Given the expression:
[tex]dx+fy=g[/tex]To solve this expression for x, means that you have to isolate the term "x" in one side of the equal sign and all other terms mus be in the other side of it.
To "pass" a term from one side of the = sign to the other you have to perform the inverse operation to both sides of the equation (this way the equality remains valid)
So, the term "fy" is adding, the inverse operation is to subtract it, first step is to subtract this term of both sides of the equation:
[tex]dx+fy-fy=g-fy[/tex]+fy and -fy cancel each other so that:
[tex]dx=g-fy[/tex]Next, the term "x" is being multiplied by "d" but you need to reach the point were x is alone.
To cancel this multiplication you have to divide it by "d", and to keep the equality valid you have to perform the operation in both sides of the = sign:
[tex]\frac{dx}{d}=\frac{(g-fy)}{d}[/tex]d/d=1, then we get that x is equal to:
[tex]x=\frac{(g-fy)}{d}[/tex]For f(2)=2-2, which gives an output of 4B?O f(-8)of()O f(4)Of(8)
For f(x)= x ^3 - x ^2 , which gives an output of 48?
_____________________
replace values directly in the expression
x ^3 - x ^2
f(2)= 2 ^3 - 2 ^2
______________________________________
f(-8) = -572
f(-4) = -80
f(4) = 48
f(8) = 448
____________________________
Answer f(4) = 48
PLEASE ANSWER QUICK I WILL GIVE BRAINLIEST IF ITS RIGHT
Step-by-step explanation:
try this option, all the details are in the attachment.
Use the compound interest formulas A=P(1+r/n)^nt and A=Pe^rt to solve. Find the accumulated value of $20,000 for 5 years at an interest rate of 6.5% if the money is compounded monthly. What is the accumulated value if the money is compounded monthly?
Given: An investment of $20000 for 5 years at an interest rate of 6.5%.
Required: To determine the accumulated value if the money is compounded monthly.
Explanation: The formula for compound interest is as follows-
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here, n=12 as the money is compounded monthly in a year. Also
[tex]\begin{gathered} P=20000 \\ t=5 \\ r=\frac{6.5}{100} \\ =0.065 \end{gathered}[/tex]Substituting the values into the formula as-
[tex]A=20000(1+\frac{0.065}{12})^{12\times5}[/tex]Further solving-
[tex]A=27,656.35[/tex]Final Answer: The accumulated value is $27,656.35
The function describes the spread of a rumor among a group of people in an enclosed space. N represents the number of people who have heard the rumor, and t is measured in minutes since the rumor was started. Which of the following statements are true?Check all that apply.A.There are 299 people in the enclosed space.B.The rumor spreads at a constant rate of 0.36 people per minute.C.It will take approximately 14 minutes for 100 people to hear the rumor.D.Initially, only one person had heard the rumor.
The statements which are true about this exponential function include the following:
C. It will take approximately 14 minutes for 100 people to hear the rumor.
D. Initially, only one person had heard the rumor.
What is an exponential function?Mathematically, an exponential function can be modeled by using this equation:
f(x) = abˣ
Where:
a represents the initial value.b represents the rate of change.At the initial time (t₀), the value of t₀ is zero (0) and the number of people who heard the rumor is given by:
N(t) = 300/(1 + 299e^{-0.36t})
Substituting the initial time (t₀) into this exponential function, we have;
N(t₀) = 300/(1 + 299e^{-0.36t₀})
N(0) = 300/(1 + 299e^{-0.36 × 0})
N(0) = 300/(1 + 299e^{0})
N(0) = 300/(1 + 299)
N(0) = 300/300
N(0) = 1 person.
At t = 14, the number of people who heard the rumor is given by:
N(t₁₄) = 300/(1 + 299e^{-0.36t₁₄})
N(14) = 300/(1 + 299e^{-0.36 × 14})
N(14) = 300/(1 + 299e^{-5.04})
N(14) = 300/(1 + 299(0.00647374831))
N(14) = 100 people.
In conclusion, there are 300 people in the enclosed space rather than 299 people.
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Help needed! please help math
Answer:
4.163 × 10^7
Step-by-step explanation:
The step by step explanation is in the image attached
hope this helps!!
I’m confused bout this, could you possibly explain and help me solve.
Solve the inequality 10>2x - 4 for x.
[tex]\begin{gathered} 10+4>2x-4+4 \\ \frac{14}{2}>\frac{2x}{2} \\ 7>x \\ x<7 \end{gathered}[/tex]So inequality for x is x < 7.
Plot the inequality on the graph.
given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=590(1.061)^x
Given the exponential function:
[tex]y=590(1.061)^x[/tex]Let's determine if the exponential function represents growth or decay.
Take the exponential function:
[tex]y=a(b)^x[/tex]Where b is the base.
• If the base of an exponential function is greater than one, the exponential function represents growth
• If the base of an exponential function is between 0 and 1, the function represents a decay function.
Here, the base of the exponential function, b is 1.061 which is greater than 1, the function represents a growth function.
SInce it is represents a growth function, let's determine the percentage rate of increase.
The general formula for exponential growth is:
[tex]y=a(1+r)^x[/tex]Where r is the growth rate.
Thus, we have:
[tex]\begin{gathered} y=590(1+(1-1.061)^x \\ \\ y=590(1+0.061)^x \end{gathered}[/tex]The growth rate, r is = 0.061
The percentage rate of increase is:
[tex]\text{percentage rate of increase = }0.061\ast100=6.1\text{\%}[/tex]Therefore, the percentage rate of increase is 6.1%
ANSWER:
The function represents growth
Percentage rate of increase = 6.1%
6pq³ x 2p⁹q²
solve this equation please and thanks
The resulting equation is 12[p^10][q^5].
The expression given to us is "6pq³ * 2(p^9)q²".The first term of the expression contains a constant that is 6.The first term of the expression contains a variable "p" raised to the power of 1.The first term of the expression contains a variable "q" raised to the power of 3.The second term of the expression contains a constant that is 2.The second term of the expression contains a variable "p" raised to the power of 9.The second term of the expression contains a variable "q" raised to the power of 2.We need to multiply the terms in the expression.In order to get the correct result, multiply the constants together and add the powers of the same variables.The final expression is "(6*2)[p^(1+9)][q^(3+2)]".The final expression is "12[p^10][q^5]".Hence, the resulting equation is 12[p^10][q^5].To learn more about equations, visit :
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In the figure below, pentagon RSTYZ is a regular polygon and m/RST = 108⁰.If m/UTY = 115°, what is m/STU?A137°OB. 223°OC. 108°OD. 115°
ANSWER
[tex]223[/tex]Option B
EXPLANATION
Given;
[tex]\begin{gathered} m\angle RST=108⁰. \\ m\angle UTY=115° \end{gathered}[/tex]Note that the pentagon is a regular polygon (all the angles are equal).
Hence;
[tex]m\angle RST=m\angle STY=108[/tex]The measure of angle STU is;
[tex]\angle STU=\angle STY+\angle UTY[/tex]Hence, substitute the values of the angles;
[tex]\begin{gathered} \operatorname{\angle}STU=\operatorname{\angle}STY+\operatorname{\angle}UTY \\ =108+115 \\ =223 \end{gathered}[/tex]Therefore, the measure of angle STU is 223 degrees
i need help with figures and dilations
7. The relationship between the latitude Lof a city in the Northern Hemisphere and its average annual temperature Tis modeled by the function T = -0.68L + 89.5. The slope of this linear function means (A) That temperature at the equator would be 89.5°. (B) For every degree increase in latitude, the average annual temperature increases by 89.5º. (C) For every degree increase in latitude, the average annual temperature increases by 0.68 (D) For every degree increase in latitude the average annual temperature decreases by 0.68º.
We are given the following function that models the temperature T as a function of the latitude L:
T = - 0.68 L + 89.5
We see that the temperature is in fact a linear function of slope -0.68 degrees/latitude.
Since the latitude of the Equator is 0 degrees, then, the equation tells us that the temperature at the Equator is:
T = - 0.68 (0) + 89.5 = 89.5 degrees of annual temperature. But this is NOT related to the slope.
The other two statements (B and C) are not correct,
The last statement D is correct, since for every degree increase in latitude, there is an annual decrease of temperature by 0.68 degrees, and this is what the slope expresses.
Please select answer D.
I dont understand what to do for this I have 5 questions of this and I dont understand how to do this please help me!
1) Whenever we're asked to find out something of like 1/7 of 35 we must proceed with a multiplication. This way:
2)
[tex]\frac{1}{7}\times35=\frac{35}{7}\text{ = 5}[/tex]3) Hence, the answer is 5
You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You neverwithdraw money from the account. How much money will be in the account after 4 years?
The formula to calculate the amount for compound interest is given to be:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
t=number of time periods elapsed
From the question provided, we have the following parameters:
[tex]\begin{gathered} P=2000 \\ r=5\%=0.05 \\ n=1(annual\text{ }compounding) \\ t=4 \end{gathered}[/tex]Therefore, we can solve as follows:
[tex]\begin{gathered} A=2000(1+\frac{0.05}{1})^{1\times4}=2000(1.05)^4 \\ A=2431.01 \end{gathered}[/tex]The amount after 4 years is $2,431.01.
Simplify the expression (x¹2)3.
Answer:
3x¹²
Step-by-step explanation:
1. Rule (x) = x
2. (x¹²) = x¹²
3. x¹²*3
4. 3x¹²
Did you get the same sum for both sets of angle measurements? What do you think that means? Create an equation to represent the situation.
If we know the measure of two of the three angles of a triangle, since the sum of the angles in a triangle aways is 180º, we can write the equation for angles a, b and c:
[tex]\begin{gathered} m\angle a=x \\ m\angle b=y \\ m\angle c=z \\ \text{Then,} \\ 180º=x+y+z \end{gathered}[/tex]Let's suppose we know x and y, then z is:
[tex]z=180º-x-y[/tex]11
Determine if the lines are parallel, perpendicular, or neither
y = 5 and y = -1
Parallel
Perpendicular
Neither
Answer:
its parallel
Step-by-step explanation:
because it is
(05.01 MC)A store sells cooking oil of two different brands in bottles of the same size. The table below and the equation each show the price (y), in dollars, of different number of bottles of oil (x):Brand ANumber of Bottles, x Price (dollars), y2 243 364 485 60Brand By = 15xHow many dollars more is the price of 9 bottles of brand B oil than the price of 9 bottles of brand A oil? (5 points)1. $32. $93. $184. $27
Solution
Step by step explanation:
Using the data, we can calculate the price per bottle for Brand A, which is:
24 / 2
= $12 per bottle
We also know that the slope of a line shows the rate of change, so the price per bottle for Brand B is $15.
The difference per bottle is 15 - 12 = Brand B is cost $3 more per bottle
The difference for 9 bottles will be: 9 * 3 = $27.
Therefore the answer will be $27
find the value of given
The value of (p² + 1/p²) and (p + 1/p)²is 18 and 20 respectively.
The above question is from algebra section and is from the topic surds and indices.
One of the standard formula is
(a - b)² = a² - 2ab +b²
(i) Here the expression is
p - 1/p = 4 and we need to find the value of p² + 1/p²
(p - 1/p)² = p² + 1/p² -2p(1/p)
4² = p² + 1/p² - 2
16 + 2 = p² + 1/p²
p² + 1/p² = 18
(ii) we need to find the value of (p + 1/p)²
(a + b)² - (a - b)² = 4ab
(p + 1/p)² - (p - 1/p)² = 4p(1/p)
(p + 1/p)² - 4² = 4
(p + 1/p)² = 4 + 16
(p + 1/p)² = 20
Therefore, the value of (p² + 1/p²) and (p + 1/p)² is 18 and 20 respectively.
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About how many times greater is the area ofthe Pacific Ocean than the Atlantic Ocean?Ocean Area (square kilometers)Pacific161.8 × 106Atlantic85,133,000
Given:
Area of Pacific ocean = 161.8 12 x 10⁶ square kilometers
Area of Atlantic ocean = 85133000 square kilometers
Let's find how many times greater is the area of the pacific ocean than the Atlantic ocean.
To find how many times greater, divide the area of the Pacific ocean by the area of the Atlantic ocean.
Thus, we have:
[tex]\begin{gathered} \frac{161.8\times10^6}{85133000} \\ \\ =\frac{161.8\times10^6}{85.133\times10^6} \\ \\ =1.9 \end{gathered}[/tex]Therefore, the area of the Pacific ocean is 1.9 times greater than the area of the Atlantic ocean.
ANSWER:
1.9 times
Find the probability of getting two or more heads.
Answer:
Step-by-step explanation: 0.50+0.25=0.75
so your answer would be 1/4 of a probability
How many solution does 19x=5x have?
Answer:
it doesn't have a solution
Step-by-step explanation:
A pipe is at least 21 feet long and you want to cut it into three pieces
The length of the each piece of pipe is 7 feet
What is Length?
Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The meter serves as the foundational unit of length in the International System of Units.
Given,
Total length of the pipe = 21feet
The pipe after 3 pieces = ?
We have to find the length of pipe after it is cut down into three piece
To find that we have to divide the length of the pipe with 3
The length of 3 pieces = 21/3
= 7 feet
Hence, The length of each piece will be 7 feet
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Which set of numbers is ordered from least to greatest? {2.82, √8. √II, 3-1} {-√16,-√17,-√18,-√19} {√5,- √6, 21/1, -3} {√10, 4, √4, 15}
A group of integers is referred to as an element and makes up a set. The set of numbers can either be an endless or a limited collection.
The set of numbers is ordered from least to greatest exists {2.82, √8. √II, 3-1}.
What is meant by the set of numbers?A set exists a grouping or collection of objects. These things exists frequently directed to as elements or set members.
Any grouping of items (elements) in mathematics and logic, whether or not they are mathematical (such as numbers and functions). A list of all the members of a set, wrapped in braces, is a typical way to represent a set. Even older than the concept of number is the intuitive conception of a set.
A group of integers is referred to as an element and makes up a set. The set of numbers can either be an endless or a limited collection. Roster notation is a method of indicating sets that uses "" and "" with commas separating the items.
Therefore, the correct answer is option a) {2.82, √8. √II, 3-1}.
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multiply the following decimals-0. 8 • (-0.3) • (-0.4) = -0. 096
Remember when we multiply negative numbers we need to be careful in the sign
[tex]-0.8\cdot-0.3\cdot-0.4=-0.096[/tex]Remember when we multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.
The markdown of a bicycle is Php1500.00 which is 20% of the original selling price. Find (a) the original selling price and (b) the new selling price.
Given:
The markdown of a bicycle = $1500
Which is 20% of the original selling price
Let the original selling price = x
so, 20% of x = 1500
so,
[tex]\begin{gathered} \frac{20}{100}\cdot x=1500 \\ \\ x=\frac{1500\cdot100}{20}=7500 \end{gathered}[/tex]so, the answer will be:
a) the original selling price = $7,500
b) the new selling price = 7500 - 1500 = $6,000
What is the measure of angle D?
(Geometry) with details and steps!!!
Answer:
See below
Step-by-step explanation:
The angle at E in the UPPER triangle
is 180 - -45 -14 = 121° ( because the angles of any triangle sum to 180 °)
The angle below this is the same value 121°
then 27 + 121 + D = 180 shows D = 32°
Answer:
32°
Step-by-step explanation:
If you look at the figure there are two distinct triangles formed by the intersection of the two lines
These are ΔAEB and ΔCED
Consider ΔAEB
Two of its angle measure are given:
m∠EAB = 14° and m∠EBA = 45°
The measure of the third angle ∠AEB can be computed from the fact that the sum of the three angles of a triangle add up to 180°
So we get the equation:
14 + 45 + m∠AEB = 180
59 + m∠AEB = 180
m∠AEB = 180 -59 = 121°
We also have
m∠AEB = m∠CED
since they are vertically opposite angles formed at intersection E by the two straight lines AD and BC
So m∠CED = 121°
Now considering the triangle ΔCED we have two angles known to us
m∠ECD = 27° and m∠CED = 59°
The sum of the measures of the three angles ∠ECD, ∠CED and ∠CDE must add up to 180°
==> 27 + 121 + ∠CDE = 180
148 + ∠CDE = 180
∠CDE = 180 - 148 = 32°
So ∠D measures 32°
What are the coordinates of the point on the directed line segment from (-9, 2) to
(5,-10) that partitions the segment into a ratio of 1 to 3?
[1.5, 4] are the coordinates that divide the section into a 3 to 1 ratio.
Using a 3:1 partitioning ratio
#Multiply the ratio by the length of the x-coordinate:
5 + 9 = 14;
1/4 of 14 is 3.5;
we take this value out of the x-max to get the point, which is 5 - 3.5 = 1.5.
#Multiply the ratio by the length of the y-coordinate:
We subtract -2 from the y-max to obtain the point,
which is equal to 2 + 2 = 4.
x length -10 + 2
=> 1/4 x -8 = - 2
Consequently, [1.5, 4] are the coordinates that divide the section into a 3 to 1 ratio.
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3) Write 3 different ratios that are equivalent to 7 : 3
From the given problem, we have a ratio of 7 : 3.
Just any number to the ratio to get as many ratios as you want.
Sinec we only need 3 ratios,
multiply, 2, 3 and 4
The ratios will be :
14 : 6
21 : 9
28 : 12
Huilan is 8 years younger than Thomas. The sum of their ages is 76. What is Thomas's age?
Let H denote the age of Hullan.
Let T denote the age of Thomas.
Huilan is 8 years younger than Thomas
Mathematically,
[tex]H=T-8\qquad eq.1[/tex]The sum of their ages is 76.
Mathematically,
[tex]H+T=76\qquad eq.2[/tex]Now let us substitute eq. 1 into eq. 2
[tex]\begin{gathered} H+T=76 \\ (T-8)+T=76 \\ T-8+T=76 \\ 2T-8=76 \\ 2T=76+8 \\ 2T=84 \\ T=\frac{84}{2} \\ T=42 \end{gathered}[/tex]Therefore, the age of Thomas is 42 years.
Need ASAP, explanation if you can :)
The probability of the complement of event E is 0.56,
How to find the probability?For any event A, we define the complement of A as:
[tex]A^c[/tex]
Where the complement refers to all the elements in the sample space that are not A, and the relation between the probabilities is:
P([tex]A^c[/tex]) = 1 - P(A).
In this case, we have an event E and we know that:
P(E) = 0.44
Then the probability of the complement will be:
P([tex]E^c[/tex]) = 1 - P(E) = 1 - 0.44 = 0.56
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