Answers
Applying the Pythagorean theorem and the trigonometric ratios, the perimeter of triangle ABC is: 68.8 units.
What is the Perimeter of a Triangle?The perimeter of a triangle = sum of its 3 sides.
Given the following:
AB = 15 BD = 9m∠C=30°Use the Pythagorean theorem to find AD considering triangle ADB as a right triangle:
AD = √(15² - 9²)
AD = 12 units
Use the trigonometric ratios to find DC and AC:
sin 30 = AD/AC
sin 30 = 12/AC
AC = 12/sin 30
AC = 24 units
tan 30 = AD/DC
tan 30 = 12/DC
DC = 12/tan 30
DC ≈ 20.8 units
BC = BD + DC = 9 + 20.8
BC = 29.8 units.
Perimeter of triangle ABC = BC + AB + AC
Perimeter of triangle ABC = 29.8 + 15 + 24
Perimeter of triangle ABC = 68.8 units.
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Related Questions
Suppose the average age of family members is 34 with a standard deviation of 4. if 100 members of the community decided to have a summer outing bonding and relaxation, find the probability that the average of these members is less than 35?
Answers
Using the normal distribution, it is found that there is a 0.9938 = 99.38% probability that the average of these members is less than 35.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, we have that the parameters are given as follows:
[tex]\mu = 34, \sigma = 4, n = 100, s = \frac{4}{\sqrt{100}} = 0.4[/tex].
The probability that the average of these members is less than 35 is the p-value of Z when X = 35, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{35 - 34}{0.4}[/tex]
Z = 2.5
Z = 2.5 has a p-value of 0.9938.
0.9938 = 99.38% probability that the average of these members is less than 35.
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Please Help I Don't Understand
Answers
Answer:
7.5
Step-by-step explanation:
10 is to 8 as x is to 6
10/8 = x/6
6 (10/8) = x = 7.5
Answer:
Step-by-step explanation:
The two triangles are similar because the corresponding angle in each is equal to the angle corresponding angles in the other.
Put in simpler language. ΔAEB ~ ΔADC by parallel lines properties. If that's the case 10/(10 + 8) = x/(x + 6)
Equation
AE/AD = AB/AC Substitute values
Solution
10/(10 + 8) = x/(x + 6) Cross Multiply
10*(x + 6) = x* (10 + 8) Combine
10*(x + 6) = 18x Remove the Brackets
10x + 60 = 18x Subtract 10x from both sides
8x = 60 Divide by 8.
x = 60/8
x = 7.5
Answer: A
4 5/6 - 2 1/2
please help!
Answers
Answer:
2.33
Step-by-step explanation:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
296−52
29
6
−
5
2
Applying the fractions formula for subtraction,
=(29×2)−(5×6)6×2
=
(
29
×
2
)
−
(
5
×
6
)
6
×
2
=58−3012
=
58
−
30
12
=2812
=
28
12
Simplifying 28/12, the answer is
=213
At 13:00, a water tank contained 180 litres of water. Water flowed from the tank at a constant rate until, at 17:30, the tank was completely empty. Calculate the rate of flow of water from the tank in litres per hour. If your answer is a decimal, give it to 1 d.p.
Answers
The drain rate is constant and thus equal to the average drain rate over the entire 4.5 hour period. This rate is
[tex]\dfrac{0 \,\mathrm L - 180 \,\mathrm L}{4.5 \,\rm h} = -40 \dfrac{\rm L}{\rm h}[/tex]
which is to say, water flows from the tank at a rate of 40 L/h.
x^2+3x-18 use factoring to determine the zeros
Answers
Answer:
x = 3
x = -6
Step-by-step explanation:
Hello!
Let's first set the equation to 0.
x² + 3x - 18 = 0To factor, first think about two numbers that multiply to -18, but add up to 3. The two numbers are 6 and -3.
Now, expand 3x to 6x and -3x. Then, factor by grouping.
Factorx² + 3x - 18 = 0x² + 6x - 3x - 18 = 0(x² + 6x) - (3x + 18) = 0x(x + 6) -1(3)(x + 6) = 0(x - 3)(x + 6) = 0Now, set each factor to 0 and solve for x
Solve(x - 3) = 0x = 3(x + 6) = 0
x = -6
x = 3, x = -6
If f(x) = 3x + 2 and g(x) = x² + 1, which expression is equivalent to (fog)(x)?
O (3x + 2)(x2 + 1)
Answers
Answer:
Hi,
Step-by-step explanation:
[tex](fog)(x)=g(f(x))=g(3x+2)=(3x+2)^2+1=9x^2+6x+5[/tex]
Answer:
hi
Step-by-step explanation:
How many solutions exist for the system of equations graphed below?
a.) none
b.) one
c.) two
d.) infinitely many
Answers
Answer:
one
Step-by-step explanation:
When a system of equations is graphed, the solution is the coordinate that is plotted at the intersection of the two lines.
If the two lines cross once, there is only one solution.
If the two lines are on top of each other then there are infinitely many solutions.
If the two lines are parallel ( and never touch ) then there are no solutions
By looking at the graph we notice the two lines intersect once. So we can conclude that there is only one solution.
Detailed Explanation:
For the graph of a system of linear equations :-
• If the lines are parallel, then the pair of equations has no solution
• If the lines are coincident, then the pair of equations has infinite solutions
• If the lines are intersecting, then the pair of equations have one solution.
In this graph, the lines formed by the equations are intersecting at a point. Hence it has a unique solution.
What type of function is f(x) = 2x³ - 4x² + 5? O Exponential O Logarithmic O Polynomial O Radical
Answers
Answer:
Polynomial
Step-by-step explanation:
⇒ It cannot be option 1 as y does not vary with an exponent
⇒ It cannot be option 2 as y does not relate to any logarithmic values of x
⇒ It cannot be a option 4 as there no irrational numbers under a root
⇒ Therefore it is a polynomial, as it is written in the form : y = ax³ + bx² + cx + d (cubic polynomial)
The function g(x) is defined as g(x)=-2x+3x the value of g(-3)is
Answers
Answer:
-3
Step-by-step explanation:
g(-3) = -2x+3x
-2(-3) +3(-3)
6+-9 = -3
give brainliest please
hope this helps :)
Answer:
just commenting so you can give the other guy brainliest !
Step-by-step explanation:
How would I solve this?
Answers
Answer:
(-2, -2)
Step-by-step explanation:
the solution of the system of equation put simply is the point of intersection between the 2 lines
hence, the answer is (-2,-2)
216, 36,6, Find the 8th term.
Answers
Answer:
1
Step-by-step explanation:
216 is term 1
36 is term 2
6 is term 3
1 is term 4
Parallelogram L M N O is shown. Angle N is (2 x) degrees and angle L is (3 x minus 20) degrees.
What is the measure of angle L in parallelogram LMNO?
Answers
X is a normally distributed random variable with mean 46 and standard deviation 22.
What is the probability that X is between 2 and 90?
A. .99
B. .95
C. .85
D. .65
Answers
Answer:
B. 0.95
Step-by-step explanation:
The probability that the value of the random variable is in the given range is the area under the normal probability distribution curve over that range. The value of this area is conveniently provided by any number of calculators, apps, or spreadsheets. It can also be determined using the "empirical rule" that tells you the probability over certain normalized ranges.
__
normalized rangeA standard normal probability density function (PDF) has a mean of 0 and a standard deviation of 1. The range in this problem can be normalized to some number of standard deviations above or below the mean. The mean is given as 46, and the standard deviation is given as 22.
In this problem, the lower limit of the range is ...
z = (2 -46)/22 = -2
standard deviations from the mean.
Similarly, the upper limit is ...
z = (90 -46)/22 = +2
standard deviations from the mean.
empirical ruleThe empirical rule tells us that 95% of the area of the PDF lies between -2 and +2 standard deviations from the mean.
P(2 < X < 90) ≈ 0.95
_____
Additional comment
The empirical rule for other ranges is ...
± 1 standard deviation: 68%
±2 standard deviations: 95%
±3 standard deviations: 99.7%
Are the equations 5x=24+2x and 3x=24 equivalent?
Answers
Answer:
Yes they are.
Step-by-step explanation:
By simply moving 2x from the LHS to the RHS we'll get it's equivalent to be 3x.
i.e 5x - 2x = 3x
Consider the graph of the linear function h(x) = -x + 5. Which could you change to move the graph down 3 units?
O the value of b to -3
the value of m to -3
the value of b to 2
O the value of m to 2
Intro
Done
Answers
Answer:
the value of b to 2
The value of b changes to 2.
The correct option is C.
What is Linear Equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
We have,
Equation: h(x) = -x + 5
Now, using the slope intercept form
y = mx + b
From which we get
m = -1 and b=5
Now, we need to move the graph 3 units down then we need to subtract given function by 3, we get
y = -x+5 -3
y = -x +2.
Here y-intercept is 2.
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NEED ANSWER ASAP HELP
Given ABC with altitude h
Prove: sin(B)/b=sin(C)/c
Answers
Using the given information in the diagram, we have proven that sin(B)/b = sin(C)/c
Proving the Sine ruleFrom the question, we are to prove that sin(B)/b=sin(C)/c
Consider the right triangle with sides a, c, and h
Using SOH CAH TOA, we can write that
sin(B) = h/c
∴ h = c × sin(B) --------- (1)
Also,
Consider the other right triangle
Using SOH CAH TOA, we can write that
sin(C) = h/b
∴ h = b × sin(C) ---------- (2)
Equate equations (1) and (2)
That is,
c × sin(B) = b × sin(C)
This can then be expressed as
sin(B)/b = sin(C)/c
Hence, the given expression is proven as shown above
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A square purple rug has a green square in the center. The side length of the green square is x inches. The width of the purple band that surrounds the green square is 3 in. What is the area of the purple band?
Answers
What is a pair of overlapping triangles?
△EDB and △DEC
△ADE and △FCB
△BDE and △EDA
Answers
Explanation: You can see the overlapping if you look very careful. You can see a little triangle formed of DFE.
The number of swimsuits purchased at a department store is positively correlated with each of these variables. a change in which variable most likely caused a change in the number of swimsuits purchased?
Answers
The variable that is most likely to have a positive correlation with the number of swimsuits purchased is the temperature changing outside.
What is positive correlation?Correlation measures the relationship between two variables. When there is a positive correlation, it means that the two variables move in the same direction. If one of the variables increases, the other variable increases. If one of the variables decreases, the other variable decreases.
When it is summer, it is expected that the number of swimsuits bought would increase. When it is winter, it is expected that the number of swimsuits bought would decrease.
Here are the options:
A. The number of swimsuit cover-ups the store has in stock
B. The number of sand castles built by store customers
C. The temperature outside changing
D. The number of minutes it takes the store's employees to get to work
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3n + 19 = 28
How do I solve this
Answers
Answer:
to solve this you need to find out what number n is to make it equal 28.
Step-by-step explanation:
19+3 =22 so 3 is not it
19+9=28
answer is 9
hopefully this is right and this gets to you on time
Answer:
err Im not sure if this is a multiple-choice but n=3
Step-by-step explanation:
3(n) + 19 is 28 meaning you have to find what multiplies with 3 to get 9 because 19+9 is 28
Hope this helps
HELP ME PLEASEEEE ANSWER MY MATH
Answers
The water consumption based on the information for three Months will be 22267m³.
How to calculate the values?The total water consumption for the three months will be:
= 7219 + 7390 + 7658
= 22267m³
In conclusion, the information simply want you to add the values of the water given.
Therefore, the water consumption based on the information for three Months will be 22267m³.
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what is the GCF of (8x-6)
sos T-T
Answers
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the G.C.F. of 8x-6.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
G.C.F. stands for Greatest Common Factor.So what is the G.C.F. of 8x-6? We can list all of their common factors and then select the greatest one, like so:
[tex]\longmapsto\bf{Factors\;of\;8x:}[/tex] 1, 2, 4, 8, x
[tex]\longmapsto\bf{Factors\;of\;-6:}[/tex] -1, 1, 2, -3, 3, -6, 6
So the GCF is:
2
Now, we can also factor it out by placing it outside the parentheses ():
2(4x-3)
See, we factored it out by dividing both terms of the expression by the G.C.F.
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{\bf{We\;factor\;out\;the\;G.C.F.\;by\;dividing\;all\;the\;terms\;of\;the\;expression\;by\;it}}[/tex]
Hope this helps you out! :D
Ask in comments if any queries arise.
~Just a smiley person helping fellow students :)
Answer: 2, you have to use math apps man it will save your life
Complete the equations below. 15.3 ÷ 3 = tenths + 3 15.3÷ 3 = tenths 15.3 ÷ 3 =
Answers
The value of the complete equation is 5.1.
We have given the equation,
15.3 ÷ 3 = tenths + 3 15.3÷ 3 = tenths 15.3 ÷ 3
What is the equation?
An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Therefore we have,
[tex]15.3/3=15+0.3 \ tenths/3\\=5+0.1 \ tenths\\=5.1[/tex]
Therefore the value of the complete equation is 5.1.
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use the tables below to find (p+q)(2).
Answers
The value of the composite function (p + q)(2) is 1
How to evaluate the function?The function expression is given as:
(p + q)(2)
As a general rule
(p + q)(x) = p(x) + q(x)
Substitute 2 for x
(p + q)(2) = p(2) + q(2)
From the table, we have:
p(2) = 3 and q(2) =-2
So, we have:
(p + q)(2) = 3 - 2
Evaluate
(p + q)(2) = 1
Hence, the value of the composite function (p + q)(2) is 1
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Answer: (p+q)(2)=1
Step-by-step explanation:
Edge
Isabelle has a five-sided chicken coop in her yard. each side has an equal length. what is the total perimeter of the chicken coop if the length of one side is yards? recall that the perimeter is the sum of all sides of a shape or boundary. yards yards yards yards
Answers
The total perimeter of the chicken coop if the length of one side is 3√5 yards is; 15√5 yards.yards
How to calculate the total perimeter?We are told that Isabelle had a five sided chicken coop in her yard and that the length was equal in all the sides.
Now, we need to find the total perimeter of the chicken coop.
The length of one side of the coop from online sources is 3√5 yards.
Since the coop is 5 sided, it means that it is a pentagon and we know that;
Perimeter of a pentagon = 5a
Where a is length of one side of the pentagon. Thus;
Perimeter = 5 x 3√5
Perimeter = 15 √5 yards
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A library checked out 20 books on Tuesday if 15 of the books are fiction find the ratio of nonfiction books to fiction books checked out
Answers
The ratio of nonfiction books to fiction books checked out is 1 : 3
How to determine the ratio?The given parameters are:
Total = 20
Fictions = 15
This means that:
Non Fictions = 20 - 15
Evaluate
Non Fictions = 5
The ratio is then represented as:
Ratio = Non Fiction : Fiction
This gives
Ratio = 5 : 15
Simplify
Ratio = 1 : 3
Hence, the ratio of nonfiction books to fiction books checked out is 1 : 3
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what is n^10/n^-5?
pls no explanation just answer
will mark brainliest!
Answers
Answer:
n¹⁵
Key:
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]Step-by-step explanation:
[tex]\frac{n^{10}}{n^{-5}}\\=n^{10-\left(-5\right)}\\n^{10} = n10\\^{-5} = -5\\n10 - -5 = n15\\= n^{15}[/tex]
can someone help me to number 2,4&5.
just 2,4&5 that's all thank you.
Answers
Answer:
See below ~
Step-by-step explanation:
According to a survey, 48% of adults in the united states believe that unidentified flying objects (ufos) are observing our planet. you ask 8 randomly chosen adults whether they believe ufos are watching earth.
Answers
The expected number of adults that believe ufos are watching earth is 4
How to determine the number of adults?The given parameters are:
p = 48%
Sample size, n = 8
The expected number of adults that believe ufos are watching earth is calculated as:
E(x) = np
This gives
E(x) = 8 * 48%
Evaluate
E(x) = 3.84
Approximate
E(x) = 4
Hence, the expected number of adults that believe ufos are watching earth is 4
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The volume of a rectangular prism is 400 cm3 . If the length is 16 cm and the width is 5cm, what is its height?
Answers
Answer:
H = 5
Step-by-step explanation:
rectangular prism:
V = L x W x H
400 cm3 = 16 x 5 x H
400 cm3 = 80 x H
400/80 = 5
h = 5 cm
95% sure this is correct! :)
Answer:
5 cm
Step-by-step explanation:
Formula used :
Volume of the rectangular prism = Length × Width × Height
=========================================================
Given :
⇒ Volume = 400 cm³
⇒ Length = 16 cm
⇒ Width = 5 cm
===========================================================
Solving :
⇒ 400 cm³ = 16 cm × 5 cm × Height
⇒ Height = 400 cm³ / 80 cm²
⇒ Height = 5 cm