Answer:
(1, 4)
Step-by-step explanation:
Lets show first the inequality. Putting in numbers what greater than one half times x plus 2 means is:
y > (1/2)x + 2
The procedure is simple: take the points and replace them in the inequality to see which verifies.
(1, 4):
4 > (1/2)*1 + 2
4> 1/2+ 2
4 > 1/2 + 4/2
4> 5/2
8/2> 5/2 ---> I verifies!!!
(-1, 1)
1 > (1/2)(-1) + 2
1> -1/2 + 2
1 > -1/2 + 4/2
1 > 3/2 ---> Not verify!!
(2, 3):
2 > (1/2)*2 + 2
2 > 1 + 2
2 > 3 ---> Not verify!!!
(0, 2)
2 > (1/2)*0 + 2
2 > 2 ---> Not verify!!!
So, the only pair that verifies is (1, 4)
3x - 3y = -3
2x - y = -5
For this case we must solve the following system of equations:
[tex]3x-3y = -3\\2x-y = -5[/tex]
To solve we follow the steps below:
We multiply the second equation by -3:
[tex]-6x + 3y = 15[/tex]
Thus, we have the equivalent system:
[tex]3x-3y = -3\\-6x + 3y = 15[/tex]
We add the equations:
[tex]3x-6x-3y + 3y = -3 + 15\\-3x = -3 + 15\\-3x = 12\\x = \frac {12} {- 3}\\x = -4[/tex]
We look for the value of the variable "y":
[tex]2 (-4) -y = -5\\-8-y = -5\\-y = -5 + 8\\-y = 3\\y = -3[/tex]
Thus, the solution of the system is given by:
[tex](x, y): (- 4, -3)[/tex]
Answer:
[tex](x, y): (- 4, -3)[/tex]
[tex] {x}^{2} + {11}^{2} = {22 }^{2} [/tex]
Answer:
See image below.
I'm not 100% sure if this is allowed or not, someone please let me know if it is not.
Step-by-step explanation:
See image below
Answer:
± 11[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Given
x² + 11² = 22², that is
x² + 121 = 484 ( subtract 121 from both sides )
x² = 363 ( take the square root of both sides )
x = ± [tex]\sqrt{363}[/tex] = ± [tex]\sqrt{121(3)}[/tex] = ± 11[tex]\sqrt{3}[/tex]
The tile back splash will be a mixture of colors of four inch square tiles. One fifth of the tiles will be indian red three tenths will be Tuscan blue one sixth will be eucalyptus and the rest will be the color of sand . What fraction of the tiles will be the color of sand .
=================================================
Explanation:
1/5 of the tiles are indian red
3/10 of the tiles are Tuscan blue
1/6 of the tiles are eucalyptus
x of the tiles are sand, where x is some fraction
The four fractions listed above add to 1. The "1" refers to a whole back splash, in which you can think of "1" as "100%"
-----------
We have the fractions 1/5, 3/10 and 1/6
To combine these fractions, we need a common denominator. In this case, the lowest common denominator (LCD) is 30 as this is the LCM of the denominators 5, 10, and 6.
Let's get each fraction to have a denominator of 30
1/5 = (6/6)*(1/5) = 6/30
3/10 = (3/3)*(3/10) = 9/30
1/6 = (5/5)*(1/6) = 5/30
-----------
So effectively we have these fractions: 6/30, 9/30, and 5/30
They add to the unknown fraction x to get 1
Let's solve for x.
-----------
(1/5) + (3/10) + (1/6) + x = 1
(6/30) + (9/30) + (5/30) + x = 1
(6/30 + 9/30 + 5/30) + x = 1
(6 + 9 + 5)/30 + x = 1
20/30 + x = 1
2/3 + x = 1
x + 2/3 = 1
x+2/3-2/3=1-2/3 ... subtract 2/3 from both sides
x = 1 - 2/3
x = 3/3 - 2/3
x = (3 - 2)/3
x = 1/3
------------
1/3 of the tiles are the color of sand
Final answer:
One third of the tiles will be the color of sand. This is found by adding the fractions of the other colors, simplifying, and subtracting from one whole set of tiles.
Explanation:
To find the fraction of the tiles that will be the color of sand, we first need to calculate the total fraction of tiles that have already been assigned colors: Indian red, Tuscan blue, and eucalyptus. Then we subtract this total from 1, which represents the whole set of tiles, to find the remaining fraction for the sand-colored tiles.
Indian red: ⅓ of the tilesTuscan blue: ⅗ of the tilesEucalyptus: ⅙ of the tilesAdding these fractions:
⅓ + ⅗ + ⅙ = ⅓ + (⅗ × 2/2) + (⅙ × 5/5)= ⅓ + ⅖ + ⅓= 10/15Now, we convert 10/15 to a simplified fraction:
10/15 = 2/3 (dividing both numerator and denominator by 5)To find the fraction for sand-colored tiles, subtract the total colored fraction from 1:
1 - 2/3 = 3/3 - 2/3= 1/3Therefore, one third of the tiles will be the color of sand.
LabTech is a company that manufactures microscopes and other laboratory instruments . On occasion, one of the microscopes is defective when it comes off of the production line. The probability that a microscope is defective is 0.17%. Find the probability that one of the first 50 microscopes is defective .
To find the probability of at least one defective microscope in a batch of 50, we first calculate the probability of all 50 being non-defective and then subtract this from 1. The resulting probability of having at least one defective microscope in the batch is approximately 7.96%.
Explanation:The question is about finding the probability that one of the first 50 microscopes manufactured by LabTech is defective. Given the probability of a microscope being defective is 0.17%, we can calculate this by multiplying the probability of a single microscope being defective by the total number of microscopes.
Firstly, convert the 0.17% to a decimal by dividing by 100, which gives us 0.0017. This is the probability of a single microscope being defective. Then, to find out the probability of at least one out of 50 being defective, we would consider the opposite - the probability of all 50 microscopes being non-defective. If one microscope has a 0.0017 chance of being defective, it has a 1-0.0017 = 0.9983 chance of being non-defective.
The chance of all 50 microscopes being non-defective is [tex](0.9983)^{50} = 0.9204.[/tex] Therefore, the probability of at least one out of 50 being defective is 1 - 0.9204 = 0.0796 or 7.96%.
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Final answer:
The probability that at least one of the first 50 microscopes manufactured is defective is calculated using the complement rule, by subtracting the probability of none being defective from 1, the answer is 0.082
Explanation:
To find the probability that at least one of the first 50 microscopes LabTech manufactures is defective, we use the complement rule. The probability that a microscope is not defective is 1 - 0.0017 (since 0.17% as a decimal is 0.0017). To find the probability that none of the microscopes out of the 50 produced are defective, we raise this to the power of 50:
P(no defective microscopes) = [tex](1 - 0.0017)^{50[/tex]
Then, to find the probability that at least one microscope is defective, we subtract this from 1:
P(at least one defective microscope) = [tex]1 - (1 - 0.0017)^{50[/tex]
P(at least one defective microscope)= 1-0.918= 0.082
Find the solution for 30 − 5n ≤ 25.
1 n ≤ -1
2 n ≤ -11
3 n ≥ -11
4 n ≥ 1
Answer:
n>=1
Step-by-step explanation:
30-5n<=25
5n<=30-25
5n<=5
n<=5/5
n<=1
n>=1
.. Jessie charges Jim $45.00 for 3 hours of tutoring. Mike charges Jim $90.00 for
5 hours of tutoring. Who offers Jim the better hourly rate of pay?
Answer:
jessie is better
Step-by-step explanation:
45/3=15
$15 per hour
90/5=18
$18 per hour
Answer:
the correct answer is jessie charges jim the better price
Step-by-step explanation:
The slope is undefined and contains the point (-3,8)
the graph of which of the following will be perpendicular to the graph of 4x- 3y= -12
a. 4x+3y=12
b. y=-3/4x-8
c.y=3/4x+1
d. 3x-4y=1
Answer:
(b) y=-3/4x-8
Step-by-step explanation:
The graph that will be perpendicular to the graph 4x - 3y = -12
If this equation is represented in form of the straight line equation y = mx + b
it will change to 3y = 4x + 12
therefore y = (4/3)x + (12/3)
y = (4/3)x + 4
which implies that m = 4/3 while b = 4
However for the line that will be perpendicular to the graph, its slope m1 must be negative inverse of the slope of the initial graph
This is because m x m1 = -1
therefore m1 = -1/m
this implies that the correct answer must have a slope of -1/(4/3) = -3/4
The correct answer can then be analysed by expressing all options with y = mx + b
(a) In form of y = m1x + b, 4x+3y=12 becomes y = -4/3x + 4 (m1 = -4/3: wrong)
(b) In form of y = m1x + b, y=-3/4x-8 has m1 = -3/4 (correct)
(c) In form of y = m1x + b, y=3/4x+1 has m1 = 3/4 (wrong)
(d) In form of y = m1x + b, 3x-4y=1 becomes y = 3/4x - 1/4 (m1 = 3/4: wrong)
Find the surface area of a conical grain storage tank that has a height of 41 meters and a diameter of 16 meters. Round the answer to the nearest square meter.
Answer:
The surface area of a conical grain storage tank that has a height of 41 meters and a diameter of 16 meters is[tex]1250.9 m^2[/tex]
Explanation:
Height of the conical grain storage tanks =41 m
Diameter of the conical grain storage tank=16 m
Hence radius = diameter/2=8 m
Suppose h is height and r is radius
Formula used:
Surface area of a cone= A
A= [tex]\pi rl +\pi r^2[/tex]
= πr(l+r)
Where[tex]l =(r^2+h^2)^1^/^2[/tex]
=[tex]\pi r(r+(h^2+r^2)^1^/^2)[/tex]
Putting the values
=[tex]3.14 \times 8\left(8+\left(41^{2}+8^{2}\right)^{1 / 2}\right)[/tex]
=1250.9368
=[tex]1250.9 m^2[/tex]
[tex]1250.9 m^2[/tex] is the surface area of a conical grain storage tank
Ifc-8 is an odd integer, which of the following could be the value of c?
-8
0
-5
10
Let's try all of the possible answer choices.
Any result that is even, we cross off the list. Otherwise we have our answer.
If c = -8, then c-8 = -8-8 = -16 which is even. Cross this off the list
If c = 0, then c-8 = 0-8 = -8, which is even. Cross this off the list.
If c = -5, then c-8 = -5-8 = -13, which is odd. We have our answer
If c = 10, then c-8 = 10-8 = 2, which is even. Cross this off the list
=============================================
Final Answer: Choice C) -5I need help !
Write an equation in point slope form (-6,3) m= -1/5
Answer:
y-3=-1/5(x+6)
Step-by-step explanation:
Jadas family has completed 30% of a trip. They have traveled 15 miles. How far is the trip
Answer:
50
Step-by-step explanation:
.3x=15
x=50
Answer:
The trip is 50miles far
Step-by-step explanation:
If they have travel 15miles which is equal to 30% of the trip.
To find how far the trip is.
Let x represent the trip in miles
Therefore:
30% of x is 15miles
30/100 * x = 15miles
x = 15 miles ÷ 30/100
x = 15 miles * 100/30
x = 1500miles/30
x = 50miles
J(x)=3x+-1 find j(-2)
Answer:
-7
Step-by-step explanation:
j(x)=3x+(-1)
j(x)=3x-1
j(-2)=3(-2)-1
j(-2)=-6-1
j(-2)=-7
Answer:
-7
Step-by-step explanation:
plug in -2 for x
(3)(-2) = -6
and then add the -1
= -7
the difference of the product of 3 and 6 minus the quotient of 6 divided by 2
Sequence 1: 32, 16, 0, –16, ...
Sequence 2: 32, 16, 8, 4, ...
Which of the following statements are true regarding Sequence 1 and Sequence 2.
This is a cool one. Sequence 1 will approach negative infinity and Sequence 2 will approach 0 but never get to it!
Sequence 1 is an arithmetic sequence with a common difference of -16. Sequence 2 is a geometric sequence with a common ratio of 1/2.
Explanation:Sequence 1 is an arithmetic sequence with a common difference of -16. Starting with 32, each term is obtained by subtracting 16 from the previous term. Sequence 2 is a geometric sequence with a common ratio of 1/2. Starting with 32, each term is obtained by multiplying the previous term by 1/2.
Sequence 1: 32, 16, 0, -16, ...
Sequence 2: 32, 16, 8, 4, ...
Statement 1: Sequence 1 is an arithmetic sequence. True.
Statement 2: Sequence 2 is a geometric sequence. True.
Statement 3: The common difference in Sequence 1 is 8. False. The common difference is -16.
Statement 4: The common ratio in Sequence 2 is 1/2. True.
Statement 5: The next term in Sequence 1 is -32. True. The next term is obtained by subtracting 16 from -16.
Statement 6: The next term in Sequence 2 is 2. True. The next term is obtained by multiplying 4 by 1/2.
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es - Multiply the binomials (5x - 1) and (2x - 8).
A)
10x2 - 42x - 8
B)
10x2 - 42x + 8
o
10x2 + 38x - 8
D)
10x2 – 38x - 8
Answer:
Our final answer is option B that is [tex]10x^2-42x+8[/tex]
Step-by-step explanation:
As we have to multiply the binomial.
Here is the work.
Using distributive law of multiplication.
Where [tex]a(b+c)=ab+ac[/tex]
⇒[tex](5x-1)(2x-8)[/tex]
[tex]5x(2x-8)-1(2x-8)[/tex]
[tex]10x^2-40x-2x+8[/tex]... [tex](-1\times -8 =8)[/tex]
As [tex]-40x[/tex] and [tex]-2x[/tex] are in negative so we will add these
numbers keeping the negative sign as it is.
[tex]10x^2-42x+8[/tex]
So the correct choice is option B that is [tex]10x^2-42x+8[/tex]
The perimeter of a rectangle is 34cm.Find the breadth of the rectangle if its length is 12cm.
What is the first term of the quotient of the following division problem ? (X^3-1)
Answer:
The question is incomplete, complete question is:
What is the first term of the quotient of the following division problem?
(x^3 – 1) ÷ (x + 2)
A. –0.5
B. 1
C. x^2
D. x^4
option C
Step-by-step explanation:
(x^3-1) divide by x+2
Use long division
x^2 -2x
-----------------------
x+2 x^3 + 0x^2 +0x -1
x^3 + 2x^2
-----------------------------------(subtract it)
- 2x^2 +0x - 1
-2x^2 - 4x
--------------------------------(subtract)
5x -1
Thus the first term of the quotient is x^2.
If 1/2 is subtracted from four times the reciprocal of a number, the result is 0. Find the number.
Answer:Include
Step-by-step explanation:
Multiply add and subtract the top. I can include the rest if you want
Answer:
The required number is 8.
Step-by-step explanation:
Given : If [tex]\frac{1}{2}[/tex] is subtracted from four times the reciprocal of a number, the result is 0.
To Find : The number ?
Solution :
Let the number be x.
The reciprocal of number is [tex]\frac{1}{x}[/tex]
[tex]\frac{1}{2}[/tex] is subtracted from four times the reciprocal of a number, the result is 0.
The equation will become,
[tex]4\times \frac{1}{x} - \frac{1}{2}=0[/tex]
Solving the equation we get,
[tex]\frac{4}{x} -\frac{1}{2}=0[/tex]
[tex]\frac{4}{x} = \frac{1}{2}[/tex]
[tex]x= 4\times 2[/tex]
[tex]x=8[/tex]
Therefore, the required number is 8.
Which equation represents the horizontal line passing through (-1,2)
Answer:
y = 2
Step-by-step explanation:
When line is horizontal, all points on this line have the same value of y.
In this case , all points have to have y = 2.
y = 2, is an equation of horizontal line.
The equation of line y = 2 represents the horizontal line passing through (-1,2).
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have given a point (-1, 2) on a coordinate plane.
The distance from origin (0, 0) and (0, 2) is 2
And line y = 2 represents the horizontal line that passes through (-1, 2)
Thus, the equation of line y = 2 represents the horizontal line passing through (-1,2).
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Which situation CANNOT be represented by this equation?
4r +7= 31
Answer:
r=6
Step-by-step explanation:
4r+7=31
4r=31-7
4r=24
r=24/4
r=6
There are 2 girls and 3 boys on a camping trip. What is the ratio of girls
to boys on the trip?
Answer:
2/3
Step-by-step explanation:
Answer:
2/3 is the answer
Step-by-step explanation:
Write as one logarithm. Simplify.
log5 125 – log5 25
Answer:
log 5 5
= 1.
Step-by-step explanation:
Use the logarithm law loga b - loga c = loga b/c:
log5 125 – log5 25
= log5 125 / 25
= log5 5.
= 1.
The expression log5 125 - log5 25 simplifies to 1.
To combine the logarithms log5 125 and log5 25 as one logarithm and simplify, we can use the properties of logarithms. Specifically, we'll use the property that states logb(x) - logb(y) = logb(x/y). Applying this property, we have:
log5 125 - log5 25 = log5 (125/25)
We simplify the fraction 125/25 to get 5. So, we have:
log5 (125/25) = log5 5
The logarithm of a number to the base of itself is always 1, so:
log5 5 = 1
Therefore, the expression log5 125 - log5 25 simplifies to 1.
(2, -3) and (6,-13)
What is the slope
Answer:
-5/2
Step-by-step explanation:
Slope = change in y over change in x or (y2-y1)/(x2-x1)
slope = (-13-(-3))/(6-2) = -10/4 = -5/2
Answer:
m=-5/2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-13-(-3))/(6-2)
m=(-13+3)/4
m=-10/4
simplify,
m=-5/2
n a recent election, Mark Benton received 780 votes for 12% of the total vote. How many people voted in the election?
A
65
B
936
C
6,500
D
9,360
Answer: Answer C
Step-by-step explanation:
12%___780 votes
100%___X= 6500 votes
(100*780)/12 = 6500
Am i doing this right?
y = -4
Answer:
Step-by-step explanation:
no but you are very close
you forgot to put the x next to the -4
because if you left it like that than it would be a horizontal line going through the y-axis at -4
the x is very important since it is the input value while y is the output
so y depends on the x
Answer:
[tex]\displaystyle YES[/tex]
Step-by-step explanation:
The equation you modeled here is [tex]\displaystyle y = -4x,[/tex]where the y-intercept and x-intercept are both located at the origin. This is what is called direct variation.
I am joyous to assist you anytime.
*Just attach the x to the equation because leaving it out would form a horizontal line [zero rate of change (slope)].
Mohammad would like to graph the line that represents the total number of baseball cards he will
have collected, T, after m months, given that he buys 5 cards each month and he started with no
cards. He would like the graph to show the number of cards after 6 and 12 months
Select from the drop-down menus to correctly complete each statement
To best show this information, the scale for the T-axis of his graph should go from 0 to at least
(Answer)
and the m-axis of his graph should go from 0 to at least (Answer)
Answer:
To best show this information, the scale for the T-axis of his graph should go from 0 to at least 60.
To best show this information, the scale for the m-axis of his graph should go from 0 to at least 12.
Step-by-step explanation:
Mohammad will have collected T cards after m months, given that he buys 5 cards each month and he started with no cards.
The relationship describing this situation is
[tex]T=5m[/tex]
When [tex]m=6,[/tex] then [tex]T=5\cdot 6=30[/tex] cards.
When [tex]m=12,[/tex] then [tex]T=5\cdot 12=60[/tex] cards.
To best show this information, the scale for the T-axis of his graph should go from 0 to at least 60.
To best show this information, the scale for the m-axis of his graph should go from 0 to at least 12.
this should be easy for someone who is smart
Answer:
Hope it helps :)
Step-by-step explanation:
Detailed answer in the attached file
A student cost for last semester at her community college was 2000.She spent $220 of that on books.what percent of last semester college costs was spent on books??
11% of college costs was spent on books.
Step-by-step explanation:
Total cost for last semester = $2000
Amount spent on books = $220
Percent of amount spent on books = [tex]\frac{Amount\ spent\ on\ books}{Total\cost\ for\ semester}*100[/tex]
Percent of amount spent on books = [tex]\frac{220}{2000}*100\\[/tex]
Percent of amount spent on books = [tex]\frac{22000}{2000}[/tex]
Percent of amount spent on books = 11%
11% of college costs was spent on books.
Keywords: percentage, division
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HELP!
Jack drove 278.2 miles on 19.6 gallons of gasoline. About how many miles did he drive per gallon of gasoline?
(Round your answer to the nearest WHOLE amount of miles. Whole = ones place)
Answer:
[tex]14\ \frac{miles}{gallon}[/tex]
Step-by-step explanation:
we know that
To find out the unit rate (number of miles per gallon of gasoline) divide the total miles driven by the total gallons of gasoline used
so
[tex]\frac{278.2}{19.6}\ \frac{miles}{gallons}=14.19\ \frac{miles}{gallon}[/tex]
Round to the nearest WHOLE amount of miles
[tex]14.19\ \frac{miles}{gallon}=14\ \frac{miles}{gallon}[/tex]