Step-by-step explanation:
y is directly proportional to x
y = kx
k represents the constant of proportionality.
when y = 20 and x = 8:
20 = 8k
Dividing both sides by 8 gives:
k = 2.5
Hence when x = 3.
y = 2.5(3)
y = 7.5 .
The value of y when x=3 is 7.5
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
y is directly proportional to x.
and, when x = 8, y = 20.
So, using proportion
8/20 = 3/y
8y = 60
y= 60/8
y= 7.5
Hence, the value of y is 7.5
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Andy is designing a dice tray in the shape of a rectangular prism to use during a role-playing game. The tray needs to be three centimeters high and have a volume of 252 cubic centimeters in order for the dice to roll properly. The length of the tray should be five centimeters longer than its width. The volume of a rectangular prism is found using the formula V = l · w · h, where l is the length, w is the width, and h is the height. Complete the equation that models the volume of the tray in terms of its width, x, in centimeters.
Answer:
Andy is designing a dice tray in the shape of a rectangular prism to use during a role-playing game. The tray needs to be three centimeters high and have a volume of 252 cubic centimeters in order for the dice to roll properly. The length of the tray should be five centimeters longer than its width.
The volume of a rectangular prism is found using the formula V = l · w · h, where l is the length, w is the width, and h is the height.
Complete the equation that models the volume of the tray in terms of its width, x, in centimeters.
3x2 + 15x = 252
Is it possible for the width of the tray to be 7.5 centimeters?
no it is too large
Step-by-step explanation:
An equation is formed when two equal expressions. The equation that models the volume of the tray in terms of its width, x, in centimeters is 3x² + 15x - 252 = 0.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the width of the rectangular prism die be represented by x.
Given that the length of the tray should be five centimeters longer than its width. Therefore, the length and the width of the prism can be written as,
Width = x
Length = x + 5
Further, it is given that the volume of die is 252 cubic centimeters in order for the dice to roll properly. Also, the height of the prism is 3 centimeters. Therefore, the Volume can be written as,
Volume = Length × Width × Height
252 = (x + 5) × x × 3
252 = 3x(x+5)
252 = 3x² + 15x
3x² + 15x - 252 = 0
Hence, the equation that models the volume of the tray in terms of its width, x, in centimeters is 3x² + 15x - 252 = 0.
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Landon is building new bookshelves for his bookstore's new mystery section. Each shelf can hold 34 books. There are 1,265 mystery books. How many shelves will he need to build?
Answer:
37.2 = 38
Step-by-step explanation:
After divideing 1265 by 34, you will get 37.2. As you cannot have books not in bookshelves, you will have to round up and have 38 bookshelves.
In the figure shown, which theorem can be used to show that ABC = ADEF?
O A The triangles are not congruent.
OB SAS Triangle Congruence Theorem
OC AAS Triangle Congruence Theorem
OD ASA Triangle Congruence Theorem
Pick choice-C ... AAS.
When I learned Geometry (during the late Pleistocene epoch), I don't remember ever using AAS.
BUT ... If you know 2 angles of a triangle, then you know all three, because they all add up to 180.
So if you have AAS=A'A'S', then you also have ASA=A'A'S', which was a congruence theorem even way back then.
Ahhh the good old days. We rarely got any homework, because the teachers all knew that the clay tablets would ruin our backpacks.
IM STUCK WITH THIS, ITS BETWEEN 22 OR 12 CAN SOMONE CHECK?
ILL MARK U BRAINIEST
Answer:
12
Step-by-step explanation:
it’s 12 because 4 x 3 = 12
How do you solve n=17
Answer:
uhm chile anyways
Step-by-step explanation:
i just want points lol
What is 3 1/3 times 3?
Answer:
10
Step-by-step explanation:
friend chicked for life
interquartile range of the wingspans of 74, 71, 75, 80, 67, 84, 77
Answer: 9
Step-by-step explanation:
Population size=7
Lower quartile=71
Upper quartile=80
67 Is or es el 67
Jajaja
(Urgent please help!!!) Maria earned $5,250; $4,800; $3,990 and $5,120 from her home business during the last four months. What was her average monthly income during this period?
Please answer correctly !!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!
The sum of two complementary angles is 90 degrees.
Angle A + Angle B = 90
Let Angle B = X
5x + 2 + x = 90
Combine like terms:
6x +2 = 90
Subtract 2 from both sides:
6x = 88
Divide both sides by 6:
x = 88/6
x = 14.67
Angle B = 14.67 degrees ( rounded to the nearest hundredth)
Write an equation of a line that is parallel to the given line.
5. y = 7
6. x = 12
if you can also help with 7 that would be amazing
7. for what value of a are the graphs of 3y=6x-5 and 9y=ax+2
Answer:
5) y=5
6)x=7
7)a=18
Step-by-step explanation:
5) y= any number will work. don't add a variable like x
6)x= any number will work. don't add a variable
My work for 7 is in the picture. If you'd like me to explain more for 7 lmk :)
C:
D:
E:
F:
G:
H:
3 a) If the first coordinate in an ordered pair is 0, where does the point lie?
3 b) If the second coordinate in an ordered pair is 0, where does the point lie?
8. How far does Cal live from Mel?
9. How far does Mia live from Amy?
10. How far apart do Amy and Cal live?
14. Whose house is a reflection of Amy’s house across the y-axis? Explain.
Answer:
its in progress so tell ur teacher.
Step-by-step explanation:
Given: x + 2y = -6.
Solve for y.
A.) y=x-6/2
B.)y=-x+6/2
C.)y=-x-6/2
Answer:
a
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Subtract x from each side so you get
2y = -x-6
Then divide them by 2 to get
y = -x-6/2
Place the steps in the correct order
Answer:
1. Add x on both sides.
2. Divide both sides by 4.
3. Add 20 to both sides.
4. Divide both sides by 3.
Brainliest Appreciated! Hope I helped!
Matthew invested $680 in an account paying an interest rate of 5.8% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 11 years?
Answer:
Step-by-step explanation:
1290
Based on the amount invested, the rate, and the period of compounding, after 11 years, the account would be $1,290.
As the rate is compounded daily, the rate and the period need to be converted to daily figures:
Rate = 5.8% / 365 days = 5.8/365 %
Period = 11 x 365 = 4,015 days
The amount in 11 years is:
= Amount x ( 1 + rate) ^ period
= 680 x (1 + 5.8/365%) ⁴⁰¹⁵
= $1,286.965
= $1,290
In conclusion, the account would have $1,290.
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If z = 1 –StartRoot 3 EndRoot i, what is z^3? please help im stressed
a) -8
b) 8
c) -8i
d) 8i
Answer:
Correct answer: a) -8
Step-by-step explanation:
Complex Numbers
A complex number z in polar form is expressed as
[tex]z=r(\cos\theta+\mathbf{i}\sin\theta)[/tex]
The nth power of a complex number in polar form is:
[tex]z^n=r^n(\cos(n\theta)+\mathbf{i}\sin(n\theta))[/tex]
If the complex number is given in rectangular form
[tex]z=x+\mathbf{i}y[/tex]
then the values of r and θ are given by:
[tex]r=\sqrt{x^2+y^2}[/tex]
[tex]\displaystyle \theta=\arctan\left(\frac{y}{x}\right)[/tex]
The given complex number is:
[tex]z=1-\mathbf{i}\sqrt{3}[/tex]
The value of r is:
[tex]r=\sqrt{1^2+(-\sqrt{3})^2}[/tex]
[tex]r=\sqrt{1+3}=2[/tex]
r=2
Calculating the angle:
[tex]\displaystyle \theta=\arctan\left(\frac{-\sqrt{3}}{1}\right)[/tex]
[tex]\displaystyle \theta=\arctan(-\sqrt{3})[/tex]
Since the number is in the quadrant IV, the angle is:
[tex]\theta=-60^\circ[/tex]
Thus, z is expressed in polar form as:
[tex]z=2(\cos(-60^\circ)+\mathbf{i}\sin(-60^\circ))[/tex]
Calculating:
[tex]z^3=2^3(\cos(-180^\circ)+\mathbf{i}\sin(-180^\circ))[/tex]
Given cos 180°=-1 and sin(-180°)=0
[tex]z^3=8(-1+0)[/tex]
[tex]z^3=-8[/tex]
Correct answer: a) -8
Answer:
A
Step-by-step explanation:
just finished test
Seth has game and education apps on his tablet. He noticed that he has 5 game apps for every 2 education apps. Which of the following is another way to write this ratio?
2:3
2:5
3:2
5:2
Question 4(Multiple Choice Worth 3 poi
Answer:
it would be 5:2
Step-by-step explanation:
none of these are equivalent to the ratio and 2:5 would be 2 to 5
Answer:
5:2
Step-by-step explanation:
The plate moved 1719 km in 150 million years what is the rate the plate traveled in 1 million years.
Answer:
11.46 km per million years
Step-by-step explanation:
divided 1719 by 150
Complete the two-column proof.
A. Alternate Exterior angles theorem / Vertical angles
B. Alternate exterior angles theorem / corresponding angles theorem
C. Symmetric property / Transitive property
The correct explanations are;
A) Vertical angles.
B) Corresponding angles theorem
C) Transitive property.
What are Parallel lines?
Parallel lines are those lines that are equidistance from each other and never intersect each other.
Given that;
Two lines x and y are parallel.
w is transversal of x and y.
Now, To prove ∠4 ≅ ∠5 we use;
Since, Two lines x and y are parallel.
So, We can apply all the properties of angles of triangles.
Statements Reasons
1. x || y 1. Given
2. w is transversal 2. Given
3. ∠4 ≅ ∠1 3. Vertically opposite angles.
4. ∠1 ≅ ∠5 4. By Corresponding angles theorem.
5. ∠4 ≅ ∠5 5. By Transitive property.
Thus, The correct explanations are;
A) Vertical angles.
B) Corresponding angles theorem
C) Transitive property.
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-3=12y-5(2y-7). Solve for y
Answer:
y = -19
Step-by-step explanation:
-3 = 12y -5(2y - 7)
distribute -5 to (2y -7)
-3 = 12y - 10y + 35
subtract 35 from both sides and simplify
-38 = 2y
divide both sides by 2 to isolate y
-19 = y
Which number is IRRATIONAL?
Answer:
I'm sure a and b is not irrational. But
Step-by-step explanation:
C and D can be
Use calculator, if the number is not repeating and non recurring, then that can be irrational
Two numbers have a sum of 136 and a difference of 32. Find the smaller of the two numbers.
Answer:
Smaller number = x
Bigger number = x +32
Why? -- the difference of the numbers is 32, this also means that one number is 32 greater than the other.
x + x+32 = 136
2x +32 = 136
2x = 104
x = 104/2
x = 52
----> The smaller number is 52 <-----
We can check by solving for the bigger number.
Bigger number = x+32
x = 52
52 + 32 = 84
Bigger number = 84
Bigger number + Smaller number = 136
84 + 52 = 136
The numbers are 84 and 52 if the two numbers have a sum of 136 and a difference of 32.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Two numbers have a sum of 136 and a difference of 32
Let x be the first number and y be the second number:
x + y = 136
x - y = 32
After solving the above linear equation by elimination method:
2x = 168
x = 168/2
x = 84
2y = 104
y = 52
Thus, the numbers are 84 and 52 if the two numbers have a sum of 136 and a difference of 32.
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For each triangle, check all that apply.
PHOTO ABOVE
⚠️TEST
Answer:
Step-by-step explanation:
Triangle A - Equilateral triangle because all the angles are equal which means all the sides will be equal.
Triangle B - Isosceles Triangle because 2 sides are equal (we know this because 2 of the angles are equal)
Triangle C - Equilateral triangle because all the sides are equal.
Triangle D - Scalene triangle because all the sides have different lengths.
I NEED HELP LIKE ASAP Which ratios are equivalent to 3 parts silver paint to 4
parts green paint? Check all that apply.
O4:5
O 6:8
O 5:6
O9:12
Answer:
its o4:5
Step-by-step explanation:
Jose tacking care of a nabers cat for 5 days he has 3 cans of food he needs to feed the cat the same amont every day howw much food shold joes feed the cat per day
Answer:
If the owner left only 3 cans of food for 5 days, that means that we have to divide those cans of food so we can just do simple math and divide 3 by 5
3/5 and you get 0.6
So the cat must eat 0.6 of each can everyday.
What is the value of x?
Which expression is equivalent to 4(x+12)
Answer:
4(x + 12) = 4x + 48
Step-by-step explanation:
Answer:
2(2x + 6)
Step-by-step explanation:
Jake has a container in the shape of a rectangular prism.The base of the container is 30 centimeters long and 20 centimeters wide. Jake pours 0.5 gallons of water into centimeters, how high, in centimeters,will the water reach the container?Note that 1 gallon is approximately equal to 3.8 liters and 1cm3 of volume can hold 1 million of water
Answer:
40 centimeters
Step-by-step explanation:
Evaluate -9x-2 when x =-4
Answer:
34
Step-by-step explanation:
So -9x is 36,36-2=34
Answer:
34
Step-by-step explanation:
-9(-4)-2
36-2
34
please show how to check the answer . that's all I'm struggling with
Answer:
For Question 3, all you have to do is subtract 5 from both sides of the equation, then divide by -3, which will leave you with 5 as the answer.
-3x + 5 = -10
-3x = -15x
x = 5
Two students are pulling an object with ropes. One student pulls with a force of 40 pounds at an angle of 30° above the ground, and the other student pulls with a force of 35 pounds at an angle 45° above the ground. What is the direction of the resultant force?
approximately 37.33° above the ground
approximately 42.27° above the ground
approximately 47.73° above the ground
approximately 53.13° above the ground
Answer: A. approximately 37.33° above the ground
Step-by-step explanation:
edge2020
The the direction of the resultant force is A. approximately 37.33° above the ground.
What's a resultant force?A resultant force simply means the single force that has same effect as two or more forces that are acting together.
In this case, a student pulls with a force of 40 pounds at an angle of 30° above the ground, and the other student pulls with a force of 35 pounds at an angle 45° above the ground.
The direction of the resultant force is 37.33° above the ground.
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