Help me sort these cards in the right column. Whether it falls in y-intercept, zeroes, axis symmetry, and max/min value. need help solving each card.
Answers
The cards can be sorted based on the function -16x³ + 80x as -
y-intercept - Card 4
Zeros - Card 1
Axis of symmetry - Card 2
Min/Max value - Card 3
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
To find the zeroes of the function, we set f(x) = 0 and solve for x -
-16x³ + 80x = 0
-16x(x² - 5) = 0
x = 0 or x = √5 or x = -√5
So the zeroes of the function are 0, √5, and -√5.
Therefore, this represents the time at which the football reaches the maximum height.
The axis of symmetry for the function is the vertical line that passes through the vertex of the parabola.
The formula for the axis of symmetry of a parabola in standard form is x = -b/2a, so for this function -
x = -80/(2 × (-16)) = 2.5
The axis of symmetry is x = 2.5.
Therefore, this represents for how long the football was in the air.
To find the y-intercept of the function, we set x = 0 -
f(0) = -16(0)³ + 80(0) = 0
So the y-intercept is 0.
Therefore, this represents the height of the football when it is kicked.
To find the maximum or minimum value of the function, complete the square to rewrite the function in vertex form.
Using the latter method, we have -
f(x) = -16x³ + 80x
f(x) = -16(x³ - 5x)
f(x) = -16(x³ - 5x + 25/4) + 16(25/4)
f(x) = -16(x - 5/2)² + 100
So the vertex of the parabola is (2.5, 100), and the maximum value of the function is 100.
Therefore, this represents the maximum height of the football.
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Related Questions
I will mark you brainiest if you can answer this
Answers
2. H (-9,-5)
3. B (-2,6)
4. E (8,-4)
5. G (-4,-2)
6. ( 6,8)
7. A (-8,4)
8. F (4,-9)
is this triangle a SSS, SAS, ASA, AAS, or HL?
Answers
Answer:
sss
Step-by-step explanation:
Answer: its a SAS triangle
Step-by-step explanation:
Unit 2: Logic & Proof
Homework 2: Compound Statements
Answers
on using disjunctive syllogism to derive Q from the second premise and the derived value of A. if P is true, then Q must also be true..
In logic, a compound statement is made up of two or more simple statements, known as premises or assumptions, that are combined using logical operators such as "and," "or," and "not." To prove a compound statement, we use rules of inference to derive a conclusion based on the given premises.
In the first proof question, we are given three premises: P, P or R, and not S or A. We need to prove the statement Q using these premises. To do so, we use the disjunctive syllogism rule, which states that if one of two disjunctive statements is false, then the other must be true. By assuming ~P, we derive ~S from the third premise using the rule of disjunction. Then, using modus ponens, we derive A from the assumption of ~P and the third premise. Finally, we use disjunctive syllogism to derive Q from the second premise and the derived value of A.
In the second proof question, we are given three premises: not P or S, not S, and R or Q. We need to prove the statement P implies Q using a conditional world proof. We assume P is true and derive S using the first premise. Using the second premise and modus tollens, we derive not R. Finally, using disjunctive syllogism, we derive Q from the third premise and the derived value of not R. Therefore, we show that if P is true, then Q must also be true..
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Help please i dint get it pls answer
Answers
Answer: 7%
(Hope this is right.)
Step-by-step explanation:
Let's solve this using the information we have and an equation.
Shane: $32,000 - (Given)
Theresa: 18,000+14x, if x=1,160 - (Given)
---------------------------------------------------------------
Step two: (Theresa) 14(1,160) =16,240 (Algebra)
Step three: (Theresa) 18,000+16,240=34,240 (Algebra, given.) - cost of Theresa's car.
---------------------------------------------------------------
Finally,
They're asking for how much more she paid for her car as a percentage of what Shane paid.
34,240-32,000=2,240 and
2,240/32,000=0.07
0.07x100=7
Answer 7% more than what Shane paid.
The mean value of 500 homes in a county is $225,000 and the standard deviation is $25,000. approximately how many of the homes in the county are between $175,000 and $225,000?
Answers
240 homes in the county are between $175,000 and $225,000.
The image attached is associated with this question and m in it refers to the mean value which is $225000 here and d refers to the standard deviation which is $25000 here.
Now since m= $225000
and $175000= $225000-$50000= $225000-(2* $25000)= m-2d
Thus, as per the image area covered between m and m-2d= $225000
and $175000 is (34%+14%)of 500 homes= 68% of 500= 240 homes, is the answer.
A random variable X is said to follow a normal distribution if its parameters are mean and standard deviation. Every other distribution can be reduced to a normal distribution.
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For a system of vectors u = {(1,2,6 ); (0,-1,-5); (2,3,7); (1,0,-4) } . a. find the number of dimensions and a basis w of the subspace generated by the vector system u . b. find the parameter k to u = (2, 3, k^2+1) is a linear combination of w , and deduce [u ]w
Answers
a. The subspace generated by the vector system u has 2 dimensions. A basis for this subspace is {(1, 2, 6), (0, -1, -5)}. b. The parameter k that makes u = (2, 3, \(k^2 + 1\)) a linear combination of the basis w is k = ±√6. The coordinate vector [u]w with respect to the basis w is [u]w = (2, 1).
a. To find the number of dimensions and a basis for the subspace generated by the vector system u, we need to determine the linearly independent vectors among the given vectors. Let's perform Gaussian elimination to determine the linearly independent vectors:
Row 2 = Row 2 - 0 * Row 1
= (0, -1, -5)
Row 3 = Row 3 - 2 * Row 1
= (2, 3, 7)
Row 4 = Row 4 - Row 1
= (1, 0, -4)
Row 3 = Row 3 - 2 * Row 2
= (2, 3, 7) - 2 * (0, -1, -5)
= (2, 3, 7) - (0, -2, -10)
= (2, 5, 17)
Now, we have the following row-echelon form:
(1, 2, 6)
(0, -1, -5)
(0, 0, 0)
(0, 0, -10)
We can see that there are 2 pivot columns in this row-echelon form, which indicates that the subspace generated by the vector system u has 2 dimensions.
b. To find the parameter k such that u = (2, 3, k² + 1) is a linear combination of the basis w, we can set up the following equation:
(2, 3, k² + 1) = a(1, 2, 6) + b(0, -1, -5)
This equation gives us the following system of equations:
2 = a
3 = 2a - b
\(k^2 + 1 = 6a - 5b\)
From the first equation, we can deduce that a = 2. Substituting this value into the second equation, we get:
3 = 2(2) - b
3 = 4 - b
b = 4 - 3
b = 1
Now, we can substitute the values of a and b into the third equation:
\(k^2 + 1 = 6(2) - 5(1)\\k^2 + 1 = 12 - 5\\k^2 + 1 = 7\\k^2 = 7 - 1\\k^2 = 6\)
k = ±√6
Therefore, the parameter k that satisfies u = (2, 3, \(k^2 + 1\)) as a linear combination of the basis w is k = ±√6. The coordinate vector [u]w represents the coefficients of the linear combination of the basis vectors w that yield the vector u. Using the basis w = {(1, 2, 6), (0, -1, -5)}, we can express u as:
u = a(1, 2, 6) + b(0, -1, -5)
Substituting the values of a = 2 and b = 1, we get:
u = 2(1, 2, 6) + 1(0, -1, -5)
u = (2, 4, 12) + (0, -1, -5)
u = (2, 4, 12) + (0, -1, -5)
u = (2, 3, 7)
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Can someone verify if this is correct
Answers
Step-by-step explanation:
f(g(x))
means we have to calculate g(x) first, and then we use that result as input value for f and calculate that as the final result.
in general, the expression for that combined function is created by putting the expression of g(x) into every place of x in f(x) :
(f○g)(x) = f(g(x)) = 2(3x + 4) + 1 = 6x + 8 + 1 = 6x + 9
therefore,
f(g(8)) = 6×8 + 9 = 48 + 9 = 57
let's try it with basic steps :
g(8) = 3×8 + 4 = 24 + 4 = 28
and then
f(28) = 2×28 + 1 = 56 + 1 = 57
so, no, the showing number "21" is not correct.
I cannot see what you did to get 21.
the only way seems to be that you calculated f(8) = 17. and then you used this 17 to replace the whole 3x and not just x and got 17 + 4 = 21.
if that is what you did, you made 2 mistakes at once.
first you used 8 as input value for f(x) and not for g(x).
so, you tried to calculate g(f(8)).
and then, as mentioned, you replaced 3x (why ? what made you think that that's a valid thing) in g(x) by that result, instead of x.
select the correct answer. a building has a triangular rooftop terrace which is modeled by triangle . in triangle , the measure of is , the measure of is , and the measure of is . which side of the terrace has the greatest length? a. cannot be determined b. c. d.
Answers
However, without specific measurements for the angles or sides of the triangle, we cannot determine the lengths of the sides or identify which side is the longest. Therefore, the answer is (a) "cannot be determined."
To determine which side of the triangular rooftop terrace has the greatest length, we need to examine the given information. The lengths of the sides of a triangle are dependent on the measures of the angles and the relative proportions between the sides.
Without knowing any specific values for the angles or sides, we cannot compare or determine the lengths of the sides accurately. Additional information is needed to identify which side has the greatest length.
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Answer:
cannot be determined
Step-by-step explanation:
Construct the confidence interval for the population mean μ c-0.95, x-4.8, σ-0.6, and n-55 A 95% confidence interval for μ is (LIL) . (Round to two decimal places as needed.)
Answers
Answer:
A 95% confidence interval for μ is (LIL) 4.61.
The confidence interval for the population mean μ is constructed as follows:
Here, x is the sample mean, σ is the population standard deviation,
n is the sample size, and
zα/2 is the z-value
that corresponds to a level of confidence of (1-α)100%.
Given that c = 0.95, x = 4.8, σ = 0.6, and n = 55.
Confidence interval is given by;
(LIL), (UIL) = (x - zα/2*σ/√n), (x + zα/2*σ/√n)
where LIL is the lower limit of the interval and UIL is the upper limit of the interval.
Now, we need to determine the value of zα/2 such that the level of confidence is 0.95.
In the standard normal distribution, the area to the left of
zα/2 is (1-α)/2 or
(1-0.95)/2 = 0.025.
Using the z-table, we can find that the z-value that corresponds to this area is 1.96.
Therefore, the 95% confidence interval for μ is given by;
(LIL), (UIL) = (4.8 - 1.96*0.6/√55), (4.8 + 1.96*0.6/√55)= (4.61, 4.99)
Therefore, a 95% confidence interval for μ is (LIL) 4.61. (Round to two decimal places as needed.)
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Yiron buys a new dress for $40. How much does she pay if there is a 7% tax?
Answers
40 divided by 7%.
The Physician prescribed Medication G 0.6 g, orally, every 12 hours. The medication label reads Medication G 100 mg per 5 mL. The nurse should prepare how many mL to administer the dose? Convert the answer to fluid ounces. __________ fl oz
Answers
The nurse is responsible for giving Medication G in a quantity of 30 mL, which is approximately equivalent to 1.014 fluid ounces.
First, we need to convert 0.6 g to mg:
0.6 g = 600 mg
Next, we need to calculate how many mL are needed to deliver 600 mg of Medication G. From the label, we know that there are 100 mg of Medication G in 5 mL, so we can set up a proportion:
100 mg / 5 mL = 600 mg / x mL
Cross-multiplying, we get:
100x = 5 * 600
Simplifying, we get:
x = 30 mL
Finally, we can convert 30 mL to fluid ounces. There are 29.5735 mL in one fluid ounce, so:
30 mL / 29.5735 mL/oz ≈ 1.014 fl oz
Therefore, the nurse should administer 30 mL (or approximately 1.014 fluid ounces) of Medication G.
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X
TY
12
1.5
18
2.25
22
2.75
26
3.25
Select all true statements about the table above.
Answers
Answer:
A
Step-by-step explanation:
Rachel enjoys exercising outdoors. Today she walked miles in hours. What is Rachel’s unit walking rate in miles per hour and in hours per mile?
Answers
Unit walking rate in miles per hour = 5 2/3 / 2 2/3 = 17/3 / 8/3 = 17/3 x 3/8 = 17/8 = 2 1/8 miles per hour.
Unit walking rate in hours per mile = 1/ 17/8 = 8/17 hours per mile.
~you did not write the question properly but i guess this your needed answer
AC is a diameter of OE, the area of
the
circle is 2897 units², and AB = 16 units.
Find BC and mBC.
B
A
C
E
Answers
Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.
Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):
AC² = AB² + BC²
Substituting the given values, we have:
(AC)² = (AB)² + (BC)²
(AC)² = 16² + (BC)²
(AC)² = 256 + (BC)²
Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.
AC = 2 * radius
To find the radius, we can use the formula for the area of a circle:
Area = π * radius²
Given that the area of the circle is 2897 units², we can solve for the radius:
2897 = π * radius²
radius² = 2897 / π
radius = √(2897 / π)
Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:
(2 * radius)² = 256 + (BC)²
4 * radius² = 256 + (BC)²
Substituting the value of radius, we have:
4 * (√(2897 / π))² = 256 + (BC)²
4 * (2897 / π) = 256 + (BC)²
Simplifying the equation gives:
(4 * 2897) / π = 256 + (BC)²
BC² = (4 * 2897) / π - 256
Now we can solve for BC by taking the square root of both sides:
BC = √((4 * 2897) / π - 256)
To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.
In summary:
BC = √((4 * 2897) / π - 256)
mBC = 90 degrees
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The pressure of a fixed volume of a certain gas is related to its temperature as shown in the table below.
Temperature of Gas vs. Pressure
Temperature (in degrees Celsius)
Pressure (in pascals)
44
91
52
93
60
95
68
97
76
99
Which type of function best models the data in the table?
exponential
logarithmic
linear
quadratic
Answers
Answer:
C: linear.
Step-by-step explanation:
The function represented in the table is a linear function given by,
⇒ y = (1/4)x + 80
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
Now, Let y represent the pressure of the gas at x temperature.
Using the point (44, 91) and (52, 93), hence:
y - 91 = (93 - 91) / (52 - 44) (x - 44)
y - 91 = 1/4 (x - 44)
y = 1/4x + 80
Thus, The function represented in the table is a linear function given by,
y = (1/4)x + 80
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Cane someone help me with this
I will mark the person brainliest who answers with an actual correct answer
Due soon!!!
Answers
Answer:
10 units
Step-by-step explanation:
Translation does not change the length of a line segment, think of it as moving the figure about the x and y axis.
FG=LM=10 units
a researcher is investigating the relationship between the restrictiveness of gun laws and gun-crime rates. she gathers a sample of states and divides them into two groups: strict gun laws or lax gun laws. she then calculates the gun crime rate in each state. which type of t-test would be appropriate for analyzing the data?
Answers
The appropriate type of t-test for analyzing the relationship between the restrictiveness of gun laws and gun-crime rates in the researcher's study would be an independent samples t-test.
In this scenario, the researcher has divided the states into two groups based on the restrictiveness of gun laws: strict gun laws and lax gun laws. The goal is to compare the mean gun crime rates between these two groups. An independent samples t-test is used when comparing the means of two independent groups. In this case, the groups (states with strict gun laws and states with lax gun laws) are independent because each state falls into only one group based on its gun laws.
The independent samples t-test allows the researcher to determine whether there is a statistically significant difference in the means of the gun crime rates between the two groups. This test takes into account the sample means, sample sizes, and sample variances to calculate a t-value, which can then be compared to the critical t-value to determine statistical significance. By using this test, the researcher can assess whether the restrictiveness of gun laws is associated with differences in gun-crime rates.
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4 Assignment
K
Question 4, 2.4.20
Part 3 of 8
Fill in the Venn diagram with the appropriate numbers based on the following information.
n(A)=33
n(B)=36
n(B n C) = 14
n(An C) = 9
n(AnBn C) = 5
n(U)= 70
n(C) = 24
n(An B) = 17
A Venn diagram is a graphical representation of sets. Remember that n(A) is the number of
elements in set A.
Region I contains 12 elements.
Region Il contains 12 elements.
Region III contains elements.
I
=
II
HW Score: 73.15%, 6.58 of S
Points: 0 of 1
VII
VI
V
с
VIII
III
IV
B
U
Answers
We can fill in the Venn diagram since the number of elements in Region VIII is negative, it means there is an error in the given information or in the calculations.
How to fill in the Venn diagram?Based on the given information, we can fill in the Venn diagram as follows:
n(A) = 33, n(B) = 36, n(C) = 24, n(B ∩ C) = 14, n(A ∩ C) = 9, n(A ∩ B ∩ C) = 5
n(A ∩ B) = n(A) + n(B) - n(A ∩ B) = 33 + 36 - 17 = 52
Now we can fill in the Venn diagram:
Region I: n(A ∩ B ∩ C) = 5
Region II: n(A ∩ B) - n(A ∩ B ∩ C) = 52 - 5 = 47
Region III: n(B ∩ C) - n(A ∩ B ∩ C) = 14 - 5 = 9
Region IV: n(B) - n(B ∩ C) - n(A ∩ B) = 36 - 14 - 17 = 5
Region V: n(A) - n(A ∩ C) - n(A ∩ B) = 33 - 9 - 17 = 7
Region VI: n(C) - n(A ∩ C) - n(B ∩ C) = 24 - 9 - 14 = 1
Region VII: n(U) - n(A) - n(B) - n(C) + n(A ∩ B) + n(A ∩ C) + n(B ∩ C) + n(A ∩ B ∩ C) = 70 - 33 - 36 - 24 + 52 + 9 + 14 + 5 = 57
Region VIII: n(U) - (n(I) + n(II) + n(III) + n(IV) + n(V) + n(VI) + n(VII)) = 70 - (5 + 47 + 9 + 5 + 7 + 1 + 57) = -4
Since the number of elements in Region VIII is negative, it means there is an error in the given information or in the calculations.
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The area of a circle is 121 pi squared meters find the area of the sector whose central angle is 28°
Answers
The circle's circumference is equal to 4 * 11 or 44 cm for a square.
What is perimeter ?It is the length of any two-dimensional geometric shape's boundary or outline.
Depending on the size, the perimeter of several figures can be the same. Consider a triangle built of an L-length wire, for instance.
If all the sides are the same length, the same wire can be used to create a square.
The length that the shape's perimeter covers is known as the perimeter.
Hence, the perimeter's units will be the same as its length units.
Perimeter is one-dimensional, as we can say. As a result, it can be measured in metres, kilometres, millimetres, etc.
Inches, feet, yards, and miles are some more perimeter measurement units that are recognised on a global scale.
The perimeter of the square = 4*11 = 44 cm
The radius of the circle = 44*7/44 = 7 cm.
Area of the circle = (22/7)*7*7 = 154 cm^2
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If Rs 42,000 is left after paying an income tax at the rate of 30%.Find the income
Answers
Answer:
Total income is 60,000
Step-by-step explanation:
I. if paid rate is 30%, that's mean 42,000 is 70%
II. Perform ratio 70/100 = 42,000/x
70*x = 100 * 42,000
70x = 4,200,000
x = 60,000
III. If you perform 30/100 = x/60,000 will be 42,000
Sorry for late.
What is the place value of the 2 in 150.1235?
Hundredths
Tenths
Tens
Thousandths
Answers
Answer:
The 2 is placed in the Hundredths place
Step-by-step explanation:
Hope it helps! =D
I'm been doing this question about an hour still can't solve so I really need your help! Really appreciate if u do :D
Answers
Explanation:
1 hat = 45 dollars
6 hats = 6*45 = 270 dollars
1 phone = 40 dollars
4 phones = 4*40 = 160 dollars
total = $270 + $160 = $430
Felicia spent a total of $430. Since this amount of money leaves her account, this means we write a negative sign out front to end up with the final answer of -430
In other words, her account balance went down by $430 which is why we use a negative. If someone gave her $430, then the answer would be positive.
Let R be a relation on a set A and suppose R is symmetric
and transitive. Prove the following: If for every x in A
there is a y in A such that x R y, then R is an equivalence
relation.
please state proof technique and explain
Answers
R is transitive. it is an equivalence relation. We used direct proof technique to prove this.
To prove that R is an equivalence relation, we need to show that it is reflexive, symmetric, and transitive.
Since for every x in A there is a y in A such that x R y, we know that R is reflexive. This is because every element in A is related to itself by R, as given by the premise of the problem.
To show that R is symmetric, let x and y be arbitrary elements in A such that x R y. Since R is symmetric, we know that y R x. But since x R y, and R is transitive, it follows that x R x. Therefore, R is symmetric.
Finally, to show that R is transitive, let x, y, and z be arbitrary elements in A such that x R y and y R z. Since R is transitive, it follows that x R z. Therefore, R is transitive.
Since R is reflexive, symmetric, and transitive, it is an equivalence relation. We used direct proof technique to prove this.
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Yesterday Jack drove 39 1/2 miles. He used 1 1/4 gallons of gasoline. What is the unit rate for miles per gallon?
Answers
Answer:
31.6 or 31 6/10 or 31 3/5
39.5/1.25 = 31.6
Jack gets 31.6 miles per gallon.
.25 = 1/4
.5 = 1/2
52 plus what equals 208
Answers
Answer:
The answer is 156 Hope it helps!
Step-by-step explanation:
Match the algebraic expressions and the algebraic equations
Answers
Answer:
The answer is as follows:
1. Algebraic Expression
2. Algebraic Expression
3. Algebraic Equations
4. Algebraic Equations
5. Algebraic Expression
6. Algebraic Equations
Step-by-step explanation:
To solve this, you need to know that expressions DO NOT have an equal sign. However, equations DO.
Here's an example of an equation:
4 + 5 = 9
Here's an example of an expression:
8x - 1 + 2x
Notice that equations have an equal sign "=" but expressions don't...that is the key difference between the two!
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
The algebraic equations are :
\(y = - 2 {x}^{} + 3\)\( {x}^{3} - 2 {x}^{2} = x\)\( {x}^{2} - 5x + 6 = 0\)The algebraic expressions are :
\(2 {x}^{2} - 3x + 1\)\(5x + 20\)\( - x - 5\)Who likes wings of fire if you do pls e-mail me E-mail in comments
Answers
Answer:
like the book series? if so yes its great
Step-by-step explanation:
Help me plzzzzzzzzzzzzz brooo!!
Answers
Answer:
x = -2
Step-by-step explanation:
Um empresário possui um espaço retangular de 100 m por 750 m para corrida. Determine quantos metros percorreu um atleta que deu apenas 6 voltas pelas extremidades do espaço: * (A) 300 (B) 1700 (C) 10200 (D) 75000 (E) 7500
Answers
Answer:
(C) 10200m
Step-by-step explanation:
Dizem-nos na pergunta que um homem de negócios tem um espaço retangular de 100 m por 750 m para correr.
O primeiro passo é calcular o perímetro do retângulo.
Perímetro de um rectângulo = 2 (Comprimento × Largura)
Da pergunta,
Comprimento = 100m
Largura = 750m
Perímetro do rectângulo = 2 ( 100 + 750)
= 2(850)
= 1700m
Perímetro do rectângulo = 1700m
Somos questionados na pergunta para determinar quantos metros (Distância) um atleta viajou que tem apenas 6 voltas ao redor das extremidades do espaço.
A distância total percorrida pelo atleta ao correr é calculada como:
6 × perímetro do rectângulo.
= 6 × 1700
= 10200m
Quantos metros percorreu um atleta que deu apenas 6 voltas pelas extremidades do espaço = 10200
inverso aditivo de +3x
Answers
Answer:
inverso aditivo de +3x
Ok so wala ko kasabot nimo baah