Given function: h(t) = -16t^2 + 96t + 5, where t represents the time in minutes.
We need to find the interval for which the arrow is going up.
The arrow is going up would be the values of time t =0 when it start and when it went to highest point.
Given function is a quadratic function and it represents a parabolic shape.
The highest point on the parabola is a vertex point.
Therefore, we need to find the x-coordinate of the vertex.
We know, formula for x-coordinate of the vertex is
[tex]\frac{-b}{2a}[/tex]
For the given quadratic a= -16 and b=96.
Plugging values of a and b in formula, we get
[tex]\frac{-96}{2(-16)}=\frac{-96}{-32} = 3.[/tex]
Therefore, after 3 seconds arrow would be at maximum height.
Therefore, the interval for which the arrow is going up is [0,3].
Tyrell went to the park to go jogging. The beginning of the running path has a elevation of -2 feet. The higest elevation on the jogging path is 14 feet . What is the difference in elevation between highest point and the beginning of the path
Leo has 32 coins and wants to make equal groups with 8 coins each.What does the answer tell him?
There would be 4 groups of 8 coins. 32/8=4 Hope I could help!!!
im terrible with graphs help me out...but explain it cuz im a math inclined typa person sooo.......idek just help i guess?
Answer:
14. The correct option is 2.
13. The correct option is 4.
Step-by-step explanation:
14.
The given function is
[tex]f(x)=4|x|[/tex]
The function is non-negative for all values of x. So, the function opens in upward direction.
The function uis in the form of
[tex]f(x)=k|x|[/tex]
Where, a is vertical stretch factor or compress factor.
If k>1, then it represent vertical stretch and if 0<k<1, then it represent vertical compression.
Since the value of k is 4, therefore it represents vertical stretch and option 2 is correct.
13.
The given function is
[tex]y=x^3[/tex]
The traslate form of given function is
[tex]y=(x+a)^3+b[/tex]
Where, a represents the horizontal shift and b represents the vertical shift.
If a>0, then the graph shifts left side by a units and if a<0, then the graph shifts right side by a units.
If b>0, then the graph shifts upward by b units and if b<0, then the graph shifts downward by b units.
Since the graph shifts vertically 5 units down and horizontally 4 units left, therefore the value of a is 4 and value of b is -5. The required equation is
[tex]y=(x+4)^3-5[/tex]
Therefore option 4 is correct.
What is 1/5-3/4 help me please i need to step up my grade just a little to get 100%
Tim is buying packages of paper plates & cups. He wants to have equal amounts of each, but plates come in 24 per pack and cups come in 16 per pack. What is the least amount of plates & cups Tim will buy to get the same number of each ? A. 8 B. 16 C. 24 D. 48
The triangle shown below must be congruent
True or false
That would be FALSE
They have the same angles, so they're similar triangles. For them to be congruent, the corresponding sides must have equal length. Here we have two sides of length 7, but they're not corresponding sides. If on the second triangle the 7 was the length of the side between the 60 and 62 degree vertices then we'd have equal corresponding sides and congruent triangles.
Answer: no
Step-by-step explanation: this answer would be FALSEEE
Kelly and Daniel wrote the following proofs to prove that vertical angles are congruent. Who is correct?
Line segment NT intersects line segment MR forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles. Kelly's Proof Statement Justification ∠2 = ∠4 Vertical angles are congruent. ∠1 = ∠3 Vertical angles are congruent. Vertical Angles are congruent. Vertical Angle Theorem Daniel's Proof Statement Justification ∠1 + ∠2 = 180° Definition of Supplementary Angles ∠1 + ∠4 = 180° Definition of Supplementary Angles ∠1 + ∠2 = ∠1 + ∠4 Transitive Property of Equality ∠2 = ∠4 Subtraction Property of Equality
Both Kelly and Daniel are correct.
Neither Kelly or Daniel is correct.
Kelly is correct, but Daniel is not.
Daniel is correct, but Kelly is not.
Answer:
The answer is Daniel is correct, but Kelly is not.
Step-by-step explanation:
Answer:
(D) Daniel is correct, but Kelly is not.
Step-by-step explanation:
It is given that Line segment NT intersects line segment MR forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles.
Kelly's Proof:∠2 = ∠4 (Vertical angles are congruent)
∠1 = ∠3 (Vertical angles are congruent)
Using Vertical Angle Theorem the vertical angles are equal.
since, we cannot use the direct information given in the question in order to prove the same.
Thus, the justification given by Kelly is incorrect.
Now, Daniel's proof:
∠1 + ∠2 = 180°(Definition of Supplementary Angles)
and ∠1 + ∠4 = 180° (Definition of Supplementary Angles)
⇒∠1 + ∠2 = ∠1 + ∠4(Transitive Property of Equality)
Hence, ∠2 = ∠4(Subtraction Property of Equality)
Thus, the justification of Daniel is correct.
Hence, option (D) is correct.
A rectangular prism has dimensions of x + 1, x - 1, and x. Write an expression for the total volume of the prism.
We have been given the dimensions of the rectangular prism.
Lets say that the length, width, and height of the rectangular prism are:
Length [tex]= x+1[/tex]
Width [tex]=x-1[/tex]
Height[tex]=x[/tex]
Volume of a rectangular prism is given by:
[tex]length \times width\times height[/tex]
Plugging the values of length, width, and height, we get:
Total volume of the prism [tex]= (x+1)\times(x-1)\times x[/tex]
[tex]=(x^2-1)x=x^3-x[/tex] (we have used [tex](a+b)\times (a-b)=a^2-b^2[/tex])
So, the expression for the total volume of the prism is:
[tex](x^3-x)[/tex]
Find all points on the x-axis that are 14 units from the point (3,-7).
Answer:
(3±√147, 0) ≈ (-9.124, 0) and (15.124, 0)
Step-by-step explanation:
The points (x, 0) satisfy the distance formula:
d = 14 = √((x -3)² +(0+7)²)
196 = (x -3)² +49 . . . . . square both sides
147 = (x -3)² . . . . . . . . . subtract 49
3 ±√147 = x . . . . . . . . . take the square root and add 3
The points at distance 14 from (3, -7) on the x-axis are (3±√147, 0).
Radhika borrowed Rs.12000 from her friends. Out of which Rs.4000 were borrowed at 18% and the remaining at 15% rate of interest per annum. What is the total interest after 3 years?
Answer-
The total interest after 3 years is Rs.5760 .
Solution-
Total money borrowed = Rs.12000
Out of those Rs.4000 is of 18% interest rate and remaining 12000-4000=8000 is of 15% interest rate.
[tex]\text{Total interest}=\frac{P_1\times r_1\times t}{100}+\frac{P_2\times r_2\times t}{100}[/tex]
Where,
P₁ = principal amount = Rs.4000
P₂ = principal amount = Rs.8000
r₁ = rate of interest of P₁ = 18%
r₂ = rate of interest of P₂ = 15%
t = time period = 3 years
[tex]\text{Total interest}=\frac{4000\times 18\times 3}{100}+\frac{8000\times 15\times 3}{100}=2160+3600=5760[/tex]
a card is chosen from a standard deck of cards. what is the probability that the card is a queen, given that the card is a club?
Answer:
Probability that card is queen given that card is club is [tex]\frac{4}{13}[/tex]
Step-by-step explanation:
Given : A card is chosen from a standard deck of cards.
To find : What is the probability that the card is a queen, given that the card is a club?
Solution : It is the conditional probability
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
Let A is probability that card is queen.
Let B is the probability that card is a club.
Probability that card is queen given card is club [tex]P(A\cap B)=\frac{4}{52}=\frac{1}{13}[/tex]
Probability that card is club from deck of 52 cards [tex]P(B)=\frac{13}{52}=\frac{1}{4}[/tex]
To find probability that card is queen given that card is club [tex]P(A|B)[/tex]
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
[tex]P(A|B)=\frac{\frac{1}{13}}{\frac{1}{4}}[/tex]
[tex]P(A|B)=\frac{1\times4}{13\times 1}=\frac{4}{13}[/tex]
Therefore, Option A is correct.
Probability that card is queen given that card is club is [tex]\frac{4}{13}[/tex]
Answer:
the correct answer was 1/13
Step-by-step explanation:
i took my test and put 4/13 which was wrong and said that 1/13 is the right answer
Two bags contain marbels. Bag A conatains 112 marbles, and bag B contains 140 marbles. What percent fewer marbles does Bag A have than bag B
Which pair is the gcf of 1, 30 and 70, 24 and 44, 12 and 30, and 16 and 21
The GCF is 1.
Explanation:
1 has: 1 (LOL)
12 has: 1,2,3,4,6,12
16 has: 1,2,4,8,16
21 has: 1,3,7,21
24 has: 1, 2, 3, 4, 6, 8, 12, 24
30 has: 1, 2, 3, 5, 6, 10, 15, 30
44 has: 1, 2, 4, 11, 22, 44
70 has: 1, 2, 5, 7, 10, 14, 35, 70
So therefore, The GCF is 1
Hope this helps!
-Queenb369
P.S Could you possible give me the brainlist if i get it right.
Each employee can essemble 28 castles per hour. How many employees worked each hour? (What is the answer to this?)
What is the unemployment rate of this economy?
6.5%
9.3%
13.6%
15.7%
The unemployment rate is calculated as the number of unemployed divided by the labor force, resulting in approximately 9.6%, which is the closest to 9.3% as listed. It is higher than the historical average and the February 2015 rate.
Explanation:The unemployment rate of an economy is calculated by taking the number of unemployed persons and dividing it by the total labor force, and then multiplying the result by 100 to get a percentage.
In this case, using the given figures, the unemployment rate is calculated as follows: 14.8 (unemployed) / 153.9 (labor force) = approximately 9.6%.
This indicates that the correct answer is not explicitly listed, but the closest answer given is 9.3%, which seems to be a typo.
Furthermore, this current unemployment rate is significantly higher than the February 2015 rate of 5.5% and above the historical average unemployment rate, which tends to range between 4% to 6% over time, according to Federal Reserve Economic Data.
write the equation in y-intercept form slope 2 passes through point (5,-2)
The equation is y = 2x - 12
ExplanationEquation in slope intercept form is
[tex]y = mx + b[/tex]
Where,
m = slope
b = y-intercept
Putting the value of slope in this equation:
[tex]y = 2x + b[/tex]
From this we can solve the equation for b
[tex]b = y - 2x[/tex]
[tex]b = -2 - 2(5)[/tex]
[tex]b = -12[/tex]
Now, the equation of y-intercept becomes
[tex]y = 2x - 12[/tex]
Angels Inscribed and circumscribed.
Remark
The diameter of the circle is AC. The hypotenuse of the right triangle is also AC. This assumes that A,B and C all lie on the circumference of the circle.
Answers
One
The center of the circle is on the diameter of the circle. In fact, the center bisects the diameter. So the center lies on AC and if the center is labeled O then AO = BO.
Answer 1: AC
Two
The answer is the single word diameter.
Factor the difference of two cubes completely.
x^3-64
can anyone verify this for me?
[tex]x^3-4^3 = (x-4)(x^2+4x+16)=(x-4)(x+4)(x+4)[/tex]
Amy wants to carpet a room that is 12 feet by 8 feet.How many square yards of carpet will she need to complete the room?
96 square yards would complete the room
If sin(x) = 1/3 and sec(y) = 17/15 , where x and y lie between 0 and π/2, evaluate the expression using trigonometric identities. (enter an exact answer.) "sin(2y)"
Answer: sin2y =240/289 where 0<y <π/2
Step-by-step explanation:
Given sin(x) = 1/3 and sec(y) = 17/15 , where x and y lie between 0 and π/2.
We now that
[tex]cosy = \frac{1}{secy} =\frac{15}{17} \\and\\\text{using identity } sin^2y+cos^2y=1\\\text{we have}\\siny=\sqrt{1-cos^2y}=\sqrt{1-(\frac{15}{17} )^2}=\sqrt{1-\frac{225}{289} }=\sqrt{\frac{64}{289} }=\frac{8}{17} \\\Rightarrow\ siny=\frac{8}{17} \\\text{Now we are using identity sin2A=2sinAcosA we have}\\sin2y=2\cdot\ siny\cdot\ cosy=2\cdot\ \frac{8}{17} \cdot\ \frac{15}{17} =\frac{240}{289}[/tex]
To solve the question, we firstly find cos(y) from 'sec(y) = 17/15' because secant is the reciprocal of cosine. Then, we use the Pythagorean identity to find sin(y). Finally, we substitute these values into the double angle identity 'sin(2y) = 2sin(y)cos(y)' to find the final answer.
Explanation:In this high school level mathematics problem, 'sin(x) = 1/3' and 'sec(y) = 17/15' are given. From 'sec(y) = 17/15', we can calculate cos(y) because secant is the reciprocal of cosine. Hence, 'cos(y) = 15/17'. The question asks for the evaluation of the expression 'sin(2y)'. Here, we can use a trigonometric identity for double angles, which states 'sin(2y) = 2sin(y)cos(y)'.
However, we are only given secant of y, not sine. To find sin(y), we can use the Pythagorean identity. According to this identity, 'sin^2(y) = 1 - cos^2(y)'. So, 'sin(y) = sqrt[1 - (15/17)^2]'.
So, the final answer becomes 'sin(2y) = 2 * √[1 - (15/17)²] * 15/17'. It's useful to note that you should always check that your angle lies within the given range when using a square root in trigonometry, to ensure your answer is correct.
Learn more about Trigonometry here:https://brainly.com/question/11016599
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If f(x) = 3x-2 what is the value of 5
A. 9
B. 13
C. 15
D. 33
B
Assuming you mean the value of f(5)
If so then substitute x = 5 into f(x)
f(5) = (3 × 5) - 2 = 15 - 2 = 13 → B
The graph of g(x) is obtained by reflecting the graph of f(x)=4|x| over the x-axis.
Which equation describes g(x)?
A) g(x)=|x−4|
B) g(x)=|x+4|
C) g(x)=−4|x|
D) g(x)=|x|−4
That would be choice C.
The graph of 4|x| is shaped like a V whose vertex is at the origin.
Every y value will be positive for y = 4|x| as |x| is always positive and a reflection in the x axis will make every y value negative.
Through moving up c units, the graphs of g can be determined from the graph of f. If we subtract c from f(x), the graph shifts downward. Let [tex]\bold{ h(x) = f(x) - c}[/tex]. Shifting downward c units yields this graph of h from the graph of f.
Given:
[tex]\bold{f(x)=4|x|}[/tex]
Calculation:
It is stated that its graph of [tex]g(x)[/tex] is obtained by reflecting a graph of [tex]f(x)=4|x|[/tex] over the x-axis.When a figure is reflected across the x-axis, the rule for reflection is [tex]\bold{(x,y) \to (x,-y)}[/tex].To use the preceding logic, if the given function is reflected from across the x-axis, then [tex]g(x)=-f (x)[/tex].[tex]\bold{g(x)=-(4|x|)}\\\\\bold{g(x)=-4|x|}\\\\[/tex]
So, the equation [tex]g(x)=-4|x|[/tex] describes [tex]g(x)[/tex].
Therefore, the final choice is "Option C".
Learn more:
brainly.com/question/6280870
You work 1.15 hours on your English Homework and 1.75 hours in your math homework. Your science homework takes 1.05 hours less than your math homework. How many more hours do you work on your homework? The answer is 4 but it's saying it's wrong
Answer:
Total time taken for doing home work = 3.6 hours.
Explanation:
Time taken for English home work = 1.15 hours.
Time taken for Mathematics home work = 1.75 hours.
Time taken for Science home work = Time taken for Mathematics home work - 1.05 hours = 1.75 - 1.05 = 0.7 hours
Total time taken for doing home work = 1.15 + 1.75 + 0.7 = 3.6 hours.
So the answer is not 4 hours, it is 3.6 hours, that is why it is showing it as wrong.
What are the place values of the 6,s in 8,462,412,104
30 points! How do I factor 6x^2+x-15
Using the Grid Box Method?
Thank you! Thanks for helping - that was all of my factoring problems! :D ^.^ Most educational sites explain the factoring methods well, but in a very confusing way! :'3 Thank you so much again; have an awesome day! :)
Now for this you would have to think what two numbers multiplied to get 6x^2. Let's say for example 3x and 2x=6x^2
And now what two numbers multiplied together make -15, For example it can be 5 and -3
Now your ANSWER: (3x+5)(2x-3)
If eight trash bags last for thirty days then how many trash bags do you need for 180 days
Set up the proportion. Then cross multiply and isolate the variable to solve.
[tex]\frac{8(trash bags)}{30 (days)} = \frac{x (trash bags)}{180 (days)}[/tex]
8(180)= 30(x)
[tex]\frac{8(180)}{30} = \frac{30x}{30}[/tex]
8(6) = x
48 = x
Answer: 48 trash bags
Please help, I would appreciate it!!
Two Angles are Supplementary when they add up to 180°.
m∠2 + m∠1 = 180° (*)
If ∠1 ≅ ∠3, then m∠1 = m∠3.
Substitute to the (*)
m∠2 + m∠3 = 180°
Therefore ∠2 and ∠3 are supplementary.
A dolphin is swimming with her friend. The dolphin jumps to a height of 4.54.54, point, 5 meters above the surface of the water as her friend swims 9.89.89, point, 8 meters directly below her. What is the position of the dolphin's friend relative to the surface of the water?
The dolphin's friend is 8.63 meters below the surface of the water relative to the dolphin's jumping point.
Explanation:To solve this problem, we can use the kinematic equation that relates initial velocity, final velocity, acceleration, and displacement:
vf² = vi² + 2ad
Knowns:Plug in the knowns: (-13.0 m/s)² = (0 m/s)² + 2(-9.8 m/s²)(d)Simplify and solve for d: d = (169 m²/s²) / (-19.6 m/s²)Calculating: d = -8.63 mThe positive value of d indicates that the dolphin's friend is 8.63 meters below the surface of the water relative to the dolphin's jumping point.
The dolphin's friend is 5.3 meters below the surface of the water.
Let's reassess the problem with the given constraints more carefully.
We need to find the position of the dolphin's friend relative to the surface of the water.
1. Dolphin's height above the water:
[tex]\[ 4.5 \text{ meters above the surface} \][/tex]
2. Distance between the dolphin and her friend:
[tex]\[ 9.8 \text{ meters below the dolphin} \][/tex]
Since the friend is swimming below the dolphin, we need to subtract this distance from the height of the dolphin above the surface to find the position of the friend relative to the water surface.
3. Calculate the position of the dolphin's friend:
[tex]\[ \text{Position of friend} = 4.5 \text{ meters} - 9.8 \text{ meters} \][/tex]
[tex]\[ \text{Position of friend} = -5.3 \text{ meters} \][/tex]
This means the dolphin's friend is 5.3 meters below the surface of the water.
The perimeter of a given parallelogram is 46 inches. If the length of one side is 14 inches , what is the length of a side adjacent to it ??
Perimeter = 2*14 + 2x where x is length of the adjacent side
46 = 28 + 2x
2x = 18
x = 9 inches Answer
what else would need to be congruent to show that abc def by aas
The answer is A=D apex
Answer:
It's the first one, I just literally got done taking the test it was my last question anyways.