Answer:
When an exponent of the power is an even number and the base is a negative number, the value is always positive.
What is the meaning of "If Y = ran(f), then f is a function onto Y"?
The statement implies that the function f has a surjective property, ensuring full coverage of the target set Y.
The statement "If Y = ran(f), then f is a function onto Y" can be understood in the context of mathematical functions and their range.
In mathematics, a function is considered "onto" or "surjective" if every element in the target set (in this case, Y) has a pre-image in the domain set. In other words, for every element y in Y, there exists at least one element x in the domain set such that f(x) = y.
The given statement is saying that if Y is equal to the range of the function f, then f is a function that covers or maps onto every element in Y. In this case, the function f has a mapping for each element in the set Y, ensuring that no element in Y is left without a pre-image in the domain set.
Thus, the statement implies that the function f has a surjective property, ensuring full coverage of the target set Y.
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Multiply out
5x(3x-2)=
The solution is the multiplication is: 5x × (3x-2) = 15x² - 10x.
Here, we have,
given that,
the expression is:
5x(3x-2)
now, we have to Multiply out
so, we have,
5x × (3x-2)
= 5x×3x - 5x×2
=15x² - 10x
Hence, The solution is the multiplication is: 5x × (3x-2) = 15x² - 10x.
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Derrick Rolls a die many times and Records the number of times he rolls a three arrange the following situations in order from the situation that gets the largest difference between relative frequency and actual probability to the situation that gives the smallest difference
The order from the situation with the largest difference between relative frequency and actual probability to the situation with the smallest difference would be:
Situation 1: Derrick rolls the die 10 times.
Situation 2: Derrick rolls the die 100 times.
Situation 3: Derrick rolls the die 1,000 times.
Situation 4: Derrick rolls the die 10,000 times.
Situation 5: Derrick rolls the die 1,000,000 times.
To determine the order of situations from the largest difference between relative frequency and actual probability to the smallest difference, we need to consider the concept of relative frequency and actual probability.
Relative frequency refers to the observed proportion of an event occurring in an experiment or trial, while actual probability represents the theoretical or expected probability of that event occurring.
Situation 1: Derrick rolls the die 10 times.
In this situation, the relative frequency of rolling a three can vary, but with a limited number of trials, the relative frequency might not accurately reflect the actual probability. Therefore, the difference between relative frequency and actual probability is likely to be larger compared to situations with more trials.
Situation 2: Derrick rolls the die 100 times.
With a larger number of trials, the relative frequency is expected to converge towards the actual probability. The difference between relative frequency and actual probability would likely be smaller compared to the previous situation.
Situation 3: Derrick rolls the die 1,000 times.
Increasing the number of trials further enhances the convergence of relative frequency to the actual probability. The difference between relative frequency and actual probability would be smaller than in the previous two situations.
Situation 4: Derrick rolls the die 10,000 times.
With an even larger number of trials, the relative frequency becomes more reliable and closely approximates the actual probability. The difference between relative frequency and actual probability would be smaller compared to the previous situations.
Situation 5: Derrick rolls the die 1,000,000 times.
In this situation, the large number of trials greatly increases the reliability and accuracy of the relative frequency. The observed relative frequency is expected to be very close to the actual probability, resulting in the smallest difference between the two.
Therefore, the order from the situation with the largest difference between relative frequency and actual probability to the situation with the smallest difference would be:
Situation 1: Derrick rolls the die 10 times.
Situation 2: Derrick rolls the die 100 times.
Situation 3: Derrick rolls the die 1,000 times.
Situation 4: Derrick rolls the die 10,000 times.
Situation 5: Derrick rolls the die 1,000,000 times.
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write an explicit formula for an the nth term of the sequence 6, 12, 18
Answer:
[tex]a_{n}[/tex] = 6n
Step-by-step explanation:
there is a common difference between consecutive terms, that is
12 - 6 = 18 - 12 = 6
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + d(n - 1)
where a₁ is the first term and d the common difference
here a₁ = 6 and d = 6 , then
[tex]a_{n}[/tex] = 6 + 6(n - 1) = 6 + 6n - 6 = 6n
The Burj Khalifa, located in Dubai in the United Arab Emirates, is the tallest building in the world as of 2022. Andre visited Dubai over winter break. He stood 1000 meters away from the building, looked up at a 39.62 degree angle using a laser rangefinder and spotted the top of the building.
Andre
If every floor is 5.079 meters tall, how many floors are there in the Buri Khalifa?
The Burj Khalifa, located in Dubai in the United Arab Emirates, is the tallest building in the world as of 2022, there are approximately 148 floors in the Burj Khalifa.
We can make use of the data given to determine the Burj Khalifa's floor count.
Andre is known to have stood 1,000 metres away from the structure and turned his head to look up at a 39.62 degree angle.
Let's write "h" for the Burj Khalifa's height and "d" for Andre's distance from the building's base.
tan(39.62°) = h / d
h = d * tan(39.62°)
h = 1000 * tan(39.62°) ≈ 753.7 meters
So, as per this, Number of floors = h / floor height
Number of floors = 753.7 meters / 5.079 meters
Number of floors ≈ 148.4 floors or 148 floors.
Thus, 148 floors are there in Burj Khalifa.
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Match the trigonometric expressions to their solutions.
cos [140°- (50° +30°)]
√3
tan 240°
-√6-√2
cos 150°
1
Reset
Next
sin 255
Hi,
cos[140˚- ( 50˚ + 30˚)] = 1/2
tan 240˚ = √3
cos 150˚ = -√3/2
sin 255˚ = -√6 - √2/4
Those above should be the correct ones
XD
Molly used 192 beads to make a necklace AND a bracelet. It takes 5 times as many beads to make a necklace as it does a bracelet. How many beads are used to make the necklace?
Examining the word problem we can say that, Molly used 160 beads to make the necklace.
How to find the number of beadsLet's assume the number of beads used to make the bracelet is x.
We also know that Molly used a total of 192 beads for both the necklace and the bracelet. and It takes 5 times as many beads to make a necklace as it does a bracelet, So,
x + 5x = 192
6x = 192
solve for x
x = 192 / 6
x = 32
Molly used 32 beads to make the bracelet.
number of beads used to make the necklace
Number of beads used for the necklace = 5 * 32
Number of beads used for the necklace = 160
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b) 9 mm 6 mm 7 mm surface area for this question
The surface area of the rectangular prism is 318 square mm
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
9 mm by 6 mm by 7 mm
The surface area of the rectangular prism is calculated as
Surface area = 2 * (Length * Width + Length * Height + Width * Height)
Substitute the known values in the above equation, so, we have the following representation
Area = 2 * (9 * 6 + 9 * 7 + 6 *7)
Evaluate
Area = 318
Hence, the area is 318 square mm
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Question
The net of a rectangular prism and its dimensions are given as 9 mm 6 mm 7 mm. What is the total surface area of the rectangular prism in square inches?
Which of the following statements are true? Check all of the boxes that apply.
f(x) = 2√x has the same domain and range as f(x)=√x
f(x) = -2√x has the same domain and range as f(x)=√x
f(x) = -√x has the same domain as f (x)=√x, but a different range.
f(x)=√x has the same domain as f(x)=√x, but a different range
0 0 0 0
DONE ✔
Intro
15 of 19
The correct statements regarding the domain and the range of the functions are given as follows:
f(x) = 2√x has the same domain and range as f(x)=√xf(x) = -√x has the same domain as f (x)=√x, but a different range.How to obtain the domain and range of a function?The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.The range of a function is defined as the set containing all the values assumed by the dependent variable y of the function, which are also all the output values assumed by the function.For the square root function, we have that:
The domain is x >= 0.The range is y >= 0.Hence if we multiply the function by a negative number, the domain of the function remains constant, but the range is changed.
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pls answer this question, I don't understand it.
The two numbers could be 0.43× 10⁻⁵ and, 0.06× 10⁻³.
Here, we have,
given that,
the product of two number in scientific notation is: 0.0258 × 10⁻⁸
now, let the two numbers be:
0.43× 10⁻⁵ and, 0.06× 10⁻³
we get,
0.43× 10⁻⁵ × 0.06× 10⁻³
= 0.43 × 0.06× 10⁻⁵ × 10⁻³
= 0.43 × 0.06 × 10⁻⁵⁻³
=0.43 × 0.06× 10⁻⁸
=0.0258 × 10⁻⁸
Hence, The two numbers could be 0.43× 10⁻⁵ and, 0.06× 10⁻³.
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x^2-2y=5 and 4y+z=7 write z in terms of x
The equation is written as z = 7 + (20 -4x²/2)
How to make the subject
From the information given, we have that the equations as;
x²-2y=5 ( 1)
4y+z=7 (2)
From equation (1), make y the subject of formula, we have;
-2y= 5 - x²
Divide both sides by the coefficient of the variables, we have;
y = 5 - x²/-2
y = -5 + x²/2
Now, substitute the value of y in (2), we have;
4 (-5 + x²/2) + z = 7
expand the bracket
-20 + 4x²/2 + z = 7
collect the like terms, we have;
z = 7 + (20 -4x²/2)
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An investment banking house conducted a survey to determine how two of its proposed investment plans for three different age categories are used. This table shows the responses they received. Plan I Plan II Neither Ages 26–35 19 14 17 Ages 36–45 14 28 8 Ages 46–55 27 21 2 What percentage of people preferring plan I are from the 36–45 age group, and what percentage of people from the 46–55 age group prefer plan II? Round your answers to the nearest whole number. A. 23% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II. B. 28% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II. C. 23% of people who prefer plan I are from the 36–45 age group, and 33% of people from the 46–55 age group prefer plan II. D. 28% of people who prefer plan I are from the 36–45 age group, and 33% of people from the 46–55 age group prefer plan II. E. 32% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II.
The Percentage of people from the 46-55 age group preferring Plan II is 42%.
The percentages, we need to calculate the ratio of people preferring Plan I in the 36-45 age group and the ratio of people preferring Plan II in the 46-55 age group.
Let's start with the first part of the question:
Percentage of people preferring Plan I from the 36-45 age group:
To calculate this percentage, we need to divide the number of people preferring Plan I in the 36-45 age group by the total number of people preferring Plan I, and then multiply by 100 to express it as a percentage.
Number of people preferring Plan I in the 36-45 age group = 14
Total number of people preferring Plan I = 14 + 28 + 21 = 63
Percentage = (14 / 63) * 100 ≈ 22.22 ≈ 22% (rounded to the nearest whole number)
So, the percentage of people preferring Plan I from the 36-45 age group is approximately 22%.
Now, let's move on to the second part of the question:
Percentage of people from the 46-55 age group preferring Plan II:
To calculate this percentage, we need to divide the number of people preferring Plan II in the 46-55 age group by the total number of people from the 46-55 age group, and then multiply by 100 to express it as a percentage.
Number of people preferring Plan II in the 46-55 age group = 21
Total number of people in the 46-55 age group = 27 + 21 + 2 = 50
Percentage = (21 / 50) * 100 = 42%
So, the percentage of people from the 46-55 age group preferring Plan II is 42%.
Based on the calculations, the correct answer is:
A. 23% of people who prefer Plan I are from the 36-45 age group, and 42% of people from the 46-55 age group prefer Plan II.
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I have 12 teams that will play each other once, but have activities that each team will only play once. How many weeks and activities do I need.
==============================================
Explanation:
The formula to use is n*(n-1)/2
Plug in n = 12 to get 12*(12-1)/2 = 12*11/2 = 132/2 = 66
That formula is from the nCr combination formula when r = 2.
---------------------
Here's a visual way to see why that rule works.
Imagine there are only 4 teams. We'll make a table that has 4 rows and 4 columns. The team names are A,B,C,D.
[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & & & & \\\cline{1-5}B & & & & \\\cline{1-5}C & & & & \\\cline{1-5}D & & & & \\\cline{1-5}\end{array}[/tex]
In the table, cross out the cells where one team pairs up with itself. That's along the main diagonal pointing to the northwest (or southeast).
[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & & X & & \\\cline{1-5}C & & & X & \\\cline{1-5}D & & & & X\\\cline{1-5}\end{array}[/tex]
Let's also cross out any cell below the main diagonal.
[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & X & X & & \\\cline{1-5}C & X & X & X & \\\cline{1-5}D & X & X & X & X\\\cline{1-5}\end{array}[/tex]
We do this because a mirrored copy is found above the diagonal.
We started with 4*4 = 16 cells. Then subtracted off the diagonal to get 16-4 = 12 cells left over. Then divide in half because we crossed off the lower half to get 12/2 = 6 different matchups among the 4 teams.
Those 6 matchups are:
A vs BA vs CA vs DB vs CB vs DC vs DThe order doesn't matter. A matchup like "A vs B" is the same as "B vs A".
We'll take this concept to extend it to n teams. We have n*n = n^2 cells to start with. Subtract off the n cells along the diagonal to get n^2-n = n(n-1) cells remaining.
Then we split that in half to get the formula n(n-1)/2.
Calculate the area of the composite figure
1. The area of composed figure is 52.26 cm².
2. The area of composed figure is 74 ft².
1. Area if Triangle
= 1/2 x b x h
= 1/2 x 6 x 8
= 24 cm²
Area of semicircle
= πr²/2
= 3.14 x 3 x 3
= 28.26 cm²
So, area of composed figure
= 28.26 + 24
= 52.26 cm²
2. Area of Trapezium
= 1/2 (7 + 13) x 5
= 1/2 x 20 x 5
= 50 ft²
Area of Triangle
= 1/2 x b x h
= 1/2 x 8 x 6
= 24 ft²
So, area of composed figure
= 24 + 50
= 74 ft²
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Given below are lease terms at the local dealership. What is the total cash due at signing?
Terms:
Length of lease: 30 months
MSRP of the car $15,500
• Purchase value of the car after lease: $9900
Down payment $2500
Monthly payment $425
-Security deposit $375
Acustion fee $500
A. 375
B. 3375
C. 3800 (✅️)
D. 3400
Given the diagram below, determine the measure of angles A, B, and C.
Hello!
A = 115° => opposite
B = 115° => corresponding angles
C = 65° => 180° - 115°
Answer:
A = 115 degrees
B = 115 degrees
C = 65 degrees
Step-by-step explanation:
A is opposite of 115 so it is 115 degrees.
B is 115 because it is on a parellel line to the one of 115
C is 180 minus B, which is 180 - 115 = 65
What is the solution to the proportion 2/3 m/9
What is the meaning of "The field of a relation R"?
The meaning of "The field of a relation R" is a constraint on the values that can be stored in that attribute.
We are given that;
The statement The field of a relation R
Now,
According to the web results, the field of a relation R is the set of all values that appear in the relation R. In other words, it is the union of all the attributes (columns) of R. For example, if R is a relation with attributes A, B, and C, then the field of R is the set of all values that appear in A, B, or C. The field of R can also be denoted by F.
The field of a relation is different from the domain of an attribute, which is the set of all possible values that an attribute can take. For example, if A is an attribute that can only take integer values, then the domain of A is the set of all integers. The domain of A may be larger than the field of A, which is the set of all values that actually appear in A. The domain of an attribute defines a constraint on the values that can be stored in that attribute.
Therefore, by the domain the answer will be a constraint on the values that can be stored in that attribute.
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find the surface area
The surface area of the triangular prism is 193.05 cm².
We have,
The figure is a triangular prism.
Now,
There are 4 triangular surfaces.
Each surface area is the same except the base surface.
So,
3 surface area.
= 3 x (1/2 x 9 x 11.3)
= 3 x 50.85
= 152.55 cm²
And,
Base surface area.
= 1/2 x 9 x 9
= 40.5 cm²
Now,
The surface area of the triangular prism.
= 152.55 + 40.5
= 193.05 cm²
Thus,
The surface area of the triangular prism is 193.05 cm².
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Simplify. Write your answers without exponents. 4^ -5/2= (1/16)^-3/2=
Please look at photo for accuracy
The value of the given expression is,
[tex]4^{- 5/2[/tex] = 1/32
[tex](1/16) ^ {- 3/2[/tex] = 64
We have to given that,
Expressions to solve are,
⇒ [tex]4^{- 5/2[/tex]
And, [tex](1/16) ^ {- 3/2[/tex]
We know that,
Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself
Now, We can simplify the given expression,
By using law of exponents
We get,
⇒ [tex]4^{- 5/2}[/tex]
⇒ [tex]2^{2(- 5/2)}[/tex]
⇒ 2⁻⁵
⇒ 1/2⁵
⇒ 1/32
Thus,
The value of [tex]4^{- 5/2[/tex] = 1/32
The given expression is,
⇒[tex](1/16) ^ {- 3/2[/tex]
By using law of exponents
We get,
⇒ [tex]16 ^{3/2}[/tex]
⇒ [tex](4^2)^{3/2}[/tex]
⇒ 4³
⇒ 64
The value of [tex](1/16) ^ {- 3/2[/tex] = 64
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6.56*10^-7 by 4.86*10^-7
6.56 × [tex]10^{-7}[/tex] by 4.86×[tex]10^{-7}[/tex] is 3.18816 × [tex]10^{-13}[/tex] is factorize.
To find the product of 6.56 × [tex]10^{-7}[/tex] by 4.86×[tex]10^{-7}[/tex]. The conventions of scientific notation can be applied. To get 31.8816, we must first multiply the coefficients, which are 6.56 and 4.86. The exponents, which are -7 and -7, are then added to provide -14.
The product of 6.56 × [tex]10^{-7}[/tex] by 4.86 × [tex]10^{-7}[/tex] is 3.18816 × [tex]10^{-13}[/tex] This, according to the conventions of scientific notation, can be calculated by multiplying the coefficients and adding the exponents.
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77th term of the sequence 16,19,22,25
The 77th term of the given Sequence is 244.
The given sequence is an arithmetic progression with a common difference of 3. To find the 77th term of the sequence, we can use the formula for the nth term of an arithmetic progression.
The formula for the nth term of an arithmetic progression is:
_ = _1 + ( − 1),
where _ is the nth term, _1 is the first term, is the position of the term in the sequence, and is the common difference.
In this case, _1 = 16 and = 3. Plugging in these values into the formula, we get:
_77 = 16 + (77 − 1) × 3.
_77 = 16 + 76 × 3.
_77 = 16 + 228.
_77 = 244.
Therefore, the 77th term of the given sequence is 244.
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(a) Dewi has £460 to buy Chinese yuan.
Calculate
.
the maximum number of CYN Dewi can buy, and
how much, to the nearest penny, this will cost him.
The maximum number of CYN Dewi can buy is 4268.8 CYN and cost in pounds is £453.20.
Maximum number of CYN Dewi can buy:
Since £1 buys 9.28 CYN, Dewi's £460 can be converted to Chinese yuan by multiplying it by the exchange rate:
Maximum CYN = £460 × 9.28 CYN/£1
To calculate this, we multiply the pound amount by the exchange rate:
Maximum CYN = £460 × 9.28 CYN/£1 ≈ 4268.8 CYN
Cost in pounds to the nearest penny:
To calculate the cost in pounds, we divide the desired amount of Chinese yuan by the exchange rate:
Cost in pounds = 4268.8 CYN ÷ 9.42 CYN/£1
To calculate this, we divide the Chinese yuan amount by the exchange rate:
Cost in pounds = 4268.8 CYN ÷ 9.42 CYN/£1
= £453.20
Therefore, the cost in pounds, to the nearest penny, will be £453.20.
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Complete question
Buying chinese yuan (CYN) £1 buys 9.28 CYN
Selling chinese yuan (CYN) 9.42 CYN buys £1
(a) Dewi has £460 to buy Chinese yuan.
Calculate the maximum number of CYN Dewi can buy, and
how much, to the nearest penny, this will cost him.
A conveyor belt carries supplies from the first floor to the second floor which is 23 feet higher. The belt makes a 60-degree angle with the ground.
How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the nearest foot.
PLEASE no spam!!
Answer:
caculations below
Step-by-step explanation:
A conveyor belt carries supplies from the first floor to the second floor which is 23 feet higher. The belt makes a 60-degree angle with the ground.
To calculate the distance traveled by the supplies from one end of the conveyor belt to the other, we can use the trigonometric function of sine.
sin(60) = opposite / hypotenuse
Here, the opposite side is the height difference between the two floors, which is 23 feet.
sin(60) = 23 / hypotenuse
To find the hypotenuse, we can rearrange the above equation:
hypotenuse = 23 / sin(60)
Using a calculator, we get:
hypotenuse = 26.5 feet
Therefore, the supplies travel approximately 26.5 feet from one end of the conveyor belt to the other.
Rounding the answer to the nearest foot, we get:
The supplies travel approximately 27 feet from one end of the conveyor belt to the other.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer: B
Step-by-step explanation: 63.3 in^2
give the rule in words of this pattern 10,13,17,238
Answer:
a set of numbers in order of least to greatest
Assume 0 is an acute angle.
cot 0 =
4
3
The value of the angle csc θ of the given problem is: 5/4
How to solve the trigonometric ratios?There are different trigonometric ratios such as:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Now, we are given that:
cot θ = 4/3
We know that cot θ = 1/tan θ
Thus:
tan θ = 3/4
Since θ is an acute angle, it means it is less than 90 degrees. Thus, using Pythagoras theorem, we can find the third side which is the hypotenuse to be 5
Now, csc θ = 1/sin θ
Thus: sin θ = 4/5
csc θ = 5/4
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40 points. I need help with this, so I can explain it to my son. Thank you in advance
The functions of the coefficients of the quadratic equation indicates that the correct statements are;
a. The y-intercept of the function is (0, c)
c. The coefficient b determines the horizontal shift of the parabola compared to the parent function
d. If a is negative, the parabola opens upwards
What are the functions of the quadratic equation?The quadratic equation is; y = a·x² + b·x + c
The functions of the coefficients of the above quadratic function are;
a = The scale factor, and the coefficient that determines the direction the projectile faces.
a < 1; Indicates that the graph is wider than the parent function
a > 1; Indicates that the graph is narrower than the parent function
a < 0; Indicates that the parabola opens downward
a > 0; Indicates that the parabola opens upwards
b = The coefficient b together with coefficients a and c determines the coordinate of the vertex of the graph of the quadratic function, which is; (-b/(2·a), -D/(4·a))
Where;
D = The discriminant
Therefore, b determines the x-value, and therefore, the horizontal shift of the parabola compared to the parent function
c = The y-coordinate of the y-intercept of the quadratic function, which is (0, c)
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NEED HELP ASAP WILL GIVE BRAINLIEST HELP!
Answer:
∠ 1 and ∠ 3 = 180°
Step-by-step explanation:
∠ 1 and ∠ 3 are same- side interior angles and sum to 180° , that is
∠ 1 + ∠ 3 = 180
These shapes are similar.
Find X.
X
5
9
27
15
21
The value of X is 7.
Given that the set of number are in pattern,
X, 5, 9, 27, 15, 21.
To find the value of X such that given numbers are in pattern.
The next three number are three times of first three numbers respectively.
Let a, b, c is the first three numbers then 3a, 3b, 3c are next three numbers.
Consider the given set of numbers, X, 5, 9, 9 × 3, 5 × 3, 21.
By using the data and the pattern set gives,
3X = 21.
Divide by 7 on both sides,
X = 7.
Hence, the value of X is 3
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