Based on the definition of the inscribed angle of a semicircle , the value of x is: A. 6.
What is an Inscribed Angle of a Semicirle?An inscribed angle of a semicircle is an angle whose vertex lies on the circumference of the semicircle and whose sides are chords of the semicircle. The measure of an inscribed angle of a semicircle is always equal to half the measure of the central angle (90 degrees) that intercepts the same arc as the inscribed angle.
Therefore, we would have:
16x - 6 = 90
16x = 90 + 6
16x = 96
16x/16 = 96/16
x = 6
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In Bill the Boring's dryer there are 3 black shirts, 8 gray shirts, 13 black sweaters, and 7 gray sweaters. Bill is going to take one of these pieces of clothing out
of the dryer at random to check if his clothes are completely dry. What is the probability that the piece of clothing Bill takes out is gray or is a shirt?
Do not round intermediate computations, and round your answer to the nearest hundredth.
Answer:
0.58
Step-by-step explanation:
First, we need to find the total number of pieces of clothing in the dryer. We do this by adding up the number of black shirts, gray shirts, black sweaters, and gray sweaters: 3 + 8 + 13 + 7 = 31
Next, we need to find the number of gray pieces of clothing in the dryer. We do this by adding up the number of gray shirts and gray sweaters: 8 + 7 = 15
Now we can find the probability of Bill taking out a gray piece of clothing by dividing the number of gray pieces of clothing by the total number of pieces of clothing: 15/31
To find the probability of Bill taking out a shirt, we add the number of black shirts and gray shirts: 3 + 8 = 11
Now we can find the probability of Bill taking out a shirt by dividing the number of shirts by the total number of pieces of clothing: 11/31
To find the probability that the piece of clothing Bill takes out is gray or is a shirt, we add the probability of Bill taking out a gray piece of clothing and the probability of Bill taking out a shirt.
So the probability that the piece of clothing Bill takes out is gray or is a shirt is: (15/31)+(11/31)= 0.58 rounded to the nearest hundredth.
lisa drove 60 miles, then increased her speed by 15 miles per hour for 135 miles. if the second part of the drive took 1 hour longer than the first part, find her average speed.
Lisa’s average speed is: 11.4 miles/hours
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formulas and procedures we will use to solve this exercise are:
vm= x(total)/t(total)t= x/vWhere:
x(total)= total distancet(total) = total timevm= average velocityv= velocityt= timeGiven info:
x1= 60 milv2=15 mi/hx2= 135 mit2=?t1= t2- 1 hApplying the time formula we get:
t2= 135 mi / 15 mi/h
t2= 9 h
Calculating t1 we get:
t1= 9h -1 h
t1= 8 h
Applying the average velocity formula we get:
vm= x(total)/t(total)
vm= (60 mil + 135 mil) /( 9h + 8h)
vm= 195 mil/17 h
vm= 11.4 mil/h
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today, most countries use the metric system of measurement while the u.s. used the imperial system. what would be the advantages and disadvantages of the u.s. converting to the metric system?
On U.S. converting to Metric System , the Advantages are Standardization , Improved Science and Technology and the Disadvantages are Cost , Resistance to change .
The Advantages of the U.S. converting to the metric system:
(i) Standardization: The metric system is used by the majority of countries in the world, making international trade and communication easier and more efficient.
(ii) Improved Science and Technology: The metric system is the standard system used in science and technology, making it easier for the U.S. to collaborate with other countries and to participate in international research.
The Disadvantages of the U.S. converting to the metric system:
(i) Cost: The conversion to the metric system would be a costly and time-consuming process, involving changes to products, labeling, and infrastructure.
(ii) Resistance to change: There may be resistance from people who are used to the imperial system and are comfortable with it.
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which graph shows solution?
Answer: The Fourth One
Step-by-step explanation:
Answer:
Bottom right corner
Step-by-step explanation:
The coordinates of the vertices of quadrilateral CDEF are C(6, 6), D(6, 8), E(8, 10), and F(10, 8). The figure is rotated 90° about the origin. What are the vertices of the resulting image, Figure C’D’E’F’? Drag numbers to complete the coordinates.
Answer:
C' - (6, -6)
D' - (8, -6)
E' - (10, -8)
F' - (8, -10)
Step-by-step explanation:
Hey there!
To solve this problem, we must first know what the rule for rotating a shape 90 degrees clockwise is:
(x, y) --> (y, -x)
Now, we can apply this rule to all of the points/vertices
C' - (6, -6)
D' - (8, -6)
E' - (10, -8)
F' - (8, -10)
These are the points and their coordinates after the rotation has been applied.
9th grade easy question i forget :// giving brainliest
Answer:
B. y -6 = 2(x -2)
Step-by-step explanation:
You want the point-slope equation of the line with slope 2 through point (2, 6).
Point-slope equationThe point-slope equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
Then the equation for the line with slope 2 through point (2, 6) is ...
y -6 = 2(x -2) . . . . . choice B
__
Additional comment
If any function goes through the point (0, 0), it can be translated so that it goes through the point (h, k) by the replacements ...
x ⇒ x -hy ⇒ y -kA line with slope 2 through the origin is y = 2x. When that is translated so it goes through (2, 6), the equation becomes ...
y -6 = 2(x -2)
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Ofeila ha a certain amount of money. If he pend $12, then he ha 1/5 of the original amount left. How much money did ofelia have orginally?
The total amount Ofelia had was $ 15.
The equations are mathematical statements with two algebraic expressions flanking the equal to the sign on either side.
It can demonstrate the equality of the relationship between the expressions printed on the left and right sides.
There are some components of an equation, that are:
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign.
The "=" sign determines on both sides must always be present when writing an equation.
Given data,
Let the equation be represented as A
Now, the value of A is equal to the original amount of money
The amount Ofelia spends = $ 12
The remaining amount of money Ofelia had=(1/5)A
So, the equation will be
subtract the original amount of money A - amount Ofelia spends = remaining amount of money Ofelia had
By substituting the values in the equation, we get
A - 12 = ( 1/5 )A
Add 12 on both sides of the equation, and we get
A = (1/5)A + 12
Subtract (1/5 )A on both sides of the equation, and we get
A - ( 1/5 )A = 12
On simplifying the equation, we get
(5A - A)/5 = 12
4A/5 = 12
Multiplying by 5 on both sides of the equation, we get
4A = 60
Divide by 4 into both sides of the equation, and we get
A = $ 15
The value of A is $ 15
Hence, the original amount is $ 15
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Which is the smallest number?13,0.13,1.03,1.3
Answer: the smallest number out of the four is 0.13
Step-by-step explanation:
First, let's think about the number 13. It's a whole number and it's pretty big. It's definitely larger than the other numbers we're looking at today.
Next, let's take a look at 0.13. This number is a decimal, which means it's a number that has a whole number part and a fractional part. The whole number part is 0 and the fractional part is 13. So, 0.13 is smaller than 13.
Now, let's move on to 1.03. This is also a decimal and it's a little bit bigger than 0.13, but smaller than 13.
Finally, we have 1.3. This number is a decimal with a whole number part of 1 and a fractional part of 3. It is bigger than 0.13 and 1.03 but smaller than 13.
So, we can see that the smallest number out of the four is 0.13.
In the figure, ABC is a right angled triangle and angle BAC = 90°. If AD perpendicular to BC and BD=DC then prove that BC² = 4AD².
2
SEE ANSWERS
If ABC is a right angled triangle and angle BAC = 90°. If AD perpendicular to BC and BD=DC then BC² = 4AD² is 4 * AD^2.
How to prove that BC² = 4AD²?
In right triangle ABC, by Pythagorean theorem, we have:
AC^2 + BC^2 = AB^2
Since AD is perpendicular to BC, by similarity, triangle ABD is similar to triangle ADC. Therefore, we have:
BD/AD = AD/DC
BD = AD^2/DC
Substituting BD into the first equation, we get:
AC^2 + BC^2 = AB^2 = AD^2 + (AD^2/DC)^2
AC^2 + BC^2 = AD^2 + AD^4/DC^2
AC^2 + BC^2 = AD^2(1 + AD^2/DC^2)
Since BD = DC, we have:
AC^2 + BC^2 = AD^2(1 + AD^2/BD^2)
And substituting DC = BD:
AC^2 + BC^2 = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2)
Since AB^2 = AC^2 + BC^2, we have:
BC^2/AD^2 = AB^2/AD^2 - AC^2/AD^2 = (AB^2 + AC^2)/AD^2 - AC^2/AD^2 = (BC^2 + AC^2)/AD^2 = 4
Therefore, BC^2 = 4 * AD^2.
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how to sketch z = 6 − 2x − 3y
The sketch of the function z = 6 − 2x − 3y is illustrated below graph.
The term in math called function is defined as special relationship where each input has a single output.
Here we have the function as z = 6 − 2x − 3y
Now, we have to plot the function into graph.
In order to plot the graph, first we have to identify the variable in the function here in the function we have 3 variable. then we plot the graph on the 3 dimensional plane.
If you want to understand how to draw 3−D plot, then assume one of the coordinate is zero and draw line of remaining two coordinate,
In a similarly draw for other two coordinates too, you will get purview of
3−D plot of that function that has been look like as follows.
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Jenny has 18 sweets in a bag. There are 11 orange sweets and 7 green sweets in the bag. Jenny takes at random 3 sweets from the bag. Calculate the probability that the 3 sweets are not all of the same colour.
Now that we have added up all three alternatives ("or" = sum), we have the general option of choosing two different colors. = 0.7316
What is meant by probability?The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.There must be some mistakes in this. But I make an effort to address the appropriate topics.
Nothing is underneath (a). I have nothing to say in response.
(a) Her purse contains 20 candies. If all 20 are yellow, then 9.
As a result, the probability is the proportion of desirable possibilities to all possible outcomes.
Hence, ta da! 9/20
That is the likelihood that Samira will choose a yellow candy.
Again, 20 candies are the starting point [1](i).
Six are green.
When she chooses the first option, her likelihood of selecting a green option is 6/20 = 3/10 = 0.3.
She chooses another candy now, assuming that her prediction came true.
Only 19 were left this time, and 5 of them are green.
Therefore, the likelihood is 5/19.
For the situation we are describing, both occurrences are now required. No overlapping, no ifs, ands, or buts exist. It is simply the sum of the two probabilities.
3/10 × 5/19 = 15/190 = 3/38
That's what I believe the description calls for.
(ii) The likelihood is that the first choice is red and the second is not, plus the first choice is green and the second is not, plus the first choice is yellow and the second is not.
so,
red and not red
5/20 = 1/4 red
15/19 not red (there are still 15 sweets of other colors in the bag, but again now only 19 total).
red and not red = 1/4 × 15/19 = 15/76 = 0.1974
green and not green
6/20 = 3/10 = green
14/19 = not green
green and not green = 3/10 × 14/19 = 52/190 = 26/95 =
= 0.2737
yellow and not yellow
9/20 = yellow
11/19 = not yellow
yellow and not yellow = 9/20 × 11/19 = 99/380 = 0.2606
Now that we have added up all three alternatives ("or" = sum), we have the general option of choosing two different colors.
= 0.7316
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Let f(x)=3x^{2}-2x+6 and g(x)=7x-4.identify the rule for f+g.(f+g)
The required simplified value of the f + g(x) = 3x² + 5x + 2.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
f(x)=3x²-2x+6
g(x) = 7x - 4
f+g = f(x) + g(x)
= 3x²-2x+6 + 7x - 4
= 3x² + 5x + 2
Thus, the required simplified value of the f + g(x) = 3x² + 5x + 2.
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Find 2/5(-3.75). Write your answer as a mixed number in simplest form.
Answer:
- 1 [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
-3.75 can be written as a fraction as -3 [tex]\frac{75}{100}[/tex] o r-3 [tex]\frac{3}{4}[/tex] if I divide the numerator and the denominator by 25.
[tex]\frac{2}{5}[/tex] (-3 [tex]\frac{3}{4}[/tex])
We can change -3 [tex]\frac{3}{4}[/tex] into an improper fraction. We can do that a few ways but I am going to the it the way that is most intuitive to me.
another name for 1 is [tex]\frac{4}{4}[/tex] because 4 ÷ 4 = 1. I am going to use that knowledge to convert -3 [tex]\frac{3}{4}[/tex] into a mixed number.
-( [tex]\frac{4}{4}[/tex] + [tex]\frac{4}{4}[/tex] + [tex]\frac{4}{4}[/tex] + [tex]\frac{3}{4}[/tex]) = - [tex]\frac{15}{4}[/tex] The negative sign can go in the numerator, denominator or in front to the fraction to show that the number is negative.
[tex]\frac{2}{5}[/tex] x -[tex]\frac{15}{4}[/tex] = - [tex]\frac{30}{20}[/tex] Divide the numerator and the denominator by 10
= [tex]\frac{3}{2}[/tex]
Which means the same thing as -( [tex]\frac{2}{2}[/tex] + [tex]\frac{1}{3}[/tex] ) which means the same thing as -(1 + [tex]\frac{1}{3}[/tex] +or - 1 [tex]\frac{1}{3}[/tex]
Find the domain and range please
Therefore , the solution of the given problem of domain comes out to be its range is [2,-2] and domain is [-1.5,-4].
What is a domain?A function's domain is the range of possible arguments that it can receive. These integers indicate the cross of a functional like f. (x). The range of potential values that can be used with a function is known as its domain. The value that method returns after inserting the x value belongs to this set. The formula for a function with y as the predictor variables and x as the predictor variables is y = f. (x). When a single value of y can be successfully produced from a value of x, that value is said to be in the domain of the function.
Here,
Given :
A graph with the extreme values of 2 and -2.
So.
Its range is [2,-2]
and
its start from [-1.5,-4]
so its domain is [-1.5,-4] .
Therefore , the solution of the given problem of domain comes out to be
its range is [2,-2] and domain is [-1.5,-4].
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The relation's domain is 0, 1, 2, 3, and 4.The relation's range is: 0, 1, 4, 9, and 16.
What is a Relation's Range?The set of x-values or relational inputs can be thought of as the domain of a relation.
The collection of all results, or y-values, that match an ordered set of pairs' x-values.
With respect to the relationship, (0, 0), (1, -1), (2, -4), (3, -9), and (4, -16)
The relation's range is 0, 1, 2, 3, and 4. (these are all the input of the relation).
The relation's range is: 0, 1, 4, 9, and 16 (these are all the output of the relation).
The relation's domain is 0, 1, 2, 3, and 4.The relation's range is: 0, 1, 4, 9, and 16
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12. (2 points) suppose {an} is arithmetic and a3 = 5, a11 = 87. what is the common difference? just give the answer, you don’t have to justify it.
The common difference of ap = 41/4 and the sum of 200 terms = 204575.
The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.
We have a3= 5 and a11=87 we have to find the value of d,
n th term of ap= An= a+(n-1)d
A3=5
5=a+2d
87=a+10d
d=41/4 and a=-31/2
the sum of 200 terms when a=3
[tex]S_n=\frac{n}{2}{(2a+(n-1)d)\\S_{200}=100(6+199*41/4)\\\\S_{200}=204575.[/tex]
The complete question is :-
suppose {an} is arithmetic and a3 = 5, a11 = 87. what is the common difference
And find [tex]\sum_{3}^{200}ak[/tex],
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3 Ib/sec ≈ ? kg/h
please help
The complete equation is 3 lb/sec ≈ 4897.0806 kg/h.
How to complete the conversionFrom the question, we have the following parameters that can be used in our computation:
3 Ib/sec ≈ ? kg/h
To convert pounds per second (lb/sec) to kilograms per hour (kg/h), we can use the conversion factor: 1 lb = 0.45359237 kg.
So, 3 lb/sec = 3 * 0.45359237 kg/sec = 1.361 kg/sec
To convert from per second to per hour, we multiply by the number of seconds per hour:
1.3607771 kg/sec * 3600 sec/hour = 4897.0806 kg/h
Therefore, 3 lb/sec ≈ 4897.0806 kg/h.
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if it takes 84 seconds for you to walk up a flight of stairs from the first floor to the third floor, how long would it take you to walk from the first floor to the fifth floor?
It is going to take 140 seconds to walk from first floor to the fifth floor.
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
According to the data problem,
Time taken for walking up 3 floors = 84 seconds
Time taken for walking up 1 floor = 84 seconds/3 = 28 seconds/floor
Time it is going to take for walking up 5 floors = 28 second/floor* 5 floor
Time it is going to take for walking up 5 floors = 140 seconds
We can conclude, it will take 140 seconds to walk from the first floor to the fifth floor.
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select all that apply
Answer:
I think I'm wrong but I Think its C and D
Step-by-step explanation: Tell me if I'm wrong that way other people know
can someone help me for 50 pts
Answer:
Answer is 382.5 square inch
Step-by-step explanation:
calculate all the area of the surface
Answer is 382.5 square inch
The surface area of the prism is given by the equation A = 382.5 inches²
What is the surface area of the prism?The surface area of the prism is calculated as
The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism
Surface Area of the prism = 2B + ph
The area of the triangular prism is A = ph + ( 1/2 ) bh
Given data ,
Let the surface area of the prism be represented as A
Now , the prism consists of 2 right angled triangles and 3 faces of rectangles
So , the base of the triangle b = 9 inches
The height of the triangle h = 10 inches
So , the area of the 2 triangles = 2 ( bh ) / 2
On simplifying the equation , we get
The area of 2 triangles = 9 x 10 = 90 inches²
The area of first rectangle = 9 x 10 = 90 inches²
The area of second rectangle = 9 x 9 = 81 inches²
The area of third rectangle = 13.5 x 9 = 121.5 inches²
So , the area of the prism = area of 2 triangles + area of first rectangle + area of second rectangle + area of third rectangle
Substituting the values in the equation , we get
The area of the prism A = 90 + 90 + 81 + 121.5
The area of the prism A = 382.5 inches²
Hence , the surface area of prism is 382.5 inches²
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7 times 10 four square in standard notation
The standard notation of the given term is 70,000.
What is standard notation?A form of writing a certain number, an equation, or an expression in a way that adheres to set norms is known as a standard notation.
Given a phrase
7 times 10 four square
so 10 four square is 10 to the power 4
10 four square = 10⁴
and 7 times 10⁴ = 7 x 10⁴
the standard form of 7 x 10⁴ is
10⁴ = 10,000
7 x 10⁴ = 7 x 10,000
7 x 10⁴ = 70,000
Hence standard form is 70,000.
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5. the coefficient of determination between two variables is .64. answer the following questions: a. what is the pearson correlation coefficient? b. how strong is the relationship? c. how much of the variance in the relationship between these two variables is unaccounted for?
The Pearson correlation coefficient = r =[tex]\\sqrt{0.64}\\[/tex] = [tex]\\pm0.80[/tex]
The absolute value of Pearson correlation coefficient is greater than 0.75, the relationship between two variables is very strong.
The Percentage of the variance in the relationship between these two variables accounted for is 0.64×100=64%
Correlation Coefficient value always lies between -1 to +1. If correlation coefficient value is positive, then there is a similar and identical relation between the two variables. Else it indicates the dissimilarity between the two variables.
The covariance of two variables divided by the product of their standard deviations gives Pearson’s correlation coefficient. It is usually represented by ρ (rho).
ρ (X, Y) = cov (X, Y) / σX.σY.
Given, coefficient of determination, [tex]r^2[/tex] = 0.64
a) Pearson correlation coefficient = r =[tex]\\sqrt{0.64}\\[/tex] = [tex]\\pm0.80[/tex]
b) Since the absolute value of Pearson correlation coefficient is greater than 0.75, the relationship between two variables is very strong.
c) Percentage of the variance in the relationship between these two variables accounted for is 0.64×100=64%
Therefore, the Pearson correlation coefficient = r =[tex]\\sqrt{0.64}\\[/tex] = [tex]\\pm0.80[/tex], the absolute value of Pearson correlation coefficient is greater than 0.75, the relationship between two variables is very strong, Percentage of the variance in the relationship between these two variables accounted for is 0.64×100=64%.
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Write x + 2 + 3x^2 in standard form
Answer: 3x^2 + x + 2
Step-by-step explanation:
A fast food meal contains 70 g of fat. What percent of the recommended daily allowance of 20 g is?
Answer:
[tex]350%[/tex]%
Step-by-step explanation:
[tex]\frac{70}{20}[/tex] x 100% = 350%
Stun is driving from Indianapolis to Albuquerque. the distance is 1,285 miles. for the first 350 miles, it cost Arun $0.27 a mile to drive. after that, his driveing cost $0.16 mile. what is Arun's total driveing cost
The total cost of Stun Arun's driving from Indianapolis to Albuquerque, a distance of 1,285 miles, is $244.10.
What is the total cost?The total cost means the sum of different expenses.
In this situation, the driving cost per mile for the first 350 miles is different from the rest of the distance.
Therefore, we find the different costs and sum them up to get the total cost incurred by Stun Arun, who is driving from Indianapolis to Albuquerque.
The total distance from Indianapolis to Albuquerque = 1,285 miles
The driving cost per mile for the first 350 miles = $0.27
The total cost for the first 350 miles = $94.50 (350 x $0.27)
The difference between 1,285 and 350 miles = 935 miles
The driving cost per mile for 935 miles = $0.16
The total cost for 935 miles = $149.60 (935 x $0.16)
The total driving cost from Indianapolis to Albuquerque = $244.10 ($94.50 + $149.60)
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the table shows several values of x and their corresponding values of y. which of the following is closest to the correlation between x and y? a. -0.98
b. -0.95
c. 0.20
d. 0.95
e. 0.98
x: 1, 2, 3, 4, 5
y: 3, 4, 7, 8, 12
The pearson correlation coefficient is equal to 4.6/1.25, or 3.68. This is approximately equal The closest answer is e. 0.98.
What is coefficient ?Coefficient is a numerical or statistical value used to measure the strength or magnitude of a relationship between two or more variables. It is commonly used in mathematics, physics, engineering, and economics to quantify the strength of a linear relationship between two variables. In mathematics, coefficients are used to measure the degree of influence of a certain variable on the relationship between two variables.
The correlation between x and y can be found by calculating the Pearson correlation coefficient. This can be done by first calculating the covariance of x and y, which is equal to 4.6, and then dividing it by the standard deviation of x multiplied by the standard deviation of y, which is equal to 1.25.
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Can you please help me? I get stuck on these, if you could I would really appreciate how you solved it as well to help me understand better! Thank you so much! <3
what is the minimum z score a data point could have to remain in top 25 percent
The top 25 percent, a data point would need to have a z score greater than 0.67.
A z score is a measure of how many standard deviations a data point is from the mean of a data set.
To determine the minimum z score, we first need to find the mean and standard deviation of the data set. The mean represents the center of the data and the standard deviation tells us how spread out the data is.
If a data point has a z score greater than 0, it is above the mean and considered in the top half of the data set.
To be in the top 25 percent, the data point would need to have a z score greater than the value that separates the top 75 percent from the bottom 25 percent.
This value can be found using a table of standard normal distributions or using software that calculates z scores.
In a standard normal distribution, the value that separates the top 75 percent from the bottom 25 percent is about 0.67.
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if an airplane's speed is 200 miles per hour, what is its speed in feet per second. (Show step by step)
Answer:
I'm sorry I don't know
Step-by-step explanation:
but I think that you do need to multiply it by 1pp just asyou multiply the amp by 100 from Ma to A
Lito drove from Manila to Lucban, Quezon to join a festival. After traveling for 2 hours at an average speed of 80 kph, he took a rest and continued with the last 200 km stretch at 60kph. The whole trip including resting time was 6 hours. How long did he spend resting? ( show solution please )
Answer:
The man took 0.7 Hours for resting
Step-by-step explanation:
Total time taken = 6 hours
We can remove the first 2 hours as it isn't necessary in this question
so Total time taken = 4 hours
Speed traveled = 60kph
distance traveled = 200km
Time taken to travel = Distance/ speed
= 200 / 60
= 3.3 Hours
Time taken for resting = Total time - Time taken for travel
= 4 hours - 3.3 hours
= 0.7 Hours
The man took 0.7 Hours for resting
Please help me out. And i will give you 20 points.
1. The slope-intercept form of the equation of each line given the slope and y-intercept are as follows:
The equation will be: y = -10x - 5The equation will be: y = 7x + 5The equation will be: y = -9/5x - 4The equation will be: y = -5/4x - 52. The given slopes are:
slope = -13/28slope = -9/7slope = 1/37slope = -11/123. Two slopes of the parallel lines are:
The slope of the line parallel is 2/3.
The slope of the line parallel is 9/5
4. The slopes of all perpendicular lines are:
The slope of a perpendicular line = 2The slope of a perpendicular line = 1What is the slope-intercept form of the equation of a line?The slope-intercept form of the equation of a line given is given below:
y = mx + cwhere;
m is the slope
c is the intercept
a. Slope-10, y-intercept = -5
The equation will be: y = -10x - 5
b. Slope 7, y-intercept = 5
The equation will be: y = 7x + 5
c. Slope = -9/5, y-intercept =- 4
The equation will be: y = -9/5x - 4
d. Slope = -5/4, y-intercept - 5
The equation will be: y = -5/4x - 5
2. Slope = y₂ - y₁ / x₂ - x₁
a. (17,-6), (-11,7)
slope = 7 - (-6) / -11 - 17
slope = -13/28
b. (3,4), (-4,-5)
slope = -5 - 4 / -4 - 3
slope = -9/7
c. (-20, 14),(17, 15)
slope = 15 - 14 / 17 - (-20)
slope = 1/37
d. (11,-18), (-1,-7)
slope = -7 - (-18) / -1 - 11
slope = -11/12
3. Two lines are parallel if the slopes are equal.
a. y = 2/3x - 4
The slope of its line is 2/3
The slope of the line parallel is 2/3.
b. y = 9/5x - 5
The slope of its line is 9/5
The slope of the line parallel is 9/5
4. The slope of all perpendicular lines is the negative reciprocal, that is, (-1/m).
a. y = -1/2x -2
slope, m = -1/2
The slope of a perpendicular line = -1/(-1/2)
The slope of a perpendicular line = 2
b. y = -x -1
slope, m = -1
The slope of a perpendicular line = -1/(-1)
The slope of a perpendicular line = 1
Learn more about slopes and intercepts of a line at: https://brainly.com/question/25722412
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