Answers
The triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.
What is the similarity?If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.
In the given triangles we can see that:-
Angle BAC is congruent to Angle DCA Angle B and Angle D are congruent.The two triangles are sharing common side which is AC.Therefore we can see that the triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.
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Related Questions
A triangle has two sides of lengths 4 and 15. What value could the length of
the third side be? Check all that apply.
A. 19
B. 11
C. 4
OD. 15
OE. 12
F. 13
Answers
The value could the length of the third side will be 11,12,13,15. Options B, D, E, and F are the correct answers.
What is the triangle?A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.
According to the triangle Inequality theorem, any two triangle sides must add up to more than the third side's length.
You may get the potential length of a triangle by multiplying the sum of two sides by the difference between two sides.
Therefore,
Let x is the possible length of the third side of a triangle.
14-4<x<15+4
10<x<19
The values of the third side is lies between the 10 and 19.The value could the length of the third side will be 11,12,13,15
Hence, options B, D, E, and F are the correct answers.
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Round 7,485 to the nearest hundred.
Answers
Answer:
7,500
Step-by-step explanation:
When you round you automatically round up unless told otherwise
so find the hundredth, which is 485 and you round that to 500
then put the 7 back → 7,500
What is the solution to the equation 3 square root 5x-4 = 3 square root7x+8?
Answers
(08.01 MC)
Find the height of a square pyramid that has a volume of 75 cubic feet and a base length of 5 feet.
A. 5 feet
B. 9 feet
C. 25 feet
D. 45 feet
Answers
Answer:
A. 5 feet
Step-by-step explanation:
Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
An investment company advertised that last year its clients, on average, made a profit of 10%. Assuming that average refers to
following claims must be true based on this information?
Note: More than one statement could be true. If none of the statements is true, mark the appropriate box.
Last year at least one of their clients made a profit of
exactly 10%.
Two years ago some of their clients made a profit of at least
10%.
Last year some of their clients made a profit of
0
10% or more.
O
O Last year all of their clients made a profit of more than 2%.
Last year, the number of their clients who made a profit of
10% or less was equal to the number of their clients who
made a profit of 10% or more.
Answers
The statements that are true based on the information are:
1. Last year at least one of their clients made a profit of exactly 10%.
3. Last year some of their clients made a profit of 10% or more.
Options 1 and 3 are the correct answer.
We have,
1. Last year at least one of their clients made a profit of exactly 10%.
- True.
The investment company advertised that, on average, their clients made a profit of 10%.
This means there must be some clients who made exactly 10% profit.
2. Two years ago some of their clients made a profit of at least 10%.
Not enough information is given to determine the accuracy of this statement.
The information provided only refers to last year's profits, not profits from two years ago.
3. Last year some of their clients made a profit of 10% or more.
- True.
The average profit of the clients was 10%, indicating that some clients made a profit of 10% or more.
4. Last year all of their clients made a profit of more than 2%.
- Not necessarily true.
The average profit was 10%, but this does not guarantee that all clients made a profit greater than 2%.
Some clients might have made less than 2% or even incurred losses.
5. Last year, the number of their clients who made a profit of 10% or less was equal to the number of their clients who made a profit of 10% or more.
- Not enough information is given to determine the accuracy of this statement.
The average profit of 10% does not tell us about the distribution of profits among clients to make this comparison.
Thus,
The statements that are true based on the information are:
1. Last year at least one of their clients made a profit of exactly 10%.
3. Last year some of their clients made a profit of 10% or more.
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transform each graph below.
(a) The graph of y=f(x) is shown. Draw the graph of y= f(2x).
(b) The graph of y=g (x) is shown. Draw the graph of y=1/2g(x).
Answers
Answer:
Step-by-step explanation:
HELP ME PLEASE
13
25
Which expression represents the volume, in cubic units,
of the composite figure?
○ π(57)(13) —π (5²)(12)
○ π(5²)(13) — π (5²)(25)
○ ~(5²)(13) + = π (5²)(12)
○pi(5²)(13) + = π (5²³)(25)
Answers
Answer:
π(5²)(13)+⅓π(5²)(12)
Step-by-step explanation:
You can find the volume of the cylinder by:
V=πr²h
which is V1=π(5²)(13)
and the volume of the crooked cone by:
⅓πr²h
which is V2=⅓π(5²)(12)
and you need the volume of the whole shape. you can find by adding V1+V2
The following graph portrays the distribution of the number of spicy chicken sandwiches sold at a nearby Wendy's for the last 141 days.
The mean number of sandwiches sold per day is 91.9 and the standard deviation is 4.67. (Round your answers to 2 decimal places.)
If we use the Empirical Rule, on 68 percent of the days sales will be between
95 percent of the days sales will be between
Answers
68% of the day's sales will be between 87.23 and 96.57 and on 95% of the days, sales will be between 82.56 and 101.24.
What is the empirical rule?If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.
We have:
The mean number of sandwiches sold per day is 91.9 and the standard deviation is 4.67.
As we know, from the empirical rule, 68% of the data will lie in one standard deviation of the mean, i.e., in the interval with the endpoints x±s
for samples and with endpoints u±б for the population.
x = 91.9
s = 4.67
x - s = 91.9 - 4.67 = 87.23
x + s = 91.9 + 4.67 = 96.57
68% of the day's sales will be between 87.23 and 96.57
95% of the data will lie within two standard deviations of the mean, which means in the interval with the endpoints x±2s for samples and with endpoints u±б population.
x - 2s = 82.56
x + 2s = 101.24
On 95% of the days, sales will be between 82.56 and 101.24
Thus, 68% of the day's sales will be between 87.23 and 96.57 and on 95% of the days, sales will be between 82.56 and 101.24.
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Which expressions are equivalent to 9b?
Choose all answers that apply
A. b+2(b+2b)
B. 3b+b
C. 2(2b)
Answers
Answer:
A. b+2(b+2b)
b + 2b + 4b = 7b
B. 3b + b = 4b
C. 2(2b) = 4b
None of them are equal to 9b
Answer:
[tex]\fbox {None}[/tex]
Step-by-step explanation:
A
b + 2(b + 2b)b + 2(b) + 2(2b)b + 2b + 4b7bB
3b + b4bC
2(2b)4bWhich graph best represents the equation shown below? 3x + y = 2 A. B. C. D.
Answers
Answer:
The plots are (0,2) (1,-1)
Step-by-step explanation:
a slanted line starting from top left corner ending in the bottom right
The volume of a can of Pepsi is 0.33liter. There are 12 cans in 1 carton
What is the volume of 5 cartons of Pepsi?
Answers
Answer:
19 liters 800 milliliters
Step-by-step explanation:
0.33 * 12 * 5 = 19.8 liters
Suppose we want to choose 2 colors, without replacement, from the 3 colors red, blue, and green . How many ways can this be done, if the order of choices is relevant
Answers
The 2 colors can be chosen in 6 different ways.
In how many ways can the colors be chosen?Here we need to identify the selections and the numbers of options for each.
Here the selections are:
Color 1.Color 2.And the numbers of options for each are:
Color 1: 3 options (there are 3 colors).color 2: 2 options (one is already taken).The total number of combinations is:
C = 3*2 = 6
The 2 colors can be chosen in 6 different ways.
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A sample of size 400 was drawn and sample mean was found t
be 99. Test whether this sample could have come from a normal
population with mean 100 and variance 64 at 5%
significance.
Answers
Answer:
etrf4f3dvef3rf3rfr2wrgwrf2rg3rf3rgerferferfef I'm
The function f(x)= –StartRoot negative x EndRoot is shown on the graph.
Answers
The range of the required function f(x) = -√-x is all real values less than or equal to 0.
The nature of the function is imaginary because of the negative sign present inside the root. Hence the range of the function exists only and only if the function gives real values in each of its outcomes.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.
As per question
f(x) = -√-x
clearly, for each positive real number the function becomes imaginary.
So the domain of the given function lies (-∞, 0).
and for every x in its domain function has its exists in range of all real values less than and equal to zero.
Thus, the range of the function f(x) ≤ 0.
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Question 15 (06.01 LC)
Classify the expression: 5x³ - 4x²
Quadratic expression
Linear expression
Cubic expression
Constant expression
Answers
Answer:
Cubic expression
Step-by-step explanation:
Polynomials with a degree of 3 are known as cubics.
Answer:
cubic expression
Step-by-step explanation:
it is cubic when raised to the power of 3
Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of the patients in the study experienced insomnia as a side effect. As random sample of 20 Clarinex-D users is obtained, and the number of patients who experienced insomnia is recorded. Find and interpret probability that 3 or fewer experienced insomnia as a side effect.
Answers
Using the binomial distribution, it is found that there is a 0.9842 = 98.42% probability that 3 or fewer experienced insomnia as a side effect, which means that it is a highly likely event.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
n = 20, p = 0.05.
The probability that 3 or fewer experienced insomnia as a side effect is given by:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.3585[/tex]
[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.3774[/tex]
[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.1887[/tex]
[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]
Then:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9842[/tex]
0.9842 = 98.42% probability that 3 or fewer experienced insomnia as a side effect.
Since this probability is greater than 95%, this is a highly likely event.
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Which expression is equivalent to...
Answers
Detailed Answer:
Following the Laws of Exponents,
• a^n * a^m = a^(n + m)
Therefore,
= 5^10 * 5^5
= 5^(10 + 5)
=> 5^15
Find the formula for the area of the shaded region in the figure.
x² = 4py
ہے
Answers
The formula for the area of the shaded region in the figure.
x² = 4py is mathematically given as
[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]
What is the formula for the area of the shaded region in the figure?Parameters
[tex]$x^{2}=4 p y$[/tex]
[tex]$y=h$[/tex]
[tex]\therefore x^{2}=4 p h \Rightarrow x=2 \sqrt{p h} \\[/tex]
Generally, the equation for the Area is mathematically given as
[tex]& A=2 \int_{0}^{2 \sqrt{p h}}\left(h-\frac{x^{2}}{4 p}\right) d x \\\\& A=2\left(h x-\frac{x^{3}}{12 p}\right]_{0}^{2 \sqrt{p h}} \\\\& A=2\left[\left[h 2 \sqrt{p h}-\frac{1}{12 p} \cdot(2 \sqrt{p h})^{3}-0\right]\right. \\[/tex]
[tex]&A=2\left[2 h^{3 / 2} \sqrt{p}-\frac{8(\sqrt{p})^{3}(\sqrt{h})^{3}}{12 p}-0\right] \\\\&A=2\left[2 h^{k / 2} \sqrt{p}-\frac{2}{3} \sqrt{p} \cdot h^{3 / 2}\right] \\\\&A=2 \times \frac{4 \sqrt{p} \cdot h^{3 / 2}}{3} \\\\&A=\frac{8}{3} \cdot \sqrt{p} \cdot \sqrt{h} \cdot h \\\\&A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]
[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]
In conclusion, the equation for the Area is
[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]
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For the regions bounded by y = 6cosx and y = one fourth x squared minus 7.
Part A: Find the limits of integration. (10 points)
Part B: Write the expression representing the total area. (10 points)
Part C: Solve for the total area. (10 points)
Answers
For the regions bounded by y = 6cosx and y = one-fourth x squared minus 7, the limits of integration, the expression representing the total area, and the total area are mathematically given as
A=27.03squnit
What are the limits of integration, the expression representing the total area, and the total area.?
Generally, the equation for expression is mathematically given as
y = 6cosx
y=(1/4)x^2-7
therefore
[tex]A=\int^{b}_a (f(x)-g(x))dx[/tex]
The limits are
a=0 b=2\pi
Hence
[tex]A=\int ^{2\pi}_0 (6cosx -((1/4)x^2-7))dx\\\\solving\\\\A=\int^{2\pi}_0 (6cosx -((1/4)x^2-7))dx[/tex]
A=27.03squnit
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Enter the correct answer in the box.
Function g has the same a value as function f, but its vertex is 2 units below and 3 units to the left.
f(x) = x² - 4x - 32
Write the vertex form of the equation modeling function g.
Answers
The equation in the vertex form of g(x) is:
[tex]g(x) = (x + 1)^2 - 38[/tex]
How to get the equation of function g?
We know that g(x) is a translation of 2 units below and 3 units to the left of f(x).
So first, let's rewrite f(x) to its vertex form:
[tex]f(x) = x^2 - 4x - 32[/tex]
The vertex is at:
[tex]x = -(-4)/2*1 = 2[/tex]
The y-value of the vertex is:
[tex]f(2) = 2^2 - 4*2 - 32 = -36[/tex]
Then the vertex form of f(x) is:
[tex]f(x) = (x - 2)^2 - 36[/tex]
If we move this vertex 2 units below, and 3 units to the left, then we have:
[tex]g(x) = f(x +3) - 2\\\\g(x) = (x - 2 + 3)^2 - 36 - 2\\\\g(x) = (x + 1)^2 - 38[/tex]
That is the equation for g(x) in vertex form.
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Which of the following statements are true?
A. Both graphs have exactly one asymptote.
B. Both graphs have been shifted and flipped.
c. Both graphs are logarithmic functions.
D. Both graphs are exponential functions.
Answers
Math: Surface Area word problem..10 pts for your help!
Answers
The formula for the surface area N(t) of the balloon after t seconds is [tex]N(t) = \frac {64}9\pi t^2[/tex]
How to determine the surface area?We have:
[tex]S(r) = 4\pi r^2[/tex]
Also, we have:
[tex]P(t) = \frac 43t[/tex]
The above can be rewritten as:
[tex]r = \frac 43t[/tex]
Substitute [tex]r = \frac 43t[/tex] in S(r) to determine the function N(t)
[tex]S(r) = 4\pi (\frac 43t)^2[/tex]
Express as N(t)
[tex]N(t) = 4\pi (\frac 43t)^2[/tex]
Expand the exponent
[tex]N(t) = 4\pi *\frac {16}9t^2[/tex]
Evaluate the product
[tex]N(t) = \frac {64}9\pi t^2[/tex]
Hence, the formula for the surface area N(t) of the balloon after t seconds is [tex]N(t) = \frac {64}9\pi t^2[/tex]
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Find x and Y pls help
Answers
Answer:
Step-by-step explanation:
Comment
The angle supplementary to x and 3x are equal.
Supplementary angles = 180
Solution
x + 3x = 180
4x = 180 Divide by 4
4x/4 = 180/4
x = 45
The angle supplementary to x is 3x
3x = 3*45
3x = 135
This angle is vertically opposite y. Vertically opposite angles are equal. So y = 135
Answer
x = 45
y = 135
Evaluate 3a-5b when a=-3 and b=-2
Answers
Answer: 1
Step-by-step explanation:
Substituting in the given values,
3a-5b=3(-3)-5(-2)=-9+10=
Find the critical point for f(x)=x^2-2x+4 and determine their nature.
Select one:
O a. (3, 1) minimum point
O b. (1, 3) minimum point
O c. (1, 3) maximum point
O d. (3, 1) maximum point
Answers
Tan + Cos / 1 + Sin = Sec
Answers
[tex]\tan x+\frac{\cos x}{1+\sin x}\\\\ =\frac{\sin x}{\cos x}+\frac{\cos x}{1+\sin x}\\\\=\frac{\sin x(1+\sin x)+\cos^{2} x}{\cos x(1+\sin x)}\\\\=\frac{\sin^{2} x+\cos^{2} x+\sin x}{\cos x(1+\sin x)}\\\\=\frac{1+\sin x}{\cos x(1+\sin x)}\\\\=\frac{1}{\cos x}\\\\=\sec x[/tex]
How do I solve for x?
Answers
Answer:
3
Step-by-step explanation:
1: Turn the mixed fraction into improper.
2: Multiply 3/5 to each side
3: The you get x = 3
You need to multiply the fraction instead of division because multiplying by the reciprocal is the same as dividing the normal fraction.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{5 = 1\dfrac{2}{3}x}[/tex]
[tex]\mathsf{1\dfrac{2}{3}x = 5}[/tex]
[tex]\mathsf{\dfrac{1\times3 + 2}{3}x = 5}[/tex]
[tex]\mathsf{\dfrac{3 + 2}{3}x = 5}[/tex]
[tex]\mathsf{\dfrac{5}{3}x = 5}[/tex]
[tex]\large\textbf{MULTIPLY }\rm{\bf \dfrac{3}{5}}\large\textbf{ to BOTH SIDES}[/tex]
[tex]\mathsf{{\dfrac{3}{5}\times\dfrac{5}{3}x= \dfrac{3}{5}\times 5}}[/tex]
[tex]\large\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathsf{x = \dfrac{3}{5}\times5}[/tex]
[tex]\mathsf{x = \dfrac{3}{5}\times\dfrac{5}{1}}[/tex]
[tex]\mathsf{x = \dfrac{3\times5}{5\times1}}[/tex]
[tex]\mathsf{x = \dfrac{15}{5}}[/tex]
[tex]\mathsf{x = 15\div5}[/tex]
[tex]\mathsf{x = 3}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A dragon flew 300 miles from his castle to visit a friend. Flying with the wind, his trip took 2 hours. His return trip against the wind took 3 hours. What was the speed of the wind and the speed of the dragon in still air?
Answers
The speed of the wind and the speed of the dragon in still air are respectively; 142.5 mph and 7.5 mph
How to calculate the speed?The dragon flew 300 miles with the wind in two hours.
After flying against the wind for two hours, he had made 270 miles of the return trip.
Let s be the speed in still air
Let w be the speed of the wind
Thus;
(s - w) = effective speed against the wind
and
(s + w) = effective speed with the wind
We know that;
distance = time * effective speed
Thus;
2(s + w) = 300
2(s - w) = 270
This can be simplified to get;
s + w = 150 -----(1)
s - w = 135 -----(2)
Add both equations to get;
2s = 285
s = 285/2
s = 142.5 mph.
Then, plane speed in still air is;
142.5 + w = 150
w = 150 - 142.5
w = 7.5 mph is the speed of the wind
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the value of a savings account can be found using the equation 300(1.03)^24. the interest is compounded monthly.
the interest rate is _____ per year
a. 12%
b. 0.25%
c. 36%
d. 1.5%
Answers
The interest rate is 36% per year if the value of a savings account can be found using the equation 300(1.03)²⁴ option (c) is correct.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We have:
The value of a savings account can be found using the equation =
= 300(1.03)²⁴
From the function:
F(x) = a(1+r)ˣ
On compare:
1 + r = 1.03
r = 0.03
or
r = 3% monthly
r = 3×12 = 36% yearly
Thus, the interest rate is 36% per year if the value of a savings account can be found using the equation 300(1.03)²⁴ option (c) is correct.
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$10,000 is invested for 4 years at an annual simple interest rate of 16%.
Answers
Answer:
$16,400
Step-by-step Explanation:
Step 1: We multiply $10,000 by 16%, getting $1,600.
Step 2: We then multiply $1,600 by 4 (which is given). That gives us $6,400.
Step 3: Add that to $10,000. We get $16,400 as the answer!
Please mark me as brainliest! I really need it!!! Thanks!Answer:
Simple interest = P x r x t
= 10,000 x 16/100 x 4
= $6400
Final amount = P (1 +rt)
= 10,000 (1 + 16/100 x 4)
= $16400
(or you can just add the simple interest to the principle amount to get the final amount)
