Answer:
a. 8 gallons
b. (11-0.75t) gallons
Step-by-step explanation:
a. Here in this question, we are told that the total amount of fuel in the fuel tank is 11 gallons and the car consumes 0.75 gallon per hour. We are interested in knowing the amount of fuel left in the tank after driving for four hours.
We proceed as follows;
Since 0.75 gallon is consumed in an hour, the amount of fuel consumed in 4 hours would be the amount consumed in an hour * 4 hours
Mathematically, that would be 0.75 * 4 = 3 gallon
Now, the amount of fuel left is simply the difference between the initial amount of fuel in the tank minus the amount of fuel present after 4 hours.
That would be; 11 - 3 = 8 gallons
b. Like above, we want to know the amount of fuel left after t hours.
Since 0.75 is used up per hour, the amount used up in t hours would be 0.75 * t = 0.75t
Now, the amount of fuel that would be left in the tank would be the difference between what we had initially and what was used up.
Mathematically, that would be 11- 0.75t
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
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:
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
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:)
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)
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
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.
please help me i offered all my points and this is really important!!! The question is attached.
Answer:
25[tex]\sqrt{3}[/tex] +60
Step-by-step explanation: The first thing you need to do is realize that, this figure is a isosceles trapezoid due to the markings on each side.
So now we know both sides are 10.
We also know the the top two angles are congruent to each other and so are the bottom two angles due to the trapezoid being isosceles.
So the top two angles are 120 degrees and bottom two angles are 60 degrees.
It seems like we can't find the sides, let's try drawing two lines from each top angle all the way down to form two right triangles.
Wow, these two triangles are special right triangles in the form of
30 - 60 - 90 degrees.
shorter side = n
longer side = n[tex]\sqrt{3}[/tex]
hypotenuse = 2n
So, 2n = 10
n = 5 for the short side
The bottom base is 4[tex]\sqrt{3}[/tex] + 5 + 5 = 10 + 4[tex]\sqrt{3}[/tex]
The longer side is 5[tex]\sqrt{3}[/tex].
The area of trapezoid = (base1 + base2)/2 * height
= (4[tex]\sqrt{3}[/tex] + 10 + 4[tex]\sqrt{3}[/tex])/2 * 5[tex]\sqrt{3}[/tex] = (10 + 8[tex]\sqrt{3}[/tex])/2 * 5[tex]\sqrt{3}[/tex] = (5+4[tex]\sqrt{3}[/tex])*5[tex]\sqrt{3}[/tex] = 25[tex]\sqrt{3}[/tex] +60
So, 25[tex]\sqrt{3}[/tex] + 60 is our answer.
Answer:
60 +25√3
Step-by-step explanation:
In the figure of the isosceles trapezoid below, the angles at C and D are supplementary to the given angle, so are 60°. That makes triangle BDE a 30°-60°-90° right triangle, which has side length ratios ...
DE : BE : BD = 1 : √3 : 2 = 5 : 5√3 : 10
Triangle BDE can be relocated to the other end of the figure to become triangle CAD'. Then the area of concern is that of the rectangle with height 5√3 and length 5+4√3. The area is then ...
Area = lh = (5√3)(5 +4√3) = 5·5√3 +5·4·3
Area = 60 +25√3 . . . square units
_____
In the figure, 6.93 = 4√3, and 8.66 = 5√3, 16.93 = 10+4√3.
Please help,thanks!(:
Answer:
<4=<2
x+30=2x+15
x=15
therefore <4=(15)+30
=45°
what is another expression equivalent to 3(8-2)
Answer:
3(6)
??
Step-by-step explanation:
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]
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.
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:
helpppppppppppppppp
Express the following English phrase using an algebraic expression.
The product of 12 and a number y.
Represent "The product of 12 and a number y " mathematically.
Answer:
12y
Step-by-step explanation:
product means multiplycation so twelve times y is 12y
Four machines give out a signal at intervals of 24 seconds, 27 seconds, 30 seconds and 50 seconds respectively. At 5.00 p.m. all four machines give out a signal simultaneously. At what time will this happen again at the earliest?
Answer:
6:30 pm
Step-by-step explanation:
Given the following :
Four machines give out a signal at intervals of 24 seconds, 27 seconds, 30 seconds and 50 seconds respectively.
Time when all four machines gave out signal simultaneously = 5:00 pm
To find the time all four will give out the next simultaneous signal :
Take the lowest common factor of the four intervals :
L. C. M of 24, 27, 30, 50
Using the Lowest Common Multiple calculator :
L. C. M. = 5400
5400 seconds.
Adding 5400 seconds to the last time a simultaneous signal was produced :
5:00 pm + 5400 seconds
5400 seconds = (5400/60) = 90 minutes = 1hour 30 minutes
5:00 pm + (1 hour 30 minutes)
= 6:30 pm
(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]
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
3.03 times 10^-3 in scientific nation
Answer:
3.03 • 10⁻³ is scientific notation
0.00303 is decimal form
Find the value of x in each case:
Answer:
x=36
Step-by-step explanation:
180-x=180-2x +180-4x
180-x = 360 -6x
5x =180
36 = x
9=m/3=4 please help!!
Answer:
Step-by-step explanation:
9 = m/3 + 4
5 = m/3
m = 15
Answer: m=15
Step-by-step explanation:
[tex]9=\frac{m}{3}+4[/tex]
subtract 4 on both sides
[tex]\frac{m}{3}+4-4=9-4[/tex]
[tex]\frac{m}{3}=5[/tex]
multiply 3 on both sides
[tex]\frac{3m}{3}=5\cdot \:3[/tex]
[tex]m=15[/tex]
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]
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:
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
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
i back at you with another question..!
Answer:
Identity Property of Multiplication
Step-by-step explanation:
The Identity Property of Multiplication states that any number multiplied by 1 will equal the same number.
Since we have one item that costs $14.50, we know that the total cost will be $14.50 since we are multiplying $14.50 by 1.
Hope this helped!
Answer:
Identity property of multiplication.
Step-by-step explanation:
When we multiply any number by 1, we will get the same number.
5 *1 = 5
-8 * 1 = -8
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:
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
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
Derivative of sin3x using first principle
[tex]\displaystyle f(x)=\sin(3x)\\\\\\f'(x)=\lim_{h\to0}\dfrac{\sin(3(x+h))-\sin(3x)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{\sin(3x+3h)-\sin(3x)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{3x+3h+3x}{2}\right)\sin\left(\dfrac{3x+3h-3x}{2}\right)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{6x+3h}{2}\right)\sin\left(\dfrac{3h}{2}\right)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{6x+3h}{2}\right)\sin\left(\dfrac{3h}{2}\right)}{\dfrac{3h}{2}}\cdot\dfrac{3}{2}[/tex]
[tex]\displaystyle f'(x)=\lim_{h\to0}2\cos\left(\dfrac{6x+3h}{2}\right)\cdot\dfrac{3}{2}\\\\f'(x)=\lim_{h\to0}3\cos\left(\dfrac{6x+3h}{2}\right)\\\\f'(x)=3\cos\left(\dfrac{6x+3\cdot 0}{2}\right)\\\\f'(x)=3\cos\left(\dfrac{6x}{2}\right)\\\\f'(x)=3\cos(3x)[/tex]
The derivative of sin 3x using first principles is; 3cos(3x)
We want to find the derivative of sin 3x using first principles.
Step 1;
f'(x) = [tex]\lim_{h \to \ 0} \frac{(sin3(x + h)) - sin(3x)}{h}[/tex]
Step 2; Expand the bracket to get;
f'(x) = [tex]\lim_{h \to \ 0} \frac{(sin(3x + 3h)) - sin(3x)}{h}[/tex]
Step 3: According to trigonometric identities, we know that;
sin A - sin B = [tex]2cos\frac{A + B}{2} sin\frac{A - B}{2}[/tex]
Applying that to the answer in step 2 gives;
f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(3x + 3h + 3x)}{2}) sin\frac{(3x + 3h - 3x)}{2})}{h}[/tex]
Step 4; Simplify the brackets to obtain;
f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(6x + 3h)}{2}) sin\frac{(3h)}{2})}{h}[/tex]
Step 5; Rewrite the denominator to get;
f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(6x + 3h)}{2}) sin\frac{(3h)}{2})}{\frac{3h}{2}*\frac{2}{3}}[/tex]
Step 6; Input the limit of 0 for h to get;
f'(x) = [tex]\frac{2(cos\frac{(6x)}{2}) sin\frac{(0)}{2})}{\frac{0}{2}*\frac{2}{3}}[/tex]
⇒ f'(x) = [tex]\frac{2(cos3x)}{2/3} \frac{ 0}{{0}}[/tex]
0/0 = 1. Thus;
f'(x) = 3cos(3x)
Read more about differentiation from first principles at; https://brainly.com/question/5313449
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°