Yes, if Trapezoid abcd has vertices a(2, 4), b(5, 4), c(7, 1), and d(0, 1) , ABCD is an isosceles trapezoid.
Since, If in a trapezoid two opposite nonparallel sides are equal then it is called isosceles trapezoid.
In trapezoid ABCD sides are AB, BC, CD and DA.
According to the question, A≡(2,4) B≡(5,4) C≡(7,1) and D≡(0,1)
After making the diagram of ABCD, we found that DA and BC are nonparallel sides.
And, by the distance formula BC = √((7 - 5)² + (1 - 4)²) =
⇒ BC =√(4 + 9)
⇒BC = √13 unit.
Similarly, DA = √((0 - 2)² + (1 - 4)²)
DA = √(4 + 9)
⇒ DA = √13 unit.
Thus, In trapezoid ABCD, two non parallel sides BC and DA are equal.
Therefore, trapezoid ABCD is a isosceles trapezoid.
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problem 3.7. suppose integer polynomials p and q satisfy that p ( x)/ q ( x ) is an integer for infinitely many integer inputs x. does it follow that q ( x ) divides p ( x ) ?
Integer polynomials p and q fulfill that for an unlimited number of inputs of integers x, p (x)/q (x) is an integer. q (x) does not necessarily divide p. (x)
Sums of terms of the form k^xn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials.This section covers the ideas of degree, standard form, monomial, binomial, and trinomial.
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HELP ASAP! Linear function k has a zero at 3 and a y-intercept of 9. Which graph best represents k?
Colleen took out a $48,000 student loan with a fixed interest rate to pay for college. Colleen did not make payments on her loan for a period of 7 years. After this time period interest had accrued, resulting in the loan balance increasing to $78,000. a. What is is the 7-year growth factor for the amount that Colleen owes on the loan? Preview b. What is the 7-year percent change for the amount that Colleen owes on the loan? % Preview c. What is is the 1-year growth factor for the amount that Colleen owes on the loan? Preview d. What is the 1-year percent change for the amount that Colleen owes on the loan? % Preview Submit
a)The 7-year growth factor for the amount on the loan is $4285.71.
b) 7-year percentage change for the amount is 6.25%.
c) 1-year growth factor for the amount $612.244.
d) 1-year percent change for the amount is 0.894%.
a)We know very well that growth factor is ratio of difference of principal amount and loan amount to the time taken, or
Growth factor=(Final loan amount-Initial loan amount)/Total time
=>Growth factor=(78,000-48,000)/7
=>Growth factor=30,000/7=$4285.71
b)To find the percentage change in amount, we need to use initial loan amount and the difference between two amounts, or
percentage change=((78000-48000)/48000)×100
=>percentage change=[(30000)/48000)]×100
=>percentage change=300/48=6.25%
c)Now, we have already find the growth factor for 7 years, we need to find growth rate in 1 year. So, we use unitary method to find it
=>In 7 years growth factor is=$4285.71
∴In 1 years growth factor is=$4285.71/7=$612.244
d)In 7 years percentage change for the given amount is =6.25%
∴In 1 year percentage change for the given amount=6.25/7=0.894%
Hence, answers are a)$4285.71 b)6.25% c)$612.244 d)0.894%
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A new movie streaming service opens and it charges a $9 sign up fee. Streaming 10 movies costs a total of $14, including the sign up fee.
Answer:
33 I guess I don't really know
Answer: ok expensive
Step-by-step explanation:
if a flock of 45 turkeys shows a constant growth rate of 2.3%, how many turkeys will be in the population after 10 years? show your work. how long would it take the flock of turkeys in the above problem to double in population?
By using the concept of growth, it can be calculated that
Number of turkeys after 10 years = 57
It took 10 years for the number of turkeys to double
What is growth?
Growth is the increase in the value of an asset or cost or population at a certain rate over a certain period of time.
Original number of turkeys = 45
Rate of growth = 2.3 %
Time = 10 years
Number of turkeys after 10 years = [tex]45 \times (1 + \frac{2.3}{100})^{10}[/tex]
= 57
Now,
New number of turkeys = 45 [tex]\times[/tex]2 = 90
[tex]90 = 45 \times (1 + \frac{2.3}{100})^n[/tex]
[tex](1 + \frac{2.3}{100})^n = \frac{90}{45}\\\\1.023^n = 2\\n\ ln (1.023) = ln( 2)\\n \times 0.023 = 0.693\\n = \frac{0.693}{0.023}\\n = 30.1 \ years[/tex]
It took 10 years for the number of turkeys to double
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How many baseballs are in the next picture in this pattern?
A. 64
B. 30
C. 32
D. 24
E. 25
find the equation of the line that contains the point (1,-1) and is perpendicular to the line x=4 write the line in slope intercept form
-2m + 11m + m + 11 = -19
Answer:
m= -3
Step-by-step explanation:
-2m+11m+m+11= -19
9m+m+11=-19
10m+11=-19
-11. -11
10m=-30
/10. /10
m= -3
Hopes this helps please mark brainliest
Answer:
hop this helps
Step-by-step explanation:
you should use the step by step calculator Symbolab
Which of the following constructions can be accomplished with paper
folding?
Check all that apply.
A. Drawing a line through a given point parallel to a given line
B. Drawing a perpendicular line segment from a given point to a
given segment
C. Finding the midpoint of a segment
D. Drawing a perpendicular line segment through a given point on a
given segment
The steps are given in option B and option C are used in paper folding.
What is Paper Folding?When we simply fold the paper in such a manner that we can achieve our objectives, the method is called Paper Folding.
Now, WE get;
Option A can not be accomplished as we need the proper equipment to construct the circle.
Option B can be done by folding the paper along the point.
Option C can be done by folding the paper in the exact half measure.
Option D can not be done.
Hence, the steps are given in option B and option C are used in paper folding.
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a researcher developing a regression equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) found a significant interaction between age and educational status (x3). educational status is a dummy variable with 0
A substantial interaction between age and educational status was discovered by a researcher who was creating a regression equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) (x3)
A dummy variable, educational status has the values 0 for no college degree and 1 for a college degree.
The regression formula is y = 0 + 1x1 + 2x2 + 3x1x2 where 0 is the intercept, 1 is the age regression coefficient, 2 is the educational status regression coefficient, and 3 is the regression coefficient for the interaction between age and educational status.
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A survey of all beings on planet Boondin found that 75% preferred alaber juice to all other juices. If 12 beings were surveyed altogether, how many of them preferred alaber juice?
The number of people who preferred alaber juice is 9 people
How many of them preferred alaber juice?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, the survey of all beings on planet Boondin found that 75% preferred alaber juice to all other juices. If 12 beings were surveyed altogether
Those who preferred alaber juice will be:
= 75% × 12
= 0.75 × 12
= 9
The number of people is 9.
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#10 i need help with my math
Answer: √6 -8√5
or 15.43905
Step-by-step explanation:
What is the equation of the line that passes through (0, 3) and is perpendicular to y = 3/4x + 5?
Answer:
3/4x + 3
Step-by-step explanation:
they both need to have the same gradient but different y intercepts and in this case the y intercept is 3
The equation of line passing through the point P ( 0 , 3 ) is given by
y = ( -4/3 )x + 3
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 0 , 3 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
The slope of the line we want to find will be the negative reciprocal of this slope, which is -4/3
Slope m = -4/3
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 3 = ( -4/3 ) ( x - 0 )
Adding 3 on both sides , we get
y = ( -4/3 )x + 3
Hence , the equation of line is y = ( -4/3 )x + 3
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Multiple Choice
1. Write the following ratio in simplest form: 32 min:36 min
08:9
08:36
032:9
128:144
The following ratio is the simplest form of 32 min: 36 min is 8: 9. The correct option is a.
What is the simplest ratio in maths?If two quantities of a ratio (i.e., antecedent and consequent) have no common factor (i.e., antecedent and consequent are co-prime), the ratio is said to be in its simplest form or in the lowest term.
The simplest form of the fraction is also known as the reduced form of a fraction. For instance, 34 is the simplest form of a fraction with a common component of one.
32/36 = 8:9. It is divided by 2.
Therefore, the correct option is a. 8:9.
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Answer:
The answer is D
Step-by-step explanation:
I hope it helps!
Jakobe earns a bi-weekly mean gross pay of $1,592. 0. What percent of his total salary will he pay if his student loan payments are $130. 00 per month for 180 months? round to the nearest tenth. (4 points) 3. 9% 3. 8% 3. 6% 3. 7%
Answer:
Step-by-step explanation:
Which logarithmic equation is equivalent to 32 = 9?
The equivalent equation to the given logarithm is log₃9=2.
Define the term logarithmic equation?An equation using the logarithm of just an expression involving a variable is referred to as a logarithmic equation. Check to verify if you can write two aspects of the equation as powers of a similar number before attempting to solve an exponential equation.A log function can be used to determine how much a given number must always be raised to reach the desired result.
aˣ = b
This can be written as;
logₐ b = c
Where an is the starting point from which the power will be raised,When power is increased, we want b to be the appropriate number,To obtain b, c must be increased to a power.For the expression;
3² = 9
Given what we know about just the logarithm, the following is how we can represent the given equation:
3² = 9
log₃9 = 2
Consequently, the equivalent equation of 3² = 9 could be expressed as log₃9=2.
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The correct question is-
Which logarithmic equation is equivalent to 3^2 = 9?
all problems concern the following wheel, which we shall call q. 1 4 16 64 (a) estimate the probabilities of the outcomes of q. (b) estimate the expected value of q. (c)
Probabilities of Q are 1,4, 16, 64 are 312 2 8181818 , E(Q)=20.88 and 12.5% information revealed. Wheel is spin twice 0.2815.
When we are not sure about the outcome we can make possible probabilities about the situation. Therefore, it is the maximum and possible chances of something to be happen.
Step 1
Angle of one complete spin = 360°
Q=16=90° Q=6490"
Q=4-450
Q=1=135°
Here
P(Q16) = P(Q= 64)
=90/36
=1/4
Step 2
Expected value E(Q) = xP(x) E(Q) = 1x+4x+16x+64 x2/8
Step 3
c)
We learn Q=4
P(Q=4)=1/8=0.125
12.5 % information is revealed.
Please refer to solution in this step.
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which needs to occur on a consistent basis and at regular intervals to determine whether execuatin of goals
Exercise needs to be consistent and done at regular times. The body can adjust more effectively and swiftly when there is consistency. Exercise should ideally be performed 3-5 times per week.
What is Exercise ?Exercise is any physical activity done to increase one's physical or mental fitness.
Exercise and physical activity not only aid to enhance physical health but also help to promote mental health.
A healthy mind follows from a healthy body.
By lowering body weight, frequent physical activity lowers the risk of developing serious conditions like heart attack, cardiovascular disease, diabetes, and high blood pressure. Regular exercise revitalizes the body and the mind.
Additionally, it raises energy levels, mood, and sleep quality.
Hence, Exercise must be performed consistently and at regular intervals. When there is consistency, the body can adjust more quickly and efficiently. The ideal number of times to exercise per week is three to five.
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does anyone know?? please help
Check the picture below.
A gym employee is paid monthly. After working for 3 months,he had earned $4,500. To determine how much money he will make over a six-month period,he created the table below.
1. If he continues to earn at the same rate, how much will he have earned after working 5 months?
2) After how many months will the gym employee have made $19,500?
3) Write an equation to represent the constant of proportionality.
1. The amount that the employee make in 5 months will be $7500.
2. The number of months that the gym employee have made $19,500 is 13 months.
3. The equation to represent the constant of proportionality is C = 1500m
What is the constant of proportionality?The constant of proportionality simply shows the ratio of two proportional values that possess a constant value.
Since after working for 3 months, he had earned $4,500. The amount per month will be:
= $4500 / 3
= $1500
The amount in 5 months will be:
= $1500 × 5
= $7500
The number of months that the gym employee have made $19,500 will be:
= $19500 / $1500
= 13 months.
The equation to represent the constant of proportionality is c = 1500m. In this case, c = total amount earned and m = number of months.
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1. Explain what a polygon is and how it is classified. Give more than one example to justify your answer.
2. What is a one-hundred sided polygon called? Why?
3. Tell whether the following is or is not a polygon and justify your answer:
Answer:
1. Polygons are flat figures formed by a closed polygonal line and its interior. Any plane figure that is made up of “straight sides” is a polygon.
2.A 100-sided polygon is called a hectogon, centagon or 100-gon. In general, any n-sided polygon with over 12 sides is called an n-gon. While there are other conventions for naming polygons with any number of sides, it is most common to use the n-gon form.
Step-by-step explanation:
Does someone know this ?
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=8\pi \\ r=2 \end{cases}\implies 8\pi =\cfrac{\pi (2)^2 h}{3}\implies 8\pi =\cfrac{4h\pi }{3} \\\\\\ 24\pi =4h\pi \implies \cfrac{24\pi }{4\pi }=h\implies 6=h[/tex]
Let A be the set of all statement forms in the three variables p, q, and r, and let R be the relation defined on A as follows.For all S and T in A, S R T ⇔ S and T have the same truth table.Prove that R is an equivalence relation. Show that it satisfies all the properties you selected in part (a), and submit your proof as a free response.
We have proved the statement that S≅W by 3 properties reflexive property, symmetric property, and transitive property.
Given that,
Let R be the relation defined on A as follows, and let A be the set of all statement forms in the three variables p, q, and r. S R T⇔ S and T have the same truth table for all S and T in A. substantiate the equivalence of R.
We have to demonstrate that it satisfies each of the properties you choose.
We know that,
By reflexive property,
S ≅ S means that S has the same truth table as S.
T≅ T denotes that T and T have the same truth table.
By symmetric property,
S ≅T denotes that S and T share the same truth table.
At that time, T and S share the same truth table.
So, T ≅ S
By transitive property,
S≅T and T≅V and V≅W
S shares a truth table with S. Truth table between T and T W's truth table is the same for V and V.
S, T, V, and W all have the same truth table as a result.
S specifically has the same truth table as W.
Then S≅T≅V≅W ---> S≅W
Therefore, We have proved the statement that S≅W by 3 properties reflexive property, symmetric property, and transitive property.
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what would happen to the width of a confidence interval if the size of the population being sampled was doubled, from 25 million to 50 million?
50 million people instead of 25 million people make up the population. The degree of assurance is reduced from 95% to 90%.
What is confidence interval?
A confidence interval in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified degree of confidence; the most popular level is 95%, but other levels, such 90% or 99%, are occasionally used.
Because the standard error is reduced as sample size increases, confidence intervals are narrower.
Therefore, we may state that when the population standard deviation rises, the width of the confidence interval will also rise.
Hence, 50 million people instead of 25 million people make up the population. The degree of assurance is reduced from 95% to 90%.
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Augusto wants to prove to his parents that watching TV while he does his homework will help him get better grades. He decides to ask 20 of his friends if they watch while they do their
homework and what their grades are. He finds that his friends who have high grades also watch TV while they do their homework. He tells his parents that he has proven that watching TV
while doing homework will cause his grades to improve. What mistake has Augusto made? (6 points)
© He did not use a random sample, and he tried to show cause and effect with an observational study.
O He did not use random sample, and he tried to show cause and effect with an experiment.
© He did not separate his friends into different groups, and he didn't apply a treatment.
© He did not separate his friends into different groups, and he used survey to collect data.
Answer:
A. He did not use a random sample, and he tried to show cause and effect with an observational study
Hope this helps! : D
Step-by-step explanation:
8.
(08.05 MC)
Augusto wants to prove to his parents that watching TV while he does his homework will help him get better grades. He decides to ask 20 of his friends if they watch TV while they do their homework and what their grades are. He finds that his friends who have high grades also watch TV while they do their homework. He tells his parents that he has proven that watching TV while doing homework will cause his grades to improve. What mistake has Augusto made? (6 points)
a runner competed in a 5 mile run. how many yards did she run (1 mile =1760 yards)
Answer:8,800
Step-by-step explanation:
1760 times 5 = 8,800
A bake sale committee wants to raise $189 for a donation to a local charity. They set aside $14 of their profit at the end of each day. How many days will it take them to raise enough money for the whole donation?
Answer:
Step-by-step explanation:
14x=189 (x represents the number of days)
189 divided by 14 = 13.5
Answer or X: Approximately = 14 days
a worn, poorly set-up machine is observed to produce components whose length x follows a normal distribution with mean 14 centimeters and standard deviation 3 centimeters. find the probability that the length of a component lies between 19 and 21 centimeters. round your answer to four decimal places.
The probability that the length of a component lies between 19 and 21 centimeters is 0.0376.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given:
Population mean, µ = 14
Population standard deviation, σ = 3
Probability that the length of a component lies between 19 and 21 centimeters
= P(19 < X < 21)
= P( (19 - 14) / 3 < (X - µ) / σ < (21 - 14) / 3)
= P(1.67 < z < 2.33)
= P(z < 2.33) - P(z < 1.67)
Using excel function:
= NORM.S.DIST(2.33,1) - NORM.S.DIST(1.67,1)
= 0.9901 - 0.9525
= 0.0376
Hence, the probability that the length of a component lies between 19 and 21 centimeters is 0.0376.
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Find f (5)
quick can someone answer meee
Answer:
f (5) = 4
Step-by-step explanation:
First we need to find f(x)
To do this we can find the gradient of the line then plug it into the formula for an equation of a line.
using the points on the line, (3,0) (0,-6)
gradient, m :
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
[tex] \frac{0 - ( - 6)}{3 - 0} = \frac{6}{3} = 2[/tex]
therefore the gradient was found to be 2.
Equation of a line:
y - y1 = m( x - x1)
y - 0 = 2( x - 3)
y = 2x - 6
Therefore the function of the line was found to be:
f(x) = 2x -6
so to find f(5) we substitute 5 in the place of x:
f(5) = 2(5) - 6
f(5) = 10 - 6
f(5) = 4
Work out the length of ab a=-1.6 b=5.3 give your answer
Answer: 6.708
Step-by-step explanation:
a(-1,6)
b(5,3)
ab =( (-1-5)^2+(6-3)^2)^(1/2)
ab=(36+9)^(1/2)
ab=6.708