The congruence theorem that would best prove the congruence of the triangles is SAS that is Side-Angle-Side.
What is congruence theorem?
Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another.
The figure, in this case a triangle, is congruent if and only if the corresponding sides and angles are equal in measurement. In this case we have BC being common to both triangles. Thus, one pair of corresponding sides is equal. Next, we have another pair of corresponding sides that are equal, AC and DC. Lastly, we have the included angles being equal to each other. Thus, the congruence theorem that would best prove the congruence of the triangles is SAS that is Side-Angle-Side.
Complete question: Triangles ABC and DBC have the following characteristics: BC is a side of both triangles ∠ACB and ∠DCB are right angles AC ≅ DC Which congruence theorem can be used to prove △ABC ≅ △DBC?
AAS
SSS
HL
SAS
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[tex]\frac{12}{y-x}[/tex] to a denominator of [tex]x-y[/tex]. What will the numerator be?
pls help
When 12 / (y -x) is a denominator of x - y the numerator will be
(x - y) (y -x)How to find the numerator of the fractionThe problem involves division of fractions
The fractions is a number type that has two major divisions,
the numerator : the number at the top
the denominator: the number below or at the bottom
The division of the fraction: In this case the denominator is the divisor
= (x - y) ÷ 12 / (y -x)
inverting the divisor of the fraction
= (x - y) * (y -x)/12
= { (x - y) * (y -x) } / 12
the numerator is (x - y)(y -x)
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The regular price of a desk is $97.98. This week, it is on sale for $94.96 off. What is the sale price of the desk?
Answer:
$3.02
Step-by-step explanation:
You just subtract 97.98-94.96.
Answer:
3.02
Step-by-step explanation:
you subtract 94.96 from 97.98
a wooden cuboid has an open flame base with a square surface with 1.2 m sides and a height of 0.25 m. Find the surface of the cuboid.
Answer:
2.64 square meters.
Step-by-step explanation:
To find the surface area of a cuboid, you need to find the area of each of the six faces and add them together. A wooden cuboid with an open flame base that has a square surface with 1.2 meter sides and a height of 0.25 meters would have a surface area of 1.2 * 1.2 + 4 * (1.2 * 0.25) = 1.44 + 1.2 = 2.64 square meters. This is because the base of the cuboid has an area of 1.2 * 1.2 = 1.44 square meters, and each of the four sides has an area of 1.2 * 0.25 = 0.3 square meters. The total surface area of the cuboid is therefore the sum of these areas: 1.44 + 4 * 0.3 = 2.64 square meters.
fifteen students are competing for 4 rotary scholarships, 1 in england, 1 in germany, 1 in brazil, and 1 in japan. in how many ways can the scholarships be awarded to different students?
The number of different ways of distributing the scholarships is 32,760.
consider the situation: fifteen students are competing for 4 Rotary scholarships.
consider each scholarship is to be a position In which a student assigned.
This is a permutation problem as:
A) each student selected from the same set.
b) No students can be selected twice.
c) The order in which students are assigned to three scholarships.
Four students are assigned in 4 activities For scholarships.
Activity A1: select a student from the set of 15 students for giving away the first scholarship.
Activity A2: select a student from remaining 14 students for giving away the second scholarship.
Activity A3: select a student from remaining 13 students for giving away the third scholarship.
Activity A4: Select a student from remaining 12 students for giving away the forth scholarship.
According to multiplication rule of accounting the number of different arrangements is A1 X A2 X A3 X A4
15 X 14 X 13 X 12=32760
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Adurey is making a scale drawing of her drawing of her rectangular bedroom. on her drawing a 10-foot wall is 8 inches. Audrey wants to add a 7-foot wall to her scale drawing. Which equation can she use to find how long she should make the wall in her drawing
The length of the wall in her drawing is given as follows:
5.6 inches.
How to obtain the length of the wall in the drawing?A scaling measurement represents the proportion of a total dimension, as it is the ratio between the length of the drawing with the actual length of the object.
On her drawing a 10-foot wall is 8 inches, hence the scale measurement for this problem is given as follows:
8 inches/10 feet = 0.8 inches per feet.
The scale means that each feet of an actual object is represented by a length of 0.8 inches on the drawing.
Audrey wants to add a 7 foot wall to the drawing, meaning that the length of the drawing is given as follows:
7 x 0.8 = 5.6 inches.
(applying the proportion found from the scale measurement).
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two fair dice are rolled. The score is the difference between the two dice.
In a dice, there is a six side
Probability of occurring a score = 1/18
= 1*2/18*2
= 2/36
= preferred outcome/ Total outcome
Only 5 is a number that has occurred twice
The score that has a probability of occurring of 1/18 is 5.
The two dice having different values 30/36 = 5/6 (because the probability of the two dice having equal values is 6/36 = 1/6.)
The probability of the second dice being less than the first dice is the same as the probability of the first dice is less than the second dice: (5/6) / 2 = 5/12.
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33) A farmer needs to construct a bridge over a stream to connect fields for his sheep to graze. He will do most
of the planning on his own. Name some measurements that will need to be made by a professional engineer.
Answer:
There are several measurements that a professional engineer would need to make in order to design and construct a bridge over a stream for a farmer's sheep to graze. These measurements may include:
Width and depth of the stream: The engineer will need to determine the width and depth of the stream in order to determine the size and type of bridge that is needed.
Soil composition and stability: The engineer will need to assess the soil composition and stability of the area surrounding the stream in order to determine the foundation and support structure needed for the bridge.
Water flow: The engineer will need to measure the water flow in the stream in order to determine the load-bearing capacity of the bridge and to ensure that it is able to withstand the forces of the water.
Distance between the two banks: The engineer will need to measure the distance between the two banks of the stream in order to determine the length of the bridge and ensure that it is long enough to span the stream.
Height of the banks: The engineer will need to measure the height of the banks of the stream in order to determine the height of the bridge and ensure that it is tall enough to allow the sheep to pass under it.
Point D, E, and F are midpoint of the ide of ΔABC. The perpendicular biector of AB i m, and the perpendicular biector of BC i n. Line m and n interect at T. If TA=5. 9, what i TC?
The value of TC = 5.9
According to the given figure of the triangle ABC, (refer to the attached figure)
The length of perpendicular bisector AC is = m
The length of perpendicular bisector BC is = n
The point at which line m and line n are intersecting = T
Given the value of TA = 5.9
According to the corner theorem.
AC = CF
So, ΔTFA ≅ ΔTFC
⇒ TA = TC = 5.9
Therefore, The value of TC = 5.9
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The price of an airline ticket from New Orleans to Boston increased to $550. This is a 30% increase.
To the nearest cent, what is the old fare?
A $397.67
B $423.08
C $412.14
D $501.40
The value of the old fare to the nearest cent will be $423.08. Then the correct option is B.
What is the percentage?Any product's quantity is presented as if it were a percentage of one hundred. The proportion can be written as 1/4 of 100. One hundred percent is symbolized by the symbol %. The sign for it is the letter "%".
The cost of an aircraft ticket from New Orleans to Boston expanded to $550. This is a 30% expansion.
Let 'x' be the old fare. Then the equation is given as,
(1 + 0.30) x = $550
Simplify the equation, then we have
(1 + 0.30) x = $550
1.30 x = $550
x = $550 / 1.30
x = $423.08
The worth of the old admission to the closest penny will be $423.08. Then the right choice is B.
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For funsies, find what w equals to.
−4w + 2 = 14
[tex]-4w+ 2 = 14[/tex]
Subtract 2 from both sides:
[tex]-4w+2-2=14-2[/tex]
[tex]-4w=12[/tex]
Divide both sides by -4:
[tex]\dfrac{-4w}{-4} =\dfrac{12}{-4}[/tex]
[tex]= \fbox{w = -3}[/tex]
Answer:
w = -3
Step-by-step explanation:
-4w + 2 = 14
-4w + 2 - 2 = 14 - 2 (Subtract 2 from both sides)
-4w = 12
-4w/-4 = 12/-4 (Divide -4 from both sides)
w = -3
Triangle A and Triangle B are right triangle. Triangle A ha a height of 8 meter and a bae of 6 meter. Triangle B ha a height that i one unit greater than triangle A and a bae that i one unit le. Part A
What i the meaure of the hypotenue of triangle A? Show your work
Triangle A and Triangle B are right triangle. Triangle A ha a height of 8 meter and a bae of 6 meter. then The length of one of the legs of the triangle is 10 units.
An isosceles triangle has a base length of 126 units and a height of 16 units. We need to find out the length of one of the legs of the triangle.
First of all, we will consider a perpendicular bisector of the triangle. This divides the given triangle into two equal right-angled triangles. Now, in the smaller triangle, we will use the Pythagorean theorem.
Let the length of the leg be represented by the variable "x". The length of the base of the right-angled triangle is half the length of the base of the original triangle.
x² = (6)² + (8)²
x = sqrt ( 36+64)
x = √100
x = 10
Hence, the length of one of the legs of the triangle is 10 units.
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a street light is mounted at the top of a 15-foot tall pole. a man 6 feet tall walks away from the pole with a speed of 5 ft/sec along a straight path. how fast is the tip of his shadow moving when he is 40 feet from the pole?
The tip of man's shadow moving with speed of 25/3 ft/sec, when he is 40 feet from the pole.
We have, height of street light on pole,
AB = 15ft.
Height of man , BC = 6 ft.
Speed of man walks away from the pole.
= 5 ft/sec
This problem is look like a time rate problem , Let us consider x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole, i.e,
length of Shadow, CE =( y -x) ft
We assume the man and pole are standing straight up, which means the 2 triangles are similar. By similarity of triangles, (y − x)/y = 6/15
=> 15(y-x) = 6y
=> 15y - 15x = 6y
=> 15y - 6y = 15x
=> 9y = 15x
=> y = (15/9)x = (5/3)x
differentiate the above equation with respect to t or time.
dy/dt = (5/3)dx/dt
We know that, dx/dt = 5 ft/sec because the man is walking that speed away from the pole. We want to calculate dy/dt, how fast the tip of the shadow is moving when y = 40 feet
dy/dt = (5/3) (5) = 25/3 ft/sec.
We see actually, the man's distance from the pole doesn't matter since only his speed affects how fast his shadow moves. Hence, the tip of the shadow is moving with speed of 25/3 ft/sec.
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for the capacitor network shown in (figure 1) , the potential difference across ab is 48 v .
The charge on the 150 nF capacitor is 3200 nF, the charge on the 120 nF capacitor is 3200 nF, the total energy stored in the network is [tex]76.8 \times 10^{-6} \mathrm{~J}[/tex], the energy stored in the 150 nF capacitor is [tex]34.1 \times 10^{-6} \mathrm{~J}[/tex], the energy stored in the 120 nF capacitor is [tex]42.67 \times 10^{-6} \mathrm{~J}[/tex], the potential difference across the 120 nF and 150 nF capacitor is 21.33V, 26.67 V.
The equivalent capacitance when the capacitors are connected in series is,
[tex]$$C_{\text {eq }}=\left(\frac{1}{C_1}+\frac{1}{C_2}\right)^{-1}=\left(\frac{1}{150 \mathrm{nF}}+\frac{1}{120 \mathrm{nF}}\right)^{-1}=66.67 \mathrm{nF}$$[/tex]
the charge on each capacitor remains the same because they connected in series. Hence, the charge on each capacitor is,
Q=C V=(66.67 nF) (48 V)=3200 nC
the charge on the 150 nF capacitor is [tex]Q_{150}[/tex]=3200 nC
the charge on the 120 nF capacitor is [tex]Q_{120}[/tex]=3200 nC
the total energy stored in the network is,
[tex]$$$U=\frac{Q^2}{2 C}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(66.67 \times 10^{-9} \mathrm{~F}\right)}=76.8 \times 10^{-6} \mathrm{~J}$$[/tex]
the energy stored in the 150 nF capacitor is,
[tex]$U=\frac{Q_{150}{ }^2}{2 C}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(150 \times 10^{-9} \mathrm{~F}\right)}=34.1 \times 10^{-6} \mathrm{~J}$$[/tex]
the energy stored in the 120 nF capacitor is,
[tex]$U=\frac{Q_{150}{ }^2}{2 \mathrm{C}}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(120 \times 10^{-9} \mathrm{~F}\right)}=42.67 \times 10^{-6} \mathrm{~J}$$[/tex]
the potential difference across the 150 nF capacitor is,
[tex]$$V_{150}=\frac{Q_{150}}{C_{150}}=\frac{3200 \times 10^{-9} \mathrm{C}}{150 \times 10^{-9} \mathrm{~F}}=21.33 \mathrm{~V}$$[/tex]
the potential difference across the 120 nF capacitor is,
[tex]$$V_{120}=\frac{Q_{100}}{C_{120}}=\frac{3200 \times 10^{-9} \mathrm{C}}{120 \times 10^{-9} \mathrm{~F}}=26.67 \mathrm{~V}$$[/tex]
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QN:-- For the capacitor network shown in (Figure 1) , the potential difference across ab is 48 V .
Find the charge on the 150 nF capacitor.
Find the charge on the 120 nF capacitor.
Find the total energy stored in the network.
Find the energy stored in the 150nF capacitor.
Find the energy stored in the 120nF capacitor.
Find the potential difference across the 150 nF capacitor.
Find the potential difference across the 120 nF capacitor.
Jessica is building a fence around her garden. For every 3 feet of fencing, the cost is $27. Complete the table below showing the length of the fence and the cost.
The complete table is
Length of fencing(feet) 1 3 6 9 10
cost($) 9 27 54 81 90
What is fencing of a wall?
A fence is a building used to enclose a space, usually outdoors. It is often made of posts joined by boards, wire, rails, or nets. In contrast to a wall, a fence lacks a firm basis over its whole length.
The cost of fencing 3 feet is $27.
Applying unitary method:
The cost of fencing 1 feet is $27/3 = $9.
The cost of fencing 6 feet is $(6×9) = $54
The cost of fencing 10 feet is $(10×9) = $90.
$27 needs to make a fencing with length 3 feet.
$1 needs to make a fencing with length 3/27 feet = 1/9
$9 needs to make a fencing with length (1/9)× 9 = 1 feet.
$81 needs to make a fencing with length (1/9)× 81 = 9 feet.
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Order the fractions below from least to greatest.
The numbers are 5/6, 2/3, and 1/2.
Please write the fractions like this
Least ____
Middle _____
Greatest ______
Answer: Least 1/2
Step-by-step explanation: Middle 2/3
Greatest 5/6
Answer:
Least 1/2
Middle 2/3
Greatest 5/6
Step-by-step explanation:
First,5 divided by 6,is 0.83(in to 1 decimal point)
Then 2 divided by 3 is 0.67(in to 1 decimal point)
Last 1 divided by 2 is 0.5(in to 1 decimal point)
So is 5/6 is greatest and 2/3 is in the middle and the least is 1/2.
when some of the variables represent categories, we can apply a useful summarization method called tabulation, where we simply count how many people or items are in each category or combination of categories. true false 1.25 points question 1 of 8 next question last questionunsaved change moving to another question will save this res
The given statement is true for tabulation method representing the variable different categories and summarize it in tabulation method makes the calculation simple.
As given in the question,
Let the variable 'x' , 'y' , and 'z' represent some different categories.To simplify the data represent the category in tabulation form.Each category represent the frequency of its own.Now to do the calculation simply count the number of items present in each category.This makes the calculation simple and easy to handle.Therefore, the given statement of representing the variable different categories and summarize it in tabulation method makes the calculation simple is a true statement.
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16.8 Divided by 0.27
Please help me with this question
many thanks
Can you help me with this
Answer:
X = add 25 Y =add 3 see 3 ,3+3=6 so i think y is 3
Step-by-step explanation:
Complete the following statement. Write your answer as a decimal or whole number % of $70 = $28
Answer:
40%
Step-by-step explanation:
You want to know what percent of $70 is $28.
EquationThe question can be written as an equation, using a variable for the unknown percentage:
x% · $70 = $28
SolutionThe percent sign can be considered to be fully equivalent to "/100". Dividing by dollars on both sides, we can rewrite the equation as ...
x/100 · 70 = 28
Dividing by the coefficient of x gives ...
x = 28/0.70
x = 40
The complete statement is ...
40% of $70 = $28
__
Additional comment
If you're comfortable with writing decimal fractions as percentages, and vice versa, you can do without the %, and simply write ...
x · 70 = 28
x = 28/70 = 0.40 = 40%
This tells you 40% of $70 is $28, which is what you want to know.
The radius of the circle is 13cm. what is the circumference of the circle 3.14
Answer:
Step-by-step explanation:
81.64
Please help me answer this question
Step-by-step explanation:
photo is not clear post again.
suppose that 90% of the patients with a certain disease can be cured with a certain drug. what is the approximate probability that, of 50 such patients, at least 45 can be cured with the drug?
The approximate probability that at least 45 of 50 patients can be cured with the drug is 0.788.
To find the approximate probability that at least 45 of 50 patients can be cured with the drug, we can use the binomial formula. The binomial formula allows us to calculate the probability of a certain number of success out of a set of trials given a certain probability of success for each trial. In this case, we have a probability of success of 0.9 and 50 trials. Therefore, the probability of at least 45 of the 50 patients being cured with the drug is 0.788. This can be calculated using the binomial formula or a binomial probability calculator.
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as we wrap this up for stat 3113, recall that in class, we talked about how the statistics and could be calculated from a sample of data but that the parameters and could not be calculated. why is this?
Parameters are values that describe the entire population, while statistics are values that describe only a sample of the population. Since there is no way to know the exact values of the parameters, they cannot be calculated from a sample of data.
Parameters are values that describe the characteristics of the entire population. They are used to make inferences about the population and provide a basis for making decisions. On the other hand, statistics are values that describe only a sample of the population. They are used to estimate the parameters of the population. Since it is not possible to know the exact values of the parameters, they cannot be calculated from a sample of data. Instead, we use statistics to estimate the parameters. This is why it is important to use a representative sample when collecting data, as it provides a better estimate for the population parameters
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solve the equations using elimination -8x+y=-8; 6x-y=6
Answer:
x = 1 y = 0
Step-by-step explanation:
-8x + y = -8
6x - y = 6
y have the same coefficient but one is negative and the other is positive therefore we add both the equations
we get:
-2x = -2
divide both sides by -2
x = 1
now as we have the value of x we can input this into any one of the starting equations
-8x + y =-8
-8(1) +y = -8
-8 + y = -8
add 8 to both sides
y = 0
Answer:
(1, 0 )
Step-by-step explanation:
- 8x + y = - 8 → (1)
6x - y = 6 → (2)
adding (1) and (2) term by term will eliminate y
- 2x + 0 = - 2
- 2x = - 2 ( divide both sides by - 2 )
x = 1
substitute x = 1 into either of the 2 equations and solve for y
substituting into (1)
- 8(1) + y = - 8
- 8 + y = - 8 ( add 8 to both sides )
y = 0
solution is (1, 0 )
what is 52,437 rounded to the nearest hundred.
Answer: 52,000
Step-by-step explanation: Because we are rounding to the nearest hundred, we only need to focus on the #'s 4, 3, and 7 in 52,437. So, 3 is less than 5, so we have to round down to 3 (stays the same) and 4 is less than 5 so, we round down to 4 (also stays the same), and since 7 is greater than 5, we can round up to 440. But, 440 is still less than 500, so your final answer should be 52,000.
what is the equation of the horizontal line that intersects the graph of the line y=4x+7 at x= -2?
Answer:
y = -1
Step-by-step explanation:
y = 4 · -2 + 7
y = -8 + 7
y = -1
Two sides of a triangle my 8 Ickes and 10 inches , respectively. Which one these is NOT a possible length for the third Sid elf a triangle please show ur work Bc I have too
A) 12 inches
B) 16 inches
C) 17inched
D)18 inches
18 inches is not a possible length for the third side of a triangle
What is the triangle inequality theorem?
The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the remaining side.
By triangle inequality theorem:
This theorem states that the sum of any two sides of a triangle must be greater than the third side.
As per the statement:
A triangle has two sides of lengths 8 inches and 10 inches.
Let the third side be x.
The Sum of the two sides is:
8 + 10 = 18
By triangle inequality theorem:
18 > x
or
x < 18
⇒ the length of the third side must be less than 18
From the given options:
Length of third sides 12, 16, and 17 which are less than 18.
the value which could the length of the third side be are: 12, 16, and 17.
Hence, 18 inches is not a possible length for the third side of a triangle
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Is the line perpendicular?
The situation is based on football. One player starts a couple of yards in the endzone while the other starts at the 8-9 yard line. The player in the endzone almost scores when he is tracked down by the guy on the 8-9 yard line. So does the starting position of these players form a perpendicular line?
Yes, the starting position of these players form a perpendicular line.
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
Using Trigonometry
sin [tex]\theta[/tex] = 33.33/100
sin [tex]\theta[/tex] = 0.3333
[tex]\theta[/tex] = [tex]sin^{-1}[/tex] (0.3333)
[tex]\theta[/tex] = 19.469
cos 19.469 = B/ 100
0.9428 = B/ 100
B= 94.28
tan [tex]\theta[/tex] = P/B
tan [tex]\theta[/tex] = 94.28/ 33.33
[tex]\theta[/tex] = 70.5
Using Angle Sum property
< 3= 180 - (70.5 + 19.5)
<3 = 180 - 90
<3 = 90
Hence, they form perpendicular line.
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the distance between parallel lines 4y=3x-1 and 8y=6x-7
Answer: The distance between the two parallel lines is 11/12.
Step-by-step explanation:
The distance between two parallel lines can be found by calculating the difference between the y-intercepts of the two lines. In this case, the y-intercept of the first line is (-1/4,0), and the y-intercept of the second line is (-7/6,0). The difference between these y-intercepts is (-1/4 - (-7/6)) = 11/12. Therefore, the distance between the two parallel lines is 11/12.