The area of the pool is the amount of space it occupies
The expression for the area and the perimeter are [tex]\mathbf{A = 15x + x^2}[/tex] and [tex]\mathbf{P = 4x +30}[/tex], respectively
Let the dimension of the pool be x and y, where x represents width and y represents length.
So, the relationship between the width and the length is given as:
[tex]\mathbf{y = 15 + x}[/tex]
The area of the pool would be:
[tex]\mathbf{A = xy}[/tex]
Substitute 15 + x for y
[tex]\mathbf{A = x(15 + x)}[/tex]
Open bracket
[tex]\mathbf{A = 15x + x^2}[/tex]
And the perimeter of the pool would be
[tex]\mathbf{P = 2(x + y)}[/tex]
Substitute 15 + x for y
[tex]\mathbf{P = 2(x +15 + x)}[/tex]
[tex]\mathbf{P = 2(2x +15)}[/tex]
Open brackets
[tex]\mathbf{P = 4x +30}[/tex]
Hence, the expression for the area and the perimeter are [tex]\mathbf{A = 15x + x^2}[/tex] and [tex]\mathbf{P = 4x +30}[/tex], respectively
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if something traveled 36 feet in 22 frames in a 60 fps video, how fast would that be in mph?
i calculated that the answer will be roughly 24.9 miles per hour.
How are expressions 1/4 of 12 and 12 divided by 4
what are the leading coefficient and degree of the polynomial?
Answer:
leading coefficient: 2degree: 7Step-by-step explanation:
The degree of a term with one variable is the exponent of the variable. The degrees of the terms (in the same order) are ...
6, 0, 7, 1
The highest-degree term is 2x^7. Its coefficient is the "leading" coefficient, because it appears first when the polynomial terms are written in decreasing order of their degree:
2x^7 -7x^6 -18x -4
The leading coefficient is 2; the degree is 7.
__
Additional comment
When a term has more than one variable, its degree is the sum of the exponents of the variables. The term xy, for example, is degree 2.
if star x 2 equals square, then star x 8 equal
Answer:
Square times 4
Step-by-step explanation:
Square divided by 2 equals star right? Now we can plug in star in terms of square and we get square divided by 2 times 8, which is just Square times 4
Suppose `h\left(t\right)=-5t^{2}+10t+3`is an expression giving the height of a diver above the water (in meters), t seconds after the diver leaves the springboard.
a. How high above the water is the springboard? Explain how you know.
Answer:
Step-by-step explanation:
a) The height of the springboard above the water should be h(0) : Read, the height at t = 0
h(0) = -5(0) + 10(0) + 3
h(0) = 0 + 0 + 3
h(0) = 3
a) 3 meters
b) The time it takes the diver to hit water should be, the positive 0 solution for t. Remember, in a quadratic equation, there are two values for t where a parabola crosses the horizontal axis, which in this case would be t. Just by looking at the function, h(t) = -5t2 + 10t + 3 , one should be able to see that it cannot be factored easily, so it requires the Quadratic Formula to find the zeros ; x = -b ±√(b2-4ac) / 2a
Substitute t for x, and use the coefficients for a, b, c:
t = (-10 ± √((102 - 4(-5)(3)))/2(-5)
t = (-10 ±√(100 + 60))/-10
t = (-10 ±√160)/-10) ; Now factor the 160 to simplify:
t = (-10 ±√(10*16))/-10
t = (-10 ±4√10)/-10 ; Factor out leading coefficient of -2 from the numerator:
t = -2(5 ± 2√10)/-10
t = (5 ± 2√10)/5
Using a calculator to find the zeros, and disregarding the negative zero (because t starts at 0):
t ≈ 2.265
b) approx. 2.265 seconds for diver to hit water.
c) To find this, set the function equal to 3 to find what other value for t would be equal to 3 (we know one is 0).
-5tt + 10t + 3 = 3
-5t2 + 10t = 0 ; factor out t
t(-5t + 10) = 0
We know t = 0:
We also know that -5t + 10 = 0
-5t = -10
t = 2
c) 2 seconds. This is the time that diver would equal height of t=0 which is where he started, and where he equals the height of the springboard.
d and e) The peak of the dive (parabola), is determined using the formula h = -b/2a (Derived from the Quadratic Formula) to find the y value (in this case, the h value, answering e) and then using that result in the function to find the x value (in this case, the t value answering d) of the point where the parabola (dive path) reaches a maximum(height), or minimum(in upward opening parabolas).
h = -10/2(-5)
h = -10/-10
h = 1
h(1) = -5(1)2 + 10(1) + 3
h(1) = -5 + 10 + 3
h(1) = 8
d) At t = 1 second, diver will have reached peak of dive.
e) At t = 1 second, diver will have reached a maximum height of 8 meters.
Find the equation of the line which passes through (0,7) at a gradient of 3
Answer:
y=3x+7
Step-by-step explanation:
y=mx+c
we have (0,7). (x,y)
so y-7/x-0=3
multiply by (x-0) both sides to get
y-7=3x take -7 to the other side of equal sign
it will be: Y=3X+7
i need a lot of help from the smartest people now right now
Answer:
K) I, II, and III
Step-by-step explanation:
Given the quadratic equation in standard form, h = -at² + bt + c, where h is the height or the projectile of a baseball that changes over time, t. In the given quadratic equation, c represents the constant term. Altering the constant term, c, affects the h-intercept, the maximum value of h, and the t-intercept of the quadratic equation.
I. The h-interceptThe h-intercept is the value of the height, h, when t = 0. This means that setting t = 0 will leave you with the value of the constant term. In other words:
Set t = 0:
h = -at² + bt + c
h = -a(0)² + b(0) + c
h = -a(0) + 0 + c
h = 0 + c
h = c
Therefore, the value of the h-intercept is the value of c.
Hence, altering the value of c will also change the value of the h-intercept.
II. The maximum value of hThe maximum value of h occurs at the vertex, (t, h ). Changing the value of c affects the equation, especially the maximum value of h. To find the value of the t-coordinate of the vertex, use the following formula:
t = -b/2a
The value of the t-coordinate will then be substituted into the equation to find its corresponding h-coordinate. Thus, changing the value of c affects the corresponding h-coordinate of the vertex because you'll have to add the constant term into the rest of the terms within the equation. Therefore, altering the value of c affects the maximum value of h.
III. The t-interceptThe t-intercept is the point on the graph where it crosses the t-axis, and is also the value of t when h = 0. The t-intercept is the zero or the solution to the given equation. To find the t-intercept, set h = 0, and solve for the value of t. Solving for the value of t includes the addition of the constant term, c, with the rest of the terms in the equation. Therefore, altering the value of c also affects the t-intercept.
Therefore, the correct answer is Option K: I, II, and III.
In a recent survey of 288 people, 72 said that their favorite color of car was white. What percent of the people surveyed didn't like white cars?Write 2 over 5 as a percent.
9514 1404 393
Answer:
75%
Step-by-step explanation:
The number for whom white was not a favorite was ...
288 -72 = 216
The percentage whose favorite was not white was ...
216/288 × 100% = 75% . . . didn't like white
The temperature in antartica is 20 degrees below freezing at night. During the day, the temperature increases
by 30 degrees. What is the daytime temperature?
Answer:
42
Step-by-step explanation:
From a group of 15 men and 12 women, how many ways can you select a group of 2?
Answer:
The total number of ways this can be done together is 105 × 66 = 6930
This is a combination question question it has to do with selection.
In order to group 2 men from 15 men, this can be expressed using the combination formula as shown;
15C2 = 15!/(15-2)!2!
15C2 = 15!/13!2!
15C2 = 15×14/2
15C2 = 105 ways
Similarly in order to group 2 women from 12 men, this can be expressed using the combination formula as shown;
12C2 = 12!/(12-2)!2!
12C2 = 12!/10!2!
12C2 = 12×11/2
12C2 = 66 ways
The total number of ways this can be done together is 105 × 66 = 6930
Learn more about combination here: https://brainly.com/question/14492965
range of the function f(x) = -x^2 - 5
Answer:
Step-by-step explanation:
Calculate the perimeter of a square with a side length of 3ft
The perimeter of a square is the length of one side multiplied by 4 ( the number of sides)
3 ft x 4 sides = 12 ft.
Perimeter = 12 ft.
Eric is helping his younger sister learn division. He is having a hard time explaining what a remainder is. Help Eric out by describing what a remainder is in your own words. What is the remainder when 76 is divided by 3?
Answer:
1
Step-by-step explanation:
The remainder is what’s left when you divide. The part you cannot divide.
You can divide 75 by 3 = 25, so the remainder is 1.
help pls home work home qork
Answer:
the answer is this sign >. it means the answer on the left is greater than the one on the right
35 if the answer is correct
Answer:
A.
Step-by-step explanation:
The attached graph has a y-intercept of -1 and a slope of 2, as the equation says it must.
__
The equation is in slope-intercept form, where the coefficient of x is the slope of the line. That is, the ratio of "rise" to "run" is 2: the line rises 2 grid squares for each grid square it runs to the right.
A local hamburger shop sold a combined total of 813 hamburgers and cheeseburgers on Saturday. There were 63 more cheeseburger sold than burgers. How many hamburgers were sold on Saturday?
9514 1404 393
Answer:
375 hamburgers
Step-by-step explanation:
Let h represent the number of hamburgers. Then h+63 is the number of cheeseburgers, and the combined total is ...
h +(h +63) = 813
2h = 813 -63 = 750
h = 750/2 = 375
375 hamburgers were sold on Saturday.
_____
Additional comment
In a "sum and difference" problem like this, the smaller number is half the difference between the sum and the difference. h = (813 -63)/2 = 375. This generic solution applies to all "sum and difference" problems.
A grocery store clerk can scan 1 product every 1/2 of a second. At what rate can she scan products?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
Write a polynomial function of the least degree that has roots of 3 and (4 + i).
Roots:
Polynomial Function:
Answer:
x³ - 11x² + 41x - 51Step-by-step explanation:
The least number of degree is 3 and the third root should be (4 - i) to make polynomial rational.
The polynomial is:
(x - 3)(x - (4 + i))(x - (4 + i)) = (x - 3)(x² -x(4 + i + 4 - i) + (4 + i)(4 - i)) = (x - 3)(x² - 8x + 16 - (-1)) = (x - 3)(x² - 8x + 17) = x³ - 8x² + 17x - 3x² + 24x - 51 = x³ - 11x² + 41x - 511 2/15 + -3 1/2 in simplest form
Rewrite 5/6 and 6/7 so they have a common denominator
Answer:
a command demonimater of 6 and 7 is 42
35/42 and 36/42
Hope This Helps!!!
Review the incomplete equation below. Select the number that makes the equation true.
35 × 64 = 1800 +_____ + 120 +20
Answer:
300
Step-by-step explanation:
find what's 35 x 64 its 2240
then you add up 1800 and 120 and 20 n you get 1940
Then you subtract to see what's missing and you get
300
if you don't understand pls tell me
Apply the distributive property to factor out the greatest common factor.
6+30=6+30
6 + 30
The greatest common factor is 6, so take it out. We get...
6 (1 + 5)
Let's verify it.
6 (1 + 5) = 6 + 30
6(6) = 6 + 30
36 = 36
LHS = RHS, Hence proved.
______
RainbowSalt2222 ☔
The recursive algorithm given below can be used to compute gcd(a, b) where a and b are non-negative integer, not both zero. procedure gcd(a, b) if a > b then gcd(a, b) := gcd(b, a) else if a = 0 then gcd(a, b) := b else if a = 1 then gcd(a, b) := 1 else if a and b are even then gcd(a, b) := 2gcd(a/2, b/2) else if a is odd and b is even then gcd(a, b) := gcd(a, b/2) else gcd(a, b) := gcd(a, b − a) Use this algorithm to compute (a) gcd(124, 244) (b) gcd(4424, 2111).
Coding the given algorithm in python 3, the greatest common divisor of the values (124 and 244) and (4424 and 2111) are 4 and 1 respectively.
The program implementation goes thus :
def gcd(a, b):
#initialize a function named gcd which takes in two parameters
if a>b:
#checks if a is greater than b
return gcd (b, a)
#if true interchange the Parameters and Recall the function
elif a == 0:
return b
elif a == 1:
return 1
elif((a%2 == 0)and(b%2==0)):
#even numbers leave no remainder when divided by 2, checks if a and b are even
return 2 * gcd(a/2, b/2)
elif((a%2 !=0) and (b%2==0)):
#checks if a is odd and B is even
return gcd(a, b/2)
else :
return gcd(a, b-a)
A sample run if the program on the values given :
print(gcd(124, 244))
print()
#leaves a space after the first output
print(gcd(4424, 2111))
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John buys a computer on sale for $450.00. He
pays $50.00 less than have the original price. How
much was the original price of the computer?
Write and solve an equation
Answer:
$450+$50= X
X=$500
Step-by-step explanation:
The sale price is $450.00, so you take that amount and $50.00 which the amount he paid less and add them both. We do this because we want to see the original price of the computer. If it mentioned the original price already and the amount $50.00 and asked the sail price instead, we would have to subtract to get the answer.
Here we have to add.
450+50=500
(add the dollar sign)
$450+$50=X
X=$500
Gene has a gasoline budget of $275 per month. He uses an average of $6 of gasoline each day he drives. Which of the following equations represents how much money is left in his gasoline budget after x days of driving?
A. y=275-6x
B. y=275+6x
C. y=6x-275
D. y=275x-6
Answer:
d because your taking away 6 from the 275
Step-by-step explanation:
What are the solutions to this quadratic equation? x2+6x-5 A. B. C. D.
8y + 15x + 3y - 12x - 3x
Answer:
11y is the exact value.
Step-by-step explanation:
What is the equation of the line in slop-intercept form?
Enter your answer in the blank spots
y= __x + __
Answer:
y = 2 1/2 x + 5
Step-by-step explanation:
We were recently going over this. Slope formula: y2 - y1 / x2 - x1. In our case the slope is 2 1/2, and the y-intercept is 5.
Tell me if I'm wrong :)
17) Which number is located the same distance on
a number line from -5 as 3 is?
Answer: -13
Step-by-step explanation:
I know that the distance between -5 and 3 is 8 so I subtracted 8 from the negative 5 so it would be the same distance and I got -13
Answer:
-13
Step-by-step explanation:
An executive has 6 skirts, 8 jackets, and 6 blouses that all coordinate. If an outfit consists of one skirt, one
jacket, and one blouse, how many different outfits does she have?
Work Shown:
6*8*6 = 288
Why does this work? Consider a table that is 6 rows by 8 columns. The rows represent the number of skirts and 8 is the number of jackets. That produces 6*8 = 48 different skirt & jacket combos. We can extend this idea out to any number of items instead of just 2.
Answer:
6
Step-by-step explanation:
you keep counting until you reach the lowest number of whatever you need to make it equal
6-1-1-1-1-1-1
6-1-1-1-1-1-1
8-1-1-1-1-1-1