When f(x) = 20
Then
5x + 10 = 20
Therefore
5x=20-10=10
x = 10 / 5 = 2
x= 2
30 points asap
The equation y = –117.5 x + 31,379.9 gives the population y of a city x years after 1975. What is the real-world meaning of the rate of change and the y-intercept?
Rate of Change: The city’s population decreases by about 118 people each year. Y-intercept: In 1975, the city’s population was about 31,380 people.
Rate of Change: The city’s population decreases by about 31,380 people each year. Y-intercept: In 1975, the city’s population was about 118 people.
Rate of Change: The city’s population decreases by about 1975 people each year. Y-intercept: In year 0, the city's population was about 118 people.
The equation y = –117.5 x + 31,379.9 gives the population y of a city in x years after 1975 , in real world ,
Rate of Change means The city’s population decreases by about 118 people each year , and Y-intercept means In 1975, the city’s population was about 31,380 people.
In the question ,
the equation that gives the population y of a city in x years is
y = –117.5 x + 31,379.9
let us find the population for 1976
So , x = 1 ,
we get , y = –117.5(1) + 31,379.9
y = –117.5 + 31,379.9
y = 31262.4
So, the population in the year 1976 is 31262.4
change in population = population in 1976 - population in 1975
= 31262.4 - 31,379.9
= -117.5
≈ -118
to find the population in the year 1977
x = 2 ,
we get , y = –117.5(2) + 31,379.9
= –235 + 31,379.9
= 31144.9
change in population = population in 1977 - population in 1976
= 31144.9 - 31262.4
= -117.5
≈ -118
From above , we can see that the population is decreasing in the year 1976 and 1977 , by 118 people,
hence , we can say that , the city’s population decreases by about 118 people each year
For population in 1975 , we put x=0 ,
So , y = –117.5(0) + 31,379.9
= 31379.9
≈ 31380
Therefore , the equation y = –117.5 x + 31,379.9 gives the population y of a city in x years after 1975 , in real world ,
Rate of Change means The city’s population decreases by about 118 people each year , and Y-intercept means In 1975, the city’s population was about 31,380 people .
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The northern hemisphere of planet earth has an inner core that is made up of iron and nickel. This iron nickel core is 30% of the volume of the northern hemisphere. If the diameter of the earth is 8,000 miles, what is the volume of iron-nickel core?
It turns out that the dynamo effect depends on the presence of up to 20% nickel in the Earth's core, a metal that behaves very differently from iron under extreme temperatures. Unlike the northern hemisphere mineral-rich crust and mantle, the core is made almost entirely of metal—specifically, iron and nickel. The shorthand used for the core's iron-nickel alloys is simply the elements' chemical symbols—NiFe. Elements that dissolve in iron, called siderophiles, are also found in the core.
Explain about the volume of iron nickel core?The core is almost entirely comprised of metal, notably iron and nickel, in contrast to the crust and mantle, which are rich in minerals. Iron-nickel alloys found in the core are denoted by their chemical symbols, NiFe. The core also contains siderophiles, or substances that dissolve in iron.volume calculation for the earth. Since the Earth is nearly spherical, its volume (V) may be determined using the formula V = 4/3 pi x r3, where r is its radius.The core of the earth is made up of iron, nickel, and other heavy metals like gold since they are the heaviest of all the metals and gravitated into the center of the planet.To learn more about iron nickel core refer to:
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please help and show steps am failing class
answer:
D. y = 3x + 9
perpendicular means negative reciprocal of the number next to x
so if its 5x perpendicular would be -1/5x
make the equation look like y = ...
2x + 6y = 6
6y = -2x + 6
y = (-2x + 6)/6
y = -2x/6 + 6/6
y = -1/3x + 1
perpendicular line would be a negative reciprocal so
-1/3x would have a perpendicular that would be 3x
D. is the only one that has 3x
Calculate the volume of liquid that would fill the bowl of the glass. SHOW ALL WORK!!
Answer:
49.7 cm³Step-by-step explanation:
We need to find the volume of the cone with:
Diameter = 5 cm andSlant height = 8 cmFirst, find the height, using Pythagorean, where hypotenuse of the triangle is 8 cm and base is the radius = 5 cm/2 = 2.5 cm:
[tex]h = \sqrt{8^2-2.5^2} =\sqrt{57.75} =7.6[/tex] (rounded)Find the volume of the cone:
[tex]V=\pi r^2h/3=3.14*2.5^2*7.6/3 = 49.7[/tex] (rounded)I need help finding the measurements of the numbered angles Question 1 and 2
In figure one the value of ∠2 = 65 ° ∠1 = 115° .
In figure two the value of ∠2 = 74° ∠1 = 106°.
What are corresponding angles in parallels lines?In the case of parallel lines, corresponding angles are congruent. Corresponding pairs are all angles that are situated in the same location with respect to the parallel and transversal lines. According to the definition of corresponding angles, when three parallel lines intersect two of them, the angles that are present at each intersection and are in the same relative position are said to be corresponding angles. Alternate angles, co-Interior angles, and matching angles are three facts regarding angles in parallel lines that we use to do this. When a transversal crosses two parallel lines, alternate and matching angle pairs coincide. Only when a transversal crosses two parallel lines perpendicularly are consecutive angles congruent. When a transversal intersects two parallel lines, however, subsequent angles are not necessary.
Figure 1
Given angle = 65°
= ∠2
Cause they are corresponding angles.
∠1 + ∠2 = 180°
∠1 = 115
Figure 2
Given angle = 74 °
= ∠ 2
Cause they are corresponding angles.
∠1 + ∠2 = 180°
∠1 = 106°
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what is the justification for step 3 in the solution process?
0.8a-0.1a=a-2.5
Step 1: 0.7a=a-2.5
Step 2: -0.3a=-2.5
Step 3: a=8.3
In step 3 each side of the equation is divided by - 0.3 to obtain the value of a = 8.3.
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Consider the expression,
0.8a - 0.1a = a - 2.5
Step 1,
Subtracting similar terms,
a( 0.8 - 0.1 ) = a - 2.5
0.7a = a - 2.5
Step 2: Subtracting the term a from each side of the equation.
0.7a - a = a - 2.5 - a
- 0.3a = - 2.5
Step 3: Multiplying each side of the equation by - 1.
- 0.3a × - 1 = - 2.5 × - 1
0.3a = 2.5
Dividing each side of the equation by 0.3.
a = 2.5/0.3
a = 8.3
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Did anybody see my question for 24 I really need help
Answer:
48
hope its right sorryyyy
I need help on this question
What is the function g(x) that results when translating the function
f(x)=|x|
to the left 12 units and reflecting it over the x-axis?
g(x) =
The image of the function after the translation is g(x) = -|x - 12|
How to determine the equation of g(x) after the transformation?From the question, the given parameters are:
f(x) = |x|
The transformation is given as
Translate the function to the left 12 units and reflect it over the x-axis
Mathematically, this transformation can be represented as
(x, y) = (x - 12, -y)
When represented as a function, we have
g(x) = -f(x - 12)
So, we have
g(x) = -|x - 12|
So, we have the following equation
f'(x) = -|x - 12|
Hence, the equation of g(x) is g(x) = -|x - 12|
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I have a question about exponential functions I will submit a photo
The values are given as:
(a) Approximate the value of e^6 to 4 decimal places:
The value of
[tex]e^6=403.42879[/tex]The approximate value to 4 decimal places is 403.4288.
(b) Approximate the value of e^(-0.66) to 4 decimal places:
[tex]\text{The value of e}^{-0.66}=0.5168513344916[/tex]Approximated value to 4 decimal places is 0.5168..
Andre is setting up rectangular tables for a party. He can fit 6 chairs around a single table. Andre lines up 10 tables end-to-end and tries to fit 60 chairs around them, but he is surprised when he cannot fit them all. IS THE RELATIONSHIP PROPORTIONAL
THIS IS DUE TODAY
Guys i need helps is this right?
please help this worth half ny grade
Answer:
see image
Step-by-step explanation:
See attached image
which expression is equivalent to 4/5-1/2
4/10-1/10
6/5-5/7
4/7-1/7
8/10-5/10
Adam's school is 12 miles from his house. It takes his older brother
20 minutes to drive him to school.
If Adam's brother drives s mph faster than usual, how fast will
they reach the school?
determine whether the function has a minimum or maximum f(x)=-2/3x+5 if x<0 -x if 0 4 -x^2+4x+4 if x>4
The function has no minimum or maximum
How to determine the minimum or the maximum of the functionThe function is given as
f(x) = -2/3x + 5 if x < 0
f(x) = -x^2 + 4x + 5 if x > 4
The above function is a piecewise function
And the type of functions in the piecewise function are
Linear functionQuadratic functionA linear function does not have a minimum or a maximum
This means that the function would have no minimum or maximum
Hence, the minimum or the maximum value of the function does not exist
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If you leave $2500 in an
account earning 9% interest, compounded daily, how
much money will be in the account after 4 years?
The amount of money that will be in the account after 4 years is $3,583.16
How many times is interest compounded annually?
The fact that the interest rate of 9% in this scenario is compounded daily means that the interest is compounded every day of the year, 365 days in a year, hence, our future value formula needs an adjustment for daily compounding as shown below:
FV=PV*(1+r/m)^(n*m)
FV=the accumulated balance in the account after 4 years=unknown
PV=amount invested or deposited initially=$2500
r=annual interest=9%
m=number of times in a year that interest is compounded=365
n=number of years=4
FV=$2500*(1+9%/365)^(4*365)
FV=$3,583.16
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Sid burrowed a single payment loan at $10,000 at an interest rate of 5.5%. The term of the loan is 120 days. What is the maturity value of his loan at exact interest?
For this case
P = 10 000
i=0.055
t=120
After you compute the formula you would get
A = 6 170 141
3
1
1. How many groups of 1/8 are in 3?
8
2. Evaluate.
5
groups
|||
Answer:
answer to question 1: 24
Explanation: (btw sorry i couldn't answer question 2) multiply 8 times 3 and you get the answer
The required group of number is 24 of 1/8 in 3.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
The given numbers are 1/8 and 3.
Let there are n number of groups of 1/8 in 3.
To find the value of number of groups n,
Use equation form,
1/8 n = 3
n = 3 x 8
n = 24.
There are 24 groups of 1/8 in 3.
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What’s the answer plss I need help asp
Answer:
I am 80% positive that it is DE but there is still that other 20% so keep in mind I am not entirely sure
Theatre tickets cost either $30 or $42. One evening twice as many $30 tickets are sold as $42 tickets and the total money taken is $18564. Find the total number of tickets that are sold.
Name a principal and interest rate where the amount of simple interest earned in 10 years would be $200. Justify your answer.
The relation between a principal and interest rate is;
⇒ P = $20 / r
Where, P is the principal amount and r is the interest rate.
What is Simple interest?
The simple interest is defined as;
Simple interest = P r t
Where, P is principal amount.
r is rate and t is time period.
Given that;
Simple interest = $200
Time period = 10 years.
Let principal amount = P
And, The interest rate = r
So, We get;
Simple interest = P r t
Substitute all the values, we get;
Simple interest = P r t
$200 = P × r × 10
Pr = $20
P = $20 / r
Thus, We get the relation between a principal and interest rate is;
⇒ P = $20 / r
Where, P is the principal amount and r is the interest rate.
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NuHome Movers charges $95 per hour for loading/unloading services and $80 per hour for packing/unpacking services. Their charge is $2.50 per mile for truck rental. Jay is moving a distance of 200 miles and needs 9 hours of loading/unloading and 7 hours of packing/ unpacking. What will his moving cost be if the service also charges 7.25% tax on the total?
Answer:
Total moving cost = $2,053.84
Step-by-step explanation:
Let's write down Jay's requirements and costs associated
9 hours of loading/unloading at $95 per hour = 95 x 9 = $855
7 hours of packing/unpacking at $80 per hour = 80 x 7 = $560
200 miles of transportation at $2.50 per mile = 2.50 x 200 = $500
Total before-tax cost of moving = $855 + $560 + $500 = $1, 915
Sales Tax is additional at 7.25%
Sales Tax amount = 1915 x 7.25%
= 1915 x 7.25/100 = 138.8375 = $138.84
Total cost including sales tax = 1915.00 + 138.84 = $2,053.84
What is the answer to the problem for sin, sec, tan. I don’t really need a detailed explanation just the answer. Thank you.
Answer:
[tex]\begin{gathered} \sin(\theta)=-0.35 \\ \\ sec(\theta)=-1.07 \\ \\ \tan(\theta)=0.38 \end{gathered}[/tex]Step-by-step explanation:
Remember that for a given terminal point of an angle, we define those trigonometric functions as following:
[tex]\begin{gathered} \sin(\theta)=\frac{y}{\sqrt{x^2+y^2}} \\ \\ sec(\theta)=\frac{\sqrt{x^2+y^2}}{x} \\ \\ \tan(\theta)=\frac{y}{x} \end{gathered}[/tex]This way, we'll have that:
[tex]\begin{gathered} \sin(\theta)=-0.35 \\ \\ sec(\theta)=-1.07 \\ \\ \tan(\theta)=0.38 \end{gathered}[/tex]What is the length of side BC to one decimal place?
Answer:
BC ≈ 9.0
Step-by-step explanation:
using the tangent ratio in the right triangle
tan42° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{10}[/tex] ( multiply both sides by 10 )
10 × tan42° = BC , then
BC ≈ 9.0 ( to 1 dec. place )
The half-life of a radioactive kind of uranium is 2 years. How much will be left after 4 years, if you start with 776 grams of it?
ANSWER
194 grams
EXPLANATION
We have that the half life of the uranium is 2 years.
This means that it will take 2 years for the uranium to decay to half of its original value.
The formula for exponential decay is:
[tex]y=ab^t[/tex]where y = the value after the decay
a = initial value
b = rate of decay.
t = number of years
First, we have to find b.
We have that 776 grams of uranium will decay to half its amount (388 grams) in 2 years. This means that:
[tex]\begin{gathered} 388\text{ = 776 }\cdot b^2 \\ \Rightarrow b^2\text{ = 388 / 776} \\ b^2\text{ = 0.5} \\ b\text{ = }\sqrt[]{0.5} \\ b\text{ = 0.707} \end{gathered}[/tex]Therefore, after 4 years (t = 4), the amount of uranium left will be:
[tex]\begin{gathered} y\text{ = 776 }\cdot(0.707)^4 \\ y\text{ = 776 }\cdot\text{ 0.25} \\ y\text{ = 194 grams} \end{gathered}[/tex]That is the amount of uranium that will be left after 4 years.
Next questionA man uses a loan program for small businesses to obtain a loan to help expand his vending machine business. The man borrows $27,000 for 3 years with a sirinterest rate of 1.5%. Determine the amount of money the man must repay after 3 years.The man must repay
Simple interest formula (not compound interest formula) is used here, as much as i know.
the formula is:
f = p * (1 + r * n).
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods
Given
[tex]\begin{gathered} P=27000 \\ r=1.5\%=\frac{1.5}{100}=0.015 \\ n=3years \end{gathered}[/tex]Therefore, we have
[tex]f=27000(1+0.015\times3)=\text{ \$}28215[/tex]Hence, the answer is
[tex]\begin{equation*} \text{\$}28215 \end{equation*}[/tex]In the space provided below, solve the inequality x/8 - 13 > -6 for x algebraically. Show all work.
Answer:
x > 56
Step-by-step explanation:
x/8 - 13 > -6
x/8 > 7
x > 56
how much more is 6.302 than 6.002 ?
Answer:
Step-by-step explanation:
0.3
Answer:
It is 0.3 more or 0.300 more
Step-by-step explanation:
6.002 + 0.3 or 0.300 = 6.302
6.302- 0.300 or 0.3 = 6.002
Hope I helped
Standard Form & Scientific Notation• 3 examples of converting from standard form to scientific notation• 3 examples of converting from scientific notation to standard form
Required:
We need to convert from standard form to scientific notation and also scientific notation to standard form.
Explanation:
a) Convert from standard form to scientific notation:
1) Consider the number 4,520,000.
The given number can be written as follows.
[tex]4,520,000=452\times10000[/tex][tex]=452\times10^4[/tex][tex]=452\times10^4\times\frac{10^2}{10^2}[/tex][tex]=452\times\frac{10^4\times10^2}{10^2}[/tex][tex]=\frac{452}{100}\times10^6[/tex][tex]=4.52\times10^6[/tex]The scientific notation of s
[tex]4.52\times10^6[/tex]2) Consider the number
[tex]35.98\times10^3[/tex]Multiply and divide by 10.
[tex]35.98\times10^3=35.98\times10^3\times\frac{10}{10}[/tex][tex]=\frac{35.98}{10}\times10^3\times10[/tex][tex]=3.598\times10^4[/tex]The scientific notation is
[tex]3.598\times10^4[/tex]3) Consider the number.
[tex]600.89\times10^{-8}[/tex]Multiply and divide by 100.
[tex]600.89\times10^{-8}=600.89\times10^{-8}\times\frac{100}{100}[/tex][tex]=\frac{600.89}{100}\times10^{-8}\times10^2[/tex][tex]=6.0089\times10^{-6}[/tex]The scientific notation is
[tex]6.0089\times10^{-6}[/tex]b) convert from scientific notation to standard form:
1)
Consider the notation:
[tex]6.285\times10^{-5}[/tex][tex]Use\text{ }10^{-5}=\frac{1}{100000}.[/tex][tex]6.285\times10^{-5}=\frac{6.285}{100000}[/tex][tex]=0.00006285[/tex]The standard form is 0.00006285.
2) Consider the notation.
[tex]7.9\times10^4[/tex][tex]Use\text{ }10^4=10000.[/tex][tex]7.9\times10^4=7.9\times10000[/tex][tex]=79000[/tex]The standard form is 79,000.
3) Consider the notation.
[tex]9.008\times10^5[/tex][tex]Use\text{ }10^5=100000.[/tex][tex]9.008\times10^5=9.008\times100000[/tex][tex]9.008\times10^5=900800[/tex]The standard form is 900,800.
