What is the reason for the third step in this proof? Corresponding sides of congruent triangles are equal in length. The diagonals of a rectangle bisect each other. SSS criterion for congruence Opposite sides of a parallelogram are congruent.
Answer: D Opposite sides of a parallelogram are congruent.
Step-by-step explanation:
The correct answer is the Opposite sides of a parallelogram are congruent.
What is a parallelogram?A parallelogram is a quadrilateral having four sides and the two opposite sides are equal and parallel to each other.
Consider a parallelogram with diagonals that are congruent and perpendicular.
In triangles Δ AOB and Δ AOD,
OA = OA (common)
OB = OD (Since the diagonals of a parallelogram bisect each other)
∠ AOB = ∠ AOD = 90° (diagonals are perpendicular)
Therefore, Δ AOB ≅ Δ AOD (By SAS postulate)
Since, corresponding parts of congruent triangles are equal,
AB = AD
Similarly, we can prove
BC = CD and CD = DA
So, AB = BC = CD = DA.
Also, it is given that AC = BD.
Therefore the correct answer is the Opposite sides of a parallelogram are congruent.
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How do I find the perimeter and area?
Which of the following statements is true?
The number 2 /3 is an irrational number.
The number -4 is a whole number.
The number 9 is a rational number.
The number 5/8 is a natural number.
Find the critical value tc for the confidence level cequals 0.95 and sample size nequals 19.
The critical values are fixed values which can be obtained from the standard t crit tables. We can find the critical value tc when the degrees of freedom and confidence level are given. The degrees of freedom is simply:
Degrees of Freedom = Number of samples – 1
Degrees of Freedom = 19 – 1
Degrees of Freedom = 18
From the t critical tables, the tc corresponding to Degrees of Freedom equal to 18 and Confidence level equal to 95% is as follows:
tc = 2.101
Therefore this means that any t value beyond 2.101, we already reject the null hypothesis.
Meghan works at an ice cream shop and makes $8.25 per hour Lucas works at a landscaper and makes $6.50 per hour how much more does Meghan makes each hour ?
A certain triangle has two 45 angles. What type of triangle is it?
A. Acute scalene
B. Right scalene
c. Right isosceles
D. Acute isosceles
Answer:
C. Right isosceles
Step-by-step explanation:
In Acute scalene triangle, all angles are acute ( less than 90 degrees ) and different,
In Right scalene triangle, two angles are acute and different, while, the third angle is of 90°.
In Right isosceles triangle, two angles are acute and equal, while, the third angle is of 90°.
In Acute isosceles, all angles are acute in which any two angles are equal.
Now, given,
The two angle of the triangles are 45° and 45°,
Let x be the third angle,
⇒ x + 45° + 45° = 180°
⇒ x + 90° = 180°
⇒ x = 90°
Hence, the angles of given triangle are 45°, 45° and 90°,
By the above definitions,
It is clear that, given triangle is right isosceles.
Option C is correct.
. In the algebraic expression mc034-1.jpg 7, 17, and –10 are _____ terms. operations. coefficients. variables.
Answer:
Coefficient
Step-by-step explanation:
The correct option is A.
In the algebraic expression 7a+17b-10c, 7, 17 , and −10 are coefficients.
A. Coefficients. The numbers 7, 17, and -10 are coefficients in the expression 7a + 17b - 10c because they are the constants that multiply the variables a, b, and c respectively.
B. Incorrect. Operations are mathematical actions like addition, subtraction, multiplication, or division, not the constants themselves.
C. Incorrect. Variables, denoted by a, b, and c, are letters or symbols representing unknown or changing quantities, not the constants.
D. Incorrect. Terms are the individual parts of an expression separated by addition or subtraction, consisting of a coefficient and possibly a variable or variables multiplied together. The numbers 7, 17, and -10 are coefficients within the terms of the expression but are not terms themselves.
So, the correct option is A. Coefficients.
The complete question is here:
In the algebraic expression 7a+17b-10c, 7, 17 , and −10 are ______
A. coefficients.
B. operations.
C. variables.
D. terms.
A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches. Find the area of the rectangle.
3 to the 2 over 3 power inches squared
3 to the 8 over 3 power inches squared
9 inches squared
9 to the 2 over 3 power inches squared
Question 4(Multiple Choice Worth 2 points)
(MC)
Rewrite the rational exponent as a radical.
5 to the 3 over 4 power, to the 2 over 3 power
the cube root of 5 squared
the twelfth root of 5
the square root of 5
the cube root of 5 the fourth power
Question 5(Multiple Choice Worth 2 points)
(MC)
Rewrite the radical as a rational exponent.
the cube root of 2 to the seventh power
2 to the 3 over 7 power
2 to the 7 over 3 power
2 to the power of 21
2 to the power of 4
The number of lines that can be drawn perpendicular to a given line at a given point on that line in a plane is
Answer:
I JUST HAD THIS QUESTION 1
Step-by-step explanation:
212 tens divided by 10 =
One-on-one mapping from one plane to the same plane is called:
congruency.
transformation.
isometry.
None of the choices are correct.
Final answer:
Isometry is the term used for a one-on-one mapping from one plane to the same plane. It is key in transformations and geometry studies.
Explanation:
Isometry is the term for a one-on-one mapping from one plane to the same plane. In mathematics, this concept is crucial in the study of transformations and geometry. An isometry preserves distances, angles, and areas in a mapping, making it a significant concept in mathematical modeling.
Enter the slope-intercept equation of the line shown below.
You want to buy a new bike, and your parents will contribute $32.50 toward the cost of the bike. If the most expensive bike is $50.00, how much will you have to spend on the bike? Solve the following inequality 50.00 > 32.50 + x and graph its solution.
A 10-foot piece of string is cut into two pieces so that the longer piece is 1 footfoot longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.
shorter piece = x
longer piece = 2x+1
3x+1 =10
3x=9
x = 9/3=3
short piece = 3 feet
long piece = 2*3+1 = 7 feet
50 POINTS FOR ANSWER!!!!!!!!!!!!!!!!!!!!!!
A mover uses a ramp to pull a 1000-Newton cart up to the floor of his truck, which is .8 meters high. If it takes 125 newtons to pull the cart, what is the length of the ramp?
What is the circumference of a circular disc with a diameter of 10 centimeters? (Round your answer to the nearest tenth.)
The circumference of the circle is 31.4 cm
What is Circumference of circle?The circumference of a circle refers to the measure of its boundary. If we open a circle and measure the boundary just like we measure a straight line, we get the circumference of the circle in terms of units of length like centimeters, meters, or kilometers.
Now let us learn about the elements that make up circumference. These are the three most important elements of a circle.
Center: The center of the circle is a point that is at a fixed distance from any other point from the circumference.Diameter: The diameter is the distance across the circle through the center, it is a line that meets the circumference at both ends and it needs to pass through the center.Radius: The radius of a circle is the distance from the center of a circle to any point on the circumference of the circle.The formula for the circumference of a circle is expressed using the radius 'r' of the circle and the value of 'pi'. It is expressed as, Circumference of a circle formula = 2πr.
Given:
diameter= 10 cm
So,
Circumference of circle is = πd
=3.14* 10
=31.4 cm
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Sarah is y years old now. How could you represent her age 5 years ago?
y + 5
5 y
y - 5
y ÷ 5
y-5..................................................
solve the equation using any method: -2x^2-4x=6
Given f(x) = x + 2 and g(x) = x2 – 4, find the function (g/f)(x).
4m - 4 = 4m
Please solve and show work
The depreciating value of a semi-truck can be modeled by y = Ao(0.87)x, where y is the remaining value of the semi, x is the time in years, and it depreciates at 13% per year. What is the value of the truck initially, Ao, and how would the graph change if the initial value was only $67,000?
Answer: 1) The value of truck initially would be $87000.
2) at t = 0 , y-axis would be cut at $67000.
Step-by-step explanation:
Since we have given that
[tex]y=A_0(0.87)^x[/tex]
Here, A₀ is the initial value.
Rate of depreciation = 13%
Number of years = x
So, The value of truck initially would be $87000.
As shown in the given figure.
If the the initial value of truck = $67000
Rate will be same but the y-intercept will change.
As change in initial value does not affect the rate but the y - intercept.
Then at t = 0 , y-axis would be cut at $67000.
2x^3+2x^2-19x+20=0 find the roots of the polynomial equation
Answer:
[tex]\frac{3+i}{2} , \frac{3-i}{2} , -4[/tex]
Step-by-step explanation:
a mail distribution center processes as many as 150,000 pieces of mail each day. the mail is sent via ground and air. each land carrier takes 1800 pieces per load and each air carrier 1500 pieces per load. the loading equipment is able to handle as many as 150 loads per day. let X be the number of loads by air carriers and y the number of loads by air carriers. write a system of inequalities that represents this situation
Final answer:
The system of inequalities representing this situation is:
1500X + 1800Y ≤ 150,000.
X + Y ≤ 150.
X ≥ 0 and Y ≥ 0.
Explanation:
Let's define X as the number of air carrier loads and Y as the number of land carrier loads. Given that the mail distribution center processes up to 150,000 pieces of mail each day and the loading equipment can handle a maximum of 150 loads per day, we can write the following system of inequalities:
The total mail processed by both air and land carriers cannot exceed 150,000 pieces:
1500X + 1800Y ≤ 150,000.
The total number of loads carried by both air and land carriers cannot exceed 150 loads:
X + Y ≤ 150.
Furthermore, since there cannot be a negative number of loads, both X and Y have to be non-negative:
X ≥ 0 and Y ≥ 0.
These inequalities model the constraints for the mail distribution center's operations.
Rewrite the equation 8x+6x^2-7=x^2
in standard form and identify a, b, and c.
To rewrite the equation 8x + 6x^2 - 7 = x^2 in standard form, subtract x^2 from both sides and combine like terms. The standard form of the equation is 5x^2 + 8x - 7 = 0. The values of a, b, and c are 5, 8, and -7 respectively.
Explanation:The given equation is 8x + 6x^2 - 7 = x^2.
To rewrite it in standard form, we need to collect like terms. Subtracting x^2 from both sides, we get: 6x^2 + 8x - x^2 - 7 = 0.
Combining like terms, the standard form of the equation is 5x^2 + 8x - 7 = 0.
Here, a = 5, b = 8, and c = -7.
Find the volume of the square pyramid with length 14.7 inches and height 18 inches.
(50 Points Please help)
Drag the expression that is the most reasonable measurement for each object.
Answer:
A. Length of a Tour Bus ↔ #2. 1.1 × 10¹ meters
B. Width of an apple ↔ #3. 4 × 10⁰ centimeters
C. Distance from Earth to a Satellite ↔ #6. 8 × 10² kilometers
D. Thickness of a human hair ↔ #5. 9 × 10¹ micrometers
Step-by-step explanation:
The length of a tour bus should be measured in meters. It sure is way less than 1 kilometer and way more than a few centimeters. It could be about some meters, more than 5 meters, may be between 10 meters and 15 meters.
The measurement in the box # 2. is 1.1 × 10¹ meters, which is equivalent to 1.1 × 10 meters = 11 meters. Thus, this is a reasonable length.
B. Width of an apple.
The most appropriate unit to measure the width of an apple should be centimeter. It certainly is shorter than 1 meter and bigger than 1 mm.
The width of an apple could be, more or less, around 8 centimeters. The only measurement in the boxes that is in that order is that in the box #3., 4 × 10⁰ centimeters, because 10⁰ = 1, so 4 × 10⁰ = 4 × 1 = 4 centimeters.
C. Distance from Earth to a Satellite
The distance from Earth to a satellite should be measured in kilometers.
You can find in the internet that the distances of the satellites are between 700 kilometers and 36,000 kilometers.
The number in the box #1 is too big, in the order of ten trillions of kilometers, because one trillion is 10¹²; thus that is nonseasonal (too big).
The number in the box #6 is 8 × 10² kilometers, which is equal to 8 × 100 = 800 kilometers.
Thus, 8 × 10² kilometers (box #6) is the most reasonable measurement for the distance from Earth to a Satellite
D. Thickness of a human hair
Of course, kilometers, meters, centimeters and even millimeters are units too big to measure the thickness of a human hair.
One micrometer is 10⁻⁶ meters or 10⁻³ millimeters.
In the internet you can find that diameter of the human hair is in the range from 17 micrometers to 181 micrometers.
The measurement in the box #5. is 9 × 10¹ micrometers, which is equivalent to 9 × 10 = 90 micrometers.
Thus, 9 × 10¹ micrometers is the most reasonable measurement for the thickness of a human hair.
A. Length of a Tour Bus ↔ 2. 1.1 × 10¹ meters
B. Width of an apple ↔ 3. 4 × 10⁰ centimeters
C. Distance from Earth to a Satellite ↔ 6. 8 × 10² kilometers
D. Thickness of a human hair ↔ 5. 9 × 10¹ micrometers
What is Satellite?
A satellite is a moon, planet or machine that orbits a planet or star. For example, Earth is a satellite because it orbits the sun. Likewise, the moon is a satellite because it orbits Earth.
What is expression?
An act, process, or instance of representing in a medium (such as words) : utterance freedom of expression. Something that manifests, embodies, or symbolizes something else this gift is an expression of my admiration for you.
According to question, we have to drag the expression that is the most reasonable measurement for each object.
Length of Tour Bus is generally between 1 meter to 2 meters.
So, Reasonable measurement for Length of a Tour Bus is [tex]1.1[/tex]× [tex]10^{1}[/tex] meters
Width of an apple is generally between [tex]2[/tex] centimeters to [tex]6[/tex] centimeters
So, Reasonable measurement for Width of an apple is [tex]4[/tex]×[tex]10^{0}[/tex] centimeters .
Distance from Earth to a Satellite is generally between [tex]700[/tex] kilometers to [tex]3600[/tex] kilometers.
So, Reasonable measurement for Distance from Earth to a Satellite is
[tex]8[/tex]×[tex]10^{2}[/tex] kilometers.
Thickness of a human hair is generally between 17 micrometers to 181 micrometers.
So, Reasonable measurement for Thickness of a human hair is [tex]9[/tex]×[tex]10^{1}[/tex] micrometers.
Hence, we can conclude that the following expression is the most reasonable measurement for each object.
A. Length of a Tour Bus ↔ 2. 1.1 × 10¹ meters
B. Width of an apple ↔ 3. 4 × 10⁰ centimeters
C. Distance from Earth to a Satellite ↔ 6. 8 × 10² kilometers
D. Thickness of a human hair ↔ 5. 9 × 10¹ micrometers
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If ABCDE is translated 2 units to the right and 4 units up, what will happen to the polygon?
Answer:
A polygon will move but won't change shape or size
Step-by-step explanation:
Given the figure
If ABCDE is translated 2 units to the right and 4 units up, then we have to choose the correct option.
A translation is a geometric transformation that moves every coordinate point of a figure by the same distance.
The result of translation transformation implies
The size, the shape and the orientation of the image after translation are same as that of the original object.
Hence, a polygon will move but won't change shape or size
Option A is correct
Which number is greatest?
a. 3.4 × 10-2
b. 4.3 × 10-3
c. 5.2 × 10-4
d. 6.1 × 10-4
Answer:
the answer is d 6.1x 10-4
Step-by-step explanation:
Four girls and three boys volunteer to represent their class at a school assembly.the teacher selects one name and then another from a bag containing the seven students names.what is the probability that both representatives will be girls
Sarah decides to take her six-year-old son to the circus the price for the child ticket is $4.75 dollars Less in the price for the adult ticket if we represent the price for the child ticket using the variable X how would you write the algebraic expression for the adult ticket price