Answer:
It is rational
Step-by-step explanation:
The pi terms cancel out when you divide. This is due to the rule x/x = 1 where x is any number you want except x cannot be zero. So replace x with pi and we have pi/pi = 1
Therefore,
(3pi)/(2pi) = (3/2)*(pi/pi)
(3pi)/(2pi) = (3/2)*1 .... use the rule mentioned above
(3pi)/(2pi) = 3/2
we get a fraction or a ratio of two whole numbers, so this proves that the given expression is rational.
Please help me answer both questions if they are correct I’ll give brainliest
Answer:
see explanation
Step-by-step explanation:
(4)
Under a counterclockwise rotation about the origin of 90°
a point (x, y) → (- y, x), hence
C(- 3, 4) → C'(- 4, - 3)
(5)
Under a clockwise rotation about the origin of 180°
a point (x , y) → (-x, - y), hence
A(- 3, 2) → A'(3, - 2)
What is the axis of symmetry for f(x) = 2x − 8x + 8? (1 point) Select one: a. x = −2 b. x = −3 c. x = 3 d. x = 2
Answer:
x=2
Step-by-step explanation:
F(x) = 2x^2 - 8x +8
Axis of symmetry lies at the x coordinate of vertex
To find x coordinate of vertex use formula
[tex]x=\frac{-b}{2a}[/tex]
from the given f(x) , a= 2 and b = -8
Plug in all the values
[tex]x=\frac{-(-8)}{2(2)}[/tex]
[tex]x=\frac{8}{4}=2[/tex]
x=2
So the axis of symmetry at x=2
Ms. Blankenship had $80 to purchase school supplies for her class. She bought 32 glue sticks and 32 boxes of crayons. Each glue stick cost $1.40, and each box of crayons cost $0.59. How much money did Ms. Blankenship have left after these purchases?
Answer:
$16.32
Step-by-step explanation:
1. Ms. Blankenship bought 32 glue sticks each for $1.40, then she spent
[tex]\$1.40\cdot 32=\$44.80[/tex]
for all sticks.
2. Ms. Blankenship bought 32 boxes each for $0.59, then she spent
[tex]\$0.59\cdot 32=\$18.88[/tex]
for all boxes.
3. Together 32 glue sticks and 32 boxes cost
[tex]\$44.80+\$18.88=\$63.68.[/tex]
4. If Ms. Blankenship had $80, then she had left
[tex]\$80-\$63.68=\$16.32.[/tex]
what is a mathematical statement consisting of a hypothesis and conclusion that has to be proven true
please help me, PLEASE!!!!!!
Tell wheather the sequence is arithmetic. If it is , what is the common difference? -12,-7,-2,3.......
A yes ;5
B yes ;8
C yes :3
D no
Answer:
C
Step-by-step explanation:
To find whether it is a arithmetic or geometric sequence it is easiest to try to subtract term a2 from a1, seeing if d or r is positive. If that does not heed an answer try dividing a2 by a1 to see if it is a geometric sequence.
The terms go as follows just in case (They would normally be in subscripts)-
a1= -12
a2= -7
a3= -2
a4= 3
Answer: Yes; 5 (choice A)
We add 5 to each term to get the next
-12+5 = -7
-7+5 = -2
-2+5 = 3
and so on. The nth term formula is
an = -12 + 5(n-1)
If you were to plug in n = 1, 2, 3, ... then it should generate the terms shown
What is the greatest common factor of the terms in the expression 21x - 18x + 28xy?
Answer:
The terms are already in lowest form. The factors of 21 are 21 and 1, and 3 and 7. The factors of 18 are 1 and 18, 2 and 9, and 3 and 6. The factors of 28 are 1 and 28, 2 and 14, and 7 and 4. None of them match up so it is as low as it can be.
Step-by-step explanation:
the greatest common factor is x. because
21, -18, and 28 do not have any shared factors
y−3=2(x+1) Complete the missing value in the solution to the equation. ( -1, _ )
Answer:
The missing value for y is 3
Step-by-step explanation:
y−3=2(x+1)
We know that x=-1 and we want to solve for y
Put in x=-1
y-3 = 2(-1+1)
y-3 = 2(0)
y-3=0
Add 3 to each side
y-3+3 = 0+3
y =3
Solve using elimination
5x-4y=-21
-2x+4y=18
Answer:
x=-1, y=4
Step-by-step explanation:
When we solve by elimination, we are getting rid of one variable, in this case y. We will add the two equations together.
5x-4y=-21
-2x+4y=18
---------------
3x = -3
Divide each side by 3
3x/3 =-3/3
x =-1
Now we need to calculate y
-2x +4y = 18
Substitute x=-1
-2(-1)+4y = 18
2+4y =18
Subtract 2 from each side
4y = 18-2
4y=16
Divide each side by 4
4y=16/4
y =4
Please answer this correctly
Answer:
$13.66
Step-by-step explanation:
Multiply the amount of Dijon mustard and mustard by its price, then add them together.
3 * 3.69 = 11.07
.5 * 5.18 = 2.59
Add these sums together.
11.07 + 2.59 = 13.66
How do you convert a fraction to a decimal? Say, [tex]\frac{2}{5}[/tex] ?
Answer:
you divide the top number by the bottom number
Step-by-step explanation:
2/5 = 0.4
the total cost of four boxes of pasta is $14 There are 16 oz of pasta in each box of the same amount what is the maximum number of boxes that can be purchased with $65
Answer:
18.5 but rounded to 19 because you cant have half of a box
Step-by-step explanation:
because each box costs 3.5 dollars because i did 1 4 divided by 4.then you want to get to 65 so i did 3.5 divided by 65 then got 18.5 which was rounded because the decimal was big This was the real decimal 18.5714286. THIS MIGHT BE WRONG
A kite is stuck in a 36-ft tree. If the angle of elevation from the kite and the ground is 12, find the length of the kite.
Answer:
173.15 ft.
Step-by-step explanation:
Please find the attachment.
Let L be the length of kite.
We have been given that a kite is stuck in 36-ft tree. The angle of elevation from the kite and the ground is 12.
We can see from our attachment that kite and tree form a right triangle. height of tree is opposite of angle of elevation and length of kite is hypotenuse.
Since we know that Sine relates the opposite and hypotenuse of a right triangle, so we will use sine to find the length of kite.
[tex]sin(12)=\frac{36}{L}[/tex]
[tex]L=\frac{36}{sin(12)}[/tex]
[tex]L=\frac{36}{0.207911690818}[/tex]
[tex]L=173.1504364105882792\approx 173.15[/tex]
Therefore, the length of kite is 173.15 ft.
Landen spent LL hours at the beach last weekend. Matéo spent 15\%15% fewer hours at the beach than Landen did. Which of the following expressions could represent how many hours Matéo spent at the beach last weekend? Choose 2 answers: Choose 2 answers:
Answer: 0.85 L or [tex]\frac{85L}{100}[/tex] or [tex]\frac{17L}{20}[/tex]
Step-by-step explanation:
Since, According to the question,
Landen spent time at the beach last weekend = L hours
And, Matéo spent 15% fewer hours at the beach than Landen did.
Therefore, Number of hours spent by Matéo = (Time spent by Landen last week - 15 % of the Time spent by Landen last week ) hours
= 85% of the Time spent by Landen last week
= [tex]\frac{85\times L}{100}[/tex]
= [tex]\frac{85L}{100}[/tex] Hours
= [tex]\frac{17L}{20}[/tex] Hours
= 0.85 L Hours
Answer:
Its L(1-0.15) and L-3/20L
Step-by-step explanation:
Trust me. i got it from Khan Academy. for mine it was B and E. :3
At a restaurant, four people ordered fried crab cakes and four people ordered a cup of gumbo, with a total of $31. If only two people had ordered the crab cakes and one person ordered the gumbo, the bill would have been $12.25. How much are each order of fried crab cakes and each cup of gumbo? (Can you please show the steps?) Thank you.
Answer:
Fried crab cakes = $4.50
Cup of gumbo = $3.25
Step-by-step explanation:
Let's make the price of fried crab cakes = x and the price of a cup of gumbo = y. Set up two equations for x and y and solve for each variable.
Setting up the equations:4 people ordered x and 4 people ordered y for a total of 31 dollars, so this equation would look like: 4x + 4y = 31
2 people ordered x and 1 person ordered y for a total of $12.25, so this equation would look like: 2x + y = 12.25
Substitution method:Now you have your two equations-- solve for a variable in one of the equations and substitute that value into the other equation.
The easiest way to start would be to solve for y in the second equation by subtracting 2x from both sides.
y = 12.25 - 2x
Substitute this value into the first equation.
4x + 4(12.25 - 2x) = 31
Now solve for x-- start by distributing 4 inside the parentheses.
4x + (49 - 8x) = 31
Combine like terms.
-4x + 49 = 31
Subtract 49 from both sides.
-4x = -18
Divide both sides by -4.
x = 4.5
Substitute this value of x into our starting equation for which we solved for y.
2(4.5) + y = 12.25
Multiply 2 and 4.5 together.
9 + y = 12.25
Subtract 9 from both sides.
y = 3.25
Each order of fried crab cakes is worth the x-value [$4.50] and each cup of gumbo is worth the y-value [$3.25].
In this system of linear equations, by denoting the cost of the fried crab cakes as x dollars, and the cost of a cup of gumbo as y dollars, we find that each order of fried crab cakes is $4.50 and each cup of gumbo is $3.25.
Explanation:The subject of this problem is linear algebra, and it can be solved using a system of linear equations. Let's denote the cost of the fried crab cakes as x dollars, and the cost of a cup of gumbo as y dollars.
From the information given in the problem, we can create the following two equations:
4x + 4y = 31 (This is from the information that four people ordered fried crab cakes and four people ordered a cup of gumbo, with a total of $31.)2x + y = 12.25 (This is from the information that if only two people had ordered the crab cakes and one person ordered the gumbo, the bill would have been $12.25.)Now, we can solve this system of equations. Divide the first equation by 2, which will give us:
2x + 2y = 15.5
Then subtract the second equation from the result, which will give us:
y = 3.25
Substitute y = 3.25 into the second equation:
2x + 3.25 = 12.25
Finally, solve for x:
x = 4.5
So, each order of fried crab cakes is $4.50 and each cup of gumbo is $3.25.
Learn more about System of Linear Equations here:https://brainly.com/question/27063359
#SPJ3
Water is drained out of tank, shaped as an inverted right circular cone that has a radius of 4cm and a height of 16cm, at the rate of 2 cm3/min. At what rate is the depth of the water changing at the instant when the water in the tank is 8 cm deep? Show all work and include units in your answer. Give an exact answer showing all work and include units in your answer
Answer:
[tex]-\frac{1}{2\pi}[/tex] cm³/min
Step-by-step explanation:
Let h = height of water and r = radius of its surface
[tex]V = \frac{ 1}{ 3}\pi r^{2}h[/tex]
At all times,
[tex]\frac{r }{h } = \frac{4 }{16 } = \frac{ 1}{4 }[/tex]
So, [tex]r = \frac{h }{4 }[/tex]
[tex]V = \frac{ 1}{ 3}\pi (\frac{h }{ 4})^{2}h[/tex]
[tex]V = \frac{ 1}{ 48}\pi h^{3}[/tex]
[tex]\frac{\text{d}V}{\text{d}h} = \frac{ 1}{ 16}\pi h^{2}[/tex]
We want [tex]\frac{\text{d}h}{\text{d}t}[/tex]
[tex]\frac{\text{d}V}{\text{d}t} = \frac{\text{d}V}{\text{d}h} \frac{\text{d}h}{\text{d}t}[/tex]
[tex]\frac{\text{d}V}{\text{d}t}[/tex] = -2 cm³/min
[tex]-2 = \frac{ 1}{ 16}\pi h^{2} \frac{\text{d}h}{\text{d}t}[/tex]
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{2}{\frac{ 1}{ 16}\pi h^{2} }[/tex]
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{\pi h^{2}}[/tex]
When h = 8 cm
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{\pi\times8^{2}}[/tex]
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{64\pi}[/tex]
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{1}{2\pi}[/tex] cm³/min
The depth of the water is decreasing at a rate of [tex]\frac{1}{2\pi}[/tex] cm³/min
.
does 1/6, -3, √7, -6/5, or 4.5 comes first when the numbers are listed from least to greatest
The arrangement is as follows:
-3<-1.2<1/6<√7<4.5
What is ascending and descending order?Ascending means smallest to largest, 0 to 9, and/or A to Z and Descending means largest to smallest, 9 to 0, and/or Z to A.
Given:
1/6= 0.16667
√7= 2.645
-6/5= -1.2
So, the least number is -3 and greatest number is 4.5.
Learn more about ascending and descending order here:
https://brainly.com/question/320500
#SPJ6
This is the section 2 test yourself test if u know the whole thing then plz tell me
Answer: D
Step-by-step explanation:
To create a perpendicular bisector:
open the compass more than half-way between points A and Buse that width and place the compass on point A and draw an arc above and below line AB use the same width and place the compass on point B and draw an arc above and below line ABDraw a line from the intersection of the arcs above and the intersection of the arcs below line ABCongrats! You just constructed a perpendicular bisector!
For two-week. John and Amanda had the following transaction occurred to their checking account a deposit of 1644 and 50 Cent Shake written for 190 45 $7.50 and a debit card transaction for $30 14514 59 another one for $7.20 and $21.30 what is the ending balance for this time frame
Answer:
$1,337.91
Step-by-step explanation:
Hello, my dear friend, I am sure the question you are intending should be corrected as follows:
For two weeks, John and Amanda had the following transactions occur to their checking account: a deposit of $1,644.50; checks written for $190, $45, and $7.50; and debit card transactions for $30, $5.59, $7.20, and $21.30. What is the ending balance for this time frame?
If this is the case, then see the operation for the transactions below:
1,644.5−190-45-7.5-30-5.59-7.2-21.3=1,337.91
Please note that Deposits are positive in your account while written checks and debit card charges are negative.
HW 7.4/7.5 backside
Answer:
9. x=10
10. x=8
11. x=9/4=2.25
12. x=28
13. x=14
14. x=35
15. x=66
16. x=77/6
Step-by-step explanation:
9. x/20=18/36
Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 18:
x/20=(18/18) / (36/18)
x/20=1/2
Solving for x: Multiplying both sides of the equation by 20:
20(x/20)=20(1/2)
x=10
10. x/12=6/9
Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 3:
x/12=(6/3) / (9/3)
x/12=2/3
Solving for x: Multiplying both sides of the equation by 12:
12(x/12)=12(2/3)
x=4(2)
x=8
11. x/3=3/4
Solving for x: Multiplying both sides of the equation by 3:
3(x/3)=3(3/4)
x=9/4=2.25
12. x/42=30/45
Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 15:
x/42=(30/15) / (45/15)
x/42=2/3
Solving for x: Multiplying both sides of the equation by 42:
42(x/42)=42(2/3)
x=14(2)
x=28
13. x/12=14/12
Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 2:
x/12=(14/2) / (12/2)
x/12=7/6
Solving for x: Multiplying both sides of the equation by 12:
12(x/12)=12(7/6)
x=2(7)
x=14
14. x/25=28/20
Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 4:
x/25=(28/4) / (20/4)
x/25=7/5
Solving for x: Multiplying both sides of the equation by 25:
25(x/25)=25(7/5)
x=5(7)
x=35
15. x/110=(160-100)/100
x/110=60/100
Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 20:
x/110=(60/20) / (100/20)
x/110=3/5
Solving for x: Multiplying both sides of the equation by 110:
110(x/110)=110(3/5)
x=22(3)
x=66
16. x/11=(x+7)/17
Solving for x: Cross Multiplication:
17x=11(x+7)
Eliminating the parentheses on the right side of the equation:
17x=11(x)+11(7)
Multiplying:
17x=11x+77
Grouping the x's on the left side of the equation: Subtracting 11x both sides of the equation:
17x-11x=11x+77-11x
Subtracting:
6x=77
Dividing both sides of the equation by 6:
6x/6=77/6
Dividing:
x=77/6
Which of the following choices is the correct translation of the statement: “the length of a rectangle if the length is twice the size of the width increased by one”?
The statement 'the length of a rectangle if the length is twice the size of the width increased by one' translates into the equation l = 2w + 1 in mathematical terms. This equation represents a relationship between the rectangle's length (l) and width (w), with the length being twice the width, increased by one.
Explanation:The correct translation of the statement 'the length of a rectangle if the length is twice the size of the width increased by one' is mathematical in nature. This sentence is describing a relationship between the length and width of a rectangle.
To put it into an equation, start by denoting the width of the rectangle as 'w'. The statement says that the length is twice this width (2w) plus one. So, the length 'l' can be represented as:
l = 2w + 1
This equation shows the relationship between the length and width of a rectangle according to given statement. For practical purposes, you can insert a numerical value for width 'w' and perform the calculation on the right side to find the length 'l'.
Learn more about Rectangle dimensions here:https://brainly.com/question/31677552
#SPJ12
The mathematical expression translating the phrase is 'L = 2W + 1', where 'L' represents length of the rectangle and 'W' represents the width. It indicates that the length is twice the width, and further increased by one.
Explanation:The correct translation of the statement 'the length of a rectangle if the length is twice the size of the width increased by one' would result in a mathematical expression for the length of the rectangle (L). If we denote the width of the rectangle as W, then we could represent the length of the rectangle as follows:
L = 2W + 1
This expression indicates that the length is twice the size of the width, and then increased by one. Depending on the value of W, we plug it into the equation to determine the length of the rectangle.
Learn more about Mathematical Translation here:https://brainly.com/question/29021969
#SPJ12
Selling price is $70.00. Rate of the sales tax is 60%. That is the sales tax?
The sales tax would be $42.00, making the total cost $112.00.
To calculate the sales tax on an item, one must first convert the sales tax rate from a percentage to a decimal. Converting 60% to a decimal by dividing by 100 gives us 0.60.
Then, multiply this decimal by the selling price to find the amount of sales tax.
Amount of sales tax = price x rate of sales tax
So for a selling price of $70.00, the sales tax would be calculated as follows:
= $70.00 x 0.60 = $42.00
The sales tax on a $70.00 item at a rate of 60% is $42.00.
To find the total cost, one must add this tax to the original selling price.
Total cost = selling price + sales tax
Total cost = $70.00 + $42.00
Total cost = $112.00
Thus, the total amount paid including sales tax would be $112.00.
X+3y=5
-X+6y=3
solve the system of equation
A.X=1,Y=2
B.X=2,Y=1
C.X=1, Y=1
D.X=0, Y=2
Answer:
That all the answer hope i helped
Answer:
The answer will be B
Step-by-step explanation:
Determine the next three terms in the following sequence: 2, 3, 5, 8, ____, ____, ____,... a. 13, 19, 26 b. 12, 17, 23 c. 12, 16, 20 d. 13, 17, 23 Please select the best answer from the choices provided A B C D
Answer:
B. 12,17,23
Step-by-step explanation:
2,3,5,8, _,_,_
2,3 is increased by 1
3,5 is increased by 2
5,8 is increased by 3. theres our pattern, each time it increases it follows the next number so the next 3 numbers it would be increased by is. 4,5,6.
Now knowing it is 4,5,6 we need to add, start adding.
8+4=12. Which answers have 12 in them? B and C.
We know 12 is the next number, now we add 5 to that.
12+5=17.
B has 17 but C doesn't, so that tells you its most likely going to be B. To make sure add 6 to 17.
17+6=23. Its true that it is B, as B is 12.17.23.
The next three terms in the sequence are 13, 21, and 34.
Explanation:The given sequence is 2, 3, 5, 8.
To find the next three terms in the sequence, we need to determine the pattern.
By observing the sequence, we can see that each term is obtained by adding the two previous terms.
For example,
3 = 2 + 1,
5 = 3 + 2, and
8 = 5 + 3.
Using this pattern, the next term would be obtained by adding 8 + 5, -
8 + 5 = 13
The two terms after that would be
13 + 8 = 21 and
21 + 13 = 34.
Therefore, the next three terms in the sequence are 13, 21, and 34.
Learn more about Sequences here:https://brainly.com/question/30262438
#SPJ11
What is the total number of unique triangles with side lengths of 4 centimeters. 5 centimeters, and 10 centimeters that can be drawn
There are 0 unique triangles that can be drawn with the side lengths 4 cm, 5 cm, and 10 cm
How to determine the total number of unique triangles that can be drawn
From the question, we have the following parameters that can be used in our computation:
Side lengths = 4 cm, 5 cm, and 10 cm
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
So, we have
4 + 5 > 10 --- false
4 + 10 > 5 --- true
5 + 10 > 4 --- true
Since one of the conditions is false, no triangles can be formed using the side lengths
show that the points p(7,12) and q(-3,-12) and r (14,5) lie on a circle with center c(2,0)
If the points P (7, 12), Q (-3, -12) and R (14, 5) lie on a circle with the center C (0, 2), then the distance OP, OQ and OR are the same.
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute:
[tex]OP=\sqrt{(2-7)^2+(0-12)^2}=\sqrt{(-5)^2+(-12)^2}=\sqrt{25+144}=\sqrt{169}\\\\\boxed{OP=13}\\\\OQ=\sqrt{(2-(-3))^2+(0-(-12))^2}=\sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}\\\\\boxed{OQ=13}\\\\OR=\sqrt{(2-14)^2+(0-5)^2}=\sqrt{(-12)^2+(-5)^2}=\sqrt{144+25}=\sqrt{169}\\\\\boxed{OR=13}[/tex]
OP = OQ = OR, therefore the points P, Q and R lie on one circle.
Use the drop-down menus to identify the values of the parabola
Answer:
What drop down menues??????????????????????
Step-by-step explanation:
Answer:
options?
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:think as it as coordinates on a graph. Time=x Amount=y. So if the time is 0 and the amount is 60 you would graph a point on (0,60)
Step-by-step explanation:
Algebra 2. Help!
Which grows faster as x increases, x3 or 3x? Explain.
As x increases, x^3 grows faster than 3x.
As x increases, the growth rate of x^3 (x cubed) is faster than that of 3x. This can be explained by comparing their respective derivatives.
The derivative of x^3 with respect to x is 3x^2, while the derivative of 3x is simply 3.
The derivative represents the rate of change, or the slope of the function at a given point. In the case of x^3, its derivative 3x^2 grows at a faster rate than the derivative of 3x, which is a constant (3).
This means that as x increases, the rate of change of x^3 (3x^2) increases faster compared to the rate of change of 3x (which is constant at 3). In other words, x^3 exhibits exponential growth, while 3x exhibits linear growth. So, as x increases, x^3 grows faster than 3x.
for such more question on growth rate
https://brainly.com/question/31098703
#SPJ3
Which is true about an equilateral triangle?
Answer: all angle measures are equal
What decimal is represented by this expanded form?
5×10,000+3×1,000+2×10+8×1+ 6×1/100+4×1/1,000
Answer:
53028.064 I think
Step-by-step explanation: