Answer:
[tex]\frac{r^2-10}{(r+4)(r+1)}[/tex]
Step-by-step explanation:
We want to evaluate:
[tex]\frac{r+2}{r+4}-\frac{3}{r+1}[/tex]
We collect the least common multiple of the denominators to get:
[tex]\frac{(r+2)(r+1)-3(r+4)}{(r+4)(r+1)}[/tex]
Expand the numerator:
[tex]\frac{r^2+3r+2-3r-12}{(r+4)(r+1)}[/tex]
[tex]\frac{r^2-3r+3r+2-12}{(r+4)(r+1)}[/tex]
[tex]\frac{r^2-10}{(r+4)(r+1)}[/tex]
Answer:
[tex]\frac{ r^2-10}{(r+4)(r+1)}[/tex]
Step-by-step explanation:
[tex]\frac{r+2}{r+4} - \frac{3}{r+1}[/tex]
To simplify the fractions we take common denominator
LCD is (r+4)(r+1)
we try to get same denominator on both fraction
multiply the first fraction by r+1 and second fraction by r+4
[tex]\frac{(r+2)(r+1)}{(r+4)(r+1)} - \frac{3(r+4)}{(r+1)(r+4)}[/tex]
(r+2)(r+1) becomes r^2 +3r+2
3(r+4) becomes 3r+12
[tex]\frac{ r^2 +3r+2}{(r+4)(r+1)} - \frac{3r+12)}{(r+1)(r+4)}[/tex]
[tex]\frac{ r^2 +3r+2-3r-12}{(r+4)(r+1)}[/tex]
combine like terms
[tex]\frac{ r^2-10}{(r+4)(r+1)}[/tex]
mean for 13, 6, 24, 18, 33, 5, 13, 48, 9, 11, 36, 28, 15, 6, 13
13+6+24+18+33+5+13+48+9+11+36+28+15+6+13(all divided by 15)
278÷15
=18.5333
The mean, or average, of the numbers 13, 6, 24, 18, 33, 5, 13, 48, 9, 11, 36, 28, 15, 6, 13 is calculated by adding up all the values and dividing the total by the number of values. The mean of these numbers is approximately 18.13.
Explanation:The subject of your question is Mathematics and it appears that you are asking about how to calculate the mean, or average, of a set of values which are 13, 6, 24, 18, 33, 5, 13, 48, 9, 11, 36, 28, 15, 6, 13. To do this, you should add up all the values and divide the total by the number of values.
Add up all the numbers: 13 + 6 + 24 + 18 + 33 + 5 + 13 + 48 + 9 + 11 + 36 + 28 + 15 + 6 + 13 = 272Count how many numbers there are in total, which is 15 in this case.Divide the total by the count: 272 ÷ 15 = approximately 18.13So the mean of these numbers is approximately 18.13.
Learn more about mean here:https://brainly.com/question/31101410
#SPJ3
Simplify the product (x-4)(x+3)
Answer:
Final answer is [tex]x^2-x-12[/tex].
Step-by-step explanation:
Given expression is [tex]\left(x-4\right)\left(x+3\right)[/tex].
Now we need to find the product of the given expression [tex]\left(x-4\right)\left(x+3\right)[/tex].
[tex]\left(x-4\right)\left(x+3\right)[/tex]
[tex]=x\left(x-4\right)+3\left(x-4\right)[/tex]
[tex]=x^2-4x+3x-12[/tex]
combine like terms
[tex]=x^2-1x-12[/tex]
[tex]=x^2-x-12[/tex]
Hence final answer is [tex]x^2-x-12[/tex].
ANSWER
[tex](x-4)(x+3) = {x}^{2} - x - 12[/tex]
EXPLANATION
The given product is (x-4)(x+3)
We expand using the distributive property to obtain:
[tex](x-4)(x+3) = x(x + 3) - 4(x + 3)[/tex]
Expand the parenthesis to obtain:
[tex](x-4)(x+3) = {x}^{2} + 3x- 4x - 12[/tex]
Combine the similar terms to get:
[tex](x-4)(x+3) = {x}^{2} - x - 12[/tex]
Five friends are splitting a 2-pound bag of candy. If they each get the same amount of candy how much does each friend get?
0.4 pounds per friend!!
help me solve this
pls include the work!!!
Answer: is C.
Step-by-step explanation: i took the test and i got 3 as the answer :P
What is 6.25 % of 14.99
Hello There! 6.25% of 14.99 is about $0.94, or 0.936875 to be exact.
To find a percentage of a number, switch the percentage into a decimal and multiply the original number by this decimal.
To convert percentages to decimals, divide them by 100.
6.25 ÷ 100 = 0.0625
Now, multiply 14.99 by 0.0625.
14.99 x 0.0625 = 0.936875.
This can be rounded to the nearest cent, or the hundredths place, and since the thousandths place is above five, round up to six. You now have a total of about $0.94.
I hope this helps & have a great day!
your answer is 0.936875
Consider the diagram below. Which of the following statements are correct? Select all that apply. (Diagram and answer options are both in the picture) thank you !
Answer:
Options 1,2,6,7 are correct statements.
Step-by-step explanation:
In the given figure lines m and n are cut by a transversal t.
Among all the statements the options that are correct are :
1)<1 and <5 are corresponding angles.(The angles in matching corners are called corresponding angles)
2)<3 and <6 are alternate interior angles .(The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles)
6)<4 and <6 are same side consecutive angles.(consecutive angles lie on the same side of the transversal)
7)<1 and <8 are alternate exterior angles.( These angles lie on the exterior side of the lines and on opposite side of the transversal)
Answer:
Step-by-step explanation:
If two sides of the triangle are 12 inches and 18 inches, what is the range of the possible lengths of the third side
A) 6
B) 12
C)7
D)15
Answer:
d is the closest to the real answer assuming the question is asking for an estimate
i would give 20 if you help me pls
C.) y = 4c is the answer
PLEASE HELP ME!
Which expression finds the length of side y of this right triangle?
the 4th one.
[tex]y = \sqrt{r {}^{2} } - x {}^{2} [/tex]
Could someone help me with 3 and 4 please.
Answer:
3) 8pigs and 2 ducks 4(legs)*8(pigs)=32(feet) and 2(legs)*2(ducks)=4(feet) 32(pigs feet)+4(ducks feet)=36(total) 2(ducks) + 8 (pigs)= 10 (total animals)
4) 4 could be a varaity of things one way is 195/5 and you get 0 busses and 39 cars. Or the more effective way is 45*4=180 and 5*3=15 and that is 4 busses and 3 cars
Step-by-step explanation:
which statement best describes the end behavior of the following function? f(x)=3x^5+x^3-x+11
Answer:
(d)
Step-by-step explanation:
(d) is correct. This being a 5th power of x, the graph starts in Quadrant III and continues growing into Quadrant I. This is true of any positive odd power of x.
The best statement describes The graph of the function starts low and ends high.
The Option (d) is correct.
The end behavior of a polynomial function is determined by its leading term, which is the term with the highest degree. The coefficients of the leading term also play a significant role.
For the function [tex]\( F(x) = 3x^5 + 4x^3 - x + 11 \)[/tex], the leading term is[tex]\( 3x^5 \)[/tex]. Since the coefficient of[tex]\( x^5 \)[/tex] is positive, as[tex]\( x \)[/tex] approaches positive infinity[tex](\( x \to \infty \))[/tex], the function [tex]\( F(x) \)[/tex] will go to positive infinity [tex](\( F(x) \to \infty \))[/tex]. Similarly, as[tex]\( x \)[/tex]approaches negative infinity [tex](\( x \to -\infty \)),[/tex] the function [tex]\( F(x) \)[/tex] will go to negative infinity [tex](\( F(x) \to -\infty \))[/tex] because the leading term, being an odd power with a positive coefficient, will dominate and the sign will be negative due to the odd power.
So, the end behavior of the function is:
- Starts low (as[tex]\( x \)[/tex] goes to negative infinity,[tex]\( F(x) \)[/tex] goes to negative infinity).
- Ends high (as[tex]\( x \)[/tex] goes to positive infinity, [tex]\( F(x) \)[/tex] goes to positive infinity).
This corresponds to option D: "The graph of the function starts low and ends high."
What is the approximate surface area of the sphere?
Question :-
What is the approximate surface area of the sphere that has a diameter of 15 yd?Answer :-
The appoximate surface area of the sphere is 707 yd².[tex] \rule{180pt}{3pt}[/tex]
Diagram :-
[tex]\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{7.5 \: yd}}\end{picture}[/tex]
Solution :-
As per the provided information in the given question, we have been given that the diameter of the sphere is 15 yd. Thus, the radius of the sphere is 7.5 yd. We have been asked to find or calculate the surface area of the sphere.
To calculate the surface area of the sphere, we will use the formula below :-
[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}[/tex]
Substitute the given values into the above formula and solve for surface area:
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(3.14)(7.5 \: yd)^2[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(3.14)(56.25 \: yd^2)[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(176.625 \:yd^2)[/tex]
[tex]\sf:\implies \bold{Surface \: Area_{(Sphere)} = 706.5 \: yd^2}[/tex]
Therefore :-
The approximate surface area of the sphere is 707 yd².[tex]\\[/tex]
Learn more about the surface area of the sphere at https://brainly.com/question/28988747
Have a great day! <33
Amanda says that a human fingernails has a thickness of about 4.2 x 10^-4 meter. Justin says that a human fingernails has a thickness of about 0.42 millimeters .
What is the width in meters written in standard notation?
Do Justin’s and Amanda’s measurements agree? Explain .
Explain why Justin’s estimate of the thickness of a human fingernail is made appropriate than Amanda’s estimate.
Answer:
See below
Step-by-step explanation:
1. Standard notation
4.2 × 10⁻⁴ m
A negative exponent indicates
A number between 0 and 1. That the decimal point is shifted that number of places to the left.4.2 × 10⁻⁴ tells you that the decimal number is 4.2, with the decimal point moved four places to the left.
The number becomes 0.000 42 .
2. Metres to millimetres
[tex]4.2 \times 10^{-4}\text{ m} \times \dfrac{10^{3}\text{ mm}}{\text{1 m}} = 4.2\times 10^{-1}\text{ mm = 0.42 mm}}[/tex]
3. Measurements agree?
Yes, because both measurements are the same as 0.42 m.
4. More appropriate measurement
Most measurements should be expressed as a number between 0.1 and 1000, because most people aren’t particularly good at visualizing larger or smaller numbers.
Justin's measurement of 0.42 mm is more appropriate than Amanda's measurement of 4.2 × 10⁻⁴ m.
The equation ey = 2x is equivalent to y = ln 2y = In x y = ln 2x.
Answer:
[tex]y=ln(2x)[/tex]
Step-by-step explanation:
we have
[tex]e^{y}=2x[/tex]
Applying ln both sides
[tex]ln(e^{y})=ln(2x)[/tex]
[tex]y*ln(e)=ln(2x)[/tex]
Remember that
[tex]ln(e)=1[/tex]
substitute
[tex]y=ln(2x)[/tex]
Answer:
Y=ln 2x
Step-by-step explanation:I just did it on edg 2020
Drag the titles to the correct boxes to complete the pairs. Match each equation with its solution
What do you want us to help with? Is there a picture?
1. An expression is a mathematical statement using numbers, operations, and variables.
2. The________measures the steepness of a line.
Answer:
slope
Step-by-step explanation:
Answer:
The slope / gradient measures the steepness of a line.
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
Help will mark you the brainiest!
Answer:
-The percentage is about 66%
-Decreased
Step-by-step explanation:
- Because it's decreasing to 60 point to get to 34 miles.
- 94 minus 34 it decreased
PLZ MARK BRANILIST I'M IN THE NEED OF IT......
66% decreasing good luck
What is 978 cm3 expressed in L? 0.978 L 9.78 L 97.8 L 978,000 L
Answer:
0.978
Step-by-step explanation:
You move the decimal from the eight three times to the left because it is cm3
Answer:
it is 0.978
Step-by-step explanation:
Drag a statement or reason to each box to complete the proof.
Answer:
The answers of the proof are the following:
2. Division Property of Equality
3. x+ 1 = -4
4. Subraction Property of Equality
5. x = -5
Solve the system of equations 8x+13y=2 y=x-2
Answer:
x = 1.33333333
y = -0.66666667
Step-by-step explanation:
The answers have to be those numbers EXACTLY.
8x + 13y = 2
8(1.33333333) + 13(-0.66666667) = 2
10.66666667 - 8.66666667 = 2
2 = 2
y = x - 2
-0.66666667 = 1.33333333 - 2
-0.66666667 = -0.66666667
Answer:
x = 1.34
y = -0.67
Step-by-step explanation:
-3x + 4y= 24; 6x+2y= -18
Answer:
x = -4; y = 3
Step-by-step explanation:
-3x + 4y = 24
6x + 2y = -18
Rewrite the first equation as it is. Divide both sides of the second equation by 2 and write it below the first equation. Then add the equations.
-3x + 4y = 24
+ 3x + y = -9
----------------------------
5y = 15
Divide both sides by 5.
y = 3
Now plug in 3 into y in the first original equation and solve for x.
-3x + 4y = 24
-3x + 4(3) = 24
-3x + 12 = 24
-3x = 12
x = 12/(-3)
x = -4
Answer: x = -4; y = 3
Anniston has a sink that is shaped like a half-sphere. plz help gets brainy
Answer:
Part A) [tex]167\ cups[/tex]
Part B) [tex]10\ cups[/tex]
Step-by-step explanation:
Part A)
we know that
The volume of the sink is
[tex]V=\frac{2,000}{3}\pi\ in^{3}[/tex]
step 1
Find the volume of the cylindrical cup
The volume is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=2/2=1\ in[/tex] ----> the radius is half the diameter
[tex]h=4\ in[/tex]
substitute the values
[tex]V=\pi (1)^{2} (4)[/tex]
[tex]V=4\pi\ in^{3}[/tex]
step 2
To find the number of cups of water, divide the total volume of the sink by the volume of the cylindrical cup
[tex](\frac{2,000}{3}\pi)/(4\pi)=\frac{2,000}{12}=166.67\ cups[/tex]
Round to the nearest whole number
[tex]167\ cups[/tex]
Part B)
we know that
The volume of the sink is
[tex]V=\frac{2,000}{3}\pi\ in^{3}[/tex]
step 1
Find the volume of the cylindrical cup
The volume is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=6/2=3\ in[/tex] ----> the radius is half the diameter
[tex]h=8\ in[/tex]
substitute the values
[tex]V=\pi (3)^{2} (8)[/tex]
[tex]V=72\pi\ in^{3}[/tex]
step 2
To find the number of cups of water, divide the total volume of the sink by the volume of the cylindrical cup
[tex](\frac{2,000}{3}\pi)/(72\pi)=\frac{2,000}{216}=9.26\ cups[/tex]
Round to the nearest whole number (Round up)
[tex]10\ cups[/tex]
The graph shows the number of employed workers in the
United States in nonfarm jobs from 2008 to 2013.
The best conclusion that can be drawn from the graph is that
the number of nonfarm jobs
remained consistent over time.
started going down in 2008.
went up every year since 2008
started going down in 2010.
Answer:
the number of non-farm jobs started going down in 2008
Step-by-step explanation:
The question presented requires the analysis and interpretation of graphical output of data.
From the graph it is true to say that the number of non-farm jobs did not remain consistent over time since the graph is moving down then up implying decrease followed by increase.
It is also true to say that the number of non-farm jobs started going up in 2010 as indicated by the upward trend of the graph.
From 2008 to around 2010 the graph is moving downwards suggesting that the number of non-farm jobs was declining.
Answer:
D
Step-by-step explanation:
given: f(x) = x + 2 and g(x) = 3x + 5
f (x)/g (x) =
For this case we have two functions of the form y = f (x). We must find the quotient of the following functions:
[tex]f (x) = x + 2\\g (x) = 3x + 5[/tex]
So, we have by definition:
[tex]\frac {f (x)} {g (x)} = \frac {x + 2} {3x + 5}[/tex]
Answer:
[tex]\frac {f (x)} {g (x)} = \frac {x + 2} {3x + 5}[/tex]
with 3x + 5 different from zero, so that the function is defined
Answer:
[tex]\frac{f(x)}{g(x)}=\frac{x+2}{3x+5}[/tex]
where [tex]x\ne -\frac{5}{3}[/tex]
Step-by-step explanation:
The given functions are:
f(x) = x + 2 and g(x) = 3x + 5
[tex]\frac{f(x)}{g(x)}=\frac{x+2}{3x+5}[/tex]
Since this is a rational function, the function will not be defined where denominator equals zero.
We need to restrict the function or define the domain.
This is a rational function defined for [tex]x\ne -\frac{5}{3}[/tex]
How u do this bro?!,?,!,!
Answer:
c=3
Step-by-step explanation:
We have 2 points, we can find the slope using
m = (y2-y1)/(x2-x1)
Substituting into this equation
-1/4 = (4-5)/(7-c)
-1/4 = -1/(7-c)
Multiply both sides by -1
1/4 = 1/(7-c)
The denominators have to be the same
4 = 7-c
Subtract 7 from each side
4-7 = 7-7-c
-3 = -c
Multiply by -1
3 =c
what is f(5) for the function -2x^2+2x-3
____________________________________________________
Answer:
Your answer would be -43
____________________________________________________
Step-by-step explanation:
To solve this problem, we would need to plug in the number "5" in x.
Therefore, your equation should look like this:
[tex]-2(5)^2+2(5)-3[/tex]
First, you would need to solve the exponent, making it equivalent to 5 × 5, then you can solve with ease.
[tex]-2(5)^2+2(5)-3\\\\-2(25)+2(5)-3\\\\-50+10-3\\\\=-43[/tex]
All we did when we solved this was plug in and solve, that's really the only thing you need to do in questions like this.
When you're done solving, you should get the answer -43.
-43 would be your FINAL answer.
____________________________________________________
A prepaid cell phone charges a preset number of minutes to use text messaging. The graph represents y, the number of minutes used for x, the number of text messages sent and received. Is there a direct variation? Which equation represents the relationship?
Answer:
Yes,y=2x
Step-by-step explanation:
Answer: option a: Yes, y=2x
Step-by-step explanation:
i did it in edu
you invested your allowance of $270 which gets 15% compounded annually for 3 years. How much will you have in 3 years
____________________________________________________
Answer:
Your answer would be $410.64
____________________________________________________
Step-by-step explanation:
In order to find the amount of money you would have in 3 years, you would have to multiply the principal each time by 15% 3 times.
We would start with our starting allowance, and multiply that by 1.15, and so on:
270 × 1.15 = 310.50
310 × 1.15 = 357.075
357.073 × 1.15 = 410.636
Since we have three numbers after the decimal, we would want to round up to the nearest hundredth because that's how the value of money works. Cents only go up to the hundredths place.
We would round the 6 to the three, in which would make the three turn into 4. When you round, the numbers 1-4 would keep the number before it the same, 5-9 would make the number before it go up by 1.
410.636 would turn into 410.64.
You would have $410.64 dollars in three years.
____________________________________________________
With a principal of $270 and an annual compound interest rate of 15%, your investment will grow to approximately $410.64 in 3 years.
To determine how much your investment of $270 will grow in 3 years with an annual compound interest rate of 15%, you can use the compound interest formula:
A = P(1 + r/n)ⁿᵗ
Where:
A = the future value of the investment/loan, including interestP = the principal investment amount ($270)r = the annual interest rate (decimal) (0.15)n = the number of times that interest is compounded per year (1, since interest is compounded annually)t = the number of years the money is invested or borrowed for (3)Now plug in the values:
A = 270(1 + 0.15/1)¹*³Simplify inside the parenthesis:
A = 270(1 + 0.15)³Then:
A = 270(1.15)³Calculate the exponent:
A = 270 * 1.520875Finally, multiply:
A ≈ 410.64After 3 years, your investment will grow to approximately $410.64.
This demonstrates the power of compound interest, which is an important concept to understand when investing.
11) Given that the points (-1, 6), (3, 6), (3, 1), and (-1, 1) are vertices of a rectangle, how much shorter is the width than the length?
A) -5 units
B) -4 units
C) -3 units
D) -2 units
E) -1 unit
-1 unit is the correct answer.
By calculating the distances between the horizontal and vertical points of the rectangle, we find that the width is 1 unit shorter than the length.
Explanation:To determine how much shorter the width is than the length of the rectangle formed by the points (-1, 6), (3, 6), (3, 1), and (-1, 1), we can calculate the distances between the points.
The length can be measured either between the first and second point or the third and fourth, as they have the same y-value but different x-value, which is a horizontal distance on the graph.
The width can be measured between the first and fourth point or the second and third point since they share the same x-value but differ in y-values, constituting a vertical measurement.
Length is distance between (-1, 6) and (3, 6) or (3, 1) and (-1, 1) which is |3 - (-1)| = 4 units. Width is the distance between (-1, 6) and (-1, 1) or (3, 6) and (3, 1) which is |6 - 1| = 5 units.
The width is longer than the length, so to find out how much shorter the width is compared to the length, we subtract the two: 4 - 5 = -1 unit.
The data sets represent the five starting players of four basketball teams. Order the teams from least to greatest based on the mean height of the teams.
69,68,72,69,76
64,74,73,69,73
68,74,69,64,77
72,67,75,60,77
Answer:
72,67,75,60,77 (mean 70.2)
68,74,69,64,77 (mean 70.4)
64,74,73,69,73 (mean 70.6)
69,68,72,69,76 (mean 70.8)
Step-by-step explanation: