If a rock released with an initial velocity = u
If it falls under gravity 'g' for 't' seconds,
Expression to find the distance covered will be,
[tex]y=ut+\frac{1}{2}t^2[/tex]
If the initial velocity is zero expression for the distance covered will be,
[tex]y=\frac{1}{2}gt^2[/tex]
Here, g = Gravitational pull Or acceleration due to gravity
A). If the distance covered 'y' = 20 m
And t = 4 seconds
By substituting these values in the expression,
[tex]20=\frac{1}{2}g(4)^2[/tex]
[tex]20=8g[/tex]
[tex]g=2.5[/tex] m per sec square
B). Average velocity of a free falling body = [tex]\frac{\text{Initial velocity}+\text{Final velocity}}{2}[/tex]
Initial velocity of the object = 0
Final velocity = [tex]g\times t[/tex]
= [tex]2.5\times 4[/tex]
= [tex]10[/tex] meter per sec.
Therefore, average velocity = [tex]\frac{0+10}{2}[/tex]
= [tex]5[/tex] meter per second
C). Since, the rock hits the bottom after [tex]4[/tex] seconds,
Velocity with which the rock will hit the ground [tex]=gt[/tex]
[tex]=10[/tex] m per sec.
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Solve 3x − x + 2 = 12.
2x=12_2 2x=10 x=5 that answer
A woman stands on a mountain at 8,000 feet above sea level. A man stands in a valley at 400 feet below sea level. What equation shows the difference in their elevations?
8,000 + (-400) =
8,000 - 400 =
8,000 - (-400) =
-8,000 - 400 =
Answer:
8,000 - (-400)
Step-by-step explanation:
Answer: 8,000 - (-400) =
Step-by-step explanation:
what is six over seven times two and three over fourteen?
and seven is equal to six times a number.
Word problems can be tricky no matter what level of math or science you are in.
First look at the question for words that indicate mathematical symbols.
"times" indicates multiplication
"and" indicates addition
"a number" means we have a variable, x, to solve for
Now we can go from left to right and write it in a mathematical equation
7x + 7 = 6x
Then, solve for x
7x + 7 = 6x
7 = 6x - 7x
7 = -1x
7/-1 = x
x = -7
Finally, we check our work.
7x + 7 = 6x
7(-7) + 7 = 6(-7)
-49 + 7 = -42
-42 = -42 √
The answer is x = -7
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Parviz F. answered • 02/11/14
TUTOR
4.8 (4)
Mathematics professor at Community Colleges
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First thing you do in word problems : choose a variable for unknown, what problem is asked you to find.
n the number
7n 7 times the number
7n + 7 7 times the number and 7
Then the problem says it is equal 6n , make the equation
7n + 7 = 6n
and solve:
7n - 6n = -7
n = -7 / is the answer
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KERITHA C. answered • 02/25/18
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If 1 is added to seven times a number, the result is equal to 2 more than six times the number. Find the number.
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Rodney S. answered • 02/16/14
TUTOR
5 (3)
Certified Math Teacher (Grades 6 and Up) for Hire
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Seven times a number and seven is equal to six times a number.
Step 1: Translate the verbal to Algebra.
7x + 7 = 6x. ("And" means addition if no other operation is present.)
Step 2: Solve for x.
7x - 6x + 7 = 6x - 6x. (subtract 6x from both sides)
1x + 7 = 0. (Simplify)
1x + 7 - 7 = 0 - 7. (subtract 7 from both sides)
1x = -7. (Simplify)
1x/1 = -7/1. (Divide both sides by 1)
x = -7. (Simplify)
Step 3: Check 7 times the number -7 and 7 is equal to six times the number -7.
7(-7) + 7 = 6(-7)
-49 + 7 = -42
-42 = -42. (Both sides are equal!)
The number again is -7.
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Vivian L. answered • 02/10/14
TUTOR
3 (1)
Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACH
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Hi Alyson;
7x+7=6x
Let's subtract 7x from both sides...
7x+7-7x=6x-7x
7=-x
Let's multiply both sides by -1...
(-1)(7)=(-1)(-x)
-7=x
Let's check our work...
7x+7=6x
[(7)(-7)]+7=(6)(-7)
-49+7=-42
-42=-42
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express each of the following in standard form 0.000000000221
Answer:
[tex]2.21 \times {10}^{ - 10} [/tex]
Step-by-step explanation:
When we shift (.) from left to right in scientific notarion, the power of 10 varies in negative numbers according to how many numbers we shift.
Refer to the number line. Find the coordinate of point H that is 1/5 of the distance from C to F.
A B C
DEF
-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7
Number lines are used to represent numbers on a line at regular intervals. The coordinate of point H is -2.2
From the number line, we have:
[tex]C = -4[/tex]
[tex]F = 5[/tex]
First, we calculate the distance between C and F using absolute functions
[tex]CF = |C - F|[/tex]
[tex]CF = |-4- 5|[/tex]
[tex]CF = |-9|[/tex]
Remove absolute bracket
[tex]CF = 9[/tex]
Point H is [tex]\frac 15[/tex] of the distance so, we have:
[tex]H = \frac 15 CF[/tex]
[tex]H = \frac 15 \times 9[/tex]
[tex]H = 1.8[/tex]
This means that point H is 1.8 from the right of C.
So, the coordinate of H is:
[tex]H = C + 1.8[/tex]
[tex]H = -4 + 1.8[/tex]
[tex]H = -2.2[/tex]
Hence, the coordinate of point H is -2.2
Read more about number lines at:
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A sailboat travels a distance of miles in of an hour. Which complex fraction represents the unit rate in miles per hour?
Answer: I think its D and A
Step-by-step explanation:
Answer:
im pretty sure its D and also A
Step-by-step explanation:
Show work please
[tex] \sqrt{ \frac{45}{5} } [/tex]
Answer: 3
Step-by-step explanation:
[tex]\sqrt{ \dfrac{45}{5}} =\sqrt{9}=\bold3[/tex]
Answer:
3
Step-by-step explanation:
We don't really need to simplify this, but if you do:
45/5 is the same as 45 ÷ 5 so
45/5 = 9
Now we have to find the square root of 45/5(or 9). The square root of a number(x for example) is the number(y) that multiplied by itself once will equal x or y · y = x.
For this you can use a calculator:
[tex]\sqrt{\frac{45}{5} }[/tex] = 3
or
[tex]\sqrt{9}[/tex] = 3
Look below :)
Everything is underneath, ty. Just need an answer by Wednesday
Answer:
Step-by-step explanation:
[tex]\dfrac{3}{6}=\dfrac{9}{18}=\dfrac{27}{54}[/tex]
[tex]\dfrac{3*3}{6*3}=\dfrac{9}{18}\\\\\\\dfrac{3*9}{6*9}=\dfrac{27}{54}[/tex]
What is the slope of the given graph?
Answer:
Looks like it's 1.
Step-by-step explanation:
Since it is a positive slope and it goes up 1 unit, the slope is 1.
Multiply and simplify completely:
(3x + 5) (2x2 – 3x + 2)
Show all work for full credit.
Answer:
[tex](3x + 5)(2 {x}^{2} - 3x + 2) \\ \\ (3x)(2 {x}^{2} - 3x + 2) + (5)(2 {x}^{2} - 3x + 2) \\ \\ 6 {x}^{3} - 9 {x}^{2} + 6x + 10 {x}^{2} - 15x + 10 \\ \\ = 6 {x}^{3} + {x}^{2} - 9x + 10[/tex]
I hope I helped you^_^
Answer:
[tex]6x^3+x^2-9x+10[/tex]
Step-by-step explanation:
[tex](3x+5)(2x^2 - 3x+2)[/tex]
Distribute
[tex]3x(2x^2-3x+2)+5(2x^2-3x+2)[/tex]
Distribute
[tex]6x^3-9x^2+6x+5(2x^2-3x+2)[/tex]
Distribute again
[tex]6x^3-9x^2+6x+10x^2-15x+10[/tex]
Combine like terms
[tex]6x^3+1x^2+6x-15x+10[/tex]
Multiply by 1
[tex]6x^3+x^2+6x-15x+10[/tex]
Combine like terms
[tex]6x^3+x^2-9x+10[/tex]
Amy owes her mother $76. She pays her mother $14 on Sunday and $24 on Monday. Use an expression to describe the situation. How much does Amy still owe her mother?
Answer:
Amy still owes her mother $38.
Step-by-step explanation:
76 - 14 - 24
76 - 14 = 62
62 - 24 = 38
18
A company is expanding its building area from 16,500 square feet to 22,605 square feet. What is the percentage increase of the
area of the building space?
the answer is 37%
: 16500*37%= 6150
6150+16500=22605 :correct
Cuantos gramos de grasas saturadas hay en 100 g de leche entera en polvo?
Answer: Well 100g is 100 grams so 100 grams?
Step-by-step explanation:
Amaya wants to jog 8 Miles this week she has jog 2 1/2 miles on Monday and 3 2/5 miles on Wednesday how many miles does amaya still need to jog to meet her goal
Answer:
2 1/10 miles.
Step-by-step explanation:
She has already jogged 2 1/2 + 3 2/5 miles. This is 2 5/10 + 3 4/10 or 5 9/10. 8 miles is also equal to 7 10/10 miles. So, to find the remaining amount of miles, we can do 7 10/10 - 5 9/10 = 2 1/10.
Amaya still needs 2.1 miles to jog to meet her goal.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
Operators who let do basic mathematical calculations.
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
Given that this week she has jog 2 1/2 miles on Monday and 3 2/5 miles on Wednesday
She has already jogged 2 1/2 + 3 2/5 miles.
⇒ [tex]2\dfrac{1}{2} + 3\dfrac{2}{5} = \dfrac{5}{2} + \dfrac{17}{5}[/tex]
Convert fractions into decimals,
⇒ 2.5+3.4
Apply the arithmetic operation,
⇒ 5.9
So, to find the remaining amount of miles,
⇒ 8 -5.9 = 2.1
Hence, Amaya still needs 2.1 miles to jog to meet her goal.
Learn more about Arithmetic operations here:
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Only answer number 37.
Step-by-step explanation:
Use the distance formula:
(x2, y2) with (x1, y1)
[tex] d \: = \sqrt{( x2 \: - \: x1) {}^{2} \: + \: (y2 \: - \: y1) {}^{2} } [/tex]
Find the lengths of each segment one at a time.
For AC:
A(-3,8) C(0,2)
[tex]d = \sqrt{( - 3 - 0) {}^{2} + (8 - 2) {}^{2} } [/tex]
[tex]d \: = \sqrt{9 + 36} [/tex]
[tex]d \: = \sqrt{45} = 3 \sqrt{5} [/tex]
For BC:
B(6,5) C(0,2)
[tex]d \: = \sqrt{(6 - 0) ^{2} + (5 - 2) {}^{2} } [/tex]
[tex]d \: = \sqrt{36 + 9} [/tex]
[tex]d \: = \sqrt{45} = 3 \sqrt{5} [/tex]
For CD:
C(0,2) D(2,-4)
[tex]d \: = \sqrt{(0 - 2) {}^{2} + (2 - ( - 4)) {}^{2} } [/tex]
[tex]d \: = \sqrt{4 + 36} [/tex]
[tex]d \: = \sqrt{40} = 2 \sqrt{10} [/tex]
With all the segment lengths found, we can conclude that segments AC and BC have the same lengths.
The size of a population of fish in a pond is modeled by the function P, where P(t) gives the number of fish and t gives the number of years after the first year of introduction of the fish to the pond for 0≤t≤10. The graph of the function P and the line tangent to P at t=4 are shown above. Which of the following gives the best estimate for the instantaneous rate of change of P at t=4 ?
The slope (m) will be "279.33". A further solution to the question is provided below.
At one moment this same instantaneous modification rate would be the same with the functionality derivative assessed somewhere at the time. In certain other terms, the pitch of such tangent line towards the curvature is somewhere at a level equivalent to that as well.
According to the question,
(x₁, y₁) = (3, 0)(x₂, y₂) = (6, 838)As we know,
⇒ [tex]Slope (m) = \frac{y_2-y_1}{x_2-x_1}[/tex]
By substituting the values, we get
⇒ [tex]=\frac{838-0}{6-3}[/tex]
⇒ [tex]=\frac{838}{3}[/tex]
⇒ [tex]=279.33[/tex]
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The instantaneous rate of change is the rate of change at a particular point or instant in the graph. The instantaneous rate of change of P at [tex]t=4[/tex] is 250
I've added as an attachment, the graph that represents the population of the fish.
To determine the instantaneous rate of change at [tex]t=4[/tex], we simply calculate the slope (m) of the tangent line using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Because of the scale of the graph, I will use the following estimated points from the tangent line
[tex](x_1,y_1) = (3,0)[/tex]
[tex](x_2,y_2) = (4,250)[/tex]
So, the slope is:
[tex]m = \frac{250 - 0}{4 - 3}[/tex]
[tex]m = \frac{250}{1}[/tex]
[tex]m = 250[/tex]
Hence, the instantaneous rate of change of P at [tex]t=4[/tex] is 250
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Which represents a unit rate ?
A. The cost of cat food is $36 per 3 bags
B. The cost of orange juice is $3 per jug
C. The cost of photocopies is $1 per 10 pages
D. The cost of roses is $50 per 2 dozen
B. The cost of orange juice is $3 per jug
A unit rate, in terms of mathematics, is a rate per unit.
Examples of unit rates are:
The car travels 25 km per hour
The cost of bags of apples is $6.00 per bag of apples.
The unit rate in these choices is Choice B:
The cost of orange juice is $3 per jug
The other choices are rates, not unit rates.
note that one movable point always defines an extremum point
Answer:
And
Step-by-step explanation:
Noted Sir. Thanks A Lot 2 U
Quick please I really need this
Answer:
y = 39
Step-by-step explanation:
550 x [tex]\pi[/tex] = [tex]\pi[/tex] [tex]r^{2}[/tex] x 11 + y
550 x [tex]\frac{7}{22}[/tex] = [tex]\frac{7}{22}[/tex] x 11 x 11 + y
550 x [tex]\frac{7}{22}[/tex] x [tex]\frac{22}{7}[/tex] = 11 x 11 + y
550 = 11 x 11 + y
[tex]\frac{550}{11}[/tex] = [tex]\frac{11}{11}[/tex] x 11 + y
50 = 11 + y
50 - 11 = y
39 = y
IF A= { a, b, c d and B={a,b,c,d}
how can I solve this
Answer:
what we have to prove or equation ?
C. Find the equation of the line perpendicular to
y = 14x-5 and passing through (2,-3).
Answer:
[tex]y = -4x + 5[/tex]
Step-by-step explanation:
We want to find the equation of the line that is perpendicular to:
[tex]\displaystyle y = \frac{1}{4} x - 5[/tex]
And which passes through the point (2, -3).
Recall that the slopes of perpendicular lines are negative reciprocals of each other.
In other words, since the slope of the original line is 1/4, the slope of the perpendicular line will be -4.
We are also given that it passes through the point (2, -3). Hence, we can consider using the point-slope form:
[tex]\displaystyle y - y_1 = m(x- x_1)[/tex]
Substitute:
[tex]\displaystyle y - (-3) = -4 (x - (2))[/tex]
Simplify:
[tex]y + 3 = -4(x - 2)[/tex][tex]y = -4x + 5[/tex]
Distribute:
[tex]y + 3 = -4x +8[/tex]
And subtract:
[tex]y = -4x + 5[/tex]
In conclusion, our equation is:
[tex]y = -4x + 5[/tex]
A rectangle has perimeter 56 cm and length 21 cm. What is its width?
hhhhhhhhhhh
Answer:
width=7 cm
Step-by-step explanation:
perimeter=2(lengths+width)
56 =2(21+x)
56 =42+2x
56-42 =2x
2x = 14
x =7
therefore the width=7 cm
2= 2.27- m/4
How do I do this?! I need this for mathematics homework!
Answer:
1.08 = m
Step-by-step explanation:
2= 2.27- m/4
Subtract 2.27 from each side
2-2.27= 2.27-2.27- m/4
-.27 = -m/4
Multiply each side by -4
-.27 * -4 = -m/4 *-4
1.08 = m
factorize the following questions
1. a^8-b^8
2. 32y^4 - 162
Answer:
1. [tex]2(16 {y}^{4} - 81)[/tex]
2. [tex]2(2y - 3) \times (2y + 3) \times (4 {y}^{2} + 9)[/tex]
Step-by-step explanation:
1. [tex] a^{8} - {b}^{8} [/tex]
➡️ [tex]( {a}^{4} - {b}^{4} ) \times ( {a}^{4} + {b}^{4} )[/tex]
➡️ [tex]( {a}^{2} - {b}^{2} ) \times ( {a}^{2} + {b}^{2} ) \times ( {a}^{4} + {b}^{4} )[/tex]
➡️ [tex](a - b) \times (a + b) \times ( {a}^{2} + {b}^{2} ) \times ( {a}^{4} + {b}^{4} )[/tex]
➡️ [tex]2(16 {y}^{4} - 81)[/tex] ✅
---------------------------------------------------
2. [tex] 32 {y}^{4} - 162[/tex]
➡️ [tex] 2(16y^{4} - 81)[/tex]
➡️ [tex]2(4 {y}^{2} - 9) \times (4 {y}^{2} + 9)[/tex]
➡️ [tex]2(2y - 3) \times (2y + 3) \times (4 {y}^{2} + 9)[/tex] ✅
93. Let f(x) = 3x - 1 and g(x) = x + 5. Evaluate the following limits. (a) lim x→3 f(g(x)]
(b) lim x→3 g[f(x)]
Answer:
a) 23 and b) 13
Step-by-step explanation:
I. If f(g(x)) is composit function
Find fog and gof
fog = 3(g) - 1
= 3(x+5) -1
= 3x + 15 -1
= 3x + 14
gof = (f) + 5
= (3x - 1) +5
= 3x + 4
II. Fill in a) and b) question
lim x -> 3 fog
= 3(x) + 14
= 3(3) + 14
= 9 + 14
a) = 23
lim x-> 3 gof
= 3x + 4
= 3(3) + 4
= 9 + 4
b) = 13
Got more question or something to discuss, leave comment below
Combine the like terms to create an equivalent expression for −5j+(−2j)+3
Answer:
-7j + 3
Step-by-step explanation:
Combine like terms:
-5j + (-2j) = -7j
-7j + 3
Answer and Step-by-step explanation:
Simply combine the values together.
-5j - 2j + 3
-7j + 3 is the answer.
#teamtrees #PAW (Plant And Water)
I hope this helps!
A(-2,3)
Triangle ABC has vertices at A(-2,3), B(-3,6), and
C(2,-1) Is triangle ABC a night triangle? If so, which
angle is the night angle?
O No, the triangle has no right angles.
O Yes, the right angle is angle A
O Yes, the right angle is angle B
O Yes, the right angle is angle C
VA
C (2-1)
B (-3,-6)
second choice i’m prolly wrong
A boy is 12 years old his mother is four times as old as he is in x years time the mother will be three times as old as. the son form an equation in x and hence find x
plzzzzzzz help
Answer:
age of boy = 12
age of mother = 4 times age of boy = 4*12 = 48
let x = years time
3(12+x) = 48+x
36+3x = 48+x
3x-x = 48-36
2x = 12
x = 6
In 6 years time the mother will be three times as old as the son.
pleasexmark me as brainlist
PLS HELP WILL MARK AS BRAINLIEST
Answer:
SEE THE IMAGE FOR SOLUTION .
HAVE A GREAT DAY
Answer:
11. D
12. C
13. D
14. B
15. E
Step-by-step explanation:
11.
1/3 + 1/2 = 2/6 + 3/6 = 5/6
A is 3/4
B is 2/3
C is 9/10
D is 4/5
E is 2/5
the closest to 5/6 is 4/5.
12.
this is totally easy. just simply additions and one subtraction (to see what is left).
8+10+9 = 27
so, he has
60 - 27 = 33 hours left
13.
the mean value of a series of equal weighted numbers is simply their sum divided by the amount of numbers.
so,
(2+5+3+6+4)/5 = 20/5 = 4
14.
a scale factor is always applied to all dimensions, otherwise the result will be distorted. and that would be especially bad for a map.
so, clearly the width of the larger map is 3 times the width of the smaller map. therefore, the length of the larger map has to be also 3 fine the length of the smaller map.
3×6 = 18
15.
3t - 10 = 8
3t = 18
t = 6
what is the constant of the proportionality in the equation y = 7x
Answer:
7
Step-by-step explanation:
The equation of direction variation is
y = kx where k is the constant of variation
y = 7x so 7 is the constant of variation
Answer:
7
Step-by-step explanation:
The equation of direction variation:-
y = kx where k is the constant of variation -> Eq 1
y = 7x -> Eq 2
Comparing Eq 1 and Eq 2,
k=7