Answer:
-1, 0, 3, 4.
Step-by-step explanation:
f(x) = x^2 - 3x
f(f(x)) = (x^2 - 3x)^2 - 3(x^2 - 3x) (Replacing the x in f(x) by x^2 - 3x).
when f(f(x) = f(x):
(x^2 - 3x)^2 - 3(x^2 - 3x) = x^2 - 3x
(x^2 - 3x)^2 - 4(x^2 - 3x) = 0
Let y = x^2 - 3x, then
y^2 - 4y = 0
y(y - 4) = 0
y = 0, 4
when x^2 - 3x = 0, x = 0 , 3.
when x^2 - 3x = 4
x^2 - 3x - 4 = 0
(x + 1)(x - 4) = 0
x = -1, 4.
Identify the volume of the sphere in terms of π. PLEASE HELP!!!
Answer:
its B
Step-by-step explanation:
Instructions: Select the correct answer.
Vector u has a magnitude of 5 units and a direction angle of 30°. Vector v has a magnitude of 7 units and a direction angle of 120°. What is the direction angle of their vector sum?
A.) 82.21°
B.) 84.46°
C.) 85.11°
D.) 86.13°
Answer:
84.463°
Step-by-step explanation:
Determine the x- and y-components of these two vectors. Sum up the x-comps and the y-comps separately, and then find the magnitude and direction of the vector sum:
x-comps:
5 cos 30° + 7 cos 120° = 5(0.866) + 7(-0.5) = 0.83
y-comps:
5 sin 30° + 7 sin 120° = 5(0.5) + 7(0.866) = 2.5 + 6.062 = 8.562
Both components are in Quadrant I, so the direction angle ∅ is between 0° and 90°: ∅ = arcctan 8.562/0.83 = arctan 10.316 = 1.474 radian, or
1.474 rad 180°
-------------- * ----------- = 84.463°
1 π
please help!!! ive been stuck on this for 30 minutes now!
Answer:
f^-1 = 4(x-3)
Step-by-step explanation:
If f(x) = 1/4(x) + 3 we ned to find f^-1.
To find the inverse function, we need to solve the equation for "x", as follows:
f(x) = 1/4(x) + 3
y = 1/4(x) + 3
y-3 = 1/4(x)
4(y-3) = x
Now, change the "x" for an "y". And change the "y" for an "x":
4(x-3) = y
The solution is the last one.
What are the new vertices of the triangle under the translation (x, y) (x − 1, y − 3)?
ANSWER
(-1,-1), (-4,-5), (-8,0)
EXPLANATION
We have a triangle with vertices:
(0,2), (-3,-2) and (-7,3).
The rule for the translation is
[tex](x, y) \to (x - 1,y - 3)[/tex]
The new vertices of the triangle will be;
[tex](0, 2) \to (0 - 1,2- 3) = ( - 1, - 1)[/tex]
[tex]( - 3, - 2) \to (- 3-1, - 2- 3) = ( -4, - 5)[/tex]
[tex]( - 7, 3) \to ( - 7 - 1,3- 3) = ( - 8, 0)[/tex]
The new vertices are:
(-1,-1), (-4,-5), (-8,0)
What is the value of C in C = 3x - 2 if x = 5
Answer:
C = 13
Step-by-step explanation:
C = 3(5) - 2
C = 15 - 2
C = 13
Answer:
C = 13
Step-by-step explanation:
Substitute x = 5 into the expression for C
C = (3 × 5) - 2 = 15 - 2 = 13
What is the angle of the elevation from the ground to the top of a 45-foot tree from 65 feet away? Round to the nearest tenth of a degree.
Answer:
34.7 degrees
Step-by-step explanation:
This is a right triangle trig problem. The angle in question, the angle of elevation, is the base angle that is NOT the right angle. The height of the tree is the side opposite the angle of elevation, and the distance away from the tree is the measure of the base of the right triangle. So the question, then, is "What is the angle that has a ratio equal to the side opposite the angle over the side adjacent to the angle?" This is the definition of the tangent of an angle. The equation will be set up as follows:
[tex]tan\beta =\frac{45}{65}[/tex]
Your calculator needs to be in degree mode when you do this operation. Press 2nd on your calculator then tan and you'll get tan^-1 on your display. This means you are looking for a missing angle. Enter the fraction as 45/65 inside the parenthesis and hit enter and you'll get an angle of 34.69515353. Round to the nearest tenth for 34.7
You will always use the 2nd and sin/cos/tan buttons to find missing angles.
The angle elevation is 34.6 9 degree.
What is Angle of Elevation?When it lies between the horizontal line and the line of sight, the angle of elevation is formed. The angle that forms when the line of sight is above the horizontal line is referred to as the angle of elevation. The line of sight, however, is to the horizontal line downward in the angle of depression.
The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
Given:
Height of tree= 45 foot
Distance= 65 feet
Now, Using Trigonometry
tan [tex]\theta[/tex] = P/ B
= 45/65
= 9/ 13
= 0.6923
[tex]\theta[/tex] = 34.69 degrees.
Hence, the angle elevation is 34.6 9 degree.
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Find the probability of randomly choosing the letter A or E from a board that contains the letters CANDLE.
Answer:
Step-by-step explanation:
There are 6 letters all together. There 2 letters that if you draw them, you will be successful.
2/6 = 1/3
That means that 1 in 3 times you should draw an A or an E.
Which of the following formulas would find the surface area of a right cone where s is the slant height r is the radius, LA is the lateral area, and BA is the base area?
Check all that apply.
Answer:
Option A and Option C
Step-by-step explanation:
The surface area of a cone can be calculated with this formula:
[tex]SA=\pi r^2+\pi rs[/tex] (This matches with the option A)
Where [tex]\pi rl[/tex] is the lateral area of the cone (Being "s" the slant height) and [tex]\pi r^2[/tex] is the area of the base of the cone (which is a circle).
You know that BA the is the area of the base and LA the lateral area of the cone.
Then, substituting into the formula for calculate the surface area of a cone, you get:
[tex]SA=BA+LA[/tex]
This matches with the option C
Answer:
a and c
Step-by-step explanation:
a p e x
Line graphs are used to show trends in categorical data. True False
Answer:
ezpz false
Step-by-step explanation:
Given the points P(2,-1) and Q(-9,-6), what are the coordinates of the point on directed line segment PQ that partitions PQ in the ratio 3/2?
ANSWER
[tex]( - \frac{23}{5} , - 4)[/tex]
EXPLANATION
Given the points P(2,-1) and Q(-9,-6),the coordinates of the point that partition the directed line segment PQ in the ratio 3:2 is given by
[tex]x = \frac{ mx_2+nx_1}{m + n} [/tex]
[tex]y= \frac{ my_2+ny_1}{m + n} [/tex]
Where m=3 and n=2
[tex]x = \frac{ 3 ( - 9)+2(2)}{3+ 2} [/tex]
[tex]x = \frac{ - 23}{5} [/tex]
[tex]y= \frac{ 3( - 6)+2( - 1)}{3 + 2} [/tex]
[tex]y= \frac{ - 20}{5} = - 4[/tex]
The point is
[tex]( - \frac{23}{5} , - 4)[/tex]
The coordinates of the point on the directed line segment PQ that partitions it in the ratio 3/2 are (-21/5, -17/5).
Explanation:To find the coordinates of the point on the directed line segment PQ that partitions it in the ratio 3/2, we can use the section formula. The section formula states that the coordinates of a point dividing a line segment with endpoints (x1,y1) and (x2,y2) in the ratio m:n are given by:
x = (m*x2 + n*x1)/(m+n)
y = (m*y2 + n*y1)/(m+n)
Plugging in the values from the given points P(2,-1) and Q(-9,-6) into the formula, we get:
x = (3*(-9) + 2*2)/(3+2) = -21/5
y = (3*(-6) + 2*(-1))/(3+2) = -17/5
So, the coordinates of the point are (-21/5, -17/5).
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The graph of f(x) = x^2 is shown.
Compare the graph of f(x) with the graph of d(x) = x^2 - 25
Answer:
D. The graph of d(x) is 25 units below the graph of f(x)
ANSWER
D. the graph of d(x) will be 25 units below the graph of f(x).
EXPLANATION
The graph of
[tex]f(x) = {x}^{2} [/tex]
is the base function.
The graph of
[tex]d(x) = {x}^{2} - 25[/tex]
is a vertical translation of the base function 25 units down.
This implies that, the graph of d(x) will be 25 units below the graph of f(x).
Therefore the correct answer is D.
The coordinate grid above shows a pentagon. The pentagon is translated 1 unit to the left and 10 units down to create a new pentagon.
Which rule describes this transformation?
A) (x, y) → (x − 1, y − 10)
B) (x, y) → (x + 1, y − 10)
C) (x, y) → (x − 1, y + 10)
D) (x, y) → (x + 1, y + 10)
The pentagon is translated 1 unit to the left, so the points move to the left by 1 unit. Moving left or right changes the x value, when you move right, the x value increases, when you move left, x decreases. Since x is going left 1 unit:
So x - 1
10 units down. Moving up down or up changes the y value, when you move down, y decreases, when you move up, y increases. Since the pentagon is going down 10 units:
y - 10
Your answer is A
The rule that describes the given transformation is (x, y) → (x - 1, y - 10). It is given that the pentagon is translated by 1 unit to the left and 10 units down.
What are the transformations on the graph?The graph is transformed into a new graph by applying certain operations like,
translationrotationreflectiondilationHow the given graph is translated?It is given that a pentagon in the graph is translated as 1 unit to the left and 10 units to the down.
Here the translation is towards the negative axes.
Towards left means subtracting the given number of units from the x-coordinateTowards down means subtracting the given number of units from the y-coordinateSo, the rule for this transformation we can write as (x, y) → (x - 1, y - 10)
Translating the points of the pentagon from the graph using this rule:
Actual coordinates Translated coordinates
(-1, 3) ((-1 - 1), (3 - 10)) = (-2, -7)
(1, 5) ((1 - 1), (5 - 10)) = (0, -5)
(2, 2) ((2 - 1), (2 - 10)) = (1, -8)
(4, 6) ((4 - 1), (6 - 10)) = (3, -4)
(5, 3) ((5 - 1), (3 - 10)) = (4, -7)
So, the new pentagon will be plotted in the graph with these translated coordinates.
The graph of the translated pentagon is shown below.
So, option A (x, y) → (x − 1, y − 10) describes the given transformation correctly.
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If a computer depreciates at a rate of 24% per year, what is the monthly depreciation rate?
8.17%
6.33%
4.33%
2.00%
I believe the correct answer is 4.33%.
Answer:
2.00%
Step-by-step explanation:
7.
Find the missing lengths of the sides.
Answer:
[tex]a=9\ in\\b= 9\ in[/tex]
Step-by-step explanation:
This straight triangle has two angles equal to 45 ° and two equal sides.
We know that the side opposite the 90 degree angle is:
[tex]c =9\sqrt{2}\ in[/tex]
Since the triangle has two equal angles, then it is an iscoceles triangle.
This means that
[tex]a = b[/tex]
We use the Pythagorean theorem to find b
[tex]c^2 = a^2 + b^2\\\\c^2 = b^2 + b^2\\\\c^2 = 2b^2\\\\(9\sqrt{2})^2 =2b^2\\\\b^2=\frac{(9\sqrt{2})^2}{2}\\\\\sqrt{b^2}=\sqrt{\frac{(9\sqrt{2})^2}{2}}\\\\b=\frac{(9\sqrt{2})}{\sqrt{2}}\\\\b=a=9[/tex]
The angle of elevation from point A to point B measures 5(x-2) The angle of depression from point B to point A measures (x+14). Find the measure of each angle.
Answer:
It's the first choice (20 degrees).
Step-by-step explanation:
These angles will be equal ( by The Alternate Angle Theorem).
5(x - 2) = x + 14
5x - 10 = x + 14
4x = 24
x = 6.
So the measure of each angle = 5(6 - 2) = 6 + 14 = 20 degrees.
The angles of elevation and depression are equal because they are alternate interior angles. Solving the given expressions yields x = 6. Therefore, both the angle of elevation and the angle of depression measure 20 degrees.
First, let's set up the problem:
The angle of elevation from point A to point B is given by the expression 5(x-2).The angle of depression from point B to point A is given by the expression (x+14).In any scenario involving angles of elevation and depression, these angles are equal because they are alternate interior angles formed by a horizontal line and a transversal.
Therefore, we can equate the two expressions:
5(x-2) = (x+14)
Now, solve for x:
Distribute the 5 on the left side: 5x - 10 = x + 14Subtract x from both sides: 4x - 10 = 14Add 10 to both sides: 4x = 24Divide both sides by 4: x = 6Now substitute x back into the expressions to find the angle measures:
For the angle of elevation: 5(x-2) = 5(6-2) = 5*4 = 20 degrees
For the angle of depression: (x+14) = (6+14) = 20 degrees
Therefore, both the angle of elevation and the angle of depression measure 20 degrees.
This confirms that our setup and calculation are correct.
The focus for this parabola is (-1,0)
[tex]x=\frac{1}{4} y^2[/tex]
A. True
B. False
Answer:
it's false
Step-by-step explanation:
If you have the equation of a parabola in vertex form y=a(x−h)^2+k, then the vertex is at (h,k) and the focus is (h,k+14a).
In this case, h = 0,k = 0 and a = 1/4
Then the focus is at (h, k +14a) = (0, 0 + 14*1/4) = ( 0, 1)
So, it's false.
Answer:
false
Step-by-step explanation:
Abigail has 5 cousins her friend suki has 3 fewer than 4 times as many cousions as abigail has write an expression for the number of cousions suki has
5=(5 x 4)-3
Hope I helped! Sorry if I'm wrong!
~Potato
^^ What they said I think that’s right but I may be wrong
John’s employer will match his contributions into his retirement plan, but only up to 3% of his salary. John decides to invest 5% of his $42,000 salary into the retirement plan. Find the future value of the annuity in 5 years if it earns 8% compounded quarterly.
$62,406.79
$20,409.79
$255,122.39
$9,909.79
I need help with this plz, im confused and im watching videos but idk how to do it. i will mark brainliest
Answer:
$20,409.79
Step-by-step explanation:
First find John’s quarterly salary. ;$42,000 / 4 = $10,500 ;Total Contributions = John’s + Employer’s ;Total Contributions = $10,500 x 0.05 + $10,500 x 0.03 ;Total Contributions = $840 ;Find the interest rate per compounding period and the number of compounding periods. ;8% / 4 = 2% ;5 x 4 = 20 periods ;The factor from the table for 2% and 20 is 24.29737. ;Amount = $840 x 24.29737 ;Amount = $20,409.79
Without graphing, describe the end behavior of the graph of the function.
As x → ∞, f (x) → −∞.
As x → −∞, f (x) → ∞.
As x → ∞, f (x) → −∞.
As x → −∞, f (x) → −∞.
As x → ∞, f (x) → ∞.
As x → −∞, f (x) → −∞.
As x → ∞, f (x) → ∞.
As x → −∞, f (x) → ∞.
Select the functions that have identical graphs.
Answer:
c. 1 and 3
Step-by-step explanation:
To quickly solve this problem, we can use a graphing tool or a calculator to plot each equation.
Please see the attached image below, to find more information about the graph
s
The equations are:
1) y = sin (3x + π/6)
2) y = cos (3x - π/6)
3) y = cos (3x - π/3)
Looking at the graphs, we can see that the identical ones
are equations one and three
Correct option:
c. 1 and 3
Using your equation, estimate the number of daylight hours in this city on the 220th day of the year.
My equation = y = 2.15sin(2pi/12)x + 10
Answer:
The answer, using your equation is: 11 hours, 51 minutes and 44 seconds, that is the number of daylight hours in that city
Step-by-step explanation:
Ok, in a normal year, the 220th day is the 8 of august, that is 08-08.
So, using x=220, we can estimate the number of daylight hours in that city:
[tex]y=2.15sin(\frac{2\pi }{12}x)+10= 2.15sin(\frac{2\pi }{12}(220))+10[/tex]
Then using a calculator in radians:
[tex]y=2.15(sin(0,524*220))+10[/tex]
[tex]y=2.15(sin(115.192))+10[/tex]
[tex]y=2.15(0,866)+10[/tex]
[tex]y=1.862+10[/tex]
[tex]y=11.862[/tex]
Then, you have that is 11 hours, but what about the 0.862 hours? We convert the to hours knowing that 1 hour has 60 minutes. Then 0,862*60 minutes= 51,72 minutes. And we do this for the 0,72 minutes as well, knowing that 1 minute has 60 seconds, then 0,72*60= 44 seconds.
The number of hours is 11 hours, 51 minutes and 44 seconds
A box contains 5 plain pencils and 5 pens. A second box contains 7 color pencils and 1 crayon. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected?
Write your answer as a fraction in simplest form.
Answer: 1 out of 5 for the first box and 1 out of 7 for the second box
( in simplest form)
Step-by-step explanation:
You play a gambling game with a friend in which you roll a die. If a 1 or 2 comes up, you win $8. Otherwise you lose $2. What is your expected value for this game?
Answer:
you expect to win on average $1.33 per round
Step-by-step explanation:
The expected value is the sum of products of probability and value:
2/6×$8 + 4/6×(-$2) = $8/3 - 4/3 = $4/3 ≈ $1.33
The expected value of the gambling game is calculated by taking into account the probability of winning $8 and losing $2. The final expected value is $1.33, which means on average, you would gain $1.33 per game played.
Explanation:To calculate the expected value for the gambling game where you roll a die, you need to account for the different outcomes and their associated probabilities. In this game, rolling a 1 or 2 means you win $8, and there are two outcomes out of six that result in a win, giving a probability of 2/6 or 1/3 for each of these outcomes. Rolling any other number (3, 4, 5, or 6) results in losing $2, with a probability of 4/6 or 2/3 for each of these losing outcomes.
The expected value (EV) can be calculated using the formula:
EV = (Probability of Winning × Amount Won) + (Probability of Losing × Amount Lost)
Substituting the values into the formula:
EV = (1/3 × $8) + (2/3 × -$2)
EV = ($2.67) + (-$1.33)
EV = $1.33
This means that the average gain per game, after many plays, is expected to be $1.33.
Segment AB is being dilated with the center at the origin. The image of A, point A" has coordinates of (3.2, 6.4). What is the scale factor of the dilation and the coordinates of point B"
The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).
The scale factor is 1.25 and the coordinates of point B" are (–3.2, –4.8).
The scale factor is 0.8 and the coordinates of point B"are (–5, –7.5).
The scale factor is 1.25 and the coordinates of point B" are (–5, –7.5).
Answer: The correct option is
(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).
Step-by-step explanation: Given that the segment AB is being dilated to A''B'' with the center at the origin. The image of A, point A" has coordinates of (3.2, 6.4).
We are to find the scale factor of the dilation and the co-ordinates of the point B''.
From the given graph, we note that
the co-ordinates of point A are (4, 8).
Now, If S is the scale factor of dilation, then we must have
[tex]S\times (4,8)=(3.2,6.4)\\\\\Rightarrow (4S,8S)=(3.2,6.4)\\\\\Rightarrow S=\dfrac{3.2}{4}=\dfrac{6.4}{8}=0.8.[/tex]
So, the scale factor is 0.8.
Now, the co-ordinates of point B are (-4, -6). So, the co-ordinates of B'' will be
[tex](-4\times 0.8,-6\times 0.8)=(-3.2,-4.8).[/tex]
Thus, the correct option is
(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).
Answer:
A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).
Step-by-step explanation:
if Judy completes a puzzle by herself, it takes her 3 hours. working with sal, it only takes them 2 hours.
what is the missing value from the table that represents Judy's rate?
A) r
B)3-r
C)1/3
D)3
Answer:
C. [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
We have been given a table showing rates of time taken by Judy and Sam to complete a puzzle.
We can see from our given table that Sal's rate is r. We are told that Judy completes a puzzle by herself, it takes her 3 hours. working with Sal, it only takes them 2 hours.
Since Judy completes the puzzle in 3 hours, so part of puzzle completed by Judy in one hour would be [tex]\frac{1}{3}[/tex], therefore, correct choice is option C.
Answer:
C.
Step-by-step explanation:
Look at Diagram.
It says,"
ST and TU are tangent to Q. What is the value of x?"
Answer:x=18
Step-by-step explanation:2x-9=x+9
When the bridge is fully raised, tan θ=5/12. What is sec θ? PLEASE HELP
Answer:
sec Ф = 13/12
Step-by-step explanation:
If tan Ф = 5 / 12, we can find the third side of this triangle (that is, the hypotenuse) by applying the Pythagorean Theorem:
hyp² = 5² + 12² = 169. Thus, the hyp is 13.
Thus, cos Ф = adj / hyp = 12/13.
The secant function is the reciprocal of the cosine function, so
sec Ф = 13/12.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Suppose a normal distribution has a mean of 16 and a standard deviation of 4.
A value of 26 is how many standard deviations away from the mean?
Answer: d) 2.5
Step-by-step explanation:
The mean is 16 so it has a z-score is 0
The standard deviation is 4 so:
z-score of 1 is: 16 + 4 = 20z-score of 2 is: 20 + 4 = 24z-score of 3 is: 24 + 4 = 28Notice that 26 is between the z-scores of 2 and 3 = 2.5
Algebraically: [tex]\dfrac{26-16}{4}=\dfrac{10}{4}=2.5[/tex]
A dartboard has a diameter of 14 inches. What are its radius and circumference? Round to the nearest hundredth. Use 3.14 for π.
Answer:
The radius is 7, and the circumference is 43.96
Step-by-step explanation:
The radius is half of the diameter, and this would just be 14/2 which is 7. The circumference is found by C=pi(diamete) or 2pi(radius). This is found by 14*3.14 this is equals 43.96
The radius of the dartboard is 7 inches and the circumference is approximately 43.96 inches.
Explanation:Radius:
The radius of a circle is half of its diameter. So, in this case, the radius is 7 inches.
Circumference:
The circumference of a circle can be found using the formula C = 2πr, where r is the radius. So, the circumference of this dartboard is 2π(7) = 14π inches, which rounds to 43.96 inches when rounded to the nearest hundredth.
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Dr. Potter provides vaccinations against polio and measles. Each polio vaccination consists of 444 doses, and each measles vaccination consists of 222 doses. Last year, Dr. Potter gave a total of 606060 vaccinations that consisted of a total of 184184184 doses. How many polio vaccinations and how many measles vaccinations did Dr. Potter give last year? Dr. Potter gave polio vaccinations and measles vaccinations.
x - number of polio vaccinations
y - number of measles vaccinations:
x + y = 60 / * ( - 2 )
4 x + 2 y = 184
--------------------------
- 2 x - 2 y = - 120
+
4 x + 2 y = 184
--------------------------
2 x = 64
x = 64 : 2
x = 32
32 + y = 60
y = 60 - 32
y = 28
Answer: There were 32 polio and 28 measles vaccinations.
Answer:
32 and 28
Step-by-step explanation: