The greatest force acting on the ball to slow it down is Gravitational force.
Which forces will act on the ball?When ball is thrown upwards then there will be two forces on the ball opposite to the motion of ball
1. Gravitational force (mg)
2. Air friction or air drag
Both forces are opposite to the motion of the ball and it will cause the decrease in the speed of the ball.
Now here due to less value of drag coefficient on the ball we will say that ball will decrease its speed more due to gravitational force compare to friction force of air.
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Explain the steps for moving three disks from one peg to another. start with moving the small disk to the right peg.
There are some ways by which move the steps from sequence and series method like
Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.
According to the statement
we have to explain the moving steps to change the position of the given three disk from one peg to another.
So, for the solution of this problem
Firstly we know that the sequence and series
An itemized collection of elements in which repetitions of any sort are allowed is known as a sequence, whereas series is the sum of all elements.
we have to use the sequence and series method.
So, according to this method
Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.
So, there are some ways by which move the steps from sequence and series method like
Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.
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A moving company’s moving rates can be represented by the function f(x) = 3x 400, where x is the number of miles for the move. another moving company’s rates can be represented by the function g(x) = 5x 200. which function represents the difference between the moving companies' rates, h(x) = f(x) – g(x)? h(x) = 2x 200 h(x) = –2x 200 h(x) = 5x – 200 h(x) = 5x 600
The function that represents the difference between the moving companies' rates is:
h(x) = -2x + 200.
How to find the difference of two functions?The difference of two functions is found subtracting the like terms from the functions.
In this problem, the functions for the rates are given as follows:
f(x) = 3x + 400.g(x) = 5x + 200Hence the difference is given by:
h(x) = 3x + 400 - (5x + 200) = 3x - 5x + 400 - 200 = -2x + 200.
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What equation can be used to find the sum of 4/10 and 7/100
Answer:
47/100
Step-by-step explanation:
First you have to make the denominators equal.
4/10 * 10/10 = 40/100
40/100 + 7/100 = 47/100
Charles is 20% heavier than Edith. If Charles weighs 60kg, what is Edith's weight?
Charles' weight = Edith's weight + 20% of Edith's weight
We'll use a variable to represent Edith's weight, x.
The decimal form of 20% is 0.2.
60 = x + 0.2x
60 = 1.2x
x = 50
Edith's weight is 50kg.
Hope this helps!
Find the third order maclaurin polynomial. Use it to estimate the value of sqrt1.3
You can use the well-known binomial series,
[tex]\displaystyle (1+x)^\alpha = \sum_{k=0}^\infty \binom \alpha k x^k[/tex]
where
[tex]\dbinom \alpha k = \dfrac{\alpha(\alpha-1)(\alpha-2)\cdots(\alpha-(k-1))}{k!} \text{ and } \dbinom \alpha0 = 1[/tex]
Let [tex]\alpha=\frac12[/tex] and replace [tex]x[/tex] with [tex]3x[/tex]; then the series expansion is
[tex]\displaystyle (1+3x)^{1/2} = \sum_{k=0}^\infty \binom{\frac12}k (3x)^k[/tex]
and the first 4 terms in the expansion are
[tex]\sqrt{1+3x} \approx 1 + \dfrac{\frac12}{1!}(3x) + \dfrac{\frac12\cdot\left(-\frac12\right)}{2!}(3x)^2 + \dfrac{\frac12\cdot\left(-\frac12\right)\cdot\left(-\frac32\right)}{3!}(3x)^3[/tex]
which simplify to
[tex]\sqrt{1+3x} \approx \boxed{1 + \dfrac32 x - \dfrac98 x^2 + \dfrac{27}{16} x^3}[/tex]
You can also use the standard Maclaurin coefficient derivation by differentiating [tex]f[/tex] a few times.
[tex]f(x) = (1+3x)^{1/2} \implies f(0) = 1[/tex]
[tex]f'(x) = \dfrac32 (1+3x)^{-1/2} \implies f'(0) = \dfrac32[/tex]
[tex]f''(x) = -\dfrac94 (1+3x)^{-3/2} \implies f''(0) = -\dfrac94[/tex]
[tex]f'''(x) = \dfrac{81}8 (1+3x)^{-5/2} \implies f'''(0) = \dfrac{81}8[/tex]
Then the 3rd order Maclaurin polynomial is the same as before,
[tex]\sqrt{1+3x} \approx f(0) + \dfrac{f'(0)}{1!} x + \dfrac{f''(0)}{2!} x^2 + \dfrac{f'''(0)}{3!} x^3 = 1 + \dfrac32 x - \dfrac98 x^2 + \dfrac{27}{16} x^3[/tex]
Now,
[tex]\sqrt{1.3} = \sqrt{1+3x} \bigg|_{x=\frac1{10}} \\\\ ~~~~~~~~ \approx 1 + \dfrac32 \left(\dfrac1{10}\right) - \dfrac98 \left(\dfrac1{10}\right)^2 + \dfrac{27}{16} \left(\dfrac1{10}\right)^3 \\\\ ~~~~~~~~ = \dfrac{18,247}{16,000} \approx \boxed{1.14044}[/tex]
Compare to the actual value which is closer to 1.14018.
[tex]\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}[/tex] is the maclaurin polynomial and estimate value of [tex]\sqrt{1.3}[/tex] is 1.14. This can be obtained by using the formula to find the maclaurin polynomial.
Find the third order maclaurin polynomial:Given the polynomial,
[tex]f(x)=\sqrt{1+3x}=(1+3x)^{\frac{1}{2} }[/tex]
The formula to find the maclaurin polynomial,
[tex]f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} + \frac{f'''(0)}{3!}x^{3}[/tex]
Next we have to find f'(x), f''(x) and f'''(x),
[tex]f'(x) = \frac{3}{2}(1+3x)^{-\frac{1}{2} }[/tex] [tex]f''(x) =-\frac{9}{4}(1+3x)^{-\frac{3}{2} }[/tex][tex]f'''(x) = \frac{81}{8}(1+3x)^{-\frac{5}{2} }[/tex]By putting x = 0 , we get,
[tex]f(0)=(1+3(0))^{\frac{1}{2} }=1[/tex] [tex]f'(0) = \frac{3}{2}(1+3(0))^{-\frac{1}{2} }=\frac{3}{2}[/tex][tex]f''(0) =-\frac{9}{4}(1+3(0))^{-\frac{3}{2} }=-\frac{9}{4}[/tex][tex]f'''(0) = \frac{81}{8}(1+3(0))^{-\frac{5}{2} }=\frac{81}{8}[/tex]Therefore the maclaurin polynomial by using the formula will be,
[tex]\sqrt{1+3x}=f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} + \frac{f'''(0)}{3!}x^{3}[/tex]
[tex]\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}[/tex]
To find the value of [tex]\sqrt{1.3}[/tex] we can use the maclaurin polynomial,
[tex]\sqrt{1.3}[/tex] is [tex]\sqrt{1+3x}[/tex] with x = 1/10,
[tex]\sqrt{1+3(1/10)}=1+\frac{3}{2} (1/10)-\frac{9}{8} (1/10)^{2} + \frac{81}{8}(1/10)^{3}[/tex]
[tex]\sqrt{1+3(1/10)}=\frac{18247}{16000} = 1.14[/tex]
Hence [tex]\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}[/tex] is the maclaurin polynomial and estimate value of [tex]\sqrt{1.3}[/tex] is 1.14.
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In △MDK, m=16.4, d=22, and k=19. Identify m∠D rounded to the nearest degree. The figure shows triangle M D K. The length of side M D is k units. The length of side D K is m units. The length of side K M is d units.
Answers;
a) 46°
b) 58°
c) 76°
d) 14°
The length of the sides,MD, DK, and KM gives the measure of the angle m<D as c) 76°
Which method can be used to find the measure of angle m<D?In triangle ∆MDK, we have;
m = 16.4
d = 22
k = 19
Using cosine rule, we get;
d² = m² + k² - 2•m•k•cos(D)
Therefore;
2•m•k•cos(D) = m² + k² - d²
[tex]D = arccos \left( \frac{ {m}^{2} + {k}^{2} - {d}^{2} }{2 \cdot m \cdot k} \right)[/tex]
Which gives;
[tex]D = arccos \left( \frac{ {16.4}^{2} + {19}^{2} - {22}^{2} }{2 \times 16.4 \times 19} \right) \approx {76}^{ \circ} [/tex]
m<D = 76°The correct option is therefore;
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Answer:
76
Step-by-step explanation:
Use the Law of Cosines to find m∠D
.The figure shows the same triangle as in the beginning of the task. Angle M D K is highlighted in red.
Set up the equation for the Law of Cosines.
d2=k2+m2−2kmcosD
Substitute the given values and solve for m∠D
.222=192+16.42−2(19)(16.4)cosD
Simplify.
484=629.96−623.2cosD
Subtract 629.96
.−145.96=−623.2cosD
Divide by −623.2
0.234=cosD
Use the inverse cosine function to find m∠D
and round to the nearest degree.
The figure shows a screen of a graphical calculator. The inverse cosine of 0 point 2 3 4 is calculated. The result is 76 point 4 6 7 3 1 6 4 6.
m∠D=cos−1(0.234)≈76∘
Therefore, m∠D≈76∘
hope it helps you!
.
5. In one game, the final score was Falcons 3, Hawks 1. What fraction and
percent of the total goals did the Falcons score? Show your work in the space
below. Remember to check your solution.
Answer:
3/4 or 75%
Step-by-step explanation:
Falcons scored 3 and Hawks scored 1, so in total 4 points were scored during the game. Falcons scored 3 out of 4 points, so they scored 3/4 of the points scored in the game.
To convert 3/4 to percentage, divide 3 by 4, multiply the quotient (result after division calculation) by 100, and add % sign after the number.
3/4 = 0.75
Therefore 3/4 is equivalent to 75%.
Answer:
[tex] \frac{3}{4} [/tex]
[tex]75\%[/tex]
Step-by-step explanation:
From the information given from the question, we can deduce:
Total goals scored by both teams = 3 + 1 = 4
Fraction of Goals Scored by Falcons =
[tex] \frac{goals \: scored \: by \: falcons}{total \: goals \: scored \: by \: both \: teams} \\ = \frac{3}{4} [/tex]
To get the percentage, we have to make sure the denominator is 100.
[tex] \frac{3}{4} \\ = \frac{3 \times 25}{4 \times 25} \\ = \frac{75}{100} \\ = 75\%[/tex]
Translate the phrase into a variable expression. Use the letter d to name the
variable. If necessary, use the asterisk (*) for multiplication and the slash
(/) for division.
the number of dollars Paul owes minus 18...
Answer here
Answer:
d - 18
Step-by-step explanation:
The question said to use d as the variable. We do not know the number of dollars Paul owes. So we put d for that amount.
Then "minus" means to subtract 18.
Writing the expression is all that is being asked for. Translating the words into algebra. We aren't solving anything. Not even writing an entire equation, just an expression, so it has no equals sign.
Which of the following linear equations corresponds to the table above?
O A. y = 4x - 3
O B. y=¹/4 x-3
OC. y=1/4x+3
OD. y = 4x + 3
The linear equations that corresponds to the table is y = 4x + 3
How to determine the linear equation?The missing table of values in the complete question is given as:
x y
0 3
3 15
7 31
10 43
Start by calculating the slope of the equation using
m = (y2 - y1)(x2 - x1)
Substitute the values on the table in the above equation
m = (15 - 3)/(3 - 0)
Evaluate the difference
m = 12/3
Evaluate the quotient
m = 4
The linear equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 4(x - 0) + 3
Evaluate the expression
y = 4x + 3
Hence, the linear equations that corresponds to the table is y = 4x + 3
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use the present value formula to determine the amount to be invested now, or the present value needed.
The desired accumulated amount is $50,000 after 14 years invested in an account with 7% interest compounded annually
The amount to be invested now, or the present value needed, is ???
(Round to the nearest cent as needed.)
The amount to be invested now, or the present value needed, is $22873.75
How to find the present value?We solve the problem using the compound interest formula for amount
A = P(1 + r)ⁿ where
P = present value, r = interest rate and n = number of years.What is the present value?Making P subject of the formula, we have
P = A/(1 + r)ⁿ
Given that
A = $50,000, r = 7% = 0.07 and n = 14Substituting the values of the variables into the equation, we have
P = A/(1 + r)ⁿ
P = 50000/(1 + 0.07)¹⁴
P = 50000/(1.07)¹⁴
P = 50000/1.7317
P = 22873.75
So, the amount to be invested now, or the present value needed, is $22873.75
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Mathew can run 16 rounds in 4 minute. How many rounds can he run in 8 minutes?
PLS HELP ME
The angle between the generator and the central axis of a double-napped cone is 60°. a plane intersecting the cone makes an angle of 50° with the central axis. which conic section is formed?
The right option is (c).
As a result of the plane intersecting the cone here at an angle of 50° being less than the angle between the generator and central axis at an angle of 50°, a conic section is created.
What is Hyperbola?A smooth curve in a plane known as a hyperbola is one whose geometric characteristics or equations for which it is the solution set characterize it. Two parts of a hyperbola, known as connected components or branches, are mirror reflections of one another and resemble two infinite bows.
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I understand that the question you are looking for is:
"The angle between the generator and the central axis of a double-napped cone is 60°. A plane intersecting the cone makes an angle of 50° with the central axis. Which conic section is formed?"
(a)circle
(b)ellipse
(c)hyperbola
(d)parabola
Solve this system of equations by using the elimination method. x+4y=9 2x-4y=-6
Answer:
[tex]x=6[/tex]
[tex]y=\frac{3}{4}[/tex]
Step-by-step explanation:
Given the following question:
[tex]x+4y=9[/tex]
[tex]2x-4y=9[/tex]
To solve using the elimination method we will add the two equations together to find the two individual values.
[tex]x+2x=3x[/tex]
[tex]4y-4y=0[/tex]
[tex]9+9=18[/tex]
[tex]3x=18[/tex]
[tex]\frac{3x}{3} =x[/tex]
[tex]18\div3=6[/tex]
[tex]x=6[/tex]
[tex]x+4y=9[/tex]
Substitute six in for x:
[tex]x=6[/tex]
[tex]6+4y=9[/tex]
Solve for y:
[tex]6-6=0[/tex]
[tex]9-6=3[/tex]
[tex]\frac{4y}{4} =y[/tex]
[tex]3=\frac{3}{4}[/tex]
[tex]y=\frac{3}{4}[/tex]
x is equal to 6, and y is equal to 3/4.
Hope this helps.
for f(x)=7x and g(x)=x+1, find the following functions. a.(fog)(x); b.(gof)(x); c.(fog)(4); d.(gof)(4)
Answer:
[tex]a.(fog)(x) = 7x + 7 \\ b.(gof)(x) = 7x + 1 \\ c.(fog)(4) = 35 \\ d.(gof)(4) = 29[/tex]
Step-by-step explanation:
Greetings !
a. (fog)(x)= f[g(x)] = 7(x+1)
(fog)(x)= 7x+7b. (gof)(x) = g[f(x)] =7x+1
c. (fog)(4)=7(4)+7=28+7=35
d. (gof)(4)= 7(4)+1=28+1=29
(fog)(x)
f(g(x))f(x+1)7x+7(gof)(x)
g(f(x))g(7x)7x+1(fog)(4)
7(4)+735(gof)(4)
7(4)+129Solve the following system using the algebraic method of substitution. Verify your solution.
x + 2y = -5
3x - y = -1
Solve the following linear system using the algebraic method of elimination. Verify your solution.
x + 2y = 2
3x + 5y = 4
I've done it on the attached pages.
I hope this helps you...
In one afternoon's shopping Seedevi spent half as much money as Georgia, but $6 more than Amy. If the three of them spent a total of $258, how much did Seedevi spend?
The amount spent by Seedevi is $66
How to determine the amount spent by Seedevi?From the question, the given parameters are:
Seedevi = half as much money as Georgia,
Seedevi = $6 more than Amy
The three of them = $258
To solve this question, we use the following representations
x = Seedevi
y = Georgia
z = Amy
So, we have the following equations
x = 0.5y
x = 6 + z
x + y + z = 258
Make y and z the subjects
y = 2x
z = x - 6
Substitute y = 2x and z = x - 6 in x + y + z = 258
x + 2x + x - 6 = 258
Evaluate the like terms
4x = 264
Divide by 4
x = 66
Hence, the amount spent by Seedevi is $66
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Answer this question please
NO FAKE ANSWERS OR I WILL REPORT
Answer:
D
Step-by-step explanation:
the figure is composed of a rectangle and a right triangle ( top )
calculate the hypotenuse h of the right triangle using Pythagoras' identity
h² = 6² + 8² = 36 + 64 = 100 ( take square root of both sides )
h = [tex]\sqrt{100}[/tex] = 10
the base of the rectangle is equal to h , then perimeter (P) of pentagon is
P = 10 + 4 + 6 + 8 + 4 = 32 cm
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
What does the problem want:
⇒ the dimensions or the perimeter of the pentagon
What information do we need to find the perimeter:
⇒ the unknown side length
Let's find the unknown side length:
[tex]\hookrightarrow \text{split the pentagon into two shapes as shown in the image below}\\\hookrightarrow \text{the hypotenuse of the right triangle is equal to the length of the unknown side}\\\hookrightarrow\text{hypotenuse}=\sqrt{6^2+8^2}= \sqrt{36+64}=\sqrt{100}=10\\[/tex][tex]\hookrightarrow \text{the unknown side length is 10}[/tex]
Perimeter = 6 + 8 + 4 + 4 + 10 = 32
Answer: 32 or (D)
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Triangle X Y Z is shown. Angle X Z Y is a right angle. The length of Z X is b, the length of Z Y is a, and the length of hypotenuse X Y is c.
Given right triangle XYZ, which correctly describes the locations of the sides in relation to ∠Y?
In triangle XYZ, angle X Z Y is a right angle. The length of Z X is b, the length of Z Y is a, and the length of hypotenuse X Y is c. Then, the side XZ which is the perpendicular, is opposite to ∠Y. Side XZ is adjacent to the ∠Y, and side ZY, which is the base, is also adjacent to ∠Y. We can say that ∠Y has been formed by the sides XZ and ZY.
It is given that,
In triangle X Y Z, angle X Z Y is a right angle or 90°.
The length of the hypotenuse XY is c.
⇒ The side with length c is adjacent to ∠Y.
The sides XZ and ZY form the right angle, thus one is base and the other is perpendicular.
Now, in relation to ∠Y, side ZY of length a is the base (adjacent to angle Y)
Similarly, side XZ of length b forms the perpendicular and is opposite to ∠Y.
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id love the help! (im not great at math)
Answer:
Area = 113.04 in^2
Step-by-step explanation:
you have the diameter which is twice the radius, the formula is in the question:
Area = πr^2
so
12: 2 = 6 (RADIUS)
Area = π6 ^ 2 =
Area = π 36 in^2
Area = 3.14 * 36
Area = 113.04 in^2
Marta’s mother shared a funny video of their cat on the Internet. The total number of people who had viewed the video over the first 30 days could be modeled using the function f(x) = 33(1.3)x where x is the number of days the video has been online.
About how many people had viewed the video once it had been online for 20 days?
190
858
6,271
86,460
The number of people that have watched the video is 858 people
What is a function?A function is a mathematic rule. We know that a function shows the rule that is to be carried out and is often written in the form of an equation.
Now we have the function shown as; f(x) = 33(1.3)x. Since we know that the term x is referred as the number of days the video has been online.
Thus, f(x) = 33(1.3)(20) thus we can now say that the number of people who have vied the video in twenty days is 858 people.
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Answer: the answer is B or 858
Step-by-step explanation: The answer is B or 858
3
Anastacio distributed 4 4/5 kg of seed among several bird feeders. He put = 3/5 kg of seed in each
feeder. Let f represent the number of bird feeders that Anastacio filled.
Select 1 multiplication and 1 division equation to represent the relationship.
Choose 2 answers:
ƒx3/5=4 4/5
fx 4 4/5=3/5
3/5 divided 4 4/5=f
4 4/5 divided 3/5 =f
The equations to represent the relationship are ƒx3/5=4 4/5 and 4 4/5 divided 3/5 =f
Ratio and proportionFractions are written as a ratio of two integers. For instance a/b is a fraction.
If Anastacio distributed 4 4/5 kg of seed among several bird feeders and put 3/5 kg of seed in each feeder, the expression that represents the number of bird feeders that Anastacio filled is given as;
Number of bird feeder = 4 4/5 ÷ 3/5
f = 4 4/5 ÷ 3/5
Multiply both sides by
f * 3/5 = 4 4/5 ÷ 3/5 * 3/5
f * 3/5 = 4 4/5
Hence the equations to represent the relationship are ƒx3/5=4 4/5 and 4 4/5 divided 3/5 =f
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-7(-w-1)-2 simplest form
Suppose thirteen people qualify for a college cheerleading squad, eight are men and 5 are women. If a 6 member squad is selected, what is the probability that the squad will have exactly two male members.
The probability that the squad will have exactly two male members is; 0.0816
How to solve probability combinations?We are given;
Total number of people in cheerleading squad = 13
Number of Men = 8
Number of Women = 5
We are told that a 6 member squad is selected and now we want to find the probability that the squad will have exactly two male members.
Thus;
P(exactly 2 male members) = (8C2 * 5C4)/(13C6)
P(exactly 2 male members) = 140/1716
P(exactly 2 male members) = 0.0816
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What does the point (1, 2) represent? parking costs $1 per hour for the entire day. parking costs $2 per hour for the entire day. the total cost of 2 hours of parking is $1. the total cost of 1 hour of parking is $2.
The point which is indicated in the task content; (1, 2) represents; parking costs $2 per hour for the entire day.
What is the interpretation of the point given in the task content; (1,2)?
It follows from convention that the coordinate systems are structured such that the independent variable, x be placed 1st and the dependent variable, y be placed second.
Consequently, since the cost of parking is dependent on the time for which the car is parked, then, it represents parking costs 2 per hour for the entire day.
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Simplify.
2[(8 ÷ 4)-(-5)] + 6
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Equation:}[/tex]
[tex]\mathsf{2[(8 \div 4)-(-5)] + 6}[/tex]
[tex]\huge\textsf{Solving:}[/tex]
[tex]\mathsf{2[(8 \div 4)-(-5)] + 6}[/tex]
[tex]\mathsf{= 2[((2 - (-5)] + 6}[/tex]
[tex]\mathsf{= 2(7) + 6}[/tex]
[tex]\mathsf{= 2 \times 7 + 6}[/tex]
[tex]\mathsf{= 14 + 6}[/tex]
[tex]\mathsf{= 20}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{20}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:▪ [tex] \sf{2[(8 ÷ 4)-(-5)] + 6}[/tex]
First, we will start with the division:
[tex]\longrightarrow \sf{2[(2) − (−5)] +6}[/tex]
Now we will resolve what is inside the bracket:
[tex]\longrightarrow \sf{2[2+5] +6}[/tex]
[tex]\longrightarrow \sf{2 \times 7 +6}[/tex]
Now we will solve the multiplication:
[tex]\longrightarrow \sf{14 +6= 20}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex] \bm{2[(8 ÷ 4)-(-5)] + 6 = \boxed{\bm {20}}}[/tex]
What is the following simplified product? Assume x greater-than-or-equal-to 0 2 StartRoot 8 x cubed EndRoot (3 StartRoot 10 x Superscript 4 Baseline EndRoot minus x StartRoot 5 x squared EndRoot)
24 x cubed StartRoot 5 x EndRoot minus 4 x squared StartRoot 10 x EndRoot
24 x cubed StartRoot 5 x EndRoot minus 4 x cubed StartRoot 10 x EndRoot
24 x cubed StartRoot 5 EndRoot minus 4 x cubed StartRoot 10 x EndRoot
24 x cubed StartRoot 5 x EndRoot + 4 x cubed StartRoot 10 x EndRoot
The simplified expression of 2√8x³(3√10x⁴ - x√5x²) is 24x³√5x - 4x³√10x
How to determine the simplified product?The complete question is added as an attachment
From the attached figure, the product expression is:
2√8x³(3√10x⁴ - x√5x²)
Evaluate the exponents
2√8x³(3√10x⁴ - x√5x²) = 2 *2x√2x(3x²√10 - x²√5)
Evaluate the products
2√8x³(3√10x⁴ - x√5x²) = 4x√2x(3x²√10 - x²√5)
Open the bracket
2√8x³(3√10x⁴ - x√5x²) = 12x³√20x - 4x³√10x
Evaluate the exponents
2√8x³(3√10x⁴ - x√5x²) = 24x³√5x - 4x³√10x
Hence, the simplified expression of 2√8x³(3√10x⁴ - x√5x²) is 24x³√5x - 4x³√10x
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Answer:
Second option
Step-by-step explanation:
edge
Marty went on a bike ride to the store 8 miles away. If it
took Marty 3/4 of an hour to get there and 1/2 of an hour
to get back, what was his average rate of speed (miles
per hour) for the entire trip?
His average rate of speed for the entire trip is 12.8 miles per hour.
How do you calculate the average rate of speed?The most popular formula for calculating average speed is the distance traveled divided by the time taken.If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time.The overall distance the object covers in a given time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.Average speed is a scalar quantity defined as the average distance traveled by the body in the total amount of time. It measures in m/s.Marty's speed is =V
[tex]\frac{3}{4} V+\frac{1}{2} V=8*2[/tex]
[tex]\frac{5}{4} V=16[/tex]
[tex]V=12.8[/tex]
The average rate of speed for the entire trip is 12.8 miles per hour.
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Express graph in slope intercept form
Answer:
2/6
Step-by-step explanation:
Count up and over going from one point to the next and you get slope intercept. This one is up 2 over 6
Answer:
y = 1/3x - 3
Step-by-step explanation:
Slope-intercept form follows the format y = mx + b, where m is the slope of the line, and b is the y-intercept.
First let's find the slope. The slope is the amount the graph rises/runs. From point (0,-3), it rises by 1, and runs to the right by 3 where it meets the next point on the graph, meaning that the slope is 1/3.
Now, let's find the y-intercept. The y-intercept is the point on the graph where the line touches the y-axis. In this line, we can clearly see that the line touches (0,-3), therefore, the y-intercept is -3.
Using this information, we can construct the equation y = 1/3x - 3
a writer wrote 10,010 words for his book on the first day of writing. he wrote 9,760 words on the second day, 9,510 words on the third day, and continued this way in an arithmetic sequence. write an explicit rule showing the equation for the number of words the writer would write on the 14th day, and solve.
Answer:
rule: an = 10010 -250(n -1)day 14: 6760 wordsStep-by-step explanation:
The first three terms of the arithmetic sequence for the number of words written are 10010, 9760, 9510. These have a common difference of 9760-10010 = -250. The first term and common difference can be used to make the explicit equation for the words written on the n-th day.
Formula for Arithmetic SequenceThe explicit formula for the n-th term of an arithmetic sequence with first term a₁ and common difference d is ...
[tex]a_n=a_1+d(n-1)[/tex]
ApplicationFor first term a₁ = 10010 and common difference d = -250, the explicit rule is ...
[tex]a_n=10010-250(n-1)[/tex]
On day 14, n=14, and the number of words written is ...
[tex]a_{14}=10010-250(14-1)\\\\a_{14}=10010-250(13)=10010-3250\\\\a_{14}=6760[/tex]
The writer would write 6760 words on the 14th day.
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
-3
Step-by-step explanation:
(-3, -1), (-5, 5)
Each point is (x, y).
slope = (difference in y)/(difference in x)
slope = (-1 - 5)/(-3 - (-5)) = -6/(-3 + 5) = -6/2 = -3
The slope is -3