Answer:
BCE= 115 ECD=65
Step-by-step explanation:
(5x+10)+(3x+2)=180
8x+12=180
8x=168
x=21
5(21)+10=115
3(21)+2=65
Answer:
<BCE=115°
<ECD=65°
And their sum is 180°
Step-by-step explanation:
< BCE + <ECD =180° ( Being sum of supplementary angle which is formed in the given diagram is 180°)
(5x + 10)° + (3x + 2)°= 180°
5x + 10 + 3x + 2 = 180°
5x + 3x + 10 +2 = 180°
8x + 12= 180°
8x = 180°-12°
8x = 168
x= 168/8
x=21°
Now,
<BCE = 5x+10
= 5*21+10
=105+10
=115
<ECD
= 3x+2
= 3*21+2
=65
find the distance between (3,4) and (4,-6) if necessary, round to the nearest tenth.
Answer:
The distance is:
d = 10.0 units (Rounded to the nearest the Tenths Place)
Step-by-step explanation:
Given the points
(3,4)(4,-6)The distance 'd' between (3,4) and (4,-6)
\(\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\)
\(d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)
substituting the points values
\(=\sqrt{\left(4-3\right)^2+\left(-6-4\right)^2}\)
\(=\sqrt{1+10^2}\)
\(=\sqrt{1+100}\)
\(=\sqrt{101}\)
\(=10.0\) units (Rounded to the nearest the Tenths Place)
Thus, the distance is:
d = 10.0 units (Rounded to the nearest the Tenths Place)
Find the solution to the system of equations below:
y = 4x + 20
y = 8x - 4
Answer:
(6, 44)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 4x + 20
y = 8x - 4
Step 2: Solve for x
Substitution
Substitute in y: 8x - 4 = 4x + 20Subtract 4x on both sides: 4x - 4 = 20Add 4 on both sides: 4x = 24Divide 4 on both sides: x = 6Step 3: Solve for y
Define equation: y = 8x - 4Substitute in x: y = 8(6) - 4Multiply: y = 48 - 4Subtract: y = 44What is the solution set for the inequality
Answer:
A solution set is the set of values which satisfy a given inequality. It means, each and every value in the solution set will satisfy the inequality and no other value will satisfy the inequality.
please help me with this
Answer: D. 3\(\sqrt[3]{20}\)
Step-by-step explanation:
Answer:
think A or B
Step-by-step explanation:
i am not sure
How would I solve this?
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)
Write an expression equivalent to: -3(6x-10)
Answer:
Pemdas:
Step-by-step explanation:
-3*6x then -3*10
-18x+30= -0.6
The shadow of the moon during a solar eclipse travels 2300 miles in 1 hour in the first 20 minutes the shadow traveled 7662/3 miles how long does it take for the shadow to travel 1150 miles
The time that it will take for the shadow to travel 1150 miles is; 30 minutes
How to solve linear equations?Let y represent the distance in miles
Let x represent the time in minutes
The shadow travels 2300 miles in 1 hour or 60 minutes and in the first 20 minutes the shadow traveled 766 ²/₃ miles or 2300/3 miles
Thus, the coordinates are;
(60, 2300) and (20, 2300/3)
The slope is;
m = (2300 - 2300/3)/(60 - 20)
m = 115/3 mi/min
Thus, the linear equation in point slope form is;
y - 2300 = (115/3)(x - 60)
This gives;
y = (115/3)x
When y = 1150 miles, we have;
1150 = (115/3)x
x = 30 minutes
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Solve by Elimination
x - y = -4
7x - 2y = 17
Answer: x=5,y=9
Step-by-step explanation:
Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.
Point Form:
(5,9)(5,9)
Answer:
17
Step-by-step explanation:
multiply
What is the period of the graph of…
READ THE PROBLEM WITH UNDERSTANDING AND SHOW THE SOLUTION
1, if I bought(2x+4) ballpens which cost(5x+1)pesos each,how much will I pay for it?
2. A box is (xx+1)cm by(x+2)cm. What is the volume of the box?
3. Eaxh book costs(15a^2b^3)pesos each. How much will(2a) of books cost?
4. Five times a number increased by 8 is 33. What is the number?
5. The product of a number and -8 gives eight times the sum of that number and
36. Find the number
Answer:
Step-by-step explanation:
1) the equation would be:
(2x+4)x(5x+1) because if the amount of ballpens are (2x+4) and the ballpens are $(5x+1) each, you would multiply them.
this is the expanded version of (2x+4)(5x+1)
{10x^2 + 2x + 20x + 4
10x^2 + 22x + 4}
2) (x^2 +1)(x+2) are multiplied to find the volume of the box
So when expanded it looks like this:
{x^3 + 2x^2 + x + 2}
3) (15a^2b^3) would be multiplied with (2a). This is because to find the total you would times the numbers.
so when expanded:
(15a^2b^3)(2a)
{(15a^3)(2ab^3)}
4) 5X(x+8)=33
5x+40=33
5x=33-40
5x=-7
X= -7/5
5) x-8=8x
8x-x = -8
7x=-8
X=-8/7
Hope this helps :)
The population of Sweden is about 1 11/16 times as great as the population of Denmark. Find the population of Sweden if the population of Denmark is as about 5,190,000 hints 8 ;] You will get 100 points for this.
Answer:8758125
Step-by-step explanation:
1.Solve by factorization method: x+1/x=11 1/11 2.Comment on the nature of roots for 4x^2-5=2(〖x+1)〗^2-7 plz, help...
Answer:
The equation
\(4\,x^2-5=2\,(x+1)^2-7\)
can be solved by first expanding all indicated operations, and later when the constant terms disappear, by factoring out 2x , leaving the equation as a product of two factors equal zero, from which it is easy to extract the roots. See below.
Step-by-step explanation:
When solving for x in the following expression, and using factoring to apply at the end the zero product theorem:
\(4\,x^2-5=2\,(x+1)^2-7\\4\,x^2-5=2\,(x^2+2x+1)-7\\4\,x^2-5=2\,x^2+4\,x+2-7\\4\,x^2-5=2\.x^2+4\,x-5\\4\,x^2=2\,x^2+4\,x\\4\,x^2-2\,x^2-4\,x=0\\2\,x^2-4\,x=0\\2\,x\,(x-2)=0\)
We observe that for the last product, to get a zero, x has to be zero (making the first factor zero), or x has to be "2" making the binomial factor zero.
30. You buy items costing $400 and finance the cost with a simple interest fixed installment
loan at 6% simple interest per year. The finance charge is $48.
a. How many years will you be paying?
b. What is your monthly payment?
Solution
A=P×(1+rt)
Where:
A = Total amount
P = principal amount = $400
r = interest rate = 6 % =6/100 = 0.06
t = time period = x
Finance charge = $48
we will first divide the interest rate by 12 to find the monthly interest rate.
\(\begin{gathered} A=P+I \\ A=400+48 \\ A=448 \end{gathered}\)To find the number of years of paying
\(\begin{gathered} I=P\times rt \\ 48=400\times0.06t \\ 48=400\times0.06t \\ 48=24t \\ t=\frac{48}{24} \\ t=2 \\ t=2\text{years} \end{gathered}\)Time = 2 years
2 years = 2 x 12 = 24 month
(b) Now to find the monthly payment, we will simply divide the total amount payable by number of months.
Monthly payment
\(\begin{gathered} A=P+I \\ A=400+48 \\ A=448 \end{gathered}\)Monthly payment =
\(\frac{448}{2(12)}=18.67\)Therefore the monthly payment = $19
A parabola can be drawn given a focus of (8,10) and a directrix of y=6. write the equation of the parabola in any form
pls help its due in 5 min
The equation of the parabola is h²-16h+8k+32=0 when parabola can be drawn with a focus of (8,10) and a directrix of y=6.
Given that,
A parabola can be drawn with a focus of (8,10) and a directrix of y=6.
We have to find the equation of the parabola in any form.
We know that,
The distance of any point P is (h,k) on a parabola form a focus is equal to its perpendicular distance from the directrix.
So,
√((h-8)²+(k-2)²) = | (k-6)/√0²+1² |
Squaring on both sides
(h-8)²+(k-2)² = (k-6)²
From th formula (a-b)² = a²-2ab+b²
We get,
h²-16h+64+k²-4k+4 = k²-12k+36
h²-16h+64+k²-4k+4 - k²+12k-36 =0
h²-16h+64-4k+4+12k-36=0
h²-16h+8k+32=0
Therefore, The equation of the parabola is h²-16h+8k+32=0 when parabola can be drawn with a focus of (8,10) and a directrix of y=6.
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Why might game theory not always be an accurate predictor of real-world situations?
Game theory might not always be an accurate predictor of real-world situations because we do not always know the exact payoffs, since payoffs involve attitudes and feelings, and monetary gains.
Game theory is a branch of applied mathematics that provides tools for analyzing situations in which parties, called players, depend on each other to make decisions. This interdependence forces each player to consider the other player's possible options or strategies when formulating a strategy.
Game theory is a branch of mathematics used primarily in economics, political science, and psychology. In this talk, we'll define what a game is and discuss different ways to categorize and describe games.
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Is a D a failing grade?
Answer:
Yes anything under a C
Step-by-step explanation:
Product of square of x and cube of y
Where’s the image? I don’t see it
solve for each of the following equations. /2x+3/=10
Answer:
/2x+3/=10
2x+3=10 or 2x+3=-10
2x=10-3 or 2x=-10-3
2x=7 or 2x=-13
X=7÷2 or X=-13÷2
X=3.5 or X=-6.5
A recent study estimated that the wild tiger population in India decreased by 2,200 tigers in 5 years. What is the average amount this tiger population changed each year?
The average amount by which this tiger population changed is
tigers per year.
Answer:
440
Step-by-step explanation:
jjjjjjjjjjjjjjjjjj
find the values of p and q in the arithmetic progression-12,p,q,18
Answer:
p=14
q=16
Step-by-step explanation:
if,
a,b,c,d.......... (Arithmetic progression)
b-a=c-b=d-c
The differences of the adjacent elements are equal.
Which expression is equivalent to
32 + 2 • 18?
A. 24 + 22. 32
B. 2 + 22. 32
C. 25 + 2 . 32
D. Not Here
Answer:
ITS D ITS NOT THERE
Step-by-step explanation:
The swim team is raising money for a charity. Irene donates $20.00 plus $1.25 for every lap she swims. Tai donates $15.00 plus $2.50 per lap. Omar donates $40.00 plus $1.50 per lap. Divya donates $25.00 plus $1.75 per lap.
Part A: Each swimmer can complete 50 or 100 laps. Complete the table for the amount each swimmer will donate based on the number of laps.
Part B: All four swimmers swam x number of laps. Write and simplify an algebraic expression for the total amount of money donated.
Answer:
I would think 10,700
Step-by-step explanation:
21.25 + 17.50 + 41.50 + 26.75 = 107
107 x 100 = 10,700
(I'm so sorry if I'm wrong)
5. A scale drawing of an elephant shows the animal as 6 inches high and 10.8 inches long. The scale used for the drawing was 3 in.:5 ft. What are the height and length of the actual elephant?
Answer:
Length = 18ft Height = 10ft
Explaination:
We know that the height of the model is 6 inches, and we know that 3in=5ft. To find the height of the real thing we need to find out how many times 3 can fit into 6 which is 2 times. Multiply 2 by 5 to get 10, which is the height for the real elephant.
To find the length, we follow the same steps. First find out how many times 3 fits into 10.8, which is 3.6 times. Then multiply 3.6 by 5 to find the height which is 18ft.
hope this helps!
The height and length of the actual elephant are 10 ft high and 18 ft long.
How are scale drawings formed?For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.
Then it means
\(\rm 1\: ft : \dfrac{s}{k}\: in.\)
All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.
The scale used for the drawing was 3 in to 5 ft
We know that one basic unit in the drawing is in fact 3 inches.
These factors need to be multiplied with the base units of 5 ft for reality.
6 inches high
6 / 3 = 2
Now the elephant is 2 units high, which means in reality
2×5 = 10 ft high.
10.8 inches long
10.8 / 3 = 3.6
Therefore, the elephant is 3.6 units long, which means 3.6×5 = 18 ft long.
Hence the height and length of the actual elephant are 10 ft high and 18 ft long.
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During the summer, Jody earns $10 per hour babysitting and $15 per hour doing yardwork. This week she worked 34 hours and earned $410. If x represents the number hours she babysat and y represents the number of hours she did yardwork, which system of equations models this situation?
A.
x + y = 34
10x + 15y = 410
B.
x + y = 410
10x + 15y = 34
C.
x + y = 34
15x + 10y = 410
D.
x + y = 410
15x + 10y = 34
Answer:
C! i’m sure off i hope i’m right
Step-by-step explanation:
Answer:
A. x+y=34
10x+15y=410
Step-by-step explanation:
First the question states that babysitting is represented by x and yard work is represented by y, so that eliminates C and D.
If x and y are the amount of hours put into babysitting and yard work you would make the equation, x+y=34 to find out how many hours of each were worked.
Then you would make the equation 10x+15y=410 with the known variables.
So in conclusion A is the correct answer.
calculate the probability of obtaining a sample result of 168 out of 200 or less if the company's claim is true. (use a table or technology. round your answer to four decimal places.)
The cumulative probability of obtaining a sample result will be approximately 0.0001
We have to apply Formula of Binomial Distribution:
P(X ≤ 168) = ΣP(X = i) for i = 0, 1, 2, .., 168, here in a sample of size n, P(X = i) is the probability of getting exactly i success
We assume that company's claim is true, 0.8 is the probability of success for each trial
P(X = i) = (200 choose i)×\(0.8^{i}\) ×\(0.2^{200- i}\)
By using this, we can easily find that cumulative probability is 0.0001
So, the probability is very low, this means that company's claim of an 80% success rate can be incorrect
So, further analysis may be needed to draw some conclusions and results
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The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.(a) What proportion of the students scored at least 26 points on this test, rounded to five decimal places?.02275(b) What is the 71 percentile of the distribution of test scores, rounded to three decimal places?24.073
a) The proportion of the students scored at least 26 points on this test is 0.02275.
b) The 71 percentile of the distribution of test scores is 24.073
What is meant by standard deviation?A low standard deviation suggests that values are often close to the mean of the collection, whereas a large standard deviation suggests that values are dispersed over a wider range.
Standard deviation, often known as SD, is most frequently represented in mathematical texts and equations by the lower case Greek letter (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.
Let the scores be X and X is normally distributed with a mean of 22 and standard deviation of 2.
μ=22
σ=2
X≈N(22,2)
a) P(X≥26)=P(((X-μ)/σ)≥(26-μ)/σ)
=1-P(Z≥2)
=1-P(Z<2)
=1-0.97725
=0.02275
b) Let a is the 71th percentile of X,
P(X≤a)=0.71
P((X-μ)/σ)≤(a-μ)/σ)=0.71
P(Z≤z)=0.71
From the standard normal table by calculating with z value, we get
a=24.073
Therefore,
a) The proportion of the students scored at least 26 points on this test is 0.02275.
b) The 71 percentile of the distribution of test scores is 24.073.
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Can someone please help me
I need help ASAP!!!!
Answer:
it would be small.
Step-by-step explanation:
bcause its the smallest one and theres only 1 softball.
Line AB and line BC form a right angle at point B. If A = (2, 5) and B = (4, 4), what is the equation of line BC?
Answer:
y = 2x - 4
Step-by-step explanation:
To solve this problem, we must first calculate the slope of the line AB using the formula:
\(\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}\)
where:
m ⇒ slope of the line
(x₁, y₁), (x₂, y₂) ⇒ coordinates of two points on the line
Therefore, for line AB with points A = (2, 5) and B = (4, 4) :
\(m_{AB} = \frac{5 - 4}{2 - 4}\)
⇒ \(m_{AB} = \frac{1}{-2}\)
⇒ \(m_{AB} = -\frac{1}{2}\)
Next, we have to calculate the slope of the line BC.
We know that the product of the slopes of two perpendicular lines is -1.
Therefore:
\(m_{BC} \times m_{AB} = -1\) [Since BC and AB are at right angles to each other]
⇒ \(m_{BC} \times -\frac{1}{2} = -1\)
⇒ \(m_{BC} = -1 \div -\frac{1}{2}\) [Dividing both sides of the equation by -1/2]
⇒ \(m_{BC} = \bf 2\)
Next, we have to use the following formula to find the equation of line BC:
\(\boxed{y - y_1 = m(x - x_1)}\)
where (x₁, y₁) are the coordinates of a point on the line.
Point B = (4, 4) is on line BC, and its slope is 2. Therefore:
\(y - 4 =2 (x - 4)\)
⇒ \(y - 4 = 2x - 8\) [Distributing 2 into the brackets]
⇒ \(y = 2x-4\)
Therefore, the equation of line BC is y = 2x - 4.
with a known population mean of 1500, and a known standard error of the mean of 42.50 what is the probablitly of selcting at random a sample whose mean is equal to 1450 or less?
The probability of selecting a sample with a mean of 1450 or less, given a known population mean of 1500 and a known standard error of the mean of 42.50, is approximately 11.90%.
Probability plays a significant role in statistics and helps us understand the likelihood of an event occurring. In this case, we will discuss the probability of selecting a sample with a mean of 1450 or less, given a known population mean of 1500 and a known standard error of the mean of 42.50.
To calculate the probability of selecting a sample with a mean of 1450 or less, we will use the concept of the standard normal distribution. The standard normal distribution is a probability distribution that has a mean of 0 and a standard deviation of 1.
We can convert any normal distribution to a standard normal distribution by using the formula z = (x - μ) / σ, where z is the standard score, x is the raw score, μ is the population mean, and σ is the standard deviation.
In this case, we know the population mean is 1500, and the standard error of the mean is 42.50. The standard error of the mean is the standard deviation of the sample means, and we can calculate it using the formula σ/√n, where σ is the population standard deviation and n is the sample size. However, in this case, we already know the standard error of the mean.
Using the formula z = (x - μ) / σ, we can find the z-score for a sample mean of 1450:
z = (1450 - 1500) / 42.50
z = -1.18
We can then use a standard normal distribution table to find the probability of a z-score of -1.18 or less.
The probability of a z-score of -1.18 or less is 0.1190, or approximately 11.90%.
Therefore, the probability of selecting a sample with a mean of 1450 or less, given a known population mean of 1500 and a known standard error of the mean of 42.50, is approximately 11.90%.
This means that if we were to randomly select samples from the population, about 11.90% of them would have a mean of 1450 or less.
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