Need help for 56 it says solve equation to the nearest tenth use the given restrictions
Answers
Problem N 56
we have
sin∅=0.8 ----------> interval [-90,90] ----> that means the angle lie in the I or IV quadrant
∅=sin^-1(0.8)
∅=53.1 degrees
In the IV quadrant, the value of sine is negative (so in the IV quadrant there is no solution)
The answer is
∅=53.1 degreesRelated Questions
Principal Shepherd reported the state test scores from some students at her school. Score Number of students 25 3 43 4 97 3 X is the score that a randomly chosen student scored. What is the expected value of X? Write your answer as a decimal.
Answers
Answer: Expected value = 53.8
GIVEN THE FOLLOWING DATA
Score: 25 43 94
number of students: 3 4 3
E(x) = 25*3 + 43*4 + 97*3 / 3 + 4 + 3
E(x) = 75 + 172 + 291 / 10
E(x) = 538/10
E(x) = 53.8
therefore, the expected value is 53.8
A retailer needs to purchase 12 printers. The first printer costs $54, and each additional printer costs 5% less than the price of the previous printer, up to 15 printers. What is the total cost of 12 printers? $368.58 $496.41 $615.60 $618.30
Answers
Given that a retailer needs to purchase 12 printers, the first printer cost $54.
It is known that each additional printer costs 5% less than than the cost of the previous printer.
[tex]\text{Cost of first printer = \$54}[/tex]Cost of the second printer
The second printer costs 5% less than the first printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the second printer = }\frac{\text{5}}{100}\times54=2.7 \\ \text{Thus the price of the second printer =54-2.7=51.3} \end{gathered}[/tex]Cost of the third printer
The third printer costs 5% less than the second printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the third printer = }\frac{\text{5}}{100}\times51.3=2.565 \\ \text{Thus the price of the third printer =51.3-2.565=}48.735 \end{gathered}[/tex]Cost of the fourth printer
The fourth printer costs 5% less than the third printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the fourth printer = }\frac{\text{5}}{100}\times48.735=2.437 \\ \text{Thus the price of the fourth printer =48.735-2.437=}46.298 \end{gathered}[/tex]Cost of the fifth printer
The fifth printer costs 5% less than the fourth printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the fifth printer = }\frac{\text{5}}{100}\times46.298=2.315 \\ \text{Thus the price of the fifth printer =46.298-2.315=}43.981 \end{gathered}[/tex]Cost of the sixth printer
The sixth printer costs 5% less than the fifth printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the sixth printer = }\frac{\text{5}}{100}\times43.981=2.199 \\ \text{Thus the price of the sixth printer =43.981-2.199=}41.782 \end{gathered}[/tex]Cost of the seventh printer
The seventh printer costs 5% less than the sixth printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the seventh printer = }\frac{\text{5}}{100}\times41.782=2.089 \\ \text{Thus, the price of the seventh printer =41.782-2.089=}39.693 \end{gathered}[/tex]Cost of the eighth printer
The eighth printer costs 5% less than the seventh printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the eighth printer = }\frac{\text{5}}{100}\times39.693=1.985 \\ \text{Thus, the price of the eighth printer =39.693-1.985=}37.708 \end{gathered}[/tex]Cost of the ninth printer
The ninth printer costs 5% less than the eighth printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the ninth printer = }\frac{\text{5}}{100}\times37.708=1.885 \\ \text{Thus, the price of the ninth printer =37.708-1.885=}35.823 \end{gathered}[/tex]Cost of the tenth printer
The tenth printer costs 5% less than the ninth printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the tenth printer = }\frac{\text{5}}{100}\times35.823=1.791 \\ \text{Thus, the price of the tenth printer =35.823-1.791=}34.032 \end{gathered}[/tex]Cost of the eleventh printer
The eleventh printer costs 5% less than the tenth printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the eleventh printer = }\frac{\text{5}}{100}\times34.032=1.702 \\ \text{Thus, the price of the eleventh printer =34.032-1.702=}32.33 \end{gathered}[/tex]Cost of the twelfth printer
The twelfth printer costs 5% less than the eleventh printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the twelfth printer = }\frac{\text{5}}{100}\times32.33=1.617 \\ \text{Thus, the price of the twelfth printer =32.33-1.617=}30.713 \end{gathered}[/tex]Thus, the total cost of 12 printers is evaluated as
[tex]\begin{gathered} 54+51.3+48.735+46.298+43.981+41.782+39.693+37.708+35.823+34.032+32.33+30.713_{_{_{}}} \\ =496.4 \end{gathered}[/tex]Thus, the sum of twelve printers is $496.4
The second option is the correct answer.
Match the following term with its definition: a. Segment b. Line c. Angle d. Congruent e. Opposite rays f. Point 8. Ray 1) Has one endpoint and extends infinitely in one direction 2) Two rays that share one endpoint and are not on the same line 3) Two rays that share one endpoint and are on the same line 4) HHaving the same size, shape, or measure 5) Has two endpoints and is part of a line
Answers
Problem
For this problem we want to math the terms with the appripate definition and we have this:
Solution
a. Segment
5) Has two endpoints and is part of a line
c. Angle
3) Two rays that share one endpoint and are on the same line
d. Congruent
4) Having the same size, shape, or measure
e. Opposite rays
1) Has one endpoint and extends infinitely in one direction
f. Point
2) Two rays that share one endpoint and are on the same line
If the unit rate is 60 miles per hour, how many miles would be driven in 2.5 hours?
Answers
Given:
Unit rate = 60 miles/hour
To find:
How many miles would be driven in 2.5 hours
Step by step solutions:
We know that:
Amount of miles = Unit rate × time
Amount of miles = 60 miles/hour × 2.5 hours
Amount of miles = 60 × 2.5 miles
Amount of miles = 150 miles
From here we can say that they have traveled 150 miles.
Russell worked 60 math problems in 15 min. At that rate, how many problems would he be able to work in 10 min. problems.
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60 problems in 15 min
X problems is 10 min
x/60 = 10/15
x = 60 (10/15) = 600/15 = 40
x = 40
Answer:
40 math problems in 10 minutes
-6x + y = -19, -6x + y = -19 *(-2. 6)ParallelAll PointsInfinite SolutionsNo SolutionSame / differentSame / Same
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The lines are the same line, as all their coefficients are the same.
A bag contains 5 blue marbles, 11 red marbles and 14 green marbles. Marbles are then chosen at random.a) Find the probability of getting a red and then a green marble, when two marbles are chosen.b) Find the probability of getting a red or a green marble, when one marble is chosen.
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EXPLANATION:
We are given a bag of marbles and the conditions are;
5 blue marbles
11 red marbles
14 green marbles
Total of 30 marbles.
To calculate the probability of an event such as the one in this experiment, we shall use the formula;
[tex]P[E]=\frac{Number\text{ of required outcomes}}{Number\text{ of all possible outcomes}}[/tex]Marbles are now chosen at random;
The probability of getting a red marble will be;
[tex]P[red]=\frac{11}{30}[/tex]Note that the number of all possible outcomes is 30 since there are 30 marbles in all (regardless of the color).
The probability of getting a green marble would now be dependent on a total of 29 marbles. Note that 1 marble has been chosen already, which means our experiment now has a total possible outcome of 29.
[tex]P[green]=\frac{14}{29}[/tex]At this point we should note that when we need to find the probability of one event and then another, what we have is a product of probabilities.
Therefore, the probability of getting a red and then a green marble when two marbles are chosen, will be;
[tex]P[red]\times P[green][/tex][tex]P[red]\text{ and }P[green]=\frac{11}{30}\times\frac{14}{29}[/tex][tex]P[red]\text{ and }P[green]=\frac{154}{870}[/tex][tex]P[red]\text{ and }P[green]=\frac{77}{435}[/tex][tex]P[red]\text{ and }P[green]=0.1770[/tex]The probability of getting a red or a green marble when one marble is chosen is calculated as follows;
[tex]P[red]\text{ Or }P[green][/tex]The probability of one event or the other occuring is simply an addition of probabilities.
Therefore, we would have;
[tex]P[red]=\frac{11}{30}[/tex][tex]P[green]=\frac{14}{30}[/tex]Take note that one marble is drawn and NOT two like the first experiment.
[tex]P[red]+P[green]=\frac{11}{30}+\frac{14}{30}[/tex][tex]P[red]+P[green]=\frac{25}{30}[/tex][tex]P[red]+P[green]=\frac{5}{6}[/tex][tex]P[red]+P[green]=0.8333[/tex]ANSWER:
[tex]\begin{gathered} (a) \\ 0.1770 \\ (b) \\ 0.8333 \end{gathered}[/tex]Use the coordinates to describe the transformation and write a rule.
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We are given the preimage points and the mapped points (image):
A(-6, -2) A'(-6, 2)
B(-3, -6) B'(-3, 6)
C(-2, -2) C'(-2, 2)
We can see the x-coordinate of the preimage and the image are the same, but the y-coordinate is negated (or inverted).
This rule corresponds to a reflection across the x-axis.
Thus, the transformation is a reflection across the x-axis and the rule is to negate the value of the y-coordinate of each point, but leave the x-value the same.
Drag the numbers to create three ratios that are equivalent to 4:12.Numbers can only be used once.Pls help
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ANWERS
20 : 60
12 : 36
2 : 6
EXPLANATION
To create equivalent ratios we have to multiply or divide the numerator (the number on the left) and the denominator (the number on the right) by the same number.
For the first equivalent ratio we have to find the denominator given that the numerator is 20. We know that 20 is 4 times 5, this means that the numerator has been multiplied by 5 and, therefore, we have to multiply the denominator by 5 as well:
[tex]12\times5=60[/tex]For the second equivalent ratio we have to find the numerator given that the denominator is 36. 36 is 3 times 12. This means that we have to multiply the numerator by 3:
[tex]4\times3=12[/tex]For the third equivalent ratio we have the denominator that's 6. In this case, instead of multiplying we have to divide, because 6 is 12 divided by 2. Therefore, we have to divide the numerator by 2:
[tex]4\colon2=2[/tex]Find the sixth term of a sequence represented by f(n)=6n-2
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Given that the sequence is represented as
[tex]\begin{gathered} f(n)=6n-2 \\ \text{where n is the nth term of the sequence} \end{gathered}[/tex]Thus, the sixth term of the sequence is evaluated to be the value of f when n equals 6.
Thus,
[tex]f(6)=6(6)-2=36-2=34[/tex]Thus, the sixth term is 34
A phone company offers two long-distance plans. The first charges a flatvalue of $5.00 per month plus $0.99 for each minute used, and thesecond charges $10.00 a month plus $0.79 for each minute used.If x represents the number of minutes used each month, which system ofequations represents the total amount of money, y, you would spend foreach long-distance plan?
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The first phone company charges a flat monthly fee of $5 plus $0.99 per minute used. Let y = the total cost of the plan and x = the number of minutes used. Thus, the equation for this company is.
y = 0.99x + 5
The second company charges a flat monthly fee of $10 plus $0.79 per min
Write the equation of the line that passes through the given points.(-12,0) and (0,1)The equation of the line is
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To find the equation of a line that passes through the points (-12,0) and (0,1)
We will follow the steps below
We will first find the slope
slope (m) = y₂-y₁ / x₂-x₁
From the question x₁= -12 y₁ =0 x₂=0 y₂=1
Substituting the above into the slope(m) formula
m = 1-0 / 0+12
m = 1/12
We will now proceed to use the formula below to find the equation of the line;
y-y₁ = m(x - x₁)
we already know our; x₁ , y₁ and the slope(m), so we will just substitute into the above formula
y-0 = 1/12 (x+12)
We can further simplify the above to give;
12y = x+ 12
or
[tex]y\text{ =}\frac{1}{12}x\text{ + 1}[/tex]Solve the equation for y.cy +h= -7
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The given equation is-
[tex]cy+h=-7[/tex]First, we subtract h on each side.
[tex]\begin{gathered} cy+h-h=-7-h \\ cy=-7-h \end{gathered}[/tex]Then, we divide the equation by c.
[tex]\begin{gathered} \frac{cy}{c}=\frac{-7-h}{c} \\ y=\frac{-7-h}{c} \end{gathered}[/tex]Therefore, the final answer is[tex]y=\frac{-7-h}{c}[/tex]Diana uses 50 grams of coffee beans to make 80 fluid ounces of coffee. When company comes, she makes 240 fluid ounces of coffee. How many grams of coffee beans does Diana use when company comes?
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We have the following:
We can solve this problem by means of a proportion, since if with 50 grams we make 80 ounces of liquid coffee, we calculate the proportion from there and then multiply by the amount we want to know that are 240 ounces of liquid coffee
[tex](\frac{50}{80}\cdot\frac{g}{oz})\cdot(\frac{240z}{g})=150g[/tex]Therefore you need an amount of 150 grams of coffee beans
You discover a termite tunnel on your home and read that they have a doubling time of 18 days. If there are typically 150 termites in 1 tunnel, how many termites will your house have in: a. 1 month (30 days)? b. 1 year?
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Okay, here we have this:
Considering the provided information, we are going to calculate the requested amount of termites, so we obtain the following:
To do this, we will replace the doubling time in the following formula:
[tex]N(t)=N_02^{\frac{t}{T_d}}[/tex][tex]\begin{gathered} N(30)=(150)2^{\frac{30}{18}} \\ \approx476 \end{gathered}[/tex][tex]\begin{gathered} N(365)=(150)2^{\frac{365}{18}} \\ \approx190682402 \end{gathered}[/tex]Finally we obtain that:
a. After 1 month (30 days) will be approximately 476 termites.
b. After 1 year (365 days) will be approximately 190'682402 termites.
Find the equation (in terms of x) of the line through the points (-4,3) and (3,1)y =
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The Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
So, given the points:
[tex]\begin{gathered} \mleft(-4,3\mright) \\ \mleft(3,1\mright) \end{gathered}[/tex]You can find the slope by using this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, you can set up that.
[tex]\begin{gathered} y_2=3 \\ y_1=1 \\ \\ x_2=-4 \\ x_1=3 \end{gathered}[/tex]Then, substituting values into the formula and evaluating, you get:
[tex]m=\frac{3-1}{-4-3}=\frac{2}{-7}=-\frac{2}{7}[/tex]Now you can substitute the slope of the line and the coordinate of one of the points given in the exercise, into the equation
[tex]y=mx+b[/tex]Then, substituting the coordinates of the point:
[tex](3,1)[/tex]And then solving for "b", you get that this is:
[tex]\begin{gathered} 1=(-\frac{2}{7})(3)+b \\ \\ 1=-\frac{6}{7}+b \\ \\ 1+\frac{6}{7}=b \\ \\ b=\frac{13}{7} \end{gathered}[/tex]Finally, knowing "m" and "b", you can determine that the equation of this line (in terms of "x"), is:
[tex]\begin{gathered} y=mx+b \\ \\ y=-\frac{2}{7}x+\frac{13}{7} \end{gathered}[/tex]The answer is:
[tex]y=-\frac{2}{7}x+\frac{13}{7}[/tex]i have a triangle whose is 19.9 and a height of 19. what is the the mease of the diagonal to nearest 10th of an inch?
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We will find it as follows:
[tex]d^2=19.9^2+19^2\Rightarrow d=\sqrt[]{19.9^2+19^2}\Rightarrow d\approx27.5[/tex]So, the diagonal will be approximately 27.5 inches.
Graph triangle JKL with vertices J(3,3), K(0,0) and L(0,-3) and it’s image after a dilation with scale factor k. List the new coordinates of the image below the graph. I need help with question 7.
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Lets start by graphing the triangle. We will add the points first and then connect them.
The points are:
[tex]\begin{gathered} J=(3,3) \\ K=(0,0) \\ L=(0,-3) \end{gathered}[/tex]So we will get the following:
Now, the dilatation will be about point (-3, 6). It is easier to make the dilatation about the origin, so we can first translate the points (-3, 6) to the origin (0, 0), make the dilatation about the origin and then translate it back to (-3, 6).
Translate (-3, 6) to (0, 0) means to add 3 to the x coordinate and substract 6 from the y coordinate. We will apply this to all vertexes of the triangle:
[tex]\begin{gathered} Center\colon(-3,6)\to(-3+3,6-6)\to(0,0) \\ J\colon(3,3)\to(3+3,3-6)\to(6,-3) \\ K\colon(0,0)\to(0+3,0-6)\to(3,-6) \\ L\colon(0,-3)\to(0+3,-3-6)\to(3,-9) \end{gathered}[/tex]We get this:
Now, we apply the dilatation about (0, 0) (remeber that our center is now at the origin). The scale factor is 1/3, so we just multiply all the coordinates by it:
[tex]\begin{gathered} Center\colon(0,0)\to(0\cdot\frac{1}{3},0\cdot\frac{1}{3})\to(0,0) \\ J\colon(6,-3)\to(6\cdot\frac{1}{3},-3\cdot\frac{1}{3})\to(2,-1) \\ K\colon(3,-6)\to(3\cdot\frac{1}{3},-6\cdot\frac{1}{3})\to(1,-2) \\ L\colon(3,-9)\to(3\cdot\frac{1}{3},-9\cdot\frac{1}{3})\to(1,-3) \end{gathered}[/tex]We get:
And now we need to translate the center back to (-3, 6), which we do by substracting 3 from x and adding 6 to y (the contrary as we did before), we do this for all the vertexes too:
[tex]\begin{gathered} Center\colon(0,0)\to(0-3,0+6)\to(-3,6) \\ J\colon(2,-1)\to(2-3,-1+6)\to(-1,5) \\ K\colon(1,-2)\to(1-3,-2+6)\to(-2,4) \\ L\colon(1,-3)\to(1-3,-3+6)\to(-2,3) \end{gathered}[/tex]Drawing this, we have:
hello I need to graph the graph g(x)= x^2+3 which is the inverse of y^2=x-3. I do not know how to graph the graph. :)
Answers
Given:
The equation is given as g(x) = x²+3.
The objective is to fin the graph of the equation.
Explanation:
Consider the values of x as -2, -1, 0, 1, 2.
At x = -2 in the given equation.
[tex]\begin{gathered} y=(-2)^2+3 \\ =4+3 \\ =7 \end{gathered}[/tex]Thus, the coordinate is (-2,7).
At x = -1 in the given equation,
[tex]\begin{gathered} y=(-1)^2+3 \\ =1+3 \\ =4 \end{gathered}[/tex]Thus, the coordinate is (-1,4).
At x = 0 in the given equation,
[tex]\begin{gathered} y=0^2+3 \\ y=3 \end{gathered}[/tex]Thus, the coordinate is (0,3).
At x = 1 in the given equation.
[tex]\begin{gathered} y=1^2+3 \\ =4 \end{gathered}[/tex]Thus, the coordinate is (1,4).
At x = 2 in the given equation,
[tex]\begin{gathered} y=2^2+3 \\ =7 \end{gathered}[/tex]Thus, the coordinate is (2,7).
To plot the graph:
Then, using the obtained coordinates the graph of the equation will be,
Hence, the graph of the equation is obtained.
Cindy buys a party sandwich that is 5 feet long. Her brother cuts off a piece of the sandwich that is 3 /4 foot long. Cindy wants to cut the remaining sandwich into 3-inch pieces to share with guests.
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Given:
Length of sandwich Cindy buys = 5 ft
Since her brother cuts off 3/4 ft of the sandwich, the remaining length would be:
[tex]\begin{gathered} =\text{ 5 - }\frac{3}{4} \\ =\text{ }\frac{20-3}{4} \\ =\text{ }\frac{17}{4}\text{ ft} \end{gathered}[/tex]She wants to cut the sandwich into 3-inch pieces. The number of pieces that she cut is the remaining length of the sandwich divided by the length of each piece.
First, let us convert 3 inches to ft:
[tex]\begin{gathered} \text{= 3 inch }\times\frac{\frac{1}{12}\text{ ft}}{1\text{ inch}} \\ =\frac{3}{12}\text{ ft} \\ =\text{ }0.25\text{ ft} \end{gathered}[/tex]Hence:
[tex]\begin{gathered} \text{Number of pieces = }\frac{\frac{17}{4}\text{ ft}}{0.25\text{ ft}} \\ =\text{ 17 pieces} \end{gathered}[/tex]Answer: 17 pieces
How much is 17 5/14 - 18
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Solution:
Given:
[tex]17\frac{5}{14}-18[/tex]To solve the expression, we convert the mixed number to an improper fraction and find the lowest common denominator (LCD) of both fractions.
The LCD is 14.
[tex]\begin{gathered} 17\frac{5}{14}-18=\frac{243}{14}-\frac{18}{1} \\ =\frac{243-252}{14} \\ =\frac{-9}{14} \end{gathered}[/tex]Therefore, the answer is;
[tex]\frac{-9}{14}[/tex]
When baking cookies, each cookie should be placed about 2 inches from one another to allow room to expand. If one cookie has a radius of 1 inch and a center at C(1, -1), find the center and equation of the cookie immediately to the right. (Assume that each cookie is uniform with a radius of 1 inch and that 1 inch = 1 unit on a coordinate plane.) A. C2 (-1,5) (x + 1)² + (y- 5)² = 1 B. C2(3,-1) (x - 3)²+ (y + 1)² = 1 C. C2 (5,-3) (x - 5)²+(y+3)²= 1 D. C2(5,- 1) (x - 5)²+(y+ 1)²= 1
Answers
Solution
For this case the center of the original cookie is given by C= (1,-1) and the radius is r= 1
Then the original equation is:
(x-1)^2 + (y+1)^2 = 1
Then for the next cookie at the right we need to satisfy the condition of 2 units from the original then the best option is:
A. C2 (-1,5)
(x+1)^2 + (y-5)^2 = 1
3. Line p intersects plane A at what point?4. Describe how planes A and B intersect.
Answers
The point of intersection between the line "p" and the plane A is the point at which they cross, in this case this is the point X.
When two planes intersect they create a line in the case of the intersection between the planes A and B is the line "k".
Solve -2(3x - 1) = 20 for x.A) x = 5B) x = -3OC) x = 2D) x = -1
Answers
we have the equation
[tex]-2\left(3x-1\right)=20[/tex]Solve for x
step 1
Divide both sides by -2
[tex]\begin{gathered} \frac{-2\left(3x-1\right)}{-2}=\frac{20}{-2} \\ simplify \\ 3x-1=-10 \end{gathered}[/tex]step 2
Adds 1 on both sides
[tex]\begin{gathered} 3x-1+1=-10+1 \\ 3x=-9 \end{gathered}[/tex]step 3
Divide both sides by 3
[tex]\begin{gathered} \frac{3x}{3}=\frac{-9}{3} \\ \\ x=-3 \end{gathered}[/tex]The answer is option BI need help with this badly and I need a good explanation please
Answers
To solve this problem, we need to apply some angles theorems and definitions.
We know that angle MTN is 90°, by given.
Angle STM = 2x+8, by given.
Angle STM = Angle OTP, by vertical angles. Remember that vertical angles only have the vertex in common, and they are always equal.
So, by substitution, we have that:
Angle OTP = 2x+8
On the other hand, we know that the maximum angle around vertex T is 360°, which is form by the sum of all angles we know so far:
STM + 90 + NTP + OTP + STQ = 360°
Now, we substitute all given data:
2x + 8 + 90 + 71 - x + 2x + 8 + STQ = 360°
Then, we reduce like terms:
3x + 177 + STQ = 360°
STQ = 360 - 177 - 3x = 183 - 3x
As you can observe, we need to know the value of the variable x to find the angle STQ.
Angles STM, MTN, NTP are supplementary, by definition, that means they are equal to 180°:
2x + 8 + 90 + 71 - x = 180
We solve the equation for x:
x = 180 - 169 = 11
Now, we use the value of the variable to find the angle STQ:
STQ = 183 - 3x = 183 - 3(11) = 183 - 33 = 150°
Therefore, angle STQ is equal to 150°.given f(x)=x^2+3,x<_ 0. sketch the graph of f and it's inverse on the same cartesian plane.
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The given function is
[tex]f(x)=x^2+3[/tex]Its inverse can be founded by this way
[tex]\begin{gathered} y=x^2+3 \\ x=y^2+3 \\ x-3=y^2 \\ y^2=x-3 \\ y=-\sqrt[]{x-3} \\ f^{-1}(x)=-\sqrt[]{x-3} \end{gathered}[/tex]Now we need to graph them with the line of symmetry y = x
Suppose that the relation H is defined as follows. H={(5,8), (-4,-6), (8,-6)} Give the domain and range of H. Write your answers using set notation.
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Domain: { 5,-4,8} or {-4,5,8}
Range: {8, -6, -6} or {-6, 8} it's double -6, but we don't repeat same number in set notation.
[tex]undefined[/tex]What is the slope of the line
Answers
We can calculate the slope of a line "m" by means of the following equation:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1,y1) and (x2,y2) are two points of a line.
We could take any point where the line passes through, for example, we can take (0,20) and (10,70), then we get:
[tex]m=\frac{70-20}{10-0}=\frac{50}{10}=5[/tex]Then, the slope of the line equals 5
As a part of his science experiment, Ethan recorded the number of days it rained in April. Over the 30 days, it rained 15 days. Ethan wants to know what percent of the days in Apri it rained
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Answer:
Explanation:
Ethan recorded that it rained 15 days over the 30 days in April.
To know what percentage it rained, we need to divide the number of days it rained by the number of days in the month, and then multiply the result by 100.
[tex]\frac{15}{30}\times100[/tex]Simplifying this, we have:
[tex]undefined[/tex]3. Natasha places a mirror on the ground 24 ft from the base of an oak tree. She walks backward until she can see the top of the tree in the middle of the mirror. At that point, Natasha's eyes are 5.5 ft above the ground, and her feet are 4 ft from the image in the mirror Find the height of the oak tree,
Answers
The figure for the Natasha height and height of tree can be draw as,
The length MO is 4ft.
The length of MQ is 24 feet.
The length of NO is 5.5 ft.
The length of tree (PQ) is x.
Consider the triangle MNO and triangle MPQ.
[tex]\begin{gathered} \angle NMO\cong\angle PMQ \\ \angle NOM\cong\angle PQM\text{ (Each right angle)} \\ \Delta NOM\cong\Delta PQM\text{ (By AA similarity)} \end{gathered}[/tex]For similar triangle ratio of sides are equal. So,
[tex]\begin{gathered} \frac{NO}{PQ}=\frac{MO}{MQ} \\ \frac{5.5}{x}=\frac{4}{24} \\ \frac{5.5}{x}=\frac{1}{6} \\ x=5.5\cdot6 \\ =33 \end{gathered}[/tex]Thus height of oak tree is 33 ft.