1. the initial value of A is 50 and B is 25 so a is bigger so A>B
2. A hits the grond on 6.53 and B on 10.477 so A is less , so A
3. A grows to 2.5 and B to 5 so A
4. the maximum of a is 2.5 and B is 5 so A
5. the maximum height of A is 81.25 and B 150 so A>B
Write each fraction in terms of the LCD.x2x + 12x - 1x + 13x22x – 111X + 1X + 13Need Help?Watch ItAdditional Materials
The given fractions are,
[tex]\frac{x^2}{2x-1},\text{ }\frac{x+1}{x+13}[/tex]The LCD of fractions is the least common multiple of the denominators.
So, the LCD of the above fractions is,
[tex](2x-1)(x+13)[/tex]Multiplying the numerator and the denominator of the fraction by a common term does not change the fraction.
So, the first fraction can be expressed in terms of the LCD as,
[tex]\frac{x^2}{2x-1}=\frac{x^2(x+13)}{(2x-1)(x+13)}[/tex]The second fraction can be expressed in terms of the LCD as,
[tex]\frac{x+1_{}^{}}{x+13}=\frac{(x+1)(2x-1)}{(2x-1)(x+13)}[/tex]Answer this question
Okay, in this case the statement talks about the sum, according with this we need to find the sum of the number blue bikes (b) and 9 red bikes.
So, in this case the correct option is A. b+9 because it says sum
Using the hottest and coolest months data, find the equation for line of best fit for this data showing all steps by hand.
Let
x -----> average temperature
y ----> Electricity Bill
we take the points
(99,150) and (69,80)
step 1
Find out the slope
m=(80-150)/(69-99)
m=-70/-30
m=7/3
step 2
Find out the equation of the line in slope-intercept form
y=mx+b
we have
m=7/3
point (69,80)
substitute and solve for b
80=(7/3)(69)+b
b=80-161
b=-81
the equation is
y=(7/3)x-81
using a graphing tool
Remember that the value of y cannot be a negative number
Estimate the product by adjusting the larger factor to the compatible number 25 and then multiply. 27 x 8 = Think about counting by 25s.
You have the following product:
27 x 8
To estimate the product by rounding 27 to 25, you consider that 25 x 8 is the same as adding 25 eight times.
Then, you have:
25 x 8 = 25 + 25 + 25 + 25 + 25 +25 + 25 +25
25 x 8 = 50 + 50 + 50 + 50 each pair of 25's add up 50
25 x 8 = 100 + 100 each pair of 50's add up 100
25 x 8 = 200
Hence, an estimation of the given product is 200, by considering 27 rounded to 25.
Given quadrilateral MNPQ which of the following set of conditons would not be enough to know that MNPQ is a parrelogram?
For a shape to be considered a parallelogram it has to meet the following conditions:
0. The opposite sides must be equal
,1. The opposite sides are equal
,2. Adjacent sides are supplementary
,3. The diagonals bisect each other
,4. The opposite sides are parallel
For the quadrilateral to be considered a parallelogram then, the conditions that should be met are:
MN=QP and MQ=NP
MN || QP and MQ || NP
The diagonals MP and NQ bisect each other.
∠M=∠P and ∠N=∠Q
From the given options, the second one and the third one are not enough to determine MNPQ as a parallelogram
slove equations with variables on both sides-4k - 10 = -5k
We will investigate how to solve an equation consisting of one variable
We have the following equation at hand:
[tex]-4k\text{ -10 = -5k}[/tex]The basic rule applied in solving equation like above is mathematical operations. We apply basic operations like:
[tex]\text{adding, subtracting, multiplying, division}[/tex]on both sides of the equation accompained by a variable or a number in an attempt to isolate the variable ( k ).
To isolate the variable ( k ) we need all the terms involving the variable ( k ) on one side of the equation.
We will add ( 4k ) on both sides of the equation as follows:
[tex]\begin{gathered} -4k\text{ -10 + 4k= -5k + 4k} \\ (\text{ 4k - 4k ) - 10 = -k} \\ -10\text{ = -k} \end{gathered}[/tex]Now to remove the negative sign accompained by ( k ) on the right hand side of the equation. We wil multiply both sides with ( -1 ) as follows:
[tex]\begin{gathered} -1\cdot(-10)\text{ = -1}\cdot(-k) \\ 10\text{ = k} \end{gathered}[/tex]Hence, the value of ( k ) is:
[tex]10[/tex]
Find the cardinal number of the setWhere N denotes the set of all natural numbers
And x is divisible by 6 . The natural number of x will be
[tex]x=\mleft\lbrace36,42,48,54\mright\rbrace[/tex]The entire graph of the function h is shown in the figure below.Write the domain and range of h using interval notion.(a) domain=(b) range=
The graph of the function is defined for x greater than or equal to -2 and less than 3. So domain of the function is,
[tex]\lbrack-2,3)[/tex]The value of the function lies between -2 and 3. The function value is greater than or equal to -2 and less than 3. So range of function is,
[tex](-2,3\rbrack[/tex]The table shows the weights of bananas at a grocery store. Complete the table so that there is a proportional relationship between the number of bananas and their weight.Number Of Bananas. Weight In Kilograms. 2 ? 0.72 15 ?
Let u make the first box x and the second box y.
If there is a proportional relationship between the number of bananas and their weights, it means that:
[tex]\frac{2}{x}=\frac{6}{0.72}=\frac{15}{y}[/tex]We can take the first pair and solve for x as follows:
[tex]\begin{gathered} \frac{2}{x}=\frac{6}{0.72} \\ 6x=2\times0.72=1.44 \\ x=\frac{1.44}{6} \\ x=0.24 \end{gathered}[/tex]We can solve for y in the same manner:
[tex]\begin{gathered} \frac{6}{0.72}=\frac{15}{y} \\ 6y=15\times0.72=10.8 \\ y=\frac{10.8}{6} \\ y=1.8 \end{gathered}[/tex]Therefore, the boxes are filled as shown below:
Which is the graph of the solution set of -2x + 5y > 15?10 1310 138896421OT810x2468 10622-4Ox681010 138642X246810
To graph the solution set, first, we know that the border of the shaded area will be delimited by the dashed line:
[tex]-2x+5y=15.[/tex]Now, to know if the shaded area will be on top or below the line, we evaluate the point (0,0):
[tex]-2(0)+5(0)=0<15,[/tex]therefore, the origin is not a point of the solution set.
Answer:Pleaee help me draw this. Construct a tangent to the circle from point R.
solution
For this case the tangent line to the circle and the point should be:
The reason is because the tangent line and the point needs to touch the circle just one time
A rectangular prism is shown below.A formula for the volume of a rectangular prism V = Bh. The volume, V, of this prism is 600 cm³. Which expression can be used to find x, the width of the prism in centimeters? A: 600/15B: 600/8C: 600/(8)(15)D: (8)(8)(15)(15)/600
Volume of a rectangular prism = base length x width x heigth
Where;
Volume = 600 cm3
base length = 15
width = x
height = 8
Replacing:
600 = (15) (x) (8)
Isolate x
600/ (15)(8) = x
x = 600/ (8)(15)
option C
The 7th grade took a field trip to the zoo. 50 students rode in cars and the rest of the students were split equally onto 4 buses. There are 142 total 7th graders. How many students were on each bus?
traveledGiven:
The total number of students is N = 142.
The number of students riding in a car is n(C) = 50.
The total number of buses is b = 4.
The objective is to find the number of students traveling on each bus.
Explanation:
Consider the number of students travelled in each bus as s.
Then, the total number of students traveling in 4 buses will be 4s.
The algebraic expression for the total number of students N can be represented as,
[tex]N=n(C)+b(s)\text{ . . . . .(1)}[/tex]On plugging the given values in equation (1),
[tex]142=50+4s[/tex]On further solving the above equation,
[tex]\begin{gathered} 142-50=4s \\ 4s=92 \\ s=\frac{92}{4} \\ s=23 \end{gathered}[/tex]Hence, the number of students traveling on each bus is 23.
What is the solution to the equation below? Round your answer to two decimal places.ln x = 0.2A.x = 1.58B.x = -0.70C.x = -1.61D.x = 1.22
Given the equation:
[tex]\ln \left(x\right)=0.2[/tex]Apply the properties of logarithms:
[tex]e^{ln(x)}=e^{0.2}[/tex]Simplify:
[tex]x=e^{0.2}=1.22[/tex]Answer: D. x = 1.22
the odds against (E) are 23:77 Find the probability of (not E) :
We can rewrite the question as the probability of getting the event E is 23:77. Find the probability of getting the event not E.
The number 23:77 is a ratio and is it equivalent to:
[tex]\frac{23}{77}[/tex]To get the probability of the event not-E, we can proceed as follows:
[tex]1-\frac{23}{77}=\frac{77}{77}-\frac{23}{77}=\frac{53}{77}\approx0.7013[/tex]So the probability for the event not-E is about 53/77 or 0.7013 (or a little more than 70%).
Please help me!A bag holds 5 pounds of pet food. If Paul uses the 5 pounds of food to fill 6 plastic containers equally, how much pet food will each container hold?0.830.80.8030.83
We must divide the 5 pound bag in 6 different containers, therefore:
[tex]\frac{5}{6}=0.83[/tex]Each container will hold 0.83 pet food
Given A = {(1, 3X-1, 5}(6, 4)), B = {(2, 0X4, EX-4, 5x0, 0)) and C = {(1, 1x0, 2x0, 3)(0, 4X-3, 5)), answer the following multiple
choice question:
From the list of sets A, B, and C above, choose the set of relations that correctly represents a function.
O Set A only
O Sets A and C only
O Sets A and B only
The functions is Set A and Set B.
What is meant by function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
A relation in a set is said to be a function, if every first element of an ordered pair in a set is related with a unique element of a second element.
No, two distinct second elements of an ordered pair, has the same first element.
For, example, {(1,2), (1,3), (4,5)}, is not a function, but it is a relation.
In Ordered pair, (x, y)
x=First Element
y= Second Element
→In Set A
First Element Second Element
1 3
-1 5
6 4
Every First element of set A has a unique second element. So, it is a function.
→In Set B
First Element Second Element
2 0
4 6
-4 5
0 0
Every First element of set B has unique second element and no two distinct Second element of set B, has same first element. So, it is a function.
→In Set C
First Element Second Element
1 1
0 2
0 3
-3 5
As, two same first elements of set C has distinct second element. So, it is not a function.
Therefore, Set A and Set B, are functions .
To learn more about function refer to:
https://brainly.com/question/25638609
#SPJ1
find the value of f (4)
we know that
f(4) is the value of the function f(x) when the value of x is equal to 4
so
For x=4
Look at the graph
The value of the function f(x) is equal to 3
therefore
f(4)=3prove that 1+3+5+......2n-1=n²
As given by the question
There are given that the series
[tex]1+3+5+\cdots+(2n-1)=n^2[/tex]Now,
For step 1:
Put n=1
Then LHS =1
And
[tex]\begin{gathered} R\mathrm{}H\mathrm{}S=(n)^2 \\ =(1)^2 \\ =1 \end{gathered}[/tex]So,
[tex]\therefore L.H.S=R.H.S[/tex]P(n) is true for n=1.
Now,
Step 2:
Assume that P(n) istrue for n=k
Then,
[tex]1+3+5+\cdots+(2n-1)=k^2[/tex]Adding 2k+1 on both sides
So, we get:
[tex]1+3+5\ldots+(2k-1)+(2k+1)=k^2+(2k+1)=(k+1)^2[/tex]P(n) is true for n=k+1
By the principle of mathematical induction P(n) is true for all natural numbers n.
Hence,
[tex]1+3+5+\cdots+(2n-1)=n^2[/tex]For all n.
Hence proved.
3. By elimination 2x - 3y =- 55x + 2y =16
By elimination, it means that we should apply algebraic operations so we find the value of one variable. So first, lets multiply the first equation by 5. We get
[tex]5\cdot(2x-3y)=5\cdot-5\text{ = 10x-15y = -25}[/tex]Now, lets multiply by 2 the second equation
[tex]2\cdot(5x+2y)\text{ = 16}\cdot2\text{ = 10x+4y=32}[/tex]With this two equations, lets subtract the second equation from the first equation
[tex]10x+4y-(10x-15y)\text{ = 32-(-25)}[/tex]We get
[tex]19y\text{ = 57}[/tex]If we divide y by 19 we get
[tex]y=\frac{57}{19}=3[/tex]Now, using this value in the second equation we get
[tex]5x+2\cdot3\text{ = 16 }=5x+6[/tex]If we subtract 6 on both sides, we get
[tex]16-6\text{ = 5x = 10}[/tex]Finally, we divide by 5 on both sides and we get
[tex]x=\frac{10}{5}=2[/tex]on a map, the scale is 5 cm = 2km what is the missing distance?town A distance to 5.6km is the actual distance
The distance on the map is 14 cm
Explanation:Parameters:
Map scale: 5 cm = 2 km
Given actual distance = 5.6km
Let x be the distance on map, then
x = 5.6 km
2x = 5 * 5.6
2x = 28
x = 28/2
= 14 cm
Simplify.4n + 12 + 7n4 n + 1923 n16 n +711 n+ 12
11 n+ 12
In this expression, to simplify means to reduce it to the simpler expression. Hence:
1) Grouping similar terms
4n + 12 + 7n =
2) Adding them up:
4n+7n+12=
11n +12
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 2 ≤ x ≤ 6.
To find the average rate of change over an interval we need to calculate how much the function has changed over that interval by subtracting the final value by the initial one and dividing by the lenght of the interval. With this in mind we have:
[tex]\begin{gathered} \text{rate}=\frac{19-13}{6-2} \\ \text{rate}=\frac{6}{4} \\ \text{rate}=1.5 \end{gathered}[/tex]The average rate of change for this interval is 1.5
the line contains the point (-3,5) and is perpendicular to the line y=3x-4
two lines are perpendicular when the multiplication of their slopes is equal to -1. The slope of y = 3x - 4 is 3. Then the slope of a perpendicular line is:
[tex]\begin{gathered} m\cdot3=-1 \\ m=-\frac{1}{3} \end{gathered}[/tex]Slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept. Replacing with point (-3, 5) and m = -1/3, we get:
5 = -1/3(-3) + b
5 = 1+ b
5 - 1 = b
4 = b
Then, the equation is:
y = -1/3x + 4
the relationship between the minutes a candle is burned and the size of the candle in millimeters is shown on the graph.
The function is a decreasin line so the more time goes the side will decrease so the correct answer is:
The candle started at 9mm and shrinks 5mm every 4 minutes
what is 12/8 × 18/16
First of all, simplify the given fractions
Question 1 of 14, Step 1 of 10/19CorrectDetermine if the following expression is a polynomial.4 – 8x + x²AnswerKeyboaO Yes O No
Solution
Given
[tex]4-8x+x^2[/tex]We want to determine if it's a Polynomial
A polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Hence 4 - 8x + x^2 is a Polynomial
Hello may you please check me work for number 5
Surface area of a rectangular prism:
[tex]SA=2(wl+hl+hw)[/tex]Substitute 1.2 for all of the variables in the formula:
[tex]SA=2[(1.2)(1.2)+(1.2)(1.2)+(1.2)(1.2)][/tex]Using a calculator, you should get an answer of:
[tex]SA=8.64\text{ }yd[/tex]The answer is that the surface area of this shape is 8.64 yards.
The current student population of Kansas City is 2700. If the population increases at a rate of 5.2% each year. What will the student population be in 4 years?Write an exponential growth model for the future population P(x) where x is in years:p(x)=What will the population be in 4 years? (Round to nearest student)
ANSWER
P(x) = 2700(1.052)^t
P(4) = 3307. (Rounded to nearest student)
EXPLANATION
Given:
1. The current student population to be 2700
2. The growth rate = 5.2% = 0.052
Desired Outcome
1. The exponential growth model
2. Population of the students in 4 years
The Exponential Growth Model
[tex]\begin{gathered} P(x)\text{ = 2700\lparen1 + 0.052\rparen}^t \\ P(x)\text{ = 2700\lparen1.052\rparen}^t \end{gathered}[/tex]Population in 4 years
[tex]\begin{gathered} P(4)\text{ = 2700\lparen1.052\rparen}^4 \\ P(4)\text{ = 2700}\times1.2248 \\ P(4)\text{ = 3306.96} \end{gathered}[/tex]Hence, the Exponential Growth Model P(x) = 2700(1.052)^t and the Population of the students in 4 years P(4) = 3307. (Rounded to nearest student)
Given the vectors u =-7j and w=-9i+4j, find 8u and u+w.Write your answers in the form ai+bj.
Recall that:
[tex]\begin{gathered} \text{For all a, b, c, d, e real numbers:} \\ (ai+bj)+(ci+dj)=(a+c)i+(b+d)j, \\ e(ai+bj)=(ea)i+(eb)j\text{.} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 8u=8(-7j)=8(0i-7j)=(8\cdot0)i+(8\cdot(-7))j=0i-56j=-56j\text{.} \\ u+w=(-7j)+(-9i+4j)=(0i-7j)+(-9i+4j)=(0-9)i+(-7+4)j \\ =-9i-3j\text{.} \end{gathered}[/tex]Answer:
[tex]\begin{gathered} 8u=-56j\text{.} \\ u+w=-9i-3j\text{.} \end{gathered}[/tex]