Answers
Check the picture below, let's use those two points on the line to get its slope.
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{0}}}\implies \cfrac{2}{2}\implies 1[/tex]
Related Questions
Nando is on a rehabilitation program following a car accident. For the first month, he needs to exercise at most five hours per week and must burn at least 2,000 calories per week. The exercise he is allowed to
do is brisk walking which burns about 350 calories per hour and biking at a moderate pace which burns
about 700 calories per hour. Which graph best represents the set of all points that satisfy the system
representing Nando's exercise options?
Answers
Answer:
See explanation
Step-by-step explanation:
Let x be the number of hours per week Nando is brisk walking and y be the number of hours per week Nando is biking at a moderate pace.
For the first month, he needs to exercise at most five hours per week, then
[tex]x+y\le 5[/tex]
Brisk walking burns about 350 calories per hour, then it burns 350x calories per x hours.
Biking at a moderate pace burns about 700 calories per hour, then it burns 700y calories per y hours.
Nando must burn at least 2,000 calories per week, so
[tex]350x+700y\ge 2,000[/tex]
You get the system of two inequalities:
[tex]\left\{\begin{array}{l}x+y\le 5\\ 350x+700y\ge 2,000\end{array}\right.[/tex]
The attached graph shows the solution set to this system of inequalities. In this diagram, red region represents the solution set to the first inequality, blue region represents the solution set to the second inequality and their intersection is the solution set to the system of two inequalities.
Which inequality has a solution set of {x ⎸x > 3 or x < –3}? Question 16 options: a) |2| < 6 b) |2| ≥ 6 c) |2| > 6 d) |2| ≤ 6
Answers
Answer:
Option C) |2x| > 6 is correct.
Step-by-step explanation:
Consider the provided solution set:
{x ⎸x > 3 or x < –3}
Now check which options are correct.
Option A) |2x| < 6
[tex]\mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex]
[tex]-6<2x<6[/tex]
[tex]-3<x<3[/tex]
Thus, the option is incorrect.
Option B) |2x| ≥ 6
[tex]\mathrm{If}\:|u|\:\ge \:a,\:a\:>\:0\:\mathrm{then}\:u\:\le \:-a\:\quad \mathrm{or}\quad \:u\:\ge \:a[/tex]
[tex]2x\le \:-6\quad \mathrm{or}\quad \:2x\ge \:6[/tex]
[tex]2x\le \:-6\quad \mathrm{or}\quad \:2x\ge \:6[/tex]
Thus, the option is incorrect.
Option C) |2x| > 6
[tex]\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad \mathrm{or}\quad \:u\:>\:a[/tex]
[tex]2x<-6\quad \mathrm{or}\quad \:2x>6[/tex]
[tex]x<-3\quad \mathrm{or}\quad \:x>3[/tex]
Thus, the option is correct.
Option C) |2x| ≤ 6
[tex]\mathrm{If}\:|u|\:\le \:a,\:a\:>\:0\:\mathrm{then}\:-a\:\le \:u\:\le \:a[/tex]
[tex]2x\ge \:-6\quad \mathrm{and}\quad \:2x\le \:6[/tex]
[tex]x\ge \:-3\quad \mathrm{and}\quad \:x\le \:3[/tex]
Thus, the option is incorrect.
Hence, Option C) |2x| > 6 is correct.
Simplify by combining like
terms:
--6x - 12 + 8y + 16x
Answers
The answer is 10x+8y-12 if the problem was -6x - 12 + 8y + 16x because you added an extra negative at the start.
4. The annual salaries of employees in a large company are approximately
normally distributed with a mean of $50,000 and a standard deviation of
$20,000:1
a) What percent of people earn less than $40,000?
b) What percent of people earn between $45,000 and $65,000?
c) What percent of people earn more than $70.000
Answers
a. What percent of people earn less than $40000?
Solution: Let S be the random variable of a salary of employee (in $), S ~ N(50000,20000). Then the random
variable X =−50000
20000
~N(0,1).
( < 40000) = ( <
40000 − 50000
20000 ) = ( < −0.5) = (−0.5) = 0.3085375.
Here Φ(x) denotes the cumulative distribution function of a standard normal distribution.
Answer: 31%.
b. What percent of people earn between $45000 and $65000?
Solution:
(45000 < < 65000) = (
45000 − 50000
20000 < <
65000 − 50000
20000 ) = (−0.25 < < 0.75)
= (0.75) − (−0.25) = 0.7733726 − 0.4012937 = 0.3720789.
Answer: 37%.
c. What percent of people earn more than $70000?
Solution:
( > 70000) = ( >
70000 − 50000
20000 ) = ( > 1) = 0.8413447.
Answer: 84%.
By converting the salary amounts to Z-scores and checking a standard normal distribution table, the percentages of people earning less than $40,000, between $45,000 and $65,000, and more than $70,000 are approximately 30.85%, 37.21%, and 15.87%, respectively.
Explanation:In this question, we are dealing with what is known as a 'normal distribution' in statistics. The properties of a normal distribution allow us to calculate the percentages requested. First, we need to convert each salary to a 'Z-score'. A z-score will tell us how many standard deviations away from the mean the salary lies.
a) For $40,000, the Z-score will be (40000-50000)/20000, yielding -0.5. Looking up this Z-score in a standard normal distribution table, or using a calculator equipped with normal distribution functions, we find that roughly 30.85% of employees would earn less than $40,000.
b) For the range $45,000 to $65,000: the Z-scores will be -0.25 and 0.75 respectively. These correspond to about 40.13% and 77.34%. The percentage of people earning between these amounts would be 77.34% - 40.13% = 37.21%.
c) For over $70,000: the Z-score is 1.0 which corresponds to around 84.13%. Therefore, the percentage earning more than $70,000 is 100% - 84.13% = 15.87%
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The local high school football team will be playing in the state championship. The coach has free tickets that he will be distributing to 52 football players for their friends and families. If he would like to give each player at least 3 tickets, what is the minimum total he must have?
Answers
Answer:
156
Step-by-step explanation:
52*3+156
45 = 5(3x – 6)
Help me
Answers
Answer is provided in the image attached.
Simplify 2x2 - y for x= 3 and y=-2.
Answers
Answer:
20
Step-by-step explanation:
2x^2-y
x = 3 and y = -2
So then we have 2*3^2--2 which equals 20.
The solution to the algebraic expression 2x² - y for x= 3 and y=-2. is: 22
How to solve Algebra Expressions?An algebraic expression in mathematics is defined as an expression which is made up of variables and constants, along with algebraic operations
We are given the algebraic expression as:
2x² - y for x= 3 and y=-2.
Thus, plugging in 3 for x and -2 for y in the given equation and we have:
2(3)² - (-2)
= (2 * 9) + 4
= 18 + 4
= 22
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A 48ft wire is cut into 3 pieces. The 2nd is three times as long as the first piece. The third piece is 4 times as long as the second piece. How long is each piece?
Answers
Answer:
3,9,and 36
Step-by-step explanation:
small=x
median=3x
big=12x
x+3x+12x=48
16x=48
x=3
3=small
3*3=9 (median)
9*4=36(big)
3+9+36 = 48
The problem is solved by setting up and solving an equation where 'x' represents the length of the first piece. The three pieces of the wire measure 3ft, 9ft, and 36ft respectively.
Explanation:The question is about finding the length of each piece of a 48ft wire when it's divided into 3 pieces, with each piece having a specific relative length. Let's denote the length of the first piece as 'x'. According to the problem, the second piece is three times as long as the first one, so it's '3x', and the third is four times as long as the second, so it's '4*3x', which simplifies to '12x'.
Combining all these pieces, we get the total length of the wire: x + 3x + 12x = 48ft. This simplifies to 16x = 48ft. Finally, solving for 'x', we find that x = 48ft / 16 = 3ft. Therefore, the three pieces of the wire measure 3ft, 9ft, and 36ft respectively.
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Enter an inequality that represents the description, and then solve.
Nine more than seven times a number (x) is at least thirty.
Inequality:
The solution to the inequality is
Answers
Answer:
7x + 9 ≥ 30
x ≥ 3
Step-by-step explanation:
7x + 9 ≥ 30
7x ≥ 21
x ≥ 3
Final answer:
The inequality 7x + 9 ≥ 30 represents the description given, and the solution is x ≥ 3, meaning any number greater than or equal to 3 satisfies the inequality.
Explanation:
The inequality that represents the description 'nine more than seven times a number (x) is at least thirty' is written as 7x + 9 ≥ 30.
To solve this inequality:
Subtract 9 from both sides of the inequality: 7x ≥ 21.Divide both sides by 7 to isolate x: x ≥ 3.Therefore, the solution to the inequality is that x must be a number greater than or equal to 3.
Help me please!!? Idk it
Answers
Answer:
do the area of the triangle formula the base × height ÷ 2
In which direction does the head of the molecules of the plasma membrane face?
O toward the head of another molecule
O toward the middle
O
away from water
O toward the outside
Answers
Answer:
toward the outside
Step-by-step explanation:
The plasma membrane is composed of the phospholipid bilayer and cholesterol.The phospholipids have a head and two tails.The head is water loving, hence it is termed as polar/hydrophilic.The tails are nonpolar/ water fearing/hydrophobic.Both inside and outside the cell, water is vital thus the phospholipid line up in two layers where the head points outwards and the tails hidden in the middle.
Answer:
to the middle
Step-by-step explanation:
The average distance from the sun to the planet mercury is about 58,000,000km the distance of a human hair is about 0.0025
What is the distance from the sun to mercury
Answers
Answer:
58,000,000 km
Step-by-step explanation:
the hair thing is just to throw you off
The average distance from the Sun to the planet Mercury is approximately 58 million kilometers, which also translates to 0.39 astronomical units (AU). Mercury's orbit varies from 46 million kilometers at its closest to 70 million kilometers at its farthest from the Sun due to its elliptical orbit.
Explanation:Distance from the Sun to Mercury
The average distance from the Sun to Mercury is about 58 million kilometers. This distance is known as the semimajor axis of Mercury's orbit. Since Mercury's orbit has a high eccentricity of 0.206, its actual distance from the Sun can vary significantly. The closest point, or perihelion, is about 46 million kilometers, and the farthest point, or aphelion, is about 70 million kilometers. The concept of astronomical unit (AU) is used as a standard measure within the solar system, defined as the average Earth-Sun distance, which is about 150 million kilometers or 1 AU. Consequently, Mercury's average distance from the Sun can also be expressed as 0.39 AU.
The length of a rectangle is 2 km less than 3 times the width. If the perimeter is 68 km,What is the length of the rectangle
Answers
Answer:
The length of the rectangle is 25 km
Step-by-step explanation:
Let
x ----> the length of rectangle
y ----> the width of rectangle
we know that
The perimeter of rectangle is
[tex]P=2(x+y)[/tex]
we have
[tex]P=68\ km[/tex]
so
[tex]68=2(x+y)[/tex]
simplify
[tex]34=(x+y)[/tex]---- > equation A
[tex]x=3y-2[/tex] ---> equation B
substitute equation B in equation A and solve for y
[tex]34=(3y-2)+y[/tex]
[tex]34=4y-2[/tex]
[tex]4y=34+2[/tex]
[tex]4y=36[/tex]
[tex]y=9\ km[/tex]
Find the value of x
[tex]x=3(9)-2=25\ km[/tex]
therefore
The length of the rectangle is 25 km
Please help me!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
a. 81.9
b. 144.7
c. 110.2
d. 48
Step-by-step explanation:
a. 120/109.2 = 90/x
x = 81.9
b. 45.6/120 = 55/x
x = 144.7
c. 304.8/96 = 350/x
x = 110.2
d. 109.2/45.6 = 115/x
x = 48
Do number one Show your work✨
Answers
Can u guys answer these 3 questions for me w/ work shown and also label the ones u guys did so I won’t get them mixed up
Answers
8:
q/6 + p
12/6 + 10
2 + 10
12
10:
15 - m/p
15 - 3/10
14.7
12:
p - 2/qp
7 - 2/(4)(7)
7 - 2/28
7 - 1/14
6.928
OMG PLZ HELP RN
Five-eighths of a number decreased by twelve is the same as one-half of the number increased by two.
5/8x-12=1/2x+2
What is the answer?
Answers
Answer:
112
Step-by-step explanation:
The number is 112 if Five-eighths of a number decreased by twelve is the same as one-half of the number increased by two the answer is 112.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
Five-eighths of a number decreased by twelve is the same as one-half of the number increased by two.
Let x be the number:
From the question:
(5/8)x - 12 = (1/2)x + 2
The above equation is a linear equation in one variable:
After solving:
(5/8)x - (1/2)x = 12 + 2
(5-4)x/8 = 14
x = 14×8
x = 112
Thus, the number is 112 if Five-eighths of a number decreased by twelve is the same as one-half of the number increased by two the answer is 112.
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which of these is not a possibe r-value?
a.1.75
b.-0.1
c.0.2
d.-0.5
Answers
Among the given options, "-0.1" is not a possible R-value. R-values represent the thermal resistance of a material, and they are always positive values.
What are R values used forR-values are used to measure the ability of a material to resist the flow of heat, and a higher R-value indicates better insulation. Therefore, values like 1.75, 0.2, and -0.5 could potentially be R-values, with 1.75 and 0.2 being good insulators and -0.5 indicating a poor insulator. However, a negative value like -0.1 does not make physical sense in the context of R-values.
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6. What is 45% of 900?
Answers
Answer:
405
Step-by-step explanation:
45% of 900
=(45/100) . 900
=405
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each description with the correct inequality.
20 POINTS ANSWER ASAP
Answers
The 2nd one goes with the 2nd box
The last one goes with the 3rd box
Use the Distributive Property to multiply 8 and 45 in your head.
What is the answer?
32 + 40 + 72
40 + 40 = 80
320 + 40 = 360
320 + 5 = 325
Answers
Answer:
320+40=360
Step-by-step explanation:
8(40+5)
320+40=360
Answer:
320+40=360
Step-by-step explanation:
First you split 45 to 40 and 5
45= 40+5
Next you multiply each piece of 45 by 8
(40x8)+ (5x8)
Simplify
320+40
Solve
320+40=360
What is the awnser to -12/-4=
Answers
[tex]\frac{-12}{-4}[/tex] is 3.
Answer:
-12/-4 is 3
Step-by-step explanation:
hope this helps !!
Someone please help!!
Answers
Answer:
I believe the answer is D, 145 degrees
Step-by-step explanation:
180 - 35 = 145
Apologies if I am incorrect.
Round 0.817 to the hundredth
Answers
Answer:
0.820
Step-by-step explanation:
7 is above five so round to the nearst tenth
What is 118 rounded to the nearest hundred
Answers
Answer:
100.
Step-by-step explanation:
118 rounded to the nearest hundred is 100
When rounding 118 to the nearest hundred, we look at the tens digit (which is 1 in this case). Since this digit is less than 5, we round down to the nearest hundred. Therefore, 118 rounded to the nearest hundred is 100.
what is the point slope form of the line with slope -1/4 that passes through the point ( -2,9 )
Answers
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{9})~\hspace{10em} \stackrel{slope}{m}\implies -\cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{-\cfrac{1}{4}}[x-\stackrel{x_1}{(-2)}]\implies y-9=-\cfrac{1}{4}(x+2)[/tex]
Any body know, 38 to the power of 5? i know its hard, it is for me.
Answers
38 to the power of 5 is written as 38^5
When a number is raised to a power, multiply that number by itself the number of the power:
38 x 38 x 38 x 38 x 38 = 79,235,168
The Plumber charges $50 to come to her home an a additional $30.75 every hour he works on the job Sarah has $234 .50 in savings for the repairs what is the maximum amount of hours that the plumber worked on her faucet.
Answers
Answer:
6 hours
Step-by-step explanation:
234.50-50.00=184.50
184.50/30.75=6
6 hours
3 in the power of ten word form
Answers
3 in the power of ten means "10^3."
[tex]10^3[/tex]
How to solve exponents is to multiply the number as many times as it's exponent. So in this case you will have to multiply ten, three times.
[tex]10\times10\times10=1000[/tex]
Which would mean that....
[tex]10^3=1000[/tex]
The answer is 10^3.
Hope this helps.
Suppose 4/5 of a different box of oranges weighs 8 pounds. How many pounds of oranges are in the full box?
Answers
Answer:
10
Step-by-step explanation:
x×4/5=8
x=8×5/4
x=10
Answer:
The correct answer is 10.
Step-by-step explanation:
One of the ways to find this answer is the following:
If 4/5 represent 8 pounds, it means that every fifth is two pounds.
If the total amount is five fifths, it is necessary to perform the following multiplication:
2 * 5 = 10, so it is the correct answer.