Answer:
Step-by-step explanation:
[tex]y^{4}\sqrt{16x^{8}y^{12}z^{4}}=y^{4}\sqrt{4*4*x^{4*2}y^{6*2}z^{2*2}}\\\\ =y^{4}\sqrt{4^{2}*(x^{4})^{2}*(y^{6})^{2}*(z^{2})^{2}}\\\\=y^{4}*4*x^{4}*y^{6}*z^{2}\\\\=4x^{4}y^{4+6}z^{2}\\\\\\=4x^{4}y^{10}z^{2}[/tex]
A planet has a circular orbit around a star. It is a distance of 59,000,000 km from the centre of the star. It orbits at an average speed of 41,000 km/h. How many Earth days does it take the planet to orbit the star? Give your answer to 2 sf.
Answer:
380 days
Step-by-step explanation:
Problem in post:
The radius of the orbit of the planet is 59,000,000 km.
The orbit is circular, so the length of the orbit is the circumference of a circle with radius 59,000,000 km.
distance = circumference of orbit = 2(pi)r = 2 * 3.14159 * 59,000,000 km = 370,707,933 km
speed = 41,000 km/h
speed = distance/time
time * speed = distance
time = distance/speed
time = (370,707,933 km)/(41,000 km/h) = 9,042 hours
Now we convert hours into earth days.
1 earth day = 24 hours
9,042 hours * (1 day)/(24 hours) = 376.73 days
Answer: 380 days
Problem in comments:
Nina and Jo both ran an 8 km race.
Nina took 45 minutes to run the whole race.
Jo started the race 4 minutes later than Nina but caught up when they had both travelled 5 km.
If Nina and Jo both ran at constant speeds, what is Jo's speed to 2 dp?
Solution:
They met at 5 km. Let's find out how long it took Nina to run 5 km.
We can use a proportion.
(8 km)/(45 min) = (5 km)/(x)
x * 8 km = 45 min * 5 km
x = [(45 * 5)/8] min
x = 28.125 min
They met after Nina was running for 28.125 minutes.
Jo started 4 minutes after Nina, so Jo ran for 4 minutes less than Nina. Jo ran 5 km in 24.125 minutes.
speed = distance/time
speed = (5 km)/(24.125 min) * (60 min)/(1 hr)
speed = 12.43523 km/h
Answer: Jo's speed is 12.44 km/h
4 (x − 1) − 4 (x + 2.5) = x − 6
Answer:
x = -8
Step-by-step explanation:
4 (x − 1) − 4 (x + 2.5) = x − 6
Distribute
4x -4 -4x -10 = x-6
Combine like terms
-14 = x-6
Add 6 to each side
-14+6 = x-6+6
-8 =x
Answer:
-8 =x
Step-by-step explanation:
4 (x − 1) − 4 (x + 2.5) = x − 6
4x -4 -4x -10 = x-6 (Distribute )
-14 = x-6 (Combine like terms )
-14+6 = x-6+6 (Add 6 to each side)
-8 =x
I hope this helps!
evaluate (m/n)(x) for x=-3
Answer:
(-3m)/n
Step-by-step explanation:
(m/n)(x)
For x = -3,
(m/n)(-3) =
-3(m/n) =
(-3m)/n
Our answer is fully simplified
Answer:
your answer is 1
Step-by-step explanation:
answer on edgen uity
A group of friends buys 15 movie tickets for a total of $147.66, which
includes a 7% sales tax.
Before tax, how much did a single movie ticket cost?
Answer: $9.20
Step-by-step explanation:
Divide the full tax price by the sales tax (7% or .07) plus 1 (always add 1 to the tax) thus
$147.66 / 1.07 = $138.00
So $138.00 is the full price without tax.
Now divide $138.00 by the amount of tickets (15) to find a single ticket price before tax!
138.00/15 = $9.20
Remember to always add 1 to the tax percentage above when dividing to get the *pre-tax* price.
If the patter below follows the rule "Starting with two, every consecutive line
has a number that is one less than twice the previous line," how many
marbles must be in the sixth line?
O A. 11
B. 13
O C. 33
O D. Need more information
[tex]answer \\ 33 \\ please \: see \: the \: attached \: picture \\ hope \: it \: helps[/tex]
C. 33 marbles must be there in the sixth line.
How to elaborate the problem ?There are 2 marbles in the 1st line, 3 marbles in the 2nd, 5 marbles in the 3rd and 9 marbles in the 4th.
The rule is " Every consecutive line has a number that is one less than twice the previous line ".
How many marbles are there in 6th line ?In 1st line , 2 marbles are there.
In 2nd line, (2×2)-1 = 3 marbles are there.
In 3rd line, (2×3)-1 = 5 marbles are there.
In 4th line, (2×5)-1 = 9 marbles are there.
In 5th line, (2×9)-1 = 17 marbles are there.
In 6th line, (2×17)-1 = 33 marbles are there.
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Evaluate f(a) = 6a2 - 38a + 4 for a = 6.
Answer:
Just plug in 6 for a.
6 * 6² - 38 * 6 + 4 = -8.
2+|6+2|
Answer please
Answer: 10
Step-by-step explanation:
2 + |6+2|
2 + 8
Answer:
10
Step-by-step explanation:
This question uses the term absolute value.
Think of it as a form of distance. If the thing inside an Absolute value bracket is negative, absolute value will make is positive. If it is positive, it will stay the same. Thinking of this, we can solve the problem quite easily.
2 + |8| = 2+8=10
There’s your answer.
In what ways are sine and cosine graph similar? Be sure to include a discussion of intercepts, maxima, minima, and period.
Answer:
The sine and cosine functions are similars in:
They are periodic functions with a period of 2π.
The domain of each function is (−∞,∞) and the range is [−1,1]. Both has maxima in 1 and a minimal in -1.
Given the graphed function below, which of the following ordered pairs are
found on the inverse function?
10
8
6
4
-6-7 6 4 4 -3 -2 -1 0
2 3 4 5 6
-4
-8
-
A. (-10,-2), (-3,-1), (-2, 0),(-1, 1), (6,2)
O B. (2, 10), (1,3), (0, 2), (-1,1),(-2,-6)
O C. (10,2), (3, 1), (2.0), (1,-1).(-6, -2)
O D. (-2, 10),(-1,3), (0,2), (1, 1), (2.-6)
Answer:
A
Step-by-step explanation:
took it on ap ex
The correct ordered pairs which are found on the inverse function are,
⇒ (-10, -2), (-3, -1), (-2, 0),(-1, 1), (6, 2)
What is mean by Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
We have to given that;
The graphed function are shown in figure.
Now, All the points on the graph are,
⇒ (- 2, - 10) , (- 1, - 3) , (0, - 2) , (1, - 1) , (2, 6)
Hence, The correct ordered pairs which are found on the inverse function are,
⇒ (-10, -2), (-3, -1), (-2, 0),(-1, 1), (6, 2)
Thus, ''Option A'' is true.
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Alice was flying a kite when a gust of wind caught the kite in a tree. Alice is standing 10 feet from the base of the
tree, looking up at her kite at an angle of 25°. If Alice is 5 feet tall, approximately how high is the kite off of the
ground?
A4.66
B 9.66
C 21.45
D 9.23
Answer:
B. 9.66
Step-by-step explanation:
To find how high the kite is off the ground, we will follow the steps below;
we will use trigonometric ratio to solve the problem. That is;
SOH CAH TOA
sinФ = opposite / hypotenuse
cosФ = opposite / hypotenuse
tanФ = opposite / adjacent
from the diagram below
Ф = 25°
opposite = x
adjacent = 10 feet
The best trig ratio to use is tan
we can now proceed to insert the values into the formula
tanФ = opposite / adjacent
tan 25° = [tex]\frac{x}{10}[/tex]
cross-multiply
x = 10 tan25°
x ≈4.66 feet
height of the kite off of the ground = x + height of Alice
=4.66 + 5
=9.66 feet
Therefore, the kite is 9.66 feet high off of the ground
Two less than the product of a number and -5 is -42.
Answer:
8
Step-by-step explanation:
(p*-5)-2=-42
-5p-2=-42
-5p=-42+2=-40
-5p/-5=-40/-5
=8
Please help this is urgent and I am being timed
Which correlation coefficient corresponds to the best-fit line that most closely models its set of data?
Question 6 options:
a)
-0.15
b)
-0.87
c)
0.13
d)
0.84
Urgent need help fast
Answer:
500
Step-by-step explanation:
400 + 100 = 500
Answer:
500
Step-by-step explanation:
Ronald's number + 100 = Jasmine's number
400 + 100 = 500
I need help with this question please & thank you
Answer:
Step-by-step explanation:
most probably secant
hope it helps
Find the angle of elevation of the plane
When it reaches 300 feet above the ground.
Answer:
36.78°
Step-by-step explanation:
Use the tangent equation to find the solution.
Tangent = opposite/adjacent
tanx° = [tex]\frac{300}{400}[/tex]
x ≈ 36.78°
Answer:
X=36.87°
Step-by-step explanation:
Tanx=opposite/adjacent
Tanx =300/400
Tanx=0.75
X=tan-¹(inverse)0.75
X=36.87°
Which system of equations best represents the situation below?
A farmer grew his own tomatoes (a), eggplants (b), and potatoes (c). He decided to package his vegetables and price them as follows:
2 tomatoes, 1 eggplant, 3 potatoes for $10
3 tomatoes, 2 eggplants, 4 potatoes for $14
4 tomatoes, 2 eggplants, 6 potatoes for $20
Answer:
A.
2a +b+3c =10
3a+2b+4c=14
4a+2b+6c=20
Step-by-step explanation:
Hi, to answer this question we have to write a system of equation with the information given:
The price of each package will be equal to sum of the products of each vegetable (a,b or c) and their respective amount :
So:
2 tomatoes, 1 eggplant, 3 potatoes for $102a +1b+3c =10
3 tomatoes, 2 eggplants, 4 potatoes for $143a+2b+4c=14
4 tomatoes, 2 eggplants, 6 potatoes for $204a+2b+6c=20
The system is:
2a +b+3c =10
3a+2b+4c=14
4a+2b+6c=20
(option A)
Feel free to ask for more if needed or if you did not understand something.
Hira is rollerblading at 9 m/s. Danni is climbing at 7 m/s. Amelia is cartwheeling at 2 m/s.
Who will travel the furthest in 15s?
Answer:
Hira
Step-by-step explanation:
They are going at the fastest speed as 9 is the most
Answer:
Hira
Step-by-step explanation:
You're choosing between two car rental companies. Company A charges an initial fee of $15 with $.25 per mile, while Company B only charges $.50 per mile. How many miles will it take for both companies to have the same service price? What's this price amount? Use the following systems of linear equations to solve by graphing. Company A: y = 0.25x + 15 Company B: y = 0.50x
Which is correct:
A. 55 miles; $25
B. 62 miles; $35
C. 60 miles; $30
D. 58 miles; $29
Answer:
60 miles; $30
Step-by-step explanation:
Given:
y = 0.25x + 15 ...........Eq1
y = 0.50x.............Eq2
Where, x = miles and y = Total cost of ranting
Find:
Total cost of ranting.
Computation:
From Eq1 and Eq2
0.25x + 15 = 0.50x
0.25x = 15
x = 15 / 0.25
x = 60 miles
From Eq 2
y = 0.50(60)
y = $30
Help I being asking for help for weeks
Answer:
The last option
Step-by-step explanation:
Mainly because its not exactly word for word what was said but instead it was paraphrased and changed to still have the same information.
Can someone help please??
Answer:
BC= 5.87 (nearest hundredth)
Step-by-step explanation:
Please see attached picture for full solution.
Another easy way for points!!! FASTEST ANSWER=BRAINLIEST!!!
What is: 1x2x3x4x5x6x7x8x9x10?
the answer is 3628800
The solution to the equation "1x2x3x4x5x6x7x8x9x10" is 362,880.
How to find the multiplication?This is a factorial, which is the product of all the positive integers less than or equal to a given number. In this case, the factorial is 10!, which is the product of all the positive integers less than or equal to 10.
To calculate 10!, use the following formula:
n! = n × (n - 1) × (n - 2) × ... × (3) × (2) × (1)
where n is the number to be taking the factorial of.
In this case, n = 10, so:
10! = 10 × (9) × (8) × (7) × (6) × (5) × (4) × (3) × (2) × (1) = 362,880
Therefore, 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 = 362,880.
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If (5, 4) and (7, 2) are the endpoints of a diameter of a circle, what is the equation of the circle? A) (x − 6)2 + (y + 3)2 = 2 B) (x − 6)2 + (y − 3)2 = 2 C) (x + 6)2 + (y +3)2 = 8 D) (x + 6)2 + (y − 3)2 = 8
Answer:
B
Step-by-step explanation:
(5+7)/2 = 6
(4+2)/2 = 3
center = (6, 3)
diameter = √(5-7)²+(4-2)² = √8 = 2√2
radius is half diameter = √2
Equation for circle is (x-6)²+(y-3)²=2
A fruit basket contains seven apples, four bananas, and eight pears. If a piece of fruit is picked at random from the basket, which of the following is closest to the probability that it is not a banana?
1) 0.21
2) 0.68
3) 0.79
4) 0.32
Answer:
1) 0.21
Step-by-step explanation:
This is because there are 4 bananas out of all 19 fruits. 4/19 is equal to 0.21052631578.
If the line segment AB is on a number line, and point A is at 4 and Point B is at 19, then the length of AB is ____. Select one: a. 15 b. - 15 c. 23 d. 12
Answer: 15
Step-by-step explanation:
If two points are together, then you subtract the numbers to get the distance
19 - 4 = 15
What is the problem with this statement?
If you taking geometry, then you are in the 9th grade
A. It does not assume that all students take geometry
B. It does not assume that all students are in the 9th grade
C. It assumes that no students taking geometry are in the 9th grade
D. It assumes that all students taking geometry are in the 9th grade
Please I need help with this
Answer:
D. It assumes that all students taking geometry are in the 9th grade
Step-by-step explanation:
If the circumference of a circle is 484 cm, what is the area and diameter
Answer:
[tex]18641.50 \: cm^2\\154.06 \: cm[/tex]
Step-by-step explanation:
[tex]C=\pi d[/tex]
[tex]484=\pi d[/tex]
[tex]\frac{484}{\pi } =d[/tex]
[tex]d=154.06198[/tex]
[tex]A=\pi r^2[/tex]
[tex]\pi (\frac{d}{2}) ^2[/tex]
[tex]\pi (\frac{154.06198}{2}) ^2[/tex]
[tex]A=18641.49898[/tex]
Answer:
The area of the circle is approximately 18641.5 because you need to round to the nearest place value. The diameter of the circle is approximately 154.06.
Step-by-step explanation:
Area=πr2
Circumference=2πr
Solving for Area
Area= C²/4 π = 484²/4·π ≈ 18641.50017
———————————————————————————
Circumference =2πr
Diameter= πr
Solving for Diameter
Diameter= C/π = 484/π≈ 154.06198
The length of a rectangle is x. The length and width add up to 10 inches. What is the maximum area of the rectangle? Please provide steps on how solve!
Answer:
[tex]Area=25\,\,in^2[/tex]
Step-by-step explanation:
The length of the rectangle is unknown and is defined with the letter "x". Notice that the width of the rectangle is also unknown, so we can name it 'y".
Recall the formula for the area of a rectangle (length times width), and notice that it is this quantity the one we need to maximize (find the maximum possible value).
We use the other information provided to represent the rectangle's with (y) in terms of "x" :
length + width = 10 inches
x + y = 10
Therefore, y = 10 - x
Now we use this expression for "y" in the product for the area;
[tex]Area= x\,*\,y\\Area=x\,(10-x)\\Area=10x-x^2\\Area=-x^2+10x[/tex]
Notice that this quadratic expression corresponds to a parabola with branches pointing down (negative leading term), so its maximum value would be given at the vertex of the parabola.
Now recall that the formula for the x-value of a parabola's vertex when its function is of the form [tex]f(x)=ax^2+bx+c[/tex]
is given by:
[tex]x_{vertex}=-\frac{b}{2a}[/tex]
which in our case where "a" = -1 and "b" = +10, gives:
[tex]x_{vertex}=-\frac{b}{2a}\\x_{vertex}=\frac{-10}{2(-1)}\\x_{vertex}=\frac{-10}{-2}\\x_{vertex}=5[/tex]
Then the maximum value for the Area can be obtained by replacing "x" with "5" in the area formula:
[tex]Area=-x^2+10x\\Area=-(5)^2+10\,(5)\\Area=-25+50\\Area=25\,\,in^2[/tex]
Therefore, the area of the rectangle is [tex]25\,\,in^2[/tex]
Find the value of x please!!
Answer:
x = 9
Step-by-step explanation:
[tex]\frac{12}{8} = \frac{x}{6}[/tex]
x = [tex]\frac{12}{8}[/tex] x 6 = 9
Find the equation of the line that contains the point (−3,−10) and is parallel to the line 6x+5y=11. Write the equation in slope-intercept form, if possible.
Answer:
y = -1.2x - 13.6
Step-by-step explanation:
1. rearrange original question to find the gradient.
2. substitute gradient and points into y - y1 = m (x - x1)
Answer:
y = -1.2x - 13.6
Step-by-step explanation:
1. rearrange original question
2. substitute points into y - y1 = m (x - x1)