Answer:
44,886 gallons
Step-by-step explanation:
We need to find the volume
V = l*w*h
V = 30ft*25ft*8ft
V =6000 ft^3
We know that 1 ft^3 = 7.481 gallons
6000 ft^3 * 7.481 gallons/1 ft^3 = 44886 gallons
Answer:
44,883 gallons
Step-by-step explanation:
The amount of water the pool can hold can be found by calculating the volume of the pool.
We know that the pool is rectangular, and it is a three dimensional shape (3 dimensions: length, width and depth). Therefore, we can use the formula for finding the volume of a rectangular prism:
V=l*w*h
We know the length is 30 feet and the width is 25 feet. The height is also the depth, so the height is 8 feet.
l= 30 feet
w=25 feet
h= 8 feet
Substitute these values into the formula.
V= 30 feet * 25 feet * 8 feet
Multiply the numbers together.
V= (30 feet * 25 feet) * 8 feet
V= 750 feet^2 * 8 feet
V=6000 feet^3
Now, let's find how many gallons the pool can hold.
1 ft^3 is equal to 7.4805 gallons. Therefore, we can multiply 6000 ft^3 and 7.4805
6000 ft^3 * 7.4805 gallons/1 ft^3
6000* 7.4805 gallons
44,883 gallons
The pool can hold 44,883 gallons of water.
PLZZZ HLPPP MEEE The S's in the SSS Similarity theorem states that two triangles are similar if they have ___________ proportional sides
Answer:
3
Step-by-step explanation:
SSS similarity states that all 3 sides must be proportional for the triangles to be similar
Part 3
1. Be sure your work is shown and steps are in order.
2. List all the possible rational roots.
3. Use synthetic division to test the possible rational roots and factor possible.
4. Identify complex roots if possible.
5. Sketch a graph of the function, please show:
a. the end behavior correctly
b. the shape of the near x-intercepts
c. (if possible) anything you can learn by considering symmetry and transformations.
3a. p(x)= 2x^5 - 9x^4 + 6x^3 + 22x^2 - 20x - 25
Answer:
possible rational roots: ±1/2, ±1, ±5/2, ±5, ±25/2, ±25
p(x) = (x +1)^2(2x -5)(x^2 -4x +5)
complex roots: 2±i
see the last attachment for a graph
Step-by-step explanation:
2. The leading coefficient of p(x) is 2, and the constant term is 25. The Rational Root Theorem tells you possible rational roots will be of the form ...
±(divisor of 25)/(divisor of 2)
That is, they are ...
±1/2, ±1, ±5/2, ±5, ±25/2, ±25
__
3. Before we get into synthetic division, we choose to see if we can reduce this list any. We note that p(0) = -25. The value of p(1) is the sum of the coefficients:
p(1) = 2 -9 +6 +22 -20 -25 = 30 -54 = -24
Similarly, the value of p(-1) is the same sum with odd-degree coefficients negated:
p(-1) = -2 -9 -6 +22 +20 -25 = 42 -42 = 0
So, we found our first root: -1. Using synthetic division, we can reduce the polynomial and start over. See the first attachment for this division.
__
The reduced polynomial is ...
p1(x) = 2x^4 -11x^3 +17x^2 +5x -25
We already know that +1 is not a of it. Checking -1, we have ...
p1(-1) = 2 +11 +17 -5 -25 = 0
So, we found our second root: -1. Using synthetic division, we can reduce the polynomial and start over. See the second attachment for this division.
__
The reduced polynomial is ...
p2(x) = 2x^3 -13x^2 +30x -25
The alternating signs tell us there are no more negative real roots. They also tell us there are 1 or 3 positive real roots. We know p2(0) = -25. Then ...
p2(1) = 2 -13 +30 -25 = 32 -38 = -6
The average rate of change between these points is (-6 -(-25))/(1 -0) = 19. At this rate, we expect a root between x=1 and x=2. Testing x=2 using synthetic division, we get a remainder of -1. (See the 3rd attachment.) Then the rate of change between x=1 and x=2 is (-1 -(-6))/(2-1) = 5, suggesting x=5/2 might be a worthwhile test value.
The synthetic division is shown in the 4th attachment. You will note that we divide the polynomial p2(x) by its leading coefficient, so the coefficients used for p2(x) in the synthetic division are 1, -13/2, 15, -25/2. The remainder of 0 tells us that (x -5/2) is a factor of p2(x)/2, or (2x -5) is a factor of p2(x).
__
The reduced polynomial is ...
p3(x) = x^2 -4x +5
This can be written in vertex form as ...
p3(x) = (x -2)^2 +1
The positive leading coefficient means the graph opens upward, and the vertex at (2, 1) means there are no real solutions.
The real solutions to p(x) are x = -1, -1, and 5/2.
__
4. The complex solutions will be the solutions to ...
(x -2)^2 +1 = 0
(x -2)^2 = -1
x -2 = ±√(-1) = ±i
x = 2 ±i . . . . complex roots of p(x)
__
5. The graph is shown in the last attachment. The odd degree and positive leading coefficient of p(x) means the overall shape will be from lower left to upper right (/). That is, the sign of the end value of p(x) will match the sign of x.
The graph will touch the x-axis from below at x = -1, and will cross at x = 2.5. There is no particular symmetry.
The final quadratic factor is graphed and its vertex shown. The vertex matches that of the vertex-form equation for p3(x), above.
Answer:
possible rational roots: ±1/2, ±1, ±5/2, ±5, ±25/2, ±25
real solutions to p(x) are x = -1, -1, and 5/2.
(x -2)^2 +1 = 0
(x -2)^2 = -1
x -2 = ±√(-1) = ±i
x = 2 ±i complex roots
kinda stuck on this question. please help?
Answer:
The answer is b
Step-by-step explanation:
I know this because a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression and since 9 is being multiplied by x that would mean 9 is a coefficient in this expression.
what is the perimeter of a rectangle 3m long amd bm broad?
[tex]answer = 6 + 2b\\ solution \\ length = 3 \: m \\ breadth = b \: m \\ perimeter \: of \: rectangle = 2(l + b) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2(3 + b) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 3 + 2 \times b \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 6 + 2b \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
The perimeter of the rectangle is P = 6 + 2b, where b is the width.
Given data:
To find the perimeter of a rectangle, we add the lengths of all its sides. In this case, the rectangle is 3 meters long and b meters broad.
The perimeter is calculated as follows:
Perimeter = 2 × (length + breadth)
Given that the length is 3 meters and the breadth is b meters, substitute these values into the formula:
Perimeter = 2 × (3 + b)
Simplifying the expression,
Perimeter = 6 + 2b
Hence, the perimeter of the rectangle is 6 + 2b meters.
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solve the equation
7h-5(3h-8) = 72
Answer:
h = -4
Step-by-step explanation:
7h-5(3h-8) = 72
Distribute
7h - 15h +40 = 72
Combine like terms
-8h +40 = 72
Subtract 40 from each side
-8h+40-40 = 72-40
-8h = 32
Divide each side by -8
-8h/-8 = -32/-8
h = -4
Steps:
Step 1: Simplify both sides of the equation.
7h−5(3h−8)=72
7h+(−5)(3h)+(−5)(−8)=72(Distribute)
7h+−15h+40=72
(7h+−15h)+(40)=72(Combine Like Terms)
−8h+40=72 −8h+40=72
Step 2: Subtract 40 from both sides.
−8h+40−40=72−40
−8h=32
Step 3: Divide both sides by -8
Answer: h=−4
The answer for this question is h=-4
Please mark me brainliest
Hope this helps.
A. (-3,5)
B. (-2,2)
C. (-1,-3)
D. (0,-1)
Need help ASAP
Explanation:
The first inequality has its shaded region below the solid boundary line. The second inequality has its shaded region above the dashed boundary line. Overlapping the two regions leads to the left-most shaded area. This shaded area is darkest of all the shaded areas, due to the overlapping colors. All points in this area make both inequalities true.
Only point B (-2, 2) is in this region. The other points are either in one shaded region only.
Find the midpoint of the line segment.
Could someone explain how to solve these aswell?
Answer:
(-2, -3)
Step-by-step explanation:
The middle of the point. It covers two blocks so find the middle.
Or you can use the midpoint formula
[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
(-2,-3) because it is in the middle of the line segment, between the two marked points
A.) 10.9
B.) 8.6
C.) 7.3
Answer:
Option (c) 7.3
Step-by-step explanation:
Since is forms a right angled traingle,
a= 3+4= 7
b = 4-2= 2
c = AB
Pythagorean theorem:
a^2+b^2 = c^2
So since we know a and B but the hypotenuse (c) is missing
7^2 + 2^2 = c^2
c^2 = 49+4
= 53
c = √53
= 7.28 rounded off to 7.3
So the length of hypotenuse or c is 7.3 units
Therefore, the length is 7.3
A eat sixth of pizza in 2 minutes.B takes 3 minutes to eat one quarter of same same pizza.If A and B starts eating one pizza each,who will finnish first?
Answer:
same time , 12 minutes
Step-by-step explanation:
'A' can eat 1÷6 pizza in 2 minutes
Therefore, 'A' can eat full pizza in 6×2 minutes=12 minutes
'B' can eat 1÷4 pizza in 3 minutes
therefore, 'B' can eat full pizza in 3×4 minutes=12 minutes
So, Both 'A' and 'B' will finish at same time.
What must be added each term to a ratio2:3 so that it may became 4:7
Step-by-step explanation:
HOPE THE ANSWER IS CORRECT AND USEFUL
An airplane change in altitude before landing is shown in the table. What equation represents this change in altitude?
Answer:
a = -4,000m + 39,000
Step-by-step explanation:
if c=12 and d=9 , what is 82-4c+d
Answer:
43
Step-by-step explanation:
multiply 4 x c(12)=48
then just plug it in and solve
82-48=34
34+9=43
Jessica decides to mix grades of gasoline in her truck. She puts in 8 gallons of regular and 8 gallons of premium for a total cost of $41.04. If premium gasoline costs $0.21 more per gallon than regular, what was the price of each grade of gasoline?
Answer:
The price of the regular gasoline is $2.46, while the premium is $2.67.
Step-by-step explanation:
Let the price of regular gasoline be "x", while the price for the premium be "y", The sum of the amount of each type of gas multiplied by its cost should be equal to the total paid, therefore:
[tex]8*x + 8*y = 41.04[/tex]
We also know that the premium gas costs 0.21 more than the regular one, therefore:
[tex]y = x + 0.21[/tex]
We can apply the second expression on the first, in order to solve for "x".
[tex]8*x + 8*(x + 0.21) = 41.04\\8*x + 8*x + 1.68 = 41.04\\16*x = 41.04 - 1.68\\16*x = 39.36\\x = \frac{39.36}{16} = 2.46[/tex]
[tex]y = 2.46 + 0.21 = 2.67[/tex]
The price of the regular gasoline is $2.46, while the premium is $2.67.
Which is the focus of a parabola with equation y2 = 4x?
0 (-1,0)
0 (0, -1)
0 (0, 1)
(1, 0)
Answer:
(1, 0)
Step-by-step explanation:
Please write this as y^2 = 4x; the " ^ " indicates exponentiation.
The appropriate equation for a horizontal parabola that opens to the right is
y^2 = 4px
Here, we are told that y^2 = 4x; this tells us that 4p = 4, and so p = 1.
Again, this parabola is a horizontal one and it opens to the right. p = 1 is the distance of the focus from the vertex, and in this case p = 1. Thus, the focus is at (1, 0) (situated on the x-axis).
Answer:
(1,0) 2022
Step-by-step explanation:
stop playing wit me
Dawn raises money for her school in a jog-a-thon. She will get three dollars for every lap she completes. If it takes 4 laps to jog 1 mile, and Dawn jogs a total of 12 miles, how much money will Dawn raise for her school?pls help
Answer:
$144
Step-by-step explanation:
[tex]\dfrac{\$3}{\text{lap}} \cdot \dfrac{4\text{ laps}}{\text{mile}}\cdot 12\text{ miles} =[/tex]
[tex]\boxed{\$144}[/tex]
Hope this helps!
Is number one congruent? If it is how?
Answer:
Yes, Triangles in (1) are congruent
Step-by-step explanation:
Two conditions must be satisfied before two triangles can be deemed or declared as being congruent.
1.) They must posses similar shape
2.) They must posses similar size ( that is the corresponding sides and angles of both triangles must be the same)
Triangles in (1) meet both criterias by possessing similar shape with the size and length of the corresponding angles also being the same.
Therefore, the two triangles are congruent.
The congruency theorem Side-Angle-Side (SAS) proves two triangles are congruent because both triangles have an included angle in between two congruent sides.
True
False
what's the justification for 2x + 0 = 22
Answer:
Additive inverse property
Step-by-step explanation:
what is the sign of -a^4/3 when a is less than zero
A positive
B negative
C zero
Reasoning:
'a' is less than 0, so we write a < 0
Since a < 0, this means a^4 > 0. Raising a negative to an even exponent will make the result positive. Example: (-2)^4 = 16
Applying the cube root to some positive number leads to some other positive number.
So far we see that the expression a^(4/3) is positive
The final result however is negative because the negative out front flips things from positive to negative.
It turns out it doesn't matter if 'a' is positive or negative. As long as 'a' is nonzero, then -a^(4/3) is negative. If a = 0, then the whole thing is 0.
Add 30 to the product of 12 and 6 and
divide the
result by
6. The final
answer
Is what?
PLEASE HELP I AM TIMED PEOPLE
A rectangular pyramid was sliced perpendicular to its base and through its vertex. What is the shape of the cross section shown in the figure?
A) a triangle that has the same dimensions as one of the sides of the pyramid
B) a triangle that does not have the same dimensions as one of the sides of the pyramid
C) a parallelogram that is not a rectangle
D) a rectangle
Answer:
B
Step-by-step explanation:
The figure shown is of an isosceles triangle.The triangle is not congruent with any of the faces of the pyramid thus the triangle does not have the same dimension as one of the sides of the pyramid
Answer: B
Step-by-step explanation:
A quadrilateral has all sides and angles congruent. Which name best describes the figure? a. rhombus b. square c. rectangle d. trapezoid
Answer:
It's a square
Step-by-step explanation:
Because a square has all equal sides, and its an quadrilateral, and we know its square bc the other shapes dont really have that.
The square is also the name of the regular quadrilateral — one in which all sides are congruent and all angles are congruent.
Which two of these are continuous data?
Answer:
B and D
Step-by-step explanation:
Age of Student --> Age of student is continues
Time taken to run one mile is also continues
Answer:
B and D
Step-by-step explanation:
How many different angle measures the two parallel and one crossing line can make?
Answer:
The answer is 2 different angles, 53° and 127°.
Explanation:
As you subtract 180° from the given angle to find the other angle, you will get only 2 angles either 53° or 127°.
Work out the percentage change to 2 decimal places when a price of £189 is decreased to £150.
Answer:
The percentage change is -21%
Step-by-step explanation:
The percentage change can be expressed by the formula;
(new price -old price)/old price * 100%
New price = £150
old price = £189
Inputing these values in the formula, we have;
(150-189)/189 * 100%
-39/189 * 100%
= -20.63% and that is approximately -21%
Help
Two distinct number cubes are rolled together. Each number cube has sides numbered 1 through 6.
What is the probability that the outcome of the roll is an even sum or a sum that is a multiple of 3?
Enter your answer, in simplest fraction form, in the box.
Answer:
The probability is 2/3
Step-by-step explanation:
The first thing to write here is the sample space.
I have shown this in the attachment.
Kindly note that the number of expected outcome is 36
The outcome we are looking at is either an even sum or a multiple of 3
These are what i have circled in the addition results
The number of circles is 24
The probability is thus 24/36 = 2/3
what is the measure angle of N???
[tex]answer \\ 61 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
Suppose f(x)=x^2 Find the graph of f(x-2) *Will make Brainliest If answered asap*
Answer:
the root is 2 . thus, the correct graph is graph 2
Which of the following linear equations corresponds to the table above?
The linear equation of the corresponding table is y = 4x+3 which is correct option(D).
What is the slope of a linear function?The slope of a linear function is defined as the angle of the line. It is denoted by m.
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a linear function —Point 1 and Point 2. Point 1 has coordinates (x₁, y₁) and Point 2 has coordinates (x₂, y₂)
We need two of those points to come up with the equation of the corresponding line.
Solution in y-intercept form y = mx+b
We can calculate the slope of the line using any 2 of the given points: I pick (0,3) and (3,15).
The formula for determining the slope of the line through 2 points (x₁,y₁) and (x₂,y₂) as m=(y₂-y₁)/(x₂-x₁)
By plugging in the corresponding values,
m = (15-3)/(3-0) = 12/3 = 4
Since the value of y when x is zero, i.e. the point (0,3) of the table, then the value of b is 3.
Now, Substitute the values in y = mx+b,
y = 4x+3
Hence, the linear equation of the corresponding table is y = 4x+3.
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Marquis has 7 cups of yogurt. He gives his sister 3 3
5 cups of the yogurt, how much of
Marquis’s yogurt remains?
Answer:
He has 3,65 cups of yogurt left.
Step-by-step explanation:
7 - 3,35 = 3,65
