Answer:
f(g(x) = 1x² + 4x + 3
Explanation:
Question: f(g(x))
Given following:
f(x) = x² - 1g(x) = x + 2While solving such function questions, solve from right to left.
⇒ f(x + 2)
⇒ (x + 2)² - 1
⇒ x² + 4x + 4 - 1
⇒ x² + 4x + 3
The time that passes between the time you see lightning and you hear the thunder depends on your distance from the lightning. With each km from the lightning 3 seconds pass.
a) Make a table of values for distances from 0 to 5 km.
b) Graph this relation. State whether it is a linear or non-linear relation.
c) Using your graphed relation, how much time passes before you hear lightning that occurs 4.5 km away?
d) Using your graphed relation, how far away are you if you hear the thunder in 1.5 seconds?
When the lightning occurs 4.5 km away then we will hear after 13.5 seconds and if we hear after 1.5 seconds then we are 0.5 km away from lightning.
Given With each km from the lightning 3 seconds passes.
a) The table of values for distances from 0 to 5 km.
Distances Time
0 0
1 3
2 6
3 9
4 12
5 15
b) The graph of lightning is a linear relation because it is increasing constantly by 3 seconds. f(x)=3x
c) When distance =1 , the time be 3 seconds
when distance =4.5 , the time=3*4.5
=13.5 seconds.
d) When time is 3 seconds = 1km
when time =1.5 seconds , the distance be 1/2=0.5 km.
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What is 12.1975 rounded to the nearest thousandth?
Answer:
12.198
hope it helps
12.198
To round over 7 into 8, the ten-thousandth place needs to be 5 or over, and as we can see the ten-thousandth place is 5.
The function f(x) is given by the set of ordered pairs.
The equation that is true and one that matches the set of ordered pairs of functions is option C. f (0) = 6
What is the equation about?Note that a function can be made to be a given set of ordered pairs such as the ordered pairs (2,4), (3,5), (4,6) can have input functions of (as domain) 2,3,4 and output functions of (as range) of 4,5,6.
So when you see the ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)} one can see that the option that matches to the set of ordered pairs of functions above is f (0) = 6 value x = 0, f (x) = y = 6, ordered pairs (0.6)
See full question below
The function f (x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)}:Which equation is true?
f(-10)=1
f(2)=-10
f(0)=6
f(1)=-10
The answer choices are :
f (-10) = 1 values x = -10, f (x) = y = 1, ordered pairs (-10,1)
f (2) = - 10 values x = 2, f (x) = y = -10, ordered pairs (2, -10)
f (0) = 6 value x = 0, f (x) = y = 6, ordered pairs (0.6)
f (1) = - 10 values x = 1, f (x) = y = -10, ordered pairs (1, -10)
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Please help ASAP
Please help ASAP
Please help ASAP
Please help ASAP
Answer:
y-intercept: (0,2)
x-intercepts: (-4,0), (2,0)
Step-by-step explanation:
y-intercepts are found where the graph intersects the y-axis
same with x-intercepts, are found where the graph intersects the x-axis
The y-intercept is 2, and the x-intercept is -4 and 2 where the line segment crosses the y-axis and x-axis.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Where the line segment crosses the y-axis is the y-intercept,
And where the line segment crosses the x-axis is the x-intercept,
From the graph,
y-intercept is at (0,2)
x-intercepts is at (-4,0), (2,0)
Thus, the y-intercept is 2, and the x-intercept is -4 and 2 where the line segment crosses the y-axis and x-axis.
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Use the figure to decide the type of angle pair that describes ∠5 and ∠6.
Reason:
These angles are both in the same corresponding direction. Both are in the same western corner, or point to the west. If the lines were parallel, then the corresponding angles would be congruent.
Mercedes receives a $25 gift card for downloading music and wants to determine how many songs she can purchase. each downloaded song costs $1.29. write and solve an inequality to determine m, the number of songs mercedes can purchase. what is the approximate solution to the inequality? round to the nearest whole number.
The solution to the inequality: [tex]1.29m\leq 25[/tex] is m=19.
What is inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Value of gift card=$25
Cost of each song=$1.29
Let m be the number of songs purchased.
Then, the required inequality is as follows:
[tex]1.29m\leq 25\\m\leq \frac{25}{1.29}\\ m\leq 19.38[/tex]
The value of m rounded to the nearest whole number is 19.
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3. If the perimeter of an equilateral triangle is 36 ft, what is the length of one side?
O 18 ft
O 6 ft
12 ft
9 ft
Answer:
The length of one side is 12ft
Step-by-step explanation:
The triangle is equilateral so all the sides are the same length.
So you are simply going to divide 36ft by the 3 sides.
36ft/3 = 12ft
In the given figure, ΔABC is a right triangle.
The figure shows the right-angle triangle ABC. B is the length of AC and a is the height of BC and c is the base of AB.
What is true about ΔABC?
A.
sin(A) = cos(C) and cos(A) = sin(C)
B.
sin(A) = sin(C) and cos(A) = cos(C)
C.
sin(A) = cos(A) and sin(C) = cos(C)
D.
sin(A) = cos(C) and cos(A) = cos(C)
The true statement about right-angle triangle ABC is that: A. sin(A) = cos(C) and cos(A) = sin(C).
How to apply basic trigonometry?In order to determine the angles, we would apply basic trigonometry. From the diagram of the right-angled triangle shown below, we can deduce the following parameters:
Angle (θ) = 45°.Opposite (Opp) side = a.Hypotenuse (Hyp) = c.Adjacent (Adj) side = b.By applying the basic trigonometry functions, we have:
sin(A) = Opp/Hyp = a/c.
sin(C) = Opp/Hyp = c/b.
cos(A) = Adj/Hyp = c/b.
cos(C) = Adj/Hyp = a/c.
From the above, we can logically deduce that sin(A) is equal to cos(C) and cos(A) is equal to sin(C).
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Answer:
Step-by-step explanation:
The true statement about right-angle triangle ABC is that: A. sin(A) = cos(C) and cos(A) = sin(C).
How to apply basic trigonometry?
In order to determine the angles, we would apply basic trigonometry. From the diagram of the right-angled triangle shown below, we can deduce the following parameters:
Angle (θ) = 45°.
Opposite (Opp) side = a.
Hypotenuse (Hyp) = c.
Adjacent (Adj) side = b.
By applying the basic trigonometry functions, we have:
sin(A) = Opp/Hyp = a/c.
sin(C) = Opp/Hyp = c/b.
cos(A) = Adj/Hyp = c/b.
cos(C) = Adj/Hyp = a/c.
From the above, we can logically deduce that sin(A) is equal to cos(C) and cos(A) is equal to sin(C).
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Find sin 0
a. 8/15
b. 15/8
c. 15/17
D 8/17
Answer:
C
Step-by-step explanation:
first you need to memorize
SOH CAH TOA
IT means
Sine =opposite/hipotenuse
Cosine = adjecent/hipotenuse
tangent = opposite/adjecent
in this case, we need to find sine
so it's SOH
opposite of theta Θ is 15
and it's hipotenuse , we don't know yet. so need to find it by using Pythagorean theorem
let it be x
x =√ 15²+ 8²
=√ 225+ 64
=√289
= 17
so the answer is 15/17
PLEASE PASS IF YOU DON'T KNOW. find the 6th derivative of cot²3x. WILL MARK BRAINLIEST FOR THE RIGHT ANSWER
Answer:
Find the derivative using the chain and power rules.
-6csc^(2 )(x^(3)-2x^(2))(3x^(2)-4x)
Step-by-step explanation:
Identify the slope and y-intercept of the line whose equation is given. write the y-intercept as an ordered pair. y = negative 2 x + 5 a. slope = negative 2; y-intercept (0, 5) b. slope = 2; y-intercept (0, 5) c. slope = 5; y-intercept (0, 2) d. slope = negative 5; y-intercept (0, 2) please select the best answer from the choices provided a b c d
The line having the equation, y = -2x + 5, has a slope = -2, and y-intercept = (0, 5). Thus, option A is the best choice.
The slope of a line is the tangent of the angle that the line makes with the positive side of the x-axis.
The y-intercept of a line is the point at which the line intersects the y-axis.
The standard form of a line is y = mx + b, where m represents the slope of the line, and b represents its y-intercept.
In the question, we are asked to identify the slope and the y-intercept of the line whose equation is y = -2x + 5.
Comparing the given equation of the line, y = -2x + 5, with the standard equation of a line, y = mx + b, we can say that,
m = -2, and b = 5.
Representing b as an ordered pair, we get (0, 5), as b represents the y-intercept which is a point on the y-axis, where the x-coordinate is always equal to zero.
Thus, we get the slope = -2, and the y-intercept = (0, 5).
The option representing the answer is option A.
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Which of the following number lines represents the solution set of x/-1 >or= -4?
The number line that shows that x ≥ -4 is; Option B
How to Interpret Number Lines?
We want to find the number line that represents x ≥ -4
Now, for greater than sign, the number line would point to the right while for less than sign the number line would point to the left.
Now, for greater than or equal to sign the dot would be shaded and as such looking at the correct number line would be that in Option B.
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3. Donnell is doing market research for a major brand by surveying customers at a local mall.
The probability of a customer agreeing to take the survey is 22%. What is the probability that
one of the first five customers agrees to take the survey?
29%
54%
071%
74%
71% is the required probability here.
What is a probability simple definition?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The probability serves as a gauge for the possibility that an event will occur. and a The probability equation is stated by the following notation: P(E) = Number of Favorable Outcomes/Number of Total Outcomes.
The number of customers out of 5 who agree to take the survey here could be modelled as a binomial distribution given as
x ` Bin (n = 5 , p = 0.22 )
Thus the probability here is computed as
P(X≥ 1) = 1 - P(X = 0) = 1 - (1 - 0.22)⁵
= 0.71 %
Therefore 71% is the required probability here.
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What is the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers
The difference is 2003.
The formula for the sum of the first n even numbers is SE = n^{2} + n, (E standing for even).
The sum of the first n odd numbers is SO = n^{2}, (O standing for odd).
Knowing this, plug 2003 for n,
SE - SO= (2003^{2} + 2003) - (2003^{2}) = 2003
The difference is 2003.
A number that can be divided into two halves, i.e. into two equal parts is called an even number. Even numbers are exactly divisible by 2 which means the remainder will be 0.
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The length of the hypotenuse of a right triangle is 7 feet, and the length of one leg is 4 feet. what is the length of the other leg to the nearest tenth of a foot
The length of the other leg to the nearest tenth of a foot is 5.7 feet.
What is Pythagorean theorem?
A theorem in geometry: the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.The Pythagoras theorem equation is expressed as, [tex]c^{2} = a^{2} + b^{2}[/tex], where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs.We can use the Pythagorean Theorem to find the length of the other leg
[tex]a^{2} + b^{2} = c^{2}[/tex]
"a" and "c" represent the two legs of the triangle and "b" represents the perpendicular.
So,
[tex]b^{2} = c^{2} - a^{2}[/tex]
= 7² - 4²
b = [tex]\sqrt{49 - 16}[/tex]
[tex]b = \sqrt{33}[/tex] ⇒ 5.7 feet
Therefore, the length of the other leg to the nearest tenth of a foot is 5.7 feet.
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Triangle WXY has the interior and exterior angles shown below.
Triangle X W Y. Angle W is (2 x minus 13) degrees and angle Y is x degrees. The exterior angle to angle X is 122 degrees.
What is Measure of angle W?
45 degrees
58 degrees
68 degrees
77 degrees
The correct option is last one 77 degrees.
Therefore the measure angle W is 77 degrees.
Step-by-step explanation:
Given:
Exterior angle = 122°
∠W = (2x-13)°
∠Y= x°
To Find:
∠W = (2x-13)° = ?
Solution:
Exterior Angle Property:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
Angle W and Angle Y are the interior angles of Exterior angle 122°.
∴
Substituting the values we get
Now Substitute 'x' in angle W we get
Therefore the measure angle W is 77 degrees.
Step-by-step explanation:
The sum of three numbers is 131. the second of three numbers is seven more than twice the first. the third number is 12 less than the first. what equation can be used to solve the problem? x x x = 131 x (x 7) (x – 12) = 131 x (2x 7) (x – 12) = 131 x (2x 7) – 12 = 131
Answer:
C. x + (2x + 7) + (x - 12) = 131
Step-by-step explanation:
Let the first number be x.
Then, given:
The second number is 2x + 7The third number is x - 12Since their sum is 131, we get the following equation:
Sum of x, (2x + 7) and (x - 12) is 131,or
x + (2x + 7) + (x - 12) = 131This is matching the answer choice C.
two numbers that equal -8 when multiplying but thoses two numbers also have to equal to -7 when adding
Answer:
-8 and 1
Step-by-step explanation:
-8 x 1 is -8
-8+1 is -7
E represents a number. For example, if E is 5, EE equals 55 and 4E equals 45. If 1E x E = 9E, what number should be in the place of E?
Answer:
E represents a number, for this question we need to keep in mind that the product of 1E and E must end in E.
E must be 6.
E = 6
Step-by-step explanation:
16 * 6 = 96
Which linear function represents the line given by the point-slope equation y 1 = –3(x – 5)? f(x) = –3x – 6 f(x) = –3x – 4 f(x) = –3x 16 f(x) = –3x 14
The linear function which represents the line given by the point slope equation y+1=-3(x-5) is f(x) =-3x+14 which is option D.
Given the equation y+1=-3(x-5) and we have to find the equation of line that represents this equation.
An equation is a relationship between two or more variables which are expressed in equal to form. Equation of two variables looks like ax+ by=c. It is solved in order to get the values of variables. Linear function is like equation whose graph shows a straight line.
We have to just find out the value of y in terms of x to find the linear function which can be done as under:
y+1=-3x(x-5)
y+1=-3x+15
y=-3x-1+15
y=-3x+14
Hence y=-3x+14 is the linear equation which represents the point slope equation y+1=-3(x-5).
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Answer:
So the shorter version of what the guy above me is saying is that it is:
[tex]f(x) = -3x + 14[/tex] or
D
Step-by-step explanation:
I got it right on the test.
This container is composed of a right circular cylinder and a right circular cone.
k
Which is closest to the surface area of the container?
C
1243 ft²
1696 ft²
754 ft²
490 ft²
24 ft-
13 ft
10 ft
The closest surface area of the container is: 1,696 ft².
What is the Volume of a Cone and a Cylinder?Curved surface area of a cone = πrl
Surface of a cylinder = 2πr(h + r)
Surface area of the container = Curved surface area of a cone + Surface of a cylinder - area of circular base
= πrl + 2πr(h + r) - πr²
r = 24/2 = 12 ft
l = 13 ft
h = 10 ft
Plug in the values
Surface area of the container = π(12)(13) + 2π×12(10 + 12) - π(12²) = 1,696.5 ft².
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which of these ratios are equivalent ratio
1:4 2:8 3:6 7:28
Answer:
1:4
2:8
7:28
Step-by-step explanation:
1:42:8 , 1:47:28, 1:4please help me find the solution
Answer:
22
Step-by-step explanation:
BD bisects <ABC, this means the half-line divided the angle into two equal parts.
If m<ABC is equal to 44 then m<ABD is
44/2 = 22
The following three shapes are based only on squares, semicircles, and quarter circles.
Find the perimeter and the area of each shaded part.
The perimeter of the shaded part is: 25.1 cm.
The area of the shaded part is: 36.6 cm².
How to Find the Perimeter and Area of the Shaded Part?Area = Area of square - 2(area of square - area of quarter circle) = s² - 2(s² - 1/4πr²).
Parameters given are:
s = 8 cmr = 8 cmPlug in the values into the equation
Area = 8² - 2(8² - 1/4π(8²)).
Area = 64 - 2(64 - 50.3)
Area = 36.6 cm²
Perimeter = 2(perimeter of quarter circle) = 2(1/4(2πr)) = 2(1/4(2π8)) = 25.1 cm
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Please help me answer all of these questions. Its a chance to get 100 points please help me. Whoever does all of them I will mark brainlest. :) Please help.
Answer:
Step-by-step explanation:
Well since the questions are related to geometric series I'm assuming the reasoning for 0.99999.... = 1, is going to be a geometric series in this instance. All though there are other ways to prove this.
1.
a. So if you think about it, 0.999 can be represented as: [tex]\frac{9}{10} + \frac{9}{100} + \frac{9}{1000}....[/tex] and so on. This is a geometric series. The geometric sequence explicit equation can be determined by realizing each term is the previous term multiplied by 1/10, since the numerator is staying the same, but the denominator is being multiplied by 1/10. So the explicit equation for the sequence is: [tex]a_n=\frac{9}{10}*(\frac{1}{10})^{n-1}[/tex]. The sum of an infinite series can be defined as: [tex]S_\infty=\frac{a_1}{1-r}[/tex] when |r| <1 , which in this case it is. So plugging the values into the equation you get: [tex]S_\infty=\frac{\frac{9}{10}}{1-0.10}=\frac{\frac{9}{10}}{\frac{9}{10}} = 1[/tex]. So the sum of this infinite series that represents [tex]0.\overline{9}[/tex] is equal to 1.
b. Another repeating decimal can easily be determined using the repeating decimal 0.9. If you multiply both sides by 10, you'll get: [tex]9.\overline9 = 10[/tex].
2.
a. So this is an arithmetic sequence and it appears to be increasing by 5, with the first term being 3. So an explicit formula can be written using these two values: [tex]a_n=3+5(n-1)[/tex] which can also be simplified by distributing the 5, to get: [tex]a_n=3+5n-5=5n-2[/tex]. A recursive rule can also be easily defined using these two values, it's simply: [tex]a_n=a_{n-1}+5\\a_1=3[/tex]
b. The 1000th term can be evaluated using the explicit formula by plugging in 1000 in as n: [tex]a_{1000} =5(1000)-2=5000-2=4998[/tex]
c. The explicit formula, since it's much easier to evaluate values, by simply plugging in 1000 as n
d. The issue with a recursive rule, is you need to know all previous values, to determine [tex]a_n[/tex], because it's doing some operation on the previous value, except to know that previous value, you need the previous previous value, and so on. This is an issue with much larger numbers, which is why the explicit formula is generally more better.
A student submitted the following work that is not correct. Can you find the mistake?
Explain the mistake the student made.
Simplify (assuming all variables are positive): √32x³y²z7
Step 1: √8.4.x².xy².26. z
Step 2: 2xyz³ √8xz
Step-by-step explanation:
so you have the equation: [tex]\sqrt{32x^3y^2z^7}[/tex] which I'm assuming is what you meant to input. and the next step I'm assuming you wrote: [tex]\sqrt{8} * \sqrt{4} * \sqrt{x^2} * \sqrt{y^2} * \sqrt{x} * \sqrt{z^6} * \sqrt{z}[/tex], although I'm not 100% sure, I'm basing this assumption off of step 3. Anyways this will simplify to [tex]2xyz^3\sqrt{8xz}[/tex] which is correct kind of, but since they were asked to FULLY SIMPLIFY, then it's not completely done. This is because 8 has a factor of 4 which is a perfect square. This is because in step 1, the student rewrote 32 as sqrt(8) * sqrt(4) instead of writing it as sqrt(2) * sqrt(16) which is the greatest factor of 32 that is a perfect square. So they could've either done that in step 1, or they could've realized in step 2, that they can further simplify sqrt(8) and then have a step 3 showing that.
Beth wanted to buy vegetables. She noticed that brand A of black beans was on sale for 4 cans for 87 cents. Brand B was 3 cans for 79 cents. Which was a better buy?
Answer:
Brand A
Step-by-step explanation:
If you divide both brands to find how much one can costs, brand B costs more per can.
79 ÷ 3 = 26.34
87 ÷ 4 = 21.75
That being said, if brand B were to sell 4 cans instead of 3 it would be more than brand A's 4 cans. Brand A is cheaper than brand B would be.
Find the condition of the expression:√3-2x-x^2
Answer:
-1 <= x <= 1
Step-by-step explanation:
√((1-2x+x^2)+2-2x^2)
= √((1-x)^2 + 2*(1-x)(1+x) )
điều kiện là 1 - x > =0 và 1+x >=0
giải 2 bất phương trình trên ta thu đc kết ququả
Riddle-if you solve it i will delete your answer and you have to post the riddle. Riddle-you enter a room. 2 dogs, 4 horses, 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.
Answer:
10
Step-by-step explanation:
2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.
The total number of legs in the room would be 10.
How to identify how many legs are on the floor of the room?From the given information, it can be inferred that none of the legs of the animals is on the floor of the room.
It is given that 2 dogs, 4 horses, 1 giraffe, and a duck are lying on the bed. 3 chickens are flying over a chair.
The legs of the bed and the chair do.
So we can say that the chair and the bed each have four legs.
so that would be two more legs.
In total we have:
4 + 4 + 2 = 10.
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Suppose a and b are real numbers such that 17^a=16 and 17^b=4. What is 1/(2^a-b) ?
Since
[tex]17^a = 16 = 4^2 \implies 17^{a/2} = 4[/tex]
it follows that
[tex]17^b = 4 \implies 17^{a/2} = 17^b \implies \dfrac a2 = b \implies a = 2b[/tex]
Then
[tex]2^{a - b} = 2^{2b - b} = 2^b[/tex]
so that
[tex]\dfrac1{2^{a-b}} = 2^{-b}[/tex]
We also have
[tex]17^b = 4 \implies b = \log_{17}(4)[/tex]
so we can go on to say
[tex]\dfrac1{2^{a-b}} = \boxed{2^{-\log_{17}(4)}}[/tex]