In Exercises 1-3, decide whether enough information is given to prove that the triangles are congruent using either the SSS Congruence Theorem (Theorem 5.8) or the HL Congruence Theorem (Theorem 5.9). Explain.
Answers
The congruency proofs that can be used for each of the triangles are;
1) SSS Congruency
2) None
3) HL Congruence
How to prove the triangle congruency postulate?
1) The SSS congruency postulate states that If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
Now, we see that we are shown 2 corresponding sides that are congruent. However, the third side is automatically congruent using the reflexive property of congruence.
Thus, we conclude that the congruency can be proved using SSS Congruency postulate.
2) In this one, we are given 2 congruent sides and the included angle and so it is SAS Congruency and neither SSS nor HL congruency can be used.
3) The HL congruence Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
In this case, we see that the hypotenuse is congruent to itself by reflexive property of congruence while the one leg is also congruent and so we can use HL Congruence Theorem
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Related Questions
The sum of two numbers is 21. One of the numbers squared plus 1 is equal to the other number. Given that both numbers are positive, what are the two numbers?
Answers
Answer:
4 and 17
Step-by-step explanation:
4 because 4^2 is 16 + 1 = 17 and the other # is 17 because 21-4 is 17
A dwarf decides to visit three of her friends. She carries 7 apples in a sack. To reach her 1st friend she has to cross a magic river. After crossing the river, the number of apples in her sack doubles. She then gives her 1st friend a number of apples. She continues her journey and then crosses the 2nd magic river. The number of apples doubles again. She gives her 2nd friend the same number of apples. She crosses the 3rd magic river. Again the number of apples doubles. She visits her 3rd friend and gives the same number. again. This time there are NO apples left.
•What number did she give to each friend?
• Investigate with different start numbers. • What numbers work out neatly?
Answers
Answer:
She gave 8 apples to each friend.
Step-by-step explanation:
2{[2(14-x)]-x} = 0 Distribute the 2
2[28-2x -x) -x = 0 Combine like terms
2(28 -3x) -x = 0 Distribute the 2
56 - 6x - x= 0 Combine like terms
56 -7x = 0 Subtract 56 from both sides
-7x = -56 Divide both sides by -7
x = 8
Check:
7 x 2 = 14
14 - 8 = 6
6 x 2 = 12
12 - 8 = 4
4 x 2 = 8
8 - 8 = 0
Checks.
Helping in the name of Jesus
What is the answer to this combination lock
Answers
Answer: 375
Step-by-step explanation:
Ruling out each number:
6: In the first two rows, the 6's placement did not change but the clue did, meaning that it is talking about a different number. Otherwise, it would say it's in the right place twice or in the wrong place twice.
3 & 5: Since we know 6 is already ruled out, both 5 & 3 would have to be correct.
2 & 4 & 8: Is proven wrong in the 4th clue.
7: 7 would have to be in the middle since the second clue says it's in the wrong place. If it was 1, it would say it's in the right space.
1: Is proven wrong after 7 is proven true.
Figuring out placement:
5: For the first clue, it says that it's in the correct place meaning that 5 is the last digit.
3: For both of the times 3 appears, it is in the wrong spot, revealing that it's the first digit.
7: In the second clue, it could either be 1 or 7. However, since 3 took the first spot and 5 took the last spot, 7 would have to be in the middle since the clue says it's in the wrong place. If it was 1, it would say it's in the right space.
An account is opened with an initial deposit of 2500 and earns 1.8% interest compounded simi annually what will the account be worth in 30 years
4,279.66
is the answer
Answers
Answer:
Final amount = $4279.667.
Step-by-step explanation:
Formula to get the final amount after 't' years is,
Final amount = \(\text{Initial amount}\times (1+\frac{r}{n} )^{nt}\)
Here 'r' = rate of interest
t = Number of years for the investment
n = Number of compounding in a year
Now we substitute the data given in the question,
Initial amount = $2500
r = 1.8% = 0.018
n = Semi annually = 2
t = 30 years
Final amount = \(2500(1+\frac{0.018}{2})^{(2\times 30)}\)
= \(2500(1.009)^{60}\)
= 4279.667
Therefore, final amount will be $4279.667.
Let S be the universal set, where:
S={1,2,3,...,28,29,30}
Let sets A and B be subsets of S, where:
Answers
Using set theory, we can find the elements of set (AUB) as follows:
AUB = {3,10,12,25,27}
Define set theory?In mathematics, a grouping of various objects is known as a set. Any collection of items, including a numerical range, a list of days of the week, several automobile models, etc., can be categorised as a set. An element of the set can be any component of the set.
A very basic set would resemble something like this. Set A = {1,2,3,4,5}. Several notations can be used to represent the elements of a set. Sets are frequently represented by a set builder form or by using a roster form.
In the question,
Universal set = {11,2,3, 4......,28,29,30}
Set A = {3,4,5,8,10,12,15,21,24,25,27,28}
Set B = {1,3,10,11,12,16,25,27,29}
So AUB = {3,10,12,25,27}
Therefore, the elements that are included in the set (AUB) is:
{3,10,12,25,27}.
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Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.15 and a standard deviation of 1.48. Using the empirical rule, what percentage of American women have shoe sizes that are greater than 11.11? Please do not round your answer.
Answers
Solution:
To find the percentage of American women who have shoe sizes that are greater than 11.11, we apply the z score formula first
The z score formula is
\(\begin{gathered} z=\frac{x-\mu}{\sigma} \\ Where\text{ } \\ The\text{ observed value, x}=11.11 \\ The\text{ mean, }\mu=8.15 \\ The\text{ standard deviation, }\sigma=1.48 \end{gathered}\)Substitute the variables into the formula above
\(\begin{gathered} z=\frac{11.11-8.15}{1.48}=\frac{2.96}{1.48}=2 \\ z=2 \end{gathered}\)Given that the z = 2
From the deduction above, the given value is 2 standard deviation away to the right of the mean.
According to the empirical rule,
Using the chart below
The percentage of American women who have shoe sizes that are greater than 11.11 is
\(=2.35+0.15=2.5\%\)Hence, the answer is 2.5%
The vector ⇀
= ⟨2, 3⟩ is multiplied by the scalar –4. Which statements about the components, magnitude, and direction of the scalar product –4⇀
are true? Select all that apply.
A. The component form of −4⇀
is ⟨–8, –12⟩.
B. The magnitude of −4⇀
is 4 times the magnitude of ⇀
.
C. The direction of −4⇀
is the same as the direction of ⇀
.
D. The vector −4⇀
is in the fourth quadrant.
E. The direction of −4⇀
is 180° greater than the inverse tangent of its components.
Answers
Answer:
Therefore, the correct statements are A, B, and E.
Explanation:
Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.
To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀
.
- The component form of −4⇀
is obtained by multiplying each component of ⇀
by –4. Therefore, −4⇀
= ⟨–8, –12⟩. This means that statement A is true.
- The magnitude of −4⇀
is obtained by multiplying the magnitude of ⇀
by 4. The magnitude of ⇀
is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀
is 4√13. This means that statement B is true.
- The direction of −4⇀
is opposite to the direction of ⇀
because the scalar –4 is negative. This means that statement C is false.
- The vector −4⇀
is in the third quadrant because its components are both negative. This means that statement D is false.
- The direction of −4⇀
is 180° greater than the inverse tangent of its components because it is opposite to ⇀
. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀
is 180° + tan^(-1)(3/2). This means that statement E is true.
Therefore, the correct statements are A, B, and E.
100 points will mark brainliest
Answers
Answer:
A is the answer
Step-by-step explanation:
if its wrong than its C
A new therapy for Psoriasis is being tested and subjects have their PASI score taken before and after treatment. The distribution of their scores are shown in the following boxplot: A. Find the approximate 25th percentile (___), median (___), and 75th percentile (____) for the PASI scores pre treatment. B. Find the approximate 25th percentile ), median ), and 75th percentile ) for the PASI scores post treatment C. The effectiveness (i.e. the lower the score, the better) of the therapy is O A. Based on the post-treatment median being much lower than the median at baseline, the treatement appears to be ineffective OB. Based on the post-treatment median being much higher than the median at baseline, the treatement appears to be effective O C. Based on the post-treatment median being much lower than the median at baseline, the treatement appears to be effective OD. Based on the post-treatment median being much higher than the median at baseline, the treatement appears to be ineffective
Answers
The answer is option (C) based on the post-treatment median being much lower than the median at baseline, the treatment appears to be effective.
A) To find the approximate 25th percentile, median, and 75th percentile for the PASI scores pre-treatment, we can look at the boxplot. The box in the plot represents the middle 50% of the data, and the line inside the box represents the median. The whiskers show the range of the data, and any points outside of the whiskers are considered outliers.
From the given boxplot, we can see that the median is around 13, the 25th percentile is around 9, and the 75th percentile is around 19 for the PASI scores pre-treatment.
B) To find the approximate 25th percentile, median, and 75th percentile for the PASI scores post-treatment, we can again look at the boxplot.
From the given boxplot, we can see that the median is around 4, the 25th percentile is around 2, and the 75th percentile is around 8 for the PASI scores post-treatment.
C) The effectiveness of the therapy can be determined by comparing the pre-treatment and post-treatment PASI scores. As the goal is to have lower PASI scores post-treatment, a lower median PASI score post-treatment as compared to pre-treatment is an indication of the effectiveness of the therapy. Therefore, based on the post-treatment median being much lower than the median at baseline, the treatment appears to be effective.
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What is the y-intercept for this line?
Y = 2/3 x + 3
A. 2
B. 2/3
C. 3
Answers
Answer:
y intercept when x is 0, so the answer is 3
Work out the perimeter of the shaded shape on the centimetre grid.
Give the answer in cm and no spam.
Answers
Answer:
The perimeter of this rectangle is 10 cm.
Simplify 16x^3 - 8x^2 + 4x^4 / 2x
A) 8x^2 - 4x + 2x^3
B) 8x^2 - 4 + 2x^3
C) 8x^3 - 4x + 2x^3
D) 8x^2 - 4x + 2x
Answers
Answer:
2 x ^3 + 8 x ^2− 4 x
Step-by-step explanation:
Just simplify!
A box has a width of 10 cm and a length of 17 cm. The volume of the box is decreasing at a rate of 527 cubic cm per minute, with the width and length being held constant. What is the rate of change, in cm per minute, of the height when the height is 6 cm?
Round your answer to the nearest hundredth. (Do not include any units in your answer.)
Answers
Therefore, the rate of change, in cm per minute, of the height when the height is 6 cm is approximately -6 cm/min.
Given,The width of the box = 10 cm Length of the box = 17 cmThe volume of the box = 527 cubic cm/minWe need to find the rate of change, in cm per minute, of the height when the height is 6 cm.We know that the volume of the box is given as:V = l × w × h where, l, w and h are length, width, and height of the box respectively.It is given that the width and length are being held constant.
Therefore, we can write the volume of the box as
:V = constant × h Differentiating both sides with respect to time t, we get:dV/dt = constant × dh/dtNow, it is given that the volume of the box is decreasing at a rate of 527 cubic cm per minute.
Therefore, dV/dt = -527.Substituting the given values in the above equation, we get:
527 = constant × dh/dt
We need to find dh/dt when h = 6 cm.To find constant, we can use the given values of length, width and height.Substituting these values in the formula for the volume of the box, we get:
V = l × w × hV = 17 × 10 × hV = 170h
We know that the volume of the box is given as:V = constant × hSubstituting the value of V and h, we get:
527 = constant × 6 cm
constant = 87.83 cm/minSubstituting the values of constant and h in the equation, we get
-527 = 87.83 × dh/dtdh/dt = -6.0029 ≈ -6 cm/min
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A bus is scheduled to leave the terminal at 10:15 in the morning and travel for 5 3/4 hours to Bally city. If the bus leaves the terminal 35 minutes late, when will it arrive in Bally city?
Answers
Answer:
Step-by-step explanation:
3/4 hours=3/4×60=45 minutes
10:15+5.45 hrs=16:00+0:35=16:35=4.35 pm
so C
3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answers
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
________________________________________________________
When making lemonade from the frozen concentrate, the directions say to add 3 containers full of water to theconcentrated mix. What is the ratio of water to concentrate?
Answers
So, the question says you'll need three containers of water per concentrated mix. The ratio of water to concentrated mix will be:
3:1
There are 4 blueberry, 6 raisins, and 2 plain bagels in a bag. Mike randomly selects two bagels without replacing the first bagel. Find the probability that he selects a raisin bagel and then a plain bagel
Answers
Answer: 1/9
Step-by-step explanation: add all the numbers up, so 4+6+2=12, which is the denominator. First, we find the rasin bagel, which 8/12=4/6=2/3 times the number of plain bagel which is 2/12, or 1/6. 2/3*1/6=2/18=1/9. Tell me if I get it right or not.
If you roll one die, what is the probability of getting an even number ora multiple of 3?
1/3
2/3
1/6
1/2
Answers
A conical water tank with vertex down has a radius of 10 feet at the top and is 24 feet high. If water flows out of the tank at a rate of 20 ft3/min, how fast is the depth of the water DECREASING when the water is 6 feet deep?
Answers
Answer:
Depth of water is increasing at 0.143 ft/min.
Step-by-step explanation:
Aris and Josiah are reading a 50-page book for their ELA class. Aris wants to know what page Josiah is reading. Josiah gives her two hints: 1. The product of the two page numbers he can see is 930. 2. The page he is reading is an odd numbered page.
Answers
Answer:
31
Step-by-step explanation:
Let x and (x + 1) be the page numbers Josiah can see
Hint 1: x(x + 1) = 930
⇒ x² + x = 930
⇒ x² + x - 930 = 0
Using quadratic formula,
\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)
a = 1, b = 1 and c = -930
\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)
\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)
Sice x is a page number, it cannot be negative
⇒ x = 30 and
x + 1 = 31
The two pages Josiah can see are pg.30 and pg.31
Hint 2: The page he is reading is an odd number
Out of the pages 30 and 31, 31 is an odd number
Thereofre, Josiah is reading page 31
Mia hired a moving company. The company charged $500 or its services, and Mia gives the movers a 16% tip.
Answers
Answer:
The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580
Step-by-step explanation:
A clothing eCommerce company has an Average Order Value of USD 65. It costs the company USD 35 to produce the clothes in the average order and USD 15 to ship it to the customer. What is the Average Order's Gross Profit?
USD 65
USD 30
USD 15
USD 50
Answers
The Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.
For the Average Order's Gross Profit for the clothing eCommerce company in this scenario, we need to subtract the cost of production and shipping from the Average Order Value as;
⇒ Gross Profit = Average Order Value - Cost of production - Cost of shipping Gross Profit
⇒ Gross Profit = USD 65 - USD 35 - USD 15
⇒ Gross Profit = USD 15
Therefore, the Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.
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The Cleveland City Cable Railway had a 14-foot-diameter pulley to drive the cable. In order to keep the cable cars moving at a linear velocity of 16 miles per hour, how fast would the pulley need to turn (in revolutions per minute)? (1 mi = 5,280 ft. Round your answer to the nearest tenth.)
Answers
Answer:
32.0 rpm
Step-by-step explanation:
16 mi/h = (16 mi)(5280 ft/mi)/(60 min) = 1408 ft/min
One revolution is a distance of ...
C = πd
C = π(14 ft) ≈ 43.98 ft
So the number of revolutions per minute is ...
(1408 ft/min)/(43.98 ft/rev) = 32.01 rev/min
The pulley needed to turn at 32.0 rpm.
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Answers
The order from least to greatest is -4.7,-4,-31/8, \(-3\frac{1}{8}\)
What is Fraction?A fraction represents a part of a whole.
The given integers are -31/8,-4.7, -4 and -3 1/8
Now let us simplify the fraction values
-31/8=-3.875
-4.7
-4 and
\(-3\frac{1}{8}\)=-24+1/8=-23/8=-2.875
As there is a negative sign, the smallest number with negative sign will be greatest and largest number with negative sign is smaller.
So -4.7,-4, -3.875, -2.875
-4.7,-4,-31/8, \(-3\frac{1}{8}\)
Hence the order from least to greatest is -4.7,-4,-31/8, \(-3\frac{1}{8}\)
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3(x+2)=2(x+5) find the solution
Answers
Answer:
x=4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3(x+2)=2(x+5)
(3)(x)+(3)(2)=(2)(x)+(2)(5)(Distribute)
3x+6=2x+10
Step 2: Subtract 2x from both sides.
3x+6−2x=2x+10−2x
x+6=10
Step 3: Subtract 6 from both sides.
x+6−6=10−6
x=4
First use the distributive property on both the left and right side of the equation.
3(x + 2) = 2(x +5) becomes —>
3x + 6 = 2x + 10.
Isolate the variables on one side of the equation and the constants on the other sides.
3x + 6 = 2x + 10.
Subtract 2x from each side to get the variables on one side.
X + 6 = 10.
Subtract 6 from both sides to get isolate the constant on the other side of the equation.
That leaves:
X = 4.
X = 4.
The graph of the linear function passes through points (2, 44) and (5, 80). What is the equation of the function?
Answers
Step-by-step explanation:
the slope-intercept form is in general
y = ax + b
a being the slope, b being the y-intercept (the y-value when x = 0).
the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.
we got 2 points identified, so, let's use them.
(2, 44) and (5, 80)
x changes by +3 (from 2 to 5).
y changes by +36 (from 44 to 80).
the slope is +36/+3 = 12.
so, we got "a" for our equation. to get "b" we need to use the coordinates of one of the given points as x and y.
I usually use the one with the smaller numbers.
here : (2, 44).
44 = 12×2 + b = 24 + b
b = 44 - 24 = 20
our equation is
y = 12x + 20
which terms are like terms in the expression 5x + 9 + (-7x)
Answers
Answer:
5x and -7x
Step-by-step explanation:
they both end in the variable "x"
12, 18, x, and 5 are used to calculate an average of 13. What is the missing number?
Answers
Answer:
17
Step-by-step explanation:
Given the data:
12, 18, x, 5
Average of the numbers = 13
The value of x will. Be
Sum of 12, 18, x and 5 divided by the number of data values.
Mean(average) = Σ(X) / n
n = number of values
13 = (12 + 18 + x + 5) / 4
13 = (35 + x) / 4
13 * 4 = 35 + x
52 = 35 + x
x = 52 - 35
x = 17
Based on surveys, 97% of students own cell phones. What is the probability that 10 randomly selected
students all own cell phones? Round your answer to 4 decimal places.
Answers
Answer:
\(Probability = 0.7374\)
Step-by-step explanation:
Given
Represent the probability that a student has a phone with p
\(p = 97\%\)
Required
Determine the probability that 10 has
This is calculated as thus:
\(Probability = p^n\)
Where n = 10
\(Probability = (97\%)^{10}\)
\(Probability = 0.97^{10}\)
\(Probability = 0.73742412689\)
\(Probability = 0.7374\) --- Approximated
Luisa's smoothie recipe uses 8 cups of milk and 2 cups of strawberries. Enter the percentage of the smoothie recipe that is strawberries
Answers
Answer:
25% is your answer
Step-by-step explanation:
2/8 = 25%
Answer:
20% strawberries
Step-by-step explanation:
Since percentages can be found using fractions, we can turn the amounts of strawberries into a fraction. First, we determine the denominator by determining what the whole is or what the two numbers equal together. In this case: 8+2 is 10 meaning we will make our fractions with a denominator of ten. As we are determining the percentage of strawberries, we put 2 over 10 to get: \(\frac{2}{10\\}\) which, when converted to a percentage, equals 20%.