Given
Two functions
[tex]\begin{gathered} f(x)=x \\ g(x)=\frac{1}{6}x \end{gathered}[/tex]Procedure
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function.
it says on top that the image is not drawn to scale.
D; Both statements are correct
Here, we want to check the correct statement
Basically from the diagram, it is confirmed that what we have is a 30-60-90 triangle
Now, for a 30-60-90 degrees triangle, the side lengths are in a particular ratio
From the diagram, MO faces the right angle and thus, it is the longest side and the hypotenuse
Now, let us take a look at the ratio of the sides in both submissions
For a 30-60-90 degrees triangle, the ratio of the sides is;
[tex]1\colon\sqrt[]{3}\text{ :2}[/tex]Hence, one side must be twice the length of the other
From Kellie's statement we can see MO is twice NO
From Eddie's statement, we can also see that MO is twice NO
Lastly, we can also see in both that dividing MN by NO yields the root of 3 in both statemets which confirms the existence of the theoretical ratio
So the conclusion here is that;
Both students are correct
Find sinθ, tanθ, and secθ, where θ is the angle shown in the figure. Give exact values, not decimal approximations.sinθ=tanθ=secθ=
1) We have here a right triangle, so we can use the Pythagorean Theorem to find the adjacent leg. Note that the hypotenuse is leg opposite to the right angle. In this case, a=4.
a²=b²+c²
4²=b²+3²
16=b²+9
16-9=b²
b=√7
2) Let's find the trigonometric functions. The first one is the sine (θ), which relates the opposite side and the hypotenuse:
[tex]\sin (\theta)\text{ =}\frac{3}{4}[/tex]2.2)Moving on, we can deal with the tangent of theta, relating the opposite side over the adjacent, for this one we have to rationalize it:
[tex]\begin{gathered} \tan (\theta)\text{ =}\frac{3}{\sqrt[]{7}} \\ \tan (\theta)=\frac{3\sqrt[]{7}}{7} \end{gathered}[/tex]Finally, let's find the reciprocal function of the cosine function by setting this as the reciprocal of the cosine, and then calculating it:
[tex]\begin{gathered} \sec \text{ (}\theta)=\frac{1}{\cos(\theta)}\Rightarrow\sec (\theta)=\frac{1}{\frac{\sqrt[]{7}}{4}}\Rightarrow\sec (\theta)\text{ =}\frac{4}{\sqrt[]{7}} \\ \sec (\theta)\text{ =}\frac{4\sqrt[]{7}}{7} \end{gathered}[/tex]5 tons of rocks cost $7,000.00. What is the price per pound ??
Answer: Per rock or pound?
Four of the twelve members of the panel were late for
the meeting. What fraction of the members were on
time?
Answer:
2/3
Step-by-step explanation:
If 4 were late, then 8 were on time.
8/12 Divide the top and bottom by 4
2/3
You are dressing a mannequin for a clothingstore display. You have 4 types of shoes, 5necklaces, 10 tops, and 7 bottoms to choosefrom. How many distinct outfits can youcréate? >
Given:
• Types of shoes = 4
,• Number if necklaces = 5
,• Number of tops = 10
,• Number of bottoms = 7
Let's find how many distinct outfits you can create.
To find the number of distinct outfits you can create, we have:
[tex]\begin{gathered} n=4*5*10*7 \\ \\ n=1400 \end{gathered}[/tex]Therefore, the number of distinct outfits you can create is 1400.
ANSWER:
1400
A person tosses a coin 14 times. In how many ways can he get 10 heads?
convert these measurements to centimeters : (a)73.1 cm and (b) 0,0012km
Answer:
(a) 73.1 cm (b) 120 cm
Step-by-step explanation:
Step-by-step explanation:
Part (a)
73.1 cm [It remains the same as it is already given in cms]
Part (b)
To convert 0.0012km to cm we multiply x 100000
=> 0.0012 x 100000
=> 120 cm
can you help me factor the expression x^2+4x-21
To factor this expression we need to find two numbers which sum is 4 and the product is -21.
Now, 21 has only 2 factors (besides 1 and 21), 7 and 3, se we need to write them in a way such that they sum 4, so
[tex]x^2+4x-21=(x+7)(x-3)[/tex]we see that 7-3=4 and 7(-3)=-21, so the factorization is correct.
2. A membership to the theme park is $48 per year. Marcos cancelled his membership early and is only required to pay for 0.25 of a year. How much will he need to pay?
Marcos needs to pay $12 for 0.25 of a year due to cancelling the membership
Membership cost to the theme park per year = $48
Payment required to be made by Marcos = 0.25 of a year
When we divide a whole into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. However, as we proceed to the right following the decimal point, we obtain the fractional portion of the decimal number.
Converting the decimal into a fraction we get:
=0.25
= 25/100
= 1/4 of a year
So, Marcos needs to pay the membership fees for only 1/4 of a year
According to which we get: 48*1/4 = $12
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Find X.
Cirucumscribed angles
Answer:
x = 64
Step-by-step explanation:
to find x add make an equation to solve for x. the equation is 90+90+44+2x+8=360. after solving for x, x will equal 64.
Use inverse matrices to find the solution to the system of equations represented by this matrix equation
if you replace it in that order, it should give you the answer
[tex]\begin{bmatrix}{2} & {-3} \\ {-3} & {5}\end{bmatrix}[/tex]Rajan climbed to a height of 15 ft from the bottom of a climbing wall. He then climbed up an additional 10 ft.
What must he do to return to the bottom of the climbing wall?
In the first blank, say whether Rajan must climb up or down. In the second blank, state the number of feet Rajan must travel up or down.
Rajan must climb_____ft to return to the bottom of the climbing wall.
Rajan must climb down 25 ft to return to the bottom of the climbing wall
Height climbed from the bottom of the wall = 15ft
Height: The measurement of an object's height from the base to the top is known as height. It is sometimes referred to as altitude in geometry. The vertical distance between the lowest and highest point is measured. In coordinate geometry, it is often the measurement along the y-axis of an object.
Additional height climbed = 10ft
Total height climbed = 25ft
He should climb down the distance, as climbing up will further move him away from the bottom of the wall
Distance to climb down to the bottom of the wall = 25ft
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Choose the equation that represents a line that passes through points (−3, 2) and (2, 1)
5x + y = −13
5x − y = 17
x − 5y = −13
x + 5y = 7
The equation that represents a line that passes through points (−3, 2) and (2, 1) is x + 5y = 7.
How to find the equation of a line?The equation of the line passes through the points (−3, 2) and (2, 1). The equation of the line can be represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope using (−3, 2) and (2, 1)
m = slope = 1 - 2 / 2 + 3
m = - 1 / 5
Therefore,
slope = - 1 / 5
Let's find the y-intercept of the line using (2, 1)
y = - 1 / 5 x + b
1 = - 1 / 5 (2) + b
b = 1 + 2 / 5
b = 5 + 2/ 5
b = 7 / 5
Therefore, the equation of the line can be represented as follows:
y = - 1 / 5 x + 7 / 5
5y = -x + 7
5y + x = 7
x + 5y = 7
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Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students. How many students chose not to take French their freshman year?
As per the given percentage, there are 147 students are not take French their freshman year.
Students:
The students are the person formally engaged in learning, especially one enrolled in a school or college.
Given,
Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students.
Here we need to find the number of students who are not take French as their freshman year.
Let x be the total number of students in the freshman year.
So according to the given question, we know that,
72% of x = 378
Therefore, we have to find the value of x, so we have to move the others,
Then we get,
x = 378/72%
x = 378 x 100/72
x = 525
So, the total number of students are 525.
Then the students who are not taken French is,
=> 525 - 378 = 147
Therefore, the students who are not taken French is 147.
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What is the exact decimal equivalent of 7/12
Answer:
0.58333333333
I dont know how to answer this pls help
The hedgehog's total change in weight is -2.5 ounces.
What is the total change in weight?A relationship is proportional if the ratio of the variables is constant. The variables can either increase or decrease at a constant rate. A proportional relationship can be modelled with a linear equation.
Ratio = change in weight / days of hibernation
-0.18 / 9 = -0.02
-0.56 / 28 = -0.02
-1.44 / 76 = -0.02
-1.96 / 98 = -0.02
Weight when the day of hibernation is 125 = number of days x ratio
125 x -0.02 = -2.5
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Jolie is redesigning a water bottle to fit better in her cup holder. The diameter will have to be no larger 2.5 in. The water bottle is straight up and down. What would the height of the bottle be if she wants it to have a 99.34 in3 volume. (Round to nearest whole number)
20in
Explanations:The water bottle in question is known to be cylindrical in shape. The formula for calculating the volume of a cylinder is expressed as:
[tex]V=\pi r^2h[/tex]where;
r is the radius
h is the height
Given the following parameters
diameter = 2.5in
radius = 2.5/2 = 1.25in
volume = 99.34 in^3
Required
Height of the water bottle
Substitute the given parameters intothe formula
[tex]\begin{gathered} 99.34=3.14(1.25)^2\times h \\ 99.36=4.90625h \\ h=\frac{99.36}{4.90625} \\ h=20.25\approx20in \end{gathered}[/tex]The height of the water bottle will be 20in
Can you please help me solve this questions. I want a clear explanation thank you.
Given:
[tex]\begin{gathered} \text{Mean}=\mu=21.4 \\ \text{Standard deviation=}\sigma=5.0 \\ \text{Smple size=n=66} \end{gathered}[/tex]The z-score for 90 percent is 1.64.
To find the 90 percent confidence interval,
[tex]\begin{gathered} \mu+(\frac{\sigma}{\sqrt[]{n}}\times1.64)=21.4+(\frac{5}{\sqrt[]{66}}\times1.64) \\ =21.4+1.0094 \\ =22.4094\ldots\ldots(\text{ upper limit)} \\ \text{And} \\ \mu-(\frac{\sigma}{\sqrt[]{n}}\times1.64)=21.4-(\frac{5}{\sqrt[]{66}}\times1.64) \\ =21.4-1.0094 \\ =20.3906\ldots\ldots\ldots(\text{lower limit)} \end{gathered}[/tex]Answer: The 90 % confidence interval is ( 20.3906 , 22.4094 )
Find the indicated angle 0. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume a = 120 and c = 136. Round your answer to two decimal places.)
Base on the given data, the triangle is shown below.
Apply law of sine to this triangle implies,
[tex]\sin \theta=\frac{a}{c}[/tex]Given that, a=120 and c=136. Thefore, the given equation becomes,
[tex]\begin{gathered} \sin \theta=\frac{120}{136} \\ \sin \theta=0.88 \end{gathered}[/tex]Take the inverse to find the the measure of indicated angle.
[tex]\begin{gathered} \theta=\sin ^{-1}0.88 \\ \theta=61.64 \end{gathered}[/tex]Therefore, the angle is 61.64 degree.
Solve tan(x){tan(%) - 1) = 0 O A. x = 5 + 27T7,X = 3 37 + 27 O B. x = -2779,x=37 + X +277, X = +27 2. C. X = +19,X = = tnx +277 O D. X = n,X = x FT 4
Given the trigonometry equation below,
[tex]\tan (x)(\tan (x)-1)=0[/tex]Solving each part separately
[tex]\begin{gathered} \tan \mleft(x\mright)=0\quad \mathrm{or}\quad \tan \mleft(x\mright)-1=0 \\ x=\tan ^{-1}0\text{ or tan(x)=1} \\ x=\pm n\pi\text{ }or\text{ }x=tan^{-1}1 \\ x=\pm n\pi\text{ or x=45} \\ x=\pm n\pi\text{ or x=}\frac{\pi}{45}\pm n\pi \end{gathered}[/tex]Therefore,
[tex]x=\pm n\pi,\text{ x=}\frac{\pi}{45}\pm n\pi[/tex]Hence, Option D is the correct answer.
(3ax - n) ÷ 5
Solve for X.
Answer:
x = 10/a; restrictions a ± 0
Answer:
[tex]x = \cfrac{n+5}{3a}[/tex]=============================
Given expression
[tex](3ax - n) : 5 = 1[/tex]Solve it for x in steps below:
[tex]3ax - n = 5[/tex][tex]3ax = n + 5[/tex][tex]x = \cfrac{n+5}{3a}[/tex]To rent a certain meeting room, a college charges a reservation fee of $46 and an additional fee of $6.70 per hour. The math club wants to spend less than$106.30 on renting the meeting room.What are the possible amounts of time for which they could rent the meeting room?Use t for the number of hours the meeting room is rented, and solve your inequality for t.
As given by the question
There are given that the college charges a reservation fee of $46.
Now,
According to the question, the inequality is:
[tex]46+6.70t<106.30[/tex]Then,
To solve the above inequality, collect the constant terms on the right side
So,
[tex]\begin{gathered} 46+6.70t<106.30 \\ 6.70t<106.30-46 \\ 6.70t<60.3 \\ t<\frac{60.3}{6.70} \\ t<9 \end{gathered}[/tex]Hence, the room could be rented for up to 9 hours less than the stated amount.
on a map where each unit represents one kilometer two marinas are located at p(4,2) and q(8,12). if a boat travels in a straight line from one marina to the other how far does the boat travel. Answer choices: 14 kilometers 2sqrt296 kilometer 2sqrt5 kilometers
Solution:
Given the points below
[tex]p\left(4,2\right)and\text{ }q\left(8,12\right)[/tex]To find the distance between two points, the formula is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where point p represents coordinates 1 and point q represents coordinates 2
Substitute the coordinates into the formula above
[tex]\begin{gathered} d=\sqrt{(8-4)^2+(12-2)^2} \\ d=\sqrt{4^2+10^2} \\ d=\sqrt{16+100} \\ d=\sqrt{116} \\ d=\sqrt{4\times29} \\ d=2\sqrt{29}\text{ units} \end{gathered}[/tex]Since, 1 unit represents 1 kilometer on the map,
Hence, the answer is
[tex]2\sqrt{29}\text{ km}[/tex]All eleven letters from the word MATHEMATICS are written on individual slips of paper and placed in a hat. If you reach into the hat and randomly choose one slip of paper, what are the odds against the paper having a vowel written on it?
Let:
A = Get a paper having a vowel written on it
N = Total number of letters = 11
a = Number of vowels = 4
so:
[tex]\begin{gathered} P(A)=\frac{a}{N} \\ P(A)=\frac{4}{11} \\ P(A)\approx0.36 \end{gathered}[/tex]Answer:
36%
Write the inequality shown by the shaded region in the graph with the boundary line y = -3x +5
Inequality is an inequality comparison of numbers or expressions.
Given inequality:
y < -3x+5, y < x+2, y < -1
Graph the above inequality using Geogebra's online graphing calculator.
Answer:
...................... Hoffe er u
PLS HELP WILL MARK YOU BRAINLIEST!!
Point B is the midpoint of AC. AB=2x and AC=3x+20.
What is the value of x?
x=-20
x=20
x=4
x=6
Answer:
X=4
Step-by-step explanation:
i got the answer on a different app
Answer: The correct answer is 20 or -20
Step-by-step explanation:
its between 20 and -20 since i selected x=6 and x=4 and they were both wrong lol
(Solve the problem down below & simplify the answer. Round to the nearest hundredth as needed.)
From the given information, we know that the decreasing function values is
[tex]V(t)=3600(3^{-0.15t})[/tex]and we need to find the time t when V(t) is equal to $1200. Then by substituting this values into the function, we have
[tex]1200=3600(3^{-0.15t})[/tex]By dividing both sides by 3600, we get
[tex]3^{-0.15t}=\frac{1200}{3600}=\frac{1}{3}[/tex]So we have the equations
[tex]3^{-0.15t}=\frac{1}{3}[/tex]From the exponents properties, we know that
[tex]3^{-0.15t}=\frac{1}{3^{0.15t}}[/tex]so we have
[tex]\frac{1}{3^{0.15t}}=\frac{1}{3}[/tex]or equivalently,
[tex]3^{0.15t}=3[/tex]This means that
[tex]0.15t=1[/tex]Then, by dividing both sides by 0.15, we obtain
[tex]t=\frac{1}{0.15}=6.6666[/tex]So, by rounding to the nearest hundreadth, the answer is 6.67 years
Given l ∥ m ∥ n, find the value of x.
Answer:
[tex]x = \frac{ - 23}{3} [/tex]
Step-by-step explanation:
everything u need is in the picture
In the distribution shown, state the mean and the standard deviation. Hint: The vertical lines are 1 standard deviation apart.
We are given a distribution graph.
The mean of the distribution is the center that is 125.
[tex]\operatorname{mean}=\mu=125[/tex]The standard deviation is given by
[tex]std=\sigma=153-125=28[/tex]Therefore, the mean of the distribution is 125 and the standard deviation is 28.
I just need to know how to work it out for future problems. (Business Calc)
Find the price elasticity of the demand function as a function of p.
1. q=D(p)=600-3p
A)E(p)= p/p-200
B)E(p)= p/600-3p
C)E(p)= p/200-p
D)E(p)= p(200-p)
The price elasticity of the demand function as a function of p is C. E(p)= p/200-p
How to illustrate the information?It should be noted that the price elasticity of demand simply means the ratio of the percentage change in quantity demanded to the percentage change in price.
In this case, the function is given as:
q = D(p) = 600-3p
Differentiate with respect to p
D'(p) = 3
The elasticity of demand will be:
= (P / 600 - 3p) × (-3)
= P / (200 - P)
In conclusion, the correct option is C.
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