Using the perpendicularity concept, the values of a and b so that x is perpendicular to y are: a = 39º, b = 38º.
What are perpendicular lines?Two lines are perpendicular if when they intersect two angles of 90º are formed.
Hence, the condition for this problem is given by:
m<2 = 90º.m<3 = 90º.From condition 2, the value of a is found as follows:
3a - 27 = 90º
3a = 117º
a = 117/3
a = 39º.
From condition 3, the value of b is found as follows:
2b + 14 = 90º
2b = 76º
b = 76/2
b = 38º.
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Using the angle addition postulate, find M
1. M
2.M
3.M
4.M
Look at picture for angle
PLEASE HELP ME WITH THIS QUESTION!!!!!!!!!!!!!!
What are all solutions of the equation x3 = 64?
A. −8 and 8
B. 8 only
C. 4 only
D. −4 and 4
Answer:
Both Choice C, D
Step-by-step explanation:
A: Choice A cannot be the correct answer due to it being negative.
B: Choice B also cannot be part of the correct answer because 8 x 3 = 24
C: Choice C is part of the correct answer
D: Choice D is also part of the correct answer
T V is tangent to the circle, and R and S are points on the circle. What is the value of x to the nearest tenth?
A 7.6
B 6.4
C 5.7
D 4.8
By applying the Tangent Secant Theorem to this circle, the value of x to the nearest tenth is equal to: A. 5.7.
What is the Tangent Secant Theorem?The Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.
By applying the Tangent Secant Theorem to this circle, we have:
(x + x + 3) × x = 9²
(x + 3)x = 81
2x² + 3x = 81
2x² + 3x - 81 = 0
Next, we would solve the quadratic equation by using the quadratic formula:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-3\; \pm \;\sqrt{3^2 - 4(2)(-81)}}{2 \times 2}\\\\x = \frac{-3\; \pm \;\sqrt{9 + 648}}{4}\\\\x = \frac{-3\; \pm \;\sqrt{657}}{4}[/tex]
x = 5.7 or -7.2
Since the line segment cannot be negative, the value of x to the nearest tenth is equal to 5.7.
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When you look at a pencil in water, it looks bent. This illusion is due to refraction, or the bending of light when it moves from one substance to the next.
c. Without measuring, determine how many degrees the path of the light changes after it enters the water. Explain your reasoning.
Answer:
The change in direction or bending of a light wave passing from one transparent medium to another; caused by the change in wave's speed is known as “Refraction”. Pencil appears bent in water because of the refraction of light rays
Step-by-step explanation:
A circle centered at the origin contains the point (4, -3).
Select all points that also lie on the circle.
A. (-3,-4)
B. (0,4)
C. (3,-2)
D. (5,0)
The two points that also lie on the circle are:
A (-3,-4) and D (5,0)
Which points also ie on the circle?We know that a all the points on a circle are equidistant to the center of the circle, and in this case, the center is the origin (0, 0).
We know that the point (4, -3) lies on the circle, so the radius of the circle is:
R = √( (4 - 0)^2 + (-3 - 0)^2) = √25 = 5
So, any point that is at 5 units of the origin will also lie on the circle.
These points are:
A: (-3, -4)
R = √( (-3 - 0)^2 + (-4 - 0)^2) = √25 = 5
And the point D: (5, 0)
R = √( (5 - 0)^2 + (0 - 0)^2) = √25 = 5
So the correct options are A and D.
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What is the inverse of RR? Graph the inverse in the window below by dragging the blue points.
The inverse of the given linear function is of:
R^(-1)(x) = (x - 2)/3
The graph is given at the end of the answer.
What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For function R, in blue, we have that when x = 0, y = 2, hence the intercept is of b = 2 and:
R(x) = mx + 2.
When x = 1, y= 5, when x = 2, y = 8, that is, when x changes by 1 y changes by 3, meaning that the slope is of m = 3, and:
R(x) = 3x + 2.
How to find the inverse function?To find the inverse function, we exchange x and y in the original function, then isolate y.
For function R(x), we have that:
y = 3x + 2.
Then the inverse is found as follows:
x = 3y + 2
3y = x - 2
y = (x - 2)/3
R^(-1)(x) = (x - 2)/3
The graph of R(x) in blue and of R^(-1)(x) in blackis given at the end of the answer. Since they are inverses, they are symmetric over the line y = x.
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10 to the -21st power
Answer:
1e+21
Step-by-step explanation:
I believe this the answer
5. Molly, Milo and Morgan shared a pan of brownies
1
baked by Mom. Molly ate of the pan of
4
2
brownies, Milo ate
of the pan of brownies and
6
1
-
-
Morgan ate of the brownies. What fraction of
3
the brownies was left over?
Please write your answer in simplest form.
6.
The fraction of the brownies left is 1/12.
We need to find out what fraction of the brownies is left.
Let " r " denote the fraction that is left.
Then we have r + 1/4 + 2/6 + 1/3 = 1
⇒ r + 1/4 + 1/3 + 1/3 = 1 (Writing the fraction 2/6 in the simplest form)
⇒ r + 1/4 + 2/3 = 1
⇒ r + (3 + 8)/12 = 1 (taking LCM of 4, 3 and adding the fractions 1/4 and 2/3)
⇒ r + 11/12 = 1
⇒ r = 1 - 11/12
⇒ r = (12 - 11)/12
⇒ r = 1/12.
Therefore, the fraction of the brownies left is 1/12.
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Disclaimer:
The fractions provided in the question are not clear.
Assuming the following to answer the given question.
Molly ate 1/4 of the brownies,
Milo ate 2/6 of the brownies, and
Morgan ate 1/3 of the brownies.
Two hikers are 22 miles apart and walking toward each other. They meet in 4 hours. Find the rate of each hiker if one hiker walks 3.3 mph faster than the other.
Two hikers are 22 miles apart and walking toward the each other, they meet in 4 hours. The rate of each hiker if one hiker walks 3.3 mph faster than the other are 2.2mph, 2.2mph, 3.3mph.
What is a speed?Distance divided by time is the dimension of speed. The SI measure of speed is the meter per second (m/s), although the most widely used unit in daily life is the kilometer per hour (km/h), or miles per hour in the US and the UK (mph). The knot is a popular choice for air and sea travel.
The instantaneous speed serves as the upper bound of the average speed as the duration of the time period gets closer to 0. The distance traveled by an object during a period of time divided by the length of the period gives the average speed of an object throughout that period. Velocity and speed are not the same thing.
Time divided by distance are the speed-related metrics. The kilometer per hour (km/h), or miles per hour in the US and UK, is the unit of speed that is most frequently used in daily life. The meter per second (m/s) is the metric unit of speed (mph). The knot is often used in air and sea transportation.
Since the hikers are moving at varying speeds, they collide in a location other than the center.
Let the distance travelled by Hiker A (slower) be x at speed s.
So, the distance travelled by Hiker B (faster) is (22 - x) at a speed (s + 1.1).
s = x / 4
s + 1.1 = 22 - x / 4
After resolving equations 1 and 2, we obtain:
x = 8.8m and s = 2.2mph
Therefore,
Speed of the Hiker A = 2.2 mph
Speed of the Hiker A = 2.2 mph
Speed of the Hiker B = 3.3 mph
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Find the value of LK
Answer:
LK = 7
Step-by-step explanation:
NK = NM + ML + LK ( substitute values )
23 = x - 6 + 9 + 2x - 19
23 = 3x - 16 ( add 16 to both sides )
39 = 3x ( divide both sides by 3 )
13 = x
Then
LK = 2x - 19 = 2(13) - 19 = 26 - 19 = 7
Given the simultaneous equations 2x - y = 1 x² + 4ky + 5k = 0 where k is a non-zero constant show that x² + 8kx + k = 0. Given that x² + 8kx + k = 0 has equal roots.
a) [tex]x^{2}[/tex]+8kx +k=0, b) k=1/16
Here we have equation is 2x -y = 1 , [tex]x^{2}[/tex]+4ky+5k=0
To show that [tex]x^{2}[/tex] +8kx +k =0, we have two equation 2x-y=1 and [tex]x^{2}[/tex] +4ky + 5k=0
So from the equation 2x - y = 1 we can find y
Therefore y = 2x-1
Now we will put the value of y in the equation [tex]x^{2}[/tex] + 4ky + 5k =0
a) We have [tex]x^{2}[/tex] + 4k(2x-1) +5k=0
[tex]x^{2}[/tex] + 8kx -4k + 5k=0
[tex]x^{2}[/tex] +8kx +k=0
b) Now we have to find the value of k, and as from the question it is given that [tex]x^{2}[/tex] + 8kx +k =0 have equal roots
Therefore we get [tex]b^{2}[/tex] + 4ac = 0 is the condition of the linear equation in two equal roots.
So from this we have b= 8k, a = -1, c= k
[tex](8k)^{2}[/tex] - 4× 1×k =0
64[tex]k^{2}[/tex] -4k =0
4k(16k -1) =0
16k-1=0
k = 1/16
As k is a non-zero constant therefore we have not taken k=0. Therefore the value of k is 1/16.
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The complete question is:
Given the simultaneous equations 2x - y = 1 x² + 4ky + 5k = 0 where k is a non-zero constant a)show that x² + 8kx + k = 0. Given that x² + 8kx + k = 0 has equal roots., b) find the value of k.
A die is rolled. find the probability of the given event. (a) the number showing is a 3;
The probability that the number showing is a 3 is [tex]\frac{1}{6}[/tex].
What is probability?Probability refers to the possibility of the occurrence of an event.
P(E) = probability of occurrence of an event E = [tex]\frac{Number Of Favourable Outcomes}{Total Number Of Outcomes}[/tex]
Now,
According to question, number of favorable outcomes = 1, i.e., the number 3 shows up on the die
And the total number of outcomes = 6
Hence, The probability that the number showing is a 3 is [tex]\frac{1}{6}[/tex].
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rob drove to the nearest hospital with an average speed of v meters per seconds in t seconds. in terms of t, if he drives home on the same path, but with an average speed of 3v meters/second, how long is the return trip home?
The time used for the return trip is t / 3
How to find how long the trip took using the average speed?He drove to the nearest hospital with an average speed of v meters per seconds in t seconds.
Therefore,
average speed = distance / time
average speed = v
time used = t
d = distance covered
Therefore,
v = d / t
d = vt
He drives home on the same path, but with an average speed of 3v meters/second. The time used for the return trip is as follows:
Recall he covered the same distance.
Therefore,
average speed = 3v
time used for the return trip = x
d = distance
Hence,
3v = vt / x
x = vt / 3v
x = t / 3
Therefore, the time used for the return trip is t / 3
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how can you describe the graph of equation ax + by = c
The standard form of a line is simply a special way of writing the equation of a line. You are probably already familiar with the slope-intercept form of a line, y = mx + b. The standard form is just another way to write this equation and is defined as Ax + By = C, where A, B, and C are real numbers, and A and B are both not zero (see note below about other requirements). As you will see in the lesson below, every line can be expressed in this form.
Note that the requirements on A, B, and C vary a bit from textbook to textbook. While they technically can be any real numbers, it is most common to write them as integers and to keep A positive. It is also common to require that A, B, and C share no common factors.
Ax+By=C
THE STANDARD FORM OF A LINE: Ax+By=C
The result is referred to as the standard form of the line: Ax+By=C. We should always be able to convert from one form of an equation to another. For example, if we are given a line in the slope-intercept form, we should be able to express it in the standard form, and vice versa
he standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations
Now ,
A=0
B=0
A and B are not both zero, the graph of Ax + By = C is always a line.
when ,
The graph of Ax + By = C, where A and B are not both zero
A[tex]\neq[/tex]0
B[tex]\neq[/tex]0, is a line.
Divide both sides by B. Because the form Ax + By = C can describe any line,
it is called the standard form of an equation for a line.
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More details : brainly.com/question/12452575
Please?? Help Needed
Sooner would be appreciated.
Answer:
2
Step-by-step explanation:
What you do to one side, you must do to the other.
When you add the 2 on one side of the = sign then you have to add the 2 on the other side. when you do that you will get 7 + 2. so the number in the green is 2. hope this helped a little!
Solve equation.
5 c=20
To solve the equation, divide both sides by 5. The solution is c = 4.
A linear equation is an equation of which the highest degree of its variables is 1.
Steps to solve linear equations:
Simplify the expressions. If there are parentheses, remove them by multiplying the corresponding terms.Combine the same terms.Isolate the variable on one side by using subtraction or addition.Use division or multiplication to find the value of the variable.Recall that if we subtract or add the same number to both sides of an equation, it does not change the equality.The given problem:
Solve 5c = 20
Notice that the variable, c, is already isolated on the left side.
Divide both sides by 5:
5c : 5 = 20 : 5
c = 4 (solved)
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PLEASE HELP & THANKS SO MUCH.
A: Domain: (1.25,0) Range: (0,1)
B: Domain: −2≤x≤2 Range: −2≤y≤3
C: Domain: −2≤x≤3 Range:−2≤y≤2
D: Domain: −4≤x≤4 Range: −4≤y≤4
E: Domain: −2≤x≤2 Range: −3≤y≤3
The Domain of the given function is −2≤x≤2 and the range of the given function are −2≤y≤3.
The domain of a graphical function refers to all the input values which are shown or plotted on the x-axis. The domain of a function may be defined as the set of values that are assumed for the function.
The range of a graphical function refers to all the input values which are shown or plotted on the y-axis. The range of a function may be defined as the set of values that the function gives after assuming the input values for the function.
Here in the graph, the set of input values on the x-axis are from -2 to 2. Thus, the domain is −2≤x≤2. Also, the set of input values on the y-axis is from -2 to 3. Thus, the range is −2≤y≤3.
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What is the midpoint of PQ?
Answer:
Mpq= (
[tex] \frac{4 \times \frac{1}{3} + - 2 \times \frac{1}{5} }{2} and \frac{3 \times \frac{1}{6} + 3 \times \frac{2}{3} }{2} [/tex]
[tex] \frac{16}{15} \: and \frac{41}{12} [/tex]
midpoint for PQ is (16/15; 41/12)
the points $(1,-2)$ and $(-4,10)$ are adjacent vertices of a square. what is the perimeter of the square?
Answer:
Use distance formula between these points to find length of one side of the square.....then multiply by 4 sides
sqrt( 5^2 + 12^2 ) = 13 units side length
Step-by-step explanation:
And i think you can go from there if not please ask me to do the rest for you
Look at both pictures before answering
only answer if you are sure it's correct
if it's not correct I'm reporting :D
answer quickly bc I'm timed
you get 5 stars, nice comment, heart, and brainliest if you are the first corret answer
TY FOR READING THIS OMG UR SO NICE <3
Answer: A
Step-by-step explanation:
A. 2.6x 10^-7
Answer:
a
Step-by-step explanation:
because you move the decimal 7 times to the right to put it into scientific notation
you are the administrator of an annual essay contest scholarship fund. this year a $52,000 college scholarship is being divided between the top two contestants so that the winner receives three times as much as the runner-up. how much will each contestant receive (in dollars)?
The amount each contestant will receive is as follows:
First position = $39,000Runner up = $13,000How to find the amount each contestant will receive?This year $52,000 college scholarship is being divided between the top two contestants .
Therefore,
Total amount to share to the top winners = 52000 dollars
The winner receives three times as much as the runner-up.
Therefore,
let
x = Amount received by the runner-up
Hence,
Amount the winner received = 3x
Therefore,
52,000 = 3x + x
52,000 = 4x
divide both sides by 4
4x / 4 = 52,000 / 4
x = 13000 dollars
Hence,
Amount the winner received =3(13000) = $39000
Amount received by the runner-up = $13,000
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I need help with this question
The graphed function is decreasing on this following interval:
(-5, 5).
When a function is decreasing, looking at it's graph?Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down on the graph, meaning that when x increases, y decreases.
From this problem, there is only one interval, from x = -5 to x = 5, hence the interval is (-5, 5).
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4x⁰y–²z³ divided by 4x
Answer:
Step-by-step explanation:
z³/xy²
in 2016, taxicabs in los angeles charged an initial fee of $2.85 plus $2.70 per mile. in equation form, fare
If the taxicabs in Los Angeles charged an initial fee of $2.85 plus $2.70 per mile, the the equation of the fare is 2.85+2.70x
Given,
The initial fee of taxi cab = $2.85
The charges per mile = $2.70
Consider the number of miles as x
Then,
The equation of the fare = 2.85+2.70x
Hence, If the taxicabs in Los Angeles charged an initial fee of $2.85 plus $2.70 per mile, the the equation of the fare is 2.85+2.70x.
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The data set shows the number of actors used in several school plays across Des Moines.
1. Which is greater the mean or median?
2. Would the mean or median be impacted more if we added the number 60 to the data set? Explain your reasoning
The box plot below show the distribution of the average amount of hours athletes were in the weight room per month.
1. Although the schools both have the same IQR, which school will have a greater variability? Explain your reasoning
2.Is the maximum value for school 1 an outlier? Explain your reasoning using the formula
3. A new athlete started attending school 2 and spends so many hours in the weight room that they are considered a outlier how many hours did the student need to spend in the weight room for school 2 to be considered an upper end outlier? Explain your reasoning using the formula.
The comparison of the mean and median of the data set of the dot plot in the first part and the variability and outlier of the dataset in the box and whiskers plot in the second part are;
First part;
1. The median is greater than the mean.
2. Both the mean and median will increase
Second part;
1. School 1 has greater variability
2. The maximum value of school 1 is not an outlier
3. The new athlete needs to spend 21 hours or more
How can the dot and box and whiskers plots be analyzed?First part;
1. The value in the dot plot are;
10, 11, 12, 12, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 19
The number of data points = 36
The mean = The sum of the above data divided by 36
Using an online calculator of data sets, we have;
The mean = 15.194The median = 15.5Therefore;
The median is greater than the mean.2. The addition of 60 to the dataset will increase the number of data points from 36 to 37, thereby changing the median, which is the middle value to the 19th number, which is 16, while the mean value will also increase to 16.405, therefore;
The mean and median will both increaseSecond part;
1. A measure of variability of a box plot is the range, which is the difference between the largest and smallest values.
The range of school 1 is; 16 - 1 = 15
The range of school 2 is; 14 - 1 = 13
Therefore;
School 1 has greater variability.2. The maximum value of school 1 is 16
The inter quartile range of school 1 is; IQR = 10 - 4 = 6
An outlier = Q3 + 1.5 × IQR
The third quartile, Q3, for school 1 = 10Which gives;
An outlier ≥ 10 + 1.5 × 6 = 19
The maximum value for school 1 = 16 < 19, is not an outlier.3. Q3 for school 2 = 12
IQR for school 2 = 12 - 6 = 6
Which gives;
Outlier for school 2 ≥ 12 + 1.5 × 6 = 21
To be considered an upper end outlier in school 2, the student needs to spend 21 hours or more in the weight room.Learn more about dot and box and whiskers plots here:
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Determine whether the stated conclusion is valid based on the given information. If not, write invalid. Explain your reasoning.Given: An angle bisector divides an angle into two congruent angles. →KM is an angle bisector of ∠J K L .
Conclusion: ∠J K M ≅ ∠M K L battery is dead.
Answer:
Step-by-step explanation:
The answer to this my friend would be valid by the law of syllogism because our P is an angle bisector and our q is km. Our r is connecting to our p and says that they are congruent. Therefore if An angle bisector divides an angle into two congruent angles, then JKM and KML are congruent.
Hope this helps!
The Conclusion: ∠J K M ≅ ∠M K L is valid
Given data
An angle bisector divides an angle into two congruent angles. →KM is an angle bisector of ∠J K L .
What is bisection?Bisection is a term in mathematics that refers to dividing into two equal parts. This term is used more in the branch of mathematics called geometry.
Bisection can be done for an angle or line, for a line the given line is divided into two equal parts. Angle bisector divides the given angle into two equal parts to give two equal angles
When angle JKL is bisected by line KM. The line will lead to two angles which are:
∠J K M ∠M K LThese two angles are congruent and are represented by the formula below: ∠J K M ≅ ∠M K L
Hence we can say that the conclusion is valid
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Find the equation of a line that is perpendicular to the line x = 11 and contains the point (7,6). some one help plsss
The equation of a line that is also perpendicular to the line [tex]x = 11[/tex] and contains the point [tex](7,6)[/tex] is [tex]y=6[/tex]
As per the question statement, we are supposed to find the equation of a line that is also perpendicular to the line [tex]x = 11[/tex] and contains the point [tex](7,6)[/tex].
Before solving that, we need to know that the given line [tex]x = 11[/tex] is parallel to the y-axis as no point is passing through y axis hence the slope [tex]m_{1}[/tex] of the given line will be [tex]\frac{1}{0}[/tex].
The required line is perpendicular to the given line, so it will be parallel to the x-axis and hence it's slope would be slope [tex]m_{2}[/tex] = [tex]0[/tex]
We know the equation of the line passing through a some point [tex]x_{1}[/tex] and [tex]y_{1}[/tex] having slope m is given by:
[tex]y-y_{1} =m_{2} (x-x_{1})[/tex]
Here the required line is passing through (7,6), hence substituting the values of [tex]x_{1}, y_{1} ,m_{2}[/tex], we get
[tex]y-6=0(x-7)[/tex]
or [tex]y-6=0[/tex]
or [tex]y=6[/tex]
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Jackets cost the retailer $75 a piece to purchase wholesale. If he has five to sell and
doesn't sell them until 30 days have gone by, how much money does he lose? Remember
a loss is shown with a negative rational number.
with Rational Numbers
Answer:
Retailer will loss $375. If he didn't sell that Jackets until 30days.Step-by-step explanation:
Given that
Jackets cost the retailer $75 a piece to purchase wholesaleHe has 5 Jackets for sell.To find
If he didn't sell that all peace until 30 days then the lost of him.So, according the question,
We have
The price of one peace Jacket = $75.The quantity of Jacket = 5So, the money he loss to don't sell that Jackets in 30 days is the total cost of all jackets.
∴ The Total cost of all Jackets = 75 × 5
= $375.
Answer: Retailer will loss $375.
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Pls help it’s due soon
Answer: the answer is c!
Step-by-step explanation:
The approximate weights of two animals are 5.36 x 10^4 lbs. and 6.2 x 10^4 lbs. Find the total weight of the two animals. Write the final answer in scientific notation with the correct number of significant digits.
Answer: The total weights of the two animals is 11. 92 × 10² Ibs
Step-by-step explanation: