Answer:
Option AStep-by-step explanation:
The amounts invested and saved are independent and their total is the combined amount.
[tex]C(t) = V(t) + S(t)[/tex][tex]C(t) = 2,800(1.025)^t + 10t[/tex]Correct choice is A
Lets see
V(t)=2800(1.025)^tS(t)=10tAdd both
C(t)=S(t)+V(t)C(t)=2800(1.025)^t+10tA hot-air balloon is released at ground level, and it rises into the air at a constant rate. After 5 seconds the height of the balloon is 20 feet. The balloon continues to rise at the same rate. Which table shows the relationship between the time in seconds, x, and the height of the balloon in feet, y?
The constant rate = 20 ft / 5 seconds = 4 feet per second
Find the chart that shows an increase of 4 feet for every second the balloon travels.
The height of the balloon over time is modeled by the linear equation y = 4x, so, the accurate choice is option D.
What are linear equations?A linear equation arises when multiple variables are connected, resulting in a linear model when graphed. This model is characterized by having a degree of one for each variable involved.
Imagine a hot air balloon taking off from the ground, ascending at a consistent speed. After 5 seconds, its altitude reaches 20 feet. The balloon maintains this rate of ascent.
The rate per second is calculated as follows:
m = 20/ 5
m = 4 ft/sec
Consequently, the equation is formulated as:
y = 4x
For x = 10 seconds, the corresponding y value will be:
y = 4 × 10
y = 40 ft
Similarly, for
x = 20 seconds:
y = 4 × 20
y = 80 ft
Hence, the linear equation representing the balloon's height over time is
y = 4x. The accurate option among the choices is D.
Find out more on linear equation here: https://brainly.com/question/2030026
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If a=2, b= -1 and c=1, then find the value of:
A- a+b-c²
B- a³-b+c
C- a-b-c
Answer:
Step-by-step explanation:
A. 2 + -1 - 1^2 = 1 - 1 = 0
B. 2^3 - -1 + 1 = 8 + 1 + 1 = 10.
C. 2 - -1 - 1 = 2 + 1 - 1 = 2.
=2+(-1-1)^2
=1-1
=0
B- a³-b+c2^3-(-1+1)
=8+1+1
= 10
C- a-b-c2-(-1-1)
=2+1-1
=2
In quadrilateral two angles are equal. The third angle is equal to the sum of the two equal angles. The fourth angle is 60degrees less than twice the sum of the other three angles. Find the measures of the angles in the quadrilateral.
Answer: 35, 35, 70, and 220
Step-by-step explanation:
– Let x = size of one of the two equal angles
The sum of angles in a quadrilateral is 360:
360 = x+ x + ( x+x ) x (2( x+ x+ x+x ) – 60)
360 = 4 + 2(4 ) – 60
360 = 4 + 8 – 60
360 = 12 – 60
12x = 420
= 35
Substituting x for 35, will get: 35, 35, 70, 220
The values of the angles are 35°, 35°, 70° and 220°
The selling price of the Robertsons family house dropped from $500,000 to $250,000. What was the percent decrease in the value of their home?
( please solve, NOT in proportion please!! )
Answer:
50%
Step-by-step explanation:
You can literally do it mentally lol
$500,000
- $250,000
$250,000
so by common sense, it's 50%
Hope it helped!
Answer:
50%
Step-by-step explanation:
50% of the value of the house dropped.
So 50% of 500,000.
50 percent *500000 =( 50:100)*500000 =( 50*500000):100 =25000000:100 = 250000The volume of a cylinder is 256pi in3. and the height of the cylinder is 1 in. What is the radius of the cylinder?
Answer:
9.03
Step-by-step explanation:
the formula is V=pir2h
(pi, radius squared, and height)
Expand & simplify
5
(
p
+
5
)
+
6
(
p
+
6
)
5(p+5) + 6(p+6)
First step: Distribute (PEMDAS --> Parenthesis)
5p + 25 + 6p + 36 Now, combine like terms
11p + 61
Thus, the answer is 11p + 61
[tex]5(p+5)+6(p+6)\\\\=5p+25+6p+36\\\\=11p+61[/tex]
what is (1/4)^2x+3=2^5x+4
find the value of x?
Answer:
[tex] x = - \frac{10}{9} [/tex]
what is. the solution to this equation: 6r=33
Answer:
5.5
Step-by-step explanation:
6 x 5.5 = 33
The solution for r is 5.5
Answer:
r = 5.5
Step-by-step explanation:
6r=33
1. divide both sides by 6
6/6=1
33/6= 5.5
2. r=5.5
what is the volume of this shape?
Answer:
480 [tex]cm^2[/tex]
Step-by-step explanation:
8 x 6 x 10
Length x Width x Height.
Express the following ratio: 20 inches to 2 feet in its simplest form. Hint: 1 feet = 12 inches
Answer:
5 inches : 6 inches
Step-by-step explanation:
20 inches : 2 feet
Use Hint: 1 feet = 12 inches
20 inches : 2·12 = 24 inches
Find the simplest form of 20 inches : 24 inches
20 inches : 24 inches , divide both numbers by 2
10 inches : 12 inches, divide both numbers by 2 again
5 inches : 6 inches
Can someone explain this step by step? I'm very confused on how to solve it. Thanks!
Answer:
x = -8
Step-by-step explanation:
I will show each step algebraically. If you need further explanation, feel free to ask questions :)
[tex]\frac{x}{2} +7=3\\[/tex] Rewrite
[tex]\frac{x}{2} =-4[/tex] Subtract 7
[tex]x =-8[/tex] Multiply by reciprocal (2/1)
I hope this helps!
Answer:
X = -8
Step-by-step explanation:
So we will start with subtracting 7 from 3, which is -4.
So now you have x/2 = -4
Now we have to find what divided by 2 equals -4 so, we do 2 x -4, which is -8.
This is how we get our answer, x = -8
Solve this system of equations:
y = x2 – 3x + 12
y = –2x + 14
1.Isolate one variable in the system of equations, if needed.
y = x2 – 3x + 12
y = –2x + 14
2.Use substitution to create a one-variable equation.
–2x + 14 = x2 – 3x + 12
3.Solve to determine the unknown variable in the equation.
What are the values of x?
{–2, 1}
{–2, 4}
{–1, 2}
{–1, 4}
Answer:
C. { - 1, 2}Step-by-step explanation:
The first two steps solved and the last step to be performed
Solve the quadratic equation
x² - 3x + 12 = - 2x + 14x² - 3x + 2x + 12 - 14 = 0x² - x - 2 = 0x² - 2x + x - 2 = 0x(x - 2) + (x - 2) = 0(x - 2)(x + 1) = 0x - 2 = 0 ⇒ x = 2x + 1 = 0 ⇒ x = - 1The solution is:
{ - 1, 2}Correct choice is C
Solving from step 3
-2x+14=x²-3x+12x²-3x+2x-2=0x²-x-2=0(x-2)(x+1)=0x=2 or -1Option C
25. The sales tax rates 7.25
Part A How much taxis added on an item that costs $56.007
Part B $36.25 in taxis added to the price of an item, what was the original price of the item? pie y pie
Answer:
A:60.14
B:3,379.95
Step-by-step explanation:
I assume that .007 is supposed to be .07
56.07*1.0725=60.14
B.
36.25 is 1.0725 of ...
3,379.95
36.25 * 0.010725
Match each word to its definition
All i know is that 1 is the fourth option and 3 is the last option. I would assume 2 is the first option, 4 is the second option, 5 is the fifth option, and 6 is the third option, but be sure to check yourself. I hope this helps!
Graphing f(x)=(x+2)^2-3 in vertex form
Answer:
Step-by-step explanation:
This is a parabola shaped like a U.
The minimum value is at (-2, -3).
Find the zeroes:
(x + 2)^2 = 3
Find the zeroes:
x + 2 = +/- √3
x = +/-√3 - 2
x = -0.27, -3.73.
So the graph cuts the x axis at (-0.27, 0) and (-3.73, 0)
when x = -4 , f(x) = 1 and when x = 1, f(x) = 6.
So you can now draw the curve through these 5 points and it will be shaped like a U, symetrical about the line x = -2
The Speed of the machine boat is 150 km per hour. How far does the machine boat go in five and a half hours?
Answer:
825km
Step-by-step explanation:
150km/h= distance/11/2 hours
150km/h divide by 11/2 hours
=825km
Answer:
825km
Step-by-step explanation:
We have the rule: speed=distance/time
in this question you are asked to calculate the distance covered by the machine boat.
so we deduce from the above rule: distance=speed*time
Given: speed=150km/hr time=5.5hr distance=??
Solution: distance=150x5.5 = 825km
what is 3x-1/5=10 equal
Answer:
x = 17
Step-by-step explanation:
3x - 1 / 5 = 10
3x - 1 = 5 * 10
3x = 50 + 1
x = 51/ 3
x = 17
Part II: Analysis
5) How many seconds does the roller coaster last?
6) What is the roller coaster's starting height? How many seconds does it take the
roller coaster to reach maximum height?
7) Describe what the roller coaster is doing in the interval 7
8) Use your knowledge of function notation and piecewise functions to determine the
following:
a. f(10) =
i. Explain what this value means in real world context.
b. f(20) =
1. Explain what this value means in real world context.
c. If 16 seconds have passed since the roller coaster started, what is the height
of the roller coaster?
Bonus: When does the roller coaster reach 100 feet above the ground?
10 divided 20,then times mo 7 to 8
Gabby has a goal to finish covering the field before 12 hours have
elapsed. She will use any remaining time to water the field. After 1 hour
has elapsed, she has covered 4,000 square yards of the field.
Explain why Gabby will be able to meet her goal by working at this rate. As
part of the explanation, determine the amount of time, in hours, Gabby
will have to water the field.
$9,000 is invested in a stock that loses 3%/yr on average. What is its worth after 6 years? Value:
credit card cash advance
borrow: $300
rate: 18% per year
time: 6 months-,5
300
6
Answer:
Assuming the question is how much interest you will pay in the given time frame with the given terms.
Step-by-step explanation:
Borrowed $300
18% per yr = 18/12 = 1.5% per month
You borrowed for 6 months so you will end up paying 1.5%*6 =9% in interest
$300*(9% or 0.09) = $27 in interest paid + $300 in principal paid if paid off in 6 months.
Total $327.
If this was an economics class you would also have to factor in the depreciation of the principal amount month to month with minimum payments but I am guessing this is just a basic question so the above answer is correct enough.
I need help with this
Answer:
75%
Step-by-step explanation:
It's over 50% and it's definitely not 100%
Help me with this please
Answer:
B
Step-by-step explanation:
its b bc its inclusive and rhe others font make much sense
Find the center and radius of the circle represented by the equation below.
(x + 5)² + (y – 5)² = 225
1
Center:
Radius:
Answer: the center is (-5, 5) and the radius is 15
Step-by-step explanation:
the standard form of a circle is
(x-h)^2 + (y-k)^2 = r ^2 where h is the x coordinate and k is the y coordinate of the center of the circle
(h,k) = the center of the circle
r = radius
therefore,
(x+5)^2 + (y-5)^2 = 225 means that x has to be -5 since subtracting a negative creates a positive and y must be 5 as it is negative in the equation
think of it as making the sum/difference 0 within the parentheses:
(x+5) -5+5 = 0 so x=-5
(y-5) 5-5 = 0 so y =5
so the center of the circle is (-5,5)
the radius is simply 225 square rooted which is 15
hope this helps :)
Which equation can be used to find the nth term of the sequence, an? 5, 20, 80, 320, 1280, ...
an=4⋅5n−1
an=1.25⋅4n−1
an=5⋅4n−1
an=4⋅1.25n−1
Answer:
C.) 5 * 4^n-1
Step-by-step explanation:
Use the given method you use for finding the sequence with the terms.
Also K12 moment.
If it's wrong, please forgive me, I'm in the middle of the test as well.
I checked and I'm 99% sure this is the answer
Hope this helped despite being a little late!
Are the ratios 2:4 and 3:6 equivalent?
Answer:
2:4 3:6 and 8:2, and 4:1 are equivalent pairs of ratios.
2 : 4 and 3 : 6 are an equivalent pair of ratios.
( to find equivalent ratios just multiply or divide both quantities by the same number. )
[30 PTS!!] Using mathematically precise language, explain in detail how you would multiply the complex number [tex]z_1=r_1(cos[/tex]θ[tex]_1+i sin[/tex]θ[tex]_1)[/tex] with the complex number [tex]z_2=r_2(cos[/tex]θ[tex]_2+isin[/tex]θ[tex]_2)[/tex].
Multiplying z₁ and z₂ involves calculating their products
The product of z₁ and z₂ is r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))
How to multiply the complex numbers?The numbers are given as:
z₁ = r₁(cosΘ₁ + isinΘ₁)
z₂ = r₂(cosΘ₂ + isinΘ₂)
The product is represented as:
z₁ * z₂ = r₁(cosΘ₁ + isinΘ₁) * r₂(cosΘ₂ + isinΘ₂)
This gives
z₁ * z₂ = r₁r₂(cosΘ₁ + isinΘ₁) (cosΘ₂ + isinΘ₂)
Expand
z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂ + i²sinΘ₁sinΘ₂ )
In complex numbers,
i² = -1.
So, we have:
z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂ - sinΘ₁sinΘ₂ )
Rewrite as:
z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂ - sinΘ₁sinΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂ )
Apply sine and cosine ratios
z₁ * z₂ = r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))
Hence, the product of z₁ and z₂ is r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))
Read more about complex numbers at:
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Calculate the side lengths using the given scale.
Someone please help me!!
Answer:
x = 12 cm
y = 2 cm
Step-by-step explanation:
Length is G are 3 times the lengths in H.
Lengths in H are 1/3 the lengths in G.
x = 3 × 4 cm = 12 cm
y = 6 cm / 3 = 2 cm
HELP PLEASE!!!! <3
Algebraically find the slope and the y-intercept of 3y - 8 = 2x.
thank you!!
Answer:
slope = 2/3 y intercept = 8/3
Step-by-step explanation:
re-arrange to slope intercept form y = mx + b
3y = 2x + 8
y = 2/3 x + 8 / 3
Answer:
[tex]Slope=\frac{2}{3}[/tex]
[tex]Y-Intercept=\frac{8}{3}[/tex]
Hope This Helps! :)
Which of the following is the best estimate for the mass of an adult rabbit?
2g, 3 kg, 200 g,
200 g, 40 kg, 50g
Answer:
50 g
Step-by-step explanation: