Determining the slopes of each side, we get the slope of [tex]\overline{AB}[/tex] is [tex]2[/tex], the slope of [tex]\overline{BC}[/tex] is -1/2, the slope of [tex]\overline{CD}[/tex] is 2, and the slope of [tex]\overline{AD}[/tex] is -1/2. Since the slopes of sides AB and CD and BC and AD are equal, it follows that [tex]\overline{AB} \parallel \overline{CD}[/tex] and [tex]\overline{BC} \parallel \overline{AD}[/tex]. Thus, ABCD is a parallelogram because it is a quadrilateral with two pairs of opposite congruent sides. However, we can also note that the slope of side AB is the negative reciprocal of that of sides BC, and thus [tex]\overline{AB} \perp \overline{BC}[/tex]. Using the fact that perpendicular lines form right angles, we can conclude that [tex]\angle ABC[/tex] is a right angle, and since ABCD is thus a parallelogram with a right angle, it must also be a rectangle.
Answer:
Answers will vary based on the method used, but the final slope-intercept form of the equation of AB↔ will be the same.Let the equation of AB↔ in slope-intercept form be y=mx+d, where m is the slope and d is the y-intercept.The coordinates of points A and B are (1, 1) and (5, 3), respectively, so the slope of AB↔ is m=yB−yAxB−xA=24=0.5.Substitute the value of m back in the equation:y = 0.5x + d.Substitute the coordinate of point A (1, 1) in the equation above, and solve for d: 1 = 0.5 + dd = 0.5.Therefore, the equation of AB↔ is y = 0.5x + 0.5. To check whether C lies on AB↔ substitute the x-coordinate of C into the right side of the equation: 0.5 (2.6) + 0.5 = 1.8.The result is equal to the y-coordinate of C. Thus, C satisfies the equation of AB↔ which means that C lies on AB↔.
Step-by-step explanation:
I did it
Can someone help me on this pls? It’s urgent, so ASAP (it’s geometry)
Write formal proofs using LA Theorem.
Given the parameters in the diagrams, we have;
4. ∆ABC ≈ ∆DEF by ASA
5. UW ≈ XZ by CPCTC
6. QR ≈ TR by CPCTC
How can the relationship between the triangles be proven?4. The given parameters are;
<B = <E = 90°
AB = DE Definition of congruency
<A = <D Definition of congruency
Therefore;
∆ABC ≈ ∆DEF by Angle-Side-Angle, ASA, congruency postulate5. Given;
XY is perpendicular to WZ
UV is perpendicular to WZ
VW = YZ
<Z = <W
Therefore;
∆UVW ≈ ∆XYZ by Angle-Side-Angle, ASA, congruency postulate
Which gives;
UW is congruent to XZ, UW ≈ XZ, by Corresponding Parts of Congruent Triangles are Congruent, CPCTC6. Given;
PQ is perpendicular to QT
ST is perpendicular to QT
PQ ≈ ST
From the diagram, we have;
<SRR ≈ <PRQ by vertical angles theorem;
Therefore;
∆QRP ≈ ∆TRS by Side-Angle-Angle, SAA, congruency postulate
Which gives;
QR ≈ TR by Corresponding Parts of Congruent Triangles are Congruent, CPCTCLearn more about congruency postulates here:
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The design of a building that has a square pyramid roof as a roof is shown. The cost of material for the outside of the building and for the roof
ranges from $25 per square foot to $50 per square foot. The budget for this material is $500,000. The rectangular front of the building has a
length twice as long as its height. The slant height of the roof is the same as the height of the rectangular front of the building.
What is the maximum possible length of the rectangular front of the building to the nearest foot?
feet
The maximum possible length of the rectangular front of the building is
A. 164
B. 41
C. 82
D. 29
The maximum possible length of the rectangular front of the building is 23 feet
How to determine the maximum possible length?The complete question is attached
Let the length of the rectangular front be x and the height be y.
So, we have:
x = 2y
The building has 4 congruent sides.
So, the area of the 4 sides is
A = 4 * (x * y)
This gives
A = 4 * (x * 2x)
Evaluate
A = 8x²
For the triangular roof, we have:
Slant height, l = y
Base, b = x
So, the area of the 4 triangular faces is
A = 0.5 * 4 * xy
This gives
A = 2xy
Recall that:
x = 2y
Make y the subject
y = 1/2x
So, we have:
A = 2x * 1/2x
A = x²
The cost of designing the buildings is
C = 25 * 8x² + 50 * x²
C = 200x² + 50x²
C = 250x²
This gives
250x² = 500000
Divide both sides by 250
x² = 2000
Square both sides
x = 45
Recall that:
y = 1/2x
This gives
y = 1/2 * 45
y = 23
Hence, the maximum possible length of the rectangular front of the building is 23 feet
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The scatter plot below represents the amount of dog food a brand recommends based on the weight of the dog.
A
B
Amount of Food per Day (cups)
6
80
no association
negative linear association
● •
20
·
•
6
6
40
60
Weight of Dog (lb)
6
•
80
Which best describes the type of association shown in the scatter plot?
100
The best that describes the type of association shown in the scatter plot is positive linear association.
Given the scatter plot below represents the amount of dog food a brand recommends based on the weight of the dog.
Amount of Food per day cups:
20
40
60
No
We are required to find the type of association shown in the given scatter plot.
It is a positive linear association. The slope is positive so the linear association is also positive and linear mean generally in a line not on a curve like a nonlinear association.
Hence the given graph is of positive linear association.
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PLEASE I NEED HELP SO BADLY
Answer:
[tex]3y^{2} -3y-5[/tex]
The sum of all but one interior angle of a heptagon is 776°. What is the measure of the final interior angle? 42º 56º 124º 304º
The measure of the seventh interior angle of the heptagon is 124°. (Correct choice: C)
What is the measure of the missing interior angle in a heptagon?
Heptagons are polygons with seven sides, seven vertices, seven interior angles and seven central angles. Herein we know the value of the sum of six interior angles and we need to know the measure of the seventh interior angle. We can determine the measure of the seven interior angles by using the following expression:
θ = (n - 2) · 180°, where n is the number of sides of the polygon. (1)
If we know that n = 7, then sum of the internal angles in the heptagon is:
θ = (7 - 2) · 180°
θ = 900°
And the measure of the final interior angle is found by subtraction:
θ₇ = 900° - 776°
θ₇ = 124°
The measure of the seventh interior angle of the heptagon is 124°. (Correct choice: C)
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The line plot (shown in the attached image) shows the prices of sunglasses at a department store.
a. Find the mean, median, and mode.
b. Which measure best describes the data? Why?
c. Which measure might be misleading in describing the average price of sunglasses? Explain your reasoning.
Please help!! show all work and be sure to give final responses in complete sentence form in context of the problem, and explain your reasoning.
a. Mean is 70.8, median is 70, and mode is 60
b. Mean describes the data best
c. Mean can be a misleading central measure in case of outliers
Calculating Mean, Median and Mode
Mean = Total sum of pries / Total number of sunglasses
Mean = (20 + 20 + 50 + 50 + 50 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 70 + 70 + 80 + 80 + 80 + 80 + 90 + 90 + 90 + 90 + 100 + 100 + 130) / 25
Mean = 70.8
Median = (n/2 + 1)th term
Here, n is the number of sunglasses.
Median = (25/2 + 1)th term
Median =13th term
Median = 70
Mode = Most occurring data
Mode = 70
Why is mean the best central measure to describe the data?
When your data distribution is continuous and symmetrical, such as when your data are normally distributed, the mean is typically the best measure of central tendency to utilize. Thus, mean describes the average price of the sunglasses here
Mean Being Misleading
In case there are outliers, the mean of the data gets highly affected. Hence, it can be misleading for analyzing average price of the data.
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The image point of A after a translation right 4 units and up 2 units is the point B(1,−3). Determine the coordinates of the pre-image point A.
The image of point A(-3, -5) after a translation right 4 units and up 2 units is the point B(1,−3)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
The point A = (1 - 4, -3 - 2) = (-3, -5)
The image of point A(-3, -5) after a translation right 4 units and up 2 units is the point B(1,−3)
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I keep getting (10,5) or (0,5) someone pls help
Answer:
(4,-3)
Step-by-step explanation:
Multiplying the bottom equation by -6, we get -6x+12y=-60.
Adding this to the first equation gives 15y=-45, and thus y=-3.
So, it follows that 6x+3(-3)=15, and thus x=4.
2. The lengths in centimeters of four line segments
are shown below.
3.12, 3.24, 31, √10
Write the lengths in order from least to greatest.
Answer:
I'm pretty sure it is √10, 3.12, 3.24, 31
Step-by-step explanation:
I don't know if you messed up but I got a question similar that is the length 31 in your quesion is actually 3 1/4 in my question. but i did the math and 31 is still the greatest number.
Explain why the following form linearly dependent sets of vectors. (solve this problem by inspection.)
u1 = (3, -l), u2 = (4, 5), u3 = (-4, 7) in r2
A set of vectors {v1,v2,...,vk} is linearly independent if the vector equation x1v1 + x2v2 + .......... + xkvk = 0 has only the trivial solution
x1 = x2 = .... = xk =0. Then the set {v1,v2,...,vk} is linearly dependent otherwise.
So putting in the formula we get
x1u1 + x2u2 + x3u3 = 0
x1u1 + x2u2 = -x3u3
au1 + bu2 = u3 ∵ (-x1/x3 = a & -x2/x3 = b)
On putting in the values
a(3,-1) + b(4,5) = (-4,7)
(3a+4b,-a+5b) = (-4,7)
On comparing we get
3a + 4b = -4 -(1)
-a + 5b = 7 -(2)
on solving these equations we get
b = 17/19 and a= -48/19
which is non trivial.
Thus the following form linearly dependent sets of vectors.
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3) angle of an isosceles triangle is 70°, find the value of If one remaining angles. a) 40°, 40° b) 45°, 45° c) 40°70° d)50⁰, 50⁰
The remaining two angles of the given isosceles triangle is Option(C) 40°,70° .
What are the remaining two angles in the isosceles triangle ?For an isosceles triangle, the two sides of the triangle are congruent and equal in length . Also the angles subtending the adjacent equal sides of the isosceles triangle are of same measure.
We also know that the sum of the three interior angles of any triangle is always equal to 180° .
In the options given, in Option(C) the angles measure 40° and 70° .
Thus as one angle of the isosceles triangle is given to be 70°, the other angle of its adjacent side is also 70° .
The sum of the interior angles of the triangle is equal to -
70° + 40° + 70° = 180° which satisfies the property.
Therefore, the remaining two angles of the given isosceles triangle is Option(C) 40°,70° .
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What is the domain of the following set of ordered pairs?
{(-2,-5), (-3,8), (12,6), (8, -3), (4,0), (-5, -7)}
○ a. {-5, 8, 6, -3, 0, -7}
O b. {-2, -5, -3, 8, 12, 6}
○ c. {8, −3, 4, 0, − 5, −7}
O d. {-2, -3, 12, 8, 4, −5}
Answer:
D. {-2, -3, 12, 8, 4, −5}
Step-by-step explanation:
The domain is the set of x coordinates, so the answer is {-2, -3, 12, 8, 4, −5}.
The number of bacteria in a certain population increases according to a continuous exponential growth model with a growth rate parameter of 4.9% per hour how many hours does it take for the size of the sample to double
Answer:
14.5 hours to the nearest tenth.
Step-by-step explanation:
4.9% = 0.049.
If the original number is 50 it will double to 100 so
100 = 50(1.049)^t
1.049^t = 2
t * log 1.049 = log 2
t = log 2 / log 1.049
= 14.49 hours,
Ilean works as a welder and
web designer. As a welder, she earns $18 per hour. Last week she
worked x hours as a welder and her friend paid her $75 to design a web page. Write an
expression to represent the total amount llean earned last week.
The expression which can be used to represent the total amount llean earned last week is 75 + 18x
EquationAmount llean earns per hour welding = $18Number of hours worked as welder = xAmount earned as a web page designer = $75An expression to represent the total amount llean earned last week = Amount earned as a web page designer + (Amount llean earns per hour welding × Number of hours worked as welder)
= 75 + (18 × x)
= 75 + 18x
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A potato was launched in the air using a potato gun. the function for the situation was h(t) = -16t2 + 100t + 10, where t was the time in seconds and h(t) was the height in feet. (3 points each) a. what was the maximum height of the potato? b. what was the lowest height of the potato? c. what was the lowest time that applies to the actual situation? d. what is the greatest time that applied to the actual situation? e. using your answers to parts a through d, what are the domain and range of the function, as they apply to this situation? use set builder notation.
The answers to all the parts are given below.
To find the answers using a function:The height equation is:
h(t) = - 16t^2 + 100t + 10
A) To find the maximum height, we must find the time where the velocity is 0, so we must derive it with respect to the time.
v(t) = - 2 * 16 * t + 100 = 0
t = 100/(2*16) = 3.125s
Now we put this time in our height equation:
h(3.125s) = -16*3.125^2 + 100*3.125 + 10 = 166.25 ft.
B) The lowest height of the potato will be h = 0ft when the potato hits the ground.
C) the lowest time that works for that function is t = 0s when the potato is fired by the gun.
D) the maximum time can be found when the potato hits the ground, after that point the equation does not work anymore, let's find it,
h(t) = 0 = -16t^2 +100t+10
we can solve it using Bhaskara's equation:
[tex]t=\frac{-100+-\sqrt{100^{2} +4*16*10} }{-2*16} =\frac{-100+-103.2}{-32}[/tex]
So the two solutions are:
t = 6.3s
t = -0.1s
We need to choose the positive time, as we already discussed that the minimum time that works for the equation is t = 0s.
so here the answer is t = 6.3s
E) the domain is 0s ≤ t ≤ 6.3s
The range is 0ft ≤ h ≤ 166.25 ft.
Therefore, the answers to all the parts are shown.
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Given the following formula, solve for a. 8=a+b+c/2
Making "a" the subject of the formula would give us: a = 8 - b - c/2
How to Solve for the Subject of Formula?Given the formula, 8 = a+b+c/2, to make a the subject of the formula, we would isolate a in the equation.
8 = a+b+c/2
8 = (2a + 2b + c)/2
2(8) = 2a + 2b + c
16 = 2a + 2b + c
16 - 2b - c = 2a
Divide both sides by 2
16/2 - 2b/2 - c/2 = 2a/2
8 - b - c/2 = a
a = 8 - b - c/2
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Tickets for a concert were \$5$5dollar sign, 5 for each child and \$8$8dollar sign, 8 for each adult.
Answer:
What exactly is the question
Step-by-step explanation:
There's no clear question.
The length of tr is 17 units. what are the lengths of sv and qt? sv = units qt = units
Applying the properties of kite, the measures are: SV = 41 units; QT = 21 units.
What is a kite?A kite is a quadrilateral that has 2 pairs of congruent adjacent sides, and has two diagonals where the longest one bisects the shorter one and divides it into equal segments.
The diagram given is a kite. Where TR = 17 units. Thus we would solve for x using the equation as shown below:
TR = RV [congruent adjacent sides of the kite]
Plug in the values
17 = 3x + 2
17 - 2 = 3x
15 = 3x
15/3 = x
x = 5
SV = TS = 9x - 4 [congruent adjacent sides of the kite]
Plug in the value of x
SV = 9(5) - 4
SV = 41 units
The length of segment QT is 41 units.
QT = QV = 4x + 1 [congruent adjacent sides of the kite]
Plug in the value of x
QT = 4(5) + 1
QT = 21 units
The length of segment QT is: 21 units.
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Answer:
SV: 41
QT:21
Step-by-step explanation:
OUICK PLEASE
Find the equation of the line
Answer:
y = 2x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = ( 0, 4) ← 2 points on the line
m = [tex]\frac{4-0}{0-(-2)}[/tex] = [tex]\frac{4}{0+2}[/tex] = [tex]\frac{4}{2}[/tex] = 2
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = 2x + 4 ← equation of line
Volume=
Help me please!! Asap! Thanks so much
The volume of the oblique prism is 16261 cubic units
How to determine the volume?The given parameters are:
Height = 23
Base area = 707
The volume is calculated as:
V = base area * height
So, we have:
V = 707 * 23
Evaluate
V = 16261
Hence, the volume of the oblique prism is 16261 cubic units
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What is 3/4 divided 1/6
Answer:
Fraction form: 9/2
Mixed number form: 4 1/2
Decimal form: 4.5
Step-by-step explanation:
To divide the two number, follow these steps.
3/4÷1/6
3/4×6/1=18/4
Reduce.
18/4=9/2 or 4 1/2
Hope this helps!
Answer:
[tex]\dfrac{9}{2} = 4 \dfrac{1}{2}[/tex]
Step-by-step explanation:
[tex] \dfrac{3}{4} \div \dfrac{1}{6} = [/tex]
To divide a fraction by a fraction, rewrite the first fraction and multiply it by the reciprocal of the second fraction. To get the reciprocal of a fraction, flip it. The reciprocal of 1/6 is 6/1.
[tex] = \dfrac{3}{4} \times \dfrac{6}{1} [/tex]
[tex] = \dfrac{3 \times 6}{4 \times 1} [/tex]
[tex] = \dfrac{18}{4} [/tex]
[tex]= \dfrac{9}{2} = 4 \dfrac{1}{2}[/tex]
A triangular face of the roof of the garage has two sides
that are √93 feet in length each and a base of length
186 feet. Is the roof a right triangle? Explain the steps
to take to determine whether the roof forms a right
triangle.
Answer:
The roof does form a right triangle.
Step-by-step explanation:
If it is a right triangle then it will obey the Pythagoras Theorem.
Now (√186)^2 = (√93)^2 + (√93)^2
186 = 93 + 93 = 186
So it obeys the theorem and is therefore a right triangle.
ales volume last weekend for four samples, each consisting of five car dealerships, were as follows: Data Point 1 2 3 4 5 Sample 1 37 15 43 25 21 Sample 2 38 31 12 19 28 Sample 3 16 21 45 32 25 Sample 4 19 10 45 37 22 What is the standard deviation of the distribution of sample means
The sample standard deviation of sample 1 is 11.54, of sample 2 is 10.21, of sample 3 is 11.25, of sample 4 is 14.15.
Given
Data point sample 1 sample 2 sample 3 sample 4
1 37 38 16 19
2 15 31 21 10
3 43 12 45 45
4 25 19 32 37
5 21 28 25 22
We have to find the sample standard deviation of each sample.
We have to first mean of each sample.
Sample mean of 1=141/5=28.2
Sample mean of 2=128/5=25.6
Sample mean of 3=139/5=27.8
Sample mean of 4=133/5=26.6
Sample standard deviation=[tex]\sqrt{}[/tex]∑[tex](x-x bar)^{2}/n-1[/tex]
∑[tex](x-x bar)^{2}[/tex] is calculated in the figure.
Sample standard deviation of sample 1=[tex]\sqrt{532.8/4}[/tex]
=[tex]\sqrt{133.2}[/tex]
=11.54
Sample standard deviation of sample 2=[tex]\sqrt{417.2/4}[/tex]
=[tex]\sqrt{104.3}[/tex]
=10.21
Sample standard deviation of sample 3=[tex]\sqrt{506.8/4}[/tex]
=[tex]\sqrt{126.7}[/tex]
=11.25
Sample standard deviation of sample 4=[tex]\sqrt{801.2/4}[/tex]
=[tex]\sqrt{200.3}[/tex]
=14.15.
Hence the sample standard deviation of sample 1 is 11.54, sample standard deviation of sample 2 is 10.21, sample standard deviation of sample 3 is 11.25, sample standard deviation of sample 4 is 14.15.
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Find the quotient: look at pic
Answer:
2y+6
Step-by-step explanation:
first, pull out the 2 from the top to separate the equation
second, factor out y
third, cancel out the common factor of y-1
fourth, remove the parenthesis from 2(y+3)
answer = 2y+6
Multiply the following numbers. Reduce the answer to lowest terms.
Answer:
B 4 1/3
Step-by-step explanation:
Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters. What is the volume of the space filled with tissue paper in the packaging box? 81.84 cubic centimeters 105.84 cubic centimeters 198.264 cubic centimeters 222.264 cubic centimeters
The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters
VolumeVolume if small, Vs = 24 cubic inchesConstant = k
= 2.1³
= 9.261
Volume of large : volume of small = k
Vl / Vs = k
Vl = Vs × k
= 24 × 9.261
= 222.264 cubic inches
Therefore,
Volume of tissue paper = volume of large - volume of small
= 222.264 cubic inches - 24 cubic inches
= 198.261 cubic inches
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SOMEONE PLEASE HELP!!! Instructions: Find the length of the arc. Round your answers to the nearest tenth.
The length of the arc is 15.70 km
Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc. Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).
The formula is given by
s = ϴ × r,
where
s is the arc length
r is the radius of the circle
θ is the central angle of the arc in radians
Given :- Radius = 10km
Angle = 90 ° = [tex]\pi[/tex]/2 radians (1 radian = 180°/[tex]\pi[/tex])
By using formula we get
Length of arc = 10 x[tex]\pi[/tex]/2 = 5[tex]\pi[/tex] km ([tex]\pi[/tex] = 3.14)
= 15.70 km
Thus the length of the arc is 15.70 km
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A printing company charges a fixed rate to set up the printing press, plus a cost of $3.50 for every 100 copies. If 800 copies cost $64.00, how much will it cost to print 1500 copies?
Answer:
88.5
Step-by-step explanation:
3.5 * 8 = 28, this is how much was spent on copies printed. If 800 copies cost $64 and 28 of that was on the 3.5 fee per 100, then the flat rate must be:
64-28 = 36.
Now, let's do 1500. For 1500 copies, you will get charged $3.5 15 times. This amounts to 52.5, then adding the fixed fee of 36 dollars, you get
88.5
Q.estimate the area of each polygon in square units.
i cant understand the question can someone help me and provide detailed explanation with the solution. please provide reasons so i can grasp the concept.
The area of the polygon is 12 square units. In mathematics and everyday life, an estimate is an approximate calculation or guess that is close to the actual value but may not be exact.
To make an estimate or guess, you can square off the parallelogram and create a rectangle and add your squares (or multiply 3x4) to = 12": This part explains a method for estimating the area of a parallelogram. It suggests that if you take a parallelogram and "square it off" (convert it into a rectangle by drawing a perpendicular line), you can then find the area of the rectangle, which is easier to calculate. In this case, the dimensions of the rectangle are given as 3 units for the base and 4 units for the height, and the estimated area is 12 square units.
You can use the formula for the exact area using base x height (3x4) you get the same answer of 12 square units": This part emphasizes that the estimation method used in step 2 (multiplying 3 by 4) produces the same result as the exact formula for finding the area of a parallelogram, which is base times height. In this case, both the estimation and the formula give an area of 12 square units.
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Which of the following statements about the scatter plot and the line of best fit are accurate? Select all that apply.
Answer:
- There are more points above the line than below
- This is not a line of best fit
Step-by-step explanation:
If we count the data points above and below the line, we can see there are about 4 below and 11 above. This means there are more points above the line than below. Since there are more points above the line than below, this is not a line of best fit.