The length of the ruler is approximately 304.8 millimeters .
Length is used to measure distance.
According to the International System of Quantities, length has the dimension of distance. In most measurement systems, length is represented by a base unit from which all other units are derived. The International System of Units (SI) system's fundamental unit of length is the metre.The longest dimension of an object is typically understood to be what is meant by length.However, this isn't always the case depending on the object's position.The length of a fixed object is referred to by a number of names, including height, also referred to as vertical length or vertical extension, and width, breadth, or depth.Given that there are approximately 25.4 millimeters in 1 inch.
Therefore the length of the ruler = 25.4 × 12 = 304.8 mm
Hence the length of the ruler is approximately 304.8 millimeters .
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Answer:
304.8
Step-by-step explanation:
12*25.4 = 304.8
Find the circumference of a circle with area
[tex] \frac{1}{ 4} \pi \: d {}^{2} cm {}^{2} [/tex]
The circumference of circle is [tex]\pi[/tex]d
What is a circle ?
A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius). The fixed point is referred to as the circle's origin or center, and the fixed distance between each point and the origin is referred to as the radius.
Given that : the circle with area =[tex]\frac{1}{4}\pi d^{2} cm^{2}[/tex]
area of circle is =[tex]\pi r^{2}[/tex]
[tex]\pi r^{2}[/tex]=[tex]\frac{1}{4}\pi d^{2} cm^{2}[/tex]
on comparing we get
r = [tex]\frac{d}{2}[/tex]
circumference of circle is 2[tex]\pi r[/tex]
= 2×[tex]\pi[/tex]×[tex]\frac{d}{2}[/tex]
=[tex]\pi[/tex]d
The circumference of circle is [tex]\pi[/tex]d
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There are 110 calories per 177.4 grams of Cereal X. Find how many calories are in 246.5 grams of this cereal.
The amount of calories in 246.5 gm of Cereal 397.5372 calories
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example,
Ram spends 36 Rs. for a dozen (12) bananas. 12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees. As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas. This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
In 177.4 gm of cereal contain 110 calories.
So, 1 gram cereal contain
= 177.4 / 110
= 1.6127
and, 246.5 gm will contain
=246.5 x 1.6127
= 397.5372 calories.
Hence, 397.5372 calories are in 246.5 grams of this cereal.
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MODELING REAL LIFE A cell phone plan costs $30 for each line.
a. Does the situation represent a function? If so, identify the independent and dependent variables.
the situation represent a function. The total cost of the cell phone plan is the
The domain is
b. You can have a maximum of four lines on a plan. Find the domain and range.
Yes :: No
The range is
:: independent variable :: dependent variable
and the number of cell phone lines is the
a. Yes, The situation represents a function.
The independent variable is number of lines and dependent variable is the total cost.
b. The range is 0 ≤ y ≤ 120 and the domain is 0 ≤ x ≤ 4.
What is Domain?
The set of all inputs of the function is called Domain of set.
Given that;
A cell phone plan costs $30 for each line.
Now, Let the number of lines be x and total cost be y.
So, We can evaluate;
y = 30x
Thus, This equation represent Linear function.
So, The situation represents a function.
The independent variable is number of lines and dependent variable is the total cost.
Since, You can have a maximum of four lines on a plan.
So, The possible values are;
x = 0, 1, 2, 3, 4
After substitute all the value of x in equation y = 30x we get;
For x = 0
y = 30 × 0 = 0
For x = 1
y = 30 × 1 = 30
For x = 2
y = 30 × 2 = 60
For x = 3
y = 30 × 3 = 90
For x = 4
y = 30 × 4 = 120
Thus, The range of the function will be 0 ≤ x ≤ 4.
And, The domain of the function will be 0 ≤ y ≤ 120.
Therefore,
a. Yes, The situation represents a function.
The independent variable is number of lines and dependent variable is the total cost.
b. The range is 0 ≤ y ≤ 120 and the domain is 0 ≤ x ≤ 4.
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Help me Plss is very hard and i need an answer
Line C has the constant of proportionality between y and x of 2/3.
What is defined by constant of proportionality?The proportionality constant is the constant value of the ratio of two proportional quantities. When the ratio or product of two varying quantities yields a constant, they are said to be in a proportional relationship.For the given question;
Constant of proportionality = change in y / change in x
Check for each line;
Line A; select any coordinate from the graph.
(7, 3); Put in the formula
Constant of proportionality = 7/3
Thus, Line A has Constant of proportionality between y and x of 7/3.
Line B; select any coordinate from the graph.
(4, 3); Put in the formula
Constant of proportionality = 4/3
Thus, Line B has Constant of proportionality between y and x of 4/3.
Line C; select any coordinate from the graph.
(2, 3); Put in the formula
Constant of proportionality = 2/3
Thus, Line C has Constant of proportionality between y and x of 2/3.
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Find the value of x,y and z
○ x=70,y=58,z=53
○ x=80,y=38,z=63
○ x=85,y=38,z=63
○ x=80,y=48,z=63
Answer:
(b) x=80, y=38, z=63
Step-by-step explanation:
You want to know the values of x, y, and z, given they are angle measures in a diagram showing two triangles.
Linear pairThe angles that form a linear pair are supplementary:
x° +100° = 180°
x = 80 . . . . . . . . . divide by °, subtract 100
Angle sum theoremThe angle sum theorem tells you that the sum of angles in a triangle is 180°.
y° +62° +80° = 180°
y = 38 . . . . . . . . . . . . divide by °, subtract 142
In the other triangle, the same relation holds:
z° +100° +17° = 180°
z = 63 . . . . . . . . . . . . divide by °, subtract 117
The values of x, y, and z are ...
(x, y, z) = (80, 38, 63)
All changes savedFor the three-part question that follows, provide your answer to each question in the given workspace.Identify each part with a coordinating response. Be sure to clearly label each part of your response asPart A, Part B, and Part C.A bag contains three blue marbles, five red marbles, and four green marbles.Part A: What is the probability of selecting a red marble?Part B: What is the probability of selecting three red marbles without replacement?Part C: In a short paragraph, explain in your own words your work to Step B.
If there are three blue marbles, five red marbles, and four green marbles, the probability of selecting a red marble is
[tex]P=\frac{5}{3+5+4}=\frac{5}{12}_{}[/tex]Remember that the probability is the ratio between the number of events and the total number of all the events. In this case, the number of events is 5 because there are 5 red marbles, and the total number of all events is the sum of all the marbles.
Therefore, the probability of selecting red marbles is 5/12.
Part B.[tex]P=\frac{5}{12}\cdot\frac{4}{11}\cdot\frac{3}{10}=\frac{5\cdot4\cdot3}{12\cdot11\cdot10}=\frac{60}{1320}=\frac{30}{66}=\frac{15}{33}[/tex]Notice that we have three different ratios, that is because each time we select a red marble it represents a different situation since we won't place back the red marble into the bag, that's why each event decreases by one and each denominator too.
Therefore, the probability of selecting three red marbles without replacement is 15/33.
Part C.As we said before, in Part B, we had to multiply each probability for each time we select a red marble. It's important to notice that the numerators decreased by 1 (5,4,3) because each time we select a marble we won't place it back, that's the reason why the denominator also decreased by 1.
17. Marlene drove 540 miles to visit a friend. She drove 3 hours and stopped
for gas. She then drove 4 hours and stopped for lunch. How many
more hours did she drive if her average speed for the trip was 60 miles
per hour?
0.5 hours
Step-by-step explanation:
60 mph for 7 hours = 60×7= 420 miles
540-420=120 miles left
60mph÷120miles= 0.5 hours
Please list what the tangent parent function.Can you make graph it scale both axes. With a short table of points+ domain and range. If there are asymptotes please identify and label.
First, use a calculator to create a table of values for the function:
[tex]y=\tan (x)[/tex]A table with inputs for x starting at -6.5 reaching the value of 6.5 with steps of 0.5 would be:
Plotting all the points and joining them with a smooth line, we can see that the graph of y=tan(x) is:
As we can see from the graph, the curve has an asymptote at
[tex]\frac{(2k+1)\pi}{2}+\pi k,k\in\Z[/tex]On the other hand, the graph reaches all the real values over the Y-axis. Then, the range of the function is the set of all real numbers.
herefore, the domain is:
[tex]x\in\R-\lbrace\frac{2k+1}{2}\pi|k\in\Z\rbrace[/tex]he range is:
[tex]y\in\R[/tex]nd the asymptotes are:
[tex]x=\frac{2k+1}{2}\pi,k\in\Z[/tex]8. If a triangle has the given side lengths of
16 and 24, determine the range of
values for the possible length of the 3rd
side.
Answer:
8 < L < 30
Step-by-step explanation:
The third side (L) can't be longer than or equal to the sum of the other two.
So. L < 30.
Also, it must be greater than 24-16 ie > 8
The price of silver dropped a total of $14 in 3 and a half hours. What was the average change in price per hour?
average change in price of silver per hour is $ 4 .
WHAT IS UNITARY METHOD ?With the unitary method, you can solve issues by first calculating the value of a single unit, then multiplying that value by the quantity of units required.
CALCUATION$14 price dropped in 3 and half hours i.e. in 3.5hrs
so in 1 hour price dropped will be = 14 / 3.5
= $ 4 per hour
therefore average drop rate of price of silver per hour is $ 4 .
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What is 12 2/3 times 19 1/4? Put in your answer as a mixed number.
243.83
Step-by-step explanation:
Multiple: 38/
3
* 77/
4
= 38 · 77/
3 · 4
= 2926/
12
= 1463 · 2/
6 · 2
= 1463/
6
Answer:
[tex]243 \frac{5}{6}[/tex]
Step-by-step explanation:
Given multiplication:
[tex]12 \frac{2}{3} \times 19 \frac{1}{4}[/tex]
Convert the mixed numbers to improper fractions:
[tex]\implies \dfrac{12 \times 3+2}{3} \times \dfrac{19 \times 4+1}{4}[/tex]
[tex]\implies \dfrac{36+2}{3} \times \dfrac{76+1}{4}[/tex]
[tex]\implies \dfrac{38}{3} \times \dfrac{77}{4}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times\dfrac{b}{d}=\dfrac{ab}{cd}:[/tex]
[tex]\implies \dfrac{38\times77}{3\times4}[/tex]
[tex]\implies \dfrac{2926}{12}[/tex]
Divide the numerator and denominator by 2:
[tex]\implies \dfrac{2926 \div 2}{12 \div 2}[/tex]
[tex]\implies \dfrac{1463}{6}[/tex]
Convert to a mixed number:
[tex]\implies 243 \frac{5}{6}[/tex]
what’s the inverse of Y equals X squared -10 X
The inverse of the function y equals x squared - 10x (y = x² - 10x) is 5 ±√(x + 25).
What is an inverse function?An inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
First of all, we would translate the given word sentence into a function as follows:
y equals x squared - 10x ⇒ y = x² - 10x
In order to determine the inverse of this function f(x) = x² - 10x, we would interchange both the input value (x) and output value (y) as follows:
y = x² - 10x
x = y² - 10y
Next, we would add (half the coefficient of the y-term)² to both sides of the function as follows:
x + (-10/2)² = y² - 10y + (-10/2)²
x + 25 = y² - 10y + 25
x + 25 = (y - 5)²
±√(x + 25) = y - 5
Adding 5 to both sides of the function, we have:
5 ±√(x + 25) = y - 5 + 5
y = f⁻¹(x) = 5 ±√(x + 25)
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10 A large fountain in a city park cycles
69.3 gallons of water every 1.5 hours.
Write an equation to model how to
find the number of gallons of water the
fountain cycles every hour.
The fountain in the city cycles 46.2 gallons of water in every hour if it cycles 69.3 gallons of water every 1.5 hours according to the model equation.
Unitary Method: What is it?The unitary technique in actuality involves first determining the actual value of a single unit, alongside followed by the value of the necessary number of units.
The unitary approach is a kind of a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Total mass = 69.3 gallons
Time taken = 1.5 hrs
For 1 hr = 69.3/1.5
= 46.2 gallons
What is an example of a unitary method?A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit.
The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one liter of gas if it travels 44 km on two liters of fuel.
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Rachel can finish the job in 5 hours, while Carl can finish the same job in 8 hours.
How long will it take them to finish the job together?
Answer:
use keywords together. So I think all you have to do is multiply or add them both together. Try multiplying or adding but I know that those are part of the answer.
Step-by-step explanation:
For x = -5, what is the value of 4x²-11x ?
Answer:
155
Step-by-step explanation:
4(-5)^2-11x
-5 squared is 25, times 4 =100, -11times-5 is 55 (positive) so 100+55=155
If line a is parallel to line b what is m ∠1?
Explanation
hen a line instersects a pair of paralle lines diverse angles are created
If you copy A of the corresponding angles and you translate it along the transversal, it will coincide with the other corresponding angle (B)
so angles A and B are called
Corresponding angles, those angles are congruents
[tex]m\measuredangle A=m\measuredangle B[/tex]hence, if the lines in the problem are parellel, is must fit
[tex]m\measuredangle1=40\text{ \degree}[/tex]therefore, the answer is
[tex]a)40\text{ \degree}[/tex]I hope this helps you
Find a with the given information.
m=-6/7 (-10,0) and (a,-6)
By using the equation to find the slope, we will see that the value of a is -3.
How to find the value of a?
Here we have two points that define a line.
Remember that a linear equation is of the form:
y = m*x + b
Where m is the slope.
And we know that if the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
m = (y₂ - y₁)/(x₂ - x₁)
In this case, we know that the points are:
(-10, 0) and (a, -6), and the slope is m = -6/7, then we can write the equation:
-6/7 = (-6 - 0)/(a + 10) = -6/(a + 10)
The denominator should be the same in both sides, so we must have:
a + 10 = 7
a = 7 - 10 = -3
Then the two points are (-10, 0) and (-3, -6).
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The airport parking lot charges $2.00 to enter and $3.00 per hour after that. Carmen has N dollars and wants to be able to determine the maximum number of hours she can park. How can Carmen determine the length of time she can afford to park her car in the parking lot?
Carmen can determine the length of time she can afford to park her car in the airport parking lot by first deducting the entrance fixed charge from her N dollars and then dividing the balance by the hourly rate.
What are the mathematical operations?The standard mathematical operations that combine numbers, variables, and operands to arrive at a defined output value are addition, subtraction, division, and multiplication.
In this situation, we can use the mathematical operations of subtraction and division to determine the length of time Carmen can park her car.
The fixed charge for entering the airport parking lot = $2
Hourly charger after the initial entrance = $3
The total amount of dollars possessed by Carmen = N dollars.
Let the length of time she can park there = l.
The maximum number of hours she can park is given by the function, F(l) = (N - 2)/3.
Thus, the best strategy for Carmen to determine her parking time at the airport parking lot based on her N dollars, the fixed entrance fee, and the variable cost per hour, is using the mathematical operations of subtraction and division.
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f(x)=7x-9, f(a +9),what’s the answer HELPME
Step-by-step explanation:
substitute a+9 in place of x in f(x) f(a+9)= 7(a+9) -9 = 7a+63-9 = 7a+54Be Precise An orchard contains 12 rows of Granny Smith apple trees, 10 rows of Fuji apple trees, 15 rows of Gala apple trees, 2 rows of Golden Delicious apple trees, and 2 rows of Jonathan apple trees. Write each ratio in three ways.
Ratio in three ways are given below.
What is ratio?The ratio is the number that can be used to represent one quantity as a percentage of another, to put it simply. A ratio's two numbers can only be compared if they share the same unit. Ratios are used to compare two objects. a connection between two values that is typically expressed as the quotient of one value divided by the other. For instance, the ratio of red to blue marbles is 6:4, or six red to four blue marbles, in the case of a box containing six red and four blue marbles. A decimal or percentage can also be used to indicate a ratio.
Given Data
An orchard contains 12 rows of Granny Smith apple trees, 10 rows of Fuji apple trees, 15 rows of Gala apple trees, 2 rows of Golden Delicious apple trees, and 2 rows of Jonathan apple trees.
a) Rows of Gala apple trees to Granny apple smith trees:
Ratio
First way = 15 to 12
Second way = 15:12
Third way = [tex]\frac{15}{12}[/tex]
b) Rows of Fuji apple trees to total number of apple trees
Total number = 12 + 10 + 15 + 2 +2
Total number = 41
Rows of Fuji apple trees = 10
First way = 10 to 41
Second way = 10: 41
Third way = [tex]\frac{10}{41}[/tex]
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What is the value of the expression -83 + (-56)
Help its due in 5 hours. And I haven’t got the answer right for 2 hours.
Explanation
the volume of a cone is given by:
[tex]\text{Volume}=\frac{1}{3}\pi\cdot r^2\cdot h[/tex]Step 1
find the radius:
let
Circumference= 6n inches
radius= r
[tex]\begin{gathered} \text{Circumference = 2 }\cdot\pi\cdot radius \\ \text{replace} \\ 6n\text{ inches=2}\cdot\pi\cdot\text{ r} \\ \text{divide both sides by 2}\pi \\ \frac{6n\text{ }}{2\pi}\text{=}\frac{\text{2}\cdot\pi\cdot\text{ r}}{2\pi} \\ so \\ r=\frac{6n\text{ }}{2\pi}=\frac{3n}{\pi} \\ r=\frac{3n}{\pi} \end{gathered}[/tex]Step 2
apply the formula for the volume of the cone:
let
h=13 inhces
[tex]\begin{gathered} r=\frac{3n}{\pi} \\ h=13\text{ inches} \end{gathered}[/tex]replace.
[tex]\begin{gathered} \text{Volume}=\frac{1}{3}\pi\cdot r^2\cdot h \\ \text{Volume}=\frac{1}{3}\pi\cdot(\frac{3\text{ n}}{\pi})^2\cdot13 \\ \text{Volume}=\frac{1}{3}\pi\frac{(9n^2)}{\pi^2}\cdot13 \\ \text{Volume}=\frac{3n^2}{\pi}\cdot13 \\ \text{Volume}=\frac{39n^2}{\pi}in^3 \end{gathered}[/tex]so, the answer is
[tex]\begin{gathered} \text{Volume}=\frac{39n^2}{\pi}in^3 \\ \text{Volume}\approx\frac{39n^2}{\pi}in^3 \\ \text{Volume=}12.41n^2inches^3 \end{gathered}[/tex]I hope this helps you
Identify the domain and range of y = [x] + 2.
DOMAIN X CAN BE ALL REAL NUMBERS.
NO MATTER THE VALUE OF X YOU INSERT IT WILL ALWAYS TURN POSITIVE PLUS A POSTIVE TWO. MEANING THERE IS NO WAY THAT YOUR Y CAN BE EQUAL TO 0 OR A NEGATIVE NUMBER THE FUNCTION IS ALWAYSINCREASING FOR ANY VALUE OF Y.RANGE: Y IS ALL THE REAL NUMBERS GREATER THAN 0.
Please help me to do this problem please.
In order to find the solution of this compound inequation, let's first divide it in two inequations:
[tex]\begin{cases}-2\le3x+4 \\ 3x+4<13\end{cases}[/tex]Solving the first inequation, we have:
[tex]\begin{gathered} -2\le3x+4_{} \\ -2-4\le3x \\ -6\le3x \\ -2\le x \end{gathered}[/tex]Now, for the second inequation, we have:
[tex]\begin{gathered} 3x+4<13 \\ 3x<13-4 \\ 3x<9 \\ x<3 \end{gathered}[/tex]Putting both solutions together:
[tex]-2\le x<3[/tex]So the correct option is C.
Logan starts an IRA (Individual Retirement Account) at the age of 24 to save for retirement. He deposits $300 each month. Upon retirement at the age of 65. his
retirement savings is $1,510,293.29. Determine the amount of money Logan deposited over the length of the investment and how much he made in interest upon
retirement.
Total deposited = $147600
Interest earned = $1362693.29
Total no. of years for saving = 65-36-24 = 41
years saving no. of months = 41 x12
= 492 Month
deposit for 1 month = $300 deposit for 492 month = 492 x $300= $147600
Total deposited = $147600
Total saving after retirement = $1,510,293.29 interest = total saving - total deposit= $1,510,293.29 - $147600
= $1362693.29
What is the Interest Rate ?Interest is a periodically paid interest amount related to the amount borrowed, deposited or borrowed (the so-called capital amount). The total interest on the amount borrowed or borrowed depends on the principal amount, the interest rate, the frequency of the interest and the time of loan, deposit or borrowing.
Annual interest is interest for one year. Other interest rates apply to different periods of time, such as a month or a day, but are usually calculated annually.
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What is the linear equation of (1, -7); slope = -1
The linear equation of given point (1, -7) and slope -1 is y = -x - 6.
What is the point-slope form of linear equations?One of the three forms we can use to express a straight line is the point-slope form, also referred to as the point-gradient form. The general form of a linear equation is y - y₁ = m(x - x₁) where m is the slope and (x₁, y₁) is the point.It draws attention to the line's slope and one of the line's points (that is not the y-intercept).Given:
Point(x₁ , y₁) = (1, -7)
Slope = -1
By using the Point-slope form of the linear equations, we get
y - y₁ = m(x - x₁)
⇒ y - (-7) = -1(x - 1)
⇒ y + 7 = -x + 1
⇒ y = -x + 1 - 7
⇒ y = -x - 6
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To support a local senior citizens center, a student club sent a flyer home to the n students in the school. The flyer said, "Please bring in money to support the senior citizens center. Paper money and coins accepted!" Their goal is to raise T dollars.
The dollar amount the club would contain if half of the students at the school each provided 50 cents T - 0.5n.
What is meant by expression?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
The dollar amount the club would contain if they reached half of their goal T + 50.
The dollar amount the club would contain if every student at the school donated 50 cents to the cause 0,5T.
The dollar amount the club could donate if they earned $50 more than their goal of 0.25n.
The dollar amount the club would still require to expand to achieve its goal after every student at the school donated 50 cents 0.5n.
The dollar amount the club would contain if half of the students at the school each provided 50 cents T - 0.5n.
The complete question is:
To support a local senior citizens center, a student club sent a flyer home to the n students in the school. The flyer said, "Please bring in money to support the senior citizens center. Paper money and coins accepted!" Their goal is to raise T dollars. Match each quantity to an expression, an equation, or an inequality that describes it. A: the dollar amount the club would have if they reached half of their goal 1: B: the dollar amount the club would have if every student at the school donated 50 cents to the cause 2: C: the dollar amount the club could donate if they made $50 more than their goal 3: D: the dollar amount the club would still need to raise to reach its goal after every student at the school donated 50 cents 4: E: the dollar amount the club would have if half of the students at the school each gave 50 cents 5: Which statement matches with T + 50?
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A train starts from rest and accelerates uniformly at 1.5m/s²
until it attains a speed of 30m/s. Find the time taken and the
distance travelled.
Answer:
V= 30m/s u=0 A=1.5, time t=? distance S=?
Step-by-step explanation:
to find time:
A=v-u/t
t=v-u/a
t =30-0/1.5
t = 20 secs
to find distance S
S= UT +½at²
S= 0×20+ 1.5×20²/2
s= 300m
Use two unit multipliers to convert 75 square inches to square feet.
In order to use two unit multipliers we will convert from square inches to cm using the following unit multiplier:
[tex]\frac{6.4516}{1^{}}\frac{cm^2}{in^2}\text{.}[/tex]and then we will convert from square cm to square feet, using the following unit multiplier:
[tex]\frac{0.00107639}{1}\frac{ft^2}{cm^2}.[/tex]Answer:
[tex]75in^2=75in^2(\frac{6.4516}{1^{}}\frac{cm^2}{in^2})(\frac{0.00107639}{1}\frac{ft^2}{cm^2})=0.520833ft^2.[/tex]How to solve for 27-30 (X, Y, Z, and W)
27)
Opposite angles are equal.
x° angle is the opposite angle of the 90° angle.
Therefore, x°=90°.
28)
The 90° angle marked in the figure and the y° angles forms a linear pair.
Hence, both angles are supplementary. Supplementary angles sum upto 180°.
Therefore, we can write
[tex]\begin{gathered} y\degree+90\degree=180\degree \\ y\degree=180\degree-90\degree \\ y\degree=90\degree \end{gathered}[/tex]Therefore, y°=90°.
29)
In the figure, let z°+46°=p°.
From figure, we can see that the p° angle is the opposite angle of y° angle.
Since opposite angles are equal, we can write
[tex]\begin{gathered} p\degree=y\degree \\ z\degree+46\degree=y\degree \end{gathered}[/tex]Since from part 28, y°=90°, we get
[tex]\begin{gathered} z\degree+46\degree=90\degree \\ z\degree=90\degree-46\degree \\ z\degree=44\degree \end{gathered}[/tex]Therefore, zh=44e.
30)
From figure,
[tex]\begin{gathered} w\degree=y\degree+90\degree+z\degree \\ \end{gathered}[/tex]Substitute the known values.
[tex]\begin{gathered} w\degree=90\degree+90\degree+44\degree \\ w\degree=224\degree \end{gathered}[/tex]Therefore, w°=224°