Answers
Answer:
thanks
Step-by-step explanation:
We can prove this by contradiction.
Let us assume that c2=a2+b2 in ΔABC and the triangle is not a right triangle.
Now consider another triangle ΔPQR. We construct ΔPQR so that PR=a, QR=b and ∠R is a right angle.
By the Pythagorean Theorem, (PQ)2=a2+b2.
But we know that a2+b2=c2 and a2+b2=c2 and c=AB.
So, (PQ)2=a2+b2=(AB)2.
That is, (PQ)2=(AB)2.
Since PQ and AB are lengths of sides, we can take positive square roots.
PQ=AB
That is, all the three sides of ΔPQR are congruent to the three sides of ΔABC. So, the two triangles are congruent by the Side-Side-Side Congruence Property.
Since ΔABC is congruent to ΔPQR and ΔPQR is a right triangle, ΔABC must also be a right triangle.
This is a contradiction. Therefore, our assumption must be wrong.
Step-by-step explanation:
We can prove this by contradiction.
Let us assume that c2=a2+b2 in ΔABC and the triangle is not a right triangle.
Now consider another triangle ΔPQR. We construct ΔPQR so that PR=a, QR=b and ∠R is a right angle.
By the Pythagorean Theorem, (PQ)2=a2+b2.
But we know that a2+b2=c2 and a2+b2=c2 and c=AB.
So, (PQ)2=a2+b2=(AB)2.
That is, (PQ)2=(AB)2.
Since PQ and AB are lengths of sides, we can take positive square roots.
PQ=AB
That is, all the three sides of ΔPQR are congruent to the three sides of ΔABC. So, the two triangles are congruent by the Side-Side-Side Congruence Property.
Since ΔABC is congruent to ΔPQR and ΔPQR is a right triangle, ΔABC must also be a right triangle.
This is a contradiction. Therefore, our assumption must be wrong
Related Questions
Determine the validity of the converse and give a counterexample if the converse is not valid.
If it is sunny, then it is 80° Fahrenheit. The converse is valid.
If it is 80° Fahrenheit, then it is sunny. The converse is valid.
If it is not sunny, then it is not 80° Fahrenheit. The converse is invalid; a counterexample is a day that is not 80° Fahrenheit and not sunny.
If it is 80° Fahrenheit, then it is sunny; The converse is invalid; a counterexample is a day that is 80° and cloudy.
Answers
Your analysis is correct. Here's a summary:
If it is sunny, then it is 80° Fahrenheit. (Original statement)
Converse: If it is 80° Fahrenheit, then it is sunny. (Valid)
If it is 80° Fahrenheit, then it is sunny. (Original statement)
Converse: If it is sunny, then it is 80° Fahrenheit. (Valid)
If it is not sunny, then it is not 80° Fahrenheit. (Original statement)
Converse: If it is not 80° Fahrenheit, then it is not sunny. (Invalid)
Counterexample: A day that is not 80° Fahrenheit and not sunny (e.g., 70° and cloudy).
If it is 80° Fahrenheit, then it is sunny. (Original statement)
Converse: If it is sunny, then it is 80° Fahrenheit. (Invalid)
Counterexample: A day that is 80° Fahrenheit and cloudy.
In cases 1 and 2, the original statements and their converses are valid because the relationship between "sunny" and "80° Fahrenheit" holds in both directions. However, in cases 3 and 4, the converses are invalid because there are counterexamples where the second part of the statement (either "not 80° Fahrenheit" or "cloudy") does not necessarily imply the first part ("not sunny" or "80° Fahrenheit").
I do not understand how they got this answer. I am stuck on the exponent party- Please see attached
Answers
Looking at the question, the answer gotten is:$4316.55. The question is related to compound interest.
What is compound interest?Compound interest is known to be the interest that is earned on a principal sum in addition to the accumulated interest previously. It is as a result of reinvesting interest.
To find the compound interest, the formula used is:
A= P(1+r/n)^nt.
Where
P is the principal sum= $3500
r is the rate = 0.035
n is the compounding period = 12 months.
t is the time = 6 years.
Substituting them in the equation, we have:
A = 3500 ( 1 + 0.035/12)^12×6
Working out the one in the bracket and multiplying the exponent, we have:
A = 3500 (1.00291667)^72
Note: We got 72 by multiplying 12 by 6.
1.00291667 raised to the power of 72 = 1.23330133
A = 3500× 1.23330133 = $4,316.55
Ans: $4,316.55
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Dr. Shaban measured the height of his daughter every year from her birth to age 14. To see the trend of growth in height, which type of graph would be appropriate to display the data?
Answers
Please mark it as the brainiest
Answer:
quadratic
Step-by-step explanation:
The type of graph that most represent the height is quadratic, where the children grew faster in the beginning and slowly slow down until adulthood, before slowly getting shorter ( trend, which is most common )
what is this answer?
Answers
Answer:
a
Step-by-step explanation:
Because I did this already
At a dance supply store dance pants cost $30 each and leotards cost $18 each you have $175 to spend you are going to buy 3 pairs of pants what is the greatest number of leotards you can buy
Answers
answer
4 pairs
Step-by-step explanation:
total is $175
when you buy three pairs of pants you have wasted $90
175-90 equals 85
an employee at the bank notices an abandoned account with a balance of $360. the bank charges a monthly fee of $8 to maintain an account. the equation for this situation is y = 360 - 8x, where x is the number of months, and y is the balance in dollars. Part A: Find the y-intercept Part B: Find the x-interceptPart C: Interpret the meaning of the x- and y-intercept in terms of the problem.
Answers
Given:
There are given the equation:
\(y=360-8x\)Explanation:
(A):
To find the y-intercept, we need to put 0 for x and solve the equation for the value of y.
So,
From the function:
\(\begin{gathered} y=360-8(0) \\ y=360 \end{gathered}\)Hence, the y-intercept is shown below:
\((0,360)\)(B):
To find the x-intercept, we need to put 0 for y and find the values for x:
So,
\(\begin{gathered} y=360-8x \\ 0=360-8x \\ 8x=360 \\ x=\frac{360}{8} \\ x=45 \end{gathered}\)Hence, the value x-intercept is shown below:
\((45,0)\)(C):
The interpret the meaning of the x- and the y-intercept is shown below:
In the given context, the y-intercept, and x-intercept, mean x = 0 and y = 0 and also refers to the starting values.
For a time-based exercise, this will be the value when we started talking we read or when we started tracking the time and its related changes.
The value of an investment property after t years can be found using the formula V =C (1 + r)^2, where V is the current
value of the property, C is the original investment,
and r is the annual rate of appreciation.
a. Solve the formula for r.
b. Lew bought a condo 20 years ago for $50,000, and the current value of the condo is $175,000. Assuming the same
rate each year, what has the annual rate of appreciation been? Round your answer to the nearest half a percent.
Answers
Answer:
0.871
Step-by-step explanation:
a. Solve the formula for r.
V = C (1 + r)²
dividing both sides by C, we have
V/C = (1 + r)²
(1 + r)² = V/C
taking square root of both sides, we have
√(1 + r)² = √(V/C)
1 + r = √(V/C)
r = √(V/C) - 1
b. Lew bought a condo 20 years ago for $50,000, and the current value of the condo is $175,000. Assuming the same
rate each year, what has the annual rate of appreciation been? Round your answer to the nearest half a percent.
Since r = √(V/C) - 1 and V = $ 175,000 and C = $ 50,000
Substituting the values of the variables into the equation for r, we have
r = √($ 175,000/$ 50,000) - 1
r = √3.5 - 1
r = 1.871 - 1
r = 0.8708
r ≅ 0.871
describe how a graph would look for the solution set for the inequality in problem 5. describe what the solution means and how the price of the balloons bought will affect the amount in the budget.
Answers
A)
i) the inequality to show the number of ballons that the dance committee can buy is: 0.80b + 65 ≤ 125
ii) solving the inequality above, we arrive at b ≤ 75
B) The graph is attached accordingly.
C) See the description of the solution below.
What is the explanation for the above?
Let's start by defining our variables. Let b be the number of balloons that the dance committee could buy.
The cost of b balloons is $0.80b. We want to make sure that the cost of the balloons plus the amount already spent on decorations ($65) is less than or equal to the budget of $125. So we can write the following inequality:
0.80b + 65 ≤ 125
Now we can solve for b:
0.80b + 65 ≤ 125
0.80b ≤ 125 - 65
0.80b ≤ 60
b ≤ 75
Therefore, the dance committee can buy up to 75 balloons to stay within their budget.
To graph the solution set, we can plot b on the horizontal axis and shade the region to the left of b = 75, since b must be less than or equal to 75.
The solution set represents all possible values of b that satisfy the inequality. In this case, the solution set is b ≤ 75, which means that the dance committee can buy up to 75 balloons and still stay within their budget.
As the number of balloons increases, the cost of the balloons also increases, and the amount of money left in the budget decreases.
Therefore, the more balloons the dance committee buys, the less money they will have left for other decorations or expenses.
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Full Question:
Since the above question is incomplete, it appears you are referring to the question below.
The dance committee has a budget of $125 to decorate the gym for a spring dance. They already spent $65. Some members want to buy helium balloons that cost $0.80 each.
A) Write and solve an inequality to show the number of balloons that the dance committee could buy.
B) Graph the solution set for the inequality.
C) Describe what the solution means and how the number of balloons affects the amount in the budget.
Multi-Step Linear Equations LC)
Solve −7x− 7 = −3x + 9 for x.
A: x = −4
B: x = −3
C: x = 3
D: x = 4
Answers
Answer:
A) x= -4
Step-by-step explanation:
-7x+3x=7+9
-4x= 16
x= 16÷ -4 = -4
Mr. Logan agrees to give you a loan of 25,000 to start your business, but charge you 7% interest. How much will you have to pay him back?
Answers
Answer:
26000
Step-by-step explanation:
A natural history museum surveyed the people visiting the museum for one month and
created a circle graph to show the age of the visitors for that month.
a. Find the number of degrees for each part of the museum visitors graph.
Age 18 and under:
Age 19 – 44:
Age 45 – 64:
Age 65 and over:
b. If 5000 people visited the museum during the month the survey was taken, how Age 18 and under:
Age 19 – 44:
Age 45 – 64:
Age 65 and over:
Answers
Answer:
20
Step-by-step explanation:
19-44=25
45-64=19 25+19=44 44-64=20
HELP SRSLY I JEED TO GET THIS RIHT ILL MARK AS BRAINLYIST AND ILL GIVE 40 POINTS 14 yd-
12 yd
30 yd
2
The triangular prism above undergoes a dilation whose scale factor is
3
What is the volume of the image? Round your answer to the nearest tenths place.
Answers
A triangular prism is a three-dimensional geometric shape that consists of two triangular bases and three rectangular faces connecting them. It is a polyhedron with six faces, nine edges, and six vertices.
The two triangular bases of a triangular prism are congruent and parallel to each other. The rectangular faces are perpendicular to the triangular bases, and their lateral edges connect the corresponding vertices of the triangular bases.
The triangular bases are identical and parallel to each other. Each base has three vertices, three edges, and one face.There are three rectangular lateral faces connecting the corresponding vertices of the triangular bases. Each lateral face has two edges and one face.
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Which graph represents the function y - 3= 3/2 (x - 4)?
Answers
Answer:
A
Step-by-step explanation:
Answer:
Step-by-step explanation:
Yes it is A i did it rn
Tutorial
A cylinder has a height of 17 centimeters and a radius of 15 centimeters. What is its volume?
Use 3.14 and round your answer to the nearest hundredth.
Answers
Answer:
Volume of the cylinder is 12016.5 cm³\( \\ \)
Step-by-step explanation:
Using formula:
\( \: \: \: \: \: \: \: \: \: \: {\underline{\boxed {\pmb{ \sf{Volume \: of \: cylinder = \pi r^2h}}}}} \: \pink\star \)
\( \\ \)
Where,
Height of cylinder is 17 cmRadius of the cylinder is 15 cm.Value of π = 3.14\( \\ \)
Substituting the required values in the above formula :
\( \\ \)
\( \dashrightarrow \sf \: \: Volume = 3.14 \times {(15)}^{2} \times 17 \\ \\ \)
\(\dashrightarrow \sf \: \: Volume = 3.14 \times 225 \times 17 \\ \\ \)
\(\dashrightarrow \sf \: \: Volume = 706.5 \times 17 \\ \\ \)
\(\dashrightarrow~~{\boxed {\pink{\pmb{\sf {Volume = 12016.5 \: {cm}^{3}}}}}} \\ \\ \)
Hence,
Volume of cylinder is 12016.5 cm³Answer :
12000 cm³⠀
Explanation :
We know,
\({ \longrightarrow \qquad{\boldsymbol {\pmb{ Volume_{(cylinder)} = \pi {r}^{2} h \: }}}}\)
Where,
r is the radius of the cylinder. Here, the radius is 15 cm . h is the height of the cylinder. Here, height is 17 cm Here, we will take the value of π as 3.14 approximately .⠀
Substituting the values in the formula :
\({ \longrightarrow \qquad{ { \sf{ Volume_{(cylinder)} = 3.14 \times ({15})^{2} \times 17 \: }}}}\)
⠀
\({ \longrightarrow \qquad{ { \sf{ Volume_{(cylinder)} = 3.14 \: \times 225 \times 17}}}}\)
⠀
\({ \longrightarrow \qquad{ { \sf{ Volume_{(cylinder)} = 3.14 \times 3825 }}}}\)
⠀
\({ \longrightarrow \qquad{ \pmb{ \sf{ Volume_{(cylinder)} = 12010.5 }}}}\)
⠀
Therefore,
The volume of the cylinder is 12000 cm³ . (Rounded to nearest hundredth)A pair of basketball shoes was originally $120, but was on sale for 17% off. What is the sale price of the shoes?
*
Answers
Summer buys a bag of cookies that contains 7 chocolate chip cookies, 8 peanut butter cookies, 5 sugar cookies and 7 oatmeal cookies.
What is the probability that Summer reaches in the bag and randomly selects 2 oatmeal cookies from the bag? Round your answer to four decimal places.
Answers
Answer:
her chance of getting otmeal cookies are 7 out of 20
Step-by-step explanation:
you can round yourself
Releas
Two cyclists, 112 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other, and they meet after 4 hours of riding.
a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.
b. What are the speeds of the two cyclists? Put both values in the answerbox, separated with a comma, and select the appropriate units.
Answers
Answer:
Speed of a= 21 miles/hr
r = Speed of b= 7 miles/hr
Speed of a = 3r
Step-by-step explanation:
The cyclist are 112 miles apart
Time traveled by two = 4 hours
Speed of a = 3 * speed of b
If a cylcles 3 times More than b, then a will cover 3*distance of b
But speed = distance/time
Time = 4hours
Total distance=112
a = 3b
3b + b = 112
4b = 112
b = 112/4
b = 28 miles
a = 3b
a = 3*28
a = 84 Miles
They bought traveled 4 hours
Speed of a = 84miles/4 hours
Speed of a= 21 miles/hr
Speed of b = 28miles/4 hours
Speed of b = 7 miles/hr
7+(24/6)+(3²/3)+10 need help solveing it out
Answers
Answer: 24
Step-by-step explanation:
7+(24/6)+(3²/3)+10
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.
7+24/6+3^1+10 Also when I say 3^1 I mean 3 and the exponent is 1
Divide 24 by 6 to get 4.
7+4+3^1+10
Add 7 and 4 to get 11.
11+3^1+10
Calculate 3 to the power of 1 and get 3.
11+3+10
Add 11 and 3 to get 14.
14+10
Add 14 and 10 to get 24.
Molly's scout troop sold 148 boxes of cookies last month and 165 boxes this month. Find the percent of increase, rounded to the nearest tenth of a percent.
Answers
The percent of the increase, rounded to the nearest tenth of a percent, concerning the sales of boxes of cookies that Molly sold last month and this month, is 11.5%.
How is the percentage increase determined?The percentage increase can be determined by finding the difference or the amount of increase in sales.
This difference is divided by the previous month's sales and multiplied by 100.
The total number of boxes of cookies Molly's Scout Troop sold last month = 148
The total number sold this month = 165
The increase = 17 (165 - 148)
Percentage increase = 11.5% (17 ÷ 148 x 100)
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What is -1.2 -29/20 =
Answers
Answer:
-2.65
Step-by-step explanation:
⦁ A landscape plan includes a rectangular flower bed that is surrounded the wood planks. In the drawing, the rectangular flower bed is 4 in. by 5 in. The length and width of the actual flower bed will be 30 times larger than the length and width in the drawing.
⦁ What is the perimeter of the drawing? Show your work.
⦁ What is the perimeter of the actual flower bed? Show your work.
⦁ What is the effect on the perimeter of the flower bed with the dimensions are multiplied by 24? Show your work.
Answers
The perimeter of the actual bed is 540 square inches
The perimeter of a rectangle
The formula for calculating the perimeter of a rectangle is expressed as:
P = 2(l + w)
l is the length
w is the width
GIven the following
l = 4in
w = 5in
P = 2(4+5)
P = 2(9)
P = 18 in
If the length and width of the actual flower bed will be 30 times larger than the length and width in the drawing, the perimeter of the actual bed is;
P = 2(4(30) + 5(30))
P = 2(120 + 150)
P = 2(270)
P = 540 square inches
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I need the answer ASAP please. I would appreciate the help
Answers
Answer:
a) 293 units
b) 5795p
Step-by-step explanation:
First, determine how many units used
Take the new reading and subtract the old reading
6538 - 6245
293 units
The first 200 is at 22p
200 * 22 p =4400p
293 -200 = 93 units at the remaining unit price.
93 * 15 p =1395p
Add the two totals together
4400p + 1395p =5795p
Solve for the following if x = 6: (Hint: substitute 6 for the letter x and work the problem. You will work more with substitution later.) Example: 10x = 10*6 = 60 9. x - 6 ( if x = 6) 10. 7 + x ( if x = 6) 11. 3x - 9 ( if x = 6) 12. 63/x ( if x = 6) 13. 5 + 5x + 10 ( if x = 6)
Answers
Using PEMDAS and substituting 6 for x, the results of the mathematical operations are as follows:
1) 482) 763) 1894) 1265) 105.What is PEMDAS?PEMDAS is the order of mathematical operations that explains the correct sequential steps for evaluating mathematical expressions.
PEMDAS means that mathematical operations must follow the following order:
ParenthesesExponentsMultiplicationDivisionAdditionSubtraction.1) 9. x - 6 ( if x = 6)
= 9 x 6 - 6
= 54 - 6
= 48
2) 10. 7 + x ( if x = 6)
= 10 x 7 + 6
= 70 + 6
= 76
3) 11. 3x - 9 ( if x = 6)
= 11 x 3(6) - 9
= 11 x 18 - 9
= 198 - 9
= 189
4) 12. 63/x ( if x = 6)
= 12 x 63/6
= 126
5) 13. 5 + 5x + 10 ( if x = 6)
= 13 x 5 + 5(6) + 10
= 65 + 30 + 10
= 105
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a) Work out w, the width of the rectangle. b) Calculate the area of the curved surface of the cylinder. Give your answers to the nearest integer and remember to give the correct units. 11 cm 7 cm W Not drawn accurately
Answers
(a) The width of the rectangle is 11 cm
(b) the curved area is 242 square centimeters
a) Working out w, the width of the rectangle.From the question, we have the following parameters that can be used in our computation:
The net of the cylinder
The width is the height of the cylinder
So, we have
Width, w = 11 cm
b) Calculating the area of the curved surface of the cylinder.The curved surface area of cylinder is calculated as
A = 2πrh
So, we have
A = 2π * 7/2 * 11
Evaluate
A = 242
Hence, the curved area is 242 square centimeters
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On a coordinate plane, DEF has vertices D(1,2), E(7,2)and F(1,9). What is the distance between point E and F?
Answers
Step-by-step explanation:
Using distance formula,
Let the distance between point E and F = ef,
\(ef = \sqrt{{(7 - 1)}^{2} + {(2 - 9)}^{2} } \\ ef = \sqrt{85} \\ = 9.219544457\)
Which pile of laundry has more shirts?
Pile 1
Three pants two shirts
Pile 2
Two shirts 4 pants
Answers
Answer:111
Step-by-step explanation:
1111
Estimate the sum of 412.02 and 513.87 to the nearest whole number?
Answers
In a village there are 60 families with 4 members each. Out of
these 28 families speak only Tamil and 20 families speak only
Urdu. How many family members speak both Tamil and
Urdu
Answers
Answer:
12
Step-by-step explanation:
28 plus 20 equals to 48 and then each divide 4
HELP PLEASE WILL MARK BRAINLIEST
Answers
Answer:
D
Step-by-step explanation:
Point B is (-2,3) then it is shifted (x, y+4)
so, x remains the same by y goes up 4 units
-2,7
Find the volume of the following figure.1.5m2.5 m6 m
Answers
Start by dividing the figure into 2 prisms
calculate the volume for both independently.
For the rectangular prism
\(V=l\cdot w\cdot h\)then,
\(\begin{gathered} V=2\cdot2.5\cdot1.5 \\ V=7.5m^3 \end{gathered}\)For the triangular prism
\(V=\frac{1}{2}l\cdot h\cdot w\)then,
\(\begin{gathered} V=\frac{1}{2}\cdot1.5\cdot4\cdot2.5 \\ V=7.5m^3 \end{gathered}\)Add both volumes together
\(\begin{gathered} V_t=7.5m^3+7.5m^3 \\ V_t=15m^3 \end{gathered}\)
