Answer:
Using the concepts of coordinate system and equation of line, we find that y ≥ (1/3)x + 3 and 3x-y > 2 are represented by the graph.
Step-by-step explanation:
Equation of line passes through points (a, b) and (c, d) is given by:
y-b = [(d-b) / (c-a)] / (x-a)
Given that the first solid line (≤ or ≥) has a positive slope and goes through (0, 3) and (3, 4).
y-3 = [(4-3) / (3-0)] / (x-0)
y-3 = x / 3
y - (1/3)x = 3
Also, everything above the line is shaded, i.e. the inequality represents the first graph: y ≥ (1/3)x + 3
The second dashed line (< or >) has a positive slope and goes through (0, - 2) and (1, 1).
y+2 = [(1+2) / (1-0)](x-0)
y+2 = 3x
3x-y = 2
Everything to the right of the line is shaded.
i.e. inequality represents the second graph: 3x-y > 2
Hence, the system of linear inequalities is represented by the graph :
y ≥ (1/3)x + 3
3x-y > 2
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Answer:
D
Step-by-step explanation:
Got it right on edge 2022
x(y − 3) + n(3 − y)
please help!! The dot plots below show the ages of students belonging to two groups of salsa classes:
Based on visual inspection, which group most likely has a lower mean age of salsa students? Explain your answer using two or three sentences. Make sure to use facts to support your answer.
Im thinking group A but at this point im just plain out confused
PLEASE HELP I WILL MARK BRAINLEST
#1
Error at sign shift due to -Correct version
[tex]\\ \rm\Rrightarrow (x^3+2x^2-x)-(3x^3-3x^2+2x-4)[/tex]
[tex]\\ \rm\Rrightarrow x^3+2x^2-x-3x^3+3x^2-2x+4[/tex]
[tex]\\ \rm\Rrightarrow x^3+5x^2-3x+4[/tex]
#2
Not multiplied 3x with x[tex]\\ \rm\Rrightarrow (x^2-3x+2)(x+1)[/tex]
[tex]\\ \rm\Rrightarrow x(x^2-3x+2)+x^2-3x+2[/tex]
[tex]\\ \rm\Rrightarrow x^3-3x^2+2x+x^2-3x+2[/tex]
[tex]\\ \rm\Rrightarrow x^3-2x^2-x+2[/tex]
can someone please help and explain its due in a littleee
[tex]f(x) = {x}^{2} - 3x + 2 [/tex]
••••••••••••••••••••••••••••••••••••••••put x = (-1)
[tex] f( - 1) = {( - 1)}^{2} - 3 \times ( - 1) + 2 \\ \\ 1 + 3 + 2 \\ \\ 6.[/tex]
••••••••••••••••••••••••••••••••••••••••put x = (z)
[tex] f(z) = {z}^{2} - 3 \times z + 2 \\ \\ {z}^{2} - 3z + 2 \\ \\ {z}^{2} - 2z - z + 2 \\ \\ z(z - 2) - 1(z - 2) \\ \\ (z - 1)( z -2 ) \\ \\ (z - 1) = 0 \: \: , \: \: (z - 2) = 0\\ \\ z = 1 \:, \: 2[/tex]
••••••••••••••••••••••••••••••••••••••••put x = (x+1)
[tex]f(x + 1) = {x}^{2} - 3x + 2 \\ \\ {(x + 1)}^{2} - 3 (x + 1) + 2 \\ \\ {x}^{2} + 1 + 2x - 3x - 3 + 2 \\ \\ {x}^{2} - x \\ \\ x(x - 1) \\ \\ x(x - 1) = 0 \\ \\ x - 1 = \frac{0}{x} \\ \\ x - 1 = 0 \\ \\ x = 1.[/tex]
•••••••••••••••••••••••••••••••••put x = (√2 + 1 )
[tex]f( \sqrt{2} + 1) = {x}^{2} - 3x + 2 \\ \\ {( \sqrt{2} + 1) }^{2} - 3( \sqrt{2} + 1) + 2 \\ \\ 2 + 1 + 2\sqrt{2} - 3 \sqrt{2} - 3 + 2 \\ \\ 3 - 1 \sqrt{2} - 1 \\ \\ 2 - \sqrt{2} \\ \\ 2 - 1.4 (optional \: \: \: steps)\\ \\ 0.6 \: \: [/tex]
A 2-column table with 6 rows. The first column is labeled t with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 12, m, 4, 0, negative 4, negative 2. If the table of the function contains exactly two potential turning points, one with an input value of –1, which statement best describes all possible values of m? m ≥ –12 –12 < m < 4 m ≤ 4 m ≥ 4 or m ≤ –12
Answer:
B
Step-by-step explanation:
right on edg3
y=-6x-8
y=-6x+8
Solve the system of linear equations
Answer: No solution
Step-by-step explanation:
Both of these equations have the same number as to coefficient of x (-6) but have a different constant (-8 and 8). This means that there are no solutions to this system of equations.
i need help finding this for clever
Answer:
The dog is 16 years old.
Step-by-step explanation:
X/4 + 6 = X/8 + 8
X/4-X/8 = 8-6
0.125X = 2
X = 2/0.125
X = 16
Answer:
16 years old
Step-by-step explanation
Dividing the dog’s age by 4 and adding 6
D÷4 + 6
dividing the dog’s age by 8 and adding 8
D÷8 + 8
equating both
D÷4 + 6 = D÷8 + 8
=> D÷4 - D÷8 = 2
multiplying by 8 both sides
=> 2D - D = 16
=> D = 16
hence, the dog is 16 years old
Maria is on a hike. if she hikes to the scenic lookout on the following map first, she will have to hike farther than if she went straight to the end of the hike. 3 connected points on a coordinate plane. the point labeled, "maria," is at 4, -4. the point labeled, "end," is at -5, 5. a solid line connect the points "maria" and "end." the point labeled, "scenic lookout," is at 2, 3. dashed lines connect "maria" to "scenic lookout" and connect "scenic lookout" to "end." coordinate values on the map are in kilometers. how much shorter is the path straight to the end of the hike than past the scenic lookout? round your final answer only to the nearest kilometer. \text{km}kmstart text, k, m, end text
The path straight to the end of the hike is 6 km farther than past the scenic lookout.
How to determine the difference in the parts?The map is not given, but the question can still be answered
From the question, the positions are given as::
Maria = (4, -4)
Scenic = (2, 3)
End = (-5, 5)
The distance between Maria and the end point is calculated using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]Route\ 1 = \sqrt{(4 + 5)^2 + (-4 -5)^2}[/tex]
[tex]Route\ 1 = 13[/tex]
The distance between Maria and the scenic lookout is calculated using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]Route\ 2 = \sqrt{(4 - 2)^2 + (-4 -3)^2}[/tex]
[tex]Route\ 2 = 7[/tex]
The distance between both routes is:
Distance = 13 - 7
Evaluate
Distance = 6
Hence, the path straight to the end of the hike is 6 km farther than past the scenic lookout.
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Which equation is equivalent to the given equation?
-4(X - 5) + 8x = 9x - 3
Answer:
-5x=-23
Or
X=23/5
Step-by-step explanation:
Calculate the AREA of the shape below. Give your answer in cm²
Answer:
[tex] \boxed{\bf 26\: cm^2} [/tex]Step-by-step explanation:
We got two shapes in the given figure,on the right we got a rectangle and on the left we have a square.
Area of rectangle:-
[tex]\bf 5 \times 2[/tex][tex]\bf 10 \:cm^{2} [/tex]Area of square :-
[tex]\bf 4 \times 4[/tex][tex]\bf 16 \: {cm}^{2} [/tex]Total area :-
[tex]\bf 10 + 16[/tex][tex]\boxed{\bf 26 \: {cm}^{2} }[/tex]_________________________Answer:
26 cm^2Step-by-step explanation:
you have two rectangles, the bigest has the base of 6cm and the height of 4cm, the area is 6 * 4 = 24cm ^ 2, the other rectangle has the base of 6 - 4 = 2 and the height of 5 - 4 = 1, 2*1=2.
we add the dimensions and we have the area of the complete figure 24 + 2 =
26 cm ^ 2
solve the inequality 5x+3> 48
Answer:
x > 9
Step-by-step explanation:
for this inequality, we want to isolate x, so that we know the inequality of x
5x + 3 > 48
- 3 -3 {subtract 3 from both sides to get x alone}
5x > 45
/5 /5 {divide both sides by 5 to find 1x}
x > 9
So , x > 9 is the inequality in terms of x {is the solution}
hope this helps! :)
Answer:
[tex]\huge\boxed{\sf x > 9}[/tex]
Step-by-step explanation:
Given inequality:5x + 3 > 48
Subtract 3 to both sides
5x > 48 - 3
5x > 45
Divide 5 to both sides
x > 9
[tex]\rule[225]{225}{2}[/tex]
Find the coordinates of the midpoint of the segment whose endpoints are given W (-3,-7) and X (-8,4)
1. (-11/2) -(11/2)
2.(-5/2)-(3/2)
3.(-5/2-(11/2)
The coordinates of the midpoint of the segment whose endpoints are W (-3,-7) and X (-8,4) will be (-11/2, -3/2). Then the correct option is D.
The complete options are given below.
1. (-11/2) -(11/2)
2.(-5/2)-(3/2)
3.(-5/2-(11/2)
4. (-11/2) -(-3/2)
What is the midpoint of line segment AB?Let C be the mid-point of the line segment AB.
A = (x₁, y₁)
B = (x₂, y₂)
C = (x, y)
Then the midpoint will be
x = (x₁ + x₂) / 2
y = (y₁ + y₂) / 2
The end points are given below.
(-3, -7) and (-8, 4)
We have
(x₁, y₁) = (-3, -7)
(x₂, y₂) = (-8, 4)
Then the mid-point will be
x = (- 3 - 8) / 2
x = -11 / 2
y = (-7 + 4) / 2
y = -3/2
Then the coordinates of the midpoint of the segment whose endpoints are W (-3,-7) and X (-8,4) will be (-11/2, -3/2).
Then the correct option is D.
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Find the Value of log10 (0.0001). Rescue me!
Let's see
[tex]\boxed{\sf log_aa=1}[/tex]
Now
[tex]\\ \rm\Rrightarrow log_{10}0.0001)[/tex]
[tex]\\ \rm\Rrightarrow log_{10}10^{-4}[/tex]
[tex]\\ \rm\Rrightarrow -4log_{10}10[/tex]
[tex]\\ \rm\Rrightarrow -4[/tex]
Answer:
This has already been answered correctly, but I'll add an additional perspective. The log of (0.0001 to the base 10 is -4.
Step-by-step explanation:
log(base 10) says give us an exponent, x, that would be required to make [tex]10^{x}[/tex] equal to a specified number, in this case 0.0001.
[tex]10^{0}[/tex] = 1
[tex]10^{1}[/tex] = 10
[tex]10^{-1}[/tex] = 0.1
[tex]10^{-2}[/tex] = 0.01
[tex]10^{-4}[/tex] = 0.0001
The log of (0.0001) to the base 10 is -4.
In a casual italian restaurant, sales for the week of september 15 are as follows: food sales: $10.000 beverage sales: $ 2.500 total $12.500 a. if the food cost is 30 percent, how much did the food actually cost? b. if the beverage cost is 25 percent of beverage sales, how much did the beverages cost?
Answer: $625
Step-by-step explanation:
Total beverage sales = $2,500
Beverage cost = 25%
So, $2,500 x 25% = $2,500 x 0.25 = $625
(Giving 80 points, Please do not answer if you don't know. The second and third answer are not 4 btw)
Point A is on the point −6 and Point B is on the point 0. Let's use the Ruler Postulate to find the length of AB¯¯¯.
AB=|a−b|
AB=|−6−0|
AB=|−6|
AB=6
The length of AB¯¯¯¯ is 6. We can also write this as AB=6 or mAB¯¯¯¯=6.
Find the Length of CD¯¯¯¯
Now, let's find the length of CD¯¯¯¯. Point C is on the point 4 and Point D is on the point 8.
CD=|c−d|
CD=|4−8|
CD=|−4|
CD=4
The length of CD¯¯¯ is 4. We can also write this as CD=4 or mCD¯¯¯=4
Your Turn
1. What is the length of BC¯¯¯? 4
2. What is the length of AC¯¯¯¯?
3. What is the length of AD¯¯¯¯?
Answer:
1. 4
2. 10
3. 14
Step-by-step explanation:
A = -6
B = 0
C = 4
D = 8
1. BC = |0 - 4| = 4
2. AC = |-6 - 4| = |-10| = 10
3. AD = |-6 - 8| = |-14| = 14
Answer:
1. BC = 4
2. AC = 10
3. AD = 14
Step-by-step explanation:
Ruler Postulate
The distance between any two points on a number line is their difference.
Question 1
Given:
Point B = 0Point C = 4Therefore, using the Ruler Postulate:
⇒ BC = |b - c|
⇒ BC = |0 - 4|
⇒ BC = |-4|
⇒ BC = 4
Question 2
Given:
Point A = -6Point C = 4Therefore, using the Ruler Postulate:
⇒ AC = |a - c|
⇒ AC = |-6 - 4|
⇒ AC = |-10|
⇒ AC = 10
Question 3
Given:
Point A = -6Point D = 8Therefore, using the Ruler Postulate:
⇒ AD = |a - d|
⇒ AD = |-6 - 8|
⇒ AD = |-14|
⇒ AD = 14
Help me with steps please!
Answer:
18, 36, 54
Step-by-step explanation:
Find the least common multiple of 6 and 9:
Multiples of 6: 6, 12, 18, ......
Multiples of 9: 9, 18, 27, ......
We see that 18 is the least common multiple of 6 and 9.
Additional multiples of 18 are 36 and 54.
If an integer is divisible by 6 and by 9 , then the integer must be divisible by 54.
How to estimate an integer which is divisible by 6 and by 9?Consider the statement as a contradiction.
The assertion exists that any natural number divisible by 6 and 9 exists also divisible by 54.
Let us consider divisible to mean that the outcome of the division of the number and 54 provides another natural number. We can take the prime factors of 6 and 9 which are {2,3} and {3,3}. We can consider that the product [tex]$2 \times 3 \times 3=18$[/tex] exists a number that exists divisible by 6 and 9 but exists not divisible by 54. Another instance exists the product of [tex]$2 \times 2 \times 3 \times 3=36$[/tex] which exists also not divisible by 54.
Therefore, the correct answer is option e) 54.
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On Tuesday, a city’s parking meter income is up $311 from Monday’s income, m. So, Tuesday’s income is m + 311
If m is 894, what is m + 311
Which of the following is equivalent to 8-3x > 2(3x - 5) ?
A. 18>9x
B. 9x<13
C. 11>9x
D. -8x>2
Answer:
A
Step-by-step explanation:
Given:
[tex]8-3x > 2(3x-5)[/tex]
Simplify by distributing:
[tex]8-3x > 6x-10[/tex]
Add 10 to left side and add 3x to the right side:
[tex]18 > 9x[/tex]
Pls help asap ily
one hour after junior space cadet had left his house, his sister gwen discovered that he had forgotten his head. if junior was driving at a speed of 50 mph, and gwen drove at a speed of 75 mph, how many hours did it take gwen to restore junior's head to his shoulders?
Answer:
2 hours
Step-by-step explanation:
you can write two linear equations and then set them equal to each other to see when they intersect. so for the first equation which will be representing the junior space cadets distance from his house. this can be written as
d = 50t + 50
where t represents time and d represents distance. there is 50 being added to the equation since he had already been traveling for an hour
the second equation which will represent his sister Gwen can be represented as
d = 75t
Now we set them equal to each other
50t + 50 = 75t
50 = 25t
2 = t
Write the rate in lowest terms a printer can print 22 pages in 55 seconds
Answer:
2/5
Step-by-step explanation:
22/11=2
55/11=5
Consider the transformation shown. 2 triangles are shown. The first is labeled pre-image and the second is labeled image. Both triangles have congruent angle measures. The pre-image has side lengths of 6, 10, and 8. The image has side lengths of 3, 5, and 4. Use the drop-down menus to complete the sentence. The transformation is because the preserved.
The transformation is non-rigid because the side lengths are not preserved.
How to complete the drop-down menus?The drop-down menus and the image of the triangles are not given.
However, the question can still be solved using the available parameters.
The given parameters are:
Pre-image: 6, 10, 8
Image: 3, 5, 8
See that the side lengths of the image and the pre-image are not the same
This means that the transformation is a non-rigid transformation
Hence, the complete statement is the transformation is non-rigid because the side lengths are not preserved.
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what 1 - 2/9 - 1/3 - 1/6 =
Answer:
5/18
Step-by-step explanation:
The LCD of 9, 3, and 6 is 18.
1 - 2/9 - 1/3 - 1/6 =
= 18/18 - 4/18 - 6/18 - 3/18
= 5/18
Answer: 5/18
Step-by-step explanation:
1/1 - 2/9 - 1/3 - 1/6
18 - 4 - 6 - 3/18
5/18
This is all the questions I need answers to:
A two-digit locker combination has two non-zero digits and no two digits are the same. Event A is defined as choosing an even digit for the first number, and event B is defined as choosing an odd digit for the second number.
If a combination is picked at random, with each possible locker combination being equally likely, what is P(B|A) expressed in simplest form?
A. 4/9
B. 1/2
C. 5/9
D. 5/8
A locker combination consists of two non-zero digits, and each combination consists of different digits. Event A is defined as choosing an even number as the first digit, and event B is defined as choosing an even number as the second digit.
If a combination is picked at random, with each possible locker combination being equally likely, what is P(A and B) expressed in simplest form?
A. 1/6
B. 5/18
C. 1/2
D. 5/9
A jar contains 5 red marbles and 8 white marbles.
Event A = drawing a white marble on the first draw
Event B = drawing a red marble on the second draw
If two marbles are drawn from the jar, one after the other without replacement, what is P(A and B) expressed in simplest form?
A. 3/13
B. 10/39
C. 5/12
D. 8/13
A bag contains 5 blue marbles, 8 green marbles, 4 red marbles, and 3 yellow marbles.
Event A = drawing a green marble on the first draw
Event B = drawing a blue marble on the second draw
If Jasmine draws two marbles from the bag, one after the other and doesn’t replace them, what is P(B|A) expressed in simplest form?
A. 2/19
B. 1/6
C. 4/19
D. 5/19
A jar contains 3 pink balls, 6 blue balls, and 3 red balls.
Event A = drawing a red ball on the first draw
Event B = drawing a pink ball on the second draw
If two balls are drawn from the jar, one after the other without replacement, what is P(A and B) expressed in simplest form?
A. 3/44
B. 4/9
C. 3/11
D. 1/4
House numbers along a street consist of two-digit numbers. Each house number is made up of non-zero digits, and no digit in a house number is repeated.
Event A is defined as choosing 8 as the first digit, and event B is defined as choosing a number less than 6 as the second digit.
If a house number along this street is picked at random, with each number being equally likely and no repeated digits in a number, what is P(A and B) expressed in simplest form?
A. 1/9
B. 5/72
C. 5/8
D. 2/3
House numbers along a street consist of two-digit numbers. Each house number is made up of non-zero digits, and no digit in a house number is repeated.
Event A is defined as choosing 8 as the first digit, and event B is defined as choosing a number less than 6 as the second digit.
If a house number along this street is picked at random, with each number being equally likely and no repeated digits in a number, what is P(A and B) expressed in simplest form?
A. 2/7
B. 5/14
C. 5/13
D. 6/13
A two-digit locker combination is made up of two non-zero digits. Digits in a combination are not repeated and range from 3 through 8.
Event A = choosing an odd number for the first digit
Event B = choosing an odd number for the second digit
If a combination is chosen at random, with each possible locker combination being equally likely, what is P(A and B) expressed in simplest form?
A. 1/5
B. 3/14
C. 5/18
D. 2/5
A locker combination consists of two non-zero digits. The digits in a combination are not repeated and range from 2 through 9.
Event A = the first digit is an odd number
Event B = the second digit is an odd number
If a combination is picked at random with each possible locker combination being equally likely, what is P(B|A) expressed in simplest form?
A. 3/8
B. 3/7
C. 1/2
D. 4/7
There are 15 tiles in a bag. Of these, 7 are purple, 5 are black and the rest are white.
Event A = drawing a white tile on the first draw
Event B = drawing a purple tile on the second draw
If two tiles are drawn from the bag one after the other and not replaced, what is P(B|A) expressed in simplest form?
A. 1/5
B. 1/3
C. 7/15
D. 1/2
I know theres a lot here but please hurry :) thx 100 points to the first person to answer all correctly! thx :)
The is probability P(B|A) expressed in simplest form is 1/2 (Option B) See computation below.
How do we derive the above?P (A) = [[tex][\mathrm{C}_{5}^{1} \mathrm{C}_{8}^{1}]/ \mathrm{A}_{9}^{2}[/tex]
= ('5 x 8)/(9 x 8)
P (A) = '5/9
P (AB) = [tex][\mathrm{C}_{5}^{1} \mathrm{C}_{4}^{1}]/ \mathrm{A}_{9}^{2}[/tex]
= ('5 x 4)/(9 x 8)
= '5/18
P(B|A) = P (AB)/P(A)
= ('5/18)/('5/9)
P(B|A) = 1/2
How do we derive P(A and B) in the simplest form?From the above we already have P (AB)
this is given as
P (AB) = [tex][\mathrm{C}_{5}^{1} \mathrm{C}_{4}^{1}]/ \mathrm{A}_{9}^{2}[/tex]
= ('5 x 4)/(9 x 8)
P(AB) = '5/18
How do we derive P(A and B) in the simplest form where a jar contains 5 red marbles and 8 white marbles?Note that:
Event A = drawing a white marble on the first draw
Event B = drawing a red marble on the second draw
P(A) = 8/13; while
P (B) = (5/12) because the first marble was not replaced, thus reducing th sample to 12.
Thus
P(A and B) = P(A)*P(B) = 8/13 * 5/12
P(A and B) = 10/39 (Option B)
If Jasmine draws two marbles from the bag, one after the other and doesn’t replace them, what is P(B|A) expressed in simplest form?Event A - Probability of Drawing a Green Marble is 8/20
Event B - Probability of Drawing a Blue Marble is 5/19
Thus P(B|A) = (8/20) * (5/19)
= [tex]\frac{8 * 5 }{20 * 19}[/tex]
= 40/380; divide numerator and denominator by 20
P(B|A) = 2/19 (Option A)
Event A = Probability of Drawing a red ball = 3/12
Event A = Probability of Drawing a pink ball without replacing the read in Event A = 3/11
Thus P (B and A) =
3/12 x 3/11
P (B and A) = 3/44 (Option A)
If a house number along this street is picked at random, with each number being equally likely and no repeated digits in a number, what is P(A and B) expressed in simplest form?The conditions given are as follows:
The house number comprises of nonzero digits and are of two digits ranging from 1 to 9.As per the condition, the First digit 8 can be selected in 9 ways; and Second digits is less than 6 can be selected in waysThe sum total of ways thus is
9 x 8
= 72 ways........X
Recall that
Event A is defined as selecting 8 as the first numeral
The only way to select this is one way
Event B is defined as choosing a number less than 6 as the second digit, that is 1, 2, 3, 4, 5
Thus, the possible number of ways to fill second digit = 5/8
Thus, the possible number of ways to form two digits 'AnB' =
('AnB') = 1 x 5 = 5 .................y
Hence Probability (AnB) = 5/72 (Option B)
Given that the non-zero digits are in a combination are not repeated and range from 3 through 8, thus the odd numbers between 3 and 8 are:
3, 5, 7
total numbers is 3, 4, 5, 6, 7, 8
Hence; Event A = choosing an odd number for the first digit = 3/6
Event B = choosing an odd number for the second digit (recall that the numbers are not repeated) = 2/5
= [tex]\frac{2*3}{3*6}[/tex]
= 6/30
= 1/5 (Option A)
If a combination is picked at random with each possible locker combination being equally likely, what is P(B|A) expressed in simplest form?
Event A = the first digit is an odd number
Event B = the second digit is an odd number
The numbers from 2 to 9 are:
2,3,4,5,6,7,8,9
The odd numbers between 2 and 9 are:
3,5,7,9
P (A) = 4/8
P (B) = 3/7
P(B|A) = (3/7)/(4/8)
P(B|A) = 3/7
Event A = drawing a white tile on the first draw
Event B = drawing a purple tile on the second draw
P(B|A) = (P(AnB)/P(A)
|n| = 15 * 14 = 210
| A| = 3*14 = 42
| AnB| = 3*7 = 21
P (A) = 42/210 = 6/30
P (AnB) = 21/210 = 1/10
P(B|A) = (1/10)/6/30)
P(B|A) = 1/10 * 30/6
P(B|A) = 30/60
P(B|A) = 1/2 (Option D)
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Find the indicated side of the
right triangle.
30°
X
X
60
= [?]√]
7
Enter
Answer:
[tex]7\sqrt{3}[/tex]
Step-by-step explanation:
This is a special triangle with the angles being 30-60-90. The adjacent side to the angle of 30 degrees has a length of x * sqrt(3). The opposite side has a length of x. Since the opposite side has a length of 7 here you simply plug that into x * sqrt(3) to find the length of the adjacent side of the angle 30 degrees which gives you 7 * sqrt(3)
Casey picked 6 pounds of strawberries. Karen picked 48 ounces of blueberries. Jude picked 2 pounds of raspberries. They are going to make berry pies. The table shows the amount of berries needed for 1 pie.Select all of the true statements below.
A.
Together, Karen and Jude picked the same weight of fruit as Casey picked.
B.
Casey picked 2 times the weight of fruit that Karen picked.
C.
There are enough berries to make 6 berry pies.
D.
If they make as many pies as they can with the berries they picked, there will be 4 pounds of strawberries left over.
E.
To make 8 berry pies, they will need 1 more pound of blueberries and 2 more pounds of raspberries.
Answer:
Option B is correct
Answer:
B there is enough raspberries to make 4 pie they can 6 pies if they 2 more of raspberries
Drag each tile to the correct box. The water level of a tank every minute since it began filling is indicated by segments A, B, and C on the graph below. A graph represents the water level to fill the tank on Y-axis per time on X-axis. Segments A, B, and C fill the tank from 10 to 60, 60 to 80, and 80 to 110 centimeters in the first 2, next 4, and last 3 minutes. Place the segments in the correct order from the least to the greatest rate of increase in the water level. B A C , ,
The least to greatest slope, the segments are B, C and A.
Given that,
Segments A, B, and C on the graph below represent the water level of the tank every minute since it started filling.
A graph shows the water level needed to fill the tank on the y axis per unit of time on the x axis.
The segment's slope indicates how quickly the water level is rising. The slope, which is determined by the segment's angle with the positive x axis, is the ratio of rise to run.
slope of segment A = 60₋10/2 = 25
slope of segment B = 80₋60/4 = 5
slope of segment C = 110₋80/3 = 10
We can see that section B has the least slope, followed by segment C, and then segment A, which has the greatest slope.
B, C, and A are the segments in descending order of least to greatest slope.
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What is the solution to this equation?
8x-5(x-3) = 18
OA. x=5
OB. x = 1
OC. x = 11
OD. x=7
Answer:
x=1
Step-by-step explanation:
8x-5(x-3) = 18
The first step is to distribute
8x -5x+15 = 18
Combine like terms
3x+15 = 18
Subtract 15 from each side
3x+15-15=18-15
3x=3
Divide by 3
3x/3 =3/3
x=1
What is the effect on the graph of f(x) = x² when it is transformed to
h(x)=x²-16?
A. The graph of f(x) is vertically compressed by a factor of 7 and
shifted 16 units down.
B. The graph of f(x) is horizontally compressed by a factor of 7 and
shifted 16 units down.
C. The graph of f(x) is vertically compressed by a factor of 7 and
shifted 16 units to the right.
D. The graph of f(x) is horizontally stretched by a factor of 7 and
shifted 16 units to the right.
The correct answer is option A which is the graph of f(x) is vertically compressed by a factor of 7 and shifted 16 units down.
What is a graph?
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given functions are:-
f(x) = x²h(x)=x²-16When we plot the graph of the two functions given in the question we will see that the graph of the function F(x) = x²-16 is compressed by the factor 7 and the vertex of the graph shifted to the 16 points down.
Therefore the correct answer is option A which is the graph of f(x) is vertically compressed by a factor of 7 and shifted 16 units down.
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In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply.
m∠R > 90°
m∠S + m∠T < 90°
m∠S = m∠T
m∠R > m∠T
m∠R > m∠S
m∠S > m∠T
Answer:
1. m∠R > 90°
2. m∠S + m∠T < 90°
4. m∠R > m∠T
5. m∠R > m∠S
Step-by-step explanation:
General strategyprove the statement starting from known facts, ordisprove the statement by finding a counterexampleHelpful fact: Recall that the Triangle Sum Theorem states that m∠R + m∠S + m∠T = 180°.
Option 1. m∠R > 90°
Start with m∠R > m∠S + m∠T.
Adding m∠R to both sides of the inequality...
m∠R + m∠R > m∠R + m∠S + m∠T
There are two things to note here:
The left side of this inequality is 2*m∠RThe right side of the inequality is exactly equal to the Triangle Sum Theorem expression2* m∠R > 180°
Dividing both sides of the inequality by 2...
m∠R > 90°
So, the first option must be true.
Option 2. m∠S + m∠T < 90°
Start with m∠R > m∠S + m∠T.
Adding (m∠S + m∠T) to both sides of the inequality...
m∠R + (m∠S + m∠T) > m∠S + m∠T + (m∠S + m∠T)
There are two things to note here:
The left side of this inequality is exactly equal to the Triangle Sum Theorem expressionThe right side of the inequality is 2*(m∠S+m∠T)Substituting
180° > 2* (m∠S+m∠T)
Dividing both sides of the inequality by 2...
90° > m∠S+m∠T
So, the second option must be true.
Option 3. m∠S = m∠T
Not necessarily. While m∠S could equal m∠T, it doesn't have to.
Example 1: m∠S = m∠T = 10°; By the triangle sum Theorem, m∠R = 160°, and the angles satisfy the original inequality.
Example 2: m∠S = 15°, and m∠T = 10°; By the triangle sum Theorem, m∠R = 155°, and the angles still satisfy the original inequality.
So, option 3 does NOT have to be true.
Option 4. m∠R > m∠T
Start with the fact that ∠S is an angle of a triangle, so m∠S cannot be zero or negative, and thus m∠S > 0.
Add m∠T to both sides.
(m∠S) + m∠T > (0) + m∠T
m∠S + m∠T > m∠T
Recall that m∠R > m∠S + m∠T.
By the transitive property of inequalities, m∠R > m∠T.
So, option 4 must be true.
Option 5. m∠R > m∠S
Start with the fact that ∠T is an angle of a triangle, so m∠T cannot be zero or negative, and thus m∠T > 0.
Add m∠S to both sides.
m∠S + (m∠T) > m∠S + (0)
m∠S + m∠T > m∠S
Recall that m∠R > m∠S + m∠T.
By the transitive property of inequalities, m∠R > m∠S.
So, option 5 must be true.
Option 6. m∠S > m∠T
Not necessarily. While m∠S could be greater than m∠T, it doesn't have to be. (See examples 1 and 2 from option 3.)
So, option 6 does NOT have to be true.
Answer: Option 1, 2, 4, & 5 or
A. m∠R > 90°; B. m∠S + m∠T < 90°; D. m∠R > m∠T; & E. m∠R > m∠S
Step-by-step explanation: Trust Me!
m∠R > 90°m∠S + m∠T < 90°m∠R > m∠Tm∠R > m∠S
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The length of a spring varies directly with the mass of an object that is attached to it. When a 30-gram object is attached, the spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s? a s = StartFraction 3 Over 10 EndFraction m b s = StartFraction 10 Over 3 EndFraction m c m = StartFraction 3 Over 10 EndFraction s d m = StartFraction 1 Over 30 EndFraction s
The equation which relates the mass and length according to the task content is; l = (3/10)m.
What is the equation of proportionality?From the task content, it follows that the proportional relationship is direct. Hence, the constant of proportionality k can be evaluated as follows;
l = k × m
Hence, k = l/m = 9/30 = 3/10.
Therefore, the proportional relationship is given by the equation; l = (3/10)m
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