Linda traveled faster than Imani because when t =1 , linda traveled 65 miles and Imani traveled 60 miles and linda travelled at a faster rate because when t=0,
She travelled 10 miles and Imani travelled 0 miles these are cοrrect answer. The prοvided graph's cοοrdinates are (2, 120) and (4, 240).
What is graph ?A graph is a structure that amοunts tο a set οf items where sοme pairs οf the οbjects are in sοme manner "cοnnected" in discrete mathematics, mοre specifically in graph theοry. The items are represented by mathematical abstractiοns knοwn as vertices (sοmetimes knοwn as nοdes οr pοints), and each pair οf cοnnected vertices is knοwn as an edge. Generally, a graph is represented diagrammatically as a cοllectiοn οf dοts οr circles fοr the vertices cοnnected by lines οr curves fοr the edges. Graphs are οne οf the tοpics studied in discrete mathematics.
Slοpe with (2, 120) and (4, 240) is
Slοpe (y2-y1)/(x2-x1)
= (240-120)/(4-2)
= 120/2
= 60
Put m=60 and (x, y)=(2, 120) in y=mx+c, we get
120=60(2)+c
c=0
Sο, equatiοn is y=60x
Put x=0, 1, 2, 3 and 4, we get
y= 0, 60, 120, 180, 240
(0, 0), (1, 60), (2, 120), (3, 180) and (4, 240)
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Evaluate 2^x for (a) x= -2 and (b) x=3. Write your answers in simplest form.
a. The expression is__
when x= -2
b. The expression is__
when x= 3
(a) When [tex]x=-2, 2^x = 2^(-2) = 1/2^2 = 1/4[/tex]. So, the expression 2^x when x=-2 is 1/4.
(b) When [tex]x=3, 2^x = 2^3 = 8[/tex]. So, the expression 2^x when x=3 is 8.
The expression 2^x represents exponential growth, where the base 2 is multiplied by itself x number of times. When x is a negative number, the expression becomes a fraction because we are dividing 1 by the base raised to the absolute value of x. In this case, 2^(-2) is equivalent to 1/2^2, which is equal to 1/4. On the other hand, when x is a positive number, the expression grows exponentially. When x=3, the expression becomes 2^3, which is equal to 2x2x2 = 8.
In summary, the evaluation of 2^x when x is a negative number produces a fraction, whereas when x is a positive number, it produces a positive integer.
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Solve for x. Please show all steps needed.
x+8/(x+3)(x+4) = 3/x+3
Answer:
[tex]x = -2[/tex]
Step-by-step explanation:
[tex] \frac{(x + 8)}{[(x + 3) (x + 4)]} = \frac{3}{(x + 3)}[/tex]
Multiplying both sides by (x + 3) (x + 4), we get:
[tex](x + 8) = 3 (x + 4)[/tex]
Expanding the right-hand side, we get:
[tex]x + 8 = 3x + 12[/tex]
Subtracting x and 8 from both sides, we get:
[tex]2x = -4[/tex]
Dividing both sides by 2, we get:
[tex]x = -2[/tex]
Therefore, the solution to the given equation is x = -2. We can check this solution by substituting x = -2 into the original equation and verifying that both sides are equal.
Someone please explain the answer to this problem
Please help super confused
Answer:
1. 4, 28, 80
2. P(x)=4x
3. P(9.1)=36.4
The perimeter is 36.4 and the side length is 9.1
Step-by-step explanation:
To find perimeter you multiple a squares side length by 4.
(Please answer quickly!!!)Simplify negative 4 and 1 over 4 minus 6 and 2 over 5.
negative 213 over 20
negative 43 over 20
negative 10 and one third
10 and 13 over 20
Since 4 and 5 have a least common denominator of 20, we can convert both fractions to have a denominator of 20:
-17/4 * 5/5 = -85/20, 32/5 * 4/4 = 128/20, -85/20 - 128/20 = -213/20
what are fractions?A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers. The depiction of fractions appears easier than when decimal values are used.
A fraction is used to denote a portion or component of a whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
To simplify:
-4 and 1/4 - 6 and 2/5
For the two mixed integers, we must identify a common denominator. The least frequent multiple of 4 and 5 is 20 since their prime components are 2 and 5. Both mixed numbers can be transformed into improper fractions with a denominator of 20 as follows:
-4 and 1/4 = -17/4
6 and 2/5 = 32/5
Now we can subtract these fractions:
-17/4 - 32/5
We must locate a common denominator in order to subtract fractions. Since 4 and 5 have a least common denominator of 20, we can convert both fractions to have a denominator of 20:
-17/4 * 5/5 = -85/20
32/5 * 4/4 = 128/20
We can now take the two fractions apart:
-85/20 - 128/20 = -213/20
Therefore, -4 and 1/4 - 6 and 2/5 simplify to -213/20.
So, the answer is negative 213 over 20.
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Please help me solve this! Please and thank you! :D PLEASE HELP I WILL GIVE BRAINLIEST
The equation that shows a proportional relationship is y = 12x; where the constant of proportionality is 12
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
A proportion relationship is in the form:
y = kx; where x is the constant of proportionality
Let y represent the number of paper towel rolls and x represent the number of cases. Hence:
y = kx
From the table, using the point (1, 12):
12 = k(1)
k = 12
The equation is y = 12x
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a shopkeeper bought 300 lanterns. he sold 2/3 of them on Saturday and 1/6 of them on Sunday how many lanterns did he have left?
Answer:
150 Lanterns
Step-by-step explanation:
Total lanterns : 300
[tex]\frac{2}{6} * 300 = 100[/tex]
[tex]\frac{1}{6} * 300 = 50[/tex]
so He sold 150 lanterns in total , leaving 300-150 = 150 Lanterns left.
how to algebraically find all the real zeros on a polynomial function
Answer:
To find all the real zeros of a polynomial function algebraically, use the Rational Root Theorem to generate a list of possible rational zeros and use synthetic division to test each possible zero. The zeros that remain after testing all the possible zeros are the real zeros of the polynomial function.
To find all the real zeros of a polynomial function algebraically, you can use the Rational Root Theorem and synthetic division. The Rational Root Theorem states that if a polynomial function has integer coefficients, then any rational zero (i.e., a zero that can be expressed as a fraction) must have a numerator that is a factor of the constant term and a denominator that is a factor of the leading coefficient.
Here are the steps you can follow:
1. Write the polynomial function in descending order of degree, with all like terms combined.
2. Use the Rational Root Theorem to generate a list of possible rational zeros. This list will be a set of all the possible fractions that can be formed by dividing a factor of the constant term by a factor of the leading coefficient.
3. Use synthetic division to test each possible zero. Start with the smallest possible denominator and work your way up. If a possible zero is not a zero of the polynomial function, cross it off the list.
4. Repeat step 3 until all the possible zeros have been tested. The zeros that remain are the real zeros of the polynomial function.
For example, let's say we have the polynomial function f(x) = x^3 - 6x^2 + 11x - 6.
Write the polynomial function in descending order of degree: f(x) = x^3 - 6x^2 + 11x - 6.
Use the Rational Root Theorem to generate a list of possible rational zeros: ±1, ±2, ±3, ±6.
Use synthetic division to test each possible zero. We start with x = 1:
1 │ 1 -6 11 -6
│ 1 -5 6
└─────────────
1 -5 6 0
Since the remainder is zero, we have found a zero of the polynomial function at x = 1. We can write the factorization f(x) = (x - 1)(x^2 - 5x + 6).
Now we use synthetic division to test the other possible zeros:
2 │ 1 -6 11 -6
│ 2 12 46
└─────────────
1 -4 23 40
x = 2 is not a zero of the polynomial function.
3 │ 1 -6 11 -6
│ 3 15 78
└─────────────
1 -3 26 72
x = 3 is not a zero of the polynomial function.
-1 │ 1 -6 11 -6
│ -1 7 -4
└────────────
1 -7 18 -10
x = -1 is not a zero of the polynomial function.
-2 │ 1 -6 11 -6
│ -2 16 -50
└────────────
1 -8 27 -56
x = -2 is not a zero of the polynomial function.
-3 │ 1 -6 11 -6
│ -3 27 -102
└────────────
1 -9 38 -108
x = -3 is not a zero of the polynomial function.
6 │ 1 -6 11 -6
Hope this helps, I'm sorry if it doesn't! :]
match the equation with its graph
[tex]y=-\frac{2}{3} x+1[/tex]
identify the slope and the y-intercept
( i already did the first part i just need help finding the slope also the y intercept )
Answer:
slope is -2/3, and the y intercept is 1.
Step-by-step explanation:
Using y=Mx+b (slope intercept form), where M=slope, and B = Y intercept , you can find which valurs are which.
need help asap pleasee
Answer:
a
Step-by-step explanation:
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
the vertex of∠5 is point M
Step-by-step explanation:
Answer: M
Step-by-step explanation: M represents the vertex. Think of the vertex almost like the starting point of an angle.
express in the form n:1
Answer:3/2
Step-by-step explanation:
[tex]\frac{9}{6} = \frac{\frac{9}{3} }{\frac{6}{3} }=\frac{3}{2}[/tex]
Find the area of the shaded parts.
[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{outer}{radius}\\ r=\stackrel{inner}{radius}\\[-0.5em] \hrulefill\\ R=4\\ r=2 \end{cases}\implies A=\pi (4^2 - 2^2) \\\\\\ A=12\pi \implies A\approx 37.70~in^2[/tex]
Answer:
12πin² = 37.7in² (3sf)
Step-by-step explanation:
area of whole circle = π(4)² = 16π
area of small circle = π(2)² = 4π
area of shaded = 16π - 4π = 12π
12π = 37.6991... ≈ 37.7in² (3sf)
Which of the following tables represents a linear function? x −4 −2 0 2 4 y 5 1 −3 −7 −11 x −3 −2 0 2 3 y 5 2 0 2 4 x 3 3 0 3 3 y −3 −2 0 2 −3 x 0 2 3 4 5 y −3 2 0 2 −3
A table that represents a linear function include the following: A.
x −4 −2 0 2 4
y 5 1 −3 −7 −11
What is a linear function?In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
This ultimately implies that, a linear function has the same (constant) slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.
Next, we would determine the slope by using the points contained in the table as follows;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (1 - 5)/(-2 + 4) = (-3 - 1)/(0 + 2) = (-7 + 3)/(2 - 0)
Slope (m) = -2.
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THERMOMETER An outdoor thermometer claims to be accurate within
2 degrees Fahrenheit. One day, the thermometer reads 72°F.
a. Write an absolute value inequality that represents the possible actual
temperature t.
b. What is the range of possible actual temperatures?
Answer:
a. An absolute value inequality that represents the possible actual temperature t is:
|t - 72| < 2
b. To find the range of possible actual temperatures, we can solve the inequality:
|t - 72| < 2
We can split this into two separate inequalities, one for when t is greater than 72 and one for when t is less than 72:
t - 72 < 2 and -(t - 72) < 2
Simplifying these inequalities, we get:
t < 74 and t > 70
Therefore, the range of possible actual temperatures is 70°F < t < 74°F.
Step-by-step explanation:
The angle between the lines of sight from a lighthouse to a tugboat and to a cargo ship is 27°. The angle between the lines of sight at the cargo ship is twice the angle between the lines of sight at the tugboat. What are the angles at the tugboat and at the cargo ship?
The angle between the line of sight from the lighthouse to the tugboat is 27° and the angle between the line of sight from the lighthouse to the cargo ship is 54°.
Let's call the angle between the line of sight from the lighthouse to the tugboat "x". Then, we know that the angle between the line of sight from the lighthouse to the cargo ship is x+27, since the given angle between the lines of sight is 27°.
We also know that the angle between the lines of sight at the cargo ship is twice the angle between the lines of sight at the tugboat. Using this information, we can set up the equation:
2x = x+27
Solving for x, we get:
x = 27
So the angle between the line of sight from the lighthouse to the tugboat is 27°. Then, we can use this to find the angle between the line of sight from the lighthouse to the cargo ship:
x+27 = 27+27 = 54
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madison started a bank account with $200. each year, she earns 5% in interest, which means the amount of money in the account is multiplied by 1.05 each year.if madison does not withdraw money from her account, how much will she have in 10 years?
Madison will have $322.65 in her bank account in 10 years. Here is the calculation to find this amount:
Starting balance: $200
Year 1: $200 x 1.05 = $210
Year 2: $210 x 1.05 = $220.50
Year 3: $220.50 x 1.05 = $231.53
...
Year 10: $279.10 x 1.05 = $322.65
Therefore, after 10 years, Madison will have $322.65 in her bank account due to the annual interest earned.
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Select the correct answer. Which equation represents a circle with center T(5,-1) and a radius of 16 units? A. (x − 5)2 + (y + 1)2 = 16 B. (x − 5)2 + (y + 1)2 = 256 C. (x + 5)2 + (y − 1)2 = 16 D. (x + 5)2 + (y − 1)2 = 256
The equation of the given circle is: (x - 5)² + (y+ 1)² = 256
How to find the equation of the circle?The center-radius form (most formally called the standard form) of a circle is usually expressed as;
(x - h)² + (y - k)² = r²
where (h, k) is the center and r is the radius.
We are given a circle with center T(5,-1) and a radius of 16 units
The equation then becomes:
(x - 5)² + (y - (-1))² = 16²
(x - 5)² + (y+ 1)² = 256
Thus, we can conclude that is the equation of the circle.
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Which equation could represent a line that is parallel to y = -2x
+ 4?
a. 1/2+y=1
b.-2x+y=8
c.-2x-y=3
d.-1/2+y=5
The calculated equation that represents a line parallel to y = -2x + 4 is (c) -2x - y = 3.
How to determine the parallel equationThe equation of a line that is parallel to y = -2x + 4 will have the same slope as -2 since parallel lines have the same slope.
Therefore, we need to look for an equation that has a slope of -2.
(a) 1/2x + y = 1 has a slope of -1/2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.
(b) -2x + y = 8 has a slope of 2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.
(c) -2x - y = 3 can be rearranged to y = -2x - 3, which has a slope of -2, so it is parallel to y = -2x + 4.
(d) -1/2x + y = 5 has a slope of 1/2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.
Therefore, the equation that represents a line parallel to y = -2x + 4 is (c) -2x - y = 3.
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A coin is flipped and a card is randomly selected from a deck of 52. What is the probability the coin will land on heads and the card will be a club? There are 13 clubs in a deck of cards.
A. 1/8
B. 1/24
C. 4/9
D. 1/2
My answer:
There are 4 cards of number eight in a deck of 52 cards, namely: 8 Spades, 8 Diamond, 8 Clubs, and 8 Hearts. So the probable outcomes are 4 and the total cards are 52. So, x 100 = 1/13. So there is a 1/13 chance for getting an eight, i.e, for every 13 cards, one card will be an eight.
hope it helps :)
also please mark brainliest it means alot
36 is 15% of what number?
54
240
360
540
Answer:
240
Step-by-step explanation:
15% of 54=8.1
15% of 240=36
15% of 360=54
15% of 540=81
so the answer is 240
36 is 15 percent of 240.
We have,
To find out what number 36 is 15% of, we can set up the equation:
36 = 0.15x
Here, x represents the unknown number we are trying to find.
To solve for x, we divide both sides of the equation by 0.15:
36 / 0.15 = x
Simplifying the right side gives:
240 = x
Therefore,
36 is 15 percent of 240.
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Score: 1/6 1/6 answered
Question 1
Given the triangle
H=
* <>
15
/33°
answer to 4 decimal places.
Question Help: Video
Submit Question
X find the length of side 2 using the Law of Cosines. Round your final
3
27 a
The length of side 2 of the given triangle is 16.22.
What is Law of Cosines?The Law of Cosines is a mathematical formula that is used to calculate the length of sides and angles in a triangle. It is based on the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides
The Law of Cosines helps to solve for the side length in triangles when we are given two sides and the angle between them. In this triangle we are given side 1 (15) and the angle between the two sides (33°). To find side 2, we will use the formula:
c² = a² + b²- 2ab*cosC
Where c is the length of the unknown side, a is the length of the given side, b is the length of the other given side, and C is the angle between the two given sides.
In this case, c is side 2, a is 15, b is unknown, and C is 33°. We will plug in the known values and solve for b:
b² = 15² + c² - 2*15*c*cos(33°)
b² = 225 + c² - 30c*cos(33°)
We can solve this equation for c:
c = (225 + b² - 30b*cos(33°))/2
Now, we can solve for b using the values for c and a given in the problem:
b²= 225 + 27² - 30*27*cos(33°)
b² = 225 + 729 - 690.8
b²= 264.2
b = 16.22
Therefore, the length of side 2 is 16.22.
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What percent of data population falls between a z-score of -1. 5 and 0. 5
Around 62.47% of the data population is situated between a z-score of -1.5 and 0.5.
Assuming a standard normal distribution, the percentage of the data population that falls between a z-score of -1.5 and 0.5 can be calculated using a standard normal table or a calculator.
Using a standard normal table, we can find the area under the curve between z = -1.5 and z = 0.5.
The area to the left of z = 0.5 is 0.6915, and the area to the left of z = -1.5 is 0.0668. Therefore, the area between z = -1.5 and z = 0.5 is:
0.6915 - 0.0668 = 0.6247
So, approximately 62.47% of the data population falls between a z-score of -1.5 and 0.5.
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Which describes a financial product offered by insurance companies that, in
return for an investment, provides fixed payments each month for the
remainder of a person's life?
The financial product described is an annuity.
An annuity is a contract offered by insurance companies, where the buyer makes a lump-sum payment or a series of payments in exchange for regular payments made over time, usually until the end of the buyer's life. An annuity can be either fixed or variable, depending on the type of investment chosen by the buyer.
In a fixed annuity, the payments are predetermined and do not change over time, while in a variable annuity, the payments are based on the performance of the underlying investments. An annuity is often used as a retirement income stream.
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Find the quotient of 40y^(4)-5y^(3)-30y^(2)-10y divided by 5y
The quotient of [tex]40y^(4)-5y^(3)-30y^(2)-10y[/tex] divided by [tex]8y^(3) - y^(2) - 6y - 2[/tex]
You can use the polynomial long division method to find the product of two polynomials. Following are the steps:
Step 1: Descending in degree, write the dividend polynomial. If any terms are absent from the polynomial, replace them with coefficients of 0.Step 2: Descend the degree of the divisor polynomial as you write it. If any terms are missing from the divisor polynomial, substitute coefficients of 0 for those terms.Step 3: To calculate the first term of the quotient, divide the dividend's first term by the divisor's first term.Step 4: Multiply the divisor by the first term of the quotient to get the first term of the partial product.Step 5: Subtract the partial product from the dividend.Step 6: Bring down the next term of the dividend.Step 7: Repeat steps 3-6 until all the terms of the dividend have been used.Step 8: The final result is the quotient, plus any remainder left over after the last subtraction.To divide [tex]40y^(4)-5y^(3)-30y^(2)-10y[/tex] by 5y, we utilize long division. Divide dividend by divisor to obtain first term of the quotient:
[tex]40y^(4) / (5y) = 8y^(3)[/tex]
Multiply divisor (5y) by first term of quotient (8y^(3)) to obtain first term of partial product:
[tex](8y^(3))(5y) = 40y^(4)[/tex]
Subtract the partial product from the dividend to obtain remainder:
[tex]40y^(4) - 40y^(4) = 0[/tex]
[tex]-5y^(3) / (5y) = -y^(2)(-y^(2))(5y) = -5y^(3)-5y^(3) - (-5y^(3)) = 0[/tex]
[tex]-30y^(2) / (5y) = -6y(-6y)(5y) = -30y^(2)-30y^(2) - (-30y^(2)) = 0[/tex]
Repeat process:
[tex]-10y / (5y) = -2(-2)(5y) = -10y-10y - (-10y) = 0[/tex]
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What is 0.06 written as a percent?
Answer:
6%
Step-by-step explanation:
0.06 is 6% as a decimal
Calculate 15% of 12000 for two (2) years
Answer:
look below
13,800
Brian wants to exchange south African Rand for British pound. If R1 is worth 0. 075199 pound, how many pounds will he get for R2100 if he must pay an agent commission of 1. 5%
After deducting a commission of 1.5%, Brian will receive 155.71 pounds in exchange for R2100.
To find out how many pounds Brian will get, we first need to calculate the amount of commission he will pay. The commission is 1.5% of R2100, which is equal to 0.015 x R2100 = R31.50.
The amount of money he will actually receive in pounds is the remaining R2100 minus the commission, which is R2068.50. To convert this to pounds, we multiply by the exchange rate of R1 = 0.075199 pound:
2068.50 x 0.075199 = 155.706675 pounds
Therefore, Brian will get 155.71 pounds for R2100 after paying the agent commission.
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if 3 Sin A + 4 cos A= 5 prove that tan A = 3/4
7.03 The Unit Circle
The concept of the unit circle is presented throughout it's answer.
What is the unit circle?The unit circle is a circle with a radius of 1 unit that is centered at the origin (0,0) of a coordinate plane. It is a fundamental concept in trigonometry and geometry, and it is used to define the trigonometric functions (sine, cosine, and tangent) of angles in the Cartesian plane.
The format of each coordinate on the unit circle is given as follows:
[tex](\cos{\theta}, \sin{\theta})[/tex].
Hence we can calculate the trigonometric measures for any angle, as the tangent, the secant, the cossecant and the cotangent of an angle are all functions of the sine and the cosine obtained by the unit circle.
Missing InformationThe problem is incomplete, hence the unit circle concept is presented in this answer.
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