Plot the following points to create a rectangle.
Find the missing vertex.(5.3): (-5,3): (-5.-1) *
Answers
Answer:
(5, -1)
Step-by-step explanation:
The three coordinates of a triangle are given as:
(5,3), (-5,3), (-5,-1).
To find:
The missing vertex = ?
Solution:
Let us label the vertices:
A (5,3),
B(-5,3),
C(-5,-1).
Let the missing vertex be ([tex]x, y[/tex]).
Let us recall the properties of a rectangle.
The opposite sides of the rectangle are equal and parallel to each other.
Let us consider the side AB, we can see that only x coordinate is changed from A to B.
Let us consider the side BC, we can see that only y coordinate is changed from B to C.
A and B are adjacent vertices.
Similarly the opposite vertices will be C and D.
Same pattern will be followed in CD as that of AB.
x coordinate will be changed by same difference as that of AB.
Change in x coordinate from D to C = [tex]-5-x[/tex]
Change in x coordinate from A to B = [tex]-5-5 =-10[/tex]
Equating them:
[tex]-5-x=-10\\\Rightarrow x = 5[/tex]
Same pattern is followed in BC and AD.
Their change in y coordinate will be same.
[tex]-1-3=y-3\\\Rightarrow y =-1[/tex]
Missing vertex is (5, -1).
Please refer to the attached image for the rectangle.
Related Questions
You have a choice between going to an in-state college where you would pay $5500 per year for tuition and an out-of-state college where the tuition is $7000 per year. The cost of Iiving is much higher at the in-state college, where you can expect to pay $1000 per month in rent, compared to $750 per month at the other college Assuming all other factors are equal, which is the less expensive choice on an annual (12-month) basis? The yearly expense of the in-state college is $_____and the yearly expense of the out-of-state college is $______. Thus on an annual basis, the less expensive choice is the (1)_______college. (Simplify your answers.) in-state out-of-state
Answers
The yearly expense of the in-state college is $16000.
We are given that;
An out-of-state college where the tuition = $7000 per year.
Now,
The yearly expense of the in-state college is:
=5500+12⋅1000
=5500+12000
=17500
By solving;
The yearly expense of the out-of-state college is:
=7000+12⋅750
=7000+9000
=16000
So, on an annual basis, the less expensive choice is the out-of-state college.
Therefore, by algebra the answer will be 16000.
More about the Algebra link is given below.
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If angle EFH(5x+1)’ angle HFG(62 degrees) and angle EFG (18x+11) find each measurement
Answers
Answer:
∠EFH = 21°
∠HFG = 62°
∠EFG = 83°
Step-by-step explanation:
The diagram showing the angles has been attached to this response.
From the diagram, it can be deduced that;
Angle EFG = angle EFH + angle HFG
=> ∠EFG = ∠EFH + ∠HFG -------------------(i)
From the question:
∠EFH = (5x + 1)° -------------(ii)
∠HFG = 62° -------------(iii)
∠EFG = (18x + 11)° -------------(iv)
Substitute these values into equation (i) as follows;
(18x + 11) = (5x + 1) + 62
=> 18x + 11 = 5x + 1 + 62
Collect like terms and solve for x
18x - 5x = 1 + 62 - 11
13x = 52
x = 4
Now, to get each measurement, substitute x = 4 into each of equations (ii) - (iv)
∠EFH = (5x + 1)°
∠EFH = (5(4) + 1)°
∠EFH = (20 + 1)°
∠EFH = 21°
∠HFG = 62° [Does not depend on x]
∠EFG = (18x + 11)°
∠EFG = (18(4) + 11)°
∠EFG = (72 + 11)°
∠EFG = 83°
Conclusion:
∠EFH = 21°
∠HFG = 62°
∠EFG = 83°
Which of the following expressions means "five factors of 3"?
Options: 3^5
5^3
5 divided by 3
I know it's definitely not the third option. Please explain your answer so I understand, thank you!
Answers
Answer:
3^5
Step-by-step explanation:
five factors of 3"
This means we have 3 multiplied 5 times
3 *3*3*3*3
3^5
7 plus another is 20
Answers
Answer:
27
Step-by-step explanation:
Answer:
the answer would 13
Step-by-step explanation:
8+9t-3+4 please help me
Answers
Answer:
t = -1
Step-by-step explanation:
8 + 9t - 3 + 4
Combine like terms
(8 - 3 + 4) + 9t
9 + 9t
9t + 9
Get t by itself
9t + 9 = 0
-9 -9
9t = -9
Divide both sides by 9 to find t
t = -1
Rewrite the equation of a straight line in a slope - intercept form x + 2y + 1 = 0
Answers
Answer:
y = -x/2 -1/2
Step-by-step explanation:
[tex]x + 2y + 1 = 0\\[/tex]
Write in the y=mx+b form
[tex]2y =-x-1+0\\2y =-x-1[/tex]
Divide both sides by 2
[tex]\frac{2y}{2} =\frac{-1x}{2} -\frac{1}{2} \\\\y = -\frac{x}{2} -\frac{1}{2}[/tex]
What are the degrees of freedom associated with the factor(s) in this study design?
Answers
Answer:
The question is unclear and incomplete.
Let me explain the degrees of freedom in statistics.
Step-by-step explanation:
Statistically, degrees of freedom which is denoted as DF is the number of independent values that can vary in an analysis without breaking any constraints. It can also be referred to as the number of independent values that a statistical analysis can estimate.
Degrees of freedom also define the probability distributions for the test statistics of various hypothesis tests.
The degree of freedom has the formula:
DF = N - 1 where N number of random variables
DF = (R - 1) x (C - 1) Where R is the number of data values and C is the number of groups
Convert 6 1/2 % to a decimal
Answers
Answer:
6.5=.065
Step-by-step explanation:
im assuming this is 6.5/100
hope this helps :)
Which formula can be used to find the nth term of a geometric sequence where the fifth term is 1/6 and the common ratio is 1/4?
Answers
Answer:
[tex] a_n = 16(\frac{1}{4})^{n - 1} [/tex]
Step-by-step explanation:
Given:
Fifth term of a geometric sequence = [tex] \frac{1}{16} [/tex]
Common ratio (r) = ¼
Required:
Formula for the nth term of the geometric sequence
Solution:
Step 1: find the first term of the sequence
Formula for nth term of a geometric sequence = [tex] ar^{n - 1} [/tex], where:
a = first term
r = common ratio = ¼
Thus, we are given the 5th term to be ¹/16, so n here = 5.
Input all these values into the formula to find a, the first term.
[tex] \frac{1}{16} = a*\frac{1}{4}^{5 - 1} [/tex]
[tex] \frac{1}{16} = a*\frac{1}{4}^{4} [/tex]
[tex] \frac{1}{16} = a*\frac{1}{256} [/tex]
[tex] \frac{1}{16} = \frac{a}{256} [/tex]
Cross multiply
[tex] 1*256 = a*16 [/tex]
Divide both sides by 16
[tex] \frac{256}{16} = \frac{16a}{16} [/tex]
[tex] 16 = a [/tex]
[tex] a = 16 [/tex]
Step 2: input the value of a and r to find the nth term formula of the sequence
nth term = [tex] ar^{n - 1} [/tex]
nth term = [tex] 16*\frac{1}{4}^{n - 1} [/tex]
[tex] a_n = 16(\frac{1}{4})^{n - 1} [/tex]
Solve the following equation using the zero product property (x+9)(4x-1)=0 LAST TRY !!!!!
Answers
Answer:
x=-9, x=1/4
Step-by-step explanation:
Split it into x+9=0 and 4x-1=0.
x+9=0; x=-9
4x-1=0; 4x=1; x=1/4
4x + 3 x - 6 equals 29 what is X
Answers
+6. +6
——————-
7x = 35
7. 7
x = 5
For each of the following studies, identify the source(s) of sampling bias and describe (i) how it might affect the study conclusions and (ii) how you might alter the sampling method to avoid the bias.
(a) To study the size distribution of rock cod (Epinephelus puscus) off the coast of southeastern Australia, scientists recorded the lengths and weights for all cod captured by a commercial fishing vessel on one day (using standard hook-and-line fishing methods).
(b) A nutritionist is interested in the eating habits of college students and observes what each student who enters a dining hall between 8:00 A.M. and 8:30 A.M. chooses for breakfast on a Monday morning.
(c) To study how fast an experimental painkiller relieves headache pain residents of a nursing home who complain of headaches are given the painkiller and are later asked how quickly their headaches subsided.
Answers
Answer:
Answer:
A first of all because the sample involves only rock cods that voluntarily get hooked to the fishing rod, this is a major source of bias as the sample does not represent the whole general population.
Rather adopt stratified sampling stratified basing on Geographical location can be suggested for this study.
II. Because convenient sampling is adopted here data is only gotten from students that eat in the hall in a given period of time so this is a source of bias
Also one study center that is the Hall of only one school is used this is also biased and may affect the result of the study
To avoid this bias a simple random sampling where each student have an equal chance of being selected in the study should be adopted
Iii. this study is using convenient samples. and the effect of head ache medicine may be affected by other medicines too so the headache medicine cannot be the only reason for painrelief so it is better to sample rando amongst patients with headache
What is 4/5 ( + ) 1/2 + ( 3/4)
Answers
Answer:
41/20
Step-by-step explanation:
Simplify the following:
4/5 + 1/2 + 3/4
Hint: | Put the fractions in 4/5 + 1/2 + 3/4 over a common denominator.
Put 4/5 + 1/2 + 3/4 over the common denominator 20. 4/5 + 1/2 + 3/4 = (4×4)/20 + 10/20 + (5×3)/20:
(4×4)/20 + 10/20 + (5×3)/20
Hint: | Multiply 4 and 4 together.
4×4 = 16:
16/20 + 10/20 + (5×3)/20
Hint: | Multiply 5 and 3 together.
5×3 = 15:
16/20 + 10/20 + 15/20
Hint: | Add the fractions over a common denominator to a single fraction.
16/20 + 10/20 + 15/20 = (16 + 10 + 15)/20:
(16 + 10 + 15)/20
Hint: | Evaluate 16 + 10 + 15 using long addition.
| 1 |
| 1 | 6
| 1 | 5
+ | 1 | 0
| 4 | 1:
Answer: 41/20
PLEASE SOMEONE HELP IM TIMED What is 3.71 as a fraction?
Answers
Answer: 3 71/100
Step-by-step explanation:
Two numbers are independently selected from the set of positive integers less than or equal to 5. What is the probability that the sum of the two numbers is less than their product? Express your answer as a common fraction.
Answers
Answer: P = 15/25
Step-by-step explanation:
The set of numbers that we have here is:
{1, 2, 3, 4, 5}
We select independently two numbers of that set (so the numbers can be repeated.
We want to find the probability where the sum of the numbers is less than the product.
if one of the selected numbers is 1, then always the sum will be larger than the product, because:
1*1 = 1 and 1 + 1 = 2
1*2 = 2 and 1 + 2 = 3.
and so on.
if both numbers are 2, the sum is equal to the product:
2*2 = 4 = 2 + 2.
if else, the product will be larger than the product.
The first step now is to calculate the total number of possible combinations of 2 numbers:
For the first number, we have 5 options.
for the second number, we have 5 options.
The total number of combinations is equal to the product of the number of options in each case:
C = 5*5 = 25
Now, the combinations where the product is LESS OR EQUAL than the sum are:
1 and 1
1 and 2
1 and 3
1 and 4
1 and 5.
2 and 1
3 and 1
4 and 1
5 and 1
2 and 2.
10 combinations.
Then the combinations where the product is larger than the sum is:
25 - 10 = 15.
Then the probability that we are looking for is:
P = 15/25
What is the solution to the system of linear equations? Please show steps 4x + 5y = 9
−11x − 9y = −20
Answers
Step-by-step explanation:
4x + 5y = 9
-11x - 9y = -20
solution
5y = 4x - 9
divide both side by 5
5y = 4x - 9
5 5
5 cancel at the L.H.S
y = 4x-9
5
insert the value of y in equation ii above
-11x -9(4x-9) = -20
5
-11x - 36x-81 = -20
5
cross multiply at the RHS
-11x- 36x-81 = -100
-47x-81 = -100
-47x = -100+81
-47x = -19
divide both side by -47
-47x = -19
-47 -47
x =
g if cot=-1/3 and sin<0 find each function value only using the appropriate trigonometric identites
Answers
Answer:
Step-by-step explanation:
Other trigonometry identities that we have includes cosθ, sinθ, tanθ, secθ, cosecθ
cosecθ = 1/sinθ
Given cotθ=-1/3 and sinθ<0, this means that θ falls in the 4th quadrant.
cotθ= 1/tanθ = -1/3
tanθ = -3/1
Since tanθ = opposite/adjacent = -3/1
opposite = -3
adjacent = 1
Using pythagoras theorem to get the hypotenuse, hyp² = opp²+adj²
hyp² = (-3)²+1²
hyp = √9+1
hyp = √10
cosθ = adjacent/hypotenuse = 1/√10
sinθ = opp/hyp = -3/√10
cosecθ = 1/sinθ = 1/(-3/√10)
cosecθ = -√10/3
secθ = 1/cosθ
secθ = 1/(1/√10)
secθ = 1*√10/1
secθ = √10
1
10 points
Simplify the expression by combining like terms.
7a - 2a - a - 13
type your answer...
Answers
Answer:
4a - 13
Step-by-step explanation:
● 7a - 2a - a - 13
● (7a - 2a - a) -13
● (5a-a) -13
● 4a -13
After he bought a new car, Nelson purchased car insurance. He must pay $75 each month for the plan.Later that month, Nelson caused a car accident when he lost control of his vehicle. He was required to pay the first $500 of his repair costs, and then the insurance company covered the rest.
Read the passage about Nelson’s car insurance.
What is the $75 payment Nelson must make each month?
premium
co-payment
deductible
payout
Answers
Answer:
Premium
Step-by-step explanation:
took the test on Edge
The $75 payment that Nelson must make each month after buying the Car is called; A: Premium
What is Insurance Premium?
Insurance Premium is defined as the amount of money that one will have to pay for an insurance contract. The insurance premium simply represents the income of the insurance company concerned.
Now, the amount of premium paid for different insurance policies usually differs depending on a number of factors. However, the greater the risks associated with an insurance policy, the higher the premium that will be paid.
Since Nelson must make $75 payment each month, then that is referred to as the Premium.
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For the third week of July, Susan Gray worked 43 hours. Susan earns $17.70 an hour. Her employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours. Calculate the following for the third week of July (round your responses to the nearest cent if necessary
Answers
Answer: $787.65
explanation:
(17.70)(40) = $708
17.70 x 1.5 = 26.55
(3)(26.55) = $79.65
$708 + $79.65 = 787.65
PLEASE HELP!!! Which expression is equivelent to 32 + 16 1. 8(4+2) 2. 8(24+8) 3. 4(2+7) 4. 7(24+8)
Answers
Answer is
1. 8(4+2)
8 × 6 = 48
What is the product of the binomials below?
(2x +5)(3x+4)
O A. 6x² +23x +20
O B. 5x2 +23x +9
O C. 6x2 + 23x +9
O D. 5x2 +23x+20
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{6 {x}^{2} + 23x + 20}}}}}[/tex]
Option A is the correct option.
Step-by-step explanation:
[tex] \sf{(2x + 5)(3x + 4)}[/tex]
Use the distributive property to multiply each term of the first binomial by each term of the second binomial
⇒[tex] \sf{2x(3x + 4) + 5(3x + 4)}[/tex]
⇒[tex] \sf{6 {x}^{2} + 8x + 15x + 20}[/tex]
Collect like terms
⇒[tex] \sf{6 {x}^{2} + 23x + 20}[/tex]
Hope I helped !
Best regards!!
Which angle is supplementary to 65 degrees
Answers
Answer:
115°
Step-by-step explanation:
Supplementary angles equal 180.
180-65=115°
Answer:
[tex]\boxed{115}[/tex]
Step-by-step explanation:
Hey there!
Supplementary angles add up to 180º, so we can set up the following.
x = 180 - 65
x = 115º
Hope this helps :)
power of a product property:states that if there is more than one factor in parenthesis,within exponent _______ the parenthesis, then the exponent is distributed to every term in the parenthesis
Answers
Answer:
The answers Outside
The 10,000-meter long-distance running event in the summer Olympics is approximately 6.2 miles. Which equation could be used to determine the time, t, it takes to run 10,000 meters as a function of the average speed, s, of the runner where t is in minutes and s in miles per minute?
Answers
The equation that could be used to determine the time, t, it takes to run 10,000 meters as a function of the average speed, s, of the runner where t is in minutes and s in miles per minute is t = 6.2/s miles/minute
What is an average speed?Average speed is defined as the rate of change in distance of a body. Mathematically;
Speed = Distance/TimeGiven the distance of the runner in miles to be;
d = 6.2milesTime taken = tAverage speed = sTo express t in terms of the average speed s and distance of 6.2miles, we will substitute the values into the formula;
s = D/tSubstituting D = 6.2miles into the formula;
s = 6.2/tCross multiply
St = 6.2Divide both sides by 's'
st/s = 6.2/s
t = 6.2/s
Hence, the equation that could be used to determine the time, t, it takes to run 10,000 meters as a function of the average speed, s, of the runner where t is in minutes and s in miles per minute is t = 6.2/s miles/minute
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Determine whether the underlined number is a statistic or a parameter. a sample of seniors selected and it is found that 25% own a computer
Answers
Answer: Statistic.
Step-by-step explanation: Statistic are used to refer to numerical measurement pertaining to a sample. A sample refers to a subset of members chosen from a population, which means a smaller representation of the larger group. Hence, in the scenario above, the population is the entire seniors which makes up the group. While the sample is the subset of seniors drawn from the whole. Hence, statistical measures calculated or derived from the sample is called statistic. Hence, the 25% obtained is a statistic.
The population of a city has increased by 27% since it was last measured. If the current population is 25400, what was the previous population
Answers
Answer:6858
Step-by-step explanation:
Find (a) PQ to the nearest tenth and (b) the coordinates of the midpoint of PQ.
P(2.6), Q(-6,1)
(a) PQ=(Round to the nearest tenth as needed.)
Answers
Answer/Step-by-step explanation:
Given:
P(2, 6)
Q(-6, 1)
Required:
a. PQ
b. Coordinate of the midpoint of PQ
SOLUTION:
a. [tex] PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] P(2, 6) = (x_1, y_1) [/tex]
[tex] Q(-6, 1) = (x_2, y_2) [/tex]
[tex] PQ = \sqrt{(-6 - 2)^2 + (1 - 6)^2} [/tex]
[tex] PQ = \sqrt{(-8)^2 + (-5)^2} = \sqrt{64 + 25} [/tex]
[tex] PQ = \sqrt{89} = 3.1 [/tex] (to nearest tenth)
b. Coordinate of the midpoint of PQ
[tex] M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) [/tex]
Let [tex] P(2, 6) = (x_1, y_1) [/tex]
[tex] Q(-6, 1) = (x_2, y_2) [/tex]
Thus:
[tex] M(\frac{2 +(-6)}{2}, \frac{6 + 1}{2}) [/tex]
[tex] M(\frac{-4}{2}, \frac{7}{2}) [/tex]
[tex] M(-2, \frac{7}{2}) [/tex]
The coordinates of the midpoint of PQ are (-2,3.5) and this can be determined by using the midpoint formula.
Given :
Coordinates -- P(2,6) and Q(-6,1)
The following steps can be used in order to determine the coordinates of the midpoint of PQ:
Step 1 - According, to the given data, the coordinates of point P(2,6) and Q(-6,1).
Step 2 - The formula of midpoint can be used in order to determine the midpoint of PQ.
Step 3 - The midpoint formula is given below:
[tex]\rm x = \dfrac{x_1+x_2}{2}[/tex]
[tex]\rm y = \dfrac{y_1+y_2}{2}[/tex]
Step 4 - Substitute the values of the coordinates in the above formula.
[tex]\rm x = \dfrac{2-6}{2} = -2[/tex]
[tex]\rm y = \dfrac{6+1}{2}=3.5[/tex]
So, the coordinates of the midpoint of PQ are (-2,3.5).
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A rectangular athletic field is twice as long as it is wide. If the perimeter of the athletic field is 270 yards what are it’s dimensions?
Answers
Answer:
Step-by-step explanation:45x90
Given a=20 and b=a/4-3 what is the value of b
Answers
Answer: b=20
Step-by-step explanation:
Subsitute a for 20.
b=20/4-3
b=20/1
b=20
Answer:
pretty positive it’s 2
Step-by-step explanation:
if a=20 then you’d use pemdas so 20/4=5 then 5-3=2 so b=2