Answers
Yes, the given pair of triangles are congruent by ASA rule.
What are congruent triangles?In geometry, two triangles are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Given are two triangles, labelling by names, (refer to the image attached)
Considering the triangles, Δ ABC and Δ DEC,
We have,
AC = DC [given]
∠ A = ∠ D [both are congruent]
∠ ACB = ∠ DCE [vertically opposite angles]
∴ Δ ABC ≅ Δ DEC
By ASA rule.
Hence, we can say, the given pair of triangles are congruent by ASA rule.
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Related Questions
Solve for x in the following circle: D X 140⁰E 160
Answers
10 degrees is the measure of angle x from the circle
Theorems in circle geometryIn order to determine the value of x from the given circle, we will use the theorem ' angle at the centre of the circle is twice the angle at the circumference.
Mathematically;
360 - 140 = 2arcED
220 = 2arcED
arcED = 220/2
arcED = 110 degrees
Hence the measure of angle x from the given figure is 110 degrees
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If point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, -x).
Answers
The statement "If point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, -x)." is incorrect.
The origin of the coordinate plane is the point (0, 0), and it is the center of rotation for many geometric transformations.
When a point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, x). This is because rotation by 90 degrees counterclockwise causes the x-coordinate to become the negative of the original y-coordinate and the y-coordinate to become the original x-coordinate.
To see this, imagine the point (x, y) on the coordinate plane and draw a line segment connecting the point to the origin. The length of this line segment is given by the Pythagorean theorem as the square root of x² + y². After rotating the point 90 degrees about the origin, the line segment will be perpendicular to the original line segment and have a length equal to y and -x.
In summary, rotating a point (x, y) at 90 degrees about the origin results in the point (-y, x) due to the change in the direction and length of the line segment connecting the point to the origin.
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Identify the x-intercept and y-intercept of the line 3x - 6y= - 12.
Answers
Answer: x intercept: -4, y intercept: 2 (look at the image for the solution)
Step-by-step explanation:
Answer:
x intercept: -4, y intercept: 2
Step-by-step explanation:
how much is a 1 gallon to litre?
Answers
The gallon is a unit of volume that represents the capacity of a liquid in both conventional and US imperial systems of measurement. 1 gallon is defined as 4.54609 liters.
Gallon:
The gallon is a common unit of volume in both English and US customary units. There are three types of gallons in use today: Imperial Gallon, US Gallon, and US Dry Gallon. There are 4 quarts in a gallon, for a total of 8 pints, and each system has a different volume.
Current use of the imperial gallon as of 2021 is still used as the standard unit of petrol in four British overseas territories. It is also the standard unit of measure for six countries: Antigua and Barbuda, Grenada and Saint Lucia.
Liter:
A liter is a metric unit of volume. A liter costs 1/1000 of a cubic meter. The liter was used as the base unit of the basic French metric system. 1 liter is the volume of a cube, i.e. 10 cm x 10 cm x 10 cm, so 1 liter = 1000 cm3 and 1 liter = 0. 2641720524 gallons.
This unit of volume can be used in the International System of Units even though it is not an SI unit. Current use of liters . The liters are primarily used for pourable items (these items can be solid or liquid). These items are measured by the size or capacity of the container. It is also used to measure non-liquid volumes such as backpacks, car trunks, etc.
Formula for Converting Gallons to liters
The formula for converting 1 gallon of water in liters is :
Liter = Gallon x 3.785411784
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elevation of 30 feeet below sea level
Answers
The elevation of the diver after the dive can be found to be 42 feet below sea level or - 42 feet.
How to find the elevation ?If the diver's elevation is -30 feet relative to sea level, and she dives down 12 feet, we can find her new elevation by adding the change in depth to her initial elevation:
New elevation = Initial elevation + Change in depth
New elevation = - 30 feet + ( - 12 feet )
New elevation = - 42 feet
Therefore, the diver's new elevation after the dive is -42 feet relative to sea level.
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The full question is :
A divers elevation is -30 feet below sea level. She dives down 12 feet. What is her elevation after the dive?
For a project in her Geometry class, Ai Mi uses a mirror on the ground to measure the height of her school building. She walks a distance of 7.95 meters from the building, then places a mirror flat on the ground, marked with an X at the center. She then walks 2.3 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the school clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.15 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.
Answers
The height of the school is approximately 5.96 meters.
What is geometry?Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.
The mirror and the triangles formed by the mirror, the top of the school, and the ground are similar. This means that the corresponding sides of the triangles are proportional.
Let x be the distance from the mirror to the top of the school. Then:
[tex]\dfrac{x} {7.95} = \dfrac{(x + h) }{ 2.3}[/tex]
We can simplify this equation by cross-multiplying and solving for x:
2.3x = 7.95(x + h)
2.3x = 7.95x + 7.95h
5.65x = 7.95h
[tex]x = \dfrac{7.95h} { 5.65}[/tex]
Now we can use the measurement of the distance from Ai Mi's eyes to the ground to find h. Let d be the distance from the mirror to Ai Mi's eyes. Then:
d = 1.15 meters
The triangles formed by Ai Mi's eye, the mirror, and the ground are similar, so:
[tex]\dfrac{h} { d} =\dfrac{ x} { (d + 2.3)}[/tex]
We can substitute the value of x from earlier:
[tex]\dfrac{h} { 1.15} = \dfrac{(\dfrac{7.95h} { 5.65)}} { 3.45}[/tex]
Simplifying:
[tex]h = \dfrac{(1.15 \times 7.95\times 3.45)}{ 5.65}[/tex]
h = 5.96 meters
Therefore, the height of the school is approximately 5.96 meters. Rounded to the nearest hundredth of a meter, the answer is 5.96 meters.
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A company sells orange juice in spherical containers that look like oranges. Each container has a surface area of approximately 50.3 sq.in. What is the volume of the container?
Answers
We can determine the radius of the container using the formula for a sphere's surface area because it resembles an orange and has a surface area of roughly 50.3 square inches:
A sphere's surface area equals [tex]4 r^2[/tex].
where r denotes the sphere's radius.
50.3 sq. = 4πr²
By multiplying both sides by 4, we obtain:
r² = 50.3 sq. / (4π)
r² ≈ 4
When we square the two sides, we obtain:
r ≈ 2
Hence, the spherical container has a radius of around 2 inches.
The volume of the container can now be calculated using the following formula:
A sphere's volume equals [tex](4/3)r^3[/tex].
Container volume = (4/3) X(23)
The container's volume is 33.5 cubic inches.
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what is -0.28125 to 6 decimal places
Answers
Answer:
[tex]-0.281250[/tex]
Step-by-step explanation:
The given number has [tex]5[/tex] after the decimal point, so add a trailing zero.
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
9
72
36
27
81
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
O The college will have about 640 students who prefer cookies.
O The college will have about 1,280 students who prefer cookies.
O The college will have about 1,440 students who prefer cookies.
Answers
Using inferential statistics, it is found that the option that is best surveyed from the collected in the survey is given by:
D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.
What is an inferential statistic?An inferential statistic is one that makes inference or predictions about a population based on a sample.
From the table, we have that cookies and cream is the most popular flavor, hence the correct option is:
D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.
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The question is in the picture.
Answers
Answer:
x = 9 , y = 5
Step-by-step explanation:
Consider the figure to be a parallelogram.
• the diagonals bisect each other
then
2x - 4 = x + 5 ( subtract x from both sides )
x - 4 = 5 ( add 4 to both sides )
x = 9
and
9y - 13 = 5y + 7 ( subtract 5y from both sides )
4y - 13 = 7 ( add 13 to both sides )
4y = 20 ( divide both sides by 4 )
y = 5
please help me!!:)
MULTIPLE CHOICE QUESTION
A car was purchased in 2010 for $20,000.
The car is depreciating by 15% each year.
What is the "a" value?
Answers
Answer:
20,000
Step-by-step explanation:
I'm assuming your class is using this model of the exponential decay function:
f(x) = a(1 - r)^x
In this case, the equation would be:
f(x) = 20,000(1 - .15)^x
or, when 1 - r is calculated:
f(x) = 20,000(.85)^x
The "a" value is basically the starting value, because on a graph, the starting value would be where x = 0. Anything to the 0th power is 1, and anything multiplied by 1 is the same thing, making "a" the same as the starting value, or the y-intercept.
Therefore, a = 20,000.
Hope this helps!
this is my question
Answers
The correct answer is B. 2
WHAT IF? The total cost of the vans for Location A is $228,500. The total cost for Location B is $153,000. What is the cost of
each type of van? Location A buys 7 large and 2 small vans, location B buys 2 large and 3 small vans
Answers
The cost of each large van is 22,323.53 and each small van is 36,117.65.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Let x be the cost of a large van and y be the cost of a small van.
The total cost of the vans for Location A is $228,500.
Location A buys 7 large and 2 small vans.
So we have a linear equation,
7x + 2y = 228,500
The total cost for Location B is $153,000.
Location B buys 2 large and 3 small vans.
So we have a linear equation,
2x + 3y = 153,000
Multiplying the first equation with 3 and the second equation with 2,
21x + 6y = 685,500
4x + 6y = 306,000
Subtracting,
17x = 379,500
x = 22,323.53
Substituting in one of the equation,
y = 36,117.65
Hence the cost of each large and small van are 22,323.53 and 36,117.65 respectively.
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A university has 36,180 students. In a random sample of 210 students, 14 speak three or more languages. Predict the number of students at the university who speak three or more languages.
The expected number of students at the university who speak three or more languages is __________.
Answers
Answer:
2,412
Step-by-step explanation:
[tex]\displaystyle E(X)=np=(36180)\biggr(\frac{14}{210}\biggr)=2412[/tex]
Therefore, we can expect 2,412 students at the university to speak 3 or more languages.
In the diagram, segment AD bisects angle BAC.
Given the following segment lengths, find the value of x.
Round to the nearest tenth.
AB: 19
AC: 17
Show all your work
Answers
The length of side x is 10 units
How to determine the length of side xFrom the question, we have the following parameters that can be used in our computation:
Segment AD bisects angle BAC.
Using the above as a guide, we have the following:
BD = DC
substitute the known values in the above equation, so, we have the following representation
x = 20 - x
Evaluate the like terms
2x = 20
Divide by 2
x = 10
Hence, the value of x is 10
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how many cubic feet to liters?
Answers
One cubic foot is equal to approximately 28.3168 liters. So to convert cubic feet to liters, you can multiply the number of cubic feet by 28.3168.
Unit conversion is the process of converting a value expressed in one unit of measurement to an equivalent value expressed in another unit of measurement. For instance, to convert 10 feet to meters, you would use the conversion factor 1 foot = 0.3048 meters.
For example, if you have a volume of 5 cubic feet, you can convert it to liters as follows:
5 cubic feet * 28.3168 liters/cubic foot = 141.584 liters
Therefore, 5 cubic feet is equivalent to 141.584 liters (approximately).
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A marketing assistant for a technology firm plans to randomly select 1000 customers to estimate the proportion who are satisfied with the firm's performance. Based on the results of the survey, the assistant will construct a 95% confidence interval for the proportion of all customers who are satisfied. The marketing manager, however, says that the firm can afford to survey only 250 customers. How will this decrease in sample size affect the margin of error and confidence interval? True Statements False Statements The margin of error will be about 2 times larger. The margin of error will be about 4 times larger The margin of error will be about the same size. The margin of error will be about half as farge. The margin of error will be about one-fourth as large. The confidence interval will be wider. The confidence interval will be narrower.
Answers
The margin of error can be calculated using the formula:
Margin of error = z * √(p * (1 - p) / n)
where z is the z-score for a desired confidence level, p is the estimated proportion of satisfied customers, and n is the sample size. As the sample size decreases, the margin of error increases. So, in this case, the margin of error will be about 4 times larger with a sample size of 250 compared to a sample size of 1000.
The width of the confidence interval is determined by the margin of error and the sample size. As the margin of error increases, the confidence interval becomes wider. So, the confidence interval will be wider with a sample size of 250 compared to a sample size of 1000.
In summary, the decrease in sample size from 1000 to 250 will result in a larger margin of error and a wider confidence interval. None of the options in the list are completely true.
3. Xavier has $43 in his savings account and plans to save $15 each week. Write an algebraic expression to represent how much Xavier will have in his savings account after w weeks.
Answers
An algebraic expression representing the amount Xavier will have in his savings account after w weeks is 43 + 15w.
What is algebraic expression?Algebraic expressions consist of numbers, variables, and the mathematical operations, especially addition, subtraction, division, and multiplication.
An algebraic expression does not have the equation symbol (=) unlike an equation because it is not a complete mathematical statement.
The amount Xavier already has in his savings account = $43
The planned weekly savings = $15
The period of savings = w
Algebraic Expression:43 + 15w
Thus, using an algebraic expression, after w weeks, Xavier will have 43 + 15w in his savings account.
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Again no rush need an answer in about 5 hours or so I’d say!
Answers
The amount of square feet that will be needed is given as follows:
122 ft².
How to obtain the amount of square feet needed?The amount of square feet needed is given by the total area of the figure, which is composed as follows:
Rectangle of dimensions 6 ft and 15 ft.Trapezoid of bases 6 ft and 10 ft, along with height 4 ft.The area of the rectangle is given by the multiplication of the dimensions, hence:
Ar = 6 x 15 = 90 ft².
The area of the trapezoid is given by half the multiplication of the sum of the bases and the height, hence:
At = 0.5 x 4 x (6 + 10) = 32 ft².
Hence the total area is given as follows:
A = Ar + At
A = 122 ft².
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The table below shows the ratios of black to white keys on pianos of various sizes.
Black A 36 63 90
White 13 B 91 C
Determine which table has the correct values for A, B, and C.
Answers
The following table contains the appropriate values for A, B, and C:
White 13 52 91 130 Black 9 36 63 90
What does "proportional relationship" mean?Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them. This parameter is referred to as the "constant of proportionality". We'll now look at an instance of a proportionate relationship in real life: The amount of money we will have to spend while filling up our automobile with gas is inversely proportional to the number of gallons we put in the tank. In other words, the amount of gas we use will determine how much we pay.The definition of a proportionate relationship is as follows:
y = kx.
where k is the proportionality constant.
The following are the input and output variables for this issue:
Number of black keys to enter.
Number of white keys is the output.
The constant k is then obtained using the formula:
91 = 63k
k = 91/63
k = 13/9.
Hence the equation is:
y = 13x/9.
Hence the values are given as follows:
A: when x = 9, y = 13.
B: when x = 36, y = 13 x 36/9 = 52.
C: when x = 90, y = 13 x 90/9 = 130.
Hence the first table is correct.
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The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: "The poll has a margin of error of plus or minus three percentage points at a 95% confidence level." You can safely conclude that
A. 95% of all Gallup Poll samples like this one give answers within ±3% of the true population value.
B. the percent of the population who jog is certainly between 15% and 21%.
C. 95% of the population jog between 15% and 21% of the time.
D. we can be 95% confident that the sample proportion is captured by the confidence interval.
E. if Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.
Answers
The correct answer is option D. We can be 95% confident that the sample proportion is captured by the confidence interval.
The margin of error of plus or minus three percentage points at a 95% confidence level means that the true proportion of people who jog regularly in the population is estimated to be between 15% and 21%. We can be 95% confident that the true proportion of people who jog regularly falls within this interval.
Therefore, option B is correct. Option A is incorrect because it implies that the margin of error always holds true for any sample size, which is not the case. Option C is incorrect because it presents a range of values for the population, not for the estimate. Option E is incorrect because it refers to the proportion of samples that would find the same sample proportion, not the range of values within which the true proportion lies.
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Camden went to the grocery store and purchased cans of soup and frozen
dinners. Each can of soup has 150 mg of sodium and each frozen dinner has
300 mg of sodium. Camden purchased a total of 7 cans of soup and frozen
dinners which collectively contain 1500 mg of sodium. Graphically solve a
system of equations in order to determine the number of cans of soup
purchased, x, and the number of frozen dinners purchased, y.
Answers
Answer:
First off that is my name.
y=-0.5x+5 is the first equation. I don't know the second.
Sorry
Step-by-step explanation:
(3c)° 42° 111°
Find the value of C in the figure
Answers
9 is the value of C.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The three given angles are (3c)° 42° 111°
We need to find the value of C.
The figure might be a triangle because there are three angles.
From angle sum property , the sum of three angles of triangle is 180 degrees.
3c+42+111=180
3c+153=180
Substitute 153 from both sides
3c=27
Divide both sides by 3
c=9
Hence, the value of c is 9.
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3.
Consider this system of equations: y = - +4
3x - 4y = 12
Solve the system by graphing.
Click the line tool and select two points to create the line.
Select the point where the lines intersect and label the point. You will need to use decimal notation instead of fraction notatic
in your label.
Answers
Answer:
(4,0)
Step-by-step explanation:
I will assume the fiorst equation is missing an "x," so I'll assume it was meant to be: y = -x + 4
See the attached graph. The lines cross at (4,0).
You are making a round flower garden in your yard. The circumference of the garden will be 60 inches. What is the diameter? Use 3.14 to approximate pi. Round to the nearest tenth.
Answers
The diameter of the circular garden round to the nearest tenth will be 19.1 inches.
What is the diameter of a circle?In a circle, an infinite number of diameters can be drawn. A diameter is a straight line passing through the center and joins two points of the circumference of a circle. The length of a diameter is twice the length of the radius.
The circumference of a circle is given by C = πd, where d is the diameter of the circle and π can be taken as 3.14.
Substitute C = 60 and π = 3.14 into the above formula and find d.
60 = 3.14×d
d = 60/3.14
≈ 19.108
≈ 19.1
Therefore, the obtained answer is 19.1 inches.
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(6e-3-4)x2. Please help me solve this
Answers
Answer:
-7.988 or -2E
Step-by-step explanation:
What are the coordinates of the point (−9, −5) after being reflected across the y-axis on a coordinate plane?
Answers
To reflect a point across the y-axis, you multiply the x-coordinate of the original point by -1 while keeping the y-coordinate the same. So, reflecting the point (-9, -5) across the y-axis results in the point (9, -5).
Answe
To reflect a point across the y-axis, you multiply the x-coordinate of the original point by -1 while keeping the y-coordinate the same. So, reflecting the point (-9, -5) across the y-axis results in the point (9, -5).
Step-by-step explanation:
What is "a" in the equation
a/2.1 = 4.34
Answers
Answer:
a = 9.114
Step-by-step explanation:
[tex]\frac{a}{2.1}[/tex] = 4.34 ( multiply both sides by 2.1 to clear the fraction
a = 2.1 × 4.34 = 9.114
(3x^3+7x-1) +4x^3-9x^2-11x+1) urgent need
STANDARD FORM
Answers
The standard form, of the expression 3x³+7x-1+4x³-9x²-11x+1 is 7x³-9x²-4x
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, 3x³+7x-1+4x³-9x²-11x+1 we need to make it in a standard form,
To arrange this expression in a standard form, we will just have to perform operations in like terms and then arrange them in decreasing order of the power of the variables,
Therefore,
3x³+7x-1+4x³-9x²-11x+1
Adding the like terms
= 4x³+3x³+7x-11x-9x²+1-1
= 7x³-9x²-4x
Hence, the standard form, of the expression 3x³+7x-1+4x³-9x²-11x+1 is 7x³-9x²-4x
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What percent of 96 is 73
Answers
Answer: 70.08
Step-by-step explanation:
0.96*73=