The acceleration was -26.04 m/s².
What are Equations of Motion?Equations of motion are a set of equations which describes the basic motion concepts like velocity, position, time and acceleration.
There are mainly three equations of motion.
v = u + at
s = ut + [tex]\frac{1}{2}[/tex] at²
v² = u² + 2as
v is the final velocity, u is the initial velocity, a is the acceleration, t is the time and s is the displacement.
Given,
Initial velocity of the motorist, u = 90 km/h = 90 × (5/18) m/s = 25 m/s
Final velocity of the motorist, v = 0 m/s (since the bike stopped)
Stopping distance, s = 12 m
Using the third equation of motion,
v² = u² + 2as
0² = 25² + (2a × 12)
24a = -625
a = -625 / 24 = -26.04 ≈ -26 m/s²
Hence the acceleration of the motorist was -26 m/s².
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A bicycle travels along with the road at an average speed of 5 m/s work out the time it takes the bicycle to travel along the road
Give your answer in seconds
The time it takes the bicycle to travel along the road is 20 seconds.
What is Speed?The rate of change of position of an object in any direction is called as Speed.
The formula for speed is Distance divided by Time.
So Time = distance / speed
we need to know the distance the bicycle travels to use this formula.
If we have this distance, we can divide it by the speed of 5 m/s to find the time.
Let the distance is 100 meters, then the time taken is:
time = distance / speed = 100 / 5 = 20 seconds
Hence, the time it takes the bicycle to travel along the road is 20 seconds.
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The complete question is given below:
A bicycle travels along with the road at an average speed of 5 m/s work out the time it takes the bicycle to travel along the road of distance 100 meters.
Give your answer in seconds
A painter is going to paint a room shaped like a cube, with square walls that are 20 ft. on each side. A gallon of paint can be used to cover 400 square feet. How many gallons of paint should the painter buy?
1 gallon
5 gallons
6 gallons
4 gallons
The number of gallons of paint that the painter should buy is; 4 gallons
How to solve Algebra Word Problems?The parameters given are;
Side length of cube = 20 ft
Area that a gallon of paint can cover = 400 square feet
Since the room is shaped like a cube, then it will have 4 equal wall areas.
Area of one wall = 20 * 20 = 400 square feet
Area of 4 walls = 4 * 400 = 1600 square feet
Since 400 sq.ft is covered by 1 gallon, then;
1600 sq.ft = (1600 * 1)/400
= 4 gallons
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The teacher shave 25$ to buy supplies. Write and evaluate a numerical expression to show how much more money they will need to buy the cups and napkins.
The requried teacher needs $59.5 more to buy cups and napkins, as of the given condition.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
To find out how much more money the teachers will need to buy cups and napkins, we can first calculate the cost of each item and then add those costs together.
Each package of cups costs $3.50
The teachers need to buy 12 cups
So the total cost of cups is = 12 cups × ($3.50 per package) = $42
Now let's do the same thing for the napkins:
Each package of napkins costs $4.25
The teachers need to buy 10 napkins
So the total cost of napkins is = 10 napkins × ($4.25 per package) = $42.50
To find out how much more money the teachers will need to buy cups and napkins,
= $42 + $42.50 - $25
= $59.50 - $25 = $59.5
Therefore, the teachers will need $59.5 more to buy cups and napkins.
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Quick and Simple Algebra 2 question
Write the equation based on 2 points
The equation of line is y = 1.5x + 5.5.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
We have the reference point as (-2, 2.5) and (-1, 4)
so, slope
= (4- 2.5)/ (-1 + 2)
= 1.5
and, the equation of line is
y- 2.5 = 1.5 (x+ 2)
y- 2.5 = 1.5x + 3
y = 1.5x + 5.5
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How you solve this I give extra points or money correct answer only
The points M(0, -1), and T(4, 6), on the diagonal [tex]\overline{MT}[/tex] of the rhombus MATH, indicates that the equation of the line containing the diagonal [tex]\overline{AH}[/tex], in slope and intercept form is; [tex]y = 3\frac{9}{14} - 4\cdot \frac{x}{7}[/tex]
What is a rhombus?A rhombus is a quadrilateral that has four congruent sides.
The specified shape of the quadrilateral MATH = A rhombus
The coordinates of the endpoints of the diagonal [tex]\overline{MT}[/tex] of the rhombus are;
M(0, -1), and T(4, 6)The equation of the line that contains the diagonal [tex]\overline{AH}[/tex] of the rhombus can be found as follows;
The diagonals of a rhombus are perpendicular, therefore, the slope of the diagonal, [tex]\overline{AH}[/tex]is -1 divided by the slope of the diagonal [tex]\overline{MT}[/tex]
The slope of [tex]\overline{MT}[/tex] = (6 - (-1))/(4 - 0) = 7/4
The slope of [tex]\overline{AH}[/tex] = -1/(7/4) = -4/7
The diagonals of a rhombus bisect each other, therefore, the diagonals [tex]\overline{MT}[/tex] and [tex]\overline{AH}[/tex] intersect at the midpoint of point [tex]\overline{MT}[/tex]
Therefore, the midpoint of [tex]\overline{MT}[/tex] is a point on the diagonal line that contains the diagonal [tex]\overline{AH}[/tex]
The midpoint of [tex]\overline{MT}[/tex] = ((0 + 4)/2, (-1 + 6)/2) = (2, 2.5)
The equation of the line containing the diagonal [tex]\overline{AH}[/tex] is therefore;
y - 2.5 = (-4/7)·(x - 2)
y = -4·x/7 + 8/7 + 2.5 = -4·x/7 + 51/14
y = -4·x/7 + 51/14 = -4·x/7 + 3 9/14
y = [tex]3\frac{9}{14}[/tex] - 4·x/7
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Solve for B, please.
Answer:
b = 30
Step-by-step explanation:
You want the value of b given line y = 20x +b passes through the points (6, 150) and (11, 250).
Solve for bThe equation y = 20x +b can be solved for b:
b = y -20x . . . . . . . . subtract 20x
Using the given point (x, y) = (6, 150), you have ...
b = 150 -20(6) = 150 -120
b = 30
Julie plans to invest her bonus of P100, 000.00 in two banks. The first bank earns an interest of 6% per annum while the other bank earns 8% interest per annum. If she wants her investment to earn a total interest of exactly P7, 200.00 after a year, how much does she need ot invest in each bank?
The amount of money that is invested in the first and second accounts will be 40,000 and 60,000, respectively.
What is the solution to the equation?The possible value of the variables that satisfy the equation which is known as the solution of the equation.
The interest is given as,
I = PRT / 100
Let 'x' be the amount invested in the first bank. Then the amount of investment in the second bank is (100,000 - x). Then the equation is given as,
x · 0.06 · 1 + (100,000 - x) · 0.08 · 1 = 7,200
0.06x + 8,000 - 0.08x = 7,200
-0.02x = -800
x = 40,000
The amount in the second bank is given as,
⇒ 100,000 - 40,000
⇒ 60,000
The amount of money that is invested in the first and second accounts will be 40,000 and 60,000, respectively.
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A polynomial function can be written as (x − 2)(x − 3)(x + 5). What are the x-intercepts of the graph of this function?
The x-intercepts of the graph of the given polynomial function as described is; 2, 3 and -5.
What are the x-intercepts of a polynomial function?The x-intercepts of a polynomial function are otherwise termed, roots, solutions or zeroes of the polynomial function.
On this note, the x-intercepts of the polynomial function which is as described in this scenario are;
x - 2 = 0; x = 2.
x - 3 = 0; x = 3.
x + 5 = 0; x = -5.
Ultimately, the x-intercepts of the polynomial function in discuss are; 2, 3 and -5.
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In this picture B,D, and F are
midpoints. AC=50, CE=60, and
BD=35
B
AE=[? ]
The measure of the side AE would be 70 units.
What is the triangle midpoint theorem?We know that the triangle midpoint theorem says that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
In the given triangle B, D, F are the midpoints of the triangle.
AC=50, CE=60,
BD=35
Then, in the given triangle if BD is connecting the midpoints of AC and CE then it must be parallel to AE and equal to FE ( half of AE).
⇒ BD ≅ FE= 1/2 AE
AE = 70 units
Then, the length of line segment AE = 70 units
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Which equation best represents the curve of best fit for this data?
Answer:yes
Step-by-step explanation:
Find |A| if A = 1 1 2 2 2 3 5 6 1 3 5 3 1 1 3 6
Answer:
1 this is the answer because 1 is more than other number
A cellular phone company uses the formula $16+ $0.04m to calculate each subscriber's monthly
bill, where m is the number of minutes used. If Angelo uses 142 minutes on his phone this month,
how much will his bill be?
Please help bro I need help solving this polynomial and terms
The expression represents a quintic polynomial with 4 terms. The constant term is -6, the leading term is x⁵/2, and the leading coefficient is 1/2.
What is a polynomial expression?A polynomial expression is a mathematical equation in which the polynomial is set to zero. The equation is made up of variables, non-negative integer exponents, coefficients, arithmetic operations, and an equal sign.
From the polynomial expression given:
[tex]\dfrac{1}{2}x^5 - 6 - x^4 -5x^2[/tex]
The degree of a polynomial is the highest degree of its terms which helps us to determine the type of polynomial (quintic polynomial). The constant term is -6.
The leading term in a polynomial is the term with the highest degree = x⁵/2. The leading coefficient of a polynomial is the coefficient of the leading term is 1/2.
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Answer:
quadrinomial, 4, -6, 1/2x^5, 1/2
Step-by-step explanation:
quadrinomials are polynomials with 4 terms
constant is the number with no variable
leading term is the term at the beginning
leading coefficient is the number at the beginning
Solve number 7 using combinations
Step-by-step explanation:
7.
the probability of picking a defective missile with the first pull is
5/22
the probability of picking a working missile with the first pull is
17/22 = ((22-5)/22)
I have to assume that the picked missiles are not put back into the main pile after the check.
and I have to assume that the sequence of the pulled missiles don't matter.
a.
all are defective.
since there are only 5 defective missiles, there is only one possibility out of all the possibilities to pull 5 out of 22 to get 5 defective missiles.
the possible combinations to pull 5 out of 22 :
C(22, 5) = 22! / ((22 - 5)! × 5!) =
= 22×21×20×19×18×17/(5×4×3×2) =
= 22×21×19×3×17 = 447,678
and we have one desired situation (all 5 are defective).
so, the probability is
1/447678 = 0.000002233748364... = 2.233748364e-006
b.
all 5 are functional.
the total possible cases to pull 5 out of 22 are still
447,678.
the desired cases are all cases to pull 5 out of the 17 (22 - 5) functional missiles.
that is
C(17, 5) = 17! / ((17 - 5)! × 5!) =
= 17×16×15×14×13 / (5×4×3×2) =
= 17×2×14×13 = 6,188
so, the probability to get one of these cases is
6188 / 447678 = 0.013822435...
The probability of picking a defective missile with the first pull is 5/22
The probability of picking a working missile with the first pull is 17/22
What is Probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
If we assume that the picked missiles are without replacements and the sequence of the pulled missiles don't matter,
Therefore, the probability that:
a. all are defective is 2.233748364e-006
Since there are only 5 defective missiles, there is only one way to get 5 defective missiles out of 22 possible outcomes.
The possible combinations to pull 5 out of 22 :
C(22, 5) = 22! / ((22 - 5)! × 5!) =
= 22×21×20×19×18×17/(5×4×3×2) =
= 22×21×19×3×17 = 447,678
and we have one desired situation (all 5 are defective).
so, the probability is 1/447678 = 0.000002233748364... = 2.233748364e-006
b. all 5 are functional is 0.013822435
the total possible cases to pull 5 out of 22 are still 447,678.
The ideal scenario is for all incidents to result in the removal of 5 of the 17 (22 - 5) operational missiles.
that is
C(17, 5) = 17! / ((17 - 5)! × 5!) =
= 17×16×15×14×13 / (5×4×3×2) =
= 17×2×14×13 = 6,188
so, the probability to get one of these cases is
6188 / 447678 = 0.013822435
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PLEASE HELP QUICKLY
Answer: 10.7 or 10.8
Step-by-step explanation:
so, first [tex]a^{2} +b^{2} =c^{2}[/tex]
while [tex]a = 3.75[/tex] and [tex]b=10[/tex] and [tex]c=?[/tex]
so, it will be written as,
[tex]3.75^{2} +10^{2} =c^{2} \\[/tex]
[tex]14.0625+100=c^2[/tex]
[tex]114.0625=c^2[/tex] then square root both sides to have an answer of:
[tex]10.7=c[/tex]
That's if you are going to use the [tex]a=3.75[/tex]. as written in the question...
while if you're going to use [tex]a=4[/tex] (as shown in the figure) then only change the 3.75 with 4.
which will equal to...
[tex]4^2+10^2=c^2[/tex]
[tex]16+100=c^2[/tex]
[tex]116=c^2[/tex] then square root both sides to have an answer of:
[tex]10.77=c[/tex]
[tex]10.8[/tex] ≈ [tex]c[/tex]
hope you've understanded.!
Find the exact value of x
Answer:
[tex] \frac{1}{2} \times 25 \times 10 = 125 [/tex]
[tex] \frac{1}{2} \times breath \times perpedicular \: hight[/tex]
Serenity is making beaded jewelry with no more than 920 beads she currently has in stock. Bracelets use 15 beads
and necklaces use 70 beads.
x= the number of bracelets
y = the number of necklaces
The inequality is written as 15x + 70y ≤ 920. Then the region below the line is the solution to inequality.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Serenity is assembling beaded jewelry with no more than 920 beads she presently has in inventory. Bracelets use 15 beads and necklaces use 70 beads.
Let 'x' be the number of bracelets and 'y' be the number of necklaces. Then the inequality is given as,
15x + 70y ≤ 920
The region below the line is the solution to inequality.
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On a standard dice, what is the probability of not landing a 3
Answer:
5/6
Step-by-step explanation:
Ezra 1:9,10 records that King Cyrus returned thirty gold chargers, one thousand silver chargers, twenty - nine knives, thirty gold basons, four hundred ten silver basons, and one thousand other vessels. How many items did Cyrus return to Israel?
Answer:
2489
Step-by-step explanation:
it would be 30+ 1,000+29+30+400+1,000+ 2489
I really hope this helps
Proverbs 4:6-7
Do not forsake wisdom, and she will protect you; love her, and she will watch over you. The beginning of wisdom is this: Get wisdom. Though it cost all you have, get understanding. Cherish her, and she will exalt you; embrace her, and she will honor you. (just a little encouragement to keep studying hard!)
Answer:
2489
Step-by-step explanation:
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 4 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 111?
On solving the provided question, we can say that in the equation,Often, there is only one variable, which also serves as the symbol. An illustration would be , [tex]D = 4(82-D)+2[/tex]
What is equation?The equal sign (=), which denotes equality, is used to unite two statements in a mathematical equation. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions.
For instance, the equal sign separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14.The two sentences on either side of a letter are connected by a mathematical formula.
Each equation has a formula. Not every equation has a formula. Equations are created with the intention of being solved for a variable. If an equation meets the requirements for a function, it is a function. But not every equation is a function.
M+D = 82 marbles
[tex]M= 82- D[/tex]
[tex]D= 4M+2[/tex]
[tex]D= 4(82-D) +2[/tex]
[tex]D= 328 - 4D+2[/tex]
[tex]5D = 330[/tex]
[tex]D= 66[/tex]
Therefore, Don has 66 and Mark has 82-66 = 16
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Solve for x
2,4, and 6 i need help with
Answer: 2: 56 degrees
4: 56 degrees
(Number 6 is not in the image)
Step-by-step explanation:
So for #2 we know the whole angle is 90 degrees, so all we have to do is 90-34 = 56
And for #4, we know the angle is 180 so all we have to do is 180-124=56
The graph of a function is showed below
Answer: a
Step-by-step explanation: it's increasing and it's a line
If {={ a, b, c, d, e } A={ a, c, e} B={ b, e }. List the members of the following set. (a) A' (b) B' (c) A'uB (d) AuB' (e) A'nB (f) AnB' (g) A'uA (h) B'nB (I) AuB (j) A'uB' (k) [AnB]' (l) A'nB'
Answer:
The complement of a set A, denoted A', is the set of all elements that are not in A. The complement of B, denoted B', is the set of all elements that are not in B.
Step-by-step explanation:
(a) A' = {b, d}
(b) B' = {a, c, d}
(c) A' U B = {a, b, c, d, e} (the union of A' and B contains all elements in both sets)
(d) A U B' = {a, b, c, e} (the union of A and B' contains all elements in both sets)
(e) A' n B = {} (the intersection of A' and B is an empty set)
(f) A n B' = {c} (the intersection of A and B' contains all elements that are in A but not in B)
(g) A' U A = {a, b, c, d, e} (the union of A' and A is the universal set, containing all elements)
(h) B' n B = {} (the intersection of B' and B is an empty set)
(i) A U B = {a, b, c, e} (the union of A and B contains all elements in both sets)
(j) A' U B' = {a, b, c, d, e} (the union of A' and B' is the universal set, containing all elements)
(k) [A n B]' = {b, d} (the complement of the intersection of A and B is the union of the complements of A and B)
(l) A' n B' = {} (the intersection of A' and B' is an empty set).
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
Their is a pair of parralle sides in the following shape 5 , 7, 6
what is the area of the shape
Answer: A = 15 units²
Step-by-step explanation:
The figure has 1 pair of parallel sides and is therefore a trapezium.
The area (A) of a trapezium is calculated as
A = h (b₁ + b₂ )
where h is the perpendicular height between bases and b₁, b₂ are bases
here h = 3, b₁ = 3 , b₂ = 7 , then
A = × 3 × (3 + 7) = 1.5 × 10 = 15 units²
PLEASE HELP!!!
A survey was conducted in which the customer service representatives of two companies were rated on a scale of 1 to 6. The graph below shows customer service ratings of 20 representatives. The interquartile range for each company is 3. The difference between the median rating for each company is approximately how many times the interquartile range?
The difference between the median rating for each company is approximately 0.3 times the interquartile range.
How to calculate the median service rating?Generally speaking, the median for 20 observations is the average of the 10th and 11th number:
Median rating of Company A = (4 + 4)/2
Median rating of Company A = 8/2
Median rating of Company A = 4.
Median rating of Company B = (3 + 3)/2
Median rating of Company B = 6/2
Median rating of Company B = 3.
Difference in median = 4 - 3
Difference in median = 1
For the required expression that models the difference between the median rating for each company and the interquartile range, we have the following:
1 = 3x
x = 1/3.
x = 0.3
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CIRCLES DRAG & DROP ACTIVITY 1: Drag & Drop the correct values to fill in each table below.
HELP ASAP WILL GIVE BRAINLIST!!!!!!!!!!
The radius, diameter, area and circumference of circle 1, 2, 3 and 4 are; (2, 4, 4π, 4π), (4, 8, 16π, 8π), (1, 2, 1π, 2π) and ( 8, 16, 64π, 16π) respectively.
What are the radius, diameter, area and circumference of each of the given circle?The diameter of a circle is 2 times the radius of the circle.
The area of a circle is expressed as: A = πr²
The circumference of a circle is expressed as: 2πr
For question 1)
Radius r = 2
Diameter = 2 × radius = 2 × 2 = 4
Area = πr² = π( 2 )² = 4π
Circumference = 2πr = 2 × π × 2 = 4π
For question 2)
Radius r = 4
Diameter = 2 × radius = 2 × 4 = 8
Area = πr² = π( 4 )² = 16π
Circumference = 2πr = 2 × π × 4 = 8π
For question 3)
Diameter d = 2
Radius = diameter / 2 = 2/2 = 1
Area = πr² = π( 1 )² = 1π
Circumference = 2πr = 2 × π × 1 = 2π
For question 4)
Diameter d = 16
Radius = diameter / 2 = 16/2 = 8
Area = πr² = π( 8 )² = 64π
Circumference = 2πr = 2 × π × 8 = 16π
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which answer is the right choice
7200+80x = 3200+120x
Reason:
Canton starts off with 7200 people. Add on 80x to represent the fact the town grows 80 people per year. That's how we end up with the expression of 7200+80x
Similarly, the expression 3200+120x represents the idea Holly Springs started off with 3200 people and grows at 120 people per year.
(a) Describe the relationship among the lengths of the segments formed by the two secants. You may use words and/or an equation.
(b) Suppose = 3 in., = 2 in. and = 5 in. Is it possible to find the length of ? If so, show how to find the length. If not, explain why not.
Answer:a
Step-by-step explanation:
Find the magnitude and vector
-22.2m
12.6m
The magnitude of the vector is 25.5 metres.
How to find magnitude of a vector?The magnitude of a vector is the length of the vector. Therefore, the magnitude of a vector can be found using Pythagoras's theorem as follows:
Hence,
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
| N | = √22.2² + 12.6²
| N | = √492.84 + 158.76
| N | = √651.6
| N | = 25.5264568634
| N | = 25.5 metres
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As a fundraiser for her soccer team, Leslie must raise at least $120 by selling keychains and t-shirts. Each keychain costs $4 and each t-shirt costs $10. She must sell at least 18 items in total.
Choose the correct system of linear inequalities that represents Leslie’s situations.
X = keychains, y = t-shirts
Answer: The correct system of linear inequalities that represents Leslie's situation is:
4x + 10y ≥ 120 (to represent the requirement to raise at least $120)
x + y ≥ 18 (to represent the requirement to sell at least 18 items in total)
x ≥ 0, y ≥ 0 (to represent that Leslie must sell a non-negative number of keychains and t-shirts)
Where x represents the number of keychains sold and y represents the number of t-shirts sold. The first inequality represents the minimum amount of money Leslie needs to raise, and the second inequality represents the minimum number of items she needs to sell. The last two inequalities represent that Leslie can only sell a non-negative number of items.
Step-by-step explanation:
