + 2
Answers
Given the function:
[tex]f(x)[/tex]You can identify that its Vertex is at the Origin.
Look at the function:
[tex]g(x)[/tex]Notice that it was obtained by reflecting the first function across the x-axis and it also was shifted 2 units down.
According to the Transformation Rules for Functions:
1. If:
[tex]-f(x)[/tex]The function is reflected across the x-axis.
2. If:
[tex]f(x)-k[/tex]The function is shifted down "k" units.
You need to remember that the Parent Function (the simplest form) of Quadratic Equations is:
[tex]y=x^2[/tex]Therefore, the equation of the blue graph is:
[tex]f(x)=x^2[/tex]Therefore, you can write the following equation for the second function using the rules shown before:
[tex]g(x)=-x^2-2[/tex]Hence, the answer is: Option A.
What additional information do you need to know in order to prove the two triangles congruent using HiL?
Answers
Given
The triangles,
To find:
What additional information do you need to know in order to prove the two triangles are congruent using HL rule?
Explanation:
It is given that,
That implies,
Since HL rule states that,
If the hypotenuse and a single leg (HL) are proportional between two right triangles, then the triangles are similar.
From, the figure,
The two right triangles have same hypotnuse YW and the leg WZ and XY are proportinal.
Therefore, the triangle WXY and WZY are congruent.
Hence, no additional information is needed to prove that the two triangles are congruent.
What is the value of p?A. 40°B. 90°C. 50°D. 60°
Answers
Let thee interior angle in the triangle at the same point as 140 degrees be T
T + 140 = 180 (sum of angles on a straight line)
T = 180 -140
T = 40
Let the interior angle in the triangle at the same point as 90 degrees be S
S + 90 = 180 (sum of angles on a straight line)
S = 180 -90
= 90
P + 40 + 90 = 180 (sum of angles in a triangle)
P + 130 = 180
P = 180 - 130
P = 50
Option C