Answers
Because angle m is shown to be congruent to angles ABC and CDE, this means that angle m has a measure of 60 degrees.
There can only be 180 degrees in a triangle, so the measure of angle ACB must be 180-60-60, which equals 60 degrees.
Using the Vertical Angles Theorem, the measure of angle ACB is the same as the measure of angle CED.
Therefore, angle CED measures 60°.
Answer:
[tex]m<CED=m\°[/tex]
Step-by-step explanation:
we know that
Triangles ABC and CDE are similar triangles, because the corresponding angles are congruent
[tex]m<BCA=m<DCE[/tex] ------> by vertical angles
[tex]m<ABC=m<CDE[/tex] ----> given problem
[tex]m<BAC=m<CED[/tex] ----> The sum of the internal angles of the triangle must be equal to [tex]180[/tex] degrees
we have
[tex]m<BAC=m\°[/tex]
so
[tex]m<CED=m\°[/tex]
Related Questions
Which equation can be used to find the answer? A playground with four sides has a perimeter of 52 ft. Three of the sides have lengths of 9 ft, 16 ft, and 19 ft. What is the length of the fourth side? A. s – 9 + 16 + 19 = 52 s =26 26 ft B. s + 9 + 16 + 19 = 52 s = 8 8 ft C. s – 52 = 9 + 16 – 19 s = 58 58 ft D. s – 9 – 16 – 19 = 52 s = 96 96 ft
Answers
Perimeter=52 ft
Perimeter=s1+s2+s3+s4
s1=9ft
s2=16ft
s3=19ft
s4=s
What we need to find: equation for given information and solution to s4=s
Perimeter=s1+s2+s3+s4
52=9+16+19+s
52=9+16+19+s
52=44+s like terms added
52-44=44-44+s additive inverse
8=s
Solution: B. s + 9 + 16 + 19 = 52 s = 8 8 ft
Option B)s + 9 + 16 + 19 = 52. Solving this gives the fourth side as 8 ft.
To find the length of the fourth side, you need to know the equation that correctly represents the given information. The perimeter of the playground is the sum of all four sides. Therefore, the correct equation to find the fourth side (s) is:
B. s + 9 + 16 + 19 = 52
9 + 16 + 19 = 44.
s + 44 = 52.
s = 52 - 44.
s = 8.
Therefore, the length of the fourth side is 8 ft.
So, the correct option is B. s + 9 + 16 + 19 = 52.
Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, two green ones, four white ones, and three purple ones. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.] She does not have all the green ones.
Answers
Explanation of calculating the probability of choosing 3 green marbles out of 10 from a bag with 50 marbles.
Explanation:
The probability of choosing exactly 3 green marbles if a total of 10 marbles are selected from a bag filled with 50 marbles, 15 of which are green, can be calculated as follows:
Calculate the total number of ways to choose 3 green marbles out of 15: C(15, 3).Calculate the total number of ways to choose 7 non-green marbles out of 35: C(35, 7).Find the total number of ways to choose 10 marbles out of 50: C(50, 10).Calculate the probability by dividing the product of the above two calculations by the total ways to choose 10 marbles.If you put all the flowers together end to end, what would be the total length of all the flowers?
Answers
1/8 + 3/4 + 1 + 5/8 + 3/4 + 7/8 + 1 =
13/8 + 6/4 + 2 =
13/8 + 12/8 + 16/8 =
41/8 =
5 1/8 inches <==
Which of the following represents the zeros of the function
g(x) = x3 - 9x2 + 2x + 48 ?
A. x= -8, x= 2 , and x= -3
B. x = 8, x = -2 , and x = 3
C. x = 6, x = -4 , and x = 9
D. x = -6, x = 4 , and x = -9
Answers
Probe some roots. When you use x = - 2
you will have: (-2)^3 - 9(-2)^2 + 2(-2) + 48 = -8 - 36 - 4 + 48 = 0
So, - 2 is a root
From that you can divide x^3 - 9x^2 + 2x + 48 by x + 2 and you will get
x^2 - 11x + 24
Then you can factor that: (x - 8)(x - 3)
So, the three roots are x = - 2, x = 3 and x = 8, which is the option B.
Answer: option B. x = 8, x = -2 , and x = 3
Cameron can display his 12 models cars
Answers
Each class at briarwood elementary collected at least 54 cans of food lduring the food drive.If tbere are 29 clases in the school what was the least numbet of cans collected?
Answers
For each class → x ≥ 54
Full School → x ≥ 54(29)
If we simplify the second inequality, we get this:
x ≥ 1566
The answer to your query is x ≥ 1566. Hope this helps and have a fantastic day!
The sum of two positive numbers is 12. what two numbers will maximize the product g
Answers
Given two numbers x and y such that:
x + y = 12 ... (1)
from equation (1)
y = 12 - x
Using this value of y, we represent xy as
xy = f(x)= x(12 - x)
f(x) = 12x - x^2
Differentiating the above function:
f'(x) = 12 - 2x
Maximum value of f(x) occurs at point for which f'(x) = 0.
Equating f'(x) to 0 we get:
12 - 2x = 0
2x = 12
> x = 12/2 = 6
Substituting this value of x in equation (2):
y = 12 - 6 = 6
Therefore, value of xy is maximum when:
x = 6 and y = 6
The maximum value of xy = 6*6 = 36
The two numbers that sum up to 12 and maximize the product are 6 and 6.
Let's denote the two numbers by x and y. We know that x + y = 12, and we want to maximize the product P = xy.
First, express y in terms of x,
y = 12 - x
P = x(12 - x)
= 12x - x²
To find the maximum value of P, we can take the derivative of P with respect to x and set it to zero,
dP/dx = 12 - 2x
Set dP/dx to 0: 12 - 2x = 0
x = 6
Since x + y = 12, if x = 6, then y = 12 - 6 = 6.
The two numbers are 6 and 6.
This combination will maximize the product, which is 6 * 6 = 36.
In conclusion, the two numbers that add up to 12 and maximize their product are both 6.
What is the probability that Eric rolls an even number or draws an ace from a standard deck of cards?
Answers
It is logic that the actions are roll a die and draw a card.
The two events are indepent, so the combined probability is the sum of the individual probabiliites.
Probability = number of positive events / number of possible events
Probability of rolling an even number = number of faces with even numbers / total number of numbers.
Probability of rolling an even number = 3 / 6 = 1/2
Probability of drawing an ace = number of aces in the deck of cards / number of cards
Probability of drawing an ace = 4 / 52 = 1 / 13
Combined probability = 1/2 + 1/13 = (13 + 2) / 26 = 15 / 26
Answer: option D. 15 / 26
The salaries of the president and the Vice President of a certain country total $562,500 a year. If the president makes $237,400 more than the Vice President , find each of their salaries.
Answers
Suppose five construction companies have the ability to build a factory overseas to produce a manufactured good. The marginal cost of building a factory for each construction company is shown in the table below: Producer Marginal Cost Company 1 $1,000,000 Company 2 $1,250,000 Company 3 $1,300,000 Company 4 $1,350,000 Company 5 $1,500,000 If the market price of an overseas factory is $ 1 470 000 , what is the surplus for these five companies?
Answers
The surplus for the five companies is amounting to $830,000
What is the surplus for the five companies?Producer Surplus is the difference between the price at which a producer is willing to spend and the price which he is getting from the market for his product.
The minimum price at which a producer is willing to spend is the Marginal Cost of producing that product.Therefore, Producer surplus is Market Price- Marginal CostProducer Marginal Cost Market Price Producer Surpus Company 1 1,000,000 1,470,000 (1,470,000-1,000,000)=470,000
Company 2 1,250,000 1,470,000 (1,470,000-1,250,000)=220,000
Company 3 1,300,000 1,470,000 (1,470,000-1,300,000)=170,000
Company 4 1,350,000 1,470,000 (1,470,000-1,350,000)=120,000
Company 5 1,500,000 1,470,000 (1,470,000-1,500,000)=-30,000
Total producer surplus= 470,000 + 220,000 + 170,000 + -30,000 = 830,000
The surplus for the five companies is amounting to $830,000
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Final answer:
The surplus for Companies 1, 2, and 3 is $470,000, $220,000, and $170,000 respectively, as their marginal costs are less than the market price of $1,470,000. Companies 4 and 5 do not have a surplus since their marginal costs are above the market price. The total surplus is $860,000.
Explanation:
The surplus for the five construction companies based on their marginal costs and the market price of an overseas factory can be calculated as the difference between the market price and the marginal cost for each company. Only the companies that have a marginal cost lower than the market price will experience a surplus. Given that the market price is $1,470,000:
Company 1 has a surplus of $470,000 ($1,470,000 - $1,000,000).
Company 2 has a surplus of $220,000 ($1,470,000 - $1,250,000).
Company 3 has a surplus of $170,000 ($1,470,000 - $1,300,000).
Companies 4 and 5 do not have a surplus because their marginal costs are higher than the market price. The total surplus for the three companies with a surplus is $860,000 ($470,000 + $220,000 + $170,000).
Find the length and width of a rectangle when the width is 4ft. Shorter than the length. The perimeter of the rectangle is greater than 72ft.
Answers
width= 34
A student correctly answers 15 of the first 20 questions on an examination.
Answers
Over the last three evenings, Raina received a total of 83 phone calls at the call center . The first evening, she received 7 more calls than the third evening. The second evening, she received 2 times as many calls as the third evening. How many phone calls did she receive each evening ?
Answers
x + y + z = 83
x = z + 7
y = 2z
z + 7 + 2z + z = 83
4z + 7 = 83
4z = 83 - 7
4z = 76
z = 76/4
z = 19 <=== 3rd evening calls
x = z + 7
x = 19 + 7
x = 26 <=== 1st evening calls
y = 2z
y = 2(19)
y = 38 <=== 2nd evening calls
If an article costs a store $7.45 and if it sells the article for $9.95, what percentage (to the nearest tenth) markup is it using?
Answers
subtract to find the difference:
9.95 - 7.45 = 2.50
divide 2.50 by cost price to get mark up percentage
2.50 / 7.45= 0.3355
= 33.6 percent to the nearest tenth
Answer:
Markup Percentage is 33.56 %
Step-by-step explanation:
Given: Cost of an article = $ 7.45
Selling price of the article = $ 9.95.
To find: Markup percentage or profit percentage
Clearly Selling price is greater we have profit in this case.
Profit amount = 9.95 - 7.45 = $ 2.50
Profit percentage = [tex]\frac{2.50}{7.45}\times100=33.5570469799=33.56[/tex] %
Therefore, Markup Percentage is 33.56 %
I need to solve and show work for 3x over4 divided by 5-1 over 8
Answers
4
Is the answer
3x
---
4
over
5x-1
------
8
To accomplish this, invert the 2nd fraction and then multiply:
3x 5x-1
--- * ------ = 15x^2-3x divided by 32.
4 8
There are 365,493 blue pens in a warehouse and 549384 black pens how many pens are there in all
Answers
365,493+549,384
Your answer would be 366,042.384
I hope this helps!
At an interest rate of 8% compounded annually, how long will it take to double the following investments?
$50
$500
$1700
Answers
recall your logarithm rules for an exponential,
[tex]\bf \textit{Logarithm of exponentials}\\\\ log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\ -------------------------------\\\\ \qquad \textit{Compound Interest Earned Amount} \\\\ [/tex]
[tex]\bf A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\$100\\ P=\textit{original amount deposited}\to &\$50\\ r=rate\to 8\%\to \frac{8}{100}\to &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annnually, thus once} \end{array}\to &1\\ t=years \end{cases} \\\\\\ 100=50\left(1+\frac{0.08}{1}\right)^{1\cdot t}\implies 100=50(1.08)^t \\\\\\ \cfrac{100}{50}=1.08^t\implies 2=1.08^t\implies log(2)=log(1.08^t) \\\\\\ [/tex]
[tex]\bf log(2)=t\cdot log(1.08)\implies \cfrac{log(2)}{log(1.08)}=t\implies 9.0065\approx t\\\\ -------------------------------\\\\ [/tex]
now, for the second amount, if the Principal is 500, the accumulated amount is 1000 when doubled,
[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\$1000\\ P=\textit{original amount deposited}\to &\$500\\ r=rate\to 8\%\to \frac{8}{100}\to &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annnually, thus once} \end{array}\to &1\\ t=years \end{cases} \\\\\\ 1000=500\left(1+\frac{0.08}{1}\right)^{1\cdot t}\implies 1000=500(1.08)^t \\\\\\ [/tex]
[tex]\bf \cfrac{1000}{500}=1.08^t\implies 2=1.08^t\implies log(2)=log(1.08^t) \\\\\\ log(2)=t\cdot log(1.08)\implies \cfrac{log(2)}{log(1.08)}=t\implies 9.0065\approx t\\\\ -------------------------------[/tex]
now, for the last, Principal is 1700, amount is then 3400,
[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\$3400\\ P=\textit{original amount deposited}\to &\$1700\\ r=rate\to 8\%\to \frac{8}{100}\to &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annnually, thus once} \end{array}\to &1\\ t=years \end{cases}[/tex]
[tex]\bf 3400=1700\left(1+\frac{0.08}{1}\right)^{1\cdot t}\implies 3400=1700(1.08)^t \\\\\\ \cfrac{3400}{1700}=1.08^t\implies 2=1.08^t\implies log(2)=log(1.08^t) \\\\\\ log(2)=t\cdot log(1.08)\implies \cfrac{log(2)}{log(1.08)}=t\implies 9.0065\approx t[/tex]
Randy school requires that there are two adult chaperones for every 18 students when the students go on a field trip to the museum if there are 99 students going to the museum how many adult shop around our need it
Answers
2 adults to 18 students is as x adults to 99 students.
2/18 = x/99
18x = 2 * 99
18x = 198
x = 11
Answer: 11 adults
Johns collection contains US, Indian and British stamos. If the stamps ratios of US to Indian stamps is 5 to 2, and the ratio of Indian stamps to British stamps is 5 to 1, what is the ratio of US to British stamps
Answers
The ratio of US to British stamps is 25 to 2.
Explanation:To find the ratio of US to British stamps, we need to consider the ratios provided in the question. The ratio of US to Indian stamps is 5 to 2, and the ratio of Indian stamps to British stamps is 5 to 1. We can combine these ratios by multiplying the two ratios together. 5/2 multiplied by 5/1 is equal to 25/2. Therefore, the ratio of US to British stamps is 25 to 2.
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What is the probability of selection for any man in a proportionate random sample, where a sample of 100 will be drawn from a population of 1,000 that is 50% male and 50% female?
Answers
nx = (Nx/N)*n
where:
nx = sample size for stratum x
Nx = population size for stratum x
N = total population size
n = total sample size
Given:
Nx = 100
N = 1000
n = 0.5*(1000) = 500
Required: Probability of Man to be selected
Solution:
nx = (Nx/N)*n
nx = (100/1000)*500 = 50 men
ny = (Nx/N)*n
ny = (100/1000)*500 = 50 women
Probability of Man to be selected = nx/(nx + ny)*100 = 50/(50+50)*100 = 50%
ANSWER: 50%
What number should I multiply 1 1/4 by to get 7/12
Answers
[tex]1 \frac{1}{4} x= \frac{7}{12} [/tex]
Now, all we need to do is convert the mixed fraction into an improper fraction:
[tex] \frac{5}{4} x= \frac{7}{12}[/tex]
Now, just multiply the reciprocal of 5/4 with 7/12, giving us:
[tex] x=\frac{4}{5}* \frac{7}{12} [/tex]
Finally, just straight up multiply to get an answer of x = 28/60, which can be simplified down to x = 7/15. Therefore, the number you have to multiply 1 1/4 to get 7/12 is 7/15. Hope this helped!
Let x represent the number:
x . 5/4 = 7/12
i.e. 5x/4 = 7/12
We want to get x on it's own so multiply both sides of equation by 4
5x = 4 . (7/12) = 28/12
now divide both sides by 5 to get x on its own
x = (28/12) / 5
This does not equate to a whole number fraction as 28 and 12 are not divisible by 5. So simply convert to decimal
x = 2.3333 / 5 = 0.46666
how do i calculate an estimated regression line with the information
n=12, ∑x=66, ∑y=588, ∑xy=2244, ∑x2=396
Answers
y = ax + b
where
a = [(Σy)(Σx²) - (Σx)(Σxy)]/D
b = [n(Σxy) - (Σx)(Σy)]/D
D = n(Σx²) - (Σx)²
Therefore,
D = 12(396) - 66² = 396
a = [588*396 - 66*2244]/396 = 214
b = [12*2244 - 66*588]/396 = -30
Answer:
The regression line is y = 214x - 30
If 4f(x)+f(5-x)=x2
What is f(x)?
Answers
Substitute x with 5-x, then the above equation becomes:
[tex]4f(5-x)+f(5-(5-x))=(5-x)^2[/tex], that is
[tex]4f(5-x)+f(x)=(5-x)^2[/tex]
So, we have the following system of equations:
i) [tex]4f(x)+f(5-x)=x^2[/tex]
ii) [tex]4f(5-x)+f(x)=(5-x)^2[/tex]
multiply the first equation by -4, so that we eliminate f(5-x)'s
i) [tex]-16f(x)-4f(5-x)=-4x^2[/tex]
ii) [tex]4f(5-x)+f(x)=(5-x)^2[/tex]
adding the 2 equations side by side we have:
[tex]-15f(x)=-4x^2+(5-x)^2[/tex]
expanding the binomial, and collecting same terms we have:
[tex]-15f(x)=-4x^2+(25-10x+x^2)[/tex]
[tex]-15f(x)=-3x^2-10x+25[/tex]
dividing by -5:
[tex]3f(x)=\frac{3}{5}x^2+2x-5[/tex]
dividing by 3:
[tex]\displaystyle{f(x)= \frac{1}{5}x^2+ \frac{2}{3}x-\frac{5}{3} [/tex]
Answer: [tex]\displaystyle{f(x)= \frac{1}{5}x^2+ \frac{2}{3}x-\frac{5}{3} [/tex]
What is the value of r, the part of the job that Marina can complete in 1 hour? 0.1 0.4 0.5 0.6
Answers
if in two hours she and Marina can be done, then Marina will do 1(the whole job)-2/10 (twice as much as she can do in an hour)=0.8 of the job. So if Marina does 0.8 of the job in two hours, each hour she will do half of it: 0.4 - and this is the correct answer
Charlie has 5 times as many stamps as Ryan. They have 1,608 stamps in all. How many more stamps does CHarlie have than Ryan?
Answers
Ryan-x 1340+268=1608
5x+x=1608 1340-268=1072
6x=1608
x=268 Charlie has 1072 more stamps then Ryan
Ryan has 268 stamps
The cost CC (in dollars) of making nn watches is represented by C=15n+85C=15n+85. How many watches are made when the cost is $385?
Answers
so, 25 whole watches and hmmmm just the wristband of another maybe.
PLEASE HELP ASAP DUE IN A DAY What is the unit rate for 768.57 m 41.1 h? Enter your answer, as a decimal, in the box.
Answers
The unit rate for 768.57 meters in 41.1 hours is approximately 18.68 meters per hour. This calculation is derived by dividing the distance by the time to find the rate of movement.
To find the unit rate, divide the distance by the time:
[tex]\[ \text{Unit rate} = \frac{\text{Distance}}{\text{Time}} \][/tex]
[tex]\[ \text{Unit rate} = \frac{768.57 \, \text{m}}{41.1 \, \text{h}} \][/tex]
[tex]\[ \text{Unit rate} \approx \frac{768.57}{41.1} \, \text{m/h} \][/tex]
[tex]\[ \text{Unit rate} \approx 18.68 \, \text{m/h} \][/tex]
So, the unit rate is approximately 18.68 meters per hour.
Which point on the x-axis lies on the line that passes through point P and is perpendicular to line MN?
(0, 1)
(0, 4)
(1, 0)
(4, 0)
Answers
1. Points M and N have coordinates (-4,0) and (4,2), respectively.
Then vector [tex]\overrightarrow{MN}=(4-(-4),2-0)=(8,2)[/tex] is perpendicular to the neede line.
2. Write the equation of line that passes through the point P(2,-4) and is perpendicular to vector [tex]\overrightarrow{MN}=(8,2):[/tex]
[tex]8(x-2)+2(y+4)=0,\\8x-16+2y+8=0,\\8x+2y-8=0,\\4x+y-4=0.[/tex]
3. Find the point on x-axis, that lies on the perpendicular line.
When y=0, then 4x-4=0, x=1 and point (1,0) lies on perpendicular line.
Answer: correct choice is C.
Some luggage pieces have wheels and a handle so that the luggage can be pulled along the ground. Suppose the length from the bottom of the bag to the place on the floor perpendicular to the hand on the bag is 14 inches, and the length of the bag with its handle is 19 inches. At which angle made by the bag and the floor would it be comfortable to roll the bag?
Answers
The trigonometric ratio cosine, relates the angle with those lengths:
cos(angle) = adjacent-leg / hypotenuse = 14 / 19
=> angle = arc cosine (14/19) = 42.5°
Answer: 42.5°
A cylindrical shaped vase has the radius of 3cm and a height of 18cm. how much water is needed to fill the vase 3/4 of the way?
Answers
Answer:
Step-by-step explanation:
To fill the entire vase:
pi(3)^2(18)= 508.9 cubic centimeters
To fill vase 3/4 of the way:
3/4= .75
So then you take what it takes to fill the vase (508.9) and multiply that by .75 which equals 381.70 cubic centimeters.
3/4 of the volume of water needed to fill the vase is 162π cm^3.
To find how much water is needed to fill the vase 3/4 of the way, we first need to calculate the volume of the vase and then determine 3/4 of that volume.
The formula to calculate the volume of a cylinder is:
[tex]Volume = \pi * radius^2 * height[/tex]
Given:
Radius (r) = 3 cm
Height (h) = 18 cm
Volume of the entire vase:
[tex]Volume = \pi * (3 cm)^2 * 18 cm\\Volume = \pi* 9 cm^2 * 18 cm\\Volume = 162\pi cm^3[/tex]
Now, to find 3/4 of the volume, multiply the total volume by 3/4:
[tex]3/4 * 162\pi cm^3 = 3 * 54\pi cm^3 = 162\pi cm^3[/tex]
So, 3/4 of the volume of water needed to fill the vase is 162π cm^3.
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