For trapezoids ABCD and A'B'C'D' on a coordinate plane, side AD's length is 8 units, A'D's length is 4 units and also the scale factor is 1/2.
The question asks for facts about the dilation of trapezoid ABCD to create trapezoid A'B'C'D' on a coordinate plane. First, we are to compare the length of side AD with side A'D'. The coordinates of AD are (-4, 0) and (4, 0), so the length is 4 - (-4) = 8 units. For A'D', using coordinates (-2, 0) and (2, 0), the length is 2 - (-2) = 4 units. This confirms that:
The length of side AD is 8 units.
The length of side A'D' is 4 units.
Next, to determine whether the image is larger than the pre-image, we examine the scale factor. As the original trapezoid has been halved in size, the scale factor is indeed 1/2. Therefore, the image is not larger; it is smaller. Hence, this option is not true.
Examining the slopes of sides CD and C'D', we can use the coordinates (2, 4) to (4, 0) and (1, 2) to (2, 0) respectively to calculate the slope. The slope of CD is (0-4)/(4-2) = -4/2 = -2, and for C'D' it is (0-2)/(2-1) = -2/1 = -2. Both slopes are indeed the same, and thus, we confirm:
Sides CD and C'D' both have the same slope, -2 not 2 as stated in the options.
The final option about the scale factor being 1/2 is true and confirms:
The scale factor is 1/2.
The true statements are:
- The length of side AD is 8 units.
- The length of side A'D' is 4 units.
- The scale factor is 1/2.
To determine which statements are true about the trapezoids, let's analyze the given information:
1. The length of side AD is 8 units.
- To find the length of side AD, we can use the distance formula between points A and D.
- Distance formula: [tex]\(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)[/tex]
- [tex]\(AD = \sqrt{(4 - (-4))^2 + (0 - 0)^2} = \sqrt{8^2} = 8\)[/tex]
- This statement is true.
2. The length of side A'D' is 4 units.
- To find the length of side A'D', we can use the distance formula between points A' and D'.
- Distance formula: [tex]\(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)[/tex]
-[tex]\(A'D' = \sqrt{(2 - (-2))^2 + (0 - 0)^2} = \sqrt{4^2} = 4\)[/tex]
- This statement is true.
3. The image is larger than the pre-image.
- We can compare the lengths of corresponding sides.
- The length of side AD is 8 units, while the length of side A'D' is 4 units.
- Since the lengths of corresponding sides are not proportional, the image is not larger than the pre-image.
- This statement is false.
4. Sides CD and C'D' both have the same slope, 2.
- The slopes of sides CD and C'D' can be calculated using the coordinates of the points.
- Slope formula:[tex]\(m = \frac{y_2 - y_1}{x_2 - x_1}\)[/tex]
- For side CD: [tex]\(m_{CD} = \frac{4 - 4}{2 - (-2)} = \frac{0}{4} = 0\)[/tex]
- For side C'D':[tex]\(m_{C'D'} = \frac{2 - 0}{1 - (-1)} = \frac{2}{2} = 1\)[/tex]
- Since the slopes are not the same, this statement is false.
5. The scale factor is 1/2.
- To find the scale factor, we can compare the corresponding side lengths of the pre-image and the image.
- The length of side AD is 8 units, and the length of side A'D' is 4 units.
- The scale factor is the ratio of corresponding side lengths: [tex]\(\frac{4}{8} = \frac{1}{2}\)[/tex]
- This statement is true.
There are 19,763 tickets available for a New York Knicks home game. If there are 41 home games in a season, about how many tickets are available for all the Knicks’ home games?
Answer:
about 800000 ticket available for all the Knicks’ home games
Step-by-step explanation:
given data
tickets for Knicks home game = 19763 ≈ 20000
no of games = 41 ≈ 40
to find out
how many tickets are available for all the Knicks’ home games
solution
we know here ticket available for a New York Knicks home game and games are approx 40
so
total ticket available = tickets for Knicks home × no of games ........1
total ticket available =20000× 40
total ticket available = approx 800000
so about 800000 ticket available for all the Knicks’ home games
If it is 5:00 pm in Bloomington, OH, what time is it in St. Louis, MO?
Answer:
Should be 4:00 pm
Step-by-step explanation:
462 grams is how many milligrams
Answer:462000 milligrams
Step-by-step explanation: you times it by 1000
3. What property describes the number
sentence?
6 +0= 6
Answer:
The Identity Property
Step-by-step explanation:
Identity Property means the number's Identity stays the same; usually either itself times 1, or plus zero
6 + 0 = 6 is an example of the Identity Property
Answer: Hello there! Just a helping hand here, its an additive identity property. Hope this helps! -Skyler
Step-by-step explanation:
The additive identity property states that the sum of any number and zero is the original number.
Which of these side lengths makes the triangle obtuse?
15, 36,
Answer:
I believe the answer is 36.
If events X and Y are independent, what must be true? Check all that apply.
P(
YX) = 0
P(
XY)=0
P(YX) = P(Y)
PY|X) = P(X)
OPXY)=P(Y)
P(X|Y) = P(X)
If events X and Y are independent, then following results are true:
[tex]P(Y/X) = P(Y)[/tex][tex]P(X/Y) = P(X)[/tex]What are independent events?" Independent events are defined as the events which are not depend on any other events."
Condition used for independent events
[tex]P(X\cap Y) = P(X) \times P(Y)[/tex]
According to the question,
Given event X and Y are independent,
[tex]P(X/Y) = \frac{P(X\cap Y)}{P(Y)}[/tex]
Substitute the value of [tex]P(X\cap Y)[/tex] we get,
[tex]P(X/Y) = \frac{P(X) \times P(Y)}{P(Y)}[/tex]
[tex]= P(X)[/tex]
Similarly for independent events X and Y we have,
[tex]P(Y/X) = \frac{P(X\cap Y)}{P(X)}[/tex]
Substitute the value of [tex]P(X\cap Y)[/tex] we get,
[tex]P(Y/X) = \frac{P(X) \times P(Y)}{P(X)}[/tex]
[tex]= P(Y)[/tex]
Hence, if events X and Y are independent, then following results are true:
[tex]P(Y/X) = P(Y)[/tex][tex]P(X/Y) = P(X)[/tex]Learn more about independent events here
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The width of a rectangular football fields is 14 meters more than half of its length. If L represents the length of the field, write an expression for the width.
Answer:
w = 14 - (L/2)
Final answer:
The width, W, of the rectangular football field is expressed as W = (1/2)L + 14, which signifies that the width is half of the field's length plus an additional 14 meters.
Explanation:
If L represents the length of the football field, the expression for the width, W, is W = rac{1}{2}L + 14. This is because the width is given as 14 meters more than half of the field's length. So, to write this relationship as an expression, we start by taking half of the length, denoted as [tex]rac{1}{2}L[/tex], and then add 14 meters to this value to account for the additional width.
please answer! ill give you brainliest :)
Answer:
answer what?
Step-by-step explanation:
9x²+7x=0 Solve quadratic equation by factoring
Answer:
Step-by-step explanation:
9x²+7x=0
x(9x+7) =0
x=0 or 9x+7 =0
x=0 or x = -7/9
Gary and Ann have a joint checking account. Their balance at the beginning of October was $9145.87.
During the month they made deposits totaling $2783.71, wrote checks for $4871.90, paid a maintenance
fee of $12, and earned $11.15 in interest on the account. What was the balance at the end of the month?
Answer:
The balance at the end of the month was $7,056.83
Step-by-step explanation:
we know that
The balance at the end of the month is equal to the balance at the beginning of the month plus deposits and interest minus checks and maintenance fee
so
9,145.87+(2,783.71+11.15)-(4,871.90+12)
9,145.87+(2,794.86)-(4,883.90)=$7,056.83
Answer:
The balance was $ 7,056.83
Step-by-step explanation:
Given,
The original balance in beginning of the month = $9145.87,
The amount of deposit = $2783.71,
So, new balance after depositing = $9145.87 + $2783.71 = $ 11929.58,
Check amount = $4871.90,
After clearing check, the new balance = $ 11929.58 - $ 4871.90 = $ 7057.68,
Also, after charging $ 12 fees, new balance = $ 7057.68 - $ 12 = $ 7045.68,
Finally getting $ 11.15 interest,
The final balance at the end of month = $ 7045.68 + $ 11 = $ 7,056.83
standard notation 6x10/3
Answer:
6 x 10/3= 6000
Step-by-step explanation:
take ur first digit,6,and either multiply it by 10/3 =1000 or place to its right as many zeroes as the exponent of ten (3)
The student is working with scientific notation, specifically converting 6 x [tex]10^{-3}[/tex] into standard notation, which results in the number 0.006.
The student in question appears to be dealing with scientific notation and its application in representing large or small numbers in a condensed form. In scientific notation, numbers are represented as a product of a base number and 10 raised to a certain power. For instance, 6 x 10/3 is a way to represent the number 0.006, indicating the decimal point has been moved three places to the left.
To convert 6x10/3 into standard notation, you need to recognize that the exponent -3 on the 10 denotes how many places to move the decimal. Since it is negative, we move the decimal to the left. Therefore, we rewrite 6 as 0.006, which is the standard notation.
The quotient of a number and 3 is 8
Hey!
----------------------------------------------
[tex]\boxed{ \bf n~/~3~=~8}[/tex]
----------------------------------------------
Solution:
Number = n
Quotient of a number and three: n / 3
Is eight: = 8
End Result: n / 3 = 8
----------------------------------------------
Hope This Helped! Good Luck!
What is 10-2 simplified in standard form
Answer:
8
Step-by-step explanation:
10 - 2 can also be written as:
10
- 2
------
8
Round 919,827 to each place value in the table
Nearest 1000: 920,000
Nearest 100: 919,800
Nearest 10: 919,830
Answer:
nearest 1000- 10,000
nearest 100- 800
nearest 10- 30
How many granola bars will Kirby pack in all?
square root 1/4 +square root 9/4 -square root 45
Answer:
[tex]-\frac{85}{2}[/tex]
Step-by-step explanation:
[tex]|\frac{1}{4} |+|\frac{9}{4}| -|45|[/tex]
Simplify the expression.
[tex]\frac{1}{4} +\frac{9}{4} = \frac{5}{2}[/tex]
[tex]\frac{5}{2}-45=-\frac{85}{2}[/tex]
Answer:
2 + 3 √5
Step-by-step explanation:
√(1/4) = 1/2
√(9/4) = 3/2
√(45)= √(9×5)= 3 √5
√(1/4)+√(9/4)+√(45) 1/2 +3/2 + 3 √5 = 2 + 3 √5
The quotient of a number 2 is 7
Answer:14
Step-by-step explanation:
7) Show 10,000 as an exponent
B) What is the value of the 5 in 52.890?
Answer:
7) 10^4
B) 50
Step-by-step explanation:
7) 10,000=10x10x10x10
turned into an exponent= 10^4
B). the 5 is in the tens place so it's value is
50
The travel time for a plane traveling at a rate of r kilometers per hour for 900 kilometers
The travel time for a plane traveling at a rate of r kilometers per hour for 900 kilometers can be calculated using the formula: Time = Distance / Speed. So, the travel time for the plane would be 900 / r hours.
Explanation:The travel time for a plane traveling at a rate of r kilometers per hour for 900 kilometers can be calculated using the formula:
Time = Distance / Speed
Since the distance is given as 900 kilometers and the rate is given as r kilometers per hour, the travel time can be written as:
Time = 900 / r
So, the travel time for the plane would be 900 / r hours.
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Write the following decimal in words.
0.63
0.09
Help me right this in word form :)
Answer:
Sixty-three hundredths.
Step-by-step explanation:
Answer:
1) sixty-three hundredths
2) nine hundredths
HOPE IT HELPED {:)
Jesse multiplied 12 by 0.23. Without calculating will the product be more or less than 12 ? Explain
Answer:
The product will be LESS than 12.
Step-by-step explanation:
When multiplying a number by something smaller than 1, the product will always be smaller than your first number. A simple way to remember this is that a decimal is the same as a fraction in almost every way. For example, 1/2 and .5 are the same number.
When a number is multiplied by a decimal less than 1, the product will always be less than the original number. Hence, if Jesse multiplies 12 by 0.23, the result will be less than 12.
To determine whether the product of multiplying 12 by 0.23 will be more or less than 12, we can use some basic estimation and mathematical reasoning without performing the actual calculation. Here's a step-by-step explanation:
Step 1: Understand the decimal value of 0.23.
- 0.23 is less than 1, which means it is a fraction of 1. In decimal form, it's less than 0.5 but greater than 0.2.
Step 2: Understand the concept of multiplication with fractions less than 1.
- When you multiply a number by a fraction less than 1, the result is smaller than the original number. The closer the fraction is to 0, the smaller the result.
Step 3: Apply this understanding to the problem.
- Since 0.23 is less than 1 and closer to 0, when you multiply 12 by 0.23, the result will be smaller than 12.
Step 4: Answer the question.
- Therefore, the product of multiplying 12 by 0.23 will be less than 12.
So, without calculating the actual product, we can confidently say that the result will be less than 12 because we are multiplying 12 by a fraction (0.23) that is less than 1.
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Victor is on his school's swim team. During his 2-week winter break, he swims 30 laps each
week to stay in shape. If each lap is 25 yards, how many feet does he swim during his winter
break?
Victor swims 4500 ft during his winter break.
It is given that,
Number of weeks in winter break: 2Laps each week: 30Yards in each lap: 25 yardsExplanation:
Laps in one week is 30. So, laps in two weeks is:
[tex]2\times 30=60[/tex]
1 lap is equal to 25 yards. So, 60 laps is equal to:
[tex]60\times 250=1500[/tex] yards
We know that,
1 yard = 3 ft
So, 1500 yards is:
[tex]1500\times 3=4500[/tex] ft
Thus, Victor swims 4500 ft during his winter break.
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What is 3(-6)2 at the top ?
[tex]\huge\boxed{108}[/tex]
The [tex]^{-2}[/tex] only affects the [tex](-6)[/tex]. Let's solve that exponent first.
[tex]3(-6)^{-2}[/tex]
[tex]3(-6*-6)[/tex]
Multiply.
[tex]3*36[/tex]
Multiply one last time.
[tex]\boxed{108}[/tex]
Answer:
108
Step-by-step explanation:
Do the parentheses first with the exponent of 2 on the outside.
Multiply -6 times -6, which gets you 36.
After, multiply 36 by 3. Which gets you 108!
Final: 108
(((PICTURE ATTACHED))) please help
Identify the property used in each of the steps
Answer: (1) Distributive (2) Commutative (3) Associative
(4) Commutative (5) Addition Property of Equality
Step-by-step explanation:
1) Distributive
(x + 4) was multiplied by 3 and (2x - y) was multiplied by 5
2) Commutative
10x and -5y switched places
3) Associative
The parenthesis changed partners
4) Commutative
(12y - 5y) and 10x switched places
5) Addition Property
Like terms were added together --> 3x + 10x = 13x and 12y - 5y = 7y
20 Points, Please explain answer.
Lia claims that a reflection over the y-axis will always carry a circle drawn on the coordinate plane to a circle with the same center and the same radius. Which statement best describes Lia's claim?
A
Lia is correct as a reflected circle will always have the same center and always have the same radius as the original circle.
B
Lia is incorrect as a reflected circle will not always have the same radius and will not always have the same center as the original circle.
C
Lia is correct in stating that the reflected circle will always have the same radius, but is incorrect in stating that the reflected circle will always have the same center.
D
Lia is incorrect in stating that the reflected circle will always have the same radius, but is correct in stating that the reflected circle will always have the same center.
Answer: YOUR ANSWER WOULD BE B
Step-by-step explanation: Your answer would be B because when you reflect something on the y-axis it always goes one cube or dashed line forward so it will not have the same radius nor the circle hope this helps you alot
Answer:
C. Lia is correct in stating that the reflected circle will always have the same radius, but is incorrect in stating that the reflected circle will always have the same center.Step-by-step explanation:
Lia's claim is not correct, because when we reflect a figure, its coordinates variate. In this case, Lisa is trying to reflect a circle over the y-axis, which will change y-axis coordinates. The center of the circle is gonna change its y-axis coordinate, for example, if the center is [tex]C(2;3)[/tex], its reflection will be [tex]C(2;-3)[/tex]
Therefore, the center of the circle will not remain the same. However, the radius will be the same, because changing y-axis coordinates don't affect the distance between the center and the circumference of the circle.
So, the correct answer is option C.
Explain the meaning of each 6 in the number 763 465 284 132
Each 6 in the number 763 465 284 132 holds an individual place value. The first is worth 6 (one's place), the second is worth 6,000 (thousand's place), and the third is worth 600,000,000 (hundred million's place).
Explanation:In the number 763 465 284 132, each 6 holds a unique positional value as per the place value system, which is a fundamental concept in Mathematics. The first 6, counting from the right, is in the one's place, so it just represents the number 6. The second 6 is in the thousands place, so it represents 6,000. The third 6 is in the hundred million's place, so it represents 600,000,000.
The number could also be read as: Seven hundred sixty-three billion, four hundred sixty-five million, two hundred eighty-four thousand, one hundred thirty-two.
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What is the value of 1 exponent 102? What is the value of any power of 1? Justify your answer.
The value of [tex]1^{102[/tex] is 1 because 1 multiply by itself results to 1.
What is Exponents and power?A number's exponent indicates how many times the number has been multiplied by itself.
: Since 2 is multiplied by itself 4 times, 2x 2 x 2x 2 can be expressed as [tex]2^4[/tex]. Here, 4 is referred to as the "exponent" or "power," while 2 is referred to as the "base."
Given:
[tex]1^{102[/tex] = ?
Now, if we have
1² = 1 x 1 = 1
1³ = 1 x 1x 1 = 1
.
.
.
[tex]1^{50[/tex]= 1 x 1 x 1 x 1 x 1 x ................(50 times) = 1
and, [tex]1^{102[/tex] = 1 x 1 x 1 x 1 x 1 x ................(102 times) = 1
Hence, the value of [tex]1^{102[/tex] is 1 because 1 multiply by itself results to 1.
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Final answer:
The value of 1 raised to any power, including 1 exponent 102, is 1. When you multiply 1 by itself any number of times, the result is always 1 because the identity property of multiplication states that any number multiplied by 1 remains unchanged.
Explanation:
The value of 1 exponent 102, or $1^{102}$, is 1. In fact, the value of any power of 1 is always 1. To understand this, let's think of the exponent as how many instances of a number are multiplied together. When you multiply 1 by itself any number of times, the result remains 1 because multiplying by 1 does not change the value of the original number. Thus, 1 to any power, whether it's 1 or 102, will still give us 1.
Using these principles, let's address another problem without entering scientific notation into your calculator. To evaluate $(4.506 \times 10^4) \times (1.003 \times 10^2)$, we can multiply the coefficients (4.506 \times 1.003) and then add the exponents of 10 (4 + 2), since when powers of 10 are multiplied together, the exponents are added. The result is approximately 4.514518 \times 10^6.
I need help, if you can help me I’ll be real thankful
Answer:
x^2-6x+7
Step-by-step explanation:
You can use synthetic division since you are dividing by a linear factor with leading coefficient 1. (You can also do synthetic division when dividing by a linear factor whose leading coefficient is not 1 but it is a bit trickier.)
So since we are dividing by x-2, 2 goes on the outside.
(If we were dividing by x+2, -2 would go on the outside.)
Now the thing that goes on top inside is the dividend, the numerator which is 1x^3-8x^2+19x-14. If you were missing any terms you would have to place a zero but we aren't. All exponents between 3 and 0 (inclusive meaning to include the 3 and the constant term) on variable x is accounted for.
2| 1 -8 19 -14
| 2 -12 14
-----------------------------
1 -6 7 0
So the remainder is 0 and the quotient is x^2-6x+7.
One of two supplementary angles is 70° greater than the second.
Find the measure of the larger angle.
Answer:
125°
Step-by-step explanation:
Supplementary angles sum to 180°
let one angle be x then the larger angle is x + 70, thus
x + x + 7 0 = 180
2x + 70 = 180 ( subtract 70 from both sides )
2x = 110 ( divide both sides by 2 )
x = 55
Hence
larger angle = x + 70 = 55 + 70 = 125°