Answer:
The water level would rise by [tex]5\; \rm cm[/tex].
Step-by-step explanation:
Assume that the initial water level is [tex]h\; \rm cm[/tex].
Before the cube was placed in the tank, the volume of the water was the same as the volume of a rectangular prism with a length of [tex]160\; \rm cm[/tex], a height of [tex]80\; \rm cm[/tex], and a height of [tex]h\; \rm cm[/tex]:
[tex]\begin{aligned} & 160\; {\rm cm} \times 80\; {\rm cm} \times h\; {\rm cm} \\ =\; & (80 \times 160) \, h \; \rm cm^{3} \end{aligned}[/tex].
Let the rise in the water level in the tank be [tex]x\; \rm cm[/tex]. The new water level would be [tex](x + h)\; \rm cm[/tex].
The volume of the water and the submerged cube, combined, would be the same as that of a rectangular prism with a length of [tex]160\; \rm cm[/tex], a width of [tex]\rm 80\; \rm cm[/tex], and a height of [tex](x + h)\; \rm cm[/tex]:
[tex]\begin{aligned} & 160\; {\rm cm} \times 80\; {\rm cm} \times (x + h)\; {\rm cm} \\ =\; & (80 \times 160) \, (x + h) \; \rm cm^{3} \end{aligned}[/tex].
In other words:
Volume of water in this tank: [tex](80 \times 160)\, h\; \rm cm^{3}[/tex], whereasVolume of water in this tank, plus the volume of the submerged cube: [tex](80 \times 160) \, (x + h) \; \rm cm^{3}[/tex].Therefore, the volume of the submerged cube could be expressed as:
[tex]\begin{aligned} & (80 \times 160) \, (x + h) \; {\rm cm^{3}} - (80 \times 160) \, h \; \rm cm^{3} \\ =\; &(80 \times 160)\, x\; {\rm cm^{3}}\end{aligned}[/tex].
On the other hand, the volume of the cube could be expressed as:
[tex](40\; \rm cm)^{3} = 64000\; \rm cm^{3}[/tex].
Equate these two expressions for the volume of the cube and solve for [tex]x[/tex], the rise in the water level in the tank:
[tex](80 \times 160)\, x = 64000[/tex].
[tex]x = 5[/tex].
In other words, the rise in the water level in this tank would be [tex]5\; \rm cm[/tex].
A store in Iowa advertises that during their Labor Day sale, everything is 25% off, plus they will pay the sales tax. Mike buys shoes for $80 and socks for $5. Since there will be no tax added, what is the final price for Mike’s purchase?
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Answer:
$63.75
Step-by-step explanation:
Mike's final price will be 1-25% = 75% of the marked price.
($80 +5)(0.75) = $63.75
The final price for Mike's purchase is $63.75.
Which of the equations below could be the equation of this parabola?
Vertex
(0, 0)
0
10
ОА
A. x = - 1 2 3 4
B. y = - 1/2 x ²
C. x = 1 / 4²
Do y = x
Answer:
the answer is "B"
the "a" (as in ax^2) is negative thus the parabola "goes downward"
Step-by-step explanation:
The equation of parabola is,
y = - 1/2x²
What is Parabola?A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix.
We have to given that;
In a parabola,
Vertex = (0, 0)
Since, We know that;
Standard form of equation of parabola is,
y = a (x - h)² + k
Where, (h, k) = (0, 0) = vertex
Hence, We get;
y = a (x - 0)² + 0
y = ax²
Here, A point on parabola is, (2, - 2)
- 2 = a (2)²
a = - 2 / 4
a = - 1/2
Hence, The equation of parabola is,
y = - 1/2x²
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A camera cost 115 Canadian dollars if each Canadian dollar is worth 0.950 to US dollars how much will the camera cost in the US dollars
Answer:
109.25 US dollars
Step-by-step explanation:
115 * 0950
2.
Match the graph of the function with the function rule.
A. [tex]y=\frac{1}{4}[/tex]·4^x
B. y = 1 • 4x
C. [tex]y=\frac{1}{2}[/tex]·4^x
D. y = 2 • 4x
Answer:
C) [tex]y = \frac{1}{2}[/tex] × [tex]4^x[/tex]
Answer:
C. y= 1/2*4^x
Step-by-step explanation:
What is the value of p?
A.60°
B. 40°
C. 90°
D. 50°
Answer:
D . p = 50
Step-by-step explanation:
To find the value of p we first need to find the values of inner angles
180 - 140 (linear pair)
= 40
180 -90 (linear pair)
= 90
now use angle sum property of triangle
40 + 90 + p = 180
130 + p = 180
p = 180 - 130
p = 50
Find the average of the list of numbers.
- 13, – 25, – 24, – 14
Answer:
-19
Step-by-step explanation:
-13-25-24-14
= -76/4
= -19
Convert 8 2/3% into a decimal.
Answer:
the answer is = 0.08666666666
The decimal value of 8 2/3% is 866.677.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
8 2/3% into decimal.
So, 8 2/3%
= 26/3 %
= 26 /3 x 100
= 8.6666667 x 100
=866.6777
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name the value of the digit 484,002,000 and the 8 is underlined.
Answer:
ITS 80,000,000
I need the answerrrrrrrrrrrrrrrrrrrrrrrr I HATE GEOMETRY AND I NEED TO GET MY GRADES UP CAUSE I NEED MY PHONE BACK.
Answer:
The bisector is line l
mq = 7
Step-by-step explanation:
To find x:
[tex]5x-3=11-2x\\\\+2x+3 +3 +2x\\\\\\7x=14\\x=2[/tex]
To find the value of mq
plug in the value of x into the equation.
[tex]11-2x\\11-2(2)\\11-4\\=7[/tex]
MQ = 7
Hope this is helpful! Please leave a review and comment below! Thanks for all your support!
b. B
Step-by-step explanation:PM = RM
[tex]5x - 3 = 11 - 2x[/tex]
[tex]5x + 2x = 11 + 3[/tex]
[tex]7x = 14[/tex]
[tex]x \times 2[/tex]
MQ = [tex]11 - 2x[/tex]
[tex]11 - 2 \times 2[/tex]
[tex]11 - 4[/tex]
[tex] = 7[/tex]
please help i will give extra points
Answer:
3^2 + 21 /3
9 + 7
16✓
Answer
Set theory Need answers quick
Answer:
4. {2,4,6,8}
5. [(-2, -1), (1, 8)}
9. {0, 2}
Step-by-step explanation:
The intersection of the given sets is the set that contains elements common to all of the given the sets.
How do I write three fourths of a number is 12 as an equation?
Answer:
[tex] \frac{3}{4} n = 12[/tex]
Step-by-step explanation:
let the number be n :
[tex] \frac{3}{4} \: of \: n = 12 \\ \\ \frac{3}{4} n = 12[/tex]
further more:
[tex]3n = 12 \times 4 \\ n = \frac{12 \times 4}{3} \\ \\ n = 4 \times 4 \\ n = 16[/tex]
Answer:
3x4=12
Step-by-step explanation:
3=g/-4-5 ((for 25 points))
Answer:
3=g/-4 -5
3+5=g/-4
8= g/-4
8x(-4)=g
g=-32
Step-by-step explanation:
A triangle has side lengths of (7n-2p)(7n−2p) centimeters, (2n+4q)(2n+4q) centimeters, and (q-5p)(q−5p) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answer:
(7n-2p)(7n−2p) + (2n+4q)(2n+4q) + (q-5p)(q−5p) OR
53n² +29p² +17q² -14np +8nq -10pq
Step-by-step explanation:
The perimeter is found by adding all the side lengths.
P = (7n-2p)(7n−2p) + (2n+4q)(2n+4q) + (q-5p)(q−5p)
We know that (a+b)(a+b) = (a+b)², and (a-b)(a-b) = (a-b)²
P = (7n-2p)² + (2n+4q)² + (q-5p)²
We know that (a+b)² = a²+b²+2ab, and (a-b)² = a²+b²-2ab
P = 49n² + 4p² - 14np +4n² +16q² + 8nq +q²+25p² -10pq
Combine like terms
P = 53n² +29p² +17q² -14np +8nq -10pqhelp with this math question plz
Answer: The length of LK is 40.
Step-by-step explanation:
LK = 6x+10
KM = 2x+8
LM = 58
so
LM = LK + KM
or, 58 = 6x+10+2x+8
or, 58 = 8x + 18
or, 58-18 = 8x
or, 8x = 40
so, x = 5
now
LK = 6x + 10
= 6*5+10
= 30 +10
= 40
Show that |3| + |10| = |3| + |10|
Answer:
/10/=/-10/=10 ; /3/=/-3/=3
=> /3/+/10/=/3/+/10/=3+10=13
Step-by-step explanation:
Determine the domain of the following function:
Step-by-step explanation:
2x-18 ≥ 0
2x ≥ 18
x ≥ 9
and
3x -27 ≠ 0
3x ≠ 27
x ≠ 9
so, the answer is <9 ; +oo >
A motorboat travels 448 kilometers in 8 hours going upstream and 440 kilometers in 5 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
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Answer:
boat: 72 km/hcurrent: 16 km/hStep-by-step explanation:
The speed difference between boat and current is the upstream rate:
(448 km)/(8 h) = 56 km/h
The sum of speeds of boat and current is the downstream rate:
(440 km)/(5 h) = 88 km/h
The rate of the boat is half the sum of these:
(56 +88)/2 = 72 . . . km/h
The rate of the current is half their difference:
(88 -56)/2 = 16 . . . km/h
The rate of the boat is 72 km/h; the rate of the current is 16 km/h.
Which of the following equations has exactly one solution?
2x + 3 – 6x=-4x – 3
3x + 12 – 9x = -11x + 12 + 5x
6x +9 - 8x = 2x + 9
7x + 3 – 8= 13x + 5 – 6x
Answer:
I belive I might be c not completely sure but pretty positive
You have a lead ball with a mass of 360 g. The density of lead is 15 g/cm3. What is the volume of the ball?
Recall that density = mass / volume.
Let's plug our known values into the equation.
15 g/cm^3 = 360g / volume
First, let's multiply both sides by volume
Volume * 15 g/cm^3 = 360g
Divide both sides by 15 g/cm^3
Volume = 24 cm^3
Density is defined as the mass per unit of volume. The volume of the ball is 24 cm³.
What is density?Density is defined as the mass per unit of volume. It is given by the formula,
Density = Mass / Volume
Given that You have a lead ball with a mass of 360 g. The density of lead is 15 g/cm³.
Now, since density is the ratio of mass and volume. Therefore, we can write the volume of the ball as,
Density = Mass / Volume
Volume = Mass / Density
Volume of the ball = 360g / 15g/cm³
= 24 cm³
Hence, the volume of the ball is 24 cm³.
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A number to be a rational number that is not an integer but a while number
Answer:
So coming back to the question; No, there is no rational number that is not an integer but is a whole number. The number is called as a rational number if it can be expressed as p/q where p & q are integers & q is not 0. All negative integers are rational numbers but those are not whole numbers.Jan 1, 2020
Step-by-step explanation:
g(x)=
Write a relationship for a function whose g(x) values are 2 more than five times the principal square root of x.
Lets do
2 more than five times the square root of x[tex]\\ \sf\longmapsto g(x)=5\sqrt{x}+2[/tex]
Lets take an example
[tex]\\ \sf\longmapsto g(4)=5\sqrt{4}+2[/tex]
[tex]\\ \sf\longmapsto 5(2)+2[/tex]
[tex]\\ \sf\longmapsto 10+2[/tex]
[tex]\\ \sf\longmapsto 12[/tex]
the money spent to buy goods is called
Answer:
l think it's consumer spending
Answer and explanation please?
Answer:
c= 13
Step-by-step explanation:
The complementary angles add up to 90° so we use some basic algebra to solve this question. like in the step by step explaination I have provided on paper
Solve the equation.
6(x + 7) = 5(x - 7) + x
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution is
(Simplify your answer.)
OB. The solution is all real numbers.
O C. There is no solution.
(Answer quickly)
Answer:C
Step-by-step explanation:
6(x+7)=5(x-7)+x
⇔6x+42=5x-35+x
⇔6x-5x-x=-35-42
⇔0x=-77
Stephanie is painting her room wich is 14' long by 9' wide and each wall is 10' tall. How many square feet of paint will she use? help.
Answer:
460 sq ft
Step-by-step explanation:
Assuming the room is a perfect rectangle and not accounting for doors and windows:
14 ft x 10 ft = 140 sq ft X 2 = 280 sq ft
9 ft x 10 ft = 90 sq ft x 2 = 180 sq ft
280 sq ft + 180 sq ft = 460 sq ft
help with this plzzzz
Answer:
point C
Step-by-step explanation:
both planes include point C so that is where they intersect
Answer:
Point C
Step-by-step explanation:
As you can see in the picture below, Point C is where both planes intersect. Point C is what both planes have in common.
what is - 7/10 + (- 5/6) =
-7/10 + (-5/6) = -(7/10 + 5/6) =
= -(21/30 + 25/30) = -46/30 =
= -1 16/30 = -1 8/15 ← the end
plzz someones help me plz I will mark brainlest diameter is 1 3/4
Answer:
The area of the circle is 2.41 in^2
Step-by-step explanation:
You are given the diameter, 1 3/4. This is a mixed fraction, so let's convert that into decimal.
1 3/4 = 7/4
7/4 = 1.74
Now, let's use the area of circle formula.
A = 1/4πd^2
A = 1/4 * π * 1.75^2
A ≈ 2.40528
Let's round the area to the nearest hundredth.
2.40528 = 2.41
235Px=235P(x-1)*(3x)
Answer:
2456
Step-by-step explanation:
