Answers
a) The triangles are congruent by the AAA criterion.
b) The triangles are congruent by the SAS criterion.
a) In the first triangle the interior angles are 40 degrees and 30 degrees.
The other interior angle would be 180 - (40 + 30) = 110 degrees.
As per the diagram, the triangles have equal proportionate-sized side lengths.
Therefore, the triangles are congruent by the AAA criterion.
b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.
Therefore, the triangles are congruent by the SAS criterion.
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Related Questions
3.3.4√20+5-43 calculate
Answers
Here are the steps to calculate the expression √20 + 5 - 43 :
Step 1: Simplify the square root of 20:
[tex]\sqrt{20}[/tex]
Step 2: Calculate the value of the square root:
[tex]\sqrt{20} = 2\sqrt{5}[/tex]
Step 3: Substitute the value of the square root into the expression:
[tex]2\sqrt{5} + 5 - 43[/tex]
Step 4: Perform addition:
[tex]2\sqrt{5} + 5 = 2\sqrt{5} + \frac{5}{1} = \frac{2\sqrt{5} + 5}{1}[/tex]
Step 5: Perform subtraction:
[tex]\frac{2\sqrt{5} + 5}{1} - 43 = \frac{2\sqrt{5} + 5 - 43}{1}[/tex]
Step 6: Simplify the numerator:
[tex]\frac{2\sqrt{5} - 38}{1}[/tex]
Step 7: Simplify the expression:
[tex]2\sqrt{5} - 38[/tex]
Therefore, the calculation √20 + 5 - 43 simplifies to 2√5 - 38.
The weight (in kilograms) of 14 patients were measured as 59, 63, 61, 62, 58, 60, 58, 57, 57, 56, 50, 69, 58 and 50. What is the range weight (in kilograms) of these patients?
Answers
Answer:
57 kilograms. .........................................................................kg
HELP ASAP PLEASE
LATE ASSIGNMENT
Answers
The measure of angle ABC is given as follows:
m < ABC = 55º.
How to obtain the measure of angle ABC?First we look to the exterior angle of angle C in the bottom parallel line, as a ray is formed, hence the missing angle measure is given as follows:
50 + 75 + x = 180
125 + x = 180
x = 55º.
The exterior angle relative to angle B is supplementary with the angle of 55º, as they are consecutive angles, hence it’s measure is obtained as follows:
y + 55º = 180
y = 125º.
By the exterior angle theorem, an interior angle is supplementary with it’s respective exterior angle, hence the measure of angle ABC is given as follows:
m < ABC + 125 = 180
m < ABC = 55º.
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The length and breadth of a rectangular flower bed are 16m and 9 m, respectively. How many plants can be planted in it, if each plant requires a space of 1.2m x 1m?
Answers
The calculated number of plants the flower bed can contain is 120
Calculating hw many plants can be planted in itFrom the question, we have the following parameters that can be used in our computation:
Dimensions = 16 m by 9 m
So, the area of the flower bed is
Area = 16 * 9
Evaluate
Area = 144
Also, we have
Each plant requires a space of 1.2m x 1m?
This means that
Plant area = 1.2 * 1
Plant area = 1.2
So, we have
Plants = 144/1.2
Evaluate
Plants = 120
Hence, the number of plants is 120
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Answer:
Step-by-step explanation:
To calculate the number of plants that can be planted in the rectangular flower bed, we need to calculate the area of the flower bed and divide it by the space required for each plant.
The area of the flower bed is calculated by multiplying its length and breadth.
So, the area of the flower bed is 16m x 9m = 144 sq.m.
Each plant requires a space of 1.2m x 1m = 1.2 sq.m.
Therefore, the number of plants that can be planted in the flower bed is:
144 sq.m. ÷ 1.2 sq.m./plant = 120 plants.
So, you can plant 120 plants in the rectangular flower bed.
What is the value of x?
Answers
Solving a simple equation, we can see that x = 35.
How to find the value of x?The 3 lines with an arrow that go to the left are parallel lines, thus, the relation between the sets of values in each of the sides must be the same ones.
Then we can take the quotients between the respective values, and these quotients must be equal, so we can write:
30/12 = x/14
And now we can solve that equation for x, we will get:
x = 14*(30/12)
x = 35
That is the value of x.
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-49 = 7i, what number is the i.
Answers
Answer:
-7
Step-by-step explanation:
divide by 7 on both sides and you get i = -7
Will give you brainly! :) Thank you for taking time out of your day to answer this!
Answers
The probability values are P(30 ≤ Amount ≤ 59) = 0.43, P(Amount ≥ 60 or Amount < 30) = 0.57 and P(Amount ≥ 40) = 0.45
Calculating the probability valuesAt least $30 but not more than $59
This means that we use the money spent from 30 to 59
So, we have
30 to 59 = 76 + 58 + 67
30 to 59 = 201
Total = 85 + 98 + 201 + 84
Total = 468
Next, we have
P(30 ≤ Amount ≤ 59) = 201/468
P(30 ≤ Amount ≤ 59) = 0.43
At least $60 or less than $30
This means that we use the money spent less than 30 and greater than or equal to 60
So, we have
At least $60 or less than $30 = 84 + 85 + 98
At least $60 or less than $30 = 267
Next, we have
P(Amount ≥ 60 or Amount < 30) = 267/468
P(Amount ≥ 60 or Amount < 30) = 0.57
At least $40
This means that we use the money spent greater than or equal to 40
So, we have
At least $40 = 58 + 67 + 84
At least $40 = 209
Next, we have
P(Amount ≥ 40) = 209/468
P(Amount ≥ 40) = 0.45
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A popular brand has introduced a new design of jeans. All major stores have stocked the jeans because the brand usually sells very well. But the cost of these jeans is much higher than those of other brands, so people don't buy them.
Answers
The price of the jeans will decrease because supply is greater than demand hence the stores will sell them at discounted prices.
How do we calculate?The store owners would be forced to cut pricing if the jeans weren't purchased at all or as frequently as the other brands. Either they choose that choice, return the goods if possible or just toss the jeans away. It generally takes some trial and error to determine the proper price.
For instance, the owner may lower the price to $75 and test whether the 25% discount works or not if the jeans initially sell for $100 and nobody buys them for a week.
The price might remain there if people continue to buy and if not, the cost might decrease even further.
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Tell whether the given value is a solution to the inequality.
y + 5 > 8l; y = 1
Answers
The solution of the inequality equation is determined as y > 3.
What is the solution of the inequality equation?A solution for an inequality in y is a number such that when we substitute that number for y we have a true statement.
For the given inequality equation, which is;
y + 5 > 8
The solution of the inequality equation is calculated as follows;
y + 5 > 8
Subtract 5 from both sides of the equation as shown below;
y + 5 - 5 > 8 - 5
y > 3
The solution of the inequality equation is determined as 3, so we can conclude that any value less than 3 is not true and the proposed solution of 1 is not true or correct for the inequality equation.
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e
B
0
14. The table shows the number of inches of
rain over five months. What would be an
appropriate display of the data? Explain.
(Lesson 2)
Month
Number
of Inches
of Rain
Jan. Feb. Mar.
1.5
2.2
3.6
Apr.
5.3
May
4.8
Answers
The graph of the given function is attached.
Given is a function for the rainfall in 5 months in inches.
We need to display the data,
So, as we can see that the data is not showing any proportion or pattern,
So, it can be displayed as a line chart.
Hence the chart is attached for the function.
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5. [0.5/1 Points] DETAILS PREVIOUS ANSWERS SALGTRIG4 7.3.112.
A rectangle is to be inscribed in a semicircle of radius 4 cm as shown in the following figure.
10
4 cm-
(a) Find the function that models the area of the rectangle.
A(0) = 16 sin (20)
Need Help? Read It
MY NOTES
4
ASK YOUR TEACHER
(b) Find the largest possible area for such an inscribed rectangle. [Hint: Use the fact that sin(u) achieves its maximum value at u=/2.]
16
cm²
(c) Find the dimensions of the inscribed rectangle with the largest possible area. (Round your answers to two decimal places.)
smaller dimension 2
x cm
larger dimension 25
x cm
PR.
Answers
The Area function [tex]A(x) = 2x * \sqrt(16 - x^2).[/tex]
(a) For a rectangle inscribed in a semicircle of radius 4 cm, let half-length be x and height be y.
Therefore, the Area function [tex]A(x) = 2x * \sqrt(16 - x^2).[/tex]
(b) Maximum area occurs when x = [tex]4 * sin(\pi/4), so A(4 * sin(\pi/4)) = 16 cm^2.[/tex]
(c) Dimensions for the largest inscribed rectangle are smaller dimension (height) ≈ of 2.83 cm, a larger dimension (base) ≈ of 5.66 cm.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Answer:
5/4 = h/44, so h = 55
The height of the tree is 55 feet.
D is correct.
The algebraic expression below is a polynomial. x-1^k, where k is a real number
Answers
Answer: True
Step-by-step explanation:
lim[tex]\frac{n^{2} +4n-5}{3n^{3}+n^{2}+7 }[/tex]
Answers
Step-by-step explanation:
limit for n going to what ?
I think you mean n going to ±infinity.
for very large n (when n goes to infinity) such a fraction is reduced to the ratio of the terms with the highest exponents of n. the terms with lower exponents simply get less and less impact with growing n, and fade away for really, really large n going to infinity.
so, this limit evaluation is reduced to
lim n²/(3n³ + n²) = 1/(3n + 1)
which is again for very large n
lim 1/(3n), which goes to 1/infinity = 0
the same for going to 1/-infinity = 0
if you meant e.g. limit for n going to 0, then for the limit we set n to 0 and see, that all terms are turning 0, except for the constants -5 in the numerator and +7 in the denominator.
so, that limit is then
-5/7 = -0.714285714...
Find area of the shape
Answers
Answer:
130.4
Step-by-step explanation:
6 x 14 = 84
8 x 4 = 32
(4 x 7.2)/2 = 14.4
................................................
Answers
Answer:
4,12,36,108,324.....
Step-by-step explanation:
The sequence represented by the equation [tex]a=4(3)^{n-1}[/tex]is a geometric sequence with first term 5 and common ratio 3. The first 4 terms of the sequence are:
[tex]a_1 = 4(3)^{1-1} =4(3)^0 = 4[/tex]
[tex]a_2 =4(3)^{2-1} = 4(3)^1 = 12[/tex]
[tex]a_3 =4(3)^{3-1} = 4(3)^2 = 36[/tex]
[tex]a_4 = 4(3)^{4-1} =4(3)^3 = 108[/tex]
[tex]a_5=4(3)^{5-1} =4(3)^4=324[/tex]
The sequence can be written as:
[tex]a_n = 4(3)^{n-1}[/tex]
where n is the term number.
Therefore, the sequence is 4,12,36,108,324.....
Answer:
The answer is 4,12,36,108,324
Step-by-step Explanation:
a1=4(3)¹‐¹=4(3)⁰=4
a2=4(3)²‐¹=4×3=12
a3=4(3)³‐¹=4(3)²=4×9=36
a4=4(3)⁴‐¹=4(3)³=4×27=108
a5=4(3)⁵‐¹=4(3)⁴=4×81=324
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
From the relationship of AC bar ≅ BD bar, we can tell that ABCD is a rectangle.
How is this a rectangle ?A quadrilateral with two sets of parallel sides is known as a parallelogram.
If ABCD is a parallelogram where AC and BD have equal lengths, then the opposite sides of ABCD are also equal. ABCD has two sets of sides that are parallel and have the same length.
The fact that ABCD possesses two sets of sides that are parallel and of equal length logically leads to the conclusion that it also has four angles that are right. One reason for this is that the angles opposite each other in a parallelogram are of equal measure, while the sum of the angles at each corner of a parallelogram is always 180 degrees.Therefore, ABCD is a rectangle.
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A telephone pole is 54 feet tall. A guy wire runs 83 feet, from point A at the top of the telephone pole, to the ground at point B. The base of the telephone pole is at point C. Triangle ABC is a right triangle.
How far from the base of the telephone pole, to the nearest tenth of a foot, is the guy wire secured to the ground at point B?
Answers
Okay, let's break this down step-by-step:
* The telephone pole is 54 feet tall
* The guy wire runs 83 feet from point A (top of pole) to point B (ground)
* So the hypotenuse (AB) of the right triangle is 83 feet
* The opposite side (AC) is 54 feet (height of pole)
To find the adjacent side (BC), we use the Pythagorean theorem:
a^2 + b^2 = c^2
54^2 + BC^2 = 83^2
Solving for BC gives:
BC = sqrt(83^2 - 54^2) = sqrt(1296 - 2916) = sqrt(1620) = 40 feet
So the guy wire is secured 40 feet from the base of the telephone pole.
Rounded to the nearest tenth is 40.0 feet.
Therefore, the final answer is:
40.0
Let me know if you have any other questions!
Pls Need this ASAP
When purchasing a home, you need a loan for $80,000. The interest rate of the
loan is 8% and you are required to make monthly payment of $587.
Answers
Answer:
1) 5m
2) 0.25tan
Step-by-step explanation:
A researcher performed an experiment with two groups. She found the difference of the means for each group. Then
she combined the groups, chose two new groups, and found the difference between the means of those groups. She
repeated this process 200 times. The normal distribution of the difference in the means she found is given below. How
great would the difference in means between the first two groups have to be in order to be considered significant?
At least 8
O At least 10
At least 9
At least 7
Answers
Answer:
Step-by-step explanation:
To determine the significance level for the difference in means between the first two groups, we need to refer to the provided normal distribution. However, you haven't provided the details or parameters of the normal distribution, such as the mean and standard deviation. Without this information, it is not possible to determine the exact significance level required.
In hypothesis testing, the significance level, typically denoted as α (alpha), is chosen by the researcher before conducting the experiment. It represents the threshold at which the researcher considers the results to be statistically significant. Commonly used significance levels are 0.05 (5%) or 0.01 (1%).
Please provide the necessary parameters or more information about the normal distribution to determine the specific significance level for the difference in means between the first two groups.
b) tan 2A cot A-1 = sec 2A
Answers
The trigonometric equation is tan 2A cot A-1 = sec 2A
We have to prove the trigonometric equation
tan 2A cot A-1 = sec 2A
Now let us take LHS
tan 2A cot A-1
2tanA/1-tan²A - 1 . cotA - 1
2-1+tan²A/1-tan²A
1+tan²A/1-tan²A
sec2A
Hence, the trigonometric equation is tan 2A cot A-1 = sec 2A
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solve for v, PV/T=pv/t
Answers
No matter the values of P, V, T, p, and t, as long as the equation PV/T = pv/t holds true, the solution for v is always equal to V.
To solve for v in the equation PV/T = pv/t, we can manipulate the equation to isolate v on one side.
Starting with the given equation:
PV/T = pv/t
To isolate v, we can cross-multiply:
PVt = pVt
Next, we divide both sides of the equation by pt:
V = v
Therefore, the solution is v = V.
In other words, v is equal to V, which means they represent the same values.
This implies that v and V are interchangeable and can be used interchangeably in the equation.
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Please help due 5 min!!!!
Answers
Cameron surveyed her friends about the number of apps they use. The responses were 15, 16, 18, 9, 18, 4, 19, 20, 17, and 36 apps. Use the range and interquartile range to describe how the data vary.
Answers
The middle half of the data values vary by:
Interquartile = [tex]Q_3-Q_1[/tex] => 19.25 - 13.5 = 5.25
The given data is :
15, 16, 18, 9, 18, 4, 19, 20, 17, and 36 apps.
We have to find:
Use the range and interquartile range to describe how the data vary.
We have to arrange the data from smallest to largest.
4, 9, 15, 16, 17, 18, 18, 19, 20, 36
Range of the data is : Highest no. - lowest no.
Range of the data is: 36 - 4 = 32
The location of the [tex]Q_1[/tex] = (n + 1) × 0.25 (where n is the total no. in the data)
The location of the [tex]Q_1[/tex] = (10 + 1) × 0.25 = 11 × 0.25 = 2.75
∴[tex]Q_1[/tex] = 15 × 0.75 + 9 × 0.25 = 13.5
The location of the [tex]Q_3[/tex] = (n + 1) × 0.75
The location of the [tex]Q_3[/tex] = 11 × 0.75 = 8.75
∴[tex]Q_3[/tex] = 19 × 0.75 + 20 × 0.25 = 19.25
Hence, The middle half of the data values vary by:
Interquartile = [tex]Q_3-Q_1[/tex] => 19.25 - 13.5 = 5.25
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During the winter, if the low temperature outside is a °C, the daily cost to heat a
building can be determined using the function f(x) = 5 (1.3) * . Find and
interpret the given function values and determine an appropriate domain for the function.
round all function values to the nearest hundredth.
f:7)= __, meaning when the low temp outside is __ celsius it would cost $__ to heat the building. this interpretation _______________ in the context of your problem.
f(9.5)=___, meaning when the low temp outside is ___ celsius it would cost & __ to heat the building. this interpretation _______________ in the context of the problem.
based on the observations above it is clear that an appropriate domain for the function is —————
PLEASE HELP
Answers
The values of the function are 5 and 1.5 and the domain is,
⇒ - ∞ < x < ∞
Here, The equation of the function is given as
f(x) = 5 (1.3)ˣ
The above function is an exponential function.
An exponential function is represented as
f(x) = abˣ
Where
a represents the initial value, b represents the rate of growth or decay
While x and f(x) are the input and output values
Hence, By comparison, we have
a = 5 and b = 1.3
This means that the function values are 5 and 1.3.
Since, the function is an exponential function.
The domain of an exponential function is the set of all real values
Hence, the domain of f(x) is the set of all real values.
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17 in. 16 in. 14 in.
Answers
The surface area of the rectangular prism is 1468 square inches
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
17 in by 16 in by 14 in
The surface area of the rectangular prism is calculated as
Area = 2 * (17 * 16 + 17 * 14 + 16 * 14)
Evaluate
Area = 1468
Hence, the area is 1468 square inches
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Question
What is the surface area of this rectangular prism?
17 in. by 16 in. by 14 in.
Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.
coordinate plane showing the points 2, 10, point 3, 5, point 4, 2.5, and point 5, 1.25
a
an = 20(one half)n − 1; average rate of change is fifteen halves
b
an = 10(one half)n − 1; average rate of change is fifteen halves
c
an = 20(one half)n − 1; average rate of change is negative fifteen halves
d
an = 10(one half)n − 1; average rate of change is negative fifteen halves
Answers
The sequence based on the information would be: B. an = [tex]10 1/2^{-1}[/tex]average rate of change is negative fifteen halves.
How to explain the functionThis question is about exponent function/series. You are given 3 points from the function, point A (1,10), point B( 2, 5), and point C(4,1.25).
If you insert point A to the function, an will give a result of 10 for n=1.
For n=0, the result would be:
an= 10([tex]1/2^{-1}[/tex])
= 10 * 2
= 20
Then the average rate of change from n=0 to n=2 would be:
Rate of change= (y₂ -y₁)/ (x₂ -x₁)
Rate of change= (5-20)/ (2-0)
= -15/2
= negative fifteen halves
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Darlene purchases $20,000 worth of stock on her brokers advice and pays her broker a 1.5% broker fee
Answers
Darlene's net proceeds from the investment into shares would be $ 8, 279 .
How to find the net proceeds ?First, find the initial broker fee:
= Initial investment × Broker fee rate
= 20, 000 x 1. 5 %
= 20, 000 x 0. 15
= $ 300
The total fees incurred to buy and sell are:
= 300 initial broker + 21 later broker
= $ 321
The net proceeds would then be:
= Final value of stock - Initial investment - Total fees
= 28, 600 - 20, 000 - 321
= 8, 600 - 321
= $ 8, 279
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Full question is:
Darlene purchases $20,000 worth of stock on her brokers advice and pays her broker a 1.5% broker fee. She sells her stock when it increases to $ 28,600 two years later, and uses a discount broker who charges $21 per trade. Compute Darlene's net proceeds after the broker fees are taken out.
Find the Value of x. Round to the nearest tenth.
hyp = x
28°
11
Answers
The calculated value of x in the right triangle is 12.5
How to calculate the value of xFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The value of x can be calculated using the following cosine rule
So, we have
cos(28) = 11/x
make x the subject of the formula
So, we have
x = 11/cos(28)
Evaluate the quotient
This gives
x = 12.5
Hence, the value of x is 12.5
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What are the solutions of the equation 2 log x = log (5x-6)? Select all that apply.
A x=1
B. x=2
C. x= 3
D. x = 5
E. x=6
Answers
Answer:
B, C
Step-by-step explanation:
x^2 = 5x - 6
x = 2 or x = 3