Answer: a ticket to an amusement park is $100 per person. you have a coupon for $20 off of the admission price. the amusement park is also having a promotion where if you bring an empty pepsi can you can take an additional $4 off of the total admission cost. how much do you have to pay to be admitted to the amusement park after the coupons? (it would be $76)
Step-by-step explanation: my brain thought this up
Answer:
Step-by-step explanation:
Mikes mom gave him 100 dollars to spend and his favorite toy shop. Mike bought a Lego set which cost him 20 dollars. When he bought a lollipop which cost him 4 dollars.
Given that the curves are formed from quarter circles, find the area of the shaded region. Give your answer in terms of T. 12m 12m
the area of the shaded region:
[tex]= 2(the \ area \ of \ a \ quarter \ circle) - (the \ area \ of \ the \ square)\\[/tex]
[tex]= 2\Big(\dfrac{\pi 12^{2} }{4}\Big) - 12^{2} = \dfrac{144 \pi}{2} - 144 = 72 \pi - 144\\[/tex]
[tex]= 72 (\pi - 2) \ m^{2}[/tex]
Answer:
72π-144 m²
Step-by-step explanation:
You want the area of a shaded region consisting of the overlap of two quarter circles in a 12 m square.
SegmentsIf we draw a diagonal from upper left to lower right through the figure, the shaded area is divided into two 90° segments of a circle of radius 12 m.
The formula for the area of a segment is ...
A = 1/2r²(θ -sin(θ))
where θ is the measure of the central angle.
For θ = π/2 radians, this is ...
A = 1/2r²(π/2 -1) . . . . . half the shaded area
Shaded areaThen the whole shaded area is ...
2 × 1/2r²(π/2 -1) = (12 m)²(π/2 -1) = 72π -144 m²
The area of the shaded region is 72π -144 m².
__
Additional comment
If we expand the shaded area formula, we get ...
A =1/2πr² -r²
This is recognizable as twice the area of a quarter circle, less the area of the square.
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Determine whether the point C3,-1) and (2,4) are on the same side of the Straight y=2x-6 then determine their distances.
The points are not on the same side. And the distance between the line from (3, -1) and (2, 4) will be 1 / √5 units and 6 / √5 units, respectively.
What is the distance between a point and a line?Let (x₁, y₁) be the point and ax + by + c = 0 be the line. Then the distance between a point and a line will be given as,
[tex]\rm d = \dfrac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}[/tex]
The diagram is given below.
The points are not on the same side of the line y = 2x - 6. Then the distance from a line to (3, -1) is given as,
d = |2 × 3 - (-1) - 6| / [√(2² + (-1)²)]
d = |7 - 6| / √5
d = 1 / √5
And the distance from a line to (2, 4) is given as,
d = |2 × 2 - 4 - 6| / [√(2² + (-1)²)]
d = |-6| / √5
d = 6 / √5
The points are not on the same side. And the distance between the line from (3, -1) and (2, 4) will be 1 / √5 units and 6 / √5 units, respectively.
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Combine each set of sentences to form one grammatically-correct sentence. You can delete or change words as needed, but your sentences need to retain important information from the original sentences. Try two different combinations for each group. 1. My sister is a graduate of Polytechnic University. My sister is a border services officer. My sister lives in North Delta A. B. 2. Jasmine left to visit her friend. Jasmine's friend lives in Alberta, Jasmine left yesterday A. B. 3. They listened to music. They did their homework. The music was relaxing. It helped them concentrate
A.
B.
A. My sister is a graduate of Polytechnic University and a border services officer who lives in North Delta.
B. Yesterday, Jasmine left to visit her friend in Alberta.
A. They listened to relaxing music while they did their homework, which helped them concentrate.
B. To help them focus on their homework, they listened to relaxing music.
Combining sentences is a useful writing technique that helps make sentences concise and easy to read. Combining two or more sentences into one sentence can also help to create smoother transitions between ideas. When combining sentences, it is important to make sure the sentence remains grammatically correct, and to retain important information from the original sentences.
Another way to combine sentences is to delete certain words or phrases. For example, in the sentence “Yesterday, Jasmine left to visit her friend in Alberta”, the phrase “yesterday” can be removed without changing the meaning of the sentence.
You can also combine sentences by changing the order of the words. For example, in the sentence “They listened to relaxing music while they did their homework, which helped them concentrate”, the order of the words can be changed to “They did their homework while they listened to relaxing music, which helped them concentrate”.
Finally, it is important to make sure that the sentence remains grammatically correct. When combining sentences, it is important to make sure that the sentence still has a subject and verb, and that the verb is still in the correct tense.
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Carter makes $15.25 per hour at his part time job. He saves (3)/(5) of his earnings. About how many hours will Carter have to work in order to save $300?
Carter will have to work about 33 hours in order to save $300.
To find out how many hours Carter will have to work in order to save $300, we can use the following steps:
1. First, we need to determine how much Carter saves per hour. Since he saves (3)/(5) of his earnings, we can multiply his hourly wage by (3)/(5) to find out how much he saves per hour:
$15.25 * (3)/(5) = $9.15
2. Next, we need to determine how many hours Carter will have to work in order to save $300. To do this, we can divide $300 by the amount he saves per hour:
$300 / $9.15 = 32.79 hours
3. Since Carter can't work a fraction of an hour, we'll round up to the nearest whole hour:
33 hours
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In the drawing, >ℎ
. Which statement about the volumes of the two cylinders is true?
The volume of the left-hand cylinder is less than the volume of the right-hand cylinder.
What is a cylinder?
One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. One of the fundamental three-dimensional shapes in geometry is the cylinder, which has two distant, parallel circular bases. At a predetermined distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.
The volume of the cylinder is given by:
V = π r² h
where r = radius
h = height
Consider the left-hand side cylinder.
radius = h
height = g
Then the volume is V1 = π h²g
Now consider the right-hand side cylinder
radius = g
height = h
Then the volume is V2 = π g²h
It is given that g > h
Taking V1/V2 = π h²g/π g²h = h/g = k
where k is a constant.
Now V1 = k V2
This means that V2 will be k times V1.
So right-hand side cylinder has the largest volume among the two.
Therefore the volume of the left-hand cylinder is less than the volume of the right-hand cylinder.
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find the degree, end behavior, x and y-intercept s zeroes of multiplicity, and a few midinterval points of the function (1)/(2)=(x+2)(x-1)^(2)(5x-2)
The degree of the function (1)/(2)=(x+2)(x-1)^(2)(5x-2) is 4, as there are 4 total x terms in the equation.
The end behavior of the function is determined by the leading term, which is (1/2)(5x^4). As the degree is even and the leading coefficient is positive, the end behavior is that the function will rise to the right and rise to the left.
The x-intercepts of the function are the values of x that make the function equal to zero. These can be found by setting each factor equal to zero and solving for x:
x+2=0 -> x=-2
x-1=0 -> x=1
5x-2=0 -> x=2/5
The x-intercepts are -2, 1, and 2/5.
The y-intercept is the value of the function when x=0. Plugging in 0 for x gives:
(1/2)(0+2)(0-1)^2(5(0)-2) = (1/2)(2)(-1)^2(-2) = -2
The y-intercept is -2.
The zeroes of multiplicity are the values of x that make the function equal to zero and the number of times they appear as a factor in the equation. In this case, the zeroes of multiplicity are:
-2 with a multiplicity of 1
1 with a multiplicity of 2
2/5 with a multiplicity of 1
A few midinterval points can be found by plugging in values of x between the x-intercepts and solving for the function value. For example, plugging in x=0.5 gives:
(1/2)(0.5+2)(0.5-1)^2(5(0.5)-2) = (1/2)(2.5)(-0.5)^2(-0.5) = -0.3125
So one midinterval point is (0.5, -0.3125).
Another midinterval point can be found by plugging in x=-1:
(1/2)(-1+2)(-1-1)^2(5(-1)-2) = (1/2)(1)(-2)^2(-7) = -7
So another midinterval point is (-1, -7).
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Imagine two cars that are traveling down the highway. The distance (in miles) each car has traveled can be represented using the following polynomials where t is the number of hours that has passed.
Car A: 7t²+50t+150
Car B: 7t²+45t
Part 1)Write a polynomial for the number of miles between the two cars
Part 2)What is the distance between the two cars after 3 hours of traveling on the highway?
Part 3) After how many hours will the distance between the two cars be 200 miles?
The polynomial for the number of miles between the two cars is d(t) = 5t + 150
The distance between the two cars after 3 hours is 165 milesThe time after traveling 200 miles apart is 10 hoursThe polynomial for the number of miles between the two carsGiven that
Car A: 7t²+50t+150
Car B: 7t²+45t
The distance function is represented as
d(t) = 7t²+50t+150 - 7t² - 45t
So, we have
d(t) = 5t + 150
The distance after 3 hoursThis means that t =3
So, we have
d(3) = 5 * 3 + 150
d(3) = 165
The time the distance after is 200 milesThis means that d(t) = 200
So, we have
5t + 150 = 200
Evaluate the difference
5t = 50
So, we have
t = 10
Hence, the time is 10 hours
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You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.49. Thus you are performing a two-tailed test. Your sample data produce the test statistic z=2.517z=2.517. Find the p-value accurate to 4 decimal places.
p-value =
The p-value for our test is 0.0120, accurate to 4 decimal places.
We are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.49. We are performing a two-tailed test and our sample data produce the test statistic z=2.517.
To find the p-value, we need to use a standard normal distribution table or calculator. We will use the table for this answer.
The first step is to find the area to the left of the test statistic z=2.517 in the standard normal distribution table. This gives us the probability of obtaining a z-score less than or equal to 2.517. The closest value in the table is 2.51, which gives us an area of 0.9940.
Since we are conducting a two-tailed test, we need to find the area in both tails of the distribution. To do this, we subtract the area to the left of the test statistic from 1: 1-0.9940 = 0.0060. This gives us the area in the right tail of the distribution.
Finally, we multiply this value by 2 to get the p-value for our two-tailed test: 0.0060 * 2 = 0.0120.
Therefore, the p-value for our test is 0.0120, accurate to 4 decimal places.
p-value = 0.0120
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Find the inverse of the following matrix if it exists :X=122434−12−1−30−3−2−111
The inverse of the following matrix X is X-1 = 3/416/4-1/4-3/44/30/4-2/41/41/4.
The inverse of a matrix is a matrix that, when multiplied by the original matrix, produces the identity matrix. To find the inverse of the following matrix X, we need to use the formula X-1 = 1/|X| adj(X), where |X| is the determinant of X and adj(X) is the adjoint of X.
First, let's find the determinant of X:
|X| = (1)(-12)(-3) + (2)(-1)(-2) + (2)(3)(-1) - (-2)(-1)(2) - (1)(3)(-2) - (4)(-1)(-3)
|X| = -36 + 4 + -6 + 4 - -6 - -12
|X| = -16
Since the determinant of X is not equal to 0, the inverse of X exists.
Now, let's find the adjoint of X:
adj(X) = -12-2-134-3024−11−3
Finally, let's use the formula X-1 = 1/|X| adj(X) to find the inverse of X:
X-1 = 1/(-16) -12-2-134-3024−11−3
X-1 = 3/416/4-1/4-3/44/30/4-2/41/41/4
Therefore, the inverse of the following matrix X is X-1 = 3/416/4-1/4-3/44/30/4-2/41/41/4.
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how to work out surds
Question 5(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
Coins are placed into a treasure chest, and each coin has a radius of 1.4 inches and a height of 0.0625 inches. If there are 230 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? Round to the nearest hundredth and approximate using π = 3.14.
0.38 in3
126.39 in3
353.88 in3
88.47 in3
The coins take up approximately 35.259 cubic inches of space inside the treasure chest.
What is Volume?Volume refers to the amount of space occupied by a three-dimensional object, measured in cubic units.
Solution:
The volume of each coin is a cylinder with radius 1.4 inches and height 0.0625 inches. The volume V of one coin is given by:
V = πr²h
= 3.14 x 1.4² x 0.0625
= 0.1533 cubic inches (rounded to four decimal places)
Since there are 230 coins in the treasure chest, the total volume of the coins is:
Total volume = 230 x V = 230 x 0.1533 = 35.259 cubic inches (rounded to three decimal places)
Therefore, the coins take up approximately 35.259 cubic inches of space inside the treasure chest.
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You will be marked as brainlest
i need correct ans now please
and extra points will be given
please
Answer:
3m-4
Step-by-step explanation:
marcie's age be x
her father age is four less than three times
the equation tht describes her father age is 3m-4=40
Write an equation in slope intercept form from the linear inequality graphed below.
Given the slope of the line and the intercept it forms with the y-axis, one of the mathematical forms used to derive the equation of a straight line is called the slope intercept form. Y = mx + b, where m is the slope of the straight line and b is the y-intercept, is the slope intercept form.
The equation of the line, as determined by the slope-intercept formula, is: y = mx + b, where m is the line's slope and b is its y-intercept. As x and y represent each point on the line, they must be maintained as variables when using the formula above.
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Mario has 1 gallon of milk. He pours 4 cups of milk for him and his 3 siblings to have with their breakfast. How much milk is left ? Simplify your answer .
Answer:
37
Step-by-step explanation:
(Quick!) Can you show work as well please?
The value of x would be equal to 20 degrees.
What is linear pair?Linear pairs of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.
We are given the parameters as;
7x and (x + 20)
The sum of angle is equal to 180.
7x + (x + 20) = 180
8x + 20 = 180
8x = 180 - 20
8x = 160
x = 160/8
x = 20
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6. 4.61 x 10^17atoms radon
4.61 x 10¹⁷ atoms of radon means that is the total number of atoms in the element and is dependent on the number of mole.
What is Avogadro constant?
This is referred to as the proportionality factor that relates the number of constituent particles in a sample with the amount of substance in that sample.
One mole of a substance is equal to 6.022 × 10²³ units of that substance (such as atoms, molecules, or ions). The number 6.022 × 10²³ is known as Avogadro's number or Avogadro's constant. The concept of the mole can be used to convert between mass and number of particles.
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PLEAAAASEEEE HELPP!!!!!!!!!!! I WILL GIVE BRAINLIEST!!!!!!!!!!
The line's y-intercept is equal to -3.
An inequality to express the possible distances Jim and Lee can travel in the taxi is 1.75x + 3.00 < 45.
What is y-intercept?In Mathematics, the y-intercept is sometimes referred to as an initial value or vertical intercept and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
Based on the information provided about the line on the graph, we have the following:
y-intercept of function P = (0, -3).
Next, we would determine the possible distances Jim and Lee can travel in the taxi:
1.75x + 3.00 < 45.
1.75x < 45 - 3
1.75x < 42
x < 42/1.75
x < 24.
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In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. A regression analysis was completed and the value for s was found to be 3.05.
Which of the following is the best interpretation of s?
The average residual is about 3.05 pretzels.
The average residual is about 3.05 centimeters.
The average handspan of a student is 3.05 centimeters.
The average number of pretzels a student could grab is 3.05 pretzels.
URGENT PLEASE HELP!!! 50 POINTSS!
Answer: A, D, and F
Step-by-step explanation:
SOH CAH TOA
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
Answer:
tanθ=6/8, sinθ=6/10, cosθ= 8/10
Step-by-step explanation:
the ratio of tan is opposite over adjacent from the angle's perspective, and 6 is opposite whereas 8 is adjacent so tan(x)=6/8
the ratio of sin is opposite over hypotenuse from the angle's perspective, where 6 is opposite from it whereas the hypotenuse will always be the side opposite to 90 so it's 10 so sin(x)=6/10
the ratio of cos is adjacent over the hypotenuse from the angle's perspective, where 8 is adjacent to it whereas 10 is the hypotenuse so the ratio will be cos(x)=8/10
A theater charges $10 for main-floor seats and $4 for balcony seats. If all seats are sold, the ticket income is $5800. At oneshow, 30% of the main-floor seats and 50% of the balcony seats were sold and ticket income was $1900. How many seats are on the main floor and how many are in the balcony?
To solve this problem, we can use a system of equations. Let's call the number of main-floor seats x and the number of balcony seats y.
The first equation can be written as:
10x + 4y = 5800
The second equation can be written as:
0.3x + 0.5y = 1900
Now we can use the elimination method to solve for one of the variables. Let's multiply the second equation by -10 to eliminate the x variable:
-3x - 5y = -19000
Adding the two equations together gives us:
7x - y = 3900
Now we can use substitution to solve for one of the variables. Let's solve for y in the first equation:
y = (5800 - 10x)/4
And substitute this value into the second equation:
7x - (5800 - 10x)/4 = 3900
Multiplying both sides by 4 gives us:
28x - 5800 + 10x = 15600
Solving for x gives us:
38x = 21400
x = 563.16
And plugging this value back into the first equation to solve for y gives us:
y = (5800 - 10(563.16))/4
y = 609.21
So there are approximately 563 main-floor seats and 609 balcony seats.
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What is most likely true about the melting times of these two types of chocolates
It can be inferred that milk chocolate does have a lower melting point than dark chocolate and that the rate at which chocolate melts is influenced by a number of variables, including composition, temperature, as well as humidity.
According to the facts provided, it is anticipated that within 64 seconds, half of the milk chocolate brands will melt. According to their composition as well as melting point, different milk chocolate brands may melt sooner or later than 64 seconds.
However, it is believed that none of the dark chocolate brands are expected to melt before 64 seconds have passed and that their melting time actually begins after 200 seconds.
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Express (x+10)^2 as a trinominal in standard form
Answer:
x^2 + 10x + 20
Step-by-step explanation: When you multiply binomials, you are practically taking each term and multiplying it with others until you are out of combinations. However, when the product is represented in standard form, it requires the terms to be set within a specific order that prompts the term at the highest order/power placed on the furthest left side of the expression. The first term x^2 can be referred to as a term of the second power, 10x is seen as one to the first power (x^1 = 1st), and 20 as 0, since it is a constant.
What are the solution (s) of the equation? -4x^(4)+25x^(2)+75x=-5x^(4)-3x^(3) The solution (s) i(s)/(a)re
The solution(s) of the equation are x = 0 and the solutions of the cubic equation x^(3)+3x^(2)+25x+75 = 0.
The solution(s) of the equation can be found by rearranging the terms and then factoring. Here are the steps:
Step 1: Rearrange the terms to have all the x terms on one side of the equation:
-4x^(4)+25x^(2)+75x+5x^(4)+3x^(3) = 0
Step 2: Combine like terms:
x^(4)+3x^(3)+25x^(2)+75x = 0
Step 3: Factor out the common factor of x:
x(x^(3)+3x^(2)+25x+75) = 0
Step 4: Use the zero product property to find the solutions:
x = 0 or x^(3)+3x^(2)+25x+75 = 0
The first solution is x = 0. The other solutions can be found by solving the cubic equation x^(3)+3x^(2)+25x+75 = 0. This equation does not have any rational solutions, so the solutions will be irrational or complex.
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Which equation would calculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder shown?
a cylinder with the diameter labeled 2.8 centimeters and the height labeled 3.7 centimeters
A. SA = 2π(1.4)2 + 2.8π(3.7)
B. SA = 2π(1.4)2 + 1.4π(3.7)
C. SA = 2π(2.8)2 + 2.8π(3.7)
D. SA = 2π(2.8)2 + 1.4π(3.7)
The equation to calculate the amount of wrapping paper is 2π(1.4)² + 2.8π(3.7) cm²
The surface area of a cylinder:
Surface area is the total area that the surface of an object occupies. It is a measure of how much area is covered by the exterior of an object. The formula for the surface area of a cylinder is:
SA = 2πr² + 2πrhWhere r = radius of the base and h = height of the cylinder.
Here we have
Diameter of the cylinder = 2.8 cm
Radius of the cylinder = 2.8/2 = 1.4 cm
Height of the cylinder = 3.7 cm
Using the formula,
The surface area of a cylinder SA= 2πr² + 2πrh
The surface area of the cylinder
= 2π(1.4)² + 2π(1.4)(3.7)
= 2π(1.4)² + 2.8π(3.7)
Here, the total surface area of the cylinder will equal the amount of wrapping paper needed to completely cover the cylinder
Therefore,
The equation to calculate the amount of wrapping paper is 2π(1.4)² + 2.8π(3.7) cm²
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hi i think its A. SA = 2π(1.4)2 + 2.8π(3.7) hope this helped have a nice day! :)
Andre and Elena knew that after 28 days they would have 228 coins, but they wanted to find out how many coins that actually is.
Andre wrote: 228= 2 x 28 = 56
Elena said, “No, exponents mean repeated multiplication. It should be 28 x 28, which works out to be 784.”
Who do you agree with? Could they both be correct or wrong? Explain your reasoning.
To find the number of coins the statement made by Elena is correct.
What are exponents?The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. It might be an integer, a fraction, a negative integer, or a decimal.
Elena is on point. The formula 228 = 28 x 2 = 56 doesn't make sense in this situation since it suggests that they only counted for 28 days and received 228 coins, when the problem states that they counted for 28 days and received 228 coins. The fact that they counted for 28 days and came up with a total of 28 times 28 coins, or 784, makes the equation 228 = 28 x 28 make sense. Elena is accurate as a result.
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Find the Value of "h" h² +4h+111=0
Answer: h=−2+i√107,−2−i√107
A circle has 36 pi square meters what is the circumference of this circle
Answer: 18cm
Step-by-step explanation:
The length of the radius of the circle with center O has a circumference of 36π is 18cm.
Create an exponential function (y=ab^x) that passes through the points (1960,19.005) and (2010,19.548). Round (a) and (b) to three decimal places.
The equation of exponential function=y = 0.054 × [tex]1.028^{x}[/tex]
What are exponential functions?As the name implies, exponents are utilised in exponential functions. But remember that a variable serves as the exponent instead of a constant as the basis of an exponential function.
A function is a power function rather than an exponential function if its base is a variable and its exponent is a constant.
If the graph of exponential function passes through the points (1960,19.005) and (2010,19.548), then the coordinates of these points satisfy the equation, y = [tex]ab^{x}[/tex]
Now, 19.005 = a × [tex]b^{1960}[/tex]
⇒ [tex]b^{1960}[/tex] = 19.005/a
Similarly, 19.548 = a × [tex]b^{2010}[/tex]
⇒ [tex]b^{2010}[/tex] = 19.548/a
⇒ [tex]b^{1960}[/tex] × [tex]b^{50}[/tex] = 19.548/a
⇒ [tex]b^{50}[/tex] = 19.548/a × a/19.005
= 1.028
Putting this value to find a,
we get a = 0.054
So, the equation of exponential function=
y = 0.054 × [tex]1.028^{x}[/tex]
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Let f(x)=x2+12x+32.
What are the zeros of the function?
Enter your answers in the boxes.
blank and blank
Step-by-step explanation:
To find the zeros of the function f(x), we need to solve the equation f(x) = 0.
f(x) = x^2 + 12x + 32
Setting f(x) equal to zero and factoring, we get:
0 = x^2 + 12x + 32
0 = (x + 4)(x + 8)
Using the zero product property, we set each factor equal to zero and solve for x:
x + 4 = 0 or x + 8 = 0
x = -4 or x = -8
Therefore, the zeros of the function f(x) are -4 and -8.
The length of a rectangular poster is 9 more inches than three times its width. The area of the poster is 30 square inches. Solve for the dimensions (length and width) of the poster.
The dimensions of the poster are 2 inches by 15 inches.
What is algebra?Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. It is used to solve problems and represent mathematical relationships and formulas. In algebra, letters and other symbols are used to represent numbers and quantities, allowing us to express mathematical relationships and patterns in a more general and abstract way. Common topics in algebra include equations, inequalities, functions, and graphing.
What are equations?An equation is a mathematical statement that shows that two expressions are equal. Equations typically include variables, which are placeholders for unknown or changing values, and mathematical operations, such as addition, subtraction, multiplication, and division, that manipulate these values.
In the given question,
Let's use algebra to solve for the dimensions of the poster.
Let w be the width of the poster in inches. Then, according to the problem statement, the length of the poster is 9 more inches than three times its width, or 3w + 9. The area of the poster is given as 30 square inches, so we can set up the equation:
A = lw = (3w + 9)w = 30
Expanding the right-hand side and simplifying, we get:
3w^2 + 9w - 30 = 0
Dividing both sides by 3, we obtain:
w^2 + 3w - 10 = 0
This is a quadratic equation that we can solve using factoring or the quadratic formula. Factoring, we can write:
(w + 5)(w - 2) = 0
This gives us two solutions: w = -5 and w = 2. Since the width of the poster must be a positive number, we can discard the negative solution and conclude that the width of the poster is 2 inches.
To find the length, we can substitute w = 2 into the expression we found earlier for the length:
l = 3w + 9 = 3(2) + 9 = 15
Therefore, the dimensions of the poster are 2 inches by 15 inches.
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