The term "altitude" is the same as "height of a triangle". It is perpendicular to the base. Since we can rotate the triangle to have any side be horizontal, there are effectively 3 possible bases. Hence, there are 3 heights. It all depends how you look at it.
Let h1, h2, and h3 be the three altitudes or heights.
Without loss of generality, we'll focus on the first two heights h1 and h2. Their respective bases are b1 and b2.
If we use b1 as the base, then the area is...
area = 0.5*base*height = 0.5*b1*h1
Similarly, the other base gives the area of:
area = 0.5*b2*h2
------------------------
Since both formulas refer to the same area (because we're working with the same triangle), we can set the expressions equal to one another
0.5*b1*h1 = 0.5*b2*h2
b1*h1 = b2*h2
Let's see what happens when b1 = b2, so,
b1*h1 = b2*h2
b1*h1 = b1*h2
b1h1 - b1h2 = 0
b1(h1 - h2) = 0
b1 = 0 or h1 - h2 = 0
b1 = 0 or h1 = h2
If the bases b1 and b2 were equal, then either those bases must be 0 which isn't possible, or the altitudes must be equal. However, the initial premise is that the heights must be different from one another.
Therefore, the bases b1 and b2 can't be the same length.
We could follow the same steps and logic to conclude that if the altitudes h1 and h3 were different, then the bases b1 and b3 can't be the same. Similarly, we would conclude that b2 and b3 can't be the same. This is where the "without loss of generality" kicks in.
In other words, we only need to focus on one subcase to extend the logic to the other cases, without having to actually do every single step. That would be a bit tedious busywork.
In conclusion, we've shown that if the heights are different, then their respective bases must be different. This leads to wrapping up the proof that we have a scalene triangle.
Side note: I used an indirect proof or proof by contradiction. I assumed that a non-scalene triangle was possible and it led to a contradiction of h1 = h2.
how many days will he cut the last section?
Solving a linear equation, we will see that after 9 days he cuts the last section.
how many days will he cut the last section?We know that the initial length of the piece of cloth is 20m, and the taylor each day cuts a piece of 2 meters of it.
So, the length as a function on the number of days, is:
L(x) = 20m - 2m*x
Here we just need to solve:
L(x) = 2m
Because the last cut is when the long piece measures 4 meters (in that case he does one cut and has the two final pieces of 2 meters).
Solving that, we get:
20m - 2m*x = 2m
20m - 2m = 2m*x
18m/2m = x = 9
After 9 days he cuts the last section.
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how do i find x? pls tell me with working
Answer:
35
Step-by-step explanation:
Angle QRS is an inscribed angle, so measure of angle QRS is half the measure of the intercepted arc, arc SPQ. Therefore arc SPQ is 125*2 = 250 degrees, and arc QRS is 360 - 250 = 110 degrees.
Angle QPS is an inscribed angle, and arc QRS is its intercepted arc. Therefore angle QPS is 110/2 = 55 degrees. Since PS is the radius of the circle, angle PQS, the angle inscribed in the semicircle, is 90 degrees. Since interior angles of the triangle QPS add up to 180 degrees, angle QSP is 180 - 90 - 55 = 35 degrees.
Angles QSP and UST are vertical angles, and by the vertical angles theorem, they are congruent. Therefore x = 35.
kelvin pumped 15.2 gallons of gas into his car. if he paid 59.13 for the total amount of gas, what was the rate per gallon that kelvin paid
Answer:
3.89
Step-by-step explanation:
if 15.2 gallons cost 59.13.What about 1
then we just divide 59.13 by 15.2 to get the cost of 1 gallon
Find all solutions of the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.A) 3 sec2(θ) − 4 = 0B) cot(θ) + 1 = 0
The solution of the assumed equation is
θ = 135 + 360k
and
θ = -45 + 360k (or 315 + 360k)
Assuming the equation is
csc^2(θ) = 2cot(θ) + 4
and not
Assuming the equation to be:
csc^2(θ) = cot^2(θ) + 1
Solving these equations usually begins with algebra and/or trigonometry. ID for transforming equations to have one or more equations of the form:
trigfunction(expression) = number
It is not always easy to understand how to perform the desired transformation. If it's not obvious, first use the trigonometric identity to reduce the number of different arguments or functions in the equation. In this expression, all arguments are θ. Therefore, there is no need to reduce the number of arguments. But he has two different functions, csc and cot.
csc^2(θ) = cot^2(θ) + 1
Substituting the right side of this equation into the left side of the equation, we get: :
cot^2 (θ) + 1 = 2 cot(θ) + 4
Now that we have only one function cot and one argument θ, we are ready to find the form we need. Subtracting the entire right-hand side from both sides gives:
cot^2(θ) - 2cot(θ) - 3 = 0
The left-hand side factorizes:
(cot(θ)-3)(cot (θ) ) + 1 ) = 0
Using the properties of the zero product,
cot(θ) = 3 or cot(θ) = -1
These two equations are now in the desired form.
The next step is to write the general solution for each equation. The general solution represents all solutions of the equation.
cot(θ) = 3
Note that 3 is not a specific angle value for cot. That's why you need a calculator. Your computer probably doesn't have the crib button, so you'll need to switch it to tan
Since tan is the reciprocal of cot, if cot = 3...
tan(θ) = 1/3
Inverse tan tan^-1(1/3) can be used to find the reference angle. You should get a reference angle of 18.43494882 degrees. Using this reference angle and cot (and tan) being positive in the 1st and 3rd quadrants, we get the general solutions
θ = 18.43494882 + 360k
and
θ = 180 + 18.43494882 + 360k
.
θ = 198.43494882 + 360k
where
cot(θ) = -1
-1 should be recognized as a special angle value for cot. So you don't need a calculator. This reference angle is 45 degrees. Using this reference angle, cot is negative in the 2nd and 4th quadrants, so
θ = 180 - 45 + 360k
and
θ = -45 + 360k (or 360 - 45 + 360k) the general solution for
must get. to:
θ = 135 + 360k
and
θ = -45 + 360k (or 315 + 360k)
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Luigi is navigating a maze. He gets to a junction and has 3 directions he can go in. For each of these choices, he eventually gets to another junction where he has 6 choices of direction.
How many different possible paths are there?
In the following expression, both AAA and BBB are variables that can take positive values.
A+\dfrac{2}{B}A+
B
2
A, plus, start fraction, 2, divided by, B, end fraction
Which of these actions will cause the expression's value to increase?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
Keeping AAA constant and increasing BBB
(Choice B)
B
Keeping AAA constant and decreasing BBB
(Choice C)
C
Increasing AAA and keeping BBB constant
(Choice D)
D
Decreasing AAA and keeping BBB constant
The value to increase is keeping A constant and decreasing the value of B
What are fractions?Fractions are written as a ratio of two integers. For instance a.b is a fraction where a and b are integers.
In the fraction a/b, the numerator is and the denominator is b. If the value of the denominator is decreasing the fraction will increase but if the value of the denominator is increasing the fraction will decrease.
Given the expression A + 2/B, the higher the value of B provided such that that A is constant, the higher the expression. Hence the expression that will cause the value to increase is keeping A constant and decreasing the value of B
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Determine what type of model best fits the given situation: the membership of the local pta increases by 3 members a day for each day during the month of september.
Type of model best fits the given situation linear. Since it has a constant of +3 everyday.
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.linear type of model best fits the given situation.the membership of the local pta increases by 3 members a day for each day during the month of September.
Since it has a constant of +3 everyday.
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The area of the trapezoid is 40 square units.
A trapezoid is shown. The lengths of the bases are 6 and 10, and the height of the altitude is h.
What is the height of the trapezoid?
3 units
5 units
10 units
12 units
The altitude of the trapezoid, based on the given parameters is 5 units
How to determine the height of the trapezoid?From the question, we have the following parameters about the trapezoid
Base length 1 of the trapezoid = 6
Base length 2 of the trapezoid = 10
Area of the trapezoid = 40
Altitude of the trapezoid = h
The area of the trapezoid is calculated using
Area = 0.5 * (Sum of the two base lengths) * Altitude of the trapezoid
Substitute the given parameters in the above formula
40 = 0.5 * (6 + 10) * h
Evaluate the sum of 6 ad 10 (do not approximate)
40 = 0.5 * (16) * h
Evaluate the product of 0.5 and 16 (do not approximate)
40 = 8 * h
Divide both sides by 8 (do not approximate)
h = 5
Hence, the altitude of the trapezoid, based on the given parameters is 5 units
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Answer:
5 units
Step-by-step explanation:
5. Betty claims the solution to the equation 4x - 5(x - 5) = 7x + 13 is x = 1.5. She shows her steps below to
justify her solution.
Given
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
4x5(x-5) = 7x + 13
4x5x + 25 = 7x + 13
-x+ 25 = 7x + 13
25 = 8x + 13
12 = 8x
1.5 = x
Select the all correct justifications for the given steps.
Step 1: Distributive Property
Step 2: Combining Like Terms
Step 3: Addition Property of Equality
Step 4: Subtraction Property of Equality
Step 5: Associative Property of Equality
Answer:
See attached image
Step-by-step explanation:
Every step holds except for step 5
In mathematics, it deals with numbers of operations according to the statements.
Here,
Step 1 is the result of the distribution of -5 while opening the parenthesis, So, Step 1 holds the distributive property.
Step 2, states adding like terms across each side, so combining as terms hold,
Step 3, Addition over the equal sign. So it also holds
Step 4, subtraction of 12 over the equal sign. So subtraction of the terms also holds.
Step 5, does not hold because the number 12 gets divided by 8 it is not an associative property.
Thus, Every step holds except for step 5.
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B is the midpoint of segment AC. Which statement best describes the relationship between triangles ABD and CBD? (1 point)
The statement that best describes the relationship between triangles ABD and CBD is 'Triangles ABD and CBD are congruent by the SSS Congruence postulate'. Option A
What are similar triangles?
It is important to note the following;
"Two triangles are similar when their corresponding angles are equal and corresponding sides are in equal proportion."
The SSS congruence states that ; "Two triangles are congruent if all three sides of a triangle are congruent to corresponding three sides of other triangle."
SSS similarity postulates that; "Two triangles are similar if all the three sides of a triangle are in proportion to the three sides of another triangle."
SAS similarity postulates that ; "Two triangles are similar if the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle between the two sides in both the triangle are equal."
SAS congruence postulates that ; "Two triangles are congruent if two sides and the angle between these two sides of one triangle are congruent to the corresponding two sides and the included angle of a second triangle."
For given question,
We have been given triangles ABD and CBD.
B is the midpoint of line AC
⇒ AB = BC
For triangles ABD and CBD,
side AB = side CB; since, B is the midpoint of line AC
side BD = side BD ; they have common sides
side AD = side CD = 15 units each
So, by SSS postulates of triangle congruence triangles ABD and CBD are congruent triangles.
Therefore, the statement that best describes the relationship between triangles ABD and CBD is 'Triangles ABD and CBD are congruent by the SSS Congruence postulate'. Option A
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Let x be a discrete random variable. if pr(x<9) = 1/6, and pr(x>9) = 1/3, then what is pr(x=9)?
Answer: 1/2
Step-by-step explanation:
The probabilities must add to 1, so:
[tex]P(x < 9) +P(X=9)+P(X > 9)=1\\\\\frac{1}{6}+P(X=9)+\frac{1}{3}=1\\\\P(X=9)=\boxed{\frac{1}{2}}[/tex]
In 2010 and 2012, gallup asked the same 50 people how many hours had they worked at a job in the past 7 days. Is there a difference in the population mean amount of hours worked at a job between 2010 and 2012? would this be an example of independent or dependent samples?.
The given case of Gallup asking the same 50 people how many hours had they worked at a job in the past 7 days. is an example of dependent sample.
What is dependent sample?The measured values in relation in a dependent sample (also called a paired sample).
Some characteristics of dependent sample are-
It is a dependent sample, for instance, if a sample of patients who have knee reconstruction is selected, and each patient is questioned during the procedure. The reason for this is that the identical person was questioned twice.If, for instance, you wish to examine if a new category of baseball bat really does have an impact on notable features and the same individuals play once from the old bat and once with new bat, you also have a dependent sample. Since each player utilized both bats, there are two measured values for each player, all measured values are likewise accessible in pairs.A variation is preselected based on the format wherein you insert your data. A series is typically a respondent and, more broadly, a case. Metric values in a sequence are therefore originally regarded as dependent.To know more about dependent sample, here
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Please answer quickly! It would be great if you could include the question # and the answer in the answer section, and then explain it below. Thank you in advance!
Answer:
[tex]\textsf{19.} \quad S_{20}=1490[/tex]
33. None of these are correct.
Step-by-step explanation:
Question 19General form of an arithmetic sequence:
[tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termd is the common difference between termsGiven values:
[tex]a_n[/tex] = 27n = 20d = -5Substitute the given values into the formula and solve for a:
[tex]\implies 27=a+(20-1)(-5)[/tex]
[tex]\implies 27=a+(19)(-5)[/tex]
[tex]\implies 27=a-95[/tex]
[tex]\implies a=27+95[/tex]
[tex]\implies a=122[/tex]
Sum of the first n terms of an arithmetic series:
[tex]S_n=\dfrac12n[2a+(n-1)d][/tex]
where:
a is the first term.d is the common difference.Given values:
a = 122n = 20d = -5Substitute the given values into the formula and solve:
[tex]\implies S_{20}=\dfrac{1}{2}(20)[2(122)+(20-1)(-5)][/tex]
[tex]\implies S_{20}=10[244-95][/tex]
[tex]\implies S_{20}=10[149][/tex]
[tex]\implies S_{20}=1490[/tex]
Question 33Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
where:
a is the first termr is the common ratioGiven values:
a₁ = 1458r = ¹/₃Substitute the given values into the formula and solve:
[tex]\implies S_6=\dfrac{1458\left(1-\frac{1}{3}^6\right)}{1-\frac{1}{3}}[/tex]
[tex]\implies S_6=\dfrac{1456}{\frac{2}{3}}[/tex]
[tex]\implies S_6=\dfrac{1456 \cdot 3}{2}[/tex]
[tex]\implies S_6=2184[/tex]
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Helppp!! pleasee i put a ss!
Answer:
-20
Step-by-step explanation:
He went back 20 and not forward 20. Everyone would want a penalty if you got to go forward.
Use the laplace transform to solve the given initial-value problem. y'' − 6y' 13y = 0, y(0) = 0, y'(0) = −5
Answer:
Laplace transforms turn a Differential equation into an algebraic, so we can solve easier.
y'= pY-y(0)
y"=p²Y - py(0)- y'(0)
Substituting these in differential equation :
p²Y -py (0) -y' (0)-6(pY-y(0)) + 13Y
Substituting in the initial conditions given , fact out Y, and get:
Y( p²-6p+13) = -3
Y=-3/ p²-6p+13
now looking this up in a table to Laplace transformation we get:
y=-3/2.e³т sin(2t)
for the last one, find the Laplace of t∧2 . which is 2/p³
pY - y(0)+ 5Y= 2/p³
Y= 2/p³(p+5)
Taking partial fractions:
Y=-2/125(p+5) + 2/125p - 2/25p² + 2/5p³
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Answer:
The integral transform that converts a function of a real variable to a function of a complex variable is called Laplace transform. first we need to substitute y' and y" in differential equation then finding Laplace transformation and at last taking partial fractions.
Given: y'= pY-y(0)
y"=p²Y - py(0)- y'(0)
Putting y' and y" in differential equation :
p²Y -py (0) -y' (0)-6(pY-y(0)) + 13Y
Substituting in the initial conditions given , fact out Y, and get:
Y( p²-6p+13) = -3
Y=-3/ p²-6p+13
by Laplace transform we get:
y=-3/2.e³т sin(2t)
for the last one, find the Laplace transform of t∧2 . which is 2/p³
pY - y(0)+ 5Y= 2/p³
Y= 2/p³(p+5)
Taking partial fractions:
Y=-2/125(p+5) + 2/125p - 2/25p² + 2/5p³
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Distribute to create an equivalent
expression with the fewest symbols
possible.
2(3 – 8y)
=
Answer:
6 - 16y
Step-by-step explanation:
2(3 – 8y) = 2 × 3 - 2 × 8y = 6 - 16y
I need help cancelling units. please help
Hello and Good Morning/Afternoon:
Let's take this problem step by step:
Let's write out the equation we would hypothetically use to convert 410 kilometers to meters:
[tex]410 kilometers * \frac{1000 meters}{1 kilometers}[/tex]
Let's see if there are any errors:
there are 1000 meters in 1 kilometerwhen converting kilometer --> meter⇒ we want to get rid of the kilometer symbol
⇒ which is done in this problem
[tex]410 kilometers * \frac{1000 meters}{1 kilometers}=\frac{410 kilometers}{1 kilometers}*1000 meters = 410000meters[/tex]
Thus the answer is true
Answer: True
Hope that helps!
each side of a 4ft x 6ft rectangular flower bed was lengthened by the same amount. the area of the new flower bed is twice the area of the old one. Find the new dimensions.
The new dimensions of the flower bed are 4√2 and 6√2
How to determine the new dimensions?The dimensions of the initial rectangular flower bed are given as:
Length = 4ft
Width = 6 ft
The area of the new flower bed is twice the area of the old one.
This means that
New Area = Old Area * 2
Substitute the dimensions of the old area in the above equation
New Area = 4 * 6 * 2
Express 2 as √2 * √2
This gives
New Area = 4 * 6 * √2 * √2
Rewrite the above equation as:
New Area = 4√2 * 6√2
The area of a rectangle is
Area = Length * Width
This means that:
Length = 4√2 ft
Width = 6√2 ft
Hence, the new dimensions of the flower bed are 4√2 and 6√2
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Answer: 6x8
Step-by-step explanation:
(4+x)(6+x)=2*24
x^2+10x+24=48
subtract 48 on both sides
x^2+10x-24=0
Solve using the quadratic formula
-10±√(100+96)÷2
simplifies to
-(10±14)÷2 = 2, -12
-12 doesn't work though because the sides can't be negative.
So x=2
To check, add both sides by 2:
2(4x6)=6x8=48
Find the number of integral solutions of x+y +z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and
z ≥ 3.
There are 59 integer solutions
Such questions are best solved by writing cases and calculating the total number of cases. So beginning with
1) x = -3. The possible combinations are as follows:-
-3 2 13
-3 3 12
-3 4 11
-3 5 10
-3 6 9
-3 7 8
-3 8 7
-3 9 6
-3 10 5
-3 11 4
10 combinations
2) x = -2
-2 2 12
through
-2 11 3
10 combinations
3) x = -1
-1 2 11
through
-1 10 3
9 combinations
4) x = 0
0 2 10
through
0 9 3
8 combinations
as we can see from the pattern at x =1 we get 7 combinations, at x =2 we get 6 combinations, at x=3 we get 5 combinations and at x =4 we get 5 combinations.
Thus total number of combinations 4+5+6+7+8+9+10+10 = 59 integer solution.
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In order for you to use the goodnees-of-fit test, the test of independence, or the test of homogeneity, the expected frequencies for each cell needs to be at least:____.
The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.
According to the statement
we have to find the condition of the expected values in the case of testing of goodness-of-fit test.
So, For this purpose we know that the
The goodness of fit test is of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected.
So, The main condition of the expected value for the goodness of fit test is
For each category, the expected frequency is at least 5.
Without this condition the test is not possible, so overall this the main condition related the goodness of fit test.
So, The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.
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The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. on the bottom shelf are 3 fiction and 5 nonfiction books. choosing which 2 books describes a pair of dependent events?
The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
What is probability?Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.To find which 2 books describe a pair of dependent events:
A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change. Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance. Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is. Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
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Question 9 of 25 a bookstore costs $105 a day to keep open, and it spends $12 for each book that it sells. if each book sells for $15, what is the break-even point for this bookstore?
The store will break even after selling 35 books.
What is the break-even point?The break-even point is the moment at which total cost and total revenue are equal, implying that your small firm has no loss or benefit. In other words, you've reached the point where the costs of production equal the revenues for a product.To find what is the break-even point for this bookstore:
Given:
The cost required per day to keep the store open = $105Amount spent on each book = $12Let, n be the number of books.
Total costs = 12n + 105
The selling price of each book = $15
Total revenue = 15n
For breaking even, costs = revenue.
12n + 105 = 15n105 = 15n - 12n105 = 3n3n = 105Dividing both sides by 3:3n/3 = 105/3n = 35Therefore, the store will break even after selling 35 books.
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Which expression is equivalent to?
Answer: [tex]\frac{2x\sqrt[4]{y^{2}}}{3}[/tex]
Step-by-step explanation:
[tex]\sqrt[4]{\frac{16}[81}} \sqrt[4]{\frac{x^{11}y^{8}}{x^{7}y^{6}}}\\\\=\frac{2}{3} \sqrt[4]{x^{4}y^{2}}\\\\=\frac{2x\sqrt[4]{y^{2}}}{3}[/tex]
What are the x-intercept and vertex of this quadratic function? Write each feature as an ordered pair: (a,b). The x-intercept of function g is The vertex of function g is
The x-intercept of the function g(x) = -5(x - 3)^2 is (3, 0) and the vertex of the function g(x) = -5(x - 3)^2 is (3, 0)
How to determine the x-intercept?The function is given as:
g(x) = -5(x - 3)^2
Set g(x) to 0, to determine the x-intercept.
-5(x - 3)^2 = 0
Divide through by -5
(x - 3)^2 = 0
Take the square root of both sides
x - 3 = 0
Add 3 to both sides
x = 3
Hence, the x-intercept of the function g(x) = -5(x - 3)^2 is (3, 0)
How to determine the vertex?The function is given as:
g(x) = -5(x - 3)^2
A quadratic function is represented as:
g(x) = a(x - h)^2 + k
Where, the vertex is
Vertex = (h, k)
By comparing g(x) = a(x - h)^2 + k and g(x) = -5(x - 3)^2, we have
(h, k) = (3, 0)
Hence, the vertex of the function g(x) = -5(x - 3)^2 is (3, 0)
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NEED HELP ASAP
Which statement is correct?
OA) 7<√72<8
OB) 8<√72 <9
OC) 9<√72 <10
OD) 10<√72 < 11
Answer:
ur answer is B
Step-by-step explanation:
Answer:
B
As root over 72 is 8.48 and after we round off we get 8.5 so no B is correct
Me and mrs corrino can complete a job in 5 hours if mr corrino works twice as long as mrs corrino if each foes the job alone how long does it take mrs corrubi to complete the job alone
Mrs. Corrubi takes 7.5 hours to complete the job alone.
Directly proportional: as one amount increases, another amount increases at the same rate. Direct variation means when one quantity changes, the other quantity also changes in direct proportion
Inversely Proportional: when one value decreases at the same rate that the other increases. An increase in the quantity A leads to a decrease in quantity B and vice versa.
Let the number of hours taken by Mrs Corrubi to do a particular work be x.
∴ The number of hours taken by Mr Corrubi to do a particular work will be 2x.
So according to the condition,
1/x + 1/2x = 1/5
(2+1)/2x = 1/5
3/2x = 1/5
2x = 15
x = 7.5 hours.
Thus Mrs. Corrubi takes 7.5 hours to complete the job alone.
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Write an algebraic expression to match the graph
please help!
the graphed equation is:
y = -|x| + 1
How to find the algebraic expression that matches the graph?On the graph, we can see an absolute value equation, which opens downwards, and passes through the points (1, 0) and (0,1).
The general absolute value equation is:
y = a*|x - b| + c
Because the vertex is at the point (0, 1), we know that:
b = 0, c = 1
Replacing that we get:
y = a*|x| + 1
Now, this must be zero when we evaluate in x = 1, then:
0 = a*|1| + 1
a = -1
Then the graphed equation is:
y = -|x| + 1
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Drag each length to the correct location on the triangle. each length can be used more than once, but not all lengths will be used. what are the missing side lengths for the triangle? 10 5
Applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.
What is Trigonometry Ratios?Trigonometric ratios are defined as the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.
According to the given information:Reference angle (∅) = 60
Adjacent = 4√3
Opposite = ?
Apply TOA:tan 60 = opp/adj
tan 60 = Opp/4√3
√3 = opp/4√3
Opposite = √3 × 4√3
Opposite = 12
Find the other missing side:Reference angle (∅) = 60
Adjacent = 4√3
Hypotenuse = ?
Apply CAH:cos 60 = adj/hyp
cos 60 = 4√3/hyp
hyp = 4√3/cos 60
hyp = 4√3/1/2
hyp = 4√3 × 2
hyp = 8√3
Therefore, applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.
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If a diameter intersects a chord of a circle at a perpendicular, what conclusion can be made?
If a diameter intersects a chord of a circle at a perpendicular then the chord is bisected.
What is the relation between the chord and diameter of a circle?The segments of a circle whose endpoints are on its perimeter are called chords.A circle's diameter is the chord that passes across its center.The circle's longest chord equals its diameter.Any line that is perpendicular to a chord on the circle cuts it in half and goes through the center.The solution to the problem:
A circle's chord is intersected perpendicularly by its diameter, which also passes through the center of the circle. The chord and diameter are perpendicular. Any line that is perpendicular to a chord on the circle and passes through its center divides it. The chord is divided equally by the diameter.
Therefore, the chord is bisected.
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A local school needs to paint the floor of its theater room, where the length of the floor, x, is at least 12 feet. The width of the floor is 4 feet less than the length. It will have a stage and a closet, and the remaining area of the floor will be painted. The dimensions are shown in the diagram:
rectangle with length of x ft and width of x minus 4 ft, right triangle inside labeled stage with height of x minus 4 ft and base of 8 ft, rectangle inside labeled closet with length of 8 ft and width of 4 ft, the rest of the rectangle is labeled floor
Let A represent the painted area, in square feet, of the floor. Choose the correct equation to solve for area (A).
The correct equation that shows the area of painted area is
A=[tex]x^{2} -8x-16[/tex].
Given that the length of the floor,x,is atleast 12 feet.The width of the floor is 4 feet less than the length.There is a right angle of height x-4 and base 8 feet. The rectangle inside has length of 8 feet and width be 4 feet.
We are required to find the painted area of the theater room in square feet.
To find the painted area of the theater the following steps must be followed:
1) Find the area of the theater room.
length =x
Breadth=x-4
Area=x(x-4)
=[tex]x^{2} -4x[/tex]
2) Area of the right triangle.
Height=x-4
Base=8
Area=1/2 *8*(x-4)
=4(x-4)
=4x-16
3) Find the area of the rectangle inside labeled closet.
Length=8
Width=4
Area=8*4
=32
Area=Area of theater room-Area of of right triangle-Area of closet.
=[tex]x^{2} -4x[/tex]-4x+16-32
=[tex]x^{2} -8x-16[/tex]
Hence the correct equation that shows the area of painted area is
A=[tex]x^{2} -8x-16[/tex].
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Answer:
A = x(x − 4) − 0.5(8)(x − 4) − 3(7)
Work:
x = length, making the width (x-4)
The stage closet will be (x-4)(8)(1/2)
The rectangle is 7(3)
which makes the painted area x(x-4) - 4(x-4)
thus giving us
x(x − 4) − 0.5(8)(x − 4) − 3(7)
Step-by-step explanation:
hope this helps :)
