Answer:It has no solution
Step-by-step explanation:
- Calculate how many pupils there are in the class if there are 21 girls.
There are 37 pupils in the class.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, the ratio of girls to boys is 4:3, this means that for every 4 girls, there are 3 boys.
We can use this ratio to find the number of boys in the class. Let's set up a proportion:
4 girls : 3 boys = 21 girls : x boys
where x is the number of boys in the class.
To solve for x, we can cross-multiply:
4 girls * x boys = 3 boys * 21 girls
4x = 63
x = 15.75
We can't have a fractional number of students, so we need to round up to the nearest whole number. This means there are 16 boys in the class.
Total number of pupils = 21 girls + 16 boys = 37 pupils
Therefore, there are 37 pupils in the class.
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Complete question:
the ratio of girls to boys is 4:3. Calculate how many pupils there are in the class if there are 21 girls.
elsa made 20,000 in taxable income last year. Suppose the income tax rate is 10% for the first 9,000 plus 16% for the amount over 9,000
Answer:
Elsa's income tax for last year was 2,660 dollars.
Step-by-step explanation:
Plot the point (−312, 434) on the coordinate plane.
The graph of the point is on the image at the end.
How to plot the point on a coordinate plane?A coordinate plane has two axes, one is horizontal and the other is vertical.
A general point (x, y) has the value "x" in the horizontal axis and "y" in the vertical one, then to graph (-312, 434 ) in a coordinate plane, you need to find -312 in the horizontal axis and 434 in the vertical one.
The graph of the point is on the image at the end.
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A farmer uses 162 pounds of fertilizer on 4 acres of crops. Each acre receives the same amount of fertilizer how much fertilizer does the farmer use on each acre of crops
Answer:
We can start by dividing the total amount of fertilizer by the number of acres:
162 pounds / 4 acres = 40.5 pounds per acre
Therefore, the farmer uses 40.5 pounds of fertilizer on each acre of crops.
Step-by-step explanation:
7/25 equivalent in percents
i need help sadly
what is 60% of 120?
A worker earns 4000 naira per month,how much does he earn in 1/2 a year
The worker will earn 24,000 naira in 1/2 year
How to calculate the amount of money that the worker will earn?A worker earns 4000 naira per month
The amount he earns in 1/2 year can be calculated as follows
1/2 of a year is 6 months
The amount of money the worker will earn in six months can be calculated as follows
= 4,000 × 6
= 24,000
Hence the worker will earn 24,000 naira in 1/2 of a year(six months)
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Even though the triangles are all different sizes,the decimal for each ratio are
Even though the triangles are all different sizes,the decimal for each ratio are equal.
What is ratio ?
Ratios are commonly used in many different fields, including finance, engineering, and science. They are used to compare quantities or values that are not necessarily in the same units or are not directly comparable.
If the ratios of the corresponding sides of different triangles are equal, then the triangles are said to be similar. In this case, if the ratios of the sides of the different triangles are equal and result in the same decimal value, then it means that the triangles are similar to each other.
When two triangles are similar, it means that their corresponding angles are equal, and the ratios of their corresponding sides are also equal. This is known as the "angle-angle" or "AA" similarity criterion.
Therefore, if the ratios of the sides of different triangles are equal.
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Please don't scam already got scammed 2 Times :(
The box plot represents the number of students who used a computer in the media center in 12 days.
A box plot uses a number line from 28 to 84 with tick marks every 1 unit. The box extends from 44 to 70 on the number line. A line in the box is at 60. The lines outside the box end at 30 and 82. The graph is titled Computer Use, and the line is labeled Number of Students.
Determine which of the following is the five-number summary of the data.
Min: 30, Q1: 48, Median: 62.5, Q3: 70, Max: 82
Min: 35, Q1: 48, Median: 61.5, Q3: 70, Max: 79
Min: 30, Q1: 44, Median: 60, Q3: 70, Max: 82
Min: 30, Q1: 48, Median: 61, Q3: 70, Max: 80
Answer: im sorry you got scamed :( but heres the answer the answer is C! Min: 30, Q1: 44, Median: 60, Q3: 70, Max: 82
Step-by-step explanation:
How do i know this? well if you look at the box plot it shows you that! it shows a tick on 30, 44, 60, 70 and 82 to its corresponding quartiles. and answer C is the only one that shows this. therefore the answer is C!
Kevin uses 48 ounces of dried apples and 22 ounces of dried
cranberries to make a fruit snack. He plans to sell the snacks
in pound containers. How many containers will he fill? Will
any fruit snack be left over?
Kevin will have 6 ounces of fruit snack left over after filling the 4 pound containers.
Describe Measurement units?There are several systems of measurement units, including the International System of Units (SI), the United States customary system, and the British imperial system. The SI is the most widely used system and is based on seven base units, including the meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), and candela (luminous intensity).
To determine how many containers Kevin can fill, we need to first calculate the total weight of the fruit snack.
Total weight of the fruit snack = Weight of dried apples + Weight of dried cranberries
= 48 ounces + 22 ounces
= 70 ounces
Since there are 16 ounces in 1 pound, we can convert the total weight to pounds as follows:
Total weight in pounds = 70 ounces ÷ 16 ounces/pound
= 4.375 pounds
Therefore, Kevin can fill 4 pound containers with fruit snack, with 0.375 pounds of fruit snack left over.
To determine if any fruit snack will be left over, we need to convert the remaining weight of 0.375 pounds back to ounces:
0.375 pounds × 16 ounces/pound = 6 ounces
Therefore, Kevin will have 6 ounces of fruit snack left over after filling the 4 pound containers.
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30 people gathered to watch a baseball game. While talking, they realized that 11 of them were Toronto Blue Jays fans. What is the probability that a randomly selected person from the group is a Toronto Blue Jays fan?
Type the answer in simple fraction form.
The probability that a randomly selected person from the group is a Toronto Blue Jays fan is 11/30.
What is the probability?Probability refers to the chance or likelihood that an expected outcome, event, or success occurs when there are many possible outcomes, events, or successes.
Probability is a fractional value that lies between one and zero depending on the degree of certainty.
Probabilities can be expressed as decimals, fractions, or percentages.
The total number of people who gathered to watch the baseball game = 30
The number of Toronto Blue Jays fans = 11
Thus, the probability of selecting a Toronto Blue Jay fan from the 30 spectators is 11/30.
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89.600-47.131 How to regroup and show my work
By using all steps below we can regroup the 89.600 - 47.131 = 42.469.
What is the tenth place?The first digit after the decimal represents the tenths place. The next digit after the decimal represents the hundredth place. The remaining digits continue to fill in the place values until there are no digits left.
To regroup and show your work for the subtraction problem 89.600 - 47.131, you can line up the numbers vertically with the decimal points aligned, like this:
89.600 - 47.131 =
Start by subtracting the one's place (0 - 1). Since 0 is less than 1, you need to borrow 1 from the tens place, which becomes 8 - 1 = 7.
The one place becomes 10 + 0 - 1 = 9.
89.600 - 47.131 = 2.469
Next, subtract the tenth place (0 - 3). Since 0 is less than 3, you need to borrow 1 from the one place, which becomes 9 - 1 = 8.
The tenth place becomes 10 + 0 - 3 = 7.
89.600 - 47.131 = 42.469
Finally, subtract the hundredth place (9 - 1), which gives 8.
89.600 - 47.131 = 42.469
Therefore, By using all the above steps we can regroup the 89.600 - 47.131 = 42.469.
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Use implicit differentiation to find the equation of the tangent line to the curve xy^3+xy= 14 at the point ( 7 , 1 ). The equation of this tangent line can be written in the form y = mx+b where m is:
and b is:
Answer: [tex]$m=-\frac{1}{22}$[/tex] [tex]$b=\frac{15}{22}$[/tex]
Step-by-step explanation:
To find the equation of the tangent line to the curve [tex]$xy^3+xy= 14$[/tex] at the point [tex]$(7,1)$[/tex] we need to first find the derivative of the equation with respect to x using implicit differentiation.
Taking the derivative of both sides with respect to x:
[tex]$\frac{d}{dx}(xy^3+xy)=\frac{d}{dx}(14)$[/tex]
Using the product rule and chain rule:
[tex]$y^3+x(3y^2\frac{dy}{dx}+y)=0$[/tex]
Simplifying and solving for [tex]$\frac{dy}{dx}$[/tex]
[tex]$\frac{dy}{dx}=-\frac{y}{3y^2+1}$[/tex]
Now we can substitute x=7 and y=1 into this equation to find the slope of the tangent line at the point (7,1):
[tex]$m=\left.-\frac{y}{3y^2+1}\right|_{(7,1)}=-\frac{1}{22}$[/tex]
So the slope of the tangent line is [tex]$-\frac{1}{22}$[/tex]
To find the y-intercept, we can use the point-slope form of the equation of a line:
[tex]$y-1 = m(x-7)$[/tex]
[tex]$y=mx+(1-7m)$[/tex]
Therefore, the equation of the tangent line to the curve [tex]$xy^3+xy=14$[/tex] at the point (7,1) can be written as:
[tex]$y=-\frac{1}{22}x+\frac{15}{22}$[/tex]
So [tex]$m=-\frac{1}{22}$[/tex] and [tex]$b=\frac{15}{22}$[/tex]
Alan and Ben had collected 360 game cards altogether. They played three games using these cards. In the first game, Alan lost 2 /5 of his cards to Ben. In the second game, Alan won 1 /4 of Ben cards. In the last game, Alan lost 1 /6 of his cards to Ben. In the end, both boys had the same number of cards. How many game cards did each boy have at first?
Answer:
Alan had 272 cards initially and Ben had 88 cards initially.
Step-by-step explanation:
Let's start by assuming that Alan had x cards and Ben had y cards initially. We know that the sum of their cards is 360, so:
x + y = 360
In the first game, Alan lost 2/5 of his cards to Ben, so he gave away (2/5)x cards to Ben. Therefore, he was left with:
(3/5)x cards
Ben received (2/5)x cards from Alan and had y cards initially, so he had:
y + (2/5)x
cards after the first game.
In the second game, Alan won 1/4 of Ben's cards, so he received (1/4)(y + (2/5)x) cards. Therefore, he had:
(3/5)x + (1/4)(y + (2/5)x)
cards after the second game.
In the third game, Alan lost 1/6 of his cards to Ben, so he gave away (1/6)(3/5)x cards to Ben. Therefore, he was left with:
(2/3)(3/5)x = (2/5)x
cards.
Ben received (1/6)(3/5)x cards from Alan in the third game, and he had y + (2/5)x cards after the first game. Therefore, he had:
y + (2/5)x + (1/6)(3/5)x = y + (9/25)x
cards after the third game.
Since both boys ended up with the same number of cards, we can set the expressions for their final card counts equal to each other:
(3/5)x + (1/4)(y + (2/5)x) = y + (9/25)x
Multiplying both sides by 100 to get rid of the fractions, we get:
60x + 25y + 50x = 100y + 36x
Simplifying, we get:
24x = 75y
Since x + y = 360, we can use this equation to solve for one of the variables in terms of the other:
x = 360 - y
Substituting into the equation we just obtained, we get:
24(360 - y) = 75y
Simplifying, we get:
8640 - 24y = 75y
99y = 8640
y = 87.27
Since y must be a whole number (since it represents the number of cards that Ben had initially), we can round it up to 88. Substituting into the equation x + y = 360, we get:
x + 88 = 360
x = 272
Therefore, Alan had 272 cards initially and Ben had 88 cards initially.
To find the initial number of game cards Alan and Ben had, we can set up an equation and solve for a variable. The equation involves using the information about the games played and the number of cards lost and gained by Alan. The solution will give us the initial numbers of cards for both boys.
Explanation:To solve this problem, let's assume that Alan had x cards and Ben had y cards at the beginning. We are given that Alan lost 2/5 of his cards to Ben in the first game, so he had (3/5)x cards left and Ben had y + (2/5)x cards. In the second game, Alan won 1/4 of Ben's cards, so he gained (1/4)(y + (2/5)x) cards, leaving him with (3/5)x + (1/4)(y + (2/5)x) cards. In the last game, Alan lost 1/6 of his cards to Ben, so he had (5/6)((3/5)x + (1/4)(y + (2/5)x)) cards left. Since both boys had the same number of cards in the end, we can set up the equation: (5/6)((3/5)x + (1/4)(y + (2/5)x)) = y + (2/5)x. After simplifying and solving for y in terms of x, we can substitute back into the equation to find the value of x.
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PLEASE ANSWER QUICK!!❌❌
Find the slope of a line perpendicular to the line whose equation is 9x - 3y = 81.
Fully simplify your answer.
Answer:
slope = 1/3
Step-by-step explanation:
9x-3y=81
-9x -9x
3y/3= -9x + 81/3
y = -3x +27
is perpendicular to...
y = 1/3x + 27
for problem 5 need p value
a) The correct null and alternative hypotheses are: given in option A:
H₀: Pkids = Padults
Ha: Pkids < Padults
b) the p-value is 0.004 (rounded to three significant figures).
a) The correct null and alternative hypotheses are:
H₀: Pkids = Padults (The proportion of kids who eat cereal for breakfast is equal to the proportion of adults who eat cereal for breakfast)
Ha: Pkids < Padults (The proportion of kids who eat cereal for breakfast is less than the proportion of adults who eat cereal for breakfast)
b) To test this claim, we can use a two-sample z-test for proportions. We calculate the test statistic as follows:
z = (phat1 - phat2) / √(p*(1-p)*(1/n1 + 1/n2))
where phat1 and phat2 are the sample proportions, n1 and n2 are the sample sizes, and p is the pooled proportion. The pooled proportion is calculated as:
p = (x1 + x2) / (n1 + n2)
where x1 and x2 are the number of successes in each sample.
Using the given data, we have:
phat1 = 70/95 = 0.737
phat2 = 35/58 = 0.603
n1 = 95
n2 = 58
x1 = 70
x2 = 35
p = (70 + 35) / (95 + 58)
= 0.680
Then, the test statistic is:
z = (0.737 - 0.603) / √(0.680*(1-0.680)*(1/95 + 1/58))
= 2.62
Using a standard normal distribution table or calculator, we find the p-value associated with a z-score of 2.62 is approximately 0.004.
Therefore, the p-value is 0.004 (rounded to three significant figures).
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the proportion of kids who eat cereal for breakfast is less than the proportion of adults who eat cereal for breakfast.
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Full Question:
Cereal for Breakfast. A parent claims that kids eat cereal for breakfast more often than adults. A statistics-loving friend of the parent does some internet research and finds the following polling data. Of 95 kids polled, 70 of them say cereal is their most common breakfast. Of 58 adults polled, 35 of them say cereal is their most common breakfast. Test the parent's claim using these data.
a) Select the correct null and alternative hypotheses
H₀: Pkids = Padults
Ha: Pkids < Padults
H₀: Pkids = Padults
Hat Pkids ≠ Padults
H₀: Pkids = Padults
Ha: Pkids > Padults
b) Find the p-value (round to three significant figures).
Are lines of latitude on a globe examples of lines in elliptic geometry? Explain why or why not.
Answer:
No, lines of latitude on a globe are not examples of lines in elliptic geometry. Elliptic geometry is a non-Euclidean geometry in which there are no parallel lines, and the sum of the angles in a triangle is greater than 180 degrees. However, lines of latitude on a globe are examples of lines in spherical geometry, which is a type of elliptic geometry. In spherical geometry, lines of latitude are great circles, which are the largest circles that can be drawn on a sphere and are analogous to the equator on Earth. Unlike lines in Euclidean geometry, great circles on a sphere do not maintain a constant distance from each other and intersect at two points on the sphere.
Step-by-step explanation:
Dan has 16 pencils. Quentin gives him
5 more pencils. Choose all the ways you
can use to find how many pencils Dan
has in all.
016 +5
o 16 + 4+
o 16-5
The way we can find the pencil Dan has in total is 16+5
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.
This word problem are interpreted to mathematical equations.
San has 16 pencils with him before,
Quentin gives him more 5 pencils
then the total pencil Dan will have is obtained by adding all the pencils together,
= 16+5
= 21 pencils
therefore the total number of pencil is found by 16+5 = 21
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Ayden filled up his car with gas before embarking on a road trip across the country. The car uses 2 gallons of gas for every hour driven, and after driving for 4 hours, there were 4 gallons of gas left in the tank. Write an equation for
�
,
G, in terms of
�
,
t, representing the number of gallons of gas remaining in Ayden's gas tank after
�
t hours of driving.
The solution is,
Total capacity: 12 gallons
Equation: G = 12 - R*t
What is mathematical expression?A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
here, we have,
Let R be rate of gas consumption by car = 2 gallons/hr
Let G be the gallons in the car left
let g be the gallons used by the car while driving
Driven time, t = 4 hrs
Remaining gas =4 gallons
according to the question,
consumption rate, R = g/t
After driving for 4 hours
2 = g/4
g = 2*4 = 8 gallons
remaining gas = 4 gallons
therefore, total capacity of the car = 8 + 4 = 12 gallons
equation in terms of gas left,
G = 12 - R*t
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A school sells tickets to the school play through an online ticket company each ticket cost $8 and the company charges a $2.50 processing fee per order write an equation to represent the relationship between the number of tickets bought t and the total cost c with an equation
Answer:
c = 8t + 2.5
Step-by-step explanation:
The total cost c of buying t tickets is given by:
c = 8t + 2.5
Answer:
The total cost of buying t tickets can be represented by the equation:
c = 8t + 2.50
Where:
c is the total cost in dollars
t is the number of tickets bought
Calculate the value of the expression 4+2(5+(-3))=
Answer:
8
Step-by-step explanation:
4 + 2 (5 - 3) = 8
hope this helps :))
HI can someone please help me with these 2 questions!!
The statement that is not correct is FG/RS = EF/OS, the correct option is C.
What are similar triangles?A side of one triangle = k times corresponding side of its similar triangle
where k is the scale factor, constant for one pair of similar triangles. Now when we will take their ratio, the value of k cancels out, leaving no difference between first triangle or second triangle, but only caring if they are similar or not(which depends on angles).
Thus, the trigonometric functions depend only on angles.
We are given that;
Triangles EFG and QRS are similar
Now,
Option A states that EF/QR = CE/SQ, which is true by the definition of similarity of triangles.
Option B states that FG/RS = EG/QS, which is also true by the definition of similarity of triangles.
Option D states that 4GE/SQ = FE/RQ, which is also true as corresponding sides are proportional.
However, option C states that FG/RS = EF/OS, which is not necessarily true. There is no direct relationship between side OS and triangle EFG, so the ratio FG/RS cannot be equated to the ratio EF/OS.
Therefore, by the given similar triangles answer will be FG/RS = EF/OS.
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In a certain study, the chances of encountering a car crash on the road are stated as "5 in 17." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answer:
Step-by-step explanation:
To convert a degree of likelihood to a probability value, we use the formula:
probability = number of favorable outcomes / total number of possible outcomes
In this case, the chances of encountering a car crash on the road are stated as "5 in 17", which means there are 5 favorable outcomes (encountering a car crash) out of 17 possible outcomes (driving on the road).
So, the probability of encountering a car crash can be calculated as:
probability = 5/17
This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case. Therefore, the probability of encountering a car crash on the road is:
probability = 5/17 ≈ 0.2941
Since the probability value is between 0 and 1 inclusive, we can express the indicated degree of likelihood as a probability value of approximately 0.2941.
Mrs. Kim buys 2 x pounds of ham. Mrs. Lee buys 2.5 less pounds than Mrs. Kim. If the amount Mrs. Lee buys is y pounds of ham, express y in terms of x.
the amount Mrs. Lee buys in pounds of ham is given by y = 2x - 2.5.
Why it is and what is pound ?
If Mrs. Kim buys 2x pounds of ham, then Mrs. Lee buys 2.5 less pounds, or (2x - 2.5) pounds of ham.
We are asked to express the amount Mrs. Lee buys in terms of x, so we can write:
y = 2x - 2.5
Therefore, the amount Mrs. Lee buys in pounds of ham is given by y = 2x - 2.5.
Pound is a unit of measurement used to quantify weight or mass. It is abbreviated as "lb" or "lbs" and is commonly used in the United States and other countries. One pound is approximately 0.45 kilograms.
The pound is defined as exactly 0.45359237 kilograms, which is based on the international avoirdupois pound. In everyday use, the pound is often used to measure the weight of objects such as food, animals, and people.
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Five years ago, Castles in the Sand Inc. issued bonds at a face value of $1,000 at a yield to maturity of 4%. Now, with eight years left until the maturity of the bonds, the company has run into hard times, and the yield to maturity on the bonds has increased to 11%.
1). What is the price of the bond now? (Assume semiannual coupon payments.)
2). Suppose that investors believe that Castles can make good on the promised coupon payments but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 50% of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive?
A. The price of the bond is $556.25.
B. The yield to maturity expected by investors is 20.36%.
What is YTM?Yield to maturity (YTM) is the total rate of return that will have been earned by a bond when it makes all interest payments and repays the original principal.
here, we have,
A. The price of the bond is calculated using the formula:
P = C × (1 − (1 + YTM/2)−2T ) ÷ (YTM/2) + (1 + YTM/2)−2T
Here, C is the coupon payment, YTM is the yield to maturity and T is the time to maturity in years.
Face value = $1,000
YTM = 8.2%
Time to maturity = 7 years
Coupon payment = 8.2% × $1,000 = $82
Substituting these values in the formula, we get:
P = $82 × (1 − (1 + 0.082/2)−14 ) ÷ (0.082/2) + (1 + 0.082/2)−14
P = $82 × (1 − 0.6774) ÷ 0.041 + 0.6774
P = $556.25
B. The yield to maturity expected by investors is calculated using the formula:
YTM = 2 × (C × (1 + YTM/2)−2T + (FV − P) × (1 + YTM/2)−2T ) ÷ P
Here, C is the coupon payment, YTM is the yield to maturity, FV is the face value of the bond and P is the price of the bond.
Expected face value at maturity = 85% × $1,000 = $850
Substituting these values in the formula, we get:
YTM = 2 × ($82 × (1 + YTM/2)−14 + ($850 − $556.25) × (1 + YTM/2)−14 ) ÷ $556.25
YTM = 2 × ($82 × (1 + YTM/2)−14 + ($293.75) × (1 + YTM/2)−14 ) ÷ $556.25
YTM = 2 × ($82 × 0.6774 + ($293.75) × 0.6774) ÷ $556.25
YTM = 2 × ($55.35 + ($198.57) ) ÷ $556.25
YTM = 2 × $253.92 ÷ $556.25
YTM = 0.2036 = 20.36%
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Mr. Clark suspended 2 out of every 5 students in the 9th grade. If there are 200 total 9th grade students, how many were suspended?
If each quadrilateral below is a rectangle, find the missing measures.
Please helpppp
The measures of the angles are JKN = 27 degrees and JNK = 126
How to determine the measures of the anglesThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The rectangle
On the rectangle, we have
JKN = NJK
Using the above as a guide, we have the following:
JKN = 27 degrees
Next, we use the sum of angles in a triangle theorem
The sum of angles in a triangle is 180
Mathematically, this is represented as
J + N + K = 180
So, we have the following representation
JNK = 180 - 27 * 2
Evaluate
JNK = 126
Hence, the measure of the angle JNK is 126 degrees
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there are a group of 80 students 90% of them are right handed. how many students are right handed?
Answer:
72 of the students are right handed.
Step-by-step explanation:
Answer:
72
Step-by-step explanation:
90 x 80
100
= 72
=. Xavier wants to buy a new TV. Before he goes to the store, he measures his TV and notes that it is 56 inches long and 33 inches wide. When Xavier gets to the store, he realizes that TVs are measured by their diagonal length! What is the diagonal length of his current TV?
The diagonal length of his current TV is 65 inches.
What is Pythagoras Theorem?Pythagoras theorem states that for a right-angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude. It can be used to find the diagonal of a rectangle if we know the length and the width.
As per the given data:
Length of the TV (l) = 56 inches
Width of the TV (b) = 33 inches
To find the diagonal length (d) of the TV:
From Pythagoras theorem:
[tex]d = \sqrt{l^2 +b^2}\\d = \sqrt{(56)^2 +(33)^2}\\d = \sqrt{3136 +1089}\\d = \sqrt{4225}\\d = 65 inches[/tex]
Hence, the diagonal length of his current TV is 65 inches.
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find the angle x in each question below. give reasons for your answer
The measure of x from the angles of the parallel lines are solved
What are Parallel Lines Cut by Transversal?Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
Let the figure be represented as A
Now , let the missing angle be represented as x
a)
Let the figure be A
Now , the measure of m∠x = 125° ( corresponding angles )
So , the measure of angle x = 125°
b)
Let the figure be A
Now , the measure of m∠x = 57° ( alternate interior angles )
So , the measure of angle x = 57°
c)
Let the figure be A
Now , the measure of m∠x = 70° ( Vertically opposite angles are same )
So , the measure of angle x = 70°
d)
Let the figure be A
Now , the measure of m∠x = 180° - 105°( co interior angles add up to 180° )
So , the measure of angle x = 75°
e)
Let the figure be A
Now , the measure of m∠x = 180° - 53°( co interior angles add up to 180° )
So , the measure of angle x = 127°
f)
Let the figure be A
Now , the measure of m∠x = 180° - 133° ( corresponding angles )
So , the measure of angle x = 47°
Hence , the measures of angles are solved
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