Which point is a solution to the inequality shown in this graph?
5
(3,-1)
(-3,-3)
O A. (5,-5)
O B. (1,5)
C. (-3,-3)
D. (3, -1)
Answers
Hey there!
To find the answer, we just need to see which point falls in this blue, which represents the inequality.
We see that the point (5,-5) is not on the blue.
We see that the point (1,5) is on the blue.
(-3,-3) is on the dotted line but not a solution of the inequality. The dotted line is excluded from the inequality. If it were a bold line, then it would be a solution of the inequality.
(3,-1) is also on the dotted line so it is not a solution.
Therefore, the answer is B. (1,5)
I hope that this helps!
We want to see which point is a solution for the graphed inequality.
We will find that the correct option is B, (1, 5)
Notice that the line that defines the inequality contains the points (-3, -3) and (3, -1)
Then the slope of that line is:
[tex]a = \frac{-1 -(-3)}{3 - (1)} = 1/2[/tex]
Then the line is something like:
y = (1/2)*x + b
To find the value of b, we use the fact that this line passes through the point (3, -1), then we have:
-1 = (1/2)*3 + b
-1 - 3/2 + b
-5/2 = b
So the line is:
y = (1/2)*x - 5/2
And we can see that the line is slashed, and the shaded area is above the line, then we have:
y > (1/2)*x - 5/2
Now that we have the inequality, we can just input the values of the points in the inequality and see if this is true.
First, options C and D can be discarded because these points are on the line, and the points on the line are not solutions.
So we only try with A and B.
A) x = 5
y = -5
then we have:
-5 > (1/2)*5 - 5/2
-5 > 0
Which clearly is false.
B) x = 1
y = 5
Then we have:
5 > (1/2)*1 - 5/2 = -4/2
5 > -4/2
This is true, then the point (1, 5) is a solution.
Thus the correct option is B.
If you want to learn more, you can read:
https://brainly.com/question/20383699
Related Questions
Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = –6. Which function could Heather be writing? f(x) = x2 + 36x + 12 f(x) = x2 – 36x – 12 f(x) = –x2 + 12x + 36 f(x) = –x2 – 12x – 36
Answers
Answer:
f(x) = –x^2 – 12x – 36
Step-by-step explanation:
The parent function, x^2, touches the x-axis at x=0. Translating it 6 units left replaces x with x-(-6) = x+6, so the function is ...
f(x) = (x+6)^2 = x^2 +12x +36
Reflecting the graph across the x-axis doesn't change the x-intercept, so Heather could be writing ...
f(x) = -x^2 -12x -36
It's D.
I have to have at least 20 characters.
At the Arctic weather station, a warning light turns on if the outside temperature is below -25 degrees Fahrenheit. Which inequality models this situation?
Answers
Temperature in °F is T
Answer:
T < -25
Step-by-step explanation:
Was correct on TTM
I NEED HELP PLEASE, THANKS! :)
A discus is thrown from a height of 4 feet with an initial velocity of 65 ft/s at an angle of 44° with the horizontal. How long will it take for the discus to reach the ground? (Show work)
Answers
Answer:
2.908 s
Step-by-step explanation:
The "work" is most easily done by a graphing calculator. We only need to tell it the equation of motion.
For speeds in feet per second, the appropriate equation for vertical ballistic motion is ...
h(t) = -16t² +v₀t +s₀
where v₀ is the initial vertical velocity in ft/s and s₀ is the initial height in feet. The vertical velocity is the vertical component of the initial velocity vector, so is (65 ft/s)(sin(44°)). We want to find t for h=0.
0 = -16t² +65sin(44°) +4
Dividing by -16 gives ...
0 = t^2 -2.82205t -0.2500
Using the quadratic formula, we find ...
t ≈ (2.82205 ±√(2.82205² -4(1)(-0.25))/2 ≈ 1.41103 +√2.24099
t ≈ 2.90802
It will take about 2.908 seconds for the discus to reach the ground.
_____
Comment on the question
You're apparently supposed to use the equation for ballistic motion even though we know a discus has a shape that allows it to "fly". It doesn't drop like a rock would.
Solve the system by graphing (Simplify your answer completely.)
Will someone please help me with this and give an explanation on how you got it? I don’t understand.
{x+y=8
{x-y=4
Answers
Answer:
(6,2)
Step-by-step explanation:
1) convert both equations to slope intercept form:
y=-x+8
and
y=x-4
now graph both equations separately by intercepts:
x int: 0=-x+8
-8=-x
8=x
y int: y=0+8
y=8
so the two coordinate points for first equation are (0,8) and (8,0)
lets move on two second equation: y=x-4
x int: 0=x-4
4=x
y int y=0-4
y=-4
so the 2 coordinate points are (4,0) and (0,4)
lets graph these two equations and see where they intersect:
(see graph below), the intersection is at (6,2) so (6,2) is our answer
hope this helps
A survey was taken of students in math classes to find
out how many hours per day students spend on social
media. The survey results for the first-, second-, and
third-period classes are as follows:
First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9, 2, 4, 3,0
Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1, 3
Which is the best measure of center for second period
and why?
Answers
I’d say the mean is the best measure for period 2. This is because it doesn’t have any extremely low or high values which could distort the mean value.
If it did ie. 8, then I would choose median as it is less affected by anomalous results
Please please please please help me. i will do anything, anything!! please
Answers
Answer:
[tex]d \approx 2.2[/tex]
Step-by-step explanation:
It is the same process as in previous problems.
Once the origin is the point (0, 0):
[tex]d=\sqrt{(x_{1}-x_{2})^2 + (y_{1}-y_{2})^2}[/tex]
[tex]d=\sqrt{(2-0)^2 + (-1-0)^2}[/tex]
[tex]d=\sqrt{2^2 + (-1)^2}[/tex]
[tex]d=\sqrt{5}[/tex]
[tex]d \approx 2.2[/tex]
Answer:
2.2
Step-by-step explanation:
The distance formula
[tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex] with
[tex]x_1=0\\y_1=0\\x_2=2\\y_2=-1[/tex]
[tex]\sqrt{(0-2)^2+(0-(-1))^2}=\sqrt{2^2+1^2}=\sqrt{5}[/tex]
[tex]\sqrt{5} =2.2360...=2.2[/tex]
Which best describes the relationship between the line that passes through the points (-9, 2) and (-5, 4) and the line that passes through the points (-3, 4) and (1, 6)?
Answers
Answer:
Parallel!
Step-by-step explanation:
If you put these points on a graph and connect the dots to be two lines, they are perfectly side to side :)
4 builders are building some new classrooms at Trinity. It takes them 5 months to build the classrooms. How long will it take 10 builders?
Answers
Answer:
it takes
[tex]\boxed {\red {2 \: \: months}}[/tex]
for 10 builders
Step-by-step explanation:
[tex]4 \: \: \: builders = 5 \: month \\ 10 \: builders = x[/tex]
Let us solve
[tex]4 = 5 \\ 10 = x[/tex]
so
[tex]4 = x \\ 10 = 5[/tex]
use cross multiplication
[tex]5 \times 4 = 10 \times x \\ 20 = 10x \\ \frac{20}{10} = \frac{10x}{10} \\ \green {x = 2}[/tex]
Answer:
[tex]\boxed{2months}[/tex]
Step-by-step explanation:
B1 = 4
M1 = 5
B2 = 10
M2 = x (we have to find this)
Since it is an inverse proportion (more builders will take less time and vive versa), we'll write it in the order of
=> B1 : B2 = M2 : M1
=> 4:10 = x : 5
Product of Means = Product of Extremes
=> 10*x = 4*5
=> 10x = 20
Dividing both sides by 10
=> x = 2 months
So, it will take 2 months to build classrooms by 10 builders.
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
Answers
Answer:
t = 5.6 day
t =5 days 14 hours 24 minutes
Step-by-step explanation:
Half life is the time it will take for the original value or quantity I'd a particular substance to decrease by half of it's original self.
N = N•e(-kt)
N• = 25
K = 0.1229
Then
N = 25/2 = 12.5
The reason because at the half life , it's original value will decrease to half.
Let's solve for the half life t
N = N•e(-kt)
12.5 = 25e(-0.1229t)
12.5/25 = e(-0.1229t)
0.5 = e(-0.1229t)
In 0.5 =-0.1229t
-0.69314 = -0.1229t
-0.69314/-0.1229 = t
5.6399 = t
To the nearest tenth
5.6 days = t
7.1 A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then she wins one-half of the value that appears on the die. Determine her expected winnings.
Answers
Answer:
1.875
Step-by-step explanation:
To find the expected winnings, we need to find the probability of all cases possible, multiply each case by the value of the case, and sum all these products.
In the die, we have 6 possible values, each one with a probability of 1/6, and the value of each output is half the value in the die, so we have:
[tex]E_1 = \frac{1}{6}\frac{1}{2} + \frac{1}{6}\frac{2}{2} +\frac{1}{6}\frac{3}{2} +\frac{1}{6}\frac{4}{2} +\frac{1}{6}\frac{5}{2} +\frac{1}{6}\frac{6}{2}[/tex]
[tex]E_1 = \frac{1}{12}(1+2+3+4+5+6)[/tex]
[tex]E_1 = \frac{21}{12} = \frac{7}{4}[/tex]
Now, analyzing the coin, we have heads or tails, each one with 1/2 probability. The value of the heads is 2 wins, and the value of the tails is the expected value of the die we calculated above, so we have:
[tex]E_2 = \frac{1}{2}2 + \frac{1}{2}E_1[/tex]
[tex]E_2 = 1 + \frac{1}{2}\frac{7}{4}[/tex]
[tex]E_2 = 1 + \frac{7}{8}[/tex]
[tex]E_2 = \frac{15}{8} = 1.875[/tex]
if a varies inversely as the cube root of b and a=1 when b=64, find b
Answers
Answer:
b = 64/a³
Step-by-step explanation:
Using the given information, we can only find a relation between a and b. We cannot find any specific value for b.
Since a varies inversely as the cube root of b, we have ...
a = k/∛b
Multiplying by ∛b lets us find the value of k:
k = a·∛b = 1·∛64 = 4
Taking the cube of this equation gives ...
64 = a³b
b = 64/a³ . . . . . divide by a³
The value of b is ...
b = 64/a³
expand the linear expression 4(10x -4)
Answers
Answer:
40x - 16
Step-by-step explanation:
(see attached for reference)
By utilizing the distributive property:
4(10x -4)
= (10x)(4) -4 (4)
= 40x - 16
Answer:
4x10x= 40x -4x4=-16 40xtimes-4<-----------thats your answer
Step-by-step explanation:
A bread recipe calls for 2 1/2 cups of whole wheat flour 2/3 cups of rice flour 2 1/4 cups of white flour how many total cups of flour are needed write your answer as a simplified mixed number
Answers
Answer:
5 5/12
Step-by-step explanation:
you find the common denominator which is 12
2 6/12
8/12
2 3/12
now u add them all
hope this helps
Answer:
5 5/12 cups
Step-by-step explanation:
The Marine Corps is ordering hats for all the new recruits for the entire next year. Since they do not know the exact hat sizes they will use statistics to calculate the necessary numbers. This is the data from a sample of the previous recruits: 7.2, 6.8, 6, 6.9, 7.8, 6.2, 6.4, 7.2, 7.4, 6.8, 6.7, 6, 6.4, 7, 7, 7.6, 7.6, 6, 6.8, 6.4 a. Display the data in a line plot and stem-and-leaf plot. (These plots don’t need to be pretty; just make sure I can make sense of your plots.) Describe what the plots tell you about the data. b. Find the mean, median, mode, and range. c. Is it appropriate to use a normal distribution to model this data? d. Suppose that the Marine Corps does know that the heights of new recruits are approximately normally distributed with a mean of 70.5 inches and a standard deviation of 1.5 inches. Use the mean and standard deviation to fit the new recruit heights to a normal distribution and estimate the following percentages. d1. What percent of new recruits would be taller than 72 inches? d2. What percent of new recruits would be shorter than 67.5 inches? d3. What percent of new recruits would be between 69 and 72 inches? d4. Between what two heights would capture 95% of new recruits?? By using statistics are the numbers changed to whole numbers?
Answers
Answer:
60-|||
61-
62-||
62
64-|||
65
66
67-|
68-|||
69-|
70-||
71
72-||
73
74-||
75
76-||
77
78-|
This is a stem and leaf plot.
mean is 138.2/20=6.91
median of 20 is half way between 10th and 11th or an ordered plot. The 10th and the 11th are both 6.8, so that is the median.
6.4 and 6.8 are modes, but they are so minimal I would say there isn't a clear mode.
The range is 1.8, the largest-the smallest
This is not a normal distribution.
z=(x-mean) sd
a.(72-70.5)/1.5=1 so z>1 is the probability or 0.1587.
b.shorter than 67.5 inches is (67.5-70.5)/1.5 or z < = -2, and probability is 0.0228.
c.Between 69 and 72 inches is +/- 1 sd or 0.6826.
95% is 1.96 sd s on either side or +/- 1.96*1.5=+/- 2.94 interval on either side of 70.5
(67.56, 73.44)units in inches
Step-by-step explanation:
4
The equation of a circle is x2 + y2 + x + Dy+ E= 0. If the radius of the circle is decreased without changing the coordinates of the center point, how are the coefficients CD,
and E affected?
O A CD, and E are unchanged.
Answers
Answer:
Step-by-step explanation:
in x²+y²+2gx+2fy+c=0
center=(-g,-f)
radius=√((-g)²+(-f)²-c)
if center is not changed ,then c will change .
Here only coefficients of E will change.
what is the axis of symmetry of f(x)=-3(x+2)^2+4
Answers
Answer:
line passes through the vertex
Step-by-step explanation:
f(x)=-3(x+2)^2+4
x=-2 it is the x of the vertex
A metal alloy is 27% copper. Another metal alloy is 52% copper. How much of each should be used to make 22 g of an alloy that is 36.09% copper?
Answers
Answer:
14.0008 grams of 27% and 7.9992 grams of 52%
Step-by-step explanation:
We know that in the end we want 22 grams of 36.09% copper, meaning in the end we want 36.09% of the 22 grams to be copper. This means we can multiply 36.09% by 22 to see how much copper we want in the end.
To find out how much of each alloy to use, we can multiply the percentage of copper in the alloy be a variable x, which will be how much of that alloy we use. For the other alloy, we can multiply the percentage by (22-x) grams as we know in the end we want 22 grams and if x+y=22, than y would equal 22-x, and in this case this simplifies it to only use a single variable.
Now finally, making the equation we get 27x+52(22-x)=36.09(22). We can solve this and get 27x+1144-52x=793.98, then combine like terms and get -25x+1144=793.98. Next you have to subtract 1144 from both sides to get -25x=-350.02. Dividing both sides by -25 we get x=14.0008. This is how many grams of 27% copper was used. Now we can subtract this from 22 to get how much 52% copper was used, and we get 22-14.0008=7.9992 grams of 52% copper.
The lengths of adult males' hands are normally distributed with mean 190 mm and standard deviation is 7.4 mm. Suppose that 45 individuals are randomly chosen. Round all answers to 4 where possible.
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
For the group of 45, find the probability that the average hand length is less than 189.
Find the third quartile for the average adult male hand length for this sample size.
For part b), is the assumption that the distribution is normal necessary?
Answers
Answer:
a. The distribution of the sample means is normal with mean 190 mm and standard deviation 1.1031 mm.
b. The probability that the average hand length is less than 189 is P(M<189)=0.1823.
c. The third quartile for the average adult male hand length for this sample size is M_75=190.7440.
d. The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.
Step-by-step explanation:
We have a normal distribution, with mean 190 and standard deviation 7.4.
We take samples of size n=45 from this population.
Then, the sample means will have a distribution with the following parameters:
[tex]\mu_s=\mu=190\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{7.4}{\sqrt{45}}=\dfrac{7.4}{6.7082}=1.1031[/tex]
The probability that the sample mean is less than 189 can be calculated as:
[tex]z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{189-190}{7.4/\sqrt{45}}=\dfrac{-1}{1.1031}=-0.9065\\\\\\P(M<189)=P(z<-0.9065)=0.1823[/tex]
The third quartile represents the value of the sample where 75% of the data is to the left of this value. It means that:
[tex]P(M<M^*)=0.75[/tex]
The third quartile corresponds to a z-value of z*=0.6745.
[tex]P(z<z^*)=0.75[/tex]
Then, we can calculate the sample mean for the third quartile as:
[tex]M=\mu_s+z^*\sigma_s=190+0.6745\cdot 1.1031=190+0.7440=190.7440[/tex]
The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.
16 square meters is equivalent to how many square yards?
Answers
Answer:
16 square meters is equivalent to 19.14 square yards
Hope this helps you
How many solutions does the system have? { y = − 3 x + 9 3 y = − 9 x + 9 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ y=−3x+9 3y=−9x+9
Answers
Answer:
no solutions
Step-by-step explanation:
y = − 3 x + 9
3 y = − 9 x + 9
Multiply the first equation by -3
-3(y )=-3( − 3 x + 9)
-3y = 9x -27
3 y = − 9 x + 9
-------------------------
0 = 0 -18
0 = -18
This is never true so there are no solutions
Answer:
for kahn academy -- b -- ( no solutions)
Step-by-step explanation:
a patient receives 65 grams of medicine if its increased by 20% how many grams is that
Answers
Responda:
13 gramas
Explicação passo a passo:
65 + 20% = 13
Find the length of UC
Answers
Answer: 25 units
Step-by-step explanation:
Simply do 40(UN)-15(CN) to get 25(UC)
Hope it helps <3
Answer:
25Option D is the correct option
Solution,
Here,
UN = 40
CN = 15
Now,
UN = UC + CN
plugging the values,
40 = UC + 15
-UC = 15 - 40
-UC = -25
The difference sign (-) will be cancelled in both sides:
UC = 25
hope this helps...
Good luck on your assignment..
The additive inverse of x/y is
Answers
Answer
The additive inverse is
-x/-y
That is equal to x/y
hope this may help you
How many multiples of 4, that are smaller than 1,000, do not contain any of the digits 6, 7, 8, 9 or 0?
Answers
Answer:
44
Step-by-step explanation:
11×4
hope it helped!
Given a triangle with: a =
150, A = 75°, and C = 30°
Using the law of sines gives: c = 0
Answers
Answer:
[tex] c = 77.6 [/tex]
Step-by-step explanation:
You may have entered the measure of a side as the measure of an angle.
[tex] \dfrac{\sin A}{a} = \dfrac{\sin C}{c} [/tex]
[tex] \dfrac{\sin 75^\circ}{150} = \dfrac{\sin 30^\circ}{c} [/tex]
[tex] c\sin 75^\circ = 150 \sin 30^\circ [/tex]
[tex] c = \dfrac{150 \sin 30^\circ}{\sin 75^\circ} [/tex]
[tex] c = 77.6 [/tex]
You are correct. Good job!
1) A grocer sold 5 kg of wheat flour at Rs 30 per kg and gained 20%. If he had sold
it at Rs 27 per kg, what would be his gain or loss percent?
Answers
Answer:
given,
selling price (sp)=rs 5 ×30
=rs 150
now, gain %=20%
cost price (cp)=
[tex] \frac{sp \times 100}{100 + gain\%} [/tex]
[tex] = \frac{150 \times 100}{100 + 20} [/tex]
therefore cp= rs125
now,
again in 2nd case
sp= rs 27×5
therefore sp=rs 135
and cp= rs125
now, sp>cp so,
[tex]gain\% = \frac{sp - cp}{cp} \times 100\%[/tex]
or, gain=
[tex] = \frac{135 - 125}{125} \times 100\%[/tex]
therefore gain %= 8%.... is answer
hope it helps..
Find the area of the irregular figure. Round to the nearest hundredth.
Answers
Answer:
23.14
Step-by-step explanation:
Solve for the area of the figure by dividing it up into parts. You can divide into a half-circle and a triangle
Half-Circle
The diameter is 6. This means that the radius is 3. Use the formula for area of a circle. Divide the answer by two since you only have a half-circle.
A = πr²
A = π(3)²
A = 9π
A = 28.274
28.274/2 = 14.137
Triangle
The base is 3 and the height 6. Use the formula for area of a triangle.
A = 1/2bh
A = 1/2(6)(3)
A = 3(3)
A = 9
Add the two areas together.
14.137 + 9 = 23.137 ≈ 23.14
The area is 23.14.
Answer:
23 sq. unitsStep-by-step explanation:
The figure consists of a semi circle and a triangle
Area of the figure = Area of semi circle + Area of triangle
Area of semi circle is 1/2πr²
where r is the radius
radius = diameter/2
radius = 6/2 = 3
Area of semi circle is
1/2π(3)²
1/2×9π
14.14 sq. units
Area of a triangle is 1/2×b×h
h is the height
b is the base
h is 6
b is 3
Area of triangle is
1/2×3×6
9 sq. units
Area of figure is
14.14 + 9
= 23.14
Which is 23 sq. units to the nearest hundredth
Hope this helps you.
Eric works for salary of $3,500 per month. He has federal income withheld at the rate of 15%, Social Security tax at the rate of 6.2%, Medicare tax at the rate of 1.45% and health insurance premiums of $48 per month. Erik also contributes to a savings plan. Each month, 2% of his gross pay is placed in the savings plan.
After Erik pays the taxes on his money what is Eric's net pay?
A. (1,448.45)
B. (1,799.05)
C. (2,589.25)
D. (2799.05)
Answers
Answer:
C. 2,589.25
Step-by-step explanation:
Salary=$3500
Less:
Federal income withheld
15% of $3500
=15/100×$3500
=$525
Social security tax of 6.2%
6.2% of $3500
=6.2/100 × $3500
=$217
Medicare tax of 1.45%
1.45% of $3500
1.45/100 × $3500
=$50.75
Health insurance premium=$48
Savings plan of 2%
2% of $3500
=2/100 × $3500
=$70
Total less:= $525 + $217 + $50.75 + $48 + $70
Eric's net pay =$3500 - $910.75
=$2,589.25
Answer:
c
Step-by-step explanation:
A line through the points (2, -9) and (j, 17) is parallel to the line 2x + 3y = 21. What is the value of j?
Answers
Answer:
j = -37
Step-by-step explanation:
First find the slope of 2x + 3y = 21
Solve for y
Subtract 2x from each side
2x-2x + 3y =-2x+ 21
3y = -2x+21
Divide by 3
3y/3 = -2x /3 + 21/3
y = -2/3 x +7
This is in slope intercept form y = mx+b where m is the slope and b is the y intercept
m = -2/3
The slope of parallel lines are equal
Using the two points
m = (y2-y1)/(x2-x1)
-2/3 = (17 - -9)/(j-2)
-2/3 = (17 +9)/(j-2)
Using cross products
-2(j-2) = 3 ( 17+9)
-2j +4 = 26*3
-2j +4 = 78
Subtract 4 each side
-2j = 78-4
-2j = 74
Divide by -2
-2j/-2 = 74/-2
j = -37
The slope of the line passing through the points (7, 5) and (21, 15) is
Answers
Answer:
5/7
Step-by-step explanation:
We are given two points so we can find the slope by using
m = (y2-y1)/(x2-x1)
= (15-5)/(21-7)
=10/14
5/7