Answer: 85 meters
Step-by-step explanation:
The maximum height is the y-value of the vertex.
h(t) = -4.9t² + 20t + 65
a=-4.9 b=20 c=65
[tex]t=\dfrac{-b}{2a} = \dfrac{-(20)}{2(-4.9)} =\dfrac{-20}{-9.8}=2[/tex]
h(2) = -4.9(2)² + 20(2) + 65
= -19.6 + 40 + 65
= 85.4
if k=[-4/2 6/-3] and m=[2/8 -2/5] what is x when 2x -k = m
[tex]k=\left[\dfrac{-4}{2},\ \dfrac{6}{-3}\right]=[-2,\ -2]\\\\m=\left[\dfrac{2}{8},\ \dfrac{-2}{5}\right]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\\\\x=[a,\ b]\\\\2x-k=m.\ \text{Substitute:}\\\\2[a,\ b]-[-2,\ -2]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\\\\\ [2a,\ 2b]-[-2,\ -2]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\\\\\ [2a-(-2),\ 2b-(-2)]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\\\\\ [2a+2,\ 2b+2]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\iff2a+2=\dfrac{1}{4}\ \wedge\ 2b+2=-\dfrac{2}{5}[/tex]
[tex]2a+2=\dfrac{1}{4}\qquad\text{subtract 2 from both sides}\\\\2a=\dfrac{1}{4}-2\\\\2a=\dfrac{1}{4}-\dfrac{8}{4}\\\\2a=-\dfrac{7}{4}\qquad\text{divide both sides by 2}\\\\\boxed{a=-\dfrac{7}{8}}\\\\2b+2=-\dfrac{2}{5}\qquad\text{subtract 2 from both sides}\\\\2b=-\dfrac{2}{5}-2\\\\2b=-\dfrac{2}{5}-\dfrac{10}{5}\\\\2b=-\dfrac{12}{5}\qquad\text{divide both sides by 2}\\\\\boxed{b=-\dfrac{6}{5}}\\\\Answer:\ \boxed{x=\left[-\dfrac{7}{8},\ -\dfrac{6}{5}\right]}[/tex]
Answer:
It's B on edge 2021
Step-by-step explanation:
...
Paul is 2 years younger than patricia. Daniel is 25% older than Patricia. Ten years ago, Daniel was 50% older than Patricia. How old is paul currently.
Daniel is 25% older than Patricia. Ten years ago, Daniel was 50% older than Patricia.
That gives us the equations 1.25d=p and 1.5(d−10)=(p−10). Solving gives us 25 for Daniel and 20 for Patricia.
Paul is two years younger than Patricia.
20−2=18
To solve the problem, we set up an equation based on the given relationships and information. After solving it, we find that Patricia is 40 years old and Paul (who is 2 years younger) is 38 years old.
Explanation:Let's denote Patricia's current age as 'P', Paul's age as 'P-2' (since Paul is 2 years younger than Patricia), and Daniel's age as 'P+0.25P' (since Daniel is 25% older than Patricia).
According to the problem, ten years ago, Daniel was 50% older than Patricia. So, we create the equation '0.5(P-10) = P+0.25P-10' to represent this situation.
Solving the equation, we find P (Patricia's current age) equals 40 years. Hence, Paul's current age would be 'P-2', which is 38 years.
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Figure ABCD is a parallelogram with point C (−4, 1). Figure ABCD is rotated 90° clockwise to form figure A′B′C′D′. What coordinate would be the output for point C'?
C' (1, 4)
C' (1, −4)
C' (−1, −4)
C' (−1, 4)
find the polynomial function
Answer:
y = 2x³ +x² -3x +6
Step-by-step explanation:
The polynomial correlation function of a graphing calculator can work with the table of function values to give you the equation. (See attached)
_____
If you want to solve this by hand, you can write the equations for the unknown coefficients in the polynomial function, then solve those. First of all, notice that you are given the y-intercept, (0, 6), so you know one of the coefficients already. That leaves a system of 3 equations in 3 unknowns that need to be solved.
___
Writing the equations
... ax³ +bx² +cx +6 = y . . . . the generic linear equation in a, b, c that you're writing
For x = -1:
... -a +b -c +6 = 8
For x = 1
... a + b + c + 6 = 6
For x = 2
... 8a +4b +2c +6 = 20
In augmented matrix terms, this set of linear equations looks like ...
[tex]\left[\begin{array}{ccc|c}-1&1&-1&2\\1&1&1&0\\8&4&2&14\end{array}\right][/tex]
___
Solving the equations
There are a number of ways to solve these. Again, a graphing calculator often has solution functions, such as reducing a matrix to row-echelon form, that will solve this in a keystroke or two.
If you add the first two equations, you get ...
... 2b = 2 ⇒ b = 1
Substituting that into the first equation allows you to simplify it to ...
... -a -c = 1
Dividing the third equation by 2 (and substituting for b) makes it ...
... 4a +c = 5
Adding these equations gives ...
... 3a = 6 ⇒ a = 2
Then ...
... c = -a -1 = -2 -1 = -3
And our polynomial function is ...
... y = 2x³ +x² -3x +6
You are required to take five? courses, one each in? humanities, sociology,? science, math, and music. You have a choice of 4 humanities? courses, 6 sociology? courses, 6 science? courses, 2 math? courses, and 8 music courses. How many different sets of five courses are? possible?
By applying the combinatorics principle in mathematics, the student has a total of 2304 possible sets of courses to choose from across the five disciplines.
Explanation:The subject of this question is a mathematical problem related to combinatorics, specifically the counting principle. When you're choosing one item from a set, like how many courses you can choose, you're often dealing with combinations or permutations. In this case, since the order of taking the courses does not matter, we're dealing with a type of combination.
To find the total number of course sets, simply multiply the number of possible courses in each discipline: 4 options in humanities, 6 in sociology, 6 in science, 2 in math, and 8 in music. So, the total number of different course sets you could take is 4 * 6 * 6 * 2 * 8 = 2304 different sets of five courses.
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Two boxes are stacked together.
What is the combined volume of the two boxes?
A. 105 cm
B. 280 cm
C. 385 cm
D. 4,200 cm
The formula of a volume of a rectangle prism:
[tex]V=lwh[/tex]
l - length
w - width
h - height
The larger rectangle prism:
[tex]l = 10cm,\ w=7cm,\ h=4cm[/tex]
Substitute:
[tex]V_1=(10)(7)(4)=280\ cm^3[/tex]
The smaller rectangle prism:
[tex]l=3cm,\ w=7cm,\ h=5cm[/tex]
Substitute:
[tex]V_2=(3)(7)(5)=105\ cm^3[/tex]
Total volume:
[tex]V=V_1+V_2\to V=280\ cm^3+105\ cm^3=385\ cm^3[/tex]
Answer: C. 385 cm³.The combined volume is 385 cm³
What is a rectangular parallelepiped?A rectangular parallelepiped is a polyhedron with six faces, which is also known as a hexahedron, each of which is a parallelogram.Volume of a rectangular parallelepiped can be calculated by multiplying its length , breadth and height.How to calculate the combined volume?The two boxes can be said to have a shape of rectangular parallelepiped.For the lower box, the volume will be = (7 x 10 x 4) cm³ = 280 cm³
For the upper box, the volume will be = (7 x 5 x 3) cm³ = 105 cm³
Now, for the combined volume, we need to add the individual volumes of the two boxes.∴ Combined volume will be equal to = ( 280 + 105) cm³ = 385 cm³
Option C is correct.
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The graphic shows the schedule network diagram (in minutes) for assembling a toy train set. What is the duration of the critical path?
A) 38 minutes
B) 41 minutes
C) 49 minutes
D) 51 minutes
The critical path in a project schedule is the longest sequence of tasks from start to finish and determines the minimum total duration for the project. Without the diagram, the correct duration from your multiple-choice options cannot be determined accurately. The correct answer represents the duration of the longest path from the given options.
Explanation:Without the graphic showing the schedule network diagram for assembling a toy train set, providing an accurate answer would be difficult. Normally, in project management, a Critical Path represents the longest sequence of tasks (or activities) in a project schedule from start to finish. It determines the minimum total duration required to complete the project. You identify the critical path by adding the times for the activities in each sequence and determining the longest path in the project.
In this case, assuming that you have the diagram in front of you and you've calculated the total duration for all paths, one of the multiple choice options (A) 38 minutes, (B) 41 minutes, (C) 49 minutes, or (D) 51 minutes would represent the duration of the critical path in the network diagram.
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If triangle ABC is congruent to triangle XYZ, then which of the following is congruent to ∠Z?
option 1. ∠A
option 2. ∠B
option3. ∠C
option 4. ∠X
Answer:
The answer is ∠CStep-by-step explanation:
There are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that gives the deer population P(t) on the reservation t years from now.
Answer:
[tex]P(t)=170\cdot (1.30)^t[/tex]
Step-by-step explanation:
We have been given that there are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year.
We can see that deer population is increasing exponentially as each next year the population will be 30% more than last year.
Since we know that an exponential growth function is in form: [tex]f(x)=a*(1+r)^x[/tex], where a= initial value, r=growth rate in decimal form.
It is given that a=170 and r=30%.
Let us convert our given growth rate in decimal form.
[tex]30\text{ percent}=\frac{30}{100}=0.30[/tex]
Upon substituting our given values in exponential function form we will get,
[tex]P(t)=170\cdot (1+0.30)^t[/tex]
[tex]P(t)=170\cdot (1.30)^t[/tex]
Therefore, the function [tex]P(t)=170\cdot (1.30)^t[/tex] will give the deer population P(t) on the reservation t years from now.
What is 2x^3-x^2+3 divided by x-3?
Answer: (A) 2x² + 5x + 15 + [tex]\bold{\dfrac{48}{x-3}}[/tex]
Step-by-step explanation:
x - 3 = 0 ⇒ x = 3
Using synthetic division:
3 | 2 -1 0 3
| ↓ 6 15 45
2 5 15 48 ← remainder
Factored polynomial is: 2x² + 5x + 15 + [tex]\dfrac{48}{x-3}[/tex]
Please help! Urgent!
Examine triangle ABC. (look at picture)
What is the value of x?
A) 37
B) 48
C) 127
D) 138
Answer:
x = 127 degrees
Step-by-step explanation:
By the external angle of a triangle theorem:-
x + 5 = 79 + m < ACB
m < ACB = 180 - x, so:-
x + 5 = 79 + 180 - x
2x = 79 + 180 - 5 = 254
x = 127 ( answer)
Answer:
If you look at my screenshot it will show you the correct answer.
Step-by-step explanation:
Eric estimated 28x48 by finding 30x50. His estimate was 1,500,but he says the actual product will be greater than that amount.Is he correct? Explain how you know
Answer:
Eric is not correct.
Step-by-step explanation:
We have been given that Eric estimated [tex]28\times 48[/tex] by finding [tex]30\times 50[/tex]. His estimate was 1500, but he says the actual product will be greater than that amount.
To find if Eric is correct or not, let us see how to estimate an answer.
While estimating our given numbers we will round to nearest tenth and change the digit to the right of the rounding place to 0.
As 8 is greater than 5, so we will round 28 to 30 and 48 to 50.
Since we are rounding up, so our estimated answer will be greater than actual answer, therefore, Eric is not correct.
DB _____ CB
Choose the relationship symbol to make a true statement.
<
=
>
Answer:
DB > CB
Step-by-step explanation:
This is a short answer, but I promise that it is 100% correct.
Hope it helps.
Find the Value of x
(a)8\3
(b)8
(c)4\3
(d)16
Answer:
(a) 8√3
Step-by-step explanation:
All of the triangles are similar, so the ratio of hypotenuse to long side is the same for all. Comparing the middle-size triangle to the largest, we have ...
... x/12 = 16/x
... x² = 192 . . . . . . . . . . . . . multiply by 12x; next take the square root
... x = √192 = 8√3 . . . . . . seems to match answer choice (a)
One side of a kite is 5 cm less than 2 times the length of another. If the perimeter is 14 cm, find the length of each side of the kite.
A) 5 cm, 5 cm
B) 4.2 cm, 3.4 cm
C) 6.3 cm, 7.7 cm
D) 4 cm, 3 cm
D) 4 cm, 3 cm
Step-by-step explanation:Let x represent the length of "another" side. Then "one side" can be represented by (2x -5 cm).
The perimeter of the kite is the sum of two sides of each length:
... P = 14 cm = 2(x) + 2(2x -5 cm)
Dividing by 2 and collecting terms, we have ...
... 7 cm = 3x -5 cm
... 12 cm = 3x
... 4 cm = x . . . . the length of "another" side
... 2(4 cm) -5 cm = 3 cm . . . . the length of "one side"
The two different side lengths are 4 cm and 3 cm.
Sam is going to the store to buy pumpkins. Small pumpkins cost $2.50 and large pumpkins cost $6.00. He needs to buy at least 20 pumpkins, and he can spend no more than $90.
What is the sum of the first 75 even numbers starting with 2? Enter your answer in the box.
Answer:
5700
Step-by-step explanation:
step 1 Address the formula, input parameters & values.
Input parameters & values:
The number series 2, 4, 6, 8, 10, 12, . . . . , 150.
The first term a = 2
The common difference d = 2
Total number of terms n = 75
step 2 apply the input parameter values in the AP formula
Sum = n/2 x (a + Tn)
= 75/2 x (2 + 150)
= (75 x 152)/ 2
= 11400/2
2 + 4 + 6 + 8 + 10 + 12 + . . . . + 150 = 5700
Therefore, 5700 is the sum of first 75 even numbers.
Final answer:
To find the sum of the first 75 even numbers starting with 2, use the sum of arithmetic sequence formula: (75/2) * (2 + 150) = 5,700.
Explanation:
The sum of the first 75 even numbers starting with 2 can be calculated using the formula for the sum of an arithmetic sequence. An arithmetic sequence is a sequence of numbers with a constant difference between consecutive terms. In this case, the common difference is 2, since we are dealing with even numbers.
To find the sum of the first 75 even numbers, we use the formula: Sum = (n/2) * (first term + last term), where 'n' is the number of terms. The first term is 2 and the 75th even number can be found by the formula: last term = first term + (n-1)*difference. Thus, the last term = 2 + (75-1)*2 = 2 + 148 = 150.
Using the sum formula: Sum = (75/2) * (2 + 150) = 37.5 * 152 = 5,700. Therefore, the sum of the first 75 even numbers starting with 2 is 5,700.
D is the midpoint of CE. E has coordinates (−8, −3), and D has coordinates (2, 3). Find the coordinates of C.
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad E(\stackrel{x_2}{-8}~,~\stackrel{y_2}{-3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{-8+x}{2}~~,~~\cfrac{-3+y}{2} \right)=\stackrel{\stackrel{midpoint}{D}}{(2,3)}\implies \begin{cases} \cfrac{-8+x}{2}=2\\[1em] -8+x=4\\ \boxed{x=12}\\[-0.5em] \hrulefill\\ \cfrac{-3+y}{2}=3\\[1em] -3+y=6\\ \boxed{y=9} \end{cases}[/tex]
Football team play $28 per jersey. They bought 16 jerseys. How much money did the team spend on jerseys
What is the correct classification of the power function?
Answer:
Cubic
Step-by-step explanation:
A cubic function is a function whose degree is 3 (the highest exponent or power on the variable). It has a distinctive sideways S shape that can either start down and end up or start up and end down. It also crosses through the x-axis an odd number of times. It will have up to three x-intercepts or roots.
Can anyone please tell me what I’m doing wrong. It’s not giving me the full marks.
Answer:
Area shaded part = 116 to three sig digs.
Step-by-step explanation:
I don't know if your answer is correct or not, but the number of sig digs is not. The way the question has been posed is not to 3 sig digs either.
The answer should be 116 if they want it to three sig digs.
Let's see if the answer is correct
Area of the whole circle.
Area of a circle = pi*r^2r = 6.5 cm Note: this is 2 sig digs.pi= 3.14Area = 3.14 * 6.5^2Area = 3.14 * 42.25Area= 132.665Area of unshaded smaller circle
pi = 3.14r = 2.3Area = 3.14 * 2.3^2Area = 3.14 * 5.29Area = 16.61Area of the shaded part
Area of shaded part = area of the whole circle - Area of smaller circleArea of the shaded part = 132.66 - 16.61Area of the shaded part = 116.01To 3 sig digs is 116Answer:
116 cm^2 to 3 significant figures.
Step-by-step explanation:
Your calculations are correct. You just haven't corrected the answer to 3 significant figures.
When navigating the maze, the robot will only need to go north, south, east, and west. It can be useful to use the complex plane to represent these directions. When using the complex plane this way, we use numbers such that their magnitude is equal to 1. If we let the value i represent the robot facing due north, what values represent the robot facing east, south, and west?
Answer:
N=i
S = -i
E =1
W = -1
Step-by-step explanation:
If facing north is represented by i, then facing south would be the opposite or -i.
We can let facing east be 1 because the magnitude has to be 1, so facing west would be the opposite or -1
On a piece of paper graph f(x)=-1
Answer:
on the y axis ( the vertical line ) circle -1
:)
Unfortunately, I'm having file upload issues so I'll just say what it is. f(x) means value of the function, which is the y-value. So you're basically plotting y=-1. No matter what your x-value is, the y-value is always -1. So, it is a horizontal line crossing -1 on the y-axis, extending to infinity on either side.
There are 8 blue marbles, 9 green marbles, 5 yellow marbles, and 6 orange marbles in a bag. What is the probability of drawing an orange marble?
Answer:
3/14
Step-by-step explanation:
Probability( Drawing an orange marble) = number of orange marbles/ total number of marbles in the bag.
= 6 / (8+9+5+6)
= 6/28
= 3/14
Noah is thinking of two fractions that have the same sum of 3/5. Each fraction has a numerator of 1. What are the denimonitors of the fractions? Enter your answers in the box
Answer:
The denominators of fractions are : 2 and 10
Step-by-step explanation:
[tex]\text{Let the two fractions be : }\frac{1}{x}\thinspace and\thinspace \frac{1}{y}\\\\\implies \frac{1}{x}+\frac{1}{y}=\frac{3}{5}\\\\\implies 5\cdot x +5\cdot y-3\cdot x\cdot y=0[/tex]
By hit and trial method, if we put x = 2 and y = 10 then the resulting equation (1) is satisfied and all the conditions hold.
So, the denominators are 2 and 10
Through the hit and trial method, the value of the denominator 'a' is 2 and the value of denominator 'b' is 10 and there is also the use of arithmetic operations.
Given :
Noah is thinking of two fractions that have the same sum of 3/5.Each fraction has a numerator of 1.To determine the denominator of the two fractions whose sum is 3/5, first, let that numbers be 1/a and 1/b.
[tex]\dfrac{1}{a}+\dfrac{1}{b}= \dfrac{3}{5}[/tex]
[tex]5a + 5b = 3ab[/tex]
Now, put a = 2 then b becomes:
[tex]10 + 5b = 6b[/tex]
b = 10
So, through the hit and trial method, the value of a is 2 and the value of b is 10.
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Find the value of X in the diagram. HELP ASAP!!
Answer:
10 =x
Step-by-step explanation:
The figure in the diagram is an equilateral triangle, which means all sides are equal and all angles are equal. If all angles are equal, each angle is equal to 60 degrees (180/3=60). Therefore <B =60.
60 = 5x+10
Subtract 10 from each side
60-10 = 5x+10 -10
50 = 5x
Divide each side by 5
50/5 = 5x/x
10 =x
PLEASE HELP! :( what is the sum of the geometric series
15
E 2(1/3)^3
x = 0
rounded to the nearest whole number???
A) 1
B) 2
C) 3
D) 4
the picture is attached! i don’t get it please help!
In a right triangle one acute angle measures 48 more than 2 times the other. If the sum of the measure of the two acute angles must equal 90 find the measure is the acute angles
A)14,76 B)16,74 C)15,78. D)13,77
Answer:
A
Step-by-step explanation:
let one acute angle be x then the other is 2x + 48
Their sum is 90 , hence
x + 2x + 48 = 90
3x + 48 = 90 ( subtract 48 from both sides )
3x = 42 ( divide both sides by 3 )
x = 14
the 2 acute angles are x = 14° and (2 × 14 ) + 48 = 28 + 48 = 76°
During the basketball season, Cory made 21 of the 60 baskets she attempted. Krista made 16 of the 40 baskets she attempted. Paula made 17 of the 50 baskets she attempted. Write the names of the players in order from the least percentage of baskets made to the greatest percentage of baskets made
Answer: Paula, Cory, Krista
Step-by-step explanation: You would divide the attempted baskets with the ones that they already did make: Cory got 35% of her attempted baskets (21 divided by 60), Krista got 40% of her attempted baskets (16 divided by 40), and Paula got 34% of her attempted baskets (17 divided by 50). Hope this helped!
Answer:
Krista cory paul
Step-by-step explanation:
saw it after searching on google
Robbie Morse has a $47,500 insurance policy. The annual premium is $987.53. Robbie pays $90.00 monthly.
How much does Robbie pay in twelve months?
$
How much more does Robbie pay?
$
What percentage does Robbie pay (to the nearest percent)?
%
Answer:
Robbie pay in twelve months $1080 .
$92.47 more Robbie pay and 9.36 %(Approx) Robbie pay.
Step-by-step explanation:
As given
Robbie Morse has a $47,500 insurance policy.
The annual premium is $987.53.
Robbie pays $90.00 monthly.
First find out the Robbie pay in twelve months .
Robbie pay in twelve months = 12 × 90
= $ 1080
Second find out how much more does Robbie pay .
Robbie pay extra = Robbie pay in twelve months - annual premium
= $ 1080 - $987.53
= $92.47
Therefore the $92.47 more Robbie pay .
Third find out the what percentage does Robbie pay .
Formula
[tex]Percentage = \frac{Robbies\ pay\ more\times 100}{annual\ premium}[/tex]
Robbies pay more = $92.47
Annual premium = $987.53
Put in the above
[tex]Percentage = \frac{92.47\times 100}{987.53}[/tex]
[tex]Percentage = \frac{9247}{987.53}[/tex]
Percentage = 9.36 % (Approx)
9.36 %(Approx) Robbie pay.
Robbie pays a total of $1,080.00 over twelve months, which is $92.47 more than the annual premium. This amount is approximately 9% more than the original annual premium.
To determine how much Robbie pays for his monthly premium over twelve months, we need to perform the following calculations:
First, calculate the total amount Robbie pays monthly. He pays $90.00 monthly, so over twelve months:
$90.00 times 12 = $1,080.00
Next, we need to find out how much more Robbie pays compared to the annual premium of $987.53:
$1,080.00 - $987.53 = $92.47
Percentage Calculation:
To find the percentage Robbie pays compared to the original annual premium, use the formula:
(difference / original amount) times 100
($92.47 / $987.53) times 100 ≈ 9%
Thus, Robbie pays approximately 9% more than the annual premium.