Answer:
a) length x = 45ftb) maximum area = 4050 ft²Step-by-step explanation:
Given the quadratic equation A=−2x2+180x that gives the area A of the yard for the length x, to maximize the area of the yard then dA/dx must be equal to zero i.e dA/dx = 0
If A=−2x²+180x
dA/dx = -4x + 180 = 0
-4x + 180 = 0
Add 4x to both sides
-4x + 180 + 4x = 0 + 4x
180 = 4x
x = 180/4
x = 45
Hence the length of the building that should border the yard to maximize the area is 45 ft
To find the maximum area, we will substitute x = 45 into the modelled equation of the area i.e A=−2x²+180x
A = -2(45)²+180(45)
A = -2(2025)+8100
A = -4050 + 8100
A = 4050 ft²
Hence the maximum area of the yard is equal to 4050 ft²
roberta is 6 times danielles age. in 12 years, roberta will only be 2 times danielles age. how old is danielle now?
Answer:
the answer is 3
Step-by-step explanation:
3.03 times 10^-3 in scientific nation
Answer:
3.03 • 10⁻³ is scientific notation
0.00303 is decimal form
The 1275 students who accepted admission to Academic University in 2016 had an average SAT score of 1356. Is 1356 a population parameter or a sample statistic?
Answer:
population parameter
Step-by-step explanation:
A population is said to be category of individuals under study.
A population parameter is a numerical value which provides a summary to a measure of an average or percentage which describes the entire population under a study.
In a Normal Curve, the population parameter can be a population mean or population standard deviation , population proportion which represent the population.
∴
The average SAT score of 1356 in the given study is a population parameter
what is another expression equivalent to 3(8-2)
Answer:
3(6)
??
Step-by-step explanation:
PLEASE HELP the vertex form of the equation of a parabola is y = (x - 3)2 + 36. what is the standard form of the equation?
Answer:
[tex]\large \boxed{\sf \bf \ \ x^2-6x+45 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
You need to develop the expression.
[tex]y=(x-3)^2+36\\\\=x^2-2 * 3 * x +3^2+36\\\\=x^2-6x+9+36\\\\=x^2-6x+45[/tex]
Thank you.
Answer:
D
Step-by-step explanation:
plz help.. plzz if you can
Answer:
C is a function
Step-by-step explanation:
We can use the vertical line test. If a vertical straight lines passes through the graph more than one, it is not a function
A and B are not functions
C is a function
Given quadrilateral MATH is similar to quadrilateral ROKS calculate the value of MH Picture is below
=====================================================
Explanation:
The double tickmarks for quadrilateral MATH show that MA = TH. Since TH is 5 units long, this makes MA the same length as well.
For quadrilateral ROKS, we have RO = 15. For "MATH" and "ROKS" we have "MA" and "RO" as the first two letters of each four-letter sequence; meaning that MA and RO correspond together.
The ratio of the corresponding segments is RO/MA = 15/5 = 3.
The larger quadrilateral has each side length 3 times longer than the smaller quadrilateral's corresponding side lengths.
--------------
In short,
larger side = 3*(smaller side)
--------------
Using this scale factor of 3, we can find MH
larger side = 3*(smaller side)
RS = 3*(MH)
21 = 3*MH
3*MH = 21
MH = 21/3
MH = 7
Weather balloons burst at an altitude of 27.5 km. What is the altitude in meters?
Answer:
27500
Step-by-step explanation:
meters are 100 times more than kilometers hope this helps:)
Which of the binomials below is a factor of this trinomial?
X^2 + 5x + 6
Answer:
(x + 2) , (x + 3) are factors
Step-by-step explanation:
Given
x² + 5x + 6
Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)
The factors are + 2 and + 3, since
2 × 3 = 6 and 2 + 3 = 5 , thus
x² + 5x + 6 = (x + 2)(x + 3)
Please help,thanks!(:
Answer:
<4=<2
x+30=2x+15
x=15
therefore <4=(15)+30
=45°
Archer receives a day's work of pay, p, for 5 days of mowing lawns. He spent half of his money on gas. Then he spent $5 on water. Now, he has $40 left. Which equation represents how much Archer would get paid each day of mowing lawns?
Answer:
Daily pay= $18
5 days pay = $90
Step-by-step explanation:
Archer's daily pay =p
Pay for 5 days= 5p
Gas = 1/2 of 5p
= 1/2 × 5p
= 5p/2
Water = $5
Balance = $40
5p = 5/2p + 5 + 40
5p - 5/2p = 45
10p -5p /2 = 45
5/2p = 45
p= 45÷ 5/2
= 45 × 2/5
= 90/5
P= $18
5p= 5 × $18
=$90
The equation to determine Archer's daily pay is
5p = 5/2p + 5 + 40
Divide both sides by 5
p = 5/2p + 45 ÷ 5
= (5/2p + 45) / 5
p= (5/2p + 45) / 5
Pens cost 15 pence each. Rulers cost 20 pence each. Write down an expression for the cost of x pens and x rulers.
Answer:
C = 35x pence
Step-by-step explanation:
1 pen costs 15 , thus x will cost 15x
1 ruler costs 20, thus x will cost 20x
Total cost (C) will then be
C = 15x + 20x = 35x pence
The total cost of pens and rulers, C = 35x pence
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Cost 1 pens is 15.
Then, cost for x pen is 15x
Cost of 1 ruler is 20
Then, cost of x ruler is 20x
So, the total cost is
= 15x + 20x
= 35x
Learn more about Equation here:
https://brainly.com/question/29538993
#SPJ2
Find the amplitude of y = -2 sin x
Answer:
Amplitude = 2
Step-by-step explanation:
The amplitude of this sine wave is 2 denoted by the coefficient -2 in front of the sin(x). The negative of the coefficient denotes that the sine wave is the opposite of the standard sine wave.
Cheers.
PROVE THAT:
cos 20° - sin 20° = \sqrt{2}sin25°
Answer:
See below.
Step-by-step explanation:
[tex]\cos(20)-\sin(20)=\sqrt{2}\sin(25)[/tex]
First, use the co-function identity:
[tex]\sin(90-x)=\cos(x)[/tex]
We can turn the second term into cosine:
[tex]\sin(20)=\sin(90-70)=\cos(70)[/tex]
Substitute:
[tex]\cos(20)-\cos(70)=\sqrt{2}\sin(25)[/tex]
Now, use the sum to product formulas. We will use the following:
[tex]\cos(x)-\cos(y)=-2\sin(\frac{x+y}{2})\sin(\frac{x-y}{2})[/tex]
Substitute:
[tex]\cos(20)-\cos(70)=-2\sin(\frac{20+70}{2})\sin(\frac{20-70}{2})\\\cos(20)-\cos(70) =-2\sin(45)\sin(-25)\\\cos(20)-\cos(70)=-2(\frac{\sqrt{2}}{2})\sin(-25)\\ \cos(20)-\cos(70)=-\sqrt{2}\sin(-25)[/tex]
Use the even-odd identity:
[tex]\sin(-x)=-\sin(x)[/tex]
Therefore:
[tex]\cos(20)-\cos(70)=-\sqrt{2}\sin(-25)\\\cos(20)-\cos(70)=-\sqrt{2}\cdot-\sin(25)\\\cos(20)-\cos(70)=\sqrt{2}\sin(25)[/tex]
Replace the second term with the original term:
[tex]\cos(20)-\sin(20)=\sqrt{2}\sin(25)[/tex]
Proof complete.
(x2 - 41)2 + (yz - Yı) to the find the length of the segment
62. Use the distance formula d =
from (6,0) and (-5, 4).
Answer:
√137
Step-by-step explanation:
[tex](x_1, y_1) = (6, 0)\\(x_2, y_2) = (-5, 4)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\d = \sqrt{(-5-6)^2+(4-0)^2}\\ d = \sqrt{(-11)^2+(4)^2}\\ d = \sqrt{121+16}\\ d = \sqrt{137}\: or \:11.7[/tex]
Answer the questions when examining the data.
What is the domain?
What is the range?
I got (-infin.,infin) for domain but I’m not sure because there can’t be less that 0 days so I was wondering if it would be (3,infin), (3,192), (-infin,infin) or another coordinate. Please answer the range too
Greetings from Brasil...
In this case, we can say:
Domain = [0; 6]
Image = [3; 192]
see attachment
Solve the system of equations algebraically. 5x-3y=6 and 6x-4y=2 a. many solutions c. no solution b. (8,14) d. (9,13)
Answer:
d. (9, 13)
Step-by-step explanation:
5x-3y=6 /*6
6x-4y=2 /*(-5)
30x - 18y = 36
-30x +20y = - 10
2y = 26
y = 13
5x-3y=6
5x - 3*13 = 6
5x - 39 = 6
5x = 45
x = 9
(9, 13)
Find the value of x.
Answer:
x = 20
Step-by-step explanation:
Intersecting Chords Theorem: ab = cd
Step 1: Label our variables
a = x
b = x - 11
c = x - 8
d = x - 5
Step 2: Plug into theorem
x(x - 11) = (x - 5)(x - 8)
Step 3: Solve for x
x² - 11x = x² - 8x - 5x + 40
x² - 11x = x² - 13x + 40
-11x = -13x + 40
2x = 40
x = 20
Answer: x=20
Step-by-step explanation:
[tex]ab=cd[/tex]
[tex]x(x - 11) = (x - 5)(x - 8)[/tex]
[tex]x^2 - 11x = x^2 - 13x + 40[/tex]
[tex]x^2 - 11x = x^2 - 8x - 5x + 40[/tex]
[tex]-11x = -13x + 40\\2x = 40\\x = 20[/tex]
Find the area of the following shape. Show all work
Best way to solve this is by using
[tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]
[tex]where \: s = \frac{a + b + c}{2} [/tex]
s=(12+8+17)/2
=18.5
using the formulae
area =43.5
solve for x 7x - 3/4 = 6x - 5/8
Answer: x=0.125 or 1/8
Step-by-step explanation:
[tex]7x-\frac{3}{4}=6x-\frac{5}{8}[/tex]
add 3/4 on both sides
[tex]7x-\frac{3}{4}+\frac{3}{4}=6x-\frac{5}{8}+\frac{3}{4}[/tex]
[tex]7x=6x+\frac{1}{8}[/tex]
subtract 6x on both sides
[tex]x=\frac{1}{8}[/tex]
Answer:
x = 1/8
Step-by-step explanation:
7x - 3/4 = 6x - 5/8
7x - 3/4 + 3/4 = 6x - 5/8 + 3/4
7x = 6x + 1/8
7x - 6x = 6x + 1/8 - 6x
x = (6x - 6x) + 1/8
x = 1/8
What is the reason: if a+c=b+c then a=b
Step-by-step explanation:
Example 1:
a+c=b+c then a=b
First let the value of a and b be different (not equal)
a=5
b=7
c=10
a+c=b+c
5+10=7+10
15≠17
Example 2:
Let the value a and b be equal (the same)
a=5
b=5
c=10
a+c=b+c
5+10=5+10
15=15
So when,
a+c and b+c is equal, a and b are always equal.
Hope this helps ;) ❤❤❤
Answer:
a=b
Step-by-step explanation:
Reason:
a+c=b+c
a-b=c-c
c-c would be 0
if a-b=c-c=0
a-b=0
Only if a=b can a-b=0
You can also take it as:
b-a=c-c (a+c=b+c)
b-a=0=c-c
Therefore b=a
By the way even I am a BTS army
5
What is the equation, in point-slope form, of the line that
is parallel to the given line and passes through the point
(-3, 1)?
4
3
2
(-3, 1)
42.27
1
5 4 3 2 1
2 3 4 5 x
y-1=-{(x+3)
y-1=-{(x + 3)
y-1= {(x + 3)
y-1= {(x + 3)
(-2, 4)
Answer: [tex]y-1=\dfrac32(x+3)[/tex]
Step-by-step explanation:
Slope of a line passes through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]
In graph(below) given line is passing through (-2,-4) and (2,2) .
Slope of the given line passing through (-2,-4) and (2,2) =[tex]\dfrac{-4-2}{-2-2}=\dfrac{-6}{-4}=\dfrac{3}{2}[/tex]
Since parallel lines have equal slope . That means slope of the required line would be .
Equation of a line passing through (a,b) and has slope m is given by :_
(y-b)=m(x-a)
Then, Equation of a line passing through(-3, 1) and has slope = is given by
[tex](y-1)=\dfrac32(x-(-3))\\\\\Rightarrow\ y-1=\dfrac32(x+3)[/tex]
Required equation: [tex]y-1=\dfrac32(x+3)[/tex]
Bill’s car gets 30 miles to the gallon. For every gallon of gas it consumes, his car runs 30 miles. Use this information to determine whether this relation is a function
write a equation for the number of miles Bill travels, y, in terms how much gas it uses, x.
Answer:
Step-by-step explanation:
No. of miles driven in 1 gallon = 30 miles.
since we have to distance traveled in miles.multiply LHS and RHS by x
No. of miles driven in 1*x gallon = 30*x miles.
No. of miles driven x gallons = 30*x = 30x miles
As given that
the number of miles Bill travels is represented by y
gas used is x
then
y = 30x
=> x = y/30
Thus, Bill's car uses y/30 gallon gas to travel Y miles.
Answer:
Part a: Bill’s car travels 30 miles per gallon of gas. If y represents the number of miles the car travels on x gallons of gas, the equation that represents this situation is y = 30x.
Part b: gallons of gas (x) miles (y)
1 30
2 60
3 90
Part c: There is no x-value that would lead to multiple y-values.
Part d: Yes, y = 30x is a function, because for every input, or x-value, there is only one output, or y-value.
Step-by-step explanation:
edmentum answers 100% correct
La fuerza necesaria para evitar que un auto derrape en una curva varía inversamente al radio de la curva y conjuntamente con el peso del auto y el cuadrado de la velocidad del mismo. Supongamos que 400 libras de fuerza evitan que un auto que pesa 1600 libras derrape en una curva cuyo radio mide 800 si viaja a 50mph. ¿Cuánta fuerza evitaría que el mismo auto derrapara en una curva cuyo radio mide 600 si viaja a 60mph ?
Answer:
768 libras de fuerza
Step-by-step explanation:
Tenemos que encontrar la ecuación que los relacione.
F = Fuerza necesaria para evitar que el automóvil patine
r = radio de la curva
w = peso del coche
s = velocidad de los coches
En la pregunta se nos dice:
La fuerza requerida para evitar que un automóvil patine alrededor de una curva varía inversamente con el radio de la curva.
F ∝ 1 / r
Y luego con el peso del auto
F ∝ w
Y el cuadrado de la velocidad del coche
F ∝ s²
Combinando las tres variaciones juntas,
F ∝ 1 / r ∝ w ∝ s²
k = constante de proporcionalidad, por tanto:
F = k × w × s² / r
F = kws² / r
Paso 1
Encuentra k
En la pregunta, se nos dice:
Suponga que 400 libras de fuerza evitan que un automóvil de 1600 libras patine alrededor de una curva con un radio de 800 si viaja a 50 mph.
F = 400 libras
w = 1600 libras
r = 800
s = 50 mph
Tenga en cuenta que desde el
F = kws² / r
400 = k × 1600 × 50² / 800
400 = k × 5000
k = 400/5000
k = 2/25
Paso 2
¿Cuánta fuerza evitaría que el mismo automóvil patinara en una curva con un radio de 600 si viaja a 60 mph?
F = ?? libras
w = ya que es el mismo carro = 1600 libras
r = 600
s = 60 mph
F = kws² / r
k = 2/25
F = 2/25 × 1600 × 60² / 600
F = 768 libras
Por lo tanto, la cantidad de fuerza que evitaría que el mismo automóvil patine en una curva con un radio de 600 si viaja a 60 mph es de 768 libras.
what is the coefficient of the variable in the expression 4-3x
As per the question,
We have to find what's the coefficient.
Let's start to seperate the expression.
Here,
x is the variable,
4 is a number.
-3 is also a number.
4, -3x
The number with x here is -3 in (-3x) as the coefficient is (-3) in the given equation.
Answer:
Hey there!
Rearrange the expression to: -3x+4
The coefficient would be -3.
Let me know if this helps :)
Black Diamond Ski Resort charges $25 for ski rental and $10 an hour to ski. Bunny Hill Ski Resort charges $50 for ski rental and $5 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same.
Answer:
25 + 10h = 50+5h
Step-by-step explanation:
Black Diamond Ski Resort
25 + 10h
Bunny Hill Ski Resort
50+5h
We want when they are equal
25 + 10h = 50+5h
Answer:
10x + 25 = 5x + 50
Step-by-step explanation:
THIS IS THE HARDEST WORK ON EART SOMEONE HELP ME
Answer:
a) 2 h 45 min
b) 2 h 50 min
c) 2 h 20 min
d) 3 h 20 min
Step-by-step explanation:
Answer:
a) hours: 9 hours 15 minutes
minutes: 555
b) hours: 9hours 10 minutes
minutes: 550
c) hours: 2hours 20 minutes
minutes: 140
d) hours: 3 hours 20 minutes
minutes: 200
Step-by-step explanation:
Please answer it now
Answer:
8
Step-by-step explanation:
x+37+x+37+90 = 180
2x + 74 = 90
2x = 16
x = 8
Answer:
x=8°
Step-by-step explanation:
JI is a diameter and K is on the circumference of a circle.
∴∠JKI=90°
also KJ=KI=x(say)
tan (x+37)=y/y=1=tan 45
so x+37=45
x=45-37=8°
The diagonal of rhombus measure 16 cm and 30 cm. Find it's perimeter
Answer:
P = 68 cmStep-by-step explanation:
The diagonals of the rhombus divide it into 4 congruent right triangles.
So we can use Pythagorean theorem to calculate side of a rhombus.
[tex](\frac e2)^2+(\frac f2)^2=s^2\\\\e=30\,cm\quad\implies\quad\frac e2=15\,cm\\\\f=16\,cm\quad\implies\quad\frac f2=8\,cm\\\\15^2+8^2=s^2\\\\s^2=225+64\\\\s^2=289\\\\s=17[/tex]
Perimeter:
P = 4s = 4•17 = 68 cm
A tank contains 15,000 L of brine with 24 kg of dissolved salt. Pure water enters the tank at a rate of 150 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate.How much salt is in the tank after t minutes
Answer:
Step-by-step explanation:
Let y(t) be the amount of salt in the tank after time t.
(A) Incoming rate = 0 (due to Pure water having no salt)
(B) Mixed solution comes out at 150 L/min. Initially the tank has 15,000 L of brine with 24 kg of salt.
concentration of salt at time t = y(t) / 15000 kg/L
Outgoing rate = y(t)/15000 * 150 = y(t) / 100
(C) we know that,
[tex]\frac{dy}{dx} =(incoming\ rate) - (outgoing\ rate)[/tex]
[tex]\frac{dy}{dx} =0-\frac{y(t)}{100} = \frac{-y(t)}{100}[/tex]
Separate variable and integrate
[tex]\int {\frac{dy}{y} } = - \int {\frac{1}{100} } \, dt[/tex]
[tex]ln|y|=-\frac{1}{100}t + D[/tex]
[tex]y=e^{D} e^{\frac{-t}{100} }[/tex]
[tex]y= Ce^{\frac{-t}{100} }\ [C=e^{D} ][/tex]
At t= 0 , y(0) = 24 kg
[tex]24=C\ e^{0}[/tex]
C= 24
(D) Therefore, the amount of salt in the tank after time t :
[tex]y(t)=24e^{\frac{-t}{100} }\ kg[/tex]
