Answers
Answer:
Table B
Step-by-step explanation:
Note that for y to vary inversely as x, an increase in x will cause a decrease in y. Therefore, by careful observation of tables A, B, C, and D, we would notice the following:
In table C:
As x increases from 1 to 2 to 3, y also increases from 26 to 52 to 78. Which means that an increase in x causes an increase in y. This is not an inverse variation.
In table D:
As x increases from 1 to 2 to 3, y also increases from -7 to -1 to 6. Which means that an increase in x causes an increase in y. This is also not an inverse variation.
We are left with options A and B
If y varies inversely as x, the following relationship must hold:
[tex]y \alpha \frac{1}{x}\\y = \frac{k}{x}[/tex]
Where k is a constant of proportionality
considering option B:
When x = 1, y = 36
36 = k/1
k = 36 * 1
k = 36
when x = 2, y = 36/2
y = 18
when x = 3, y = 36/3
y = 12
These tally with all that is indicated in the table. Option B is an inverse variation
Related Questions
The speed at which a bike travels can be determined by the formula s=d/t, where S represents speed, D represents distance, and T represents time. Select yes or no to indicate if the measurement unit given is an appropriate measurement unit for the speed at which a bike travels
Answers
Answer:
Yes, No, Yes
Step-by-step explanation:
Yes for m/s which is meters per second.
No for min/ft which is reversed and should be feet per minute.
Yes for km/h which is kilometers per hour.
The correct unit for speed is distance per time.
Answer:
MPH
Step-by-step explanation:
Which represents the solution(s) of the system of equations, y + 4 = x2 and y – x = 2? Determine the solution set by graphing.
(–2, 0)
(–2, 0) and (2, 0)
(–2, 0) and (3, 5)
no solutions
Answers
Answer:
c
Step-by-step explanation:
c
Answer:
the answer is C ;D
Step-by-step explanation:
what is
5/14 mulitypled by 4 in simplest form
Answers
Answer:1 3/7
Step-by-step explanation:When you multiply the nominator and 4you get 20.So it would 20/14 but if you find the simplest form of fraction you would get 1 3/7
Miriam is setting up a fishing game in a kiddie pool for her niece's birthday party. The pool has a circular base with a diameter of 4 feet and a height of 0.75 feet. She wants to fill the pool halfway so there is plenty of space left for the plastic fish. Approximately how many cubic feet of water does she need? 9.4 1.5 2.4 4.7
Answers
Answer:
4.7 feet³ of water
Step-by-step explanation:
Diameter of 4 feet
Radius = 2 feet
Height = 0.75 feet
Formula for Volume = 2·[tex]\pi[/tex]·radius·height
But she only wants to fill half, so divide by 2, cancels the 2 in the formula for volume, giving us: [tex]\pi[/tex]·radius·height
[tex]\pi[/tex]·2·0.75 = 4.71 feet³
6 root 5 plus 6 root 5
Answers
Answer:
12√5
Step-by-step explanation:
6√5 + 6√5 = (6 + 6) * √5 = 12 * √5 = 12√5.
Answer:
12 [tex]\sqrt{5}[/tex]
Step-by-step explanation:
When you add the surds which are the same type, (both are root 5), just add the integers before them together.
A 14 foot ladder is leaning against a building. The ladder makes a 45 degree angle with the building. How for up the building does the ladder reach?
Answers
Answer:
[tex]7\sqrt{2}[/tex]
Step-by-step explanation:
Use trigonometry.
sin 45 degrees = x/14
plug in values and you get x = [tex]7\sqrt{2}[/tex]
Answer:
72
Step-by-step explanation:
What is the simplified form of y^2+7y+12/y^2-2y-15? Choices:
Answers
Answer:
[tex] \frac{y + 4}{y - 5} [/tex]Option C is the correct option
Step-by-step explanation:
[tex] \frac{ {y}^{2} + 7y + 12}{ {y}^{2} - 2y - 15 } [/tex]
Write 7y as a sum
[tex] \frac{ {y}^{2} + 4y + 3y + 12}{ {y}^{2} - 2y - 15} [/tex]
Write -2y as a difference
[tex] \frac{ {y}^{2} + 4y + 3y + 12}{ {y}^{2} + 3y - 5y - 15} [/tex]
Factor out y from the expression
[tex] \frac{y(y + 4) + 3y + 12}{ {y}^{2} + 3y - 5y - 15 } [/tex]
Factor out 3 from the expression
[tex] \frac{y(y + 4) + 3(y + 4)}{ {y}^{2} + 3y - 5y - 15 } [/tex]
factor out y from the expression
[tex] \frac{y(y + 4) + 3(y + 4)}{y(y + 3) - 5y - 15} [/tex]
Factor out -5 from the expression
[tex] \frac{y(y + 4) + 3(y + 4)}{y(y + 3) - 5( y + 3)} [/tex]
factor out y + 4 from the expression
[tex] \frac{(y + 4)(y + 3)}{y(y + 3) - 5(y + 3)} [/tex]
Factor out y + 3 from the expression
[tex] \frac{(y + 4)(y + 3)}{(y + 3)(y - 5)} [/tex]
Reduce the fraction with y + 3
[tex] \frac{y + 4}{y - 5} [/tex]Hope this helps..
Best regards!!
Help help help help help
Answers
for example with 4-6a
you would put 4 = 2•2 so 2 is it’s GCF
and 6= 3•2 so 3 is it’s GCF
however the question is asking for the combined GCF (meaning the whole problem)
so 4-6a’s GCF would be 2 considering it is the only greatest common factor between BOTH numbers
for 12a^2 - 8a you would use the same method:
12a^2= 3a•2a•2 and 3a is it’s GCF
8a = 2•2•2a and 2a is it’s GCF
but combined, the greatest factor BOTH numbers have in common is 2a, so 2a is the answer!
i hope i helped you :)!❤️
[tex]( \frac{1 + i}{1 - i} ) {}^{2} [/tex]
Please tell me the answer i need help
Answers
Answer:
- 1
Step-by-step explanation:
Given
( [tex]\frac{1+i}{1-i}[/tex] )²
= [tex]\frac{(1+i)^2}{(1-i)^2}[/tex]
= [tex]\frac{(1+i)(1+i)}{(1-i)(1-i)}[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{1+2i+i^2}{1-2i+i^2}[/tex] ← simplify using i² = - 1
= [tex]\frac{1+2i-1}{1-2i-1}[/tex]
= [tex]\frac{2i}{-2i}[/tex]
= - 1
Solve the following system using substitution.
Answers
Answer/Step-by-step explanation:
3. By substitution method, let's substitute [tex] \frac{2}{3}x- 4 [/tex] for y in the first equation.
Thus,
[tex] \frac{1}{3}x + 2(\frac{2}{3}x- 4) = 1 [/tex]
Solve for x
[tex] \frac{x}{3} + \frac{4x}{3} - 4 = 1 [/tex]
Add 4 to both sides
[tex] \frac{x}{3} + \frac{4x}{3} - 4 + 4 = 1 + 4 [/tex]
[tex] \frac{x}{3} + \frac{4x}{3} = 5 [/tex]
[tex] \frac{x + 4x}{3} = 5 [/tex]
[tex] \frac{5x}{3} = 5 [/tex]
Multiply both sides by 3
[tex] \frac{5x}{3}*3 = 5*3 [/tex]
[tex] 5x = 15 [/tex]
Divide both sides by 5
[tex] x = 3 [/tex]
Now, substitute 3 for x in the equation.
[tex] y = \frac{2}{3}x- 4 [/tex]
[tex] y = \frac{2}{3}(3) - 4 [/tex]
[tex] y = 2 - 4 [/tex]
[tex] y = -2 [/tex]
The solution of the equation is x = 3, y = -2
4. Solving by elimination, let's try to eliminate the x-variable by adding both equation together.
[tex] 3x - 2y = 11 [/tex]
[tex]-3x - y = 4[/tex]
[tex] -3y = 15 [/tex] => [tex] (-3x +(-3x) = 0; -2y +(-y) = -3y; 11 + 4 = 15) [/tex]
Divide both sides by -3 to solve for y
[tex] \frac{-3y}{-3} = \frac{15}{-3} [/tex]
[tex] y = -5 [/tex]
Substitute -5 for y in the first equation to find x
[tex] 3x - 2(-5) = 11 [/tex]
[tex] 3x + 10 = 11 [/tex]
Subtract 10 from both sides
[tex] 3x + 10 - 10 = 11 - 10 [/tex]
[tex] 3x = 1[/tex]
Divide both sides by 3
[tex] \frac{3x}{3} = \frac{1}{3} [/tex]
[tex] x = \frac{1}{3} [/tex]
The solution is [tex] x = \frac{1}{3}, y = -5 [/tex]
Determine whether the function shown in the graph is even or odd. The graph starts at the top left, continues down through the x axis at negative two to a minimum around y equals negative five, goes up to a maximum on the x axis at y equals negative one, goes back down to a minimum around y equals negative five, and goes back up through the x axis at two.
Answers
Answer:
Might be D
Step-by-step explanation:
took the test and that was the other one i was thinking
Answer: D: The function is odd because it is symmetric with respect to the origin.
Step-by-step explanation:
Pam works as an office administrator. She spends $7500 of her income on personal expenses each year. If this represents 18% of her salary, how much money does Pam earn in one year? Round your answer to the nearest whole dollar.
Answers
Answer: Pam earns $41,667 in one year.
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
Pam's salary (x) multiplied by the percentage represented by expenses (18%) in decimal form (divided by 100) must be equal to $7500.
Mathematically speaking:
x (18/100) = 7500
Solving for x:
x (0.18) = 7500
x = 7500/0.18
x = 41,667
Pam earns $41,667 in one year.
Feel free to ask for more if needed or if you did not understand something.
17.A company produces three sizes of a dog
25 house: small, medium, and large. The
small dog house sells for $80, the
medium size for $110, and the large for
$140. The small dog houses cost $50
each to make, medium $70 each, and
large $79 each. Let s represent the
number of small size dog houses, m
represent the number of medium size
dog houses and L represent the number
of large size dog houses. Write an
expression in simplest form for the net
profit.
Answers
Answer:
10s+40m+61l=net profit
Step-by-step explanation:
subtract the value you pay from the value you charge
Hope is the coach of the Wilson High School girls' soccer team. There are 3 minutes left in the game they are currently playing, and they are losing by 1 goal. In the past, when losing by 1 goal, Hope has pulled a defender out of the game and replaced her with a forward a total of 9 times. When in the same position, she has left the defender in the game 10 times. In the situations when Hope has pulled her defender, the team has lost 4 times, tied 2 times, and won 3 times. In situations when she has left her defender in the game, the team has lost 1 time, tied 3 times, and won 6 times. Based on the information above, if the goal is to either tie or win the game, should Hope pull the defender or leave her in the game?
Answers
Answer:
Hope should not pull her defender.
Step-by-step explanation:
When Hope has pulled her defender:
The team had lost 4 times, tied 2 times, and won 3 times.
Hence, the total number of times she meets her goal is:
6 times (Since the goal is to either tie or win the game )
Hence, the probability that she meets her goal is = 6/9=2/3=0.66
When she left her defender in the game:
The team has lost 1 time, tied 3 times, and won 6 times.
Hence, the total number of times she meets her goal is: 9
Hence, the probability that she meets her goal is: 9/10=0.9
As the probability of meeting her goal is more when she left her defender in the game is more.
Hence, Hope should not pull her defender.
. Factorize a² +3ab - 5ab - 15b²
Answers
Answer:
a² +3ab - 5ab - 15b² = (a+3b) (a-5b)
Step-by-step explanation:
We need to factorize a² +3ab - 5ab - 15b². Firstly we need to rearrange the expression such that,
[tex]a^2-5ab+3ab-15b^2=(a^2-5ab)+(3ab-15b^2)[/tex]
Now taking a common from the first two terms and 3b from last two terms, then :
[tex](a^2-5ab)+(3ab-15b^2)=a(a-5b)+3b(a-5b)[/tex]
In the above expression, a factor (a-5b) is in both the terms. It would mean that,
[tex]a(a-5b)+3b(a-5b)=(a+3b)(a-5b)[/tex]
So, the factors of a² +3ab - 5ab - 15b² are (a+3b) (a-5b).
Factor this polynomial expression, and wrote it in its fully factored form 3x^3 + 3x^2 - 18x
Answers
Answer:
fourth option
Step-by-step explanation:
Given
3x³ + 3x² - 18x ← factor out 3x from each term
= 3x(x² + x - 6) ← factor the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)
The factors are + 3 and - 2, since
3 × - 2 = - 6 and 3 - 2 = + 1, thus
x² + x - 6 = (x + 3)(x - 2) and
3x³ + 3x² - 18x = 3x(x + 3)(x - 2) ← in factored form
Jose unlocks his cellphone by placing his right thumb on a square of 1 centimeter by 1 centimeter at the center of the screen. Upon recognizing his thumbprint, the square expands outward. The cellphone unlocks when the perimeter reaches 32 centimeters, taking a total of 2.5 seconds. What is the perimeter of the square after 1.5 seconds?
Answers
Answer: 20.8 cm
Step-by-step explanation:
Notice that the corners of the squares form a line.
Set the x-axis to time and the y-axis to length of a side (not perimeter) to create coordinates.
At 0 seconds the side length is 1 --> (0, 1)
At 2.5 seconds the perimeter is 32 (side length is 32/4 = 8) --> (2.5, 8)
First, find the slope between the coordinates using [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Let (x₁, y₁) = (0, 1) and (x₂, y₂) = (2.5, 8)
[tex]m=\dfrac{8-1}{2.5-0}\quad =\dfrac{7}{2.5}\quad =\dfrac{7}{\frac{5}{2}}\quad =\dfrac{14}{5}\quad =2.8[/tex]
Next, use the Point-Slope formula to find the equation of the line:
[tex]y-y_1=m(x-x_1)\\\\y-1=2.8(x-0)\\\\y=2.8x+1[/tex]
Lastly, find the side length (y) when x = 1.5
y = 2.8(1.5)x + 1
= 4.2 + 1
= 5.2
Perimeter of a square = 4 times the side length
P = 4(5.2)
= 20.8
How much material would you need to fill the following cylinder? Radius 13 in. and Height 9 in.
39π in3
117π in3
1053π in3
1521π in3
Answers
Answer:
1521 pi in^3
radius x radius x height x pi = volume
13 x 13 x 9 = 1521
We do not multiply by pi because it is already included
Hope this helps
Step-by-step explanation:
what is a measure ∠x
Answers
Answer:
x = 138
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
x = B+ C
x = 68+ 70
x =138
Answer:
138 degrees
Step-by-step explanation:
A triangle is made up of 180 degrees, it lists 2 values already, 68&70. when added that equals 138.
So 180-138 is 42 degrees, which would be the last angle within the triangle.
Since a line is also 180 degrees, its 180-42, which makes x 138 degrees
How many 5-digit palindromes contain only even digits?
Answers
Answer:
400
Step-by-step explanation:
There are 400.
Assuming the number must be at least 10,000, then:
In a 5 digit palindrome, the first and last digits must be the same, and the second and fourth digits must be the same; and:
For the first and last digit there is a choice of 4 digits {2, 4, 6, 8};
For each of these there is a choice of 10 digits {0, 1, ..., 9} for the second and fourth digits;
For each of the above choices these is a choice of 10 digits {0, 1, ..., 9} for the third digit;
Making 4 x 10 x 10 = 400 possible even 5 digit palindromes.
HELP MEEEEEEE please
Answers
Answer:
scale factor = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Consider the ratio of corresponding sides, image to original, that is
scale factor = [tex]\frac{T'V'}{TV}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
THE LANDSCAPER IS PLANTING A TREE THAT IS NOW 55 CM TALL. THE TREE WILL GROW 4 CM PER MONTH FOR X MONTHS. THE TREE WILL GROW TO BE AT MOST Y CM TALL. WRITE AN INEQUALITY SHOWING THIS RELATIONSHIP.
Answers
Answer: 55cm + X*4cm < Y.
Step-by-step explanation:
The initial height of the tree is 55cm
The tree will grow 4cm per month, for X months.
then the height of the tree is the initial height, plus X times 4cm
H = 55cm + X*4cm
If Y is the maximum height that this tree can grow, then we can write the inequality as:
H < Y.
55cm + X*4cm < Y.
If the m1 = 40, what is the m 3
Answers
Explanation:
m1 = 40
m3 = 40 x 3
m3 = 120
Answer:
Your Answer is 120Step-by-step explanation:
m1=40
Taking m3
m3=40 ×3
m3= 120
Hope It helps USelect the correct answer.
Which table shows a proportional relationship between x and y?
x y
1
5
2
6
3
7
x y
2
3
4
6
6
9
x y
4
16
8
64
12
144
x y
1
3
2
9
3
27
Answers
Answer:
I think
x y
2
3
4
6
6
9
Step-by-step explanation:
but i don't see any table
Please answer this in two minutes
Answers
Answer:
20/29
Step-by-step explanation:
SOH CAH TOA
so its opposite/hyp...
20/29
is the answer
Help please!!!!!thxxxx
Answers
Answer:
144
Step-by-step explanation:
An angle of a regular pentagon is of 180(5-2)/5=108°
and that all the sides are equal so angle MNL=108/3=36
then MNK=180-MNL=180-36=144
I don't know if you understand this but it's hard to work without more points :)
Question 7(Multiple Choice Worth 1 points)
(06.02 MC)
The radius of the cone is 5 in and y = 13 in. What is the volume of the cone in terms of n?
40nt in
43n in
O
100nt in
108n in
Answers
Hey there! I'm happy to help!
I assume that n is supposed to be π. To find the volume of a cone, you multiply the base by the height and then divide by three.
First, we find the area of the base, which is a circle. To find the area of a circle, you square the radius and multiply by π.
5²=25
And we multiply by π.
25π
Now we multiply by the height.
25π×13=325π
We divide by three.
325π/3≈108π
Therefore, the answer is 108π in.
Have a wonderful day! :D
Please answer this question now
Answers
Answer:
[tex] Area = 538.5 m^2 [/tex]
Step-by-step Explanation:
Given:
∆XVW
m < X = 50°
m < W = 63°
XV = w = 37 m
Required:
Area of ∆XVW
Solution:
Find side length XW using Law of Sines
[tex] \frac{v}{sin(V)} = \frac{w}{sin(W)} [/tex]
W = 63°
w = XV = 37 m
V = 180 - (50+63) = 67°
v = XW = ?
[tex] \frac{v}{sin(67)} = \frac{37}{sin(63)} [/tex]
Cross multiply
[tex] v*sin(63) = 37*sin(67) [/tex]
Divide both sides by sin(63) to make v the subject of formula
[tex] \frac{v*sin(63)}{sin(63)} = \frac{37*sin(67)}{sin(63)} [/tex]
[tex] v = \frac{37*sin(67)}{sin(63)} [/tex]
[tex] v = 38 [/tex] (approximated to nearest whole number)
[tex] XW = v = 38 m [/tex]
Find the area of ∆XVW
[tex] area = \frac{1}{2}*v*w*sin(X) [/tex]
[tex] = \frac{1}{2}*38*37*sin(50) [/tex]
[tex] = \frac{38*37*sin(50)}{2} [/tex]
[tex] Area = 538.5 m^2 [/tex] (to nearest tenth).
Find the legs of a 30° -60°-90° triangle whose hypotenuse is:
10 in.
PLEASE ANSWER ASAP IM really STRUGGLING!!
Answers
You use Pythagoras' Theorem and the theorem of 30-60-90 triangle
Can someone please help me Just the answer no need to explain it.
Answers
Answer:
C
Step-by-step explanation:
When you use pemdas, it gives the value of 1/32