Determine whether ∆MNO=∆QRS. Explain using rigid motions.
M(4, 7), N(5, 4), O(2, 3), Q(2, 5), R(3, 2), S(0, 1)
Answers
∆MNO and ∆QRS are congruent with each other.
What are rigid motions in congruency of triangles?
Two plane figures are congruent if and only if one can be obtained from the other through a series of rigid motions (that is, reflections, translations, and/or rotations). A landscape architect designs the landscape around a mall using a grid. Trace the landscape elements to ensure that they are congruent.
For the given coordinates M(4, 7), N(5, 4), O(2, 3), Q(2, 5), R(3, 2), S(0, 1).
Let's draw the triangles on graph paper,
You can map MNO to QRS with a translation left 2 units and
down 2 units. The planters are congruent because there is a rigid
transformation that maps one to the other.
Hence, ∆MNO and ∆QRS are congruent with each other.
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Related Questions
Can walk 4 miles in one hour and can run 8 miles in one hour what percent of average running speed is her average walking speed 
Answers
Answer: 50% of her average running speed is her average walking speed
Step-by-step explanation:
60 ÷ 4 = 15
60 ÷ 8 = 7.5
7.5 is half of 15, making it 50% of her running speed.
I need help please im so confused
Answers
Step-by-step explanation:
the x-intercept is the point, where the curve intercepts the x-axis (that means y = 0).
the y-intercept is the point, where the curve intercepts the y-axis (that means x = 0).
y = 10 - 2x
when x = 0, that means y = 10 - 2×0 = 10.
when y = 0, that means 0 = 10 - 2x, 2x = 10, x = 5
x-intercept = (5, 0)
y-intercept = (0, 10)
4y + 9x = 18
x = 0, 4y = 18, y = 18/4 = 9/2 = 4.5
y = 0, 9x = 18, x = 18/9 = 2
x-intercept = (2, 0)
y-intercept = (0, 4.5)
6x - 2y = 44
3x - y = 22
x = 0, -y = 22, y = -22
y = 0, 3x = 22, x = 22/3 = 7 1/3
x-intercept = ( 7 1/3, 0)
y-intercept = (0, -22)
2x = 4 + 12y
x = 2 + 6y
x = 0, 6y = -2, y = -2/6 = -1/3
y = 0, x = 2 + 6×0 = 2
x-intercept = (2, 0)
y-intercept = (0, -1/3)
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents:
three to the one third power all over three to the one sixth power
A. the square root of three to the one sixth power
B. the ninth root of three squared
C. the square root of three to the sixth power
D. the sixth root of three
Answers
Answer:
D. The sixth root of three
Step-by-step explanation:
Translate from words to math symbols:
three to the one third power all over three to the one sixth power
[tex]\frac{3^{\frac{1}{3} } }{3^{\frac{1}{6} } } \\[/tex]
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents:
[tex]\frac{\sqrt[3]{3} }{\sqrt[6]{3} }[/tex]
Simplify:
[tex]\frac{\sqrt[3]{3} }{\sqrt[6]{3} } = \frac{\sqrt[3]{3} }{\sqrt[6]{3} } * \frac{\sqrt[6]{3^{5} } }{\sqrt[6]{3^{5} } } = \frac{\sqrt[3]{3} *\sqrt[6]{3^{5} } }{\sqrt[6]{3^{6} } } = \frac{3^{\frac{1}{3} }*3^{\frac{5}{6} } }{3^{\frac{6}{6} } } = \frac{3^{(\frac{1}{3} +\frac{5}{6} )} }{3} = \frac{3^{(\frac{2}{6} +\frac{5}{6} )} }{3} = \frac{3^{\frac{7}{6} } }{3} = \frac{3^{\frac{1}{6} } *3}{3} = \\\\3^{\frac{1}{6} } = \sqrt[6]{3}[/tex]
Answer:
[tex]\sqrt[6]{3}[/tex]
D. the sixth root of three
A hall can accommodate 600 chairs arranged in rows Each row has the same number of chairs The chairs are rearranged such that the number of row is increased by 5 but the number of chairs per row is decreased by 6 a) Find the original number of rows of chairs in the hall b) After the re-arrangement 450 people were seated in the hall leaving the same number of empty chairs in each row. Calculate the number of empty chairs per row.
Answers
The 600 chairs capacity of the hall and the arrangement such that an increase in the number of rows by 5 decreases the number of chairs per row by 6 is a word problem that indicates;
(a) There are originally 20 rows of chairs in the hall
(b) The number of empty chairs per row is 6 empty chairs
What is a mathematics word problem?A word problem is a question in which the information required to find the solution and the description of the situation is provided using sentences, or regular verbal statements rather that symbols, expressions or operators.
(a) The number of chairs the hall can accommodate = 600
Let x represent the number of rows of chairs, therefore;
The number of chairs per row = 600/x
When the number of rows is increased by and the number of shares per row is decreased by 6, we get;
New number of rows = x + 5
New number of chairs per row = (600/x) -6
The equation for the number of chairs in the hall becomes;
(x + 5) × ((600/x) - 6) = 600
600·x + 6·x² - 570·x - 3000 = 0
6·x² + 30·x - 3000 = 0
x² + 5·x - 500 = 0
(x + 25)·(x - 20) = 0
x = -25 and x = 20
The number of rows is a positive number, therefore;
The original number of rows, x = 20(b) After re-arrangement, the number of rows, x = 20
The new number of chairs per rows = (600/20) - 6 = 24
The new number of rows = 20 + 5 = 25
Let E represent the number of empty chairs, the number of people in each row becomes 24 - E, which indicates;
25 × (24 - E) = 450
450 ÷ 25 = 18 = 24 - E
E = 24 - 18 = 6
The number of empty chairs per row, E = 6
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the gram-schmidt process produces from a linearly independent set {x1, x2, . . . , xp} an orthogonal set {v1, v2, . . . , vp} with the property that span{v1, . . . , vk}
Answers
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.
Given that,
From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.
Whether the claim is true or false must be determined.
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.
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What is the formula for simple interest
Answers
Answer: The formula for simple interest is P*R*T/100
Step-by-step explanation: Where P stands for Principal and R for Rate T for Time
What is 3x+6 I don’t know what this is
Answers
Answer:
it is a function.
Step-by-step explanation:
The answer is just 3x+6
Answer:
3x+6 can be be the result of 3(x+2) and then you distribute to get 3x+6
If you are asking how to solve you need an equal sign in the equation for example: 3x+6=27 you would have to solve to figure out wht x is. x is any unknown number we use x or any letter in the alphabet to fill in. You have to olve for the variable now.
A General Rule for Solving Equations
Simplify each side of the equation by removing parentheses and combining like terms.
Use addition or subtraction to isolate the variable term on one side of the equation.
Use multiplication or division to solve for the variable.
Step-by-step explanation:
Helppppp, I don’t know what to do, I just really need the answer
Answers
The completed statement on the exponential model that fits the data in the question is presented as follows;
The exponential model indicates that the plastic production has a 7.88% growth per year. The model predicts that the production 15 years after 1960 was closest to 30 million metric tons, because the correlation coefficient indicates a strong correlation between the model and the data, this prediction is correct.
What is a correlation coefficient?The correlation coefficient is an indication of the level at which the variables are interdependent.
The table of values in the question can be entered into a spreadsheet application as follows;
In the spreadsheet application, enter Year since 1960 values in a column, and the Plastic Production in an adjacent columnSelect the all the data entered into the spreadsheet document such as MS Excel, then select the Insert tabIn the charts section select scatter plot to create a scatter plot of the dataIn the Design tab, that appears when the chart is selected, select the Add Chart Element button access the Trendline functionSelect the Exponential trendline from the menu for trendlinesThe exponential trendline is then created by the spreadsheet applicationThe equation for the trendline obtained from MS Excel is presented as follows; f(x) = 9.2179·e^(0.0788·x)
The growth rate from the above exponential function is 7·88% per year
The production 15 years after 1960 is therefore;
f(15) = 9.2179·e^(0.0788 × 15) ≈30.06
The number of plastic produced 15 years after 1960 is about 30 million metric tons
The correlation coefficient obtained from MS Excel is R² = 0,9157, which indicates a strong correlation between the data and the model
The prediction is correct based on the strong correlation between the year and the number of plastic produced.
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Given that z=x + i y, find the values of real numbers x and y such that z - 4iz' + 3 = 0, when z' is the conjugate of z.
THANKS IN ADVANCE!!!
Answers
The value of z = 0 + 0i
What is complex numbers ?
A complex number can be represented in the form a + bi, where a and b are real numbers. A complex number is a part of a number system that extends the real numbers by adding an element designated by the symbol I sometimes known as the imaginary unit, and meeting the equation displaystyle i2=-1.
( x + iy ) - 4i ( x - iy ) = 0
x + iy - 4ix + 4i²y = 0
x + i (-4x + y ) + 4y = 0
x + 4y + ( - 4x + y )i = 0
Now two complex numbers are equal if both the real and imaginary parts are equal, which gives you the system of equation
x + 4y = 0 ⇒(1)
-4x + y = 0 ⇒ (2)
Multiplying equation (1) with 4
4x + 16y = 0
Solving the equations
4x + 16 y = 0
-4x + y = 0
17 y = 0
y = 0
Putting the value of y in (1)
x + 4(0) = 0
x = 0
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Activity class has 20 women and 13 men. A committee of five is chosen at random. Find (a) p(the committee consists of all women). (b) p(the committee consists of all men) (c) p(the committee consists of all of the same sex) Activity Suppose that a die is loaded (biased) such that 3 appears twice as often as each other number but that the other 5 numbers are equally likely. What is the probability that an odd number appears when we roll this die?
Answers
the probability of the committee consisting of all women is 6.53%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
number of women = 20
number of men = 13
Total number of persons = 20+ 13 = 33
A committee of 5 people is chosen at random. Total number of ways in which the committee of 5 can be chosen N
N = C(33 5) = 33! / 5!*28!
N = 237336
p(the committee consists of all women) = C (20 3)*C(13 0)/N
p = 15504 / 237336
p = 0.0653
Hence, the probability of the committee consisting of all women is 6.53%
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A drawing ha a cale of 1:30. An a drawing, a kitchen i a rectangle meauring 12cm by 27cm. A bedroom ha an actual area of 300000cm
which ha the bigger actual area, the kitchen or the bedroom?
you mut how your working
Answers
Actual area of bedroom is bigger than the kitchen as per the given measurements and scale.
As per the given question,
Given drawing scale is:
1 : 30
Shape of the kitchen is rectangle with measurements = 12cm by 27cm
Using scale :
Length = 12cm
Actual length = 12 × 30
= 360cm
Width = 27cm
Actual width = 27 × 30
= 810 cm
Actual area of kitchen = 360 × 810
= 291,600 cm²
Actual area of bedroom = 300,000cm²
300,000 > 291,600
Actual area of bedroom > Actual area of kitchen
Therefore, actual area of bedroom is bigger than the actual area pf kitchen.
The complete question is:
A drawing has a scale of 1:30 On the drawing, a kitchen is a rectangle measuring 12 cm by 27 cm A bedroom has an actual area of 300 000 cm² Which has the bigger actual area, the kitchen or the bedroom? You must show your working.
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a spring has a spring constant of 283 n/m. how far is the spring compressed to the right if 129 n of force are used
Answers
The spring is compressed to 95.5 cm to the right if 129 N of force are used.
In this question, we have been given the spring constant k = 283 N/m
if 129 N of force are used then we need to find distance that the spring compressed to the right.
Let the spring stretch from the equilibrium position x.
An equation for the spring's potential energy is,
PE = 1/2 kx^2
129 = 1/2 * 283 * x^2
2 * 129 = 283 * x^2
258/283 = x^2
x^2 = 0.9117
x = 0.9548 m
x = 95.5 cm
Therefore, the spring is compressed to 95.5 cm to the right if 129 N of force are used.
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Use the zero-product property to solve the equation.
(x + 3)^2 = 0
Answers
this is because -3+3=0 and 0^2= 0
jadaa maake 55 ccups of blueberry jam and divided the jam equally amoung 4 containers how much jam went in each container a 2t third of a cup b 1 cup c 3over 2 of a cup and d 24 cups
Answers
When the denominator is bigger than the numerator, a fraction is expressed as one with a numerator and a denominator. 55 cups of jam divided equally into 4 containers yields 13.75 cups per container. 13.75 cups of jam are contained in each container.
What is a fraction?When the denominator of a fraction is greater than the numerator, the fraction is expressed as a pair of numbers. A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A proper fraction has a numerator that is lower than its denominator. Example: 1/2, 1/3 is a fraction.We have,
55 cups of blueberry jam were produced by Jada, who then evenly distributed the jam across 4 containers.
jam content of each container.
= 55 cups / 4 container
= 13.75 cups / 1 container
This indicates that there are 13.75 cups of jam in each container.
55 cups of jam are divided into 4 equal containers in this manner.
13.75 cups / 1 container
The amount of jam in each container is 13.75 cups of jams.
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What is 5% of 60 use a double number line diagram to show your work
Answers
Using the proportion , the 5% of 60 would be 3.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We are given that the number of 5% of 60.
5% of 60
= 0.05 x 60
= 3
Therefore, the 5% of 60 would be 3.
Using the proportion , the 5% of 60 would be 3.
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Evaluate the expression when b=9
4b+10-b
Group of answer choices
37
47
27
17
Answers
Answer:
37
Step-by-step explanation:
4b+10-b = 3b + 10 = 3(9) + 10 = 27 + 10 = 37
please help im suffering right now
Answers
Answer:
C
Step-by-step explanation:
If we use the distributive property for 4 (2x + 1), we see that 4 (2x) = 8x and that 4 (1) = 1. That means 4 (2x + 1) = 8x + 4 which is not equivalent to 2x + 4y. So this limits our answer to either C or D. C is the correct answer because if we use the distributive property again here for 4 (2x + y), we see that 4 (2x) = 8x and 4 (y) = 4y. That means that 4 (2x + y) = 8x + 4y which is the answer we're looking for.
May I please have brainliest for this? Thank you very much!
Dan buys a car for £700.
It depreciates at a rate of 5.5% per year.
How much will it be worth in 6 years?
Give your answer to the nearest penny where appropriate.
Answers
The value of car after 6 years is £498.53
Define Modeling Exponential Decay
A model for decay of a quantity for which the rate of decay is directly proportional to the amount present.A(1 - r)^tA = Present value , r = rate, t = timeGiven that,
Dan buys a car = £700
Depreciates at a rate of = 5.5% per year
The value after 6 years = 700 (1 - 5.5 / 100) ^6
= 498.527 or 498.53
Therefore, the value of car after 6 years is £498.53
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A mountain climber found that the relationship between his altitude and the surrounding air temperature is linear. The function
represents this relationship, where is the altitude in meters and is the temperature in degrees Fahrenheit. According to this function, by how much is the temperature decreasing for every meter that the mountain climber’s altitude increases?
Answers
The temperature decrease for every meter that the mountain climber's altitude increases is given by:
-100 ºF.
What is the temperature decrease?The function that models this situation is a linear function, which has the format defined as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope of the function, representing by how much y changes when x is increased by one.b is the y-intercept of the function, representing the numeric value of y when x = 0.In the context of this problem, the function is defined as follows:
f(a) = -100a + 75.
Hence the slope of the function is of:
-100.
Representing the temperature decrease for each meter of altitude increase of the climber.
Missing InformationThe function is defined as:
f(a) = -100a + 75.
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The bill for two book came to $28. 48. One book cot $7. 44. What wa the cot of the other one
Answers
Answer:
Step-by-step explanation:
Ok:
If the two books together costs $28.48 and one of them cost $7.44 Subtract to get the other book's price
2. 28.45-7.44=$21.01
3. Answer: The cost of the other one is $21.01
help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!
Answers
a. [tex]123.1(1.069)^3 \approx 150.4[/tex]
b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]
helpppppp maeeeeeeee
Answers
Answer:
x= -7
Step-by-step explanation:
The sum of the angles in a triangle is 180°. This can be abbreviated to ∠ sum of ∆.
Adding the angles in the triangle,
84° +(x +59)° +(x +51)°= 180° (∠ sum of ∆)
2x= 180 -84 -59 -51
2x= -14
Divide both sides by 2:
x= -14 ÷2
x= -7
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Tracy is saving to buy a new guitar that costs $253. 77 (including tax). Tracy has saved $136. 27, and she can save $23. 50 each week. How many more weeks will it take her to save enough money?.
Answers
Tracy need 5 weeks to save enough money to buy a new guitar.
Given that,
Tracy is saving to buy a new guitar. Which having costs $253.77(including tax).
Tracy has already saved $136. 27.
Now she needs = 253. 77- 136. 27
= $117.50
she can save each week = $23. 50
Tracy will take weeks to save enough money
= [tex]\frac{117.50}{23.50}[/tex]
= 5 weeks.
Therefore, Tracy need 5 weeks to save enough money to buy a new guitar.
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Which expression is equivalent to log2-log6
Answers
Answer: log2-log6=-log3
Step-by-step explanation:
[tex]\displaystyle\\log2-log6=\\\\log\frac{2}{6} =\\\\log\frac{2(1)}{2(3)}=\\\\log\frac{1}{3} =\\\\log3^{-1}=\\\\-log3[/tex]
How to solve Solve 3! what the exclamation point means but it part of the problem
Answers
Answer:
3! = 3*2*1 = 6
Step-by-step explanation:
! is factorial meaning that you multiply that number by all of the number below it
9! = 9*8*7*6*5*4*3*2*1
1011 = 1011*1010*1009*1008...3*2*1
what does it mean for two shapes to be proportional.
Answers
Answer:
It means that the quantities have the same relative size. In other words they have the same ratio.
Step-by-step explanation:
For example look at the attached files
ABCD is a rectangle, where AB= x cm and
BC is 1.5 cm less than AB.
If the area of the rectangle is 52 cm³, form
an equation in x and solve it to find the
dimensions of the rectangle.
Answers
Answer:
AB = 8cm ; BC = 6.5 cm
Step-by-step explanation:
BC = x- 1.5
x * (x-1.5) = 52
x^2 - 1.5x - 52 = 0
Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25
We are searching only positive value
(1.5 + 14.5)/2 = 16 / 2 = 8 cm
AB = 8 cm
BC = 8 - 1.5 = 6.5 cm
PLEASE ILL DO ANYTHING I ALREADY OFFERED AS MUCH POINTS AS POSSIBLE
Answers
Answer:
A, B, D, E
Step-by-step explanation:
Given expression:
(0.06) · (0.154)When multiplying decimals, multiply as if there are no decimal points:
[tex]\implies 6 \times 154 = 924[/tex]
Count the number of digits after the decimal in each factor:
0.06 → 2 digits0.154 → 3 digitsTherefore, there is a total of 5 digits.
Put the same number of total digits after the decimal point in the product:
[tex]\implies (0.06) \cdot (0.154)=0.00924[/tex]
-----------------------------------------------------------------------------------------------
Answer option A
[tex]\boxed{6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}}[/tex]
When dividing by multiples of 10 (e.g. 10, 100, 1000 etc.), move the decimal point to the left the same number of places as the number of zeros.
Therefore:
6 ÷ 100 = 0.06154 ÷ 1000 = 0.154[tex]\implies 6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}=(0.06) \cdot (0.154)[/tex]
Therefore, this is a valid answer option.
Answer option B
[tex]\boxed{6 \cdot 154 \cdot \dfrac{1}{100000}}[/tex]
Multiply the numbers 6 and 154:
[tex]\implies 6 \times 154 = 924[/tex]
Divide by 100,000 by moving the decimal point to the left 5 places (since 100,000 has 5 zeros).
[tex]\implies 6 \cdot 154 \cdot \dfrac{1}{100000}=0.00924[/tex]
Therefore, this is a valid answer option.
Answer option C
[tex]\boxed{6 \cdot (0.1) \cdot 154 \cdot (0.01)}[/tex]
Again, employ the technique of multiplying decimals by first multiplying the numbers 6 and 154:
[tex]\implies 6 \cdot 154 = 924[/tex]
Count the number of digits after the decimal in each factor:
0.1 → 1 digit0.01 → 2 digitsTherefore, there is a total of 3 digits.
Put the same number of digits after the decimal point in the product:
[tex]\implies 0.924[/tex]
Therefore, as (0.06) · (0.154) = 0.00924, this answer option does not equal the given expression.
Answer option D
[tex]\boxed{6 \cdot 154 \cdot (0.00001)}[/tex]
Again, employing the technique of multiplying decimals.
As there are a total of 5 digits after the decimals:
[tex]\implies 6 \cdot 154 \cdot (0.00001)=0.00924[/tex]
Therefore, this is a valid answer option.
Answer option E
[tex]\boxed{0.00924}[/tex]
As we have already calculated, (0.06) · (0.154) = 0.00924.
Therefore, this is a valid answer option.
Select all correct answers. one solution to a quadratic equation is . what is true about any remaining solutions? there are at least two more real solutions. there are no other real solutions. there is exactly one complex solution. there are two or more complex solutions. there are no complex solutions. there is exactly one more real solution.
Answers
There is exactly one more real solution or there is exactly one more complex solution
Given,
One solution to a quadratic equation is x = -5/3
We have to find the correct statements from the given ones;
A polynomial of degree two is a quadratic equation.
This implies that a polynomial has two solutions.
We already have an answer to the query, which is a true root.
Then, the additional response that we lack can appear in the form of two responses.
It may be a real root or a complicated root, depending on the situation.
The following is the response to this query:
There is exactly one more real solution or there is exactly one more complex solution
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What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.
∠Z ≅ ∠G and XZ ≅ FG
∠Z ≅ ∠G and ∠Y ≅ ∠E
XZ ≅ FG and ZY ≅ GE
XY ≅ EF and ZY ≅ FG
∠Z ≅ ∠G and XY ≅ FE
intuitive distortion
Answers
The additional information that could be used to prove that ΔXYZ ≅ ΔFEG by ASA or AAS are:
∠Z ≅ ∠G and XZ ≅ FG
∠Z ≅ ∠G and XY ≅ FE .
What is ASA and AAS?The AAS is a theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent angles and a pair of non-included sides.
The SAS is also another theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent sides and a pair of included congruent angles.
From the image attached below, we are only given one pair of congruent angles, which is ∠X ≅ ∠F.
Therefore, for both triangles to be congruent by AAS or SAS, the additional information needed are:
∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE .
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