Answer:
The volume of water in the pool over time from when the hose is placed in the pool until the pool is full is defined by the equation and its graph is given below.
Explanation:
The total capacity of the pool is 20,000 gallon.
It is given that the pool contains 5000 gallons of water when a hose is placed in the pool and begins adding water at a rate of 1250 gallons per hour. So the initial volume of water is 5000.
Let the time is defined by t. So, the volume of water in the pool after time t is defined as,
The capacity of the pool is 20,000 gallon, therefore the maximum value of V(t) is 20,000.
The maximum value of t is 12, since the time is always positive, therefore we can say that,
The below graph representing the volume of water in the pool over time from when the hose is placed in the pool until the pool is full. The initial point is (0,5000) and the other point is (12,20000).
Answer:
the two points will be (0,5000) and (12,20000
Step-by-step explanation:
What is the value of 6k^-4 if k = -1?
A. -24
B. 1
C. 6
D. 24
Answer: 6
Step-by-step explanation:
[tex]6\left(-1\right)^{-4}[/tex]
[tex]6\cdot \frac{1}{\left(-1\right)^4}[/tex]
[tex]6\cdot \:1[/tex]
[tex]6[/tex]
Answer:
C, the answer is 6.
Step-by-step explanation:
If you substitute -1 into the variable "k", it would look like this equation, 6(-1)[tex]6(-1)^{-4}[/tex], if you then raise -1 to the power of -4, you would then get the value 1. Thus, 6 * 1 equals 6. C would be the correct answer.
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The sum of the digits of a two-digit number is 12. The number formed by reversing the digits is 54 more than the original number. What is the original number?
Answer:
39
Step-by-step explanation:
let the 2 digit number be ab = 10a + b ( considering place value )
The reversed 2 digit number is ba = 10b + a
The sum of the 2 digit number is
a + b = 12 ( subtract b from both sides )
a = 12 - b → (1)
Expressing as an equation
ba = ab + 54 , that is
10b + a = 10a + b + 54
Substitute a = 12 - b into the equation
10b + 12 - b = 10(12 - b) + b + 54 , simplify both sides
9b + 12 = 120 - 10b + b + 54
9b + 12 = - 9b + 174 ( add 9b to both sides )
18b + 12 = 174 ( subtract 12 from both sides )
18b = 162 ( divide both sides by 18 )
b = 9
Substitute b = 9 into (1)
a = 12 - 9 = 3
Thus
the original 2 digit number = ab = 39
The reversed 2 digit number = ba = 93
which is 54 more than the original number
Let g be a polynomial function of x where g(x) = 2x^3+ 3x^2-5x-6 . If (x+2) is a factor of g, write an equation for g as the product of linear factors
Answer:
[tex]2x^3+ 3x^2-5x-6 = (x+2)(x+1)(2x+3)[/tex]
Step-by-step explanation:
Given polynomial [tex]g[/tex]:
[tex]g(x) = 2x^3+ 3x^2-5x-6[/tex]
A factor of polynomial is [tex](x+2)[/tex].
To find:
Equation of the polynomial as the product of linear factors.
Solution:
First of all, let us divide the polynomial [tex]g[/tex] with [tex](x+2)[/tex] to find the other factors.
As degree of polynomial is 3, when divided by a linear equation, it will result in a quadratic.
That quadratic will have 2 solutions.
Solving the quadratic in linear will give us the answer.
Result of division:
[tex]\dfrac{2x^3+ 3x^2-5x-6}{x+2} =2x^2-x-3[/tex]
Now, solving the quadratic:
[tex]2x^2-x-3 = 2x^2-3x+2x-3 \\\Rightarrow x(2x-3)+1(2x-3)\\\Rightarrow (x+1)(2x-3)[/tex]
So, the linear equation can be written as:
[tex]2x^3+ 3x^2-5x-6 = (x+2)(x+1)(2x+3)[/tex]
Which graph shows y = 2x – 12?
Answer:
(0,6) (0,-12)
Step-by-step explanation:
The equation y = 2x - 12 represents a linear function with a slope of 2 and a y-intercept of -12.
The equation y = 2x - 12 represents a linear function with a slope of 2 and a y-intercept of -12. This means that the graph will have a positive slope, indicating a upward trend, and it will intersect the y-axis at the point (0, -12).
To sketch the graph, you can start by plotting the y-intercept at (0, -12). From there, use the slope of 2 to determine additional points by moving 1 unit horizontally (to the right) and 2 units vertically (upward) to plot another point. Repeat this process to plot more points, then connect them to form a straight line.
Keep in mind that a visual representation is essential for accurately identifying the specific graph of y = 2x - 12.
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Give 3 examples of integers which are greater than −2
Answer: -1 would be greater than negative two, along with 20, 1000.
-2 is a negative number, so any number that is -1 or higher is greater than -2
Answer:
1,2,3
Step-by-step explanation:
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which number best represents the slope of the graphed line?
Answer:( -10,10), (-,+)
Step-by-step explanation:
Awnser:
-2
Step by Step:
To find a slope, you need to find 2 points. You can't have a line with only 1 point.
The equation for a slope is: y2-y1/x2-x1.
It doesn't matter which order you put them in.
I used (-4,1) and (-6,2).
So: 2-1/-6-(-4)
1/-6+4
1/-2
-2
The varsity club wants to make 1000 dollars for a NYC trip. They are selling t-shirts for 9.00 dollars each. The fee for printing lancers logos is 30 dollars if the number of t-shirts is represented by x write and solve an inequality to find the number of t-shirts they have to sell in order to reach their goal
Answer:
26
Step-by-step explanation:
Given that:
Target amount for NYC trip = $1000
Cost of T - shirt = $9 each
Logo printing fee = $30
Number of T - shirts = x
Number of T - shirts to be sold in other to reach their goal :
[(Cost of logo + Cost of T shirt) * number of shirts sold] ≥ target amount
[($30 + $9) * x] ≥ $1000
$39x ≥ 1000
x ≥ 1000/ 39
x ≥ 25.64
Hence, they have to sell at least 26 t shirts with logo printed to raise $1000
Subtract and reduce: 2 2/3 - 1 1/2
Step-by-step explanation:
I used a calculator but the answer is 1 1/6
At a football stadium, 4% of the fans in attendance were teenagers. If there were 120 teenagers at the football stadium, what was the total number of people at the stadium?
74 is a rational number but not a whole number. 74 is a whole number but not a rational number. 74 is a whole number and a rational number. 74 is not a rational number, and it is not a whole number.
Answer:
Option C: 74 is both a whole number and a rational number.
Step-by-step explanation:
A rational number is defined as a number which can be written as a fraction of two integers, an integer, a whole number and a natural number. The integer could be positive or negative.
Examples include -1/4, 1/2, 12
So it's obvious that the given number of 74 is a rational number.
Now, a whole number is simply a non - negative integer.
An integer is a number that is not a fraction.
Thus, examples of whole numbers are 0, 1, 2, 3, 4...
So 74 is clearly a whole number.
Therefore, we can conclude that 74 is both a whole number and a rational number.
for the function f(x) = 2(8)^x evaluate f(2)
Answer:
f(2)=128
Step-by-step explanation:
f(x) = 2(8)^x evaluate f(2)
f(2)= 2(8)^2
f(2)=2(64)
f(2)=128
0.6 divided by what equals 2.5
Answer:
1.5
Step-by-step explanation:
Do the reverse/opposite/check division with multiplication.
2.5 · 0.6 = 1.5
Kaley and Tom both work at Publix as cashiers for $7.68 per hour. This week Kaley worked 5 more hours than Tom in overtime. Write an expression that represents the weeks' wages for Kaley and Tom combined if h represents the number of hours Tom worked?
Answer:
X=5+h
Step-by-step explanation:
Write an equation in standard form of the line that passes through the given point and the given slope. (-9, -4); m = -1/3
First, we must determine b using slope-intercept form*, the given point, and the given slope.
[tex]-4 = -\frac{1}{3}(-9) + b\\\\-4 = -3 + b\\\\-1 = b[/tex]
Second, we need to set up the equation of the line in slope-intercept form.
[tex]y = -\frac{1}{3}x - 1[/tex]
Third, we convert the above equation to STANDARD FORM**.
[tex]y = -\frac{1}{3}x - 1\\\\\frac{1}{3}x + y = -1[/tex]
We now have our equation: [tex]\frac{1}{3}x - y = -1[/tex]
*Slope-intercept form: y = mx + b
**Standard form: ax + by = c
Cual es la raíz cuadrada de 48?
√48 = 4√3
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Dee spends $0.25, $0.30, $0.10 and $0.04.
How much $ does she spend in all?
Answer:
$0.69
Step-by-step explanation:
Add them all up.
Answer:
$0.64
Step-by-step explanation:
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From points A and B, the distance between which is 1020 mi, two trains left simultaneously towards each other. The speed of one train was 10 mph greater than the speed of the other one. In 5 hours the trains had
Complete question :
From points A and B, the distance between which is 1020 mi, two trains left simultaneously towards each other. The speed of one train was 10 mph greater than the speed of the other one. In 5 hours the trains had not met yet and were 170 mi apart. Find the speed of the trains.
Answer:
Train A = 80 miles per hour
Train B = 90 miles per hour
Step-by-step explanation:
Given that :
Distance between A and B = 1020
Let the speed of A = x
Speed of B = x + 10
Since they both left simultaneously;
Distance traveled after 5 hours will be :
Distance = speed * time
A = x * 5 = 5x
B = (x + 10) * 5 = 5x + 50
After the distance traveled by each of A and B, they are still 170 miles apart
Hence, distance covered after 5 hours ;
Total miles - miles left
1020 - 170 = 850 miles
Hence,
5x + 5x + 50 = 850
10x = 850 - 50
10x = 800
x = 80
Train A = 80 miles per hour
Train B = 80 + 10 = 90 miles per hour
__7. Cooling Tea: A freshly made cup of tea is served at a temperature of about 180°F. The tea
cools rapidly at first, and then slows down gradually as it approaches room temperature.
Independent Quantity:
Dependent Quantity:
Review the graph of complex number z.
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (5, negative 5).
What is the polar form of z?
Answer:
It is D
Step-by-step explanation:
Looking at the Graph the point is at 5-5i
the only polar form that solves to 5-5i is D.
Also I did it on Edge.. Good Luck!
The complex number z represented on the graph (5, -5) is given as 5√2[cos(-π/4) + isin(-π/4)] in polar form
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the complex number z represented on the graph as (5, -5). Therefore:
r = √(5² + 5²) = 5√2
Ф = tan⁻¹(-5/5) = -π/4
The complex number z represented on the graph (5, -5) is given as 5√2[cos(-π/4) + isin(-π/4)] in polar form
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c). The local bus service has 2 lines of buses that start together at 8
a.m. Buses on line A leave after every 15 minutes while Buses on line
B leave after every 20 minutes. In a day, how many times do buses on
both line A and B leave together between 8 a.m. and 11 a.m.
Answer:
3 times
Step-by-step explanation:
Firstly we calculate the number of minutes between 8 and 11 am
The number of hours is 3 hours
The number of minutes is 180 minutes since 1 hour is 60 minutes
Now out of 180, to know the number of times that they both leave, we need to get the multiples of both between 0 and 180
The multiples are;
60, 120, 180
This means that they leave together 3 times
Find the solutions using the Quadratic Formula.
x2 – 5x-14 = 0
HELP ASAP. ABC is an isosceles triangle.
Answer:
please make it more clear
Step-by-step explanation:
what you are asking
determine the angle of x :p
Answer:
x=-10 I think?? because they are congruent
2/3 ( 12 n + 6 ) − 1 5 ( 10 n − 2 )
Answer:
34-158n
Step-by-step explanation:
First factor:
8n+4-150n+30
Then combine like terms
34-158n
Answer: -142n+34
Step-by-step explanation:(2/3)(12n)+(2/3)(6)+(-15)(10n)+(-15)(-2)
=-142n+34
You buy 2.6 pounds of grapes for $1.40 per pound. You hand the cashier a $5 bill. How much change will you receive?
Which statement would be included in the proof of why Measure of angle C + measure of angle G + measure of angle H = 180 degrees.?
A. Angles F and H are congruent.
B. Angles A and G are congruent.
C. Angles A and H are congruent.
D. Angles E and C are congruent.
I think c
Step-by-step explanation:
I did it a min ago
Answer:
ur answer would be C. Angles A and H are congruent.
Step-by-step explanation:
right on edge 2021 for math
Will give BRAINLIEST The two points and (–3, –2) and (4, 8) are part of a line with a slope of:
Answer:
slope of 10/1 or simplified to 10
Step-by-step explanation:
Answer:
slope is 10/7
Step-by-step explanation:
use the formula or plot the points on a graph to get the slope is 10/7
If f(x) = 4x - 8, what is the value of f(-3)?
Answer:
-20
Step-by-step explanation:
f(x)= 4x-8 f(-3)
y= 4(-3) -8
y= -12 -8
y= -20
HELP ASAP PLS BRAINLIEST
Answer:
for the 10 column it is $150.00 the next column is 15 and for 200 it is $250.00
Step-by-step explanation: