the number 6 is plotted on the number line below. Answer the following questions.
Answers
Starting point = 6
a.
To obtain a point 2 units to the right add 2.
6 + 2
b.
To obtain a point 2 units to the left, subtract 2.
6 + (-2)
6-2
Related Questions
Biologists have discovered that the shoulder height h (in centimeters) of a male African elephant can be modeled by where t is the age of the elephant in years. Estimate the height of an elephant
Answers
GIVEN:
We are given a function that models the shoulder height of an African Elephant as shown below;
[tex]h(t)=62.5\sqrt[3]{t}+75.8[/tex]T is the age of the Elephant in years.
Required:
To estimate the height of an Elephant that is 10 years old.
Step-by-step solution;
To solve this problem, we have the age of the Elephant as t in the function. Where the age is now given as 10 years, we will simply substitute for t equals 10 into the function.
We now have;
[tex]\begin{gathered} h(t)=62.6\sqrt[3]{t}+75.8 \\ \\ Where\text{ }t=10 \\ \\ h(10)=62.5\sqrt[3]{10}+75.8 \\ \\ h(10)=(62.5\times2.15443469003)+75.8 \\ \\ h(10)=134.652168127+75.8 \\ \\ h(10)=210.452168127 \end{gathered}[/tex]We can now approximate this to the nearest whole number and we'll have;
[tex]h(10)=210[/tex]Therefore,
ANSWER:
For a 10 year old Elephant, the height is 210 cm.
The last option is the correct answer.
2) A number in the set {50, 51, 52, 53, ..., 999} is randomly selected. What is the probability that thenumber selected is a two-digit number? Express your answer as a common fraction.
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To answer this questions we have to count how many numbers are in the set and how many of them are two digits numbers.
In the set given there are 950 numbers, of those numbers there are 49 two digits numbers, then the probability is:
[tex]P=\frac{49}{950}[/tex]When preparing a fresh one, my mother used 3 L of Water, .0.5 L of fruit pulp, 0.5 L of orange juice and 0.5 L of Syrup, so how many liters of soda did she prepare?
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As it is a soft drink, for this you can add the amounts given that the mother used in the preparation, that is,
[tex]3+0.5+0.5+0.5=4.5[/tex]Therefore, the mother prepared 4.5 liters of soda.
Tim earns $120 plus $30 for each lawn he mows. Write an inequality to represent how many lawns he needs to mow to make more than $310.how much he will make if he mows 9 lawns?
Answers
Let's use the variable x to represent the number of lawn Tim mows.
If he earns $120 plus $30 for each lawn, we can write the following equation for his earnings:
[tex]\text{Earning}=120+30x[/tex]Then, we want an earning greater than $310, so we have the following inequality:
[tex]\begin{gathered} \text{Earning}>310 \\ 120+30x>310 \end{gathered}[/tex]Now, to find the earning for 9 lawns, let's use x = 9 and calculate the total earning:
[tex]\begin{gathered} \text{Earning}=120+30\cdot9 \\ \text{Earning}=120+270 \\ \text{Earning}=390 \end{gathered}[/tex]Therefore his earning after mowing 9 lawns is $390.
x + 9y = 3 x - 4y = -10
Answers
Given data:
The first equation is x + 9y = 3.
The second equation is x - 4y = -10.
Subtract second equation from the first equation.
[tex]\begin{gathered} (x+9y)-(x-4y)=3-(-10) \\ 9y+4y=3+10 \\ 13y=13 \\ y=1 \end{gathered}[/tex]Substitute 1 for y in the first equation.
[tex]\begin{gathered} x+9(1)=3 \\ x=-6 \end{gathered}[/tex]Thus, the value of x is -6 and the value of y is 1.
Ahmad buys candy that costs $8 per pound. He will spend at least $56 on candy. What are the possible numbers of pounds he will buy?Use p for the number of pounds Ahmad will buy.Write your answer as an inequality solved for p.
Answers
Solution
Step 1
Cost of candy per pound = $8
Step 2
[tex]\begin{gathered} 8p\text{ }\ge\text{ 56} \\ \\ p\text{ }\ge\text{ }\frac{56}{8} \\ \\ p\text{ }\ge\text{ 7} \end{gathered}[/tex]Final answer
what is the slope of this question because i don't really get slope
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
Case A:
Line A :
Two points : ( -3, 4) and (-1,0)
[tex]\text{slope,m = }\frac{y_2-y_1}{x_2-x_1}=\text{ }\frac{0-4}{-1-(-3)\text{ }}\text{ =}\frac{-4}{-1+3}=\frac{-4}{2}=-2\text{ (COR}\R ECT)[/tex]Case B:
Line B:
Two points: ( -1, 4 ) and ( 1, 0 )
[tex]\text{slope, m = }\frac{y_2-y_1}{x_2-x_1}=\text{ }\frac{0-4}{1\text{ - (-1)}}=\frac{-4}{1+1}=\frac{-4}{2}=\text{ -2 (COR}\R ECT)[/tex]
Case C:
Line C:
Two points: ( 1, 4 ) and ( -1, 0 )
[tex]\text{slope, m = }\frac{y_2-y_1}{x_2-x_1}=\text{ }\frac{0-4}{-1-1}=\frac{-4}{-2}=\text{ 2 ( NOT COR}\R ECT)[/tex]Case D:
Line D:
Two points : ( 3,4 ) and ( 1,0)
[tex]\text{slope, m =}\frac{y_2-y_1}{x_2-x_1}=\frac{0-4}{1-3}=\frac{-4}{-2}=2\text{ (NOT COR}\R ECT)[/tex]CONCLUSION:
We have seen clearly that:
Line A and Line B have a slope of -2
need help with this. Both these pictures are all one problem. Please help with a b and c
Answers
Given:
A function:
[tex]g(x)=\sqrt{x+5}[/tex]To find:
a. The domain of the function.
b. Graph of the function.
c. The range of the function.
Solution:
a.
The domain of a function is the set of all x values for which g(x) exists as a real number.
For the given function, x can only take values greater than -5 because if we take x value less than -5, the value in the root becomes negative and g(x) becomes an imaginary number.
Thus, the domain of the function is :
[tex][-5,\infty)[/tex]b.
The first graph has the required domain.
Thus, the first graph is correct.
c.
From the graph, it is clear that the curve of the function lies above the y-axis. So, the range of the function is :
[tex][0,\infty)[/tex]Find the perimeter of the polygon with the vertices 01 - 3, 2), R(1,2), (1, - 2), and 77 - 3. - 2).The perimeter isunits.
Answers
Approximately 30.47 units
To find the Perimeter of this polygon, we can find by calculating the distance between each point
Considering the points are:
1 (3,2) R (1,2) (7,7) and (-3,-2)
1) Let's calculate the distance between each of them, using the formula of the distance derived from the Pythagorean Theorem.
d1 = (3,2) and (1,2)
d_2 =(1,2) and (7,7)
d_3= (7,7) and (-3,-2)
d_4= (-3,-2) and (3,2)
[tex]\begin{gathered} d_{}=\sqrt{(x_{_2-}x_{1\text{ }})^2+(y_2-y_1)^2^{_{}}} \\ d_{_1=}\sqrt{(1-3)^2+(2-2)^2}=2 \\ d_2=\sqrt{(7-1)^2+(7-2)^2}=\sqrt{61} \\ d_3=\sqrt{(-3-7)^2+(-2-7)^2}=\sqrt{181} \\ d_4\text{ =}\sqrt{(3+3)^2+(2+2)^2}=2\sqrt{13} \end{gathered}[/tex]2) Since we have four points then let's consider them as our vertices, and add those line segments do calculate its Perimeter (2P)
[tex]2P\text{ = 2 +}\sqrt{61}+2\sqrt{13}+\sqrt{181}\text{ }\approx\text{ 30.47}[/tex]Notice that for those radicals are not perfect squares they are irrational so approximating these we have.
Derrick borrowed an 18-foot extension ladder to paint his house. If he sets thebase of the ladder 5 feet from the house, how far up along the side of the house willthe top of the ladder reach? (Round your answer to the nearest tenth.)
Answers
ANSWER
17.3 ft (rounded to the nearest tenth)
EXPLANATION
Given:
Desired Outcome:
The height the top of the ladder will reach.
Apply the Pythagorean Theorem
[tex]\begin{gathered} Hyp^2=Opp^2+Adj^2 \\ AC^2=AB^2+BC^2 \\ 18^2=x^2+5^2 \\ 324-25=x^2 \\ x^2=299 \\ x=\sqrt{299} \\ x=17.29ft \end{gathered}[/tex]Hence, the top of the ladder will reach 17.3 ft (rounded to the nearest tenth) up along the side of the house.
Calculate the pay for the following day of a weekly time card given a wage of $12/ (round your answer to the nearest hundredth)
Answers
A day of a weekly time card is given. It is required to find the pay for the day given a wage of $12/hr.
To do this, calculate the number of hours worked for the day and multiply by the wage per hour.
It is given that the person worked in the morning from 08:15 to 12:15.
The difference gives the number of hours worked in the morning:
[tex]12:15-8:15=4\text{ hours}[/tex]It is also given that the person worked in the afternoon from 13:00 to 17:30.
The difference gives the number of hours worked in the afternoon:
[tex]17:30-13:00=4\text{ hours }30\text{ mins.}=4.5\text{ hours}[/tex]Hence, the total number of hours worked for the day is:
[tex]4+4.5=8.5\text{ hours}[/tex]Multiply this by the wage earned per hour to get the pay for the day:
[tex]8.5\times12=102[/tex]Hence, the pay for the day is $102.
Pay=$
Name two angles that form a linear pair OA 2COD and 2DOE OB 2COD and cCOB O O D LBOE and cBOD C BOA and cBOC
Answers
The answer is option A
The angles that form a linear are The sum of the two angles = 180
solve if possible. if not, indicate what information is needed. sally raises pigs and chickens. it has 420 animals, with a total of 1240 legs. How many pigs does Sally raise?
Answers
Sally has 200 pigs
Explanations:Let the number of pigs be p
Let the number of chickens be c
Since there are a total of 420 animals:
p + c = 420..........................(1)
A pig has 4 legs
A chicken has two legs
The total number of legs = 1240
Therefore:
4p + 2c = 1240.............................(2)
Make p the subject of the formula in equation (1)
p = 420 - c............(3)
Substitute equation (3) into equation (2)
4(420 - c) + 2c = 1240
1680 - 4c + 2c = 1240
4c - 2c = 1680 - 1240
2c = 440
c = 440/2
c = 220
Substitute the value of c into equation (3)
p = 420 - c
p = 420 - 220
p = 200
Sally has 220 chickens and 200 pigs
What is the equivalent form to the equation y = (1 - 1)2? Fill in the blanks below (pay attention to the signs in the equation). 2. +
Answers
Answer:
x^2 - 2x + 1
Explanation:
Given the below equation;
[tex]y=(x-1)^2[/tex]The above can be rewritten as;
[tex]y=(x-1)(x-1)_{}[/tex]To expand the above, all we need to do is use all the terms in the 1st parentheses and multiply all the terms in the 2nd parentheses as shown below;
[tex]\begin{gathered} y=x^2-x-x+1 \\ y=x^2-2x+1 \end{gathered}[/tex]Find the area of the shaded region in the figure. Use the pi key for pi.The area of the shaded region in the figure is approximately: ft or ft^2(Type an integer or decimal rounded to the nearest tenth as needed.)
Answers
The area of the shaded region is equal to the area of the circle minus the area of the square, let's rember the formula to calculate the area of these figures:
[tex]\begin{gathered} A_{\bigcirc}=\frac{\pi d^{2^{}}}{4} \\ \\ A_{\square}=l^2 \end{gathered}[/tex]Remember that d is the diameter and l is the square length, then, let's apply these formulas:
[tex]\begin{gathered} A_T=A_{\bigcirc}-A_{\square} \\ \\ A_T=\frac{\pi d^2}{4}-l^2 \end{gathered}[/tex]The diameter is 3.1 ft and the length is 2.5 ft, then
[tex]\begin{gathered} A_T=\frac{\pi(3.1)^2}{4}-(2.5)^2 \\ \\ A_T=1.3\text{ ft}^2 \end{gathered}[/tex]Therefore, the area of the shaded region is 1.3 ft^2.
Bob got a raise and he's hourly wage increased from $10 to $18 what is the percent increase?
Answers
In order to find the percent increase, let's first find the absolute increase, by subtracting the new value and the old value:
[tex]18-10=8[/tex]Now we just need to divide the absolute increase by the old value, then we will find the percent increase:
[tex]\frac{8}{10}=0.8=80\text{\%}[/tex]So the percent increase is 80%.
Find the volume and the lateral area of concrete column in the form of a right prism whose base is a regular hexagon of side 50 cm and whose altitude is 10m.
Answers
Given that the concrete column is in the form of a right prism with a hexagonal base, the formula for the volume is given below:
[tex]\begin{gathered} \frac{3\sqrt[]{3}}{2}a^2h \\ \text{where a=50cm}=(\frac{50}{100})m=0.5m \\ h=10m \end{gathered}[/tex]The volume of the concrete column would be:
[tex]\begin{gathered} \frac{3\sqrt[]{3}}{2}\times0.5^2\times10m \\ =6.495m^3 \end{gathered}[/tex]To get the lateral area, the lateral area is given by:
[tex]\begin{gathered} \text{Lateral area=}6ah \\ \text{where a is the side and h is the height} \\ \text{Lateral area = }6\times0.5m\times10m \\ \text{Lateral area = }30m^2 \end{gathered}[/tex]Hence, the volume of the concrete column is 6.495 cubic metres and the lateral area is 30 square metres.
A circle is a set of points, all of which are the same distance away from a fixed point. What is the name of this fixed point?
Answers
EXPLANATION
The name of the fixed point is CENTER.
Darren went shopping and spent $19 on scarves. If he spent $.75 total, what percentage did he spend on scarves? Round your answer to the nearest percent.
Answers
The amonunt spent on scarves is $19.
The total amount spent is $75
To determine the percentage he spend on scarves .
amount spent/total amount×100
[tex]\frac{19}{75}\times100=25.34[/tex]The percentage he spent on scarves is 25.34 %.
The function g is given in three equivalent forms.Which form most quickly reveals the zeros (or "roots") of the functionChoose 1 answer:A) g(x) = 1/2(x – 8)^2 – 8B) g(x) = 1/2x^2 – 8x + 24C) g(x) = 1/2(x – 12)(x – 4)Write one of the zeros.x =
Answers
The answer to your question is letter C, because there the function is factored, and we can easily indentify the roots in this form.
The answer is C
Any question?
ok
x - 12 = 0 or x - 4 = 0
x = 12 x = 4
Given that R is between A and X on a segment, draw a picture and write an equationusing the Segment Addition Postulate. Then find AR and RX if AR = 5x - 15,RX = 3x + 1, and AX = 58.
Answers
The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC
if and only if the distances between the points meet the requirements of the equation AB + BC = AC.
The picture can look roughly like this:
We can see that "R" is in-between "A" and "X".
From the postulate, we can write:
AR + RX = AX
Now,
Given
AR = 5x - 15
RX = 3x + 1
AX = 58,
We put it into the equation and find x first. Shown below:
[tex]\begin{gathered} AR+RX=AX \\ (5x-15)+(3x+1)=58 \\ 5x+3x-15+1=58 \\ 8x-14=58 \\ 8x=58+14 \\ 8x=72 \\ x=\frac{72}{8} \\ x=9 \end{gathered}[/tex]Since, we got x, we can easily find AR and RX. Shown below:
AR = 5x - 15
AR = 5(9) - 15
AR = 45 - 15
AR = 30and
RX = 3x + 1
RX = 3(9) + 1
RX = 27 + 1
RX = 28find the area of the shaded regions in the figures below, whose measures of radius or diameters are given. take [tex]\pi 3.14[/tex]
Answers
a) The area is comprised of a semicircle and a rectangle so the combined area is given by:
[tex]\frac{\pi(10)^2}{2}+25\times20=657m^2[/tex]So the area is 657 square meters.
b) The area of required region is the difference between the area of large circle and small circle. The radius of large and small circles are 12 cm and 10 cm respectively.
So the area is given by:
[tex]\pi(12)^2-\pi(10)^2=144\pi-100\pi=44\pi=138.16cm^2[/tex]Hence the area is 138.16 square centimeters.
What does slope mean in context?Answer Choices: A. For every 1% increase in 4th grade pass rate, the predicted 8th grade pass rate will increase by 25.6%B. For every 1% increase in 8th grade pass rate, the predicted 4th grade pass rate will increase by 1.1%C. For every 1% increase in 4th grade pass rate, the predicted 8th grade pass rate will increase by 1.1%D. For every 1% increase in 8th grade pass rate, the predicted 4th grade pass rate will increase by 25.6%
Answers
Answer: The mathematical meaning of the slope in the following context is as described below:
(A):
[tex]\begin{gathered} S=\frac{\text{ 8th grade pass rate}}{\text{ 4th grade pass rate}} \\ \\ S=\frac{25.6\%}{1\%} \\ \end{gathered}[/tex](B):
[tex]\begin{gathered} S=\frac{\text{ 4th grade pass rate}}{\text{ 8th grade pass rate}} \\ \\ S=\frac{1.1\%}{1\%} \end{gathered}[/tex](C):
[tex]\begin{gathered} S=\frac{\text{ 8th grade pass rate}}{\text{ 4th grade pass rate}} \\ \\ S=\frac{1.1\%}{1\%} \end{gathered}[/tex](D): Finally the answer for the last part is:
[tex]\begin{gathered} S=\frac{\text{ 4th grade pass rate}}{\text{ 8th grade pass rate}} \\ \\ S=\frac{25.6\%}{1\%} \end{gathered}[/tex]How do the lower quartiles of the two sets of data compare?
Answers
Step 1
The first quartile is the value separating the lower quarter and the higher three-quarters of the data set.
The first quartile is sorted by taking the median of the lower of a sorted set.
Find the lower quartile of Milton
Arrange the data in ascending order
[tex]0,\: 54,\: 73,\: 85,\: 86,\: 89,\: 90,\: 91,\: 94,\: 95,\: 97[/tex]Take the lower half of the ascending set
[tex]0,54,73,85,86[/tex]Hence, the lower quartile of Milton is 73
Step 2
Find the lower quartile of Makenzie
Arrange the data in ascending order
[tex]84,\: 91,\: 92,\: 92,\: 93,\: 95,\: 97,\: 98,\: 98,\: 100,\: 100[/tex]Take the lower half of the ascending set
[tex]81,91,92,92,93[/tex]Hence the lower quartile of Makenzie = 92
The lower quartile of Milton is 73 and the lower quartile of Makenzie is 92. This means that the lower quartile of Makenzie is higher than the lower quartile of Milton and this is by (92-73)=19
Find the derivatives of the following using increment method.1. y= 4x - 12
Answers
Given:
y= 4x - 12
Required:
Find the derivatives of the following using increment method.
Explanation:
x=4y-12
just simply switchx and y is the inverse
Required answer:
x=4y-12
1) What number am I? » I am less than 10. I am not a multiple of 2. I am a composite number.
Answers
9
Explanations:Numbers less than 10 = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Numbers less than 10 that are not multiples of 2 = 0, 1, 3, 5, 7, 9
Note that composie numbers are numbers that can be divided by more than two numbers
Therefore:
A composite number that is less than 10 and not a multiple of 2 = 9
This is because 9 has 3 factors which are 1, 3, and 9
Quadrilateral ABCD is similar to quadrilateral EFGH. Find the measure of side FG.
Round your answer to the nearest tenth if necessary
Answers
Solution
For this case we can do the following proportion:
[tex]\frac{CB}{DA}=\frac{FG}{EH}[/tex]And solving for FG we got:
[tex]FG=EH\cdot\frac{CB}{DA}=47\cdot\frac{23}{11}=\frac{1081}{11}=98.3[/tex]Then the answer is 98.3
Which shapes have an area of 36 square units? Circle the letter for all that apply. A a square with sides that are 18 units long B a rectangle with a length of 9 units and a width of 4 units С a square with sides that are 6 units long D a rectangle with a length of 8 units and a width of 4 units
Answers
Given that the area(A) of the shapes is given as 36 square units.
Testing the correct options for confirmation
Option B
A rectangle with a length of 9units and width of 4units.
The formula for the area of a rectangle(A) is,
[tex]\begin{gathered} A=\text{length }\times width \\ A=9\times4=36unit^2 \end{gathered}[/tex]Therefore, the area of the rectangle is 36unit².
Option C
A square with sides that are 6 units long.
The formula for the area of a square is,
[tex]\begin{gathered} A=\text{length}\times length=l^2 \\ A=6\times6=36unit^2 \end{gathered}[/tex]Therefore, the area of the square is 36unit².
Hence, the correct options are Option B and C.
Given: f(x) = -3x³ + x² - 3, find f(1). -1 1 -5 5
Answers
Answer:
f(1) = - 5
Step-by-step explanation:
substitute x = 1 into f(x)
f(1) = - 3(1)³ + (1)² - 3 = - 3(1) + 1 - 3 = - 3 + 1 - 3 = - 5
all you need is in the photo please show your work step by step and fast
Answers
Answer:
Kim is younger than 5 years. Kim could 1, 2, 3 or 4 years old.
Explanation:
Let Kim's age be z.
From the question, Josh's age can be as represented below;
[tex]Josh^{\prime}s\text{ age =}4z+6[/tex]We're also told that the sum of their ages is less than 31, we can express this as per below;
[tex]z+(4z+6)<31[/tex]So let's go ahead and find Kim's age, z;
[tex]\begin{gathered} 5z<31-6 \\ z<\frac{25}{5} \\ z<5 \end{gathered}[/tex]So Kim is younger than 5 years. Kim could 1, 2, 3 0r 4 years old.