Answer:
The function describing the relationship of V and t is V = 3t²
Step-by-step explanation:
* Lets explain the meaning of direct variation
- The direct variation is a mathematical relationship between two
variables that can be expressed by an equation in which one
variable is equal to a constant times the other
- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the
constant of variation
* Now lets solve the problem
# V is varies directly with the square of t
- Change the statement above to a mathematical relation
∴ V ∝ t²
- Chang the relation to a function by using a constant k
∴ V = kt²
- To find the value of the constant of variation k substitute V and t
by the given values
∵ t = 6 when V = 108
∵ V = kt²
∴ 108 = k(6)² ⇒ simplify the power 2
∴ 108 = 36k ⇒ divide both sides by 36 to find the value of k
∴ 3 = k
- The value of the constant of variation is 3
∴ The function describing the relationship of V and t is V = 3t²
The length of a rectangle is 2 cm more than four times the width. If the perimeter of the rectangle is 84 cm, what are its dimensions
Answer:
Length 34 cm
Width 8 cm
Step-by-step explanation:
Let
x-----> the length of the rectangle
y----> the width of the rectangle
we know that
The perimeter of rectangle is equal to
P=2(x+y)
P=84 cm
so
84=2(x+y)
42=x+y ----> equation A
x=4y+2 -----> equation B
substitute equation B in equation A and solve for y
42=(4y+2)+y
5y=42-2
y=40/5=8 cm
Find the value of x
x=4y+2 ----> x=4(8)+2=34 cm
The dimensions are
Length 34 cm
Width 8 cm
The width of the rectangle is 8 cm and the length is 34 cm.
To determine the dimensions of the rectangle, we need to set up equations based on the given information.
Let's denote the width of the rectangle by W (in cm). According to the problem, the length L is 2 cm more than four times the width. Therefore, we can express the length as:
L = 4W + 2
The perimeter of a rectangle is calculated using the formula:
Perimeter = 2L + 2W
Given that the perimeter is 84 cm, we can substitute the expressions for L and W into the perimeter formula:
84 = 2(4W + 2) + 2W
Simplify the equation:
84 = 8W + 4 + 2W84 = 10W + 4Subtract 4 from both sides: 80 = 10WDivide both sides by 10: W = 8Now that we have the width, we can find the length:
L = 4(8) + 2 = 32 + 2 = 34
Thus, the dimensions of the rectangle are:
Width: 8 cmLength: 34 cm.Find the simple interest paid one $600 is borrowed for three years at 6% per
Answer:
Principal amount= $600
Time= 3 years
Rate of Interest = 6%
SI= PRT/100
= 600x6x3/100
= $108
Interest is $108
Step-by-step explanation:
Please Help Quickly!!
What is the first step to prove that 9^n - 4^n is divisible by 5?
the answer should be,
A. shows that 9^1 - 4^1=5
hope this helps! :)
what is the other binomial?
Answer:
11x² -3x
Step-by-step explanation:
We have the product of a sum, of two binomials and one of the initial binomials but we'd like to know the other one.
It's very much like A + B = C, and we have both B and C, but looking to find A.
What would you do in the ABC scenario?
You'd isolate A by transforming the equation to: A = C - B
In this case, C = 12x² - 5x and B = x² - 2x...
A = (12x² - 5x) - (x² - 2x) = 12x² - 5x - x² + 2x
A = 11x² -3x
Evaluate the dot product of (2,4) and (1,2)
ANSWER
The dot product is 10.
EXPLANATION
The given vectors are (2,4) and (1,2).
If we have the vectors
u=(a,b) and v=(c,d)
Then the dot product of the two vectors is given by
[tex]u \bullet \: v = ac + bd[/tex]
This implies that,
[tex](2,4) \bullet(1,2) = 2 \times 1 + 4 \times 2[/tex]
This simplifies to;
[tex](2,4) \bullet(1,2) = 2 + 8 = 10[/tex]
Answer:
-6
Step-by-step explanation:
took test
dani buys. a movie. at walmart on sale. the original. cost is $18 bit is 30% off. and there eis 5% sales tax. what the total cost she will pay for the movie
The total cost Dani will pay for the movie including discount and sales tax is $13.23
To find the total cost Dani will pay for the movie:
Calculate the discount: $18 x 0.30 = $5.40
Subtract the discount from the original price: $18 - $5.40 = $12.60
Calculate the 5% sales tax: $12.60 x 0.05 = $0.63
Total cost: $12.60 + $0.63 = $13.23
If f(x) = 5x - 2 and g(x) = 2x + 1, find (f + g)(x)
Answer:
(f + g)(x) = 7x - 1
Step-by-step explanation:
Given : f(x) = 5x – 2 and g(x) = 2x + 1
We have to find (f + g)(x)
Consider (f + g)(x) = f(x) + g(x)
Also, given f(x) = 5x – 2 and g(x) = 2x + 1
Substitute, we have,
f(x) + g(x) = 5x - 2 + 2x + 1
Like Terms are terms having same variable with same degree.
Simplify by adding like terms, we have,
f(x) + g(x) = 5x + 2x - 2 + 1
f(x) + g(x) = 7x - 1
Thus, (f + g)(x) = 7x - 1
Answer:
Thus, (f + g)(x) = 7x - 1
Step-by-step explanation:
(f + g)(x) = 7x - 1
Step-by-step explanation:
Given : f(x) = 5x – 2 and g(x) = 2x + 1
We have to find (f + g)(x)
Consider (f + g)(x) = f(x) + g(x)
Also, given f(x) = 5x – 2 and g(x) = 2x + 1
Substitute, we have,
f(x) + g(x) = 5x - 2 + 2x + 1
LIKE TERMS are terms having same variable with same degree.
Simplify by adding like terms, we have,
f(x) + g(x) = 5x + 2x - 2 + 1
f(x) + g(x) = 7x - 1
Thus, (f + g)(x) = 7x - 1
I need help on my math homework
Answer: the first one is True and the second one is false
Step-by-step explanation:
3 + 5x = 23
so replace x with 4 you get 3 + 5 * 4 = 3 + 20 = 23
this is equal to 23 so it is true
2x - 6 = 9
do the same you get
2 * 8 - 6 = 9
16 - 6 = 10
the answer is 10 not nine therefore it is false
If I make 180 dollars a week. How many weeks does it take to reach 7,500 dollars?
Answer:
it would take you 41 weeks
(rounded to 42 if that is a choice answer because when you divide 7500 by 180 it gives you 41.66666)
Step-by-step explanation:
7cm
10cm
4cm
The area of the compound shape is 106cm.
work out the size of x.
Answer: 9cm
Step-by-step explanation:
[tex]7x10=70cmx^{2}[/tex]
4(x)=4x
1.) 70+4x=106 (subtract 70 on both sides)
2.)4x=36 (divide 4 on both sides)
3.)x=9
answer=9
7x10=70cmxsquare
4(x)=4x
70+4x=106
4x=36
x=36/4
x=9
If 5 x 6 = 20 + y, what is the value of y?
5*6=20+y
30=20+y
30-20=20-20+y
10=y
Check answer by using substitution method
5*6=20+y
30=20+10
30=30
Answer is y=10
5 x 6 = 30
y + 20 = 30
y + 20 - 20 = 30 - 20
y = 10
Perform the indecated operation. 5 over 9 times 3 over 7
Answer:
[tex]\frac{5}{21}[/tex]
Step-by-step explanation:
[tex]\frac{5}{9}[/tex] × [tex]\frac{3}{7}[/tex] = [tex]\frac{15}{63}[/tex] = [tex]\frac{5}{21}[/tex]
Answer:
5/63
Step-by-step explanation:
that would be:
5 3 5
----- * ------ = (after reduction) ----------- = 5/63
9 7 3(21)
Barry is 8 years older than his sister. In 3 years, he will be twice as old as she will be then. How old is each now?
Final answer:
Barry is currently 13 years old and his sister is 5 years old. This is determined by setting up a system of equations based on the given information and solving for their current ages.
Explanation:
The question involves solving a system of equations to find the current ages of Barry and his sister. Let's let B represent Barry's current age and S represent his sister's current age. According to the problem, Barry is 8 years older than his sister (B = S + 8). In 3 years, Barry will be twice as old as his sister will be then (B + 3 = 2(S + 3)).
Write down the two equations: B = S + 8 and B + 3 = 2(S + 3).
Substitute B from the first equation into the second equation: (S + 8) + 3 = 2(S + 3).
Simplify and solve for S: S + 11 = 2S + 6.
Rearrange the equation to find S: S = 5.
Substitute the value of S back into the first equation to find B: B = 5 + 8, so B = 13.
Therefore, Barry is currently 13 years old and his sister is 5 years old.
In triangle JKL, m of angle J = 90, m of angle K = 30, and m of angle L = 60. Which of the following statements about triangle JKL are true? Check all that apply.
A) KL= root 3 (JL)
B) KL= 2(JL)
C) JK= root 3 (JL)
D) JK= 2(JL)
E) JL= root 3/2 (KL)
F) JK= root 3/2 (KL)
Answer:
# Answer B is true ⇒ KL = 2(JL)
# Answer C is true ⇒ JK = √3(JL)
# Answer F is true ⇒ JK = √3/2(KL)
Step-by-step explanation:
* Lets explain the ratio between the sides of the triangle
- In Δ JKL
∵ The measure of angle J is 90°
∴ KL is the hypotenuse
∵ The measure of angle K is 30°
∴ JL is the opposite side to angle 30°
∵ The measure of angle L is 60°
∴ JK is the opposite side to the angle 60°
- There is a fact in the triangle which has angles 30° , 60° , 90°
# The length of the side opposite to the angle of measure 30° is
half the length of the hypotenuse
∵ KL is the hypotenuse
∵ JL is the opposite side to the angle of measure 30°
∴ JL = 1/2 KL OR KL = 2 JL
# The length of the side opposite to the angle of measure 60° is
√3 the length of the opposite side to the angle 30°
∵ JK is the opposite side to the angle of measure 60°
∵ JL is the opposite side to the angle of measure 30°
∴ JK = √3 JL
# The length of the side opposite to the angle of measure 60° is also
half √3 the length of the hypotenuse
∵ JK is the opposite side to the angle of measure 60°
∵ KL is the hypotenuse
∴ JK = √3/2 KL
- From the relation above
# Answer B is true ⇒ KL = 2(JL)
# Answer C is true ⇒ JK = √3(JL)
# Answer F is true ⇒ JK = √3/2(KL)
Answer:
It is a and B in C & D
Step-by-step explanation:
These are the closest answers
Driving across country, mike drove for 3 hours at a certain rate and for 4 hours at a rate 10 mph faster. If his total distance covered was 495 miles, then what was his slower rate?
Mike's slower rate of driving across country was 65 mph.
Explanation:Let the slower rate be represented as r mph. The faster rate will be r+10 mph. The total distance covered (495 miles) is the product of the time and the rate:
The distance covered at the slower rate is 3r miles.The distance covered at the faster rate is 4(r+10) miles.Adding up the distances, we get:
3r + 4(r+10) = 495Simplifying the equation:
3r + 4r + 40 = 495Combining like terms:
7r + 40 = 495Subtracting 40 from both sides:
7r = 455Dividing by 7:
r = 65Therefore, the slower rate is 65 mph.
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The correct answer for the slower rate at which Mike drove is 65 mph.
To find the slower rate at which Mike drove, let's denote the slower rate as r mph. Mike drove at this rate for 3 hours. He then drove for 4 hours at a rate that is 10 mph faster than the slower rate, which would be r + 10 mph.
The total distance covered by Mike is the sum of the distances covered at each rate. We can set up an equation to represent this:
[tex]\[ 3r + 4(r + 10) = 495 \][/tex]
Expanding the equation, we get:
[tex]\[ 3r + 4r + 40 = 495 \][/tex]
Combining like terms, we have:
[tex]\[ 7r + 40 = 495 \][/tex]
Now, we need to solve for r We can do this by subtracting 40 from both sides of the equation:
[tex]\[ 7r = 495 - 40 \] \[ 7r = 455 \][/tex]
Dividing both sides by 7 to solve for r, we get:
[tex]\[ r = \frac{455}{7} \] \[ r = 65 \][/tex]
Therefore, the slower rate at which Mike drove is 65 mph.
The sum of two integers is -8.if one integer is 12 then the other is?
Answer:
2 and -10
Step-by-step explanation:
let the two integers be x and y.
so, x+y=-8---‐-------(1)
and,
x=y+12-------‐-----(2)
from (1) and (2),
(y+12)+y=-8
or, 2y=-8-12
or, y=-20/2
or, y=-10
substitutting the value of y in (2),
x=-10+12=2
therefore the required integers are 2 and -10.
Answer:
-20
Step-by-step explanation:
→ The sum of two integers is -8.
⇒ One will be called "x" and the other will be called "y"
→ One integer is 12 ( "y" )
Let's set up an equation x = ? and y = 12 so,
→ x + y = -8
( Substitute y for 12 )
→ x + 12 = -8
( -12 from both sides to isolate x )
→ x = -20
Tania analyzed the relationship between student test scores and the number of hours studied. She calculated the trend line to be y = 6.8x + 60, where x is the number of hours studied and y is the score. Which closet is to the score for a student who studied 3 hours?
A 80
B 85
C 90
D 95
Answer:
A: 80
Step-by-step explanation:
As we know that the trend line is [tex]y=6.8x+60[/tex], we can plug in x=3 in order to find out the estimated score for 3 hours of studying
[tex]y=6.8x+60\\\\y=6.8(3)+60\\\\y=20.4+60\\\\y=80.4[/tex]
y=80.4 is closest to A: 80
Answer:
Option A, 80
Step-by-step explanation:
Trend line is given by y = 6.8x + 60
where x = number of hours she studied
y = score
Now we have to calculate the score for a student for studied for 3 hours.
y = 6.8 × 3 + 60
= 20.4 + 60
= 80.40
≈ 80
Option A will be the answer.
(x 4 - 3x 3 + 3x 2 - 3x + 6) (x - 2)
Answer:
x^5 - 5 x^4 + 9 x^3 - 9 x^2 + 12 x - 12
Step-by-step explanation:
(x ^4 - 3x^3 + 3x^2 - 3x + 6) (x - 2)
Distribute the x to all the terms in the first parentheses
(x^ 4 *x - 3x^ 3 *x + 3x^ 2 *x - 3x *x + 6*x)
Then simplify
(x^5 - 3x^4 + 3x^ 3 - 3x2 + 6x)
Distribute the -2 to all the terms in the first parentheses
(x^ 4 *(-2) - 3x^ 3 *(-2) + 3x^ 2 *(-2) - 3x *(-2) + 6*(-2))
Then simplify
(-2x^4 +6x^3 -6x^ 2 +6x -12)
Add the terms together
(x^5 - 3x^4 + 3x^ 3 - 3x2 + 6x) +(-2x^4 +6x^3 -6x^ 2 +6x -12)
x^5 - 5 x^4 + 9 x^3 - 9 x^2 + 12 x - 12
Answer:
x^3 -x^2 + x -1 + 4/x-2
Step-by-step explanation:
;)
Find the mode of this set of data 18,27,28,44,44,50,67
Answer:
44
Step-by-step explanation:
the mode of a set of data is the value that occurs most often, in this case it is 44
44 would be the mode of the data.
The mode of the data is the number that occurs the most. It is always best to put the numbers in order from least to greatest so we can see what number appears more than once.
18,27,28,44,44,50,67
When we look at this set of numbers, we can see that 44 appears more than any other number. Therefore, the mode of these numbers is 44.
Fernando bought a new watch set that includes 5 watch faves and 7 colored bands . From how many different watches can he choose?
Answer:
35 different watches
Step-by-step explanation:
I don't know if this is correct so sorry if it's not.
5 faces x 7 bands.
So, 5 x 7
=
35
i hope that helps... it might not, sorry
Answer:
35 different watches/combos.
Step-by-step explanation:
5 watches, 7 different wrist bands
5 x 7 = 35
1 watch consist of 1 watch and 1 band so he can have 35 different watch combinations.
A right rectangular prism has a length of 5 centimeters, a width of 8 centimeters, and a height of 4
centimeters.
What is the volume of the prism?
Enter your answer in the box.
cm3
Answer:
160cm^3
Step-by-step explanation:
V=Lwh
so, (5x8x4)
v=160cm^3
Hope my answer has helped you!
Determine whether the piece of paper can be used to wrap the rectangular prism exactly once without any gaps or overlaps.
Answer:
No, because they do not have the same area.
Step-by-step explanation:
For the piece of paper to cover once without overlap or gaps, it must have the same area as the the total surface area of the prism.
The total surface area of the rectangular prism is: [tex]2(3.5\times2+3.5\times1.5+2\times1.5)=30\frac{1}{2}in^2[/tex]
The area of the rectangular sheet is:[tex]5\times 8=40in^2[/tex]
Since the area of the piece of paper is more than the surface area of the rectangular prism there will be an overlap.
if f(x) and f^-1(x) are inverse functions of each other adn f(x) - 2x+5, what is f^-1(8)?
Answer:
[tex]f^{-1}(8)=1.5[/tex]
Step-by-step explanation:
If y=f(x)=2x+5, to find the inverse function express x n terms of y:
[tex]y=2x+5\\ \\2x=y-5\\ \\x=\dfrac{y-5}{2}[/tex]
Now, change y into x and x into y:
[tex]y=\dfrac{x-5}{2}\\ \\f^{-1}(x)=\dfrac{x-5}{2}[/tex]
Substitute x=8 into [tex]f^{-1}(x)[/tex] expression:
[tex]f^{-1}(8)=\dfrac{8-5}{2}\\ \\f^{-1}(8)=\dfrac{3}{2}=1.5[/tex]
Answer:
3/2
Step-by-step explanation:
f(x) = 2x+5
f⁻¹(2x+5) = x
2x+5 = 8 => 2x+5 = 8 => 2x = 3 =>
=> x = 3/2
=> f⁻¹(8) = 3/2
The perimeter of a rectangular herb garden is 74 feet. If the length is 5 feet longer then 3 times it’s width what is the gardens width?
Answer:
width = 8 feet and length = 29 feet
Step-by-step explanation:
perimeter of a rectangle P = 2(L + W)
width W = x
length L = 3x + 5
P = 74 feet
74 = 2(3x + 5 + x)
37 = 3x + 5 + x
37 = 4x + 5
4x = 37 -5
4x = 32
x = 8
W = 8 feet
Much of Ann’s investments are in Cilla Shipping. Ten years ago, Ann bought seven bonds issued by Cilla Shipping, each with a par value of $500. The bonds had a market rate of 95.626. Ann also bought 125 shares of Cilla Shipping stock, which at the time sold for $28.00 per share. Today, Cilla Shipping bonds have a market rate of 106.384, and Cilla Shipping stock sells for $30.65 per share. Which of Ann’s investments has increased in value more, and by how much? a. The value of Ann’s bonds has increased by $45.28 more than the value of her stocks. b. The value of Ann’s bonds has increased by $22.64 more than the value of her stocks. c. The value of Ann’s stocks has increased by $107.81 more than the value of her bonds. d. The value of Ann’s stocks has increased by $8.51 more than the value of her bonds.
Answer:
A.
The value of Ann’s bonds has increased by $45.28 more than the value of her stocks.
Step-by-step explanation:
The value of Ann’s bonds has increased by $45.28 more than the value of her stocks. Option A is correct.
We have given that,
Much of Ann’s investments are in Cilla Shipping.
What is the stock increase?
By this, we mean that share prices change because of supply and demand. If more people want to buy a stock (demand) than sell it (supply), then the price moves up.
Ten years ago, Ann bought seven bonds issued by Cilla Shipping, each with a par value of $500. The bonds had a market rate of 95.626.
Ann also bought 125 shares of Cilla Shipping stock, which at the time sold for $28.00 per share.
Today, Cilla Shipping bonds have a market rate of 106.384, and Cilla Shipping stock sells for $30.65 per share.
The value of Ann’s bonds has increased by $45.28 more than the value of her stocks. Option A is correct.
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15 POINTS
Using Euler's Formula: F+V=E+2
A geometric solid has thirty-two faces and ninety edges. Find the number of vertices.
SHOW WORK
Answer:
V -E +F = 2
Vertices = 2 + Edges -Faces
Vertices = 2 + 90 -32
Vertices = 60
Step-by-step explanation:
Solve for X in this equation
Answer: x=e
Step-by-step explanation:
x= ln(e^e)
using ln(e^x)= x x ln (e), transform the expression
x= e x ln (e)
the natural logatithm of e equals 1
x=e x 1
any expression multiplied by 1 remains the same
x=e alternative form: x= 2.71828
ANSWER
[tex]x = e[/tex]
EXPLANATION
The given logarithmic equation
[tex]x = ln_{e}(e) [/tex]
Note that
[tex] ln(e) = 1[/tex]
Using the power rule of logarithms,
[tex]x =e \ln(e)[/tex]
This gives us:
[tex]x =e (1)[/tex]
Simplify to get:
[tex]x = e[/tex]
Find negative square root of 36. ±6 −6 6 18
Answer:
The answer is -6
Step-by-step explanation:
Hope it helped you!
Answer:
B. [tex]-6[/tex]
Step-by-step explanation:
We are asked to find the negative square root of 36.
We can write our given problem as [tex]-\sqrt{36}[/tex].
We can write 36 as 6 to second power.
[tex]-\sqrt{36}=-\sqrt{6^2}[/tex]
Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:
[tex]-\sqrt{6^2}=-6[/tex]
Therefore, the negative square root of 36 is negative six and option B is the correct choice.
what is the average of these numbers 23 33 31?
Answer:
29
Step-by-step explanation:
Answer: 29
Step-by-step explanation:
It is important to know the definition.
The average of a set of number is defined as the sum of all these numbers divided by the total numbers that are in this set.
So, knowing this, we know that if we have a set of three numbers:"a", "b" and "c" , we can calculate the average of them with this procedure:
[tex]average=\frac{a+b+c}{3}[/tex]
Therefore, we can calculate the average of the numbers 23, 33 and 31. This is:
[tex]average=\frac{23+33+31}{3}=\frac{87}{3}=29[/tex]
ASAP RIGHT NOW NEW FOR ME
Answer:8m+20
Step-by-step explanation:
U have too add the perimeter than multiple area