This question has two parts. First, answer Part A. Then, answer Part B.
Part A
USE EFFICIENT METHODS Determine whether Δ D E F P ≅ ΔP Q R.
D(-7,-3), E(-4,-1), F(-2,-5), P(2,-2), Q(5,-4), R(0,-5)
Find the side lengths of each triangle.
A) D E=√13, P Q=√13, E F=2 √5, Q R=√13, D F=√29, P R=√13
B) D E=√13, P Q=√13, E F=√5, Q R=√26, D F=√29, P R=√13
C) D E=√13, P Q=√13}, E F=2 √5, Q R=√26, D F=2 √29, P R=√13
D) D E=√13}, P Q=√13, E F=2 √5, Q R=√26, D F=√29, P R=√13
Answers
The side lengths of each triangle are given as follows:
D. [tex]DE = \sqrt{13}, PQ = \sqrt{13}, EF = 2\sqrt{5}, QR = \sqrt{26}, DF = \sqrt{29}, PR = \sqrt{13}[/tex]
How to obtain the side lengths of each triangle?The side lengths of each triangle are given by the distances between the vertices.
These vertices are in the coordinate plane, hence the distance between them is found using the equation for the distance between two points.
Suppose two points in the coordinate plane with notation given as follows:
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Then the distance between them is given by the equation presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Thus the side lengths are given as follows:
DE: [tex]\sqrt{3^2 + 2^2} = sqrt{13}[/tex]PQ: [tex]\sqrt{3^2 + 2^2} = sqrt{13}[/tex]EF: [tex]\sqrt{2^2 + 4^2} = \sqrt{20} = 2\sqrt{5}[/tex]QR: [tex]\sqrt{5^2 + 1^2} = \sqrt{26}[/tex]DF: [tex]\sqrt{5^2 + 2^2} = \sqrt{29}[/tex]PR: [tex]\sqrt{2^2 + 3^2} = sqrt{13}[/tex]Meaning that option D is correct.
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Related Questions
Terri is sawing wood into shorter pieces of equal lengths. Some original pieces are 30 inches long, some are 48 inches long, and some are 72 inches. She cannot waste any wood. What is the longest possible length of the shorter pieces that Terri saws?
Answers
Answer:
24 inches
Step-by-step explanation:
To find the longest possible length of the shorter pieces that Terri can saw, you need to find the greatest common factor (GCF) of the three original lengths: 30 inches, 48 inches, and 72 inches.
The GCF of 30, 48, and 72 can be found by finding the prime factorization of each number and taking the lowest exponent for each prime factor.
30 = 2 * 3 * 5
48 = 2^4 * 3
72 = 2^3 * 3^2
The GCF is 2^3 * 3 * 5, or 24 inches. Therefore, the longest possible length of the shorter pieces that Terri can saw is 24 inches.
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I hope you and your family are doing well!
To find the GCF is to use the Euclidean algorithm, which involves repeatedly dividing the larger of the two numbers by the smaller one until the remainder is 0. This can be a quicker method for finding the GCF of larger numbers.
For example:
72 / 30 = 2 with a remainder of 12
30 / 12 = 2 with a remainder of 6
12 / 6 = 2 with a remainder of 0
The last non-zero remainder is 6, so the GCF is 6.
Regardless of the method used, the GCF of 30, 48, and 72 is 6, so the longest possible length of the shorter pieces that Terri can saw is 6 inches.
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ANALYZE PROBLEMS The midpoints of the sides of a triangle are located at (a, 0),(2 a, b) and (a, b). If one vertex is located at the origin, what are the
coordinates of the other vertices?
,( ______0) and (______,______)
Answers
The coordinates of the other vertices of the triangle are (2a, 0), (2a, b), and (a, b).
What are the coordinates of the vertices of the triangle?
The coordinates of the vertices of a triangle are (x1,y1), (x2,y2), and (x3,y3). The line joining the first two is divided in the ratio l:k and the line joining this point of division to the opposite angular point is then divided in the ratio m:k+l.
To find the coordinates of the other vertices of the triangle, you can use the fact that the midpoint of a line segment is located at the average of the coordinates of the endpoints of the segment.
If the midpoint of one side of the triangle is located at (a, 0), then the coordinates of the two endpoints of this side must be (a, 0) and (2a, 0). The coordinates of one of the vertices is (2a, 0), and since this vertex is not the one located at the origin, the coordinates of the other vertex must be the origin, or (0, 0).
If the midpoint of another side of the triangle is located at (2a, b), then the coordinates of the two endpoints of this side must be (2a, b) and (2a, 0). One of the endpoints is (2a, 0), which we already know is a vertex of the triangle. The other endpoint, (2a, b), is also a vertex of the triangle.
Finally, if the midpoint of the third side of the triangle is located at (a, b), then the coordinates of the two endpoints of this side must be (a, b) and (0, 0). One of the endpoints is (0, 0), which we already know is a vertex of the triangle. The other endpoint, (a, b), is also a vertex of the triangle.
Hence, the coordinates of the other vertices of the triangle are (2a, 0), (2a, b), and (a, b).
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am i doing well on this
Answers
Answer:
The last option is the correct answer.
Step-by-step explanation:
lake front company is considering investing in a new dock that will cost 560,000 the company expects to use the dock for 5 years after which it will be sold for 300,000 lake front aticipates annual cash flows of 110,000 resulting from the new dock the companys borrowing rate is 8% while its cost of capital is 10% calculate the net present value of the dock and indicafe whether lake front should make the investment
Answers
The lakefront company should make the investment as in 5 years they'll have a profit of 10000.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, the lakefront company is considering investing in a new dock that will cost 560,000.
So, a Capital cost of 10% is (560000/10) = 56000
The company's borrowing rate is 8%.
∴ SI = (560000×8×5)/100.
SI = 5600×8×5.
SI = 224000.
So, The total cost is (560000 + 56000 + 224000) = 840000.
After 5 years they can sell it for 300000.
And has a cash flow of 110000, so in 5 years it is 550000.
So, total earnings is (300000 + 550000) = 850000.
Total profit is (850000 - 840000) = 10000 so it is profitable.
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Consider the simultaneous equations
3x² + 2xy = 4
x + y = a
where a is a real constant.
Find the complete set of values of a for which the equations have two distinct real solutions for x.
There are no values of a.
-2 < a < 2
-1 < a < 1
a = 0
a < -1 or a < 1
a < -2 or a < 2
All real values of a
Answers
The correct option is All real values of a.
What is the real number?
The positive and negative integers, as well as the fractions created from them (also known as rational numbers), as well as the irrational numbers, are all real numbers.
We have,
3x² + 2xy = 4 ...................(1)
x + y = a ...................(2)
By converting the second equation equals to y:
y = a - x .....................(3)
By substituting the (3)rd equation into (1), we get
3x² + 2xy = 4
3x² + 2x(a - x) = 4
3x² + 2ax - 2x² = 4
x² + 2ax = 4
x² + 2ax - 4 = 0
Discriminant = 4a² + 16 >= 0
2 distinct solutions & is ok for all a.
hence, the correct option is All real values of a.
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Need answer will mark Brainliest
Answers
Answer:
see explanation
Step-by-step explanation:
from the table we can obtain that
f(x ) = 6x³ + 8x - 12 ( 6 0 8 - 12 , being the coefficients of the polynomial )
f(x) is divided by (x + 7) , since evaluated at - 7
the quotient is
6x² - 42x + 302 ( 6 - 42 302, are the coefficients of the quotient )
with remainder - 2126
It takes Eddie 2 hours to shovel the snow from a driveway and sidewalk. Brad can shovel the snow from the same driveway and sidewalk in 5 hours. How long would it take them working together to shovel the snow?
How do I solve it?
Answers
Eddie and Brad together shovel the snow in 1 hour 26 minutes.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that it takes Eddie 2 hours to shovel the snow from a driveway and sidewalk.
Brad can shovel the snow from the same driveway and sidewalk in 5 hours.
We now find how long would it take them working together to shovel the snow.
Eddie does 1/2 in 1 hour or x/2 in x hours
Brad does 1/5 in 1 hour or x/5 in x hours
the sum is 1 full job
(x/2)+(x/5)=1
multiply both sides by 10
7x=10
x=(10/7) hours or 600/7 minutes =86 minutes
As we know 1 hour has 60 minutes.
We can write 86 minutes as 1 hour and 26 minutes.
Hence, 1 hour 26 minutes is the time taken by Eddie and Brad to shovel the snow.
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The graph shows a translation of the function f(x) = |x|. What absolute value function is represented by the graph?
A V shape with vertex at negative 1 point 5 comma zero and passing through the points negative 2 comma 1 and negative 1 comma 1.
A. f(x) = |x| + 1.5
B. f(x) = |x| − 1.5
C. f(x) = |x − 1.5|
D. f(x) = |x + 1.5|
Answers
The absolute value function that is represented in the graph is f(x) = |x + 1.5| So the correct option is D.
What absolute value function is represented by the graph?The general absolute value function is:f(x) = |x|This absolute value function has a vertex at the point (0, 0). We know that the graphed function has a vertex at the point (-1.5, 0).
So basically we had a horizontal translation of -1.5 units or 1.5 units to the left. That is written as: g(x) = f(x + 1.5)
Replacing the absolute value function we get:g(x) = |x + 1.5|
Then the correct option is D.
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The length of a rectangle is 3 less than twice the width. If the perimeter of the rectangle is 78 inches, find the dimensions (length and width) of the rectangle.
Answers
Length of the rectangle is 25 and width of the rectangle is 14.
What do you mean by algebraic expression?
A combination of terms through addition, subtraction, multiplication, division, and other operations is known as an algebraic expression (or variable expression). An algebraic expression is composed of various parts.
Any algebraic expression's variables, constants, terms, and coefficients.
A variable is a symbol that doesn't have a set value. Any value may be used.
It is given that the length of a rectangle is 3 less than twice the width and the perimeter of the rectangle is 78 inches.
Let the width of the rectangle be x
Length of the rectangle become 2x - 3
Perimeter of rectangle = 2(length + width)
78 = 2(2x - 3 + x)
78 = 2(3x - 3)
78 = 6x - 6
78 + 6 = 6x
84 = 6x
x = 84/6
x = 14
length of the rectanle is 2x - 3 = 2(14) - 3 = 28 - 3 = 25
Width of the rectangle is x = 14
Therefore, length of the rectangle is 25 and width of the rectangle is 14.
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An independent group of food service personnel conducted a survey on tipping practices in a large metropolitan area. They collected information on the percentage of the bill left as a tip for 20 randomly selected bills. The average tip was 11.1% of the bill with a standard deviation of 2.8%. Assume that the tips are approximately normally distributed. Construct an interval to estimate the true average tip (as a percent of the bill) with 90% confidence. Round the endpoints to two decimal places, if necessary.
Answers
Assuming that the tips are approximately normally distributed, an interval to estimate the true average tip (as a percent of the bill) with 90% confidence is (10.47, 11.73).
How to construct the confidence interval?Assuming that the tips are approximately normally distributed, we would determine both the lower limit and upper limit for the confidence interval where 90% of the sample means occur as follows;
Lower limit = μ - σ/√x
Lower limit = 11.1 - 2.8/√20
Lower limit = 11.1 - 0.63
Lower limit = 10.47
For the upper limit, we have:
Upper limit = μ - σ/√x
Upper limit = 11.1 + 2.8/√20
Upper limit = 11.1 + 0.63
Upper limit = 11.73
For 90% of the sample means to occur, the confidence interval is as follows;
Confidence interval = (10.47, 11.73)
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Write the equation of the line which passes
through the point (2. −3) and has a slope of -2/5
A. 2x + 5y = 4
C. 2x+ 5y = −11
B. 2x+5y = −9
D. 2x-5y = −16
Show work for this question please & thank u
Answers
y = -2/5 x -11/5 is the equation of line with slope -2/5 that passes through the point (2, -3).
What is the equation of line?The slope of the line is the rise to run ratio, or the rise divided by the run. It expresses the slope of a line in the coordinate plane.
The standard form of an equation is y = mx+c.
Here given,
A line with a slope of -2/5 that passes through the point (2, -3).
Simplify y = mx+c with m=2/5 and (x, y)=(2, -3). That is to say,
-3 = -2/5 (2)+c
⇒ -3 = -4/5 +c
⇒ c = -3 + 4/5
⇒ c = (-15 + 4) / 5
=> c = -11/5
When m = -2/5 and c = -11 /5 are substituted in y = mx+c, we get
y = -2/5 x -11/5
As a result, an equation for a line with a slope of -2/5 that passes through the point (2,-3) is y = -2/5 x -11/5.
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Answer:
C. 2x+ 5y = −11
Step-by-step explanation:
You want the equation of the line with slope -2/5 through point (2, -3).
Point-slope equationThe equation of a line with slope m through point (h, k) can be written as ...
y -k = m(x -h)
Then the equation of the line with slope -2/5 through point (2, -3) will be ...
y +3 = -2/5(x -2)
Standard formWe can put this in standard form by ...
5(y +3) = -2(x -2) . . . . . multiply by 5
5y +15 = -2x +4 . . . . . . eliminate parentheses
2x +5y = -11 . . . . . . . . . add 2x-15 to both sides
The desired equation is 2x +5y = -11.
Can you answer 2 and 3
Answers
Answer: 2. 37.8%
3. 30% decrease
Step-by-step explanation:
Increase = New Number - Original Number
Then: divide the increase by the original number and multiply the answer by 100.
% increase = Increase ÷ Original Number × 100.
36.99-22.99=14
100(14/36.99)
37.8%
First: work out the difference (decrease) between the two numbers you are comparing.
Decrease = Original Number - New Number
Then: divide the decrease by the original number and multiply the answer by 100.
% Decrease = Decrease ÷ Original Number × 100
2.50-1.75=0.75
100(0.75/2.5)
30%
The formula for estimating the population variance from the sample involves taking the sum of squared deviations and dividing it by ___
Answers
The formula for estimating the population variance from the sample involves taking the sum of squared deviations and dividing it by N - 1
Population variance is a measure of dispersion that determines how far each data point is from the population mean.
On the population, the population variance is calculated. When the number of observations grows, a few data points are chosen to represent the entire population.
The variance calculated on these specific data points is referred to as the sample variance. The population variance can be estimated using the sample variance.
When the population variance is unknown , we estimate the population variance by using sample variance
The formula for estimating the population variance from the sample involves taking the sum of squared deviations and dividing it by N-1
Formula of sample variance = [tex]s^2 = \frac{\sum f_i(x_i - \bar{x})}{N-1}[/tex]
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Please help
Whats
30-19+29+30-29-10=
Answers
Answer:
31Step-by-step explanation:
[tex]\tt 30-19+29+30-29-10[/tex]
[tex]\tt 11+29+30-29-10[/tex]
[tex]\tt 40+30-29-10[/tex]
[tex]\tt 70-29-10[/tex]
[tex]\tt 41-10[/tex]
[tex]\tt 31[/tex]
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what are the cooridinates of the point that is 1/6 of the way from A(14, -1) to B(-4, 23)?
Answers
Answer:
(11, 3)
Step-by-step explanation:
You want the point 1/6 of the way from A(14, -1) to B(-4, 23).
Dividing pointThe point P that divides AB into the fractional parts k and (1 -k) is ...
P = (1-k)A +kB
ApplicationFor k = 1/6, the dividing point is ...
P = (5/6)(14, -1) +(1/6)(-4, 23) = (5·14 -4, 5(-1) +23)/6 = (66, 18)/6
P = (11, 3)
The point 1/6 of the way from A to B is (11, 3).
Question 10
What is the equation of the line shown?
Answers
does it want the answer in a specific form?
slope intercept form; y = mx + b
slope = 2
b = -1
plug the values in
y = 2x -1 or y = 2/1x -1
a line with a slope of -3 passes through the point -3,8 what is its equation in slope intercept form
Answers
Then put the point and you will have the c
Y=-3x-1
PLEASE best explanation gets brainliest
Answers
Answer:
55
Step-by-step explanation:
Because you would minus 180-125 to get angle 1 and they said that angle 2 is parallel so they would be the same anwser so the answer is 55.
If two balls with different speeds roll off the edge of a table at the same time, which one hits the floor first, the faster or the slower ball? Why or why not?
Answers
Both balls will strike the ground simultaneously, but the faster ball will do so farther away from the table.
What is acceleration due to gravity ?The unit g stands for gravitational acceleration. At sea level, the standard value of g on earth's surface is 9.8 m/[tex]s^{2}[/tex]
They will strike the ground simultaneously if the table and the ground are both flat.
It is customary to divide an object's motion into a vertical component and a horizontal component. While they are on the table, neither of the balls is moving vertically. Both balls begin to accelerate downward as soon as they leave the table due to the effects of gravity. Given that both balls experience the same acceleration from gravity, they will fall at the same rate and with the same downward velocity.
Both balls will strike the ground simultaneously, but the faster ball will do so farther away from the table.
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Find the circumference and the area of a circle with radius 9m .
Use the value 3.14 for , and do not round your answers. Be sure to include the correct units in your answers.
Answers
The circumference of the circle will be 56.52 m.
And, The area of a circle will be 254.34 m².
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The radius of circle = 9 m
Now,
Since, The area of circle = πr²
Hence, The area of circle = 3.14 × 9²
= 3.14 × 81
= 254.34 m²
And, The circumference of the circle = 2πr
= 2 × 3.14 × 9
= 56.52 m
Thus, The circumference of the circle will be 56.52 m.
And, The area of a circle will be 254.34 m².
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Find the direction of the sum of these two vectors:
Answers
By using the concept of vector, it can be calculated that
Direction of the sum is 10.87° below the horizontal.
What is vector?
Anything that has both magnitude and direction and follow the vector addition law is called vector.
A = 2.71 m
[tex]A_x = 2.71 cos 60 = 1.355 \ m\\A_y = -2.71 sin 60 = -2.35 \ m[/tex]
B = 3.14 m
[tex]B_x = 3.14 cos 30 = 2.71 \ m\\B_y = 3.14 sin 30 = 1.57 \ m[/tex]
Sum of A and B = (1.355 +2.71) i + (-2.35 + 1.57) j
= 4.065i - 0.78j
Let the angle be [tex]\theta[/tex]
[tex]tan\theta = \frac{0.78}{4.065}\\tan\theta = 0.192\\\theta = tan^{-1}(0.192)\\\theta = 10.87^{\circ}[/tex]
Direction of the sum is 10.87° below the horizontal.
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Use the given measurements to solve the triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.
a=400, b=300
Answers
[tex]\frac{\sin \theta}{300}=\frac{\sin 2\theta}{400} \\ \\ \frac{\sin \theta}{300}=\frac{2\sin \theta \cos \theta}{400} \\ \\ \frac{1}{300}=\frac{\cos \theta}{200} \\ \\ \cos \theta=\frac{2}{3} \\ \\ \theta=\arccos(2/3) \\ \\ \theta \approx \boxed{48^{\circ}}[/tex]
During summer, the height of the water in Scott's pool decreases by 4 inches each week, due to evaporation. How many weeks does it take for the water to decrease by 20 inches?
Responses
A −5
B 5
C 20
D −20
Answers
Answer:
5 weeks
Step-by-step explanation:
20 inches / ( 4 inches/week ) = 5 weeks
Simplify the inequality
Answers
Add number
Divide numbers
2x>22
Solution
X>11
2. 2x > 14
3. divide 2 on each side
4. x> 11
Solve using quadratic formula: 5x^2+9=4x+5
Answers
Answer:
No real solutions.
Step-by-step explanation:
No real solutions.
Mrs.Barrera learned that 21 of her 25 students ride the school bus every morning.What percent of her students ride the school bus every morning?
Answers
The percentage of her students that ride the school bus every morning would be = 84%
What is percentage expression?A percentage expression is an representation of a data set to a fraction of 100.
The total number of students = 25 students
The number of students that ride the school bus = 21
To calculate the percentage of the students that ride the bus the following is done;
= 21/25 × 100
= 2100/25
= 84%
Therefore, the percentage of her students that ride the school bus every morning is 84%
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if three sides of a triangle are in ratio of 3:5:7 and the perimeter of the triangle is 12xm. what is the length of the longest side?
Answers
The required length of the longest side will be 28/5 cm in the triangle.
What is the perimeter of a triangle?The perimeter of a triangle is defined as the addition of the lengths of the triangle's three sides.
We have been given that the three sides of a triangle are in the ratio of 3:5:7
Let's assume the sides are 3x, 5x, 7x
Since the perimeter of the triangle is 12 cm.
So, 3x+5x+7x = 12
Apply the addition operation,
15x = 12
x = 12/15
Reduce the above fraction to the simplest form
x = 4/5
So, longest side = 7x = 28/5 cm
Thus, the required length of the longest side will be 28/5 cm in the triangle.
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Which statement is true about the diagram?
R
S
يحة
Ο Δ QRC ~Δ SCU
O ARQCA SUC by SSS
O A CRQA CSU by SAS
O No triangles are congruent
U
Answers
Answer:
[tex]\triangle CRQ \cong \triangle CSU[/tex] by SAS
Step-by-step explanation:
[tex]\angle QCR \cong \angle SCU[/tex] because of vertical angles.
TIME SENSITIVE
(2,6)
x-y=4
(a) write an equation of the line that passes through the point and is parallel to the given line
(b) write an equation of the line that passes through the point and is perpendicular to the given line
Answers
Answer:
(a) Equation of parallel line is y = x + 4
(b) Equation of perpendicular line is y = - x + 8
Step-by-step explanation:
Given line is
x - y = 4
Rewrite this as
x - 4 = y
or
y = x - 4
This is the equation of a line in slope intercept form which is generally
y = mx + b
where m is the slope and b the y-intercept
Here m = 1, b = -4
(a) A parallel line will have the same slope but a different y-intercept
So for starters we can write the equation of the parallel line as
y = x + b
Since this passes through (2,6) sub 2 for x and 6 for y to get
6 = 2 + b
==> b = 4
Equation of the line is
y = x + 4
(b) A perpendicular line will have as slope -1/m where m is the slope of the original line
Here m = 1, so -1/m = -1/1 = -1
Equation will be of the form
y = -x + b
Since this also passes through (2,6)
6 = -2 + b
==> b = 6 + 2 = 8
Equation of perpendicular line is
y = -x + 8
Help with this plsss !!!
Answers
Answer:
:))
Step-by-step explanation:
The maximum value is 22 as the last small line (end of the "whisker") is marked at 22. Hope this helps!! Pls mark as brainliest and lots of points, help ya girl out!!!