Answers
Answer:
The aircraft has a height of 1000 m at t=2 sec, and at t=8 sec
Step-by-step explanation:
Finding Exact Roots Of Polynomials
A polynomial can be expressed in the general form
[tex]\displaystyle p(x)=a_nx^n+a_{n-1}\ x^{n-1}+...+a_1\ x+a_0}[/tex]
The roots of the polynomial are the values of x for which
[tex]P(x)=0[/tex]
Finding the roots is not an easy task and trying to find a general solution has been discussed for centuries. One of the best possible approaches is trying to factor the polynomial. It requires a good eye and experience, but it gives excellent results.
The function for the trajectory of an aircraft is given by
[tex]\displaystyle h(x)=0.5(-t^4+10t^3-216t^2+2000t-1200)[/tex]
We need to find the values of t that make H=1000, that is
[tex]\displaystyle 0.5(-t^4+10t^3-216t^2+2000t-1200)=1000[/tex]
Dividing by -0.5
[tex]\displaystyle t^4-10t^3+216t^2-2000t+1200=-2000[/tex]
Rearranging, we set up the equation to solve
[tex]\displaystyle t^4-10t^3+216t^2-2000t+3200=0[/tex]
Expanding some terms
[tex]\displaystyle t^4-8t^3-2t^3+200t^2+16t^2-1600t-400t+3200=0[/tex]
Rearranging
[tex]\displaystyle t^4-8t^3+200t^2-1600t-2t^3+16t^2-400t+3200=0[/tex]
Factoring
[tex]\displaystyle t(t^3-8t^2+200t-1600)-2(t^3-8t^2+200t-1600)=0[/tex]
[tex]\displaystyle (t-2)(t^3-8t^2+200t-1600)=0[/tex]
This produces our first root t=2. Now let's factor the remaining polynomial
[tex]\displaystyle t^2(t-8)+200(t-8)=0[/tex]
[tex]\displaystyle (t^2+200)(t-8)=0[/tex]
This gives us the second real root t=8. The other two roots are not real numbers, so we only keep two solutions
[tex]\displaystyle t=2,\ t=8[/tex]
Related Questions
9.
A wholesaler buys pairs of sunglasses
for $5.50 each. He then marks up the
wholesale cost 80% to create a retail
price for his customers. Customers must
then pay an additional 7% tax on the
retail price. What is the total cost of a
pair of sunglasses to the wholesaler's
customers, including tax, rounded to
the nearest penny?
Answers
A customer will pay $10.59, including sales tax, for a pair of sunglasses.
Step-by-step explanation:
Given,
Purchase price of sunglasses = $5.50
Mark up = 80%
Amount of mark up = 80% of purchase price
Amount of mark up = [tex]\frac{80}{100}*5.50=0.80*5.50[/tex]
Amount of mark up = $4.40
Retail price = Purchase price+mark up
Retail price = 5.50+4.40 = $9.90
Sales tax = 7% of retail price
Sales tax = [tex]\frac{7}{100}*9.90=0.07*9.90[/tex]
Sales tax = $0.69
Total paid by customer = retail price + sales tax
Total paid by customer = 9.90 + 0.69 = $10.59
A customer will pay $10.59, including sales tax, for a pair of sunglasses.
Keywords: addition, percentage
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PLEASE SOLVE THE QUESTION BELOW
Answers
Answer:
There are 4 chairs in one row.
Step-by-step explanation:
Let [tex]$ x $[/tex] be the number of chairs in one row.
That is the length of one row.
Now, from the given data, three rows of length 3x can be formed with one chair left.
Or, if 15 extra chairs given, we can form 7 rows of the same length.
This means that there are [tex]$ 3x + 1 $[/tex] chairs in the first case. And since with 15 extra chairs we can form 7 rows, the equation would be
[tex]$ (3x + 1) + 15 = 7x $[/tex]
Solving this for '[tex]$ x $[/tex]', we get:
[tex]$ 3x + 16 = 7x $[/tex]
[tex]$ \implies 4x = 16 $[/tex]
[tex]$ \implies x = 4 $[/tex]
Therefore, the length of each row is four.
That is, there are four chairs in one row.
Solve the following equation for x.
3x - (2x - 3) = 2x + 9
Answers
Let’s first rewrite the equation
3x-(2x-3)=2x+9
Now now distribute the -1•2x and the -1•-3
3x-2x+3=2x+9
Let’s now combine the like terms on the left side
x+3=2x+9
To get x alone on the left side, subtract it on both sides
3=x+9
To get your final answer, subtract 9 on both sides
-6=x
And that’s your answer for x! Hope this helps comment below for more questions :)
Answer:
x=-6
Step-by-step explanation:
3x-(2x-3)=2x+9
3x-2x+3=2x+9
x+3=2x+9
3=2x-x+9
3=x+9
x=3-9
x=-6
Can you spend 1/5 of his allowance on a movie 3/8 on snacks and 2/7 on games if his allowance was $20 how much did Ken have
Answers
For this case we assume that the initial amount of money is $20.
So:
[tex]\frac{1} {5}[/tex] of $20 in movies:[tex]\frac {1} {5} (20) = 4[/tex]
[tex]\frac {3} {8}[/tex] of $20 in snacks:[tex]\frac {3} {8} (20) = 7.5[/tex]
[tex]\frac {2} {7}[/tex] of $20 in games:[tex]\frac {2} {7} (20) = 5.71[/tex]
Adding we have:
[tex]4 + 7.5 + 5.71 = 17.21[/tex]
Ken has:
[tex]20-17.21 = 2.79[/tex]
Answer:
Ken can spend what he planned and he has $2.79 left.
This Christmas, your brother Jack will be 2 years from being twice as old as your sister Jen. The sum of Jacks age and three times Jen's age is 66. How old is Jen?
Answers
Age of Jen is 13.6 years old
Solution:
Let "x" be the age of Jack and "y" be the age of Jen
Given that This Christmas, your brother Jack will be 2 years from being twice as old as your sister Jen
The above sentence can be written mathematically as:
Jack age + 2 = twice of age of Jen
[tex]x + 2 = 2y\\\\x = 2y - 2---- eqn 1[/tex]
The sum of Jacks age and three times Jen's age is 66
Jack age + three times Jen age = 66
x + 3y = 66 ---- eqn 2
Substitute eqn 1 in eqn 2
2y - 2 + 3y = 66
5y - 2 = 66
5y = 68
y = 13.6Thus age of Jen is 13.6 years old
2(5x-1)-(2x-5) simplify
Answers
Answer:
c
Step-by-step explanation:
c
Answer:
Step-by-step explanation:
2(5x - 1) - (2x - 5) =
10x - 2 - 2x + 5 =
8x + 3 <===
In winter, a sporting good stores sells 5 times as many snowboards as it as it sells during summer the store sells 132 snowboards in the summer how many so much does a store sale in winter
Answers
Solve the problem.
5) The odds in favor of Carl beating his friend in a round of golf are 7:2. Find the probability that
Carl will beat his friend.
A)
Answers
Answer:
0.7
Step-by-step explanation:
Find Explanation attached
help pleaseeeeeeeeee
Answers
Answer: Area of Δ DUO = 12.0 square units.
Step-by-step explanation:
From the diagram, Δ DPA is a right angled triangle and right angled at P.
Therefore ∠D will be
Tan ∅° = PA/DP ie, opposite side all over the adjacent.
= 4.5/3.75
Tan∅° = 1.2
to calculate ∅°, we know find the inverse of Tan 1.2
∅ = Tan^-1 1 .2 from your log tables or calculator
∅° = 50.20°.
= 50°
Since line DR is ⊥ to line OP
∠ADR = 90° - 50°
= 40°.
From the diagram,
∠ADR = ∠UDR = 40°
Therefore,
∠ODU = 180 - ( 40 + 40 + 90 ) { Angle on a straight line }
= 180 - 170
= 10°
From Δ UDM , line MU is he height of the required Δ DUO whose area is to be determined.
Now find the height MU
Tan10.0° = MU/10, where MU is the opposite side and 10.0 is the adjacent from the diagram given.
MU = Tan10.0 x 10.0
= 0.1763 x 10.0
= 1.763
Therefore to calculate the area of Δ DUO
= 1/2 x base x height
= 1/2 x line OD x line MU
= 1/2 x 14.0 x 1.763
= 7 x 1.763
= 12.341
= 12.0 square units.
=
A group of 21 people need to take an
elevator to the top floor. They will go in
groups of seven. They are deciding who
will go in the first group.
Answers
Answer:
The numbers are 18, 22.5, and 13.5
Step-by-step explanation:
You first need to figure out what number you use to multiply to find your answer. I found 4.5
Now, multiply all numbers by 4.5
4 x 4.5 = 18
5 x 4.5 = 22.5
3 x 4.5 = 13.5
Step-by-step explanation:
The tens digit of a two-digit number is 3 less than the units digit. Find the original number, if the sum of that number and the number reversed is 143.
Answers
Let...
x=ones digit
x-3=tens digit
The number in terms of x would be...
10(x-3)+x = 11x-30
The number with its digits reversed would be...
10(x)+x-3 = 11x-3
And...
11x-30+11x-3=143 We can solve for x!
22x=176
x=8
The number would be 58.
answer: 58
The two digit number needed is valued 58.
Given that:
The tens of a two digit number = unit's digit - 3
Number reversed + The number itself = 143
Let the ones digit of that two digit number be x and the tens digit be y. Then by place value concept, we have:
[tex]10(y) + x[/tex]
Since the tens digit = unit digit - 3
Thus we have:
[tex]y = x - 3[/tex]
or the number is :
[tex]10(x-3) + x = 11x - 30[/tex]
Now sum of the number and the number reversed is 143, which means:
[tex]143 = 10(x) + (y) + 10(y) + x = 10x + (x-3) + 11x - 30\\143 = 22x - 3 - 30\\x = 8[/tex]
Thus, the number is [tex]10(x-3) + x = 50 + 8 = 58[/tex]
Thus, the two digit number needed is valued 58.
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Which situation is modeled by the equation 24 = 15x + 8?
Answers
Answer:
Exact form : x = 16/15
Decimal form : x=1.06666666666...
Mixed Number form : x=1 1/15
Step-by-step explanation: Move all term that don't contain x to rightside and solve.
Hope this helps you out.
Answer:
A classroom of 24 students will go on a field trip to a museum. Each student pays $8 to go. So far, 15 of the students have paid to go. How much money, x, will be collected from all 24 students?
Let b = 7
What is the value of the expression 4b2+b−5 ?
Answers
58.....2wt.r3y2teyt3y2.te.32ty.32tye.t32y.tey32t..enkuuhuh
1.What is the circumference of a circle with a diameter of 2.9 cm?
Use 3.14 for pi.
Enter your answer as a decimal in the box.
___ cm
------------------------------
2.What is the circumference of a circle with a radius of 7.9 inches?
Use 3.14 for pi.
Enter your answer as a decimal in the box.
____ in.
Answers
Answer:
(1) 9.106 cm
(2) 49.612 inches
Step-by-step explanation:
Answer:
1. C =9.106 cm 2.C =49.612 inches
Step-by-step explanation:
To solve these problems, we will follow the steps below;
First write down the formula for calculating the circumference of the circle
C= 2πr
where c is the circumference of the circle and r is the radius of the circle
1) From the question diameter = 2.9 cm, but radius is half of the diameter, this implies that radius = [tex]\frac{d}{2}[/tex]= [tex]\frac{2.9}{2}[/tex]=1.45 cm
We can now proceed to insert the values into the formula;
C= 2πr
= 2×3.14×1.45
=9.106 cm
C =9.106 cm
2) From the question, radius = 7.9 inches and π=3.14
We can now go ahead to insert the values into the formula C= 2πr
C = 2×3.14× 7.9
=49.612 inches
C =49.612 inches
Four speed skaters, Marco
Answers
Answer:
???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
Step-by-step explanation:
plz help I don't want to be awake the whole night
Answers
Answer:
Therefore
[tex]75\div 5 - [(9-7)\times 3 ]\times 2 = 3[/tex]
Step-by-step explanation:
To Find:
Value of expression
75 ÷ 5 - [( 9 - 7 ) × 3 ] × 2
Solution:
PEDMAS rule
It explains the order of operations to solve an expression.
According to Pedmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.),
then division, multiplication, addition and subtraction from left to right.
P - parenthesis
E- exponent
D/M - Div or Multiply which ever comes first
A/S - Add or Sub which ever comes first.
So first we will solve the Parenthesis we get
Step 1. Parenthesis operation
75 ÷ 5 - [( 2 ) × 3 ] × 2
Step 2. Parenthesis operation
[tex]75\div 5 - [(2)\times 3 ]\times 2[/tex]
Step 3. Division
[tex]15 - [6]\times 2[/tex]
Step 4. Multiplication
[tex]15 - 12[/tex]
Step 5. Subtraction
3
Therefore
[tex]75\div 5 - [(9-7)\times 3 ]\times 2 = 3[/tex]
come on somebody plz help
Answers
Answer:
A=πr^2 and A=πr'^2 by the definition of area
Grandma baked
96
cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received
c
cc fewer cookies than she would have received had all of the cookies been evenly divided among the
8 grandchildren.
Answers
Answer:
[tex]12-c[/tex] Cookies
Step-by-step explanation:
The question is to find how many cookies did Cindy receive (write as an expression)?
Total cookies baked = 96
If evenly divided among 8 grandchildren, each would get:
[tex]\frac{96}{8}=12[/tex]
Each grandchildren would have gotten 12 cookies
Now, Cindy received "c" fewer than this (12), so Cindy received:
12 - c Cookies
Cindy Received = 12 - c Cookies
Answer:
96/8 - c.
Step-by-step explanation:
She is divideing among the grandkids so it would be 98/8-c
Can u please help me wit these 2 please I don't get it...
Answers
Answer:
0,-9,-5
Step-by-step explanation:
Write as a mixed number:
25/3
Answers
Answer:
8 1/3
Step-by-step explanation:
To write an improper fraction as a mixed number,
we divide the denominator into the numerator.
My work is attached below.
how manet times dose 50 go into 1,000
Answers
Answer:
20 times
Step-by-step explanation:
1,000 divided by 50 will be 20 try using lone division :)
Answer:
20 times
Step-by-step explanat
Help pls multiply 3.96584 by 100
Answers
Answer:
396.584
Step-by-step explanation:
just move the decimal right 2 spaces when multiplying by 100
Answer:
396.584
Step-by-step explanation:
A line contains the points (4, 2) and (0, -1). What is the equation of the line? Show your work.
Answers
Answer:
[tex]\large\boxed{y=\dfrac{3}{4}x-1}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept (0, b)
We have two points (4, 2) and (0, -1) → b = -1.
Calculate the slope:
[tex]m=\dfrac{-1-2}{0-4}=\dfrac{-3}{-4}=\dfrac{3}{4}[/tex]
Finally:
[tex]y=\dfrac{3}{4}x-1[/tex]
The equation of the line that passes through the points (4, 2) and (0, -1) is y = 0.75x + 1.
Explanation:The subject of this question is Mathematics, and it involves finding the equation of a line given two points. To find the equation of the line that contains the points (4, 2) and (0, -1), we first find the slope (m) using the formula m = (y2 - y1) / (x2 - x1).
Substituting the given points into the formula, we get m = (-1 - 2) / (0 - 4) = -3 / -4 = 0.75.
We then use the point-slope form of a linear equation, y - y1 = m(x - x1), and substituting m = 0.75, x1 = 4, and y1 = 2, we get the equation of our line as: y - 2 = 0.75(x - 4), which simplifies to y = 0.75x + 1.
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if a pint of milk cost $0.76 what is the cost per cup
Answers
Answer:
$0.38
Step-by-step explanation:
Since there are two cups in a pint so you divide 0.76 by 2
Answer:
.38 cents
Step-by-step explanation:
Since there are 2 cups in one pint, you have to divided .76 (cents) by 2 and you get .38 (cents)
Which of the following statements is true about the values of the coordinate points in a figure when the figure is reflected over the y-axis
Answers
Answer:
they will have the same y-coordinate from the point it was reflected because it is reflected over the y-axis.
but you didn't provide the following statements, so i do not know.
The values of the coordinates will be same for y ordinate but will be negated for x abscissa , which means (x,y) will become (-x, y)
How does the reflection works?When the graph is reflected over y axis, then all the x coordinates of all points become negation of themselves. It is because those x coordinates who were on the positive sides now are on the negative sides and those who were on the negative side are now on the positive side.
Thus:
(x,y) turns to (-x,y)
Thus, the values of the coordinates will be same for y ordinate but will be negated for x abscissa , which means (x,y) will become (-x, y)
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15. Mr. Clements painted his barn for hours in the morning. He painted
the barn for 5 hours in the afternoon. For 154-15c, select True or False
for each statement.
15a. A common denominator of
the mixed numbers is 20.
O True
False
O True
O False
15b. The amount of time spent
painting in the morning can be
rewritten as 3 hours.
False
15c. Mr. Clements spent 2 hours O True
longer painting in the afternoon
than the morning
16. Tom exercised hour on Monday and hour on Tuesday.
Answers
Answer:
15a) True 15b) False 15c) True
16)[tex]\frac{4*2}{5*2}=\frac{8}{25}=\frac{4*3}{5*3}=\frac{12}{15}[/tex]
[tex]\frac{5*2}{6*2}=\frac{10}{12}=\frac{5*3}{6*3}=\frac{15}{18}[/tex]
Step-by-step explanation:
*Rewriting the question with Retrieved missing information:
15. Mr. Clements painted his barn for hours in the morning. He painted his barn [tex]3\frac{3}{5}[/tex] hours in the morning. He painted the barn for [tex]5\frac{3}{4}[/tex] hours in the afternoon.Select True or False for each statement.
15a. A common denominator of the mixed numbers is 20.
15b. The amount of time spent painting in the morning can be rewritten as [tex]3\frac{15}{20}[/tex]
15c. Mr. Clements spent [tex]2\frac{3}{20}[/tex]
hours longer painting in the afternoon than the morning.
16. Tom exercised:
[tex]\frac{4}{5}[/tex]
hour on Monday and
[tex]\frac{5}{6}[/tex]
hour on Tuesday. Part A. Complete the calculations below to write equivalent fractions with a common denominator.
15a) True
Turning the Mixed Numbers into Improper ones:
He painted the his barn:
[tex]3\frac{3}{5}=\frac{18}{5}[/tex] Keep the denominator, and for the numerator multiply the denominator 5 by 3 and add 3 = 18. (In the morning).
[tex]5\frac{3}{4}=\frac{23}{4}[/tex] (In the afternoon)
The Prime factorization [tex]\frac{23}{4},\frac{18}{5}[/tex] help us to obtain the common denomination, i.e. 20
15b) False
This is a matter of simplification. In this mixed number, the fraction can be simplified this way:
[tex]3\frac{15}{20}=3\frac{15:5}{20:5}\Rightarrow 3\frac{3}{4}[/tex]
15c) True
Subtracting the working hours, knowing the common denominator by prime factorization is 20.
For Mixed Numbers:
[tex]5\frac{3}{4}-3\frac{3}{5}=5\frac{15}{20}-3\frac{12}{20}=2\frac{3}{20}[/tex]
For the same mixed numbers turned into improper fractions:
[tex]\frac{23}{4}-\frac{18}{5}=\frac{115-72}{20}=\frac{43}{20}[/tex]
Notice that:
[tex]2\frac{3}{20}==\frac{43}{20}=2.15[/tex]
16A
Equivalent fractions are fractions multiplied by a same constant, on the numerator and denominator:
[tex]\frac{4*2}{5*2}=\frac{8}{25}=\frac{4*3}{5*3}=\frac{12}{15}[/tex]
[tex]\frac{5*2}{6*2}=\frac{10}{12}=\frac{5*3}{6*3}=\frac{15}{18}[/tex]
15a is False as a common denominator isn't clear; 15b is False because the time in the morning is undefined; 15c is True assuming the morning was 3 hours. 16 needs further clarification.
15a ⇒False. To find the common denominator, we need to look at the fractions given. If there are fractions involved, more context is needed to validate this statement. Please provide relevant fractions.15b ⇒False. There is no concrete information given about the exact time spent in the morning to confirm this statement. If he spent 5 hours in the afternoon and the total time spent isn't specified, we cannot conclude the morning time is 3 hours.15c ⇒True. Since he painted for 5 hours in the afternoon, and we assume the morning time to be 3 hours (as per previous interpretations), Mr. Clements painted 2 hours longer in the afternoon (5 - 3 = 2).So, correct answer is 15a. False 15b. False 15c.True
in the right triangle shown, angle A=30 and AC=18 how long is AB?
Answers
Answer:
[tex]AB=9\sqrt{3}\ units[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle ABC
The cosine of angle of 30 degrees is equal to divide the adjacent side to angle of 30 degrees by the hypotenuse
so
[tex]cos(30^o)=\frac{AB}{AC}[/tex]
we have
[tex]cos(30^o)=\frac{\sqrt{3}}{2}[/tex]
[tex]AC=18\ units[/tex]
substitute
[tex]\frac{\sqrt{3}}{2}=\frac{AB}{18}[/tex]
solve for AB
[tex]AB=(18)\frac{\sqrt{3}}{2}[/tex]
[tex]AB=9\sqrt{3}\ units[/tex]
Answer:
T
Step-by-step explanation:
There are between 50 & 60 eggs in a basket. When roza counts by 3's there are 2 leftover and when she counts by 5's there are 4 leftover. How many eggs are in the basket?
(is there a way to solve this without having to go through all the options)
Answers
There are 59 eggs in the basket
Step-by-step explanation:
There are between 50 & 60 eggs in a basket
When Roza counts by 3's there are 2 leftoverWhen she counts by 5's there are 4 leftoverWe need to find how many eggs in the basket
∵ When Roza counts by 3's there are 2 leftover
∵ When she counts by 5's there are 4 leftover
- That means the number of eggs when divided by 3 give
remainder 2 and when divided by 5 give remainder 4
- To find the number look for the numbers that divisible by 5 and
add 4 to them and then check the remainder when they divided
by 3
∵ Between 50 and 60 there is only one number divisible by 5
is 55 (not including 50 or 60)
∵ 55 + 4 = 59
∴ 59 gives remainder 4 when divided by 5
Let us check them with 3
∵ 59 - 2 = 57
∵ 57 is divisible by 3 ⇒ (57 ÷ 3 = 19)
∴ 59 when divide by 3 gives remainder 2
∴ 59 gives remainder 4 when divided by 5 and remainder 2 when
divided by 3
∴ The number of eggs in the basket is 59
There are 59 eggs in the basket
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Anita and Susanna are in a 5-mile bike race. The graph shows each racers distance from the start as a function of time. What could describe Anita's race from minute 3 to minute 5
Answers
Answer:
The best could describe Anita's race from minute 3 to minute 5, She was standing, not moving, she could have been in an accident.
Step-by-step explanation:
See the attached figure.
As shown in the figure, we can note that the distance from minute 3 to minute 5 is constant which is equal to the distance at minute 3.
So, the average distance from minute 3 to minute 5 will be zero and hence the speed of Anita will be zero
So, From minute 3 to minute 5, She was standing, not moving.
Note: speed of Anita from minute 3 to minute 5
= ( distance difference) / (time difference) = zero / (5-3) = 0/2 = 0
To describe the race from minute 3 to 5, analyze the graph paying attention to the x and y axis and the slope of the curve. A straight line suggests constant speed, an upward line implies acceleration, and a downward line denotes deceleration.
Explanation:To describe Anita's race from minute 3 to minute 5, we need to analyze the provided graph which depicts the distance from the start as a function of time for both racers. In this case, we do not have the actual graph so it's important that when you are presented with a graph you pay attention to the
x and y axis
, which in this instance are time and distance. It's vital to also look at the slope of the curve during those minutes 3 to 5 for Anita. If it's a straight line, it means Anita was biking at a
constant speed
. If the line is going upward, Anita was accelerating, and if the line is going downward, she was decelerating. Without the graph itself, it's hard to provide a definitive answer. But the basic method of reading the graph will help you understand the function of time and distance in the context of a race.
Learn more about Analyzing Graphshttps://brainly.com/question/14256886
Mark and Henry win some money and share it in the ratio 3:4. Mark gets £27. How much did they win in total?
Answers
Answer:
They won [tex]\£63[/tex] in total
Step-by-step explanation:
Let
x ----> Mark's money
y ----> Henry's money
we know that
[tex]x=27[/tex] ----> equation A
[tex]\frac{x}{y}=\frac{3}{4}[/tex] ----> equation B
substitute equation A in equation B
[tex]\frac{27}{y}=\frac{3}{4}[/tex]
solve for y
[tex]y=27(4)/3\\y=36[/tex]
we have that
[tex]x+y=27+36=\£63[/tex]