What is wrong with the following equation?x2+x−20/x−4=x+5a. (x−4)(x−5)≠x2+x−20b. The left-hand side is not defined for x = 0, but the right-hand side is.c. The left-hand side is not defined for x = 4, but the right-hand side is.d. None of these - the equation is correctIn view of part (a), explain why the equation lim x rightarrow 3 x2+x-12/x-3= lim x rightarrow 3 (x+4) is correct. 1. Since x2+x-12/x-3 and x + 4 are both continuous, the equation follows. 2. Since the equation holds for all x 3, it follows that both sides of the equation approach the same limit as x Rightarrow 3. This equation follows from the fact that the equation in part (a) is correct. 4. None of these 5. the equation is not correct.
Answers
Answer:
The answer to this question can be defined as follows:
In part (i), the answer is "option d".
In part (ii), the answer is "option 2".
Step-by-step explanation:
Given:
Part (a)
\(\Rightarrow \bold{\frac{x^2+x-20}{x-4}=x+5}\\\\\)
Solve the above equation:
\(\Rightarrow x^2+x-20=(x+5)(x-4)\\\\\Rightarrow x^2+x-20=(x^2-4x+5x-20)\\\\\Rightarrow x^2+x-20=x^2-4x+5x-20\\\\\Rightarrow \boxed{x^2+x-20=x^2+x-20}\\\)
Given:
Part (b)
\(\Rightarrow \bold{ \lim_{x \to \3} \frac{x^2+x-12}{x-3}= \lim_{x \to 3} (x+4)}\\\\\)
Solve the above equation:
factor of \(\Rightarrow x^2+x-20 =(x-3)(x+4)\)
\(\Rightarrow \lim_{x \to \3} \frac{(x-3)(x+4)}{x-3}= \lim_{x \to 3} (x+4)\\\\\Rightarrow \lim_{x \to \3} (x+4)= \lim_{x \to 3} (x+4)\\\\\)
apply limit value:
\(\Rightarrow (3+4)= (3+4)\\\\\Rightarrow 7= 7\)
Related Questions
Dot Plots and Histograms-Quiz-Level F
Briana is learning to play the guitar. At the end of each week, she records the number of days
she practiced. Her data is shown below.
2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6
OFReady
Which dot plot displays the data distribution?
1
2
2
3
4
Number of Days
3
Number of Days
:
5
6
7
567
0
+
0
1
2
3
4
Number of Days
2
5
...
3
4
Number of Days
5 6
..
Answers
The dot plot that displays the data distribution is the dot plot on the lower left corner of the options with
Two dots at 0
One dot at 2
Two dots at 3
Four dots each at 4, 5, and 6
One dot at 7
A dot plot is a graphical presentation of data, on a number line, with the number of points of dot representing the frequency of data at each value on the number line.
The data can be presented as follows;
2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6
The above data can be arranged in increasing order as follows; 0, 0, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
Therefore, the frequencies of 0s is two, the frequencies of 4s, 5s and 6s are four each, and the frequency of 7 is one, which corresponds to the third graph or the graph in the bottom left corner of the figure.
Learn more on dot plots here: https://brainly.com/question/14217166
#SPJ1
can You pls Help me In steps I will Give you 20 points and mark you brainiest pls help
Answers
Answer:
612
Step-by-step explanation:
We can break this into two rectangles. One of them has lengths 12 and 11 the other one 30 and 16.
30 x 16 = 480
12 x 11 =132
Then we add the areas of these shapes to get the total area being 612.
please help ASAP ;)
Answers
Answer: use PEMDAS
Step-by-step explanation:
The average low temperatures in international falls minnesota are shown in the graph f(x) represents the function that contains these points find each of the following
Answers
The Relative Maximum will be (7, 50) and minimum is (12, 0).
We have the graph showing average low temperatures in international falls minnesota.
From the graph the maximum y coordinate is 50.
So, the Relative Maximum will be (7, 50).
and, the minimum y coordinate is 0.
So, the Relative minimum is (12, 0)
Learn more about Relative Maximum and Minimum here:
https://brainly.com/question/29158306
#SPJ1
100 POINTS!!!!
Two cylinders are similar with diameters 6 in and 9 in.
a. Find the ratio of the circumference of their bases
b. Find the ratio of the surface areas.
c. Find the ratio of the volumes.
Answers
circumference:-
\(\\ \sf\longmapsto \dfrac{2\pi r_1}{2\pi r_2}\)
\(\\ \sf\longmapsto \dfrac{6\pi}{9\pi}\)
\(\\ \sf\longmapsto \dfrac{2}{3}\)
\(\\ \sf\longmapsto 2:3\)
LSA:-
\(\\ \sf\longmapsto \dfrac{2\pi r_1h}{2\pi r_2h}\)
\(\\ \sf\longmapsto \dfrac{6}{9}\)
\(\\ \sf\longmapsto \dfrac{2}{3}\)
\(\\ \sf\longmapsto 2:3\)
TSA
\(\\ \sf\longmapsto \dfrac{2\pi r_1(h+r_1)}{2\pi r_2(h+r_2)}\)
\(\\ \sf\longmapsto \dfrac{6(h+6)}{9(h+9)}\)
\(\\ \sf\longmapsto \dfrac{6h+36}{9h+81}\)
\(\\ \sf\longmapsto \dfrac{h(6+36)}{h(9+81)}\)
\(\\ \sf\longmapsto \dfrac{42}{90}\)
\(\\ \sf\longmapsto \dfrac{7}{15}\)
\(\\ \sf\longmapsto 7:15\)
Volume:-\(\\ \sf\longmapsto \dfrac{\pi r_1^2h}{\pi r_2^2h}\)
\(\\ \sf\longmapsto \dfrac{6^2}{9^2}\)
\(\\ \sf\longmapsto \dfrac{2}{3}\)
\(\\ \sf\longmapsto 2:3\)
how to express 1 cm as a fraction of 1 meter in decimal form
Answers
\(\qquad\qquad\huge\underline{{\sf Answer}}♫\)
Let's see ~
Remember : value of 1 meter = 100 centimeters
\(\qquad \sf \dashrightarrow \:1 \: m = 100 \: cm\)
\(\qquad \sf \dashrightarrow \:1 \: cm = \frac{1}{100} \: m\)
\(\qquad \sf \dashrightarrow \:1 \: cm = 0.01 \: m\)
・ ．━━━━━━━†━━━━━━━━━．・
As we know
100cm=1mSo
turn down to fraction
\(\\ \rm\rightarrowtail \dfrac{1}{100}\)
Turn to decimal
\(\\ \rm\rightarrowtail 0.01m\)
Need help 100 points
Answers
A translation followed by what is known as a dilation, but the name for dilation may vary depending on your country of origin. A translation would cause ABCD to slide into the location of the second shape. A dilation would scale ABCD to the size of A'B'C'D.
A cylinder circumference 11 pi in and height 10in. What is the volume of the cylinder?
Please helpppp me!!!
Answers
Answer:
950.455in^3
Step-by-step explanation:
Given data
Circumference= 11π
Also, the expression for circumference is
C=2πr
11π=2πr
solve for r
r= 11π/2π
r= 5.5in
Given that the Height h= 10in
The expression for the volume is
V= πr^2h
V=3.142*5.5^2*10
V=3.142*30.25*10
V=950.455 in^3
Hence the volume is
950.455in^3
Find the slope of the line.
Answers
Answer:
-5/4
Step-by-step explanation:
slope(m)= y2-y1/x2-x1
from the graph 5-0/-2-2
=5/-4
answer = -5/4
15.3
21. A squirrel is standing on the branch of a tree. The angle of elevation from a point on the ground to the squirrel
is 48°. The ground distance from the point to the tree is 28ft. How high above the ground is the squirrel?
Round your answer to the nearest foot.
48⁰
28 ft
21
Answers
Answer:
The height of the squirrel is 31 feet.
Step-by-step explanation:
You need to know your Right Triangle Trigonometry to do this problem.
Rt Triangle trig is all about ratios. Angles and ratios.
In your question, there is a rt triangle. The side measure given, 28 is next to the angle. The math word for "next to" is "adjacent" You know the adjacent side. The squirrel's height is the opposite side. The ratio that puts together adjacent and opposite is tangent.
tan Angle = opposite/adjacent
tan 48° = x/28
multiply both sides by 28
28•tan48° = x
You have to use a calculator that has trig functions. It will have buttons that say "sin", "cos", and "tan"
Enter 28 × tan48° =
It will return 31.0971504152
Your question asks you to round to the nearest whole.
x = 31
The squirrel's height in the tree is 31ft.
P=W (1+a)/1-a Make a the subject
Answers
The variable a as the subject is a = (P -W)/(W + P)
How to make a the subject of the formulaFrom the question, we have the following parameters that can be used in our computation:
P=W (1+a)/(1-a)
Cross multiply the equation
So, we have the following representation
P - Pa = W + Wa
Collect the like terms
This gives
Wa + Pa = P - W
So, we have
a(W + P) = P - W
Divide
a = (P -W)/(W + P)
Hence, the solution is a = (P -W)/(W + P)
Read more about subject of formula at
https://brainly.com/question/657646
#SPJ1
Which expressions are completely factored?
Select each correct answer.
Responses
16a5−20a3=4a3(4a2−5)
16 a begin power 5 end power minus 20 a cubed equals 4 a cubed left parenthesis 4 a squared minus 5 right parenthesis
12a3+8a=4(3a3+2a)
12 a cubed plus 8 a equals 4 left parenthesis 3 a cubed plus 2 a right parenthesis
30a6−24a2=3a2(10a4−8)
30 a begin power 6 end power minus 24 a squared equals 3 a squared left parenthesis 10 a begin power 4 end power minus 8 right parenthesis
24a4+18=6(4a4+3)
24 a begin power 4 end power plus 18 equals 6 left parenthesis 4 a begin power 4 end power plus 3 right parenthesis
Answers
The expressions that are completely factored are:
16a5−20a3=4a3(4a2−5) is correct.12a3+8a=4(3a3+2a) is correct.24a4+18=6(4a4+3) is correct.Why are they considered to be correct?The expressions are considered correct because they have been completely factored, meaning they have been written in the form of "a common factor times another expression". This means that the expression on the right side of the equal sign can be simplified into its simplest form.
For example, in the expression 16a5−20a3=4a3(4a2−5), the 4a3 factor is common to both 16a5 and 20a3, so it can be factored out. The expression then becomes 4a3 times (4a2−5), which is the completely factored form.
Similarly, in the expression 12a3+8a=4(3a3+2a), the factor of 4 is common to both the expressions on the right side, so it can be factored out. This results in the completely factored form of 4 times (3a3+2a).
learn more about factorization: https://brainly.com/question/10718512
#SPJ1
Answer:
16a^5−20a^3=4a^3(4a^2−5)
and
24a^4+18=6(4a^4+3)
Step-by-step explanation:
PLEASE HELP ILL GIVE 5* AND THANKS
Answers
Each time 5 sticks are added. So pattern 6 would have 25 stickers added to the original 7 sticks equaling 32 sticks
B)n=5x+7
A spinner has 10 equally sized sections, 5 of which are gray and 5 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue? Write your answer as a fraction in the simplest form.
Answers
Answer:
\(P(Gray\ and\ Blue) = \frac{1}{4}\)
Step-by-step explanation:
Given
\(Sections = 10\)
\(n(Gray) = 5\)
\(n(Blue) = 5\)
Required
Determine P(Gray and Blue)
Using probability formula;
\(P(Gray\ and\ Blue) = P(Gray) * P(Blue)\)
Calculating P(Gray)
\(P(Gray) = \frac{n(Gray)}{Sections}\)
\(P(Gray) = \frac{5}{10}\)
\(P(Gray) = \frac{1}{2}\)
Calculating P(Gray)
\(P(Blue) = \frac{n(Blue)}{Sections}\)
\(P(Blue) = \frac{5}{10}\)
\(P(Blue) = \frac{1}{2}\)
Substitute these values on the given formula
\(P(Gray\ and\ Blue) = P(Gray) * P(Blue)\)
\(P(Gray\ and\ Blue) = \frac{1}{2} * \frac{1}{2}\)
\(P(Gray\ and\ Blue) = \frac{1}{4}\)
A baker is stocking up on ingredients for the next day. She needs to bake between 32 and 48 loaves of bread. Each loaf requires 3.5 cups of flour plus an additional 0.25 cup for dusting. Complete the statement to describe the amount of flour the baker should buy to have enough flour to meet her Needs without any left over.
Answers
Answer:
32and 48
Step-by-step explanation:
2) The mean mathematics SAT score in 2012 was 514 with a standard deviation of 117 ("Total group profile," 2012). Assume the mathematics SAT score is normally distributed. a. State the random variable. b. Find the probability that a person has a mathematics SAT score over 700. c. Find the probability that a person has a mathematics SAT score of less than 400. d. Find the probability that a person has a mathematics SAT score between a 500 and a 650. e. Find the mathematics SAT score that represents the top 1% of all scores.
Answers
The mathematics SAT score representing the top 1% of all scores is approximately 780.
a. The random variable in this case is the mathematics SAT score.
b. To find the probability that a person has a mathematics SAT score over 700, we need to calculate the z-score first.
The z-score is calculated as \(\frac{(X - \mu )}{\sigma}\),
where X is the value we're interested in, μ is the mean, and σ is the standard deviation.
In this case, X = 700, μ = 514, σ = 117.
Using the formula, the z-score is \(\frac{(700 - 514)}{117 } = 1.59\).
To find the probability associated with this z-score, we can consult a standard normal distribution table or use a calculator.
The probability is approximately 0.0564 or 5.64%.
c. To find the probability that a person has a mathematics SAT score of less than 400, we again calculate the z-score using the same formula.
X = 400, μ = 514, and σ = 117.
The z-score is \(\frac{(400 - 514) }{117 } = -0.9744\).
Looking up the probability associated with this z-score, we find approximately 0.1635 or 16.35%.
d. To find the probability that a person has a mathematics SAT score between 500 and 650, we need to calculate the z-scores for both values.
Using the formula, the z-score for 500 is \(\frac{(500 - 514)}{117 } = -0.1197\),
and the z-score for 650 is \(\frac{(650 - 514)}{117 } = 1.1624\).
We can then find the area under the normal curve between these two z-scores using a standard normal distribution table or calculator.
Let's assume the probability is approximately 0.3967 or 39.67%.
e. To find the mathematics SAT score that represents the top 1% of all scores, we need to find the z-score corresponding to the top 1% of the standard normal distribution.
This z-score is approximately 2.33.
We can then use the z-score formula to calculate the corresponding SAT score.
Rearranging the formula,
\(X = (z \times \sigma ) + \mu\),
where X is the SAT score, z is the z-score, μ is the mean, and σ is the standard deviation.
Substituting the values,
\(X = (2.33 \times 117) + 514 = 779.61\).
Rounded to the nearest whole number, the mathematics SAT score representing the top 1% of all scores is approximately 780.
For such more questions on mathematics
https://brainly.com/question/29892643
#SPJ8
I only have 10 points left right now I'm using it on this so please be a real answer
Answers
Answer:
B
Step-by-step explanation:
Tuesday: 16.0
Wednesday: 16.1
Thursday: 16.0
Friday: 15.1
Tuesday's and Thursday's rounded number of pounds of paper recycled is 16.
What do the following two equations represent? y=-3x+1 y+5= -3(x-2) a) the same line b) distance parallel lines c) perpendicular lines d) intersecting, but not perpendicular lines
Answers
Answer:
a) the same line
Step-by-step explanation:
The first equation is the "slope-intercept form" of the equation of a line with slope -3 and y-intercept +1. The second equation is the "point-slope form" of the equation of the same line. The "point" in this form is (x, y) = (2, -5), which is a point that satisfies the first equation:
y = -3x +1
-5 = -3(2) +1 . . . . true
The two equations represent the same line.
The perimeter of the triangle shown is 225 feet, find the length of each side
X feet = How many Feet?
5x feet = how many feet?
(6x - 3) feet = for many feet?
Answers
Answer:
I have solved it and attached in the explanation.
Step-by-step explanation:
TRUE OR FALSE??
3 Parallel lines A and B ore cut
by transversal X as shown
below.
A.The value of x can be found using
12x – 18 = 8x + 10.
B. Each of the marked ongles measures 56.
C. The marked ongles are classified as vertical
angles.
REWRITE THE FALSE STATEMENT TO MAKE IT TRUE
pls help this hw is due today!!
Answers
Answer:
Step-by-step explanation:
A. True. Vertical angles have equal measure.
B. False. 12x-18=8x+10 -> x=7 -> the angles measure 66 degrees.
C. True. They're formed by a pair of intersecting lines.
1. What is the rate of change(slope) of the following linear equation x-3y = 12?
Answers
Answer:
m= 1/3
Step-by-step explanation:
The box above is 15 centimeters long,
4 centimeters wide, and 3 centimeters tall. What is the length of the diagonal s of the bottom side?
O:44 cm
O:14.5 cm
O :15.5 cm
O :19 cm
Answers
Answer:
It should be b(14.5), or c
Step-by-step explanation:if you think about it its like the same length for the top of the box
Awnser if this is a function or not yes or no please.
Answers
Answer: NO
Step-by-step explanation:
This is not a function, since there are multiple outputs for ONE input.
Answer:
no
Step-by-step explanation:
to be a function, the x's can only have one partner. Here, 7 has two partners (7 goes to 20 and also to 18) and the 11 has two partners also. This relation is not a function.
1,368 rounded to the nearest hundred
Answers
Dmitri wants to cover the top and sides of this box with glass tiles that are 1 cm square. How many tiles will he need? Dmitri will need [Blank] glass tiles. The dimentions are...26 , 15, 8.
Answers
The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.
What is the Surface Area of a Box?The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.
What is the Surface Area of a Box?SA = 2(lw + lh + hw), where:
l = lengthw = widthh = height of the boxThe image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:
The surface area to be covered = surface area of the box - area of the bottom rectangular face
The surface area to be covered = 2(lw + lh + hw) - (l)(w)
l = 26
w = 15
h = 8
Substitute
The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =
The surface area to be covered = 1436 - 390 = 1,046 cm
Area of one tile = 1 cm square
Number of tiles needed = 1,046/1
Number of tiles needed = 1,046 tiles.
Learn more about Surface Area of a Box on:
https://brainly.com/question/26161002
#SPJ1
Which of the following shows a 90° counterclockwise rotation of the blue figure
Answers
The volume of a cylinder is 1,200 yd^3 if it’s height is multiplied by 1/4, what will be the new volume of the cylinder?
Answers
Therefore , the solution of the given problem of volume comes out to be
you would then possess 1/9 of the volume.
What is volume used for?The term "volume" refers to how much general space an object occupies. Unlike mass, volume changes depending on the surroundings. The mass of a substance in a given volume is referred to as its "density." It describes the relationship between mass and volume.
Here,
A cylinder has a volume of V = r2h.
As a result, V = r2[(1/3)]h is obtained by multiplying h by 1/3.
The (1/3) can be moved to the front to obtain V = [(1/3)]r2h because you are free to multiplied in any ratio you choose.
Thus, you would receive one-third of the initial mass.
What would occur if you increased the radius by 1/3 in contrast to this?
Next, you would have
=> V = π[(1/3)r]2h
=> V = π(1/9)r2h
=> V = (1/9)πr2h
You would then possess 1/9 of the volume.
Therefore , the solution of the given problem of volume comes out to be
you would then possess 1/9 of the volume.
To know more about volume , visit
brainly.com/question/1578538
#SPJ1
Find the area of this triangle. Round to the nearest tenth. PLEASE HELP
Answers
Answer:
74.8 m²
Step-by-step explanation:
\(\boxed{\begin{minipage}{7.6 cm}\underline{Area of a triangle} \\\\$A=\dfrac{1}{2}ab \sin C$\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides enclosing the angle. \\\end{minipage}}\)
From inspection of the given triangle:
C = 115°a = 11 mb = 15 mSubstitute the values into the formula and solve for area:
\(\implies A=\dfrac{1}{2} \cdot 11 \cdot 15 \cdot \sin 115^{\circ}\)
\(\implies A=\dfrac{165}{2} \sin 115^{\circ}\)
\(\implies A=74.77039243\)
\(\implies A=74.8\; \sf m^2\;(nearest\;tenth)\)
Therefore, the area of the triangle is 74.8 m² rounded to the nearest tenth.
What is the solution to the equation 4x + 2(x − 2) = 4x + x − 12? (1 point)
Question 13 options:
1)
−8
2)
−1
3)
1
4)
8
Answers
Answer:
It's -8
Step-by-step explanation:
DISTRIBUTE :
4x + 2( x - 2 ) = 4x + x - 12
4x + 2x - 4 = 4x + x - 12
COMBINE LIKE TERMS :
4x + 2x - 4 = 4x + x - 12
6x - 4 = 4x + x - 12
COMBINE LIKE TERMS :
6x - 4 = 4x + x - 12
6x - 4 = 5x - 12
ADD 4 TO BOTH SIDES :
6x - 4 = 5x - 12
6x - 4 + 4 = 5x - 12 + 4
ADD THE NUMBERS/ SIMPLIFY :
6x = 5x - 8
SUBTRACT 5x FROM BOTH SIDES :
6x = 5x - 8
6x - 5x = 5x - 8 - 5x
SIMPLIFY :
x = -8
20x - 2 = 8
What is X?
Answers
Answer:
1/2
Step-by-step explanation:
20 times 1/2 = 10
10-2 = 8