the initial statement is y ∝ x
to convert to an equation multiply by k the constant of variation
[tex]y = kx[/tex]
to find k use the given condition
[tex]y = 27 \\ \\ when \\ \\ x = 3[/tex]
[tex]y = kx \\ \\ k = \frac{y}{x} = \frac{27}{3} = 9[/tex]
equation is y = 9x
when x = 4 then
[tex]y = 9 \times 4 = 36.[/tex]
Answer:
y = 36
Step-by-step explanation:
given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 27 when x = 3 , then
27 = 3k ( divide both sides by 3 )
9 = k
y = 9x ← equation of variation
when x = 4 , then
y = 9 × 4 = 36
PLEASE HELP FAST!!! Write and solve an inequality or multiple inequalities to describe the possible values of x.
Options:
A. -4/7 < x < 14
B. x < 8/7
C. 0 < x < 14
An inequality that can be used to describe the possible values of x is; C. 0 < x < 14
How to calculate the angle in a triangle?
From the given image, let us first use sine rule to find the angles in the triangle with sides 12, 6 and 7 and angle 120°. Thus;
7/sin α = 12/sin 102
sin α = (7/12) * sin 102
sin α = 0.570586
α = sin⁻¹0.570586
α = 34.8°
We know that sum of angles in a triangle is 180°. Thus;
34.8° + 90° + (7x + 4) = 180°
124.8 + 7x + 4 = 180
7x = 180 - 128.4
x = 51.6/7
x = 7.37
Looking at the given options, x cannot be negative and that rules out the first option. x is greater than 8/7 and that rules out the second option but x is greater than 0 and less than 14 and so option C is correct.
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Find the measure of angle RPQ help me please thank u
Answer:
[tex]\boxed {54^{o}}[/tex]
Step-by-step explanation:
By Inscribed Angle Theorem, the value of an inscribed angle enclosed by an arc is the half the value of that arc.
⇒ ∠RPQ = 108°/2
⇒ ∠RPQ = 54°
help me to find b please
Answer:
its right there.
Step-by-step explanation:
please help!!!!
picture below
Answer:
7 ^ 6x + 2 = 7^15
taking log on both the sides
log 7^6x + 2 = log 7^15
6x + 2 log 7 = 15 log 7
log 7
7. Solve the inequality. c – 12 > –1 c < –13 c > 11 c > –13 c > 13
To solve a one-variable-inequality, isolate the variable on one side of the inequality. This can be done by using the four mathematical operations.
What is the four mathematical operations?
The four mathematical operations include the following:
AdditionSubtractionMultiplicationDivisionThese operations can be used to solve equations, inequalities, and more.
[Solving] Simplifying the inequality:Given inequality:
c – 12 > –1As stated in the previous section, let's isolate the variable (c) using the four mathematical operations. Clearly, we have to add both sides by 12 of the inequality as "c" is being subtracted by 12. Therefore, we get:
⇒ c – 12 + 12 > –1 + 12⇒ c > –1 + 12Simplify the right-hand-side to obtain the simplified inequality:
⇒ c > 11Therefore, option B is the correct/best choice.
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Construct a circle through points X, Y, and Z.
The image of the Constructed circle that passes through points X, Y, and Z is given in the image attached.
How is the circle constructed?The steps to construct the circle are:
Step one- Draw 3 circles and the center of each of then is one where one acts as one of the points, and the other side of the compass is said to be at another point.
Step two: Then the draw the circle and follow the way for each point and the three point do cross some where of each other in the middle.
Step three: Place your compass on that point and then begin to drawing side to link the points and so all 3 point will be on the circle.
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[39/(15-2)|-(2*9)
please solve and show steps! thx!
Answer:
- 15
Step-by-step explanation:
1) Simplify 15 - 2 to 13.
39/13 - 2 × 9
2) Simplify 39/13 to 3.
3 - 2 × 9
3) Simplify 2 × 9 to 18.
3 - 18
4) Simplify.
- 15
On the unit circle centered at the origin [tex]\left(x^{2}+y^{2}=1 \right)[/tex], we pick three points at random. We cut the circle into three arcs at those points. What is the expected length of the arc containing the point (1,0)?
The expected length of the arc containing the point (1,0) is; π
How to solve Unit Circle Problems?First of all, it is pertinent to note that the lengths of the four arcs in which the circle is divided by the three points and (1, 0) have identical distributions.
The problem is same as dividing a circle of length 2π at four points chosen at random, and labelling one of them (1, 0). Now, let us make L₁, L₂, L₃, L₄ to be the lengths of the four arcs determined by those four points.
Thus, we have;
L₁ + L₂ + L₃ + L₄ = 2π
Whereas, the expected value of several random variables is additive as;
E[ L₁ + L₂ + L₃ + L₄] = [EL₁] + [EL₂] + [EL₃] + [EL₄]
By symmetry the lengths have the same probability distribution and as such; [EL₁] = [EL₂] = [EL₃] = [EL₄] and the sum must be 2π. Thus, we can say that each expected value is 2π/4 = π/4.
Finally, the expected value of the arc containing the point (1, 0) is the sum of the expected values of the two arcs that are adjacent to (1, 0), i.e.,
π/2 + π/2 = π
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My rule is:y=1/3x+11/15 find x if y=6
Answer:
x=79/5 or 15.8
Step-by-step explanation:
....................
Answer:
[tex]\frac{79}{5}[/tex]
Step-by-step explanation:
Combine [tex]\frac{1}{3}[/tex] and x.
[tex]\frac{x}{3} +\frac{11}{15}=6[/tex]
Move all terms not containing x to the right side of the equation.
[tex]\frac{x}{3}=\frac{79}{15}[/tex]
Multiply both sides of the equation by 3.
3[tex]\frac{x}{3}[/tex]=3([tex]\frac{79}{15}[/tex])
Then 3 cancels out on the left side so all is left is 3.
On the right side, you need to multiply.
3 times 79 is 237.
Now simplify and you get:
79/5
Hope this helped!
Find six rational numbers between -2 and 5
Answer:
1/4, 0.5, -4/6, 4.5, 1/3, 7/8
explanation: it is the ratio of two integers
a/b where b is not = to 0
Mahek owns a holiday tree farm. There are currently 800 trees on the property. Each year 20% of the trees are harvested and sold, and 200 seedlings are planted. Write a recursive definition for the number of trees on the farm at the beginning of the nth year.
1. a1 = 800, an = 0.20an-1 +200
2. a1 = 200, an = 0.80an-1 + 800
3. a1 = 800, an = 0.80an-1 + 200
4. a1= 0.20, an=0200an-1
The equation of the sequence will be [tex]\rm a_n = 0.8 \times a_{n -1} +200[/tex],
where a₁ = 800. Then the correct option is C.
What is the geometric sequences?Let a₁ be the first term and r be the common ratio. Then the geometric sequences will be
[tex]\rm a_n = a_{n -1} \cdot r[/tex]
Mahek owns a holiday tree farm.
There are currently 800 trees on the property.
Each year, 20% of the trees are harvested and sold, and 200 seedlings are planted.
Then the equation of the sequence will be
[tex]\rm a_n = 0.8 \times a_{n -1} +200[/tex]
Where a₁ = 800.
Then the correct option is C.
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Answer:
3. a1 = 800, an = 0.80an-1 + 200
Step-by-step explanation:
REARRANGE EQUATIONS PLEASE HELP ITS DUE IN TOMORROW
Answer:
from top to bottom:
x = y(v-w)
x = (yv/w)/2
x = (6+w)/v
x = (y-2w)/v
Step-by-step explanation:
The two-way table shows the estimated number of students who will enroll in three area high schools next year. a 5-column table has 4 rows. the first column has entries mount woodson high school, valley high school, riverside high school, total. the second column is labeled tenth grade with entries 110, 180, 160, 450. the third column is labeled eleventh grade with entries 120, 150, 140, 410. the fourth column is labeled twelfth grade with entries 80, 120, 200, 400. the fifth column is labeled total with entries 310, 450, 500, 1,260. in decimal form, to the nearest tenth, what is the probability that a randomly selected riverside high school student is in twelfth grade? 0.2 0.3 0.4 0.5
Answer:
A. 0.2
Step-by-step explanation:
First make the table.
10-grade 11-grade 12-grade Total
Woodson high school | 110 | 120 | 80 | 310 |
Valley high school | 180 | 150 | 120 | 450 |
Riverside high school | 160 | 140 | 200 | 500 |
Total | 450 | 410 | 400 | 1260 |
Question: In decimal form, to the nearest tenth, what is the probability that a randomly selected riverside high school student is in twelfth grade?
First, find 12-grade and riverside high school number. 200. Take the total lined up with total number, which is 1260, and divide 200 divided by 1260.
200/1260=0.2
The answer is 0.2.
Hope this helps!
If not, I am sorry.
Answer:
its .4
Step-by-step explanation:
i got it wrong when i tried it says it is .4 or the third option c
A car travels at an average speed of 50 km/h for 1.5 hours. How far did the car travel in km?
Answer:
75 km
Step-by-step explanation:
(50km/h)(1.5h) = 75km
How do I do this? Subtract the expressions (3x+3)-(4x+6)
Answer:
-x - 3
Step-by-step explanation:
1) Distribute
(3x+3)-(4x+6)
3x + 3 - 4x - 6
2) Subtract the numbers
3x + 3 - 4x - 6
3x - 3 - 4x
3) Combine like terms
3x - 3 - 4x
-x - 3
Does the chart below represent a proportional relationship? What is the rate of change?
x y
1 4
2 8
3 12
4 16
This chart represents a proportional relationship. The rate of change will be 4.
What is the constant of proportionality?Firstly, there is a proportional relationship.
Two values x and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.
The constant k is called the constant of proportionality.
Given;
x y
1 4
2 8
3 12
4 16
Here, x = ky
put the first value
k = 1/4
This chart represents a proportional relationship.
So the rate of change will be
[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}\\\\Rate = \dfrac{8 - 4}{2 - 1}\\\\Rate = 4[/tex]
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The radius of a sphere is 3 inches. Which represents the volume of the sphere? 12Ï€ cubic inches 36Ï€ cubic inches 64Ï€ cubic inches 81Ï€ cubic inches.
Answer: 113 inches cubed
Step-by-step explanation:
Volume of a sphere = 4/3 Pi r^3
Radius = 3 inches
Volume = 113 inches cubed
Hope I helped!
Y = 4x -2 and y = x +3
Answer:
(0.5,2) and (-3,3)
Step-by-step explanation:
Answer:
Y = 4x -2 is (0.5,2)
y = x +3 is (-3,3)
Today’s weather map shows the jet stream flowing west to east toward Washington, D.C., at a speed of 70 knots. If the ground speed needs to be 450 knots to make it from Washington to Kansas City on time, what does the plane’s speed need to be?
Considering the direction of the wind, it is found that the plane's speed needs to be of 520 knots.
What is the ground speed?The ground speed, considering that the wind is flowing from Kansas City to Washington, and the trip is Washington to Kansas City, is given by:
G = Plane speed - Wind speed.
Hence:
450 knows = Plane speed - 70 knots.
Plane speed = 520 knots.
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The scatter plot shows the height of an alfalfa plant over a period of time. Click on the table that best matches the data in the scatter plot.
Based on the information provided, the table that best matches the data in the scatter plot is shown below.
What is a scatter plot?A scatter plot is a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
Based on the information provided, the table that best matches the data in the scatter plot is given by:
Data 1 2 4 5.5 6.3
Height (cm) 1 2 3 4 5
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What is 2/5 divided by 4/7 equal too
3. What mathematical symbol is appropriate to use given the
word?
4. What word is appropriate to use given the symbol?
Answer:
X
Step-by-step explanation:
Simplify 14(1−23)2+13
Answer:
-603Step-by-step explanation:
Simplify 14(1−23)2+13
Remember PEMDAS
14 * (1 - 23) * 2 + 13 =
14 * (-44) * 2 + 13 =
-308 * 2 + 13 =
-616 + 13 =
-603
james brewer purchased 100 shares of stock for $73 a share. james also paid a $60 commission. what was the total purchase price for this transaction?
Answer:
$ 7360.00
Step-by-step explanation:
100 shares * $ 73/share + $60 = $ 7360
Based on the calculation below, the total purchase price for this transaction is $7,360.
How do we calculate the total purchase price of shares of stock?The total purchase price for this transaction can be calculated using the following formula:
Total purchase price = (Price per share * Units of shares purchased) + Commission ...................................... (1)
Substituting all the values into equation (1), we have:
Total purchase price = ($73 * 100) + $60 = $7,360
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A ball is thrown from the top of the school. The height of the ball (in feet) written in
terms of the time (in seconds) is modeled by f (t) = -16t² + 32t + 48. At what time
will the ball hit the ground?
Answer:
3 seconds
Step-by-step explanation:
When the ball hits the ground, the height will be 0. Therefore, you can substitute 0 in for the value of f(t), hence the equation will be:
0 = -16t^2 + 32t + 48
You can then factor out -16:
0 = t^2 - 2t - 3
Factor:
0 = (t-3)(t+1)
t = 3, -1
However -1 is an extraneous solution because time cannot be negative. Therefore, the answer is 3 seconds.
Construct a square inscribed in a circle. Please help asp.
please help thank you !
Answer:
6.6 cm and 14.6 cm
Step-by-step explanation:
(a)
the length of arc AB is calculated as
AB = circumference of circle × fraction of circle
= 2πr × [tex]\frac{95}{360}[/tex]
= 2π × 4 × [tex]\frac{95}{360}[/tex]
= 8π × [tex]\frac{95}{360}[/tex]
= [tex]\frac{8\pi (95)}{360}[/tex]
≈ 6.6 cm ( to the nearest tenth )
(b)
the perimeter (P) of sector AOB is
P = r + r + AB = 4 + 4 + 6.6 = 14.6 cm
Step-by-step explanation:
3.
the circumference of a circle is
2×pi×r
r = 4 cm
so, we know, the full circle circumference is
2×pi×4 = 8×pi = 25.13274123... cm
a.
the arc length of AB is the part of the whole circumference that corresponds to 95° out of the full 360° of a whole circle.
arc AB = 8×pi × 95/360 = pi × 95/45 = pi × 19/9 =
= 6.632251158... cm
b.
the perimeter of OAB (the "pie slice") is then the arc AB plus 2 radius lengths (from the end points on the arc to the center of the circle) :
pi × 19/9 + 2×4 = pi×19/9 + 8 = 14.632251158... cm
What is the quotient in scientific notation?
the equation is 6a³+3b² when a=4 and b=1
Answer:
387
Step-by-step explanation:
6(4)³ + 3(1)²
6(64) + 3(1)
384 + 3
= 387
Talia is writing a coordinate proof to show that the diagonals of a square are perpendicular. Which sentence describes what Talia should do to show that the diagonals of the square are perpendicular?
Answer:
D
Step-by-step explanation:
The product of the slopes of two perpendicular lines is -1.
If the slopes of the diagonals are 1 and -1, then their product is -1, and they are perpendicular.
Answer: D
A sentence that describes what Talia should do to show that the diagonals of the square are perpendicular is: D. show that the slope of SQ is 1 and the slope of PR is -1.
How to determine whether the quadrilateral is a square by using slope?In order for a quadrilateral to be a square, the two (2) pairs of its sides must be equal (congruent) and perpendicular to each other.
Therefore, we would have to calculate the slope of each side by using this mathematical equation:
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m₁) of SQ = (a - 0)/(a - 0)
Slope (m₁) of SQ = a/a = 1.
Slope (m₂) of PR = (a - 0)/(0 - a)
Slope (m₂) of PR = -a/a = -1.
Based on the condition for two (2) perpendicular lines, we have:
m₁ × m₂ = -1
1 × -1 = -1
-1 = -1
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