Answer:
Step-by-step explanation:
f(x) = 8 sin [2(x+3)] + 9
x = 8 sin [2(y+3)] + 9
isolate y [tex](f^{-1}(x))[/tex]:
x/8 - 9 = sin[2(y+3)]
[tex]sin^{-1}(\frac{x}{8} - 9) = 2(y+3)[/tex]
= 2y + 6
[tex]sin^{-1}(\frac{x}{8} - 9) = 2y + 6\\sin^{-1}(\frac{x}{8} - 9) - 6 = 2y\\\frac{sin^{-1}(\frac{x}{8} - 9) - 6}{2} = y[/tex]
AIM: SWBAT solve two-step equations using a balance model
THINK ABOUT IT!
Mark is working at a grocery store and is stacking apples. Before he stacks them, he puts them on a
balance to weigh them. On the right side of the balance, he put 15 apples. On the other side of the
balance, he puts two boxes of apples and three additional apples (pictured below). The weight on
either side of the balance is equal, which keeps the balance balanced.
Step A: Write an equation to represent the balance.
Step B: If there is the same number of apples in each box, how many apples are in each box
A. The equation that represents the balance is, 2x + 3 = 15.
B. Each box contains, x = 6 apples.
How to Write and Solve an Equation?Given the problem above, to write an equation that would represent the balance, we would assume both sides of the balance are separated by the equal sign, "=".
Therefore, let the unknown number of apples in each box be be represented as x.
A. Apples in the two boxes would be 2x, the total apples on the left of the balance would be expressed as:
2x + 3
On the right, we have 15 apples, therefore, the equation that represents the balance is: 2x + 3 = 15
B. Solve to find x, the number of apples in each box:
2x + 3 = 15
2x + 3 - 3 = 15 - 3
2x = 12
x = 12/2
x = 6
This means that there were 6 apples in each box.
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Which expressions are equivalent to
[tex] {5}^{18} [/tex]
select all that apply
Answer:
B and C
Step-by-step explanation:
(5⁷)¹¹ = 5⁷⁷
5⁹ × 5² = 5¹¹
Answer:
[tex] {5}^{12} \times {5}^{6} and \: \frac{ {5}^{24} }{ {5}^{6} } \\ option \: b \: and \: c[/tex]
Step-by-step explanation:
[tex] {a}^{b} \times {a}^{c} = {a}^{(b + c)} \\ \frac{ {a}^{b} }{ {a}^{c} } = {a}^{(b - c)} [/tex]
[tex] {5}^{12} \times {5}^{6} = {5}^{(12 + 6} = {5}^{18} \\ \frac{ {5}^{24} }{ {5}^{6} } = {5}^{(24 - 6)} = {5}^{18} [/tex]
Jeremy spent a total of $79.16 on a shirt and one pair of jeans. He knows the jeans cost $49.95 but he does not know the cost of the shirt, s. He created the model shown to find the cost of the shirt.
The model to show the cost of the shirt is x+49.95=79.16. Therefore, the cost of shirt is $29.21.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Jeremy spent a total of $79.16 on a shirt and one pair of jeans.
Let the cost of shirt be x.
The jeans cost is $49.95
Now, the cost of shirt + the cost of jeans = Total cost
⇒ x+49.95=79.16
⇒ x=79.16-49.95
⇒ x=$29.21
Therefore, the cost of shirt is $29.21.
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The factors of the function are (x + 1), (x - 1) and (x-4). Which equation could describe the function?
The function having the factors (x+1), (x-1) and (x-4) is x³-4x²-x+4 = 0
What are factors?
A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
Factors can be found using either division or multiplication. Rules of divisibility can also be applied.
Given, the factors of a function are (x+1), (x-1) and (x-4)
We know that if the factors of a function are (x-a) and (y-b), it would mean that the function is (x-a)(y-b) = 0
Similarly, taking the above factors given in a function, the function would be:
(x+1)(x-1)(x-4)=0
⇒ (x²-1)(x-4)=0
⇒ x³-4x²-x+4 = 0
Hence, the function having the factors (x+1), (x-1) and (x-4) is x³-4x²-x+4 = 0
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in a poll, respondents were asked whether they were planning to vote in the local election. 315 respondents indicated that they were planning to vote and 217 said that they were not. what is the probability that the next respondent questioned will indicate that they are planning to vote?
The probability that the next respondent questioned would say they plan to vote is 0.59.
What is probability?
The ratio of the number of favorable outcomes to the total number of outcomes of an event is defined as probability.
We know that the probability of an occurrence =the number of favorable outcomes divided by the total number of events.
Given that, 315 respondents stated they planned to vote, while 217 said they did not.
Now, the probability of voting is:
P(voting)=315(315+217)
= 315/532
= 0.59
As a result, the likelihood that the next respondent questioned would say they plan to vote is 0.59.
The probability that the next respondent questioned would say they plan to vote is 0.59.
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What is the result of this operation?
Answer: B
Step-by-step explanation:
If you chose D it would be wrong because you have to remember that the two negatives cancel out!
hii please help I'm super confused !
Answer:
Below
Step-by-step explanation:
Two points are given....calculate the slope, m = (y1-y2) / (x1-x2)
= ( 3-1) / ( 0 - - 8) = 2/8 = 1/4
Only equation II has slope = 1/4
at a certain gas station, 35% of the customers use regular unleaded gas, 35% use extra unleaded gas, and the remainder use premium unleaded gas. of those using regular gas, only 50% fill their tanks. of those customers using extra unleaded, 30% fill their tanks, whereas of those using premium unleaded, 30% fill their tanks. if the next customer fills the tank, what is the probability that extra unleaded gas was requested? (give your answer in percentage terms with one decimal point of precision.)
The probability that extra unleaded gas was requested is 35%.
To find the probability that the next customer requested extra unleaded gas, we need to first find the total probability that any customer requests extra unleaded gas.
Since 35% of customers request extra unleaded gas, the probability that a customer requests it is 35%. Of those customers, 30% fill their tanks, so the probability that a customer requesting extra unleaded gas fills their tank is 30%.
Therefore, the probability that a customer requesting extra unleaded gas fills their tank is (35%) * (30%) = 0.105, or about 10.5%.
This is the probability that the next customer requested extra unleaded gas and fills their tank. To find the probability that the next customer simply requested extra unleaded gas, regardless of whether they fill their tank or not, we need to add the probabilities of them requesting extra unleaded gas and either filling or not filling their tank.
The probability that the next customer requested extra unleaded gas and filled their tank is 0.105, as we calculated above. The probability that the next customer requested extra unleaded gas and did not fill their tank is (35%) * (70%) = 0.245, or about 24.5%.
To find the total probability that the next customer requested extra unleaded gas, we need to add these two probabilities: 0.105 + 0.245 = 0.35, or 35%. This is the probability that the next customer requested extra unleaded gas.
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Harry owns a rare baseball card that is valued at $13.00. If he originally purchased the card for $5.00, by what percentage has its value increased?
Answer: The Value has increased by 800%
Step-by-step explanation:
When Mike and Travis go fishing, the probability that Mike catches at least one fish is 23. The probability that Travis catches at least one fish is 35. The probability that both Mike and Travis catch at least one fish is 12.
Let M = the event that Mike catches at least one fish.
Let T = the event that Travis catches at least one fish.
Are M and T independent events? Why or why not?
A) yes, because P(M)×P(T)=P(M and T)
B) yes, because P(M)+P(T)>P(M and T)
C) no, because P(M)×P(T)≠P(M and T)
D) no, because P(M)+P(T)>P(M and T)
The correct option regarding the probabilities and if the events are independent is given as follows:
C) no, because P(M)×P(T)≠P(M and T).
How to calculate the probabilities?In the context of an experiment, a probability is calculated as the division of the number of desired outcomes in the context of the problem by the number of total outcomes in the context of the experiment.
The probabilities of at least one fish for each are given as follows:
Mike: P(M) = 2/3.Travis: P(T) = 3/5.The probability that both catch at least one is:
P(M and T) = 1/2.
The multiplication of the probabilities of each is given as follows:
P(M) x P(T) = 2/3 x 3/5 = 2/5.
Different from P(M and T), hence these are not independent events, and option c is correct.
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Stanley had a poster made from a picture of
his dog Tasha. The poster image is eight
times the size of the picture. If the poster
image is 120 cm. in height, what was the
height of Stanley's original picture of Tasha
(in centimeters)?
Answer:
15 c m.
Step-by-step explanation:
120 divided by 8 =15
A rectangle park had two walking pathe as shown if PS=115m and PR=216m, find the length of QT
Answer:
QT = 108 m
Step-by-step explanation:
the diagonals of a rectangle are congruent and bisect each other, so
QS = PR = 216 , then
QT = [tex]\frac{1}{2}[/tex] QS = [tex]\frac{1}{2}[/tex] × 216 = 108 m
Answer: 108
Step-by-step explanation:
diagonals of a rectangle are equal in length
∴ PR = QS = 216
Diagonals of a rectangle bisect each other
=> QT = QS = [tex]\frac{QS}{2} \\= > \frac{216}{2}\\ = 108[/tex]
each student at william elementary can only participate in one fall activity. there are 65 students on the football team and twice that number in band. there are 61 students on each of the two soccer teams. how many students participate in fall activities
Answer:191
Step-by-step explanation:
65x2=130
130+61=191
Rugged cabin co. provides pre-made materials to build cabins. to ensure materials are in supply and ready for quick delivery, the company offers cabins in only three sizes. each cabin has rectangular floor plan where the length is equal to 5 feet more than twice the width. which expression represents the area, in square feet, for each cabin size?A. 2w^2 + 5w, where w is the widthB. 2w^2 + 5, where w is the widthC. 2w^2, where w is the widthD. 10w^2 + 5 w, where w is the width
The expression that represent the area of the cabin for rectangular floor plan is 2w² + 5w.
What is the area of rectangular shape?
In essence, the area of a rectangle is equal to the sum of its length and breadth. In contrast, the circumference of a rectangle is equal to the product of its four sides. Consequently, we can say that the area of a rectangle equals the space enclosed by its perimeter.
Given that the length of a cabin is equal to 5 feet more than twice the width.
Assume that the width of the cabin be w.
Then the mathematical expression of twice the width is 2w.
Then the mathematical expression of 5 feet more than twice the width is 2w + 5.The length of the cabin is 2w + 5 feet.
The area of rectangular shape is product of length and width.
The area of the cabin is (2w + 5)w
Apply distributive property:
= 2w × w + 5 × w
= 2w² + 5w
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make g the subject of 3e+4g=7+9eg
Answer:
the answer is g = (7 - 3e) / (4 - 9e)
Step-by-step explanation:
The subject of an equation is the value or values being solved for. An equation typically consists of two parts: an expression on the left side of an equal sign and an expression on the right side of the equal sign.
The given equation subject of equation is 3e + 4g = 7 + 9eg
Subtraction of 9eg from both sides of the equation
3e + 4g - 9eg = 7 + 9eg - 9eg
3e + 4g - 9eg = 7
Subtract 3e on both sides of the equation
3e + 4g - 9eg - 3e = 7 - 3e
4g - 9eg = 7 - 3e
Factorize g on left side of the equation,
g (4 - 9e) = 7 - 3e
Then divide (4 - 9e) on both sides of the equation,
g = (7 - 3e) / (4 - 9e)
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AHH PLEASE HELP I NEED TO HAVE THIS DONE IN 30 MIN AND THIS IS THE QUESTION I NEED HELP WITH I WILL GIVE 95 POINTS AND MARK BRAINLIEST
A linear relationship is given.
The slope of the linear relastionship is ?
The slope of the linear relationship is 15.
Define slope.Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run"). The slope of a line tangent to a function's graph in differential calculus is determined by the derivative of that function and serves as a representation of the function's instantaneous rate of change with regard to changes in the independent variable. The slope of a tangent line in the graph of a position function, which plots the distance travelled by an object against the passage of time, corresponds to the object's instantaneous velocity.
Given
A linear relationship is given.
y₁ = -9
y₂ = 6
x₁ = 0
x₂ = 1
Slope:
m = y₂ - y₁/x₂ - x₁
m = 6 + 9/1 - 0
m = 15/1
m = 15
The slope of the linear relationship is 15.
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Answer:
Slope = 15
Step-by-step explanation:
Now we have to,
→ find the slope of linear relationship.
Formula we use,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Coordinates we use from table,
→ x1 = 0, y1 = -9
→ x2 = 1, y2 = 6
Then the required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (6 -(-9))/(1 - 0)
→ m = (6 + 9)/1
→ m = (15)/1
→ [ m = 15 ]
Hence, the required slope is 15.
[140,166,132,165,152,168,181,158,173,180,182,163,177,180,142,147,149,178]
Answer: Mode: 180
Quartiles:
Q1 --> 149
Q2 --> 165.5
Q3 --> 178
Mean: 162.944....
Median: 165.5
Step-by-step explanation:
In a school Auditorium, there are three types of rows arrangement
possible for watching programs: rows of 20 students per row, or rows
of 25 students ver row, or rows of 40 students per row. Find the least
number of students required for any one of these arrangements so
that all the students can be accommodated in each of these
arrangements.
I think
it should be 200 as it's the first common multiple of 20 40 and 25
The r in the simple interest formula stands for rate which best describes how to use rate in formula
The best option is to Convert it to a decimal and multiply is the best way to describe rate in simple interest formula. The correct option is A.
What is simple Interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest.
Simple Interest (S.I.) is a method for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows Rs. 5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.
Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount. The correct option is A.
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Solve
e + 0.05 = 9.21
Answer: e = 9.16
Step-by-step explanation: Although it's not necessary, I would first get rid of the decimals by multiplying both sides of the equation by 100.
That gives is 100e + 5 = 921 which has no decimals.
Now just subtract 5 from each side to get 100e = 916 and
dividing both sides by 100 from here, e = 9.16.
Which expression is equivalent to −6(b − 7)? −6b − 42 −6b + 42 −6b − 7 6b + 7
The expression that is equivalent to −6(b − 7) is: B. -6b + 42.
How to Find Equivalent Expressions?Expressions that are equivalent to each other will give the same value when simplified and solved in their simplest forms.
Simply put, two expressions will be equivalent if they have the same number of terms or they will give the same quantity when you plug in the values of all the variables that are given in the expressions.
Given the expression, -6(b - 7), the steps below shows how we can simplify to determine the expression that is equivalent to it
-6(b - 7) [given]
Open the parentheses by using the distributive property of equality, which involves multiplying each of the terms within the parentheses by the term outside of the parentheses:
-6(b) -6(-7) [distributive property]
-6b + 42
-6b + 42 is the equivalent expression of -6(b - 7).
Thus, the answer is: B. -6b + 42.
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What is the simplified form of -24m^5 n^4/8m^-7 n^-2 ? Assume m≠0,n≠0.
[tex]-3m^{12}n^{6}[/tex] is the correct option
What is simplified form?
A fraction is a number that falls between the whole numbers but is not a whole number. It belongs to the entire. A fraction also consists of a denominator and a numerator. We obtain the fraction in its simplest form when both the numerator and denominator can no longer be independently reduced to any lower integer.
[tex](-24m^{5}*n^{4})/( 8m^{-7}*n^{-2} )\\[/tex]
taking [tex]m^{-7}*n^{-2}[/tex] in numerator to make [tex]m^{7}*n^{2}[/tex]
we get,
[tex]-3m^{4}*n^{4}*m^{7}*n^{2}\\-3m^{12}*n^{6}\\-3m^{12}n^{6}[/tex]
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Find the sum of the finite arithmetic sequence.
Sum of the first 80 positive odd integers
Answer:
6400
Step-by-step explanation:
We have 1 + 3 + 5 + ... + 155 + 157 + 159.
We can use Gauss's strategy.
Since we are adding 80 numbers, there are 40 pairs. Each pair adds up to 1 + 159 = 160. (Notice that 3 + 157, 5 + 155 = 160)
Thus, because there are 40 pairs and each pair adds up to 160, we have 160 * 40 = 6400.
I hope this helps!
find f(20) if f(x)=[tex]\frac{1}{4}x+5[/tex]
Answer:
f(20) = 10
Step-by-step explanation:
Can you please give me the answer you don’t have to solve all but please!!!!!!
Answer: Reduction: 1/3
Step-by-step explanation:
Remember that if you are dilating it to be larger, it will be a whole number. If it is less than one, then it is dilating to be smaller.
Answer: Reduction 1/3.
Step-by-step explanation: When a shape is transformed into a smaller version of the original, it's a reduction. Reductions are less than 1 so the answer I provided above is what you're looking for.
Have a great day! :)
The instructions for a fashion design project require three different cuts of silk The
longest piece must be twice the length of the middle-sized piece, and the shortest
piece must be ten inches shorter than the middle sized piece. The total length of the
piece of silk you are given to work with is 70 inches. How long should each of the
three cut pieces be?
The three cut pieces should be 10 inches, 20 inches, and 40 inches for the shortest, middle-sized and longest respectively
How to determine how long should each of the three cut pieces be?This is a word problem. We need to understand the sentence in order to translate it correctly.
To find the length of each of the three cut pieces, we can use the given information to set up a system of equations.
Let L, M and S be the length of the longest, middle-sized and shortest piece respectively
So we can set up the following equation:
L = 2M
S = M-10
L + M + S = 70
2M + M + (M - 10) + = 70
We can combine like terms to get:
4M - 10 = 70
4M = 80
We can divide both sides by 4 to get:
M = 20
Therefore, the length of the middle-sized piece is 20 inches.
Since L = 2M
L = 2 × 20 inches = 40 inches.
Since S = M - 10
S = 20 - 10 = 10 inches.
Therefore, the three cut pieces should be 10 inches, 20 inches, and 40 inches for the shortest, middle-sized and longest respectively
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Is 9,40,41 a right triangle
Using pythagoras theorem, the values given in the question 9, 40 and 41 represents a right angle triangle
Pythagoras TheoremThis theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides. The sides of this triangle are named the perpendicular, base and hypotenuse. In this case, the hypotenuse is always longest side, as it is opposite to the angle 90°
Mathematically Pythagoras theorem is given as;
x² = y² + z²
x = hypothenusey = legz = legLet's substitute the values into the formula and check if the values are a right angle triangle.
41² = 40² + 9²
1681 = 1600 + 81
1681 = 1681
The values 9, 40, 41 represents a right angle triangle
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Point B is on the graph of the function f(x) = -3x2. If the x-coordinate of point B is 2, which ordered pair gives the location of point B?
The ordered pair gives the location of point B is (2, f(2)).
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, B is a point on the graph of the function f(x) = - 3x² and the
x-coordinate of point B is 2.
To obtain the value of the y-coordinate we'll simply replace 2 in place of x.
Therefore, f(2) = - 3(2)².
f(2) = - 3(4).
f(2) = - 12.
Observing the given option the only correct answer would be
(2, - 12) and (2, f(2)).
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9. Solve for x.
12x + 3
11x +9
a. x = 9
b. x = 12
C. X = 6
d. x = 23
10. Open-Ended Complete the addends so you need to regroup to add. Then find the sum. 4, _ 37 + 1,28_
The addends 4, _ 37 + 1,28_ is completed so there will be need to regroup to add.
the addends. 4, 837 + 1,287
the sum is 6124
What is regrouping?Regrouping refers to rearranging numbers into groups according to place value to assist kids in handling greater numbers.
When performing operations like addition and subtraction on two-digit integers or bigger, regrouping is the process of forming groups of tens. Regrouping refers to the process of performing an operation by rearranging groups in place value.
Using regrouping for the addition problem
addend 4 8 3 7
addend 1 2 8 7
sum 4
1 regrouped to tens column
addend 4 8 3 7
addend 1 2 8 7
sum 2 4
1 regrouped to hundreds column
addend 4 8 3 7
addend 1 2 8 7
sum 1 2 4
1 regrouped to thousands column
addend 4 8 3 7
addend 1 2 8 7
sum 6 1 2 4
the sum is 6124
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