The answer you are looking for is letter A, x=30.
Solution/Explanation:
First, write out the equation,
1200-5(3x+30)=600
Next, using the Distributive Property,
1200-15x-150=600
Simplify the left side of the equation just a little bit more,
1050-15x=600
Reverse order of terms on the left side, to make it a little bit easier to solve,
-15x+1050=600
Now, subtract 1050 from both sides,
-15x+1050-1050=600-1050
Now, simplify this part of the equation,
-15x=-450
Finally, divide both sides by -15,
So, therefore, the final answer is x=30.
I hope this helped you. Enjoy your day, and take care!
Determine, to one decimal place, the length, width & height of the rectangular prism that would have the greatest volume, with a surface area of 200 cm^2.
Answer:
The length = The width = The height ≈ 5.8 cm
Step-by-step explanation:
The volume of a rectangular pyramid, V = l × w × h
The surface area of the pyramid = 2 × l × h + 2 × w × h + 2 × l × w = 200
∴ l × h + w × h + l × w = 200/2 = 100
We have that the maximum volume is given when the length, width, and height are equal and one length is not a fraction of the other. Therefore, we get;
At maximum volume, l = w = h
∴ l × h + w × h + l × w = 3·l² = 100
l² = 100/3
l = 10/√3
Therefore, the volume, v = l³ = (10/√3)³
The length = The width = The height = 10/√3 cm ≈ 5.8 cm
for the function g(x)=3-8(1/4)^2-x
a) State the y-intercept
b) State the equation of the horizontal asymptote
c) State whether the function is increasing or decreasing.
d) State the domain and range
e) Sketch the graph
Could anyone help?
Using function concepts, it is found that:
a) The y-intercept is y = 2.5.b) The horizontal asymptote is x = 3.c) The function is decreasing.d) The domain is [tex](-\infty,\infty)[/tex] and the range is [tex](-\infty,3)[/tex].e) The graph is given at the end of the answer.------------------------------------
The given function is:
[tex]g(x) = 3 - 8\left(\frac{1}{4}\right)^{2-x}[/tex]
------------------------------------
Question a:
The y-intercept is g(0), thus:
[tex]g(0) = 3 - 8\left(\frac{1}{4}\right)^{2-0} = 3 - 8\left(\frac{1}{4}\right)^{2} = 3 - \frac{8}{16} = 3 - 0.5 = 2.5[/tex]
The y-intercept is y = 2.5.
------------------------------------
Question b:
The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.
[tex]\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2+\infty} = 3 - 8\left(\frac{1}{4}\right)^{\infty} = 3 - 8\frac{1^{\infty}}{4^{\infty}} = 3 -0 = 3[/tex]
--------------------------------------------------
[tex]\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2-\infty} = 3 - 8\left(\frac{1}{4}\right)^{-\infty} = 3 - 8\times 4^{\infty} = 3 - \infty = -\infty[/tex]
Thus, the horizontal asymptote is x = 3.
--------------------------------------------------
Question c:
The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.
--------------------------------------------------
Question d:
Exponential function has no restrictions in the domain, so it is all real values, that is [tex](-\infty,\infty)[/tex].From the limits in item c, the range is: [tex](-\infty,3)[/tex]--------------------------------------------------
The sketching of the graph is given appended at the end of this answer.
A similar problem is given at https://brainly.com/question/16533631
helphelphelphelphelphelp
Answer:
E - (8,-9)
F - (9,-9)
G - (9,-4)
Step-by-step explanation:
The first number in the bracket relates to the x-axis
The second number relates to the y-axis
find the missing length indicated
Answer:
x = 240
Step-by-step explanation:
Apply the leg rule to find the value of x.
Leg rule is given as:
Hypotenuse/leg 1 = leg 1/part 1
Hypotenuse = 400
Leg 1 = x
Part 1 = 144
Plug in the known values into the formula
400/x = x/144
Cross multiply
x*x = 144*400
x² = 57,600
Take the square root of both sides
√x² = √57,600
x = 240
ncert maths class 10 solution 5.1 4
Can you attach a picture to your question?
I would love to help you out.
Answer:
Step-by-step explanation:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.1
where is question ??
Pressure varies inversely as volume. When the pressure is 8 Pascals, the volume is 22 liters. What would the volume be if the pressure were increased to 16 pascals?
Answer:
we can use 2 formule to solve your question: One is P*V=n(mol)*R*T(KELVIN)
Step-by-step explanation:
And other is P(first)*V(first)=P(last)*V(last)
8*22=16*?
the ?=11
(cos^2x-sin^2x)-sin4x+sin^22x=0
Answer:
x=22.5
Step-by-step explanation:
(there's a correction in the question since the I did this one before, so I know)
(cos²x-sin²x)²-sin4x+sin²2x=0
or, cos²2x-sin4x+sin²2x=0
or, 1-sin4x=0
or, sin4x=1
or, 4x=90
or, x=22.5
Please Help !
Which of the following describes point D? (-4, 0) (0, -4) (0, 4) (4, 0)
Answer:
D(0 , 4)
Step-by-step explanation:
Point D is on the y axis. So, x-coordinate = 0
y- coordinate is the vertical length from origin which is 4
Answer:
D(0 , 4)
Step-by-step explanation:
Determine what type of model best fits the given situation: the temperature of a cup of coffee decreases by 5 F every 20 minutes.
A. liner
B. exponential
C. quadratic
D. none of these
Answer: T = -t / 4 + T0 where t is the temperature in minutes elapsed, T is the final temperature, and T0 is the initial temperature
Explanation: This is a linear equation in T and t
(-1 / 4 represents -5 deg / 20 min = - 1 deg / 4min
solve the quadratic equation
give your answer to 2 decimal places
: 3x^2+x-5=0
Given:
The quadratic equation is:
[tex]3x^2+x-5=0[/tex]
To find:
The solution for the given equation rounded to 2 decimal places.
Solution:
Quadratic formula: If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have,
[tex]3x^2+x-5=0[/tex]
Here, [tex]a=3,b=1,c=-5[/tex]. Using the quadratic formula, we get
[tex]x=\dfrac{-1\pm \sqrt{1^2-4(3)(-5)}}{2(3)}[/tex]
[tex]x=\dfrac{-1\pm \sqrt{1+60}}{6}[/tex]
[tex]x=\dfrac{-1\pm \sqrt{61}}{6}[/tex]
[tex]x=\dfrac{-1\pm 7.81025}{6}[/tex]
Now,
[tex]x=\dfrac{-1+7.81025}{6}[/tex]
[tex]x=1.13504167[/tex]
[tex]x\approx 1.14[/tex]
And
[tex]x=\dfrac{-1-7.81025}{6}[/tex]
[tex]x=-1.468375[/tex]
[tex]x\approx -1.47[/tex]
Therefore, the required solutions are 1.14 and -1.47.
express the ratio 7day to 6weeks as a decimal fraction
Answer:
6 weeks=6*7 days=42days
7/42 =1/6 =0.16667
OR
7 days=1 week
therefore 1/6=0.16667
Note that both must be in the same unit.
what is the relation that represents the relation
Answer:
what can i help u with
Step-by-step explanation:
I really can't help u with that sorry i am bad at math
Pepe and Leo deposit money into their savings accounts at the end of each
month. The table shows the account balances.
If their patterns of saving continue, and neither earns interest nor withdraws
any of the money, how will the balances compare after a very long time?
Pepe's balance will be greater as it is increasing exponentially while Leo's is increasing linearly
(see graph, where red is Pepe and blue is Leo)
Pepe's balance will be greater because Pepe's balance is growing exponentially option (A) is correct.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent [tex]y = a^x[/tex]
where a is a constant and a>1
We have:
Pepe and Leo deposit money into their savings accounts at the end of each month.
From the table, we can plot a graph on a coordinate plane.
As we can see in the graph:
Because Pepe's balance is growing exponentially and Leo's is growing linearly, it will be bigger.
Thus, Pepe's balance will be greater because Pepe's balance is growing exponentially option (A) is correct.
Learn more about the exponential function here:
brainly.com/question/11487261
#SPJ5
Plz help similarity theorems
Answer:
b is the answer bro and try first then ask questions
Find the area of the bolded outlined sector.
Outlined sector:
2 πr x 225/360 +2r
=2x3.14x10 x 225/360 +20
=59.25 cm
Hope this helped!
Write an equation of the graph (shown below) in slope intercept form.
Will Give Brainliest!
Solve for r.
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
35r - 21 < -35r + 19
Answer:
r < 4/7
Step-by-step explanation:
35r - 21 < -35r + 19
35r + 35r < 19 + 21
70r < 40
r < 4/7
Answer:
r < 4/7
Step-by-step explanation:
log 55 is the power to which ---- must be raised in order to produce a value of 55
Answer:
10
Step-by-step explanation:
just took the quiz
Please help out need explanation so I can know how to do it
Answer:
B = 60in^2
H = 4in
P = 34in
SA = 280
Step-by-step explanation:
Base - The base I assume would be the red rectangle, and 12x5 would be the area of that, so the answer is 60
Height - I assume that the height is 12, if the prism is vertical, if horizontal, then the height would be 4.
Perimeter - The length of the side lengths, so the base is the red sqaure 12+12+5+5=34
Surface Area - Base=60*4 (There are 4 "bases") =240, and then we have 5*4 (For the little squares, and times this by 2 becasue there are 2 of them) = 20*2=40
40+240=280
Find all complex numbers z such that z^4 = -4.
Note: All solutions should be expressed in the form a+bi, where a and b are real numbers.
evelins room has an area of 45 squar feet. the length of her room is 5. what is the perimeter of her room?
Answer:
28 feet
Step-by-step explanation:
Since the area is 45 and length is 5.In order to find the width we divide the area by the side given
45 ÷ 5 = 9 is the width
Perimeter is the sum of all the side of a figure.
9 + 9 + 5 + 5
= 28
I hope this helps :)
If a wheel has a radius of 5cm
how much is one rotation of the wheel
How many rotations can the wheel do within a distance of 50km
Answer:
circumference = 2*PI*radius
circumference = 2 * PI * 5 cm
circumference = 31.4159265358979 cm
50 km = 500,000 centimeters
rotations = 500,000 / 31.4159 cm
15,915.51 rotations
Step-by-step explanation:
If the length of the shorter arc AB is 22cm and C is the center of the circle then the circumference of the circle
is:
Answer:
22= 2(pi)(r)(45/360)
28.01
C=176
Step-by-step explanation:
equivalent expression: 3 + 4(2z - 1)
Answer:
8z - 1
Step-by-step explanation:
Given
3 + 4(2z - 1) ← multiply each term in the parenthesis by 4
= 3 + 8z - 4 ← collect like terms
= 8z - 1
Answer:
-1 + 8z
Step-by-step explanation:
First use the distributive property of multiplication (Just multiply 4 with all numbers in the parenthesis):
3 + 4(2z - 1)
3 + 8z - 4
Group like terms:
3 + 8z - 4
-1 + 8z
The answer is -1 + 8z
Hope this helped.
Help anyone can help me do the question,I will mark brainlest.
Answer:
Step-by-step explanation:
S=pi*R^2=(area of the sector)*(360/angle of AOB)
so 22/7*9^2=99*360/angle of AOB
-> AOB=140
perimeter of circle: 2*pi*R
permiter of sector : 2*pi*140/360*R+ 2R=22+9*2=40
32 x square Y - 2 y cube
Answer:
207y
Step-by-step explanation:
Jim removed 27 gallons of water from a rainwater storage tank. There are 59 gallons left in the tank. What equation can Jim use to find how much water was in the tank earlier? Use x to represent the amount of water originally in the tank.
Answer: X = 86 gallons
Step-by-step explanation:
X-27=59
X=59+27
Determine the quotient of .    
Solve 4 sinx + 9 cosx=0 for 0°
4 sin(x) + 9 cos(x) = 0
4 sin(x) = -9 cos(x)
tan(x) = -9/4
x = arctan(-9/4) + nπ … … … (in radians)
or
x = arctan(-9/4) + 180n ° … … … (in degrees)
where n is any integer.
I'm guessing you're solving for x over some domain, probably 0° ≤ x < 360°. In that case, you would have two solutions for n = 1 and n = 2 of
x ≈ 113.96° and x ≈ 293.96°
If I start a road trip with 10,425 miles on my auto meter and I end it with 23,840 miles showing how many miles was my trip
Answer:
13,415 miles
Step-by-step explanation:
Final position - initial position = Miles traveled:
23,840 miles - 10,425 miles = 13,415 miles
