Answer:
Approximately 11.99 years
Step-by-step explanation:
This is just a type of problem like finding how long it will take for you to get somewhere. Like in finding how fast you need to go to go to a place that is 60 miles in one hour. All you have to do is divide the distance of the star by the speed of light, and you get the amount of time it will take for the star's light to reach the Earth.
The time taken by the light to travel from a star to Earth is required.
It would take 12 years for the light to reach Earth.
Distance of star from Earth = [tex]1.135\times 10^{14}\ \text{km}[/tex]
Speed of light from star = [tex]9.4607\times 10^{12}\ \text{km/year}[/tex]
Time is given by
[tex]t=\dfrac{\text{Distance}}{\text{Speed}}\\\Rightarrow t=\dfrac{1.135\times 10^{14}}{9.4607\times 10^{12}}\\\Rightarrow t=11.996\approx 12\ \text{years}[/tex]
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A polynomial function has a root of zero with multiplicity one, and root of two with multiplicity four. If the function has a negative leading coefficient, and is of odd degree, which of the following is true.
- the function is positive on (-infinity, 0)
-the function is negative on (0,2)
-the function is negative on (2,infinity)
-the function is positive on (0, infinity)
Answer: A, B, and C
Step-by-step explanation:
root of zero (x = 0) with multiplicity of 1 (x = 0)¹ means that the graph CROSSES the axis at x = 0
root of two (x = 2) with multiplicity of 4 (x = 2)⁴ means that the graph TOUCHES the axis at x = 2
WHY?
odd numbered multiplicity crosses the x-axiseven numbered multiplicity touches the x-axis (it is a turning point)Leading Coefficient (end behavior of right side):
If the leading coefficient is positive, then right side goes to +∞If the leading coefficient is negative, then right side goes to -∞Degree of polynomial (left side behavior):
If degree is even, then left side is the same as the right sideIf the degree is odd, then left side is opposite of right sideThe given polynomial has a negative leading coefficent and odd degree so the left side goes to +∞ and the right side goes to -∞
OBSERVE INTERVALS:
(-∞, 0) is above the x-axis so POSITIVE(0, 2) is below the x-axis so NEGATIVE(2, +∞) is also below the x-axis x=2 was a turning point so NEGATIVESee graph to confirm statements above
Answer:
A, B, and C
Step-by-step explanation:
Had the same question on Edge :)
PLEASE ANSWER THIS QUESTION TOO !! FOR 30 POINTS AND BRAINLIEST!!
Answer:
3000 books
Step-by-step explanation:
We know the author receives a one time fee of $2500. On top of that, the author will receive $1.50 per book sold. This is a constant rate and is linear because of this. We can use y=mx+b. M is the slope or rate of change. M here is $1.50. B is the starting value which is $2500 here.
We write y=1.5x+2500.
This equation will give the amount of money the author earns for x number of books sold. If y=7000 for the author earning 7000. We will use inverse operations to isolate and find x.
7000=1.5x+2500
7000-2500=1.5x+2500-2500
4500=1.5x
4500/1.5=x
3000=x
Answer:
The author must sell 300 books.
Step-by-step explanation:
The total amount earned = advance + books sold * money per book
We know they want to make 7000
The advance is 2500
They earn 1.50 for each book sold
b= number of books sold
Substituting in
7000= 2500 + 1.5b
Subtract 2500 from each side
7000-2500 = 2500-2500 + 1.5 b
4500 = 1.5 b
Divide each side by 1.5
4500/1.5 = 1.5b/1.5
3000 = b
Curtis traveled a distance of 12 miles in 2 hours from the park to his home. What was his average speed in miles per hour?
The graph of the function f(x) is shown below. When f(x) = 0, determine x
Answer:
When f(x) is 0, then x is -1.8.
Step-by-step explanation:
To find this, you simply have to look for the place where the line crosses the x axis. This is where y (or f(x)) is equal to 0. Since this graph only crosses that axis at x = -1.8, that is the number we are looking for.
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
If the table is that of f(x), find a point that lies on the graph of f-^1(x).
Answer: D
Step-by-step explanation:
Inverse is when the x's and y's are swapped
x | y Inverse
-3 | 5 (5, -3)
-2 | -3 (-3, -2)
0 | 3 (3, 0)
1 | -5 (-5, 1) ← this matches choice D
2 | 6 (6, 2)
3 | 10 (10, 3)
Which equation represents this problem?
Carol's age is three more than two times Lindsay's age. Carol is 39 years old. How old is Lindsay?
Let l = Lindsay's age in years.
3l + 2 = 39
2l–3=39
3l–2=39
2l + 3 = 39
Answer:
2l + 3 = 39
Step-by-step explanation:
the equation is 3 + 2L = C, where L is Lindsay's age and C is Carol's age
3 + 2L = 39
What is the length of cloth needed to make 18 shirts if each shirt is made from 0.8 yards of material?
Answer:
14.4 yards
Step-by-step explanation:
Each shirt needs 0.8 yards so 18 shirts needs 18 * 0.8 = 14.4 yards of material.
14.4 yards of material will be needed to make 18 shirts.
What is multiplication?Multiplication is when you take one number and add it together a number of times.
Given that, one shirt is of 0.8 yards of material,
18*0.8 = 14.4
Hence, 14.4 yards of material will be needed to make 18 shirts.
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how can we write 128 in exponent form?
Answer: 2⁷
Step-by-step explanation:
128
∧ 2 64 ∧ 2 32 ∧ 2 16 ∧ 2 8 ∧ 2 4 ∧ 2 2128 = 2 * 2 * 2 * 2 * 2 * 2 * 2
= 2⁷
The average speed of an airplane is four times as fast as the average speed of a passenger train. To travel 1440 km, the train requires 12 h more than the airplane. Determine the average speeds of the train and the airplane.
Answer
Average speed of the train = 90 km/h and average speed of the airplane = 360 km/h.
Explanation:-
If speed of train = x then the speed of airplane = 4x km/h and we have the 2 equations
x = 1440 / (t + 12) (t = time taken by the train)
4x = 1440 / t................................(1) (t = time taken by train)
Multiply the first equation by 4:-
4x = 5760 / (t + 12).....................(2)
Combining equations (1) and (2):-
1440 / t = 5760 / (t + 12)
Cross multiplying:-
5760t = 1440t + 17,280
4320t = 17,280
t = 17280/4320
t = 4 hours
speed of train = 1440/ (4 + 12) = 90 km/h and speed of plane = 4*90 = 360 km/h.
Find the length of the hypotenuse
We know that : In a Triangle, If Two Angles are Equal then Corresponding Sides with Respect to those Two Angles Should be Equal.
In the Given Right Angled Triangle, There are Two Angles which are Equal to 45°. It means The Lengths of the Sides Corresponding to those Equal 45° Angles should be Equal.
It Means The Given Right Angled Triangle is also an Isosceles Triangle
⇒ The Other Side of the Triangle is [tex]3\sqrt{2}[/tex]
As it is a Right Angled Triangle :
[tex]\mathsf{\implies (Hypotenuse)^2 = (3\sqrt{2})^2 + (3\sqrt{2})^2}[/tex]
[tex]\mathsf{\implies (Hypotenuse)^2 = 18 + 18}[/tex]
[tex]\mathsf{\implies (Hypotenuse)^2 = 36}[/tex]
[tex]\mathsf{\implies (Hypotenuse) = 6}[/tex]
The Length of Hypotenuse is 6
A seamstress uses 12 yards of fabric to make 3 costumes for students in the chorus. How many yards will she need to make costumes for all 25 students in chorus?
Answer:
100 yards
Step-by-step explanation:
It takes 4 yards of fabric to make a costume for one student. She needs to make costumes for every student in chorus, so you just multiply this number by 25 and get 100 yards.
Answer:
100 yards.
Step-by-step explanation:
We have been given that a seamstress uses 12 yards of fabric to make 3 costumes for students in the chorus.
We will use proportions to solve the given problem.
[tex]\frac{\text{Yards of fabric}}{\text{Costumes}}=\frac{12}{3}[/tex]
[tex]\frac{\text{Yards of fabric}}{25}=\frac{12}{3}[/tex]
[tex]\frac{\text{Yards of fabric}}{25}*25=\frac{12}{3}*25[/tex]
[tex]\text{Yards of fabric}=4*25[/tex]
[tex]\text{Yards of fabric}=100[/tex]
Therefore, 100 yards of fabric is needed to make costumes for 25 students.
PLEASE NEED HELP ASAP WILL GIVE 50 POINTS
What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 32
Step-by-step explanation:
This is an equilateral triangle, all three sides equal. Since all three sides are equal, all three angle are equal. 180/3 = 60. That means each angle is equal to 60 degrees.
2x-4 = 60
Add 4 to each side
2x-4+4 = 60+4
2x =64
Divide each side by 2.
2x/2 = 64/2
x = 32
Results from choosing a counter 20 times, green 10, yellow 3, blue 7. What is the experimental probability of geting blue?
which of the following are roots of the polynomial function below? F(x)=x^3-3x^2+2
The roots of the polynomial function F(x)=x^3-3x^2+2 can be found by reducing the function to zero and solving for x, likely by applying synthetic division or the Rational Root Theorem, as the polynomial is of third order.
Explanation:In Mathematics, especially in algebra, we often encounter the concept of finding the roots of polynomial functions. The roots of the function F(x)=x^3-3x^2+2 can be found by setting the function equal to zero and solving for the variable x:
Step 1: Set the equation to zero: x^3-3x^2+2 = 0.Step 2: Try to factor the polynomial or use a solving method such as the quadratic formula if it was a second-order polynomial. But in this case, the polynomial is of third order, and in such cases you typically apply synthetic division or the Rational Root Theorem to find the roots.Note: This explanation suggests general approaches. The actual solution would require longer calculations.
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The only root of the polynomial function F(x) = x³ - 3x² + x + 5 is 2 + i.
Explanation:Let's go through the possible roots of this polynomial function one by one and see which of them will make the function equal to zero. Recall that if a number p is a root of a polynomial, then when we substitute p into the polynomial, the resulting value will be zero.
A. First, let's consider 2+i as a possible root.
We would evaluate F(2+i) = (2+i)³ - 3(2+i)² +(2+i) + 5 = 0.
Upon evaluation, it turns out that F(2+i) does indeed equal 0.
B. Now let's see if -2+i is a root.
We evaluate F(-2+i) = ((-2+i)³ - 3(-2+i)² + (-2+i) + 5. This happens not to equal 0. Therefore, -2+i is not a root.
C. Then, we check if 1 is a root by computing
F(1) = 1³ - 3×1² +1 +5. Upon computing, we find that this doesn't result in 0 either. So, 1 is not a root
D. Finally, let's check if 2 is a root.
We compute F(2)= 2³ - 3×2² +2 +5. This computation also doesn't result in 0, therefore 2 is not a root of the polynomial function.
In conclusion, the only given number that is a root of the function is 2 + i.
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Question:Which of the following are roots of the polynomial function below?
F(x)=x³-3x²+x+5
A. 2+i
B. -2+i
C. 1
D. 2
if f(x)=5x-7 then f^-1=__ _
Answer:
f^-1(x) = (x +7)/5
Step-by-step explanation:
Set x = f(y) and solve for y.
... x = 5y -7
... x+7 = 5y
... (x+7)/5 = y . . . . this is the inverse function
f^-1(x) = (x +7)/5
Help me with these math questions........ WITH SCREENIES
Answer: 6.3093
Step-by-step explanation:
[tex]3^{\frac{x}{5}} = 4[/tex]
[tex]ln3^{\frac{x}{5}} = ln4[/tex]
[tex]\frac{x}{5} ln3 = ln4[/tex]
xln3 = 5ln4
[tex]x = \frac{5ln4}{ln3}[/tex]
x = 6.3093
************************************************************
Answer: 5, 3, [tex]\frac{1}{5}[/tex], D
Step-by-step explanation:
a) x ≤ 0 so, f(-5) = | -5 | = 5
x ≤ 0 so, f(-3) = | -3 | = 3
x > 0 so, f(5) = [tex]\frac{1}{5}[/tex]
b) graph D
************************************************************
Answer: [tex]\frac{\pi}{12}[/tex]
Step-by-step explanation:
[tex]\frac{25\pi}{12} - \frac{2\pi}{}[/tex]
= [tex]\frac{25\pi}{12} - \frac{24\pi}{12}[/tex]
= [tex]\frac{\pi}{12}[/tex]
Does anyone know how to do this?
[tex]2)\\\\6+5k+2=18\\\\(6+2)+5k=18\\\\8+5k=18\qquad\text{subtract 8 from both sides}\\\\5k=10\qquad\text{divide both sides by 5}\\\\\boxed{k=2}\\\\4)\\\\-8(a-8)=96\qquad\text{divide both sides by (-8)}\\\\a-8=-12\qquad\text{add 8 to both sides}\\\\\boxed{a=-4}[/tex]
[tex]6)\\7m+35=7(5m-3)\qquad\text{divide both sides by 7}\\\\m+5=5m-3\qquad\text{subtract 5 from both sides}\\\\m=5m-8\qquad\text{subtract 5m from both sides}\\\\-4m=-8\qquad\text{divide both sides by (-4)}\\\\\boxed{m=2}[/tex]
Ralph sold brownies for ?$0.27 a piece in order to earn money to buy baseball cards. If the cards cost ?$0.81 per? pack, and if Ralph had no money left over after buying? them, what is the least number of brownies he must have? sold
Answer:
3 brownies
Step-by-step explanation:
To find this answer we need to divide the 0.81 by 0.27 to find out how many brownies total 0.81:
0.81 ÷ 0.27 = 3
So he needs to sell 3 brownies.
3q, –3p, 3pq, 13p
Question 4 options:
3 q and 3 pq
3q, –3p, and 3pq
–3p and 13p
–3p, 3pq, and 13p
(4b) A rocking horse has a weight limit of 60 pounds. What percentage of the weight limit is 114 pounds? *
Answer:
190 percentage of the weight limit is 114 pounds.
Step-by-step explanation:
Given: A rocking horse has a weight limit of 60 pounds.
We have to find what percentage of the weight limit is 114 pounds.
x percentage of the weight limit is 114 pounds.
⇒ x% of 60 = 114
[tex]\frac{x}{100} \times 60 = 114[/tex]
Solve for x;
[tex]\frac{6x}{10} = 114[/tex]
Multiply both sides by 10 we get;
[tex]\frac{6x}{10} \times 10 = 114 \times 10[/tex]
[tex]6x = 1140[/tex]
Divide both sides by 6 we get;
[tex]x = \frac{1140}{6}[/tex]
Simplify:
x = 190%
Therefore, 190 percentage of the weight limit is 114 pounds.
To find the percentage, divide the given weight by the weight limit and multiply by 100. 114 pounds is 190% of the weight limit of 60 pounds.
To find the percentage of the weight limit, we need to divide the given weight (114 pounds) by the weight limit (60 pounds) and then multiply the result by 100. So, the calculation would be:
Percentage = (114 pounds / 60 pounds) * 100
Simplifying this equation, we get:
Percentage = 190%
Therefore, 114 pounds is 190% of the weight limit of 60 pounds.
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Identify a pattern and sequence and fine the next number in the pattern. 54,52,26,24,_,_,_
Answer:
54, 52, 26, 24, 22, -6, -4
Step-by-step explanation:
Use the Distance Formula and the Pythagorean Theorem to find the distance between each pair of points. M (5, −3) and N (4, −8)
well, we don't have to use the pythagorean theorem per se, only the distance formula, since the distance formula is really the pythagorean theorem in disguise.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ M(\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\qquad N(\stackrel{x_2}{4}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ MN=\sqrt{[4-5]^2+[-8-(-3)]^2}\implies MN=\sqrt{(4-5)^2+(-8+3)^2} \\\\\\ MN=\sqrt{(-1)^2+(-5)^2}\implies MN=\sqrt{26}[/tex]
The graph of f(t) = 6 x 2^t shows the value of a rare coin in year t. What is the meaning of the y-intercept?
Answer: The meaning y-intercept is the initial value of a rare coin is 6.
Step-by-step explanation:
Given : The graph of [tex]f(t) = 6\times 2^t[/tex] shows the value of a rare coin in year t.
The y- intercept is the point on Cartesian plane when the graph intersects y axis. It given the initial value of the function by substituting the value of independent variable as zero.
i.e. , we need to put t=0, we get
[tex]f(0) = 6\times 2^0=6[/tex]
The meaning y-intercept is the initial value of a rare coin is 6.
Beth and Carley are selling candy bars to raise money for new cheerleading uniforms. Beth has sold one less than twice the number of candy bars that Carley has sold. If they have sold 188 candy bars in all, how many has Beth sold?
Answer:
125 candy bars
Step-by-step explanation:
[tex]\text{Let the number of candy bars sold by Carley is }x\\\text{Then since Beth has sold one less than twice the number of candy bars}\\\text{that Carley has sold, so number of candy bars sold by Beth}=2x-1\\\\\text{also given that they have sold 188 candy bars in all, so we have}\\\\\text{Candy bars sold by Carley + Candy bars sold by Beth}=188\\\\\Rightarrow (x)+(2x-1)=188\\\\\Rightarrow 3x-1=188\\\\\Rightarrow 3x=189\\\\\Rightarrow x=\frac{189}{3}=63[/tex]
[tex]\text{Hence the candy bars sold by Beth are:}\\=2x-1\\\\=2(63)-1\\\\=126-1\\\\=125\\\\\text{Hence, Beth sold 125 candy bars.}[/tex]
Montel sold 13 popcorn buckets and sold 13 fruit baskets for a fundraiser. The fruit baskets coast $20.75 each . If Montel raised a total of $469, how much did each popcorn buckets coast
Answer:
The popcorn buckets each cost around $15.34.
Step-by-step explanation:
What is the value of [tex]\alpha[/tex] in this function?
Answer:
hello :
the graph passes by ( -4; 7/128) : f(-4) = 7/128
a/ (-4)^4 = 7/128
a / 256 = 7/128
a/2 = 7
a = 14
We have the point:
[tex]\left(-4,\ \dfrac{7}{128}\right)[/tex]
Put the coordinates of the point to the equation of the function f:
[tex]f(x)=\dfrac{a}{x^4}\to y=\dfrac{a}{x^4}\\\\\left(-4,\ \dfrac{7}{128}\right)\to x=-4,\ y=\dfrac{7}{128}\\\\\dfrac{a}{(-4)^4}=\dfrac{7}{128}\\\\\dfrac{a}{256}=\dfrac{7}{128}\qquad\text{multiply both sides by 256}\\\\a=\dfrac{7}{128}\cdot256\\\\\boxed{a=14}[/tex]
A manufacturer of shipping boxes has a box shaped like a cube. The side length is (5a + 4b). What is the volume of the box in terms of A and b
The volume of the cube would be S^3, where S is the length of the side.
Volume = (5a + 4b)^3
Which becomes:
(5a+4b)(5a+4b)(5a+4b)
Multiply the first two sets of parenthesis by each other:
(25a^2+40ab+16b^2)(5a+4b)
Now multiply that by the 3rd set of parenthesis to get:
125a^3+300a^2b + 240ab^2 + b^3
a soccer team hopes to win at least 3 games for every 2 lost during the season. if there are 15 games scheduled, how many games can the team lose and still achieve its goal
Answer:
This team can lose 6 games and still achieve this goal.
Step-by-step explanation:
In order to find this, we can create a proportion and solve by cross multiplying. The proportion should compare amount of losses to total games.
Ratio = Total
2/5 = x/15
Now cross multiply
15*2 = 5x
30 = 5x
6 = x
This means the team can lose 6 games and still keep the necessary ratio.
Dean has 6 2/5 cups of yogurt. If it takes 4/5 cup of yogurt to make a fruit smoothie, how many smoothies can he make?
Answer:
8
Step-by-step explanation:
Change mixed number to decimal 6 2/5 = 6.4
Change needed fraction to decimal 4/5 = 0.8
Divide yogurt by yogurt needed 6.4 / 0.8 = 8
Working the problem like this will help you with any same type of problem.
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Answer: He can make 8 smoothies.
Step-by-step explanation:
Given : The total amount of yogurt Dean has = [tex]6\dfrac{2}{5}[/tex] cups
In Improper fraction , it will be :
[tex]6\dfrac{2}{5}=\dfrac{6\times5+2}{5}=\dfrac{32}{5}[/tex]
Also, the amount of yogurt required for a fruit smoothie = [tex]\dfrac{4}{5}[/tex]
Now , The number of smoothies he can make = (Total amount of yogurt Dean has) ÷ (amount of yogurt required for a fruit smoothie )
[tex]=\dfrac{32}{5}\div\dfrac{4}{5}\\\\=\dfrac{32}{5}\times\dfrac{5}{4}=8[/tex]
Hence, he can make 8 smoothies.
Find the measure of 1
A. 104
B.38
C.76
Answer:
a
Step-by-step explanation:
104 is the only number inside the box
The value of ∠1 is 38 degree , Option B is the correct answer.
What is a Parallelogram ?Parallelogram is a polygon with four sides , Opposite sides are parallel and equal.
From the figure given
One of the angle is 104 degree
when two lines are parallel and intersected by a transversal
then the sum of the consecutive interior angles is 180 degree
∠1 + ∠2 = 180 -104 = 76 degree
similarly the other two lines are parallel with each other
so ∠1 = ∠4
∠3 = ∠2
Therefore the diagonals are bisecting the angle and so
the value of ∠1 = 76 / 2 = 38 degree
Therefore , The value of ∠1 is 38 degree , Option B is the correct answer.
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