Part I: Angle Sum Relationships
Arrange the three congruent triangles so that angles 1 and 3 are adjacent to one another, and angle 2 is adjacent to angles 1 and 3.
B. What do you notice about the three angles?
C. What do they appear to form?
D. What can you conclude about the sum of the angles in a triangle?
Answers
They appear to form a straight line.
It means that the sum of the three angles of a triangle is appears to be 180 degrees.
Answer with explanation:
→→The three Angles form a Linear pair.That is
⇒∠1+∠2+∠3=180°
→→When these three congruent triangles are joined they form a Trapezoid.
→→Sum of angles in a trangle is given by Angle sum property Axiom of triangle which states that sum of the angles in a triangle is 180°.
Related Questions
Assume the least squares equation is ŷ = 10 + 20x. what does the value of 10 in the equation indicate? when x = 0, y = 10. x increases by 10 for each unit increase in y. y increases by 10 for each unit increase in x. it is the error of estimation.
Answers
in the equation ŷ = 10 + 20x
the value of 10 is the predicted value of Y, given X=0 value.
It is also known as Y intersect
The value of 10 in the equation ŷ = 10 + 20x represents the y-intercept, which is the value of y when x equals zero.
Explanation:The value of 10 in the equation ŷ = 10 + 20x represents the y-intercept. In the context of the least squares equation, the y-intercept is the value of y when x equals zero. So when x = 0, y = 10, indicating that the initial value of y is 10.
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sqrt= Square Root
A student is attempting to calculate the square root of 18. His work is shown below. Which statement below best applies to his mathematical reasoning?
Givin sqrt 18 I observe that 18 is not a perfect square. I notice the perfect squares closest to 18 are 16 and 25, so I estimate the answer to fall somewhere between those numbers. Since 18 is closer to 16, I estimate that sqrt 18= 17
A.
18 is a perfect square, and the radical could have been evaluated directly.
B.
16 and 25 are not perfect squares, and therefore the student should not have chosen those numbers to estimate sqrt 18
C.
The student did not evaluate sqrt 16 and sqrt 25 before estimating sqrt 18
D.
The student has made no error. sqrt 18= 17
Answers
The balance on a car loan after 4 years is $8,996.32. The interest rate is 5.6% compounding annually. What was the initial value of the loan?
Answers
A=P(1+r)^n
where
A=future value
P=principle amount
r=rate
n=time
thus plugging in our values we get:
8996.32=P(1+5.6/100)^4
solving for p we shall have:
8996.32=1.2435P
hence:
P=$7234.5
Thus the initial amount was $7234.5
How do you solve this
Answers
An item is called "price elastic" if you drop the price and revenue goes up. Last week you sold 10 sodas for $2 each; this week you sold 30 sodas for $1 each. Is soda price elastic?
Answers
Final answer:
Soda is price elastic because lowering the price from $2 to $1 resulted in an increase in total revenue from $20 to $30, indicating that a decrease in price caused a larger increase in quantity sold.
Explanation:
When determining whether an item is price elastic or not, we look at the effect that changing the price has on the total revenue. If a decrease in price leads to an increase in total revenue, the demand for the product is considered price elastic. In the example given, soda was sold at different prices and quantities: 10 sodas at $2 each last week, and 30 sodas at $1 this week. We use these numbers to calculate the total revenue for each week:
Last week: 10 sodas × $2/soda = $20
This week: 30 sodas × $1/soda = $30
Since the total revenue increased from $20 to $30 when the price was lowered from $2 to $1, we can see that the revenue increased as a result of the price drop, indicating that the demand for soda is indeed price elastic.
Which value of r indicates a stronger correlation: requals0.811 or requalsnegative 0.861? explain your reasoning?
Answers
r=-0.861 indicates stronger correlation than r=0.811 because |-0.861| > |0.811|.
Using the law of cosines, a=_ rounded to the nearest tenth.
Answers
= 4.865
a = 2.2 to nearest tenth.
Answer: a = 2.2
Given that: b = 4.0, c = 3.7, A=33.
The law of cosine is:
[tex]a^2=b^2+c^2-2bccosA\\a^2=4.0^2+3.7^2-2(4.0)(3.7)cos(33)\\a^2=4.86535118882\\a=\sqrt{4.86535118882}\\a=2.20575410888\\a=2.2[/tex]
So a = 2.2
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What is a potential source of bias if an) if you are surveying students to find out their opinion of a new teacher with the following question: Is Mr Wilson a terrible teacher?
No source of bias.
Not specific Enough.
Implies that Mr. Wilson is a bad teacher.
Names the teacher.
Answers
Answer:
pronoun-antecedent number agreement error.
PLZ HELP ASAP INSCRIBED QUADRILATERALS
Answers
117 + D = 180
D = 63 degrees
A book club offers a choice of 8 books from a list of 40. In how many can a member make a collection?
Answers
This is a math combination problem. The number of ways a member can choose 8 books from a list of 40 is 76,904,685 ways.
Explanation:This is a combinatorics problem, specifically a combination problem. A combination is a selection of items from a larger set where the order does not matter. In this case, we have a set of 40 books and want to know how many ways one can select 8 books from those 40. The formula for calculating combinations is nCr = n! / [(n - r)! * r!] where 'n' represents the total number of items, 'r' represents the number of items to choose, 'nCr' represents the number of combinations of n items taken r at a time, and '!' denotes factorial, the product of all positive integers up to that number.
Applying the combination formula, a member can make the choice of 8 books from a list of 40 in:
40C8 = 40! / [(40 - 8)! * 8!] = 76,904,685 ways
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The function P(x) = 3,113(1.2795)^x models the population, in millions, of California since 1990. Use the function to complete the following.
The number 3.113 represents
(a) The current population, in millions, of California.
(b) The population, in millions, of California in 1990
(c) The amount, in millions, that the population increases each year
The number 1.2795 represents
(a) The population, in millions, of California in 1990.
(b) The amount, in millions, that the population increases each year.
(c) The rate the population of California is increasing each year.
Answers
y = A (b) ^ x
Where,
A: initial amount
b: growth rate
x: time
We then have the following function:
P (x) = 3,113 (1.2795) ^ x
Where,
The number 3.113 represents:
(b) The population, in millions, of California in 1990
The number 1.2795 represents:
(c) The rate of the population of California is increasing each year.
Write the related series for the finite sequence –7, –10, –13, . . ., –22. then find the sum.–7 + (–10) + (–13) + (–16) + (–19) + (–22) = –87
–7 + (–10) + (–13) + (–15) + (–18) + (–22) = –85
–7 + (–10) + (–13) + (–14) + (–18) + (–22) = –84
–7 + (–10) + (–13) + (–17) + (–20) + (–22) = –89
Answers
Answer: [tex]-7+(-10)+(-13)+(-16)+(-19)+(-22)=-87[/tex]
Step-by-step explanation:
Given finite sequence : -7, -10, -13, . . ., -22.
Difference between first and second term=[tex]-10-(-7)=-10+7=-3[/tex]
Difference between second and third term =[tex]-13-(-10)=-13+10=-3[/tex]
Hence, the common difference = -3
The next term after -13 =[tex]-13+(-3)=-13-3=-16[/tex]
The next term after -16 =[tex]-16+(-3)=-16-3=-19[/tex]
The next term after -19 =[tex]-19+(-3)=-19-3=-22[/tex].........which is the last term of the sequence.
Now, the sum of the given sequence =[tex]-7+(-10)+ (-13) + (-16) + (-19) + (-22) [/tex]
[tex]=-7-10-13-16-19-22= -87[/tex]
hello can you please help me posted picture of question
Answers
Probability in this case will be = Area of favorable outcome/Total Area
Let the total area be A.
Area of each section will be A/10
So probability of landing on 3 will be = (A/10) / A = 1/10
So the correct answer will be option C
Hakim invests $700 in a bank that pays 5% simple interest annually. After one year he uses the money in his account to buy a computer. The original cost of the computer is $750.00 . The computer is on sale for a 20% discount off of the original cost. The sales tax is 4% of the sale price.
After purchasing the computer, how much does Hakim have left in his bank account? Show your work.
Answers
(original cost)*(1 -0.20)*(1 +0.04)
= $750*0.80*1.04 = $624.00
The ending balance on Hakim's bank account is
$700 +700*.05 = $735.00
The amount remaining after Hakim pays for the computer is
$735.00 -624.00 = $111.00
Hey can you please help me posted picture of question
Answers
Two transformations occur on F(x)
1) Shift 8 units left
So, the expression will be | x + 8 |
2) Shift 3 units down
So, the expression will be |x + 8| - 3
Thus,
G(x) = |x +8| - 3
So, option D is the correct answer
A minus number on the right of an equal sign (where f(x) or y or something like it is on the left of the equal sign) that is negative means that the function is going down. So any positive number in the answer is wrong if it greater than 0.
f(x) = | x | - 3 is going down.
Comment 2
Anything inside the | | which is plus goes left (not right) so you want y = |x + 8| - 3
D<<<< answer
If Teresa counts 9 leaves on September 1, how will the number of leaves change from may 1 to September 1
Answers
The difference in the number of leaves is:
9 - 2 = 7
Hence, the number of leaves has increased by 7 units.
A pair of dice are rolled. What is the probability of rolling 4 or greater?
A: 5/36
B: 1/18
C: 1/36
D: 11/12
Answers
Explanation:
1) The sample space is formed by 36 pairs: 6×6 = 36.
2) Roolling 4 or more is the same that not rolling 3 or less
3) Rolling 3 or less are (1,1), (1,2), and (2,1). Those are 3 outcomes out of 36.
4) Therefore, not rolling 3 or less (the same that rolling 4 or more) has 36 - 3 = 33 outcomes out of 36.
5) The probability of 33 out of 36 is 33/36
6) Simplify the fraction 33/36 = 11/12
And that is the answer.
Which is equivalent to sin^-1(tan(pi/4)) ? Give your answer in radians.
Answers
First we evaluate tan(π/4). The value of tan(π/4) is 1.
So,
[tex]sin^{-1}(tan( \frac{ \pi }{4})) =sin^{-1} (1)[/tex]
sin(π/2) = 1
So,
[tex]sin^{-1}(1)= \frac{ \pi }{2} [/tex]
Thus, we can write:
[tex]sin^{-1}(tan( \frac{ \pi }{4}))= \frac{ \pi }{2} [/tex] radians.
So, the answer to this question is π/2 radians.
Answer:
the answer is b
Step-by-step explanation:
algebra 2 chapter 7
1-15 !!!
Answers
13) 5 + 8log_7 (v + 10) = 298log_7 (v + 10) = 24log_7 (v + 10) = 37^3 = v + 10343 = v + 10v = 333
14) log_5 (x^2) + log_5 (4) = 1log_5 (4x^2) = 15^1 = 4x^25/4 = x^2x = +/- sqrt(5) / 2 = +/-1.1180
*No extraneous solutions here, since the equation only uses x^2, not x.
15) -6*12^(b+7) +1 = -6-6*12^(b+7) = -712^(b+7) = 7/6
log 12^(b+7) = log(7/6)(b+7) log 12 = log (7/6)b+7 = log(7/6) / log(12) = 0.06203b = -6.9380
What are the zeroes of y = x^2 – 4x – 5?
Answers
That means your factors are (x - 5) and (x + 1). You can double check this by foiling and seeing if you get your original equation.
Since you want to find the zeroes for that equation, that means y = 0. Remember that anything multiplied by 0 is 0, so you can set each of your factors equal to zero and solve for x. The x-values are your zeros:
x - 5 = 0
x = 5
x + 1 = 0
x = -1
-----
Answer: 5 and -1
Answer:
x=5 or x=-1
Step-by-step explanation:
The zeroes of the equation is when the x values when y=0.
We can determine this using a method that when we times out the brackets of our simplification we arrive at the original equation. We know that we must get -5 and -4x and x^2:
We can write:
[tex]y=x^2-4*x-5=0[/tex]
[tex](x-5)*(x+1)=0[/tex]
If we use the rules of algebra and multiply each term with each other:
[tex]x*x+x*1-5*x-5*1=0[/tex]
We can simplify:
[tex]x^2-4*x-5=0[/tex]
We end up with the original equation:
Therefore the zeros of the equation is when:
[tex](x-5)*(x+1)=0[/tex]
[tex]x-5=0[/tex] and [tex]x+1=0[/tex]
[tex]x=5[/tex]
[tex]x=-1[/tex[
x=5 or x=-1
Can someone please answer all these please?
a) When Lucia buys olives at the deli, the scale shows 0.325 kg at $18.88 per kg. How much should she pay?
b) John’s weekly wage is $1510.99 and he pays 2/3 of his weekly income in rent. How much rent does he pay each week?
c) A farmer owns 780 hectares of land. During a bushfire, 195 hectares are burnt. What percentage of his land was burnt?
d) Candles are $14.95 each. Estimate how much I need if I want to buy 17 of them.
Show your working.
e) Decrease 5000 by 13 %.
f) Ray bought a computer for $1600 and then a year later sold it for $1200.
Calculate his loss =
Calculate his loss as a percentage of the original price of the computer =
g) John spent $80 on dinner last Friday night. If this $80 is equal to 40% of his weekly income, calculate his weekly income.
h) Mr Jenkins invested $7500 at his local bank at 6.5% Simple Interest per annum.
What was his investment worth at the end of the first year?
Question 5
a) Express this ratio in lowest terms: 50 minutes : 2 ½ hours
b) Divide $120 in the ratio 5:7
c) Jane and Ben share in their lottery win in the ratio of 7: 3.
If Jane’s share of the money is $5600, how much does Ben receive?
Answers
b) $997.25
c) 25%
d) $254.15
e) 4350
f) $400, 25% loss
g) $200
h) $7,987,50
5
a) 1min: 3min
b) $50:$70
c) $2400
Volume and Surface Area
Math help 100 points
Answers
volume smaller solid=512 cm³
volume larger solid=2197 cm³
we know that
volume larger solid=[scale factor]³*volume smaller solid
scale factor=∛[volume larger solid/volume smaller solid]
scale factor=∛[2197/512]-----> scale factor=1.625
Part 2)
the ratio of the surface areas is equal to [scale factor]²
1.625²-------> 2.64
Part 3)
surface area smaller solid=960 cm²
then
surface area larger solid=scale factor²*surface area smaller solid
surface area larger solid=[1.625]²*960-----> 2535 cm²
surface area larger solid is 2535 cm²
Answer:
1 - V = Smaller solid=512 cm³
V = Larger solid=2197 cm³
2- 1.625² = 2.64
3 - SA of big solid is found 2535 cm²
Jason wants to choose 9 players for his track team. There are 12 players to choose from. How many different teams can Jason make?
Answers
12C9 = 12!/(12-9)!*9!
= 12*11*10/6 = 220
Jason wants to form a team of 9 players out of total 12 players.
Here the order of selection does not matter because there is no particular post for any player. So we need to use Combinations and choose 9 players out of 12 players.
We know the formula for Combinations is given as follows :-
[tex]nCr=\frac{n!}{r!*(n-r)!} \\\\ Choosing \;9 \;out \;of \;12 \\\\ 12C9 = \frac{12!}{9!*(12-9)!} =\frac{12!}{9!*3!} =\frac{12*11*10*9*8*7*6*5*4*3*2*1}{(9*8*7*6*5*4*3*2*1)*(3*2*1)} \\\\ 12C9 = \frac{12*11*10}{3*2*1} =\frac{1320}{6} =220 \;combinations[/tex]
Hence, all the possible number of different teams = 220 combinations.
A fluorite crystal is shaped like a regular octahedron with edges that are 2.1 inches. Which of these is the volume of the fluorite crystal in cubic inches? Round to the nearest hundredth
Answers
1. You have the following information given in the problem above: The regular octahedron with edges that are 2.1 inches.
2. Therefore, you must apply the formula for calculate the volume of a octahedron, which is:
V=(a^3√2)/3
3. Therefore, you have:
V=((2.1 inches)^3√2)/3
V=178.30 inches^3
To find the volume of the fluorite crystal, you can use the formula for the volume of an octahedron with the given edge length of 2.1 inches, rounded to the nearest hundredth to be approximately 7.69 cubic inches.
The volume of the fluorite crystal can be calculated as follows:
Identify the formula for the volume of an octahedron: V = (1/3) × [tex]\sqrt{2}[/tex] × a³, where 'a' is the edge length.
Substitute the given edge length: V = (1/3) × [tex]\sqrt{2}[/tex] × 2.1³.
Calculate the volume: V = 7.69 cubic inches (rounded to the nearest hundredth).
1. You can afford a monthly mortgage payment of $1,650 and can get a 15-year 5.625% loan. What is the maximum loan you can get so your payment does not exceed $1,650?
2. You apply for a home equity loan. The lender gets an appraisal on your home, showing a value of $183,500. You have a first mortgage with a current balance of $87,435. Based on a 75% LTV ratio, what is the maximum line of credit you can get?
Answers
$200,307.94
2. .75*$183,500 -87,435 = 50,190
The maximum line of credit you can get is $50,190.
A lunch counter sells two types of sandwiches, roast beef and chicken salad. The profit on the sandwiches is $2 for chicken salad and $3 for roast beef. The amount of bread available is enough for 30 sandwiches. There are 2 hours available to prepare sandwiches. If chicken salad sandwiches take 3 minutes to prepare and roast beef sandwiches take 5 minutes, how many of each type of sandwich should be prepared to maximize the profit? Assume all sandwiches get sold
Answers
x: roast beef sandwiches
y: chicken salad sandwiches
We write the system of equations:
x + y = 30
5x + 3y = 120
Solving the system we have:
x = 15
y = 15
The profit is:
P = 3 * (15) + 2 * (15)
P = 75 $
Answer:
should be prepared to maximize the profit:
15 roast beef sandwiches
15 chicken salad sandwiches
Calculate the surface area of the portion of the surface z=x^2 + y that lies above the triangular region t wth vertices 0,0 4,0 and 4,2
Answers
Z=(0)^2+0=0
Z=(4)^2+0=16
Z=(4)^2+2=18
Z total = 34
Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1
Answers
[tex]f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}[/tex]
For [tex]f(x)[/tex] to be differentiable, it necessarily has to be continuous. For this condition to be met, we need
[tex]\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)[/tex]
[tex]\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)[/tex]
[tex]\iff2=b+c[/tex]
For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have
[tex]f'(x)=\begin{cases}2&\text{for }x<1\\2bx+c&\text{for }x>1\end{cases}[/tex]
[tex]\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)[/tex]
[tex]\iff2=2b+c[/tex]
Now we solve for [tex]b[/tex] and [tex]c[/tex]:
[tex]\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2[/tex]
To make the function differentiable, we need to make it continuous at x = 1 by ensuring that both sides of the function have the same value. The values of the constants b and c are b = 1 - c, where c is any real number.
Explanation:The function given is:
f(x)={2xbx2+cxx ≤ 1 x > 1
To determine the values of the constants b and c such that the function is differentiable, we need to make sure that the function is continuous at x = 1 and both sides of the function have the same derivative at x = 1.
To do this, we need to find the limits of the function as x approaches 1 from both the left and the right sides.
From the given function, we can see that when x ≤ 1, the function is a polynomial and is differentiable for any value of b and c.
However, when x > 1, the function is not differentiable unless we choose the values of b and c such that the function becomes continuous at x = 1.
To make the function continuous, we need to make sure that both sides of the function have the same value at x = 1.
Substituting x = 1 into the given function, we have 2b(1)(1) + c(1) = b + c = 1 (since the function should be continuous at x = 1).
Therefore, the values of the constants b and c that make the function differentiable are b = 1 - c, where c is any real number.
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10) Given that two tangent lines are constructed from the shared point A outside a circle with the center O and points of tangency B and C, what is the relationship between ∠OAB and ∠OAC?
Answers
_____
The angles are corresponding parts of congruent triangles (CPCT). Triangles OBA and OCA are right triangles congruent by the HL postulate. The "H" is segment OA. The "L" is the radius, OB or OC. Of course the angles at B and C are 90° as with any radius and tangent line.
A beach ball has a diameter of 12 inches.what is the volume to the nearest tenth
Answers
V = (4/3) * pi * r^3
The radius is half the diameter.
r = d/2 = (12 in.)/2 = 6 in.
V = (4/3) * 3.14159 * (6 in.)^3
V = 904.7786... in.^3
Answer: The volume is 904.8 in.^3
The volume of a beach ball with a diameter of 12 inches is approximately 904.3 cubic inches.
To find the volume of a beach ball with a diameter of 12 inches, we first need to find the radius. The radius is half of the diameter, so the radius is 6 inches.
The formula for the volume of a sphere is:
V = (4/3)πr³
Where V is the volume and r is the radius. Plugging in our radius:
V = (4/3)π(6)³
V ≈ (4/3)π(216)
V ≈ (4/3)(678.24)
V ≈ 904.32 cubic inches
To the nearest tenth, the volume of the beach ball is approximately 904.3 cubic inches.