1) The new points of dilation for parallelogram ABCD are:
A (-3,2)
B(-1.333, 2)
C (0, 1)
D (-2, 1)
2) the new points of dilation for kite EFGH are:
E (-6, -6)
F (0, 8)
G (6, -6)
F( 0, -10)
See the attached images for the dilated shapes.
What is dilation in Math?A dilation is a function f from a metric space M into itself that fulfills the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real integer. Such a dilatation is a resemblance of space in Euclidean space.
Parallelogram ABCD
Original Point are:
A (-9,6)
B(-4, 6)
C (0, 3)
D (-6, 3)
Since the scale factor is 1/3 which is less than one, this means that the shpe will be reduced in size.
We can do this by multiplying each of the the original coordinates by 1/3 to get:
A (-3,2)
B(-1.333, 2)
C (0, 1)
D (-2, 1)
Plotting the above on the cartesian coordinate plane will given the new position and size. See the attached imge.
Kite EFGH
In this case the scale factor is 2. This means the image will be getting bigger.
The original coordinates are:
E (-3, -3)
F (0, 4)
G (3, -3)
H ( 0, -5)
Multiplying each by two, we have:
E' (-6, -6)
F' (0, 8)
G' (6, -6)
H' ( 0, -10)
Plotting the above will given the dilated coordinates will result in the new shape.
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Simplify the expression. Write your answers using integers or improper fractions.
− 3/2(1/2 n+2n−3)+4n
The expression is simplified to n - 16/ 4
What are algebraic expressions?
Algebraic expressions are expressions comprising of terms, variables, factors, constants and coefficients.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, bracket, etc.
Given the expression;
− 3/2(1/2 n+2n−3)+4n
Solve the variables in the bracket, we have;
- 3/ 2 { n + 4n - 6 / 2} + 4n
-3/2 { 5n - 6/ 2 } + 4n
expand the bracket
- 15n - 18/ 4 + 4n
Fin the LCM
-15n - 16 + 16n /4
n - 16/ 4
Thus, the expression is simplified to n - 16/ 4
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what is limit definition of a derivative?
The limit definition of a derivative is a mathematical method used to calculate the instant rate of change of a characteristic at a particular point. it is based at the idea of the limit of a function because the input techniques a certain cost.
The limit definition of a derivative is expressed as follows:
\(f'(x) = lim (h → 0) [f(x + h) - f(x)] /h\)
Wherein f'(x) represents the derivative of the function f(x) at a particular factor x. The expression \(( f(x + h) - f(x)) / h\) represents the common price of alternate of the characteristic over a small interval of size h, focused at x. The limit of this expression as h approaches 0 represents the instant fee of change of the characteristic at x, or the slope of the tangent line to the function at that factor.
The limit definition of a derivative is a fundamental concept in calculus and is used to calculate the slopes of tangent lines, to find maximum and minimum factors, and to clear up optimization issues in a huge variety of packages.
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Joanie is 11 5 6 years old. Nancy is 1 1 3 years older than Joanie and Jane is 1 1 4 years older than Nancy. How old is Jane?
Answer:
jane is 1383 years old!!
Step-by-step explanation:
Which is the correct first step in finding the area of the base of a cylinder with a volume of 140pi cubic meters and a height of 12 meters?
Answer:
CCCC
Step-by-step explanation:
a certain bacteria population increases continuously at a rate proportional to its current number. the initial population of the bacteria is 70. the population increases to 360 bacteria in 4 hours. approximately how many bacteria are there in 7 hours? round your answer to the nearest whole number.
Rounding the result to the nearest whole number, we find that approximately 24,108 bacteria are expected to be present after 7 hours.
To solve this problem, we can use the exponential growth formula for population growth:
N(t) = N₀ * e^(kt),
where:
N(t) is the population at time t,
N₀ is the initial population,
e is the base of the natural logarithm (approximately 2.71828),
k is the growth rate constant,
t is the time in hours.
We are given the initial population N₀ = 70 and the population after 4 hours N(4) = 360.
Using this information, we can solve for the growth rate constant k:
N(4) = 70 * e^(4k) = 360
Dividing both sides of the equation by 70:
e^(4k) = 360/70
Taking the natural logarithm (ln) of both sides:
4k = ln(360/70)
Simplifying:
k = ln(360/70) / 4
Now that we have the value of k, we can find the population N(7) after 7 hours:
N(7) = 70 * e^(7k)
Substituting the value of k:
N(7) = 70 * e^(7 * ln(360/70) / 4)
Using a calculator, we can evaluate this expression:
N(7) ≈ 70 * e^(7 * ln(360/70) / 4) ≈ 70 * 345.828 ≈ 24107.96
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How can you write the value of 6 hundred thousandths?
We can write the value of 6 hundred thousandths by using multiplication and the required value is 6,00,000.
This problem can be done by using multiplication. Like 6 hundred can be multiplied with the thousand then the value gets. We can write the value of 6 hundred thousandths by using multiplication and the required value is 6lakhs.
In mathematics, the number has ones place, tens place and hundreds place, thousands place. So, by that we can conclude the required value.
The value can be get by multiplying the given terms
Given 600 and multiplied by thousandths
600 * 1000 = 6,00,000
So, the required value is 6 lakhs or 6,00,000.
Therefore, this problem can be done by using multiplication. Like 6 hundred can be multiplied with the thousand then the value gets. We can write the value of 6 hundred thousandths by using multiplication and the required value is 6lakhs.
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Hey could anyone help? Bit stuck on this question
Some important concept before solving answer :-
\( \\ \)
When ever there is three dimensional figure remember, where one figure is related to other then there's always relation with volume.
So it may get pretty difficult to understand therefore I am dividing into small parts for better understanding.
\( \\ \)
\( \pmb{ \bf \dag\cal{Part \ One:}}\)
As we know there will be relation of volume, so let's find volume of the cone first.
\( \\ \)
Given :-
⭑Height = 10 cm
⭑radius = 3cm
\( \\ \)
To find :
⭑volume of cone
\( \\ \)
Let represent :-
⭑Height as : h
⭑radius as : r
⭑volume of cone as : v
\( \\ \\ \)
Formula to find volume of cone :-
\( \\\)
\( \bigstar\boxed{ \rm v = \pi {r}^{2} \times \frac{h}{3} }\)
\( \\ \)
So let's find v!
\( \\ \)
\( \dashrightarrow\sf v = \pi {r}^{2} \times \dfrac{h}{3} \)
\( \\ \\ \)
\( \dashrightarrow\sf v = \dfrac{22}{7} \times {3}^{2} \times \dfrac{10}{3} \)
\( \\ \\ \)
\( \dashrightarrow\sf v = \dfrac{22}{7} \times {3} \times 3\times \dfrac{10}{3} \)
\( \\ \\ \)
\( \dashrightarrow\sf v = \dfrac{22}{7} \times {\cancel3} \times 3\times \dfrac{10}{\cancel3} \)
\( \\ \\ \)
\( \dashrightarrow\sf v = \dfrac{22}{7}\times 3\times \dfrac{10}{1} \)
\( \\ \)
\( \dashrightarrow\sf v = \dfrac{22}{7}\times 3\times10\)
\( \\ \\ \)
\( \dashrightarrow\sf v = \dfrac{22\times 3\times10}{7}\)
\( \\ \\ \)
\( \dashrightarrow\sf v = \dfrac{22\times 30}{7}\)
\( \\ \\ \)
\( \dashrightarrow\sf v = \dfrac{660}{7}\)
\( \\ \\ \)
\( \dashrightarrow\bf v =94.3 {cm}^{3} \)
\( \\ \\ \)
\( \pmb{ \bf \dag\cal{Part \: \: Two:}}\)
So remember that cone filled with water is equal to volume of cone.
volume of water filled in cone = volume of water in cuboid.
So you probably thinking that above sentence is wrong , cause they haven't told volumes of cuboid and cone are equal, but we have to find depth of water filled not depth of cuboid.
\( \\ \\ \)
Given :-
⭑Volume of cuboid = 94.3 cm³
⭑Length of cuboid = 5cm
⭑Width of cuboid = 3cm
\( \\ \)
To find :-
⭑Depth of water in cuboid
\( \\ \)
Let represent:-
⭑Volume of cuboid as : V'
⭑Length of cuboid as : L
⭑Width of cuboid as : W
⭑Depth of water in cuboid as : D
\( \\ \\ \)
Formula to find volume of cuboid :-
\( \\ \\ \)
\( \bigstar\boxed{ \rm V'= W \times L \times D }\)
By using this formula we can find depth of cuboid.
\( \\ \\ \)
\( : \implies \sf V'= W \times L \times D \)
\( \\ \\ \)
\( : \implies \sf 94.3= D \times 3 \times 5\)
\( \\ \\ \)
\( : \implies \sf \dfrac{943}{10\times 3 \times 5} = D \)
\( \\ \\ \)
\( : \implies \sf \dfrac{943}{10 \times 15} = D \)
\( \\ \\ \)
\( : \implies \sf \dfrac{943}{150} = D \)
\( \\ \\ \)
\( : \implies \sf D = \dfrac{943}{150} \)
\( \\ \\ \)
\( : \implies \bf D = 6.3cm\)
\( \\ \\ \)
Required Answer:-
Depth = 6.3 cm
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Step-by-step explanation:
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You did it please don't delete
Which is the correct graph?
Question 17
The slope is 1 and the y-intercept is 1.
Answer is A.Question 18
The slope is -3/5 and the y-intercept is 1.
Answer is B.Answer:
17: A
18: B
Step-by-step explanation:
17: this is because there are only 2 positive graphs and only A has the y intercept of 1
18: there are only 2 negative graphs and only B has an intercept of 1
Examination practice
Exam-style questions
1 The quadratic equation x2 - 5x – 3 = 0 has solutions a and b. Find the value of:
i a - b
ii a + b
Leave your answers in exact form.
Answer:
Please refer to the attachment
Hope it helps
Please mark me as the brainliest
Thank you
5) Annalisa’s favorite snack is Triscuits. Her mom buys her a big box for a special treat, and Annalisa wants to figure out exactly how much of her sweet and salty snack is in the box. The box has a volume PLS help omg
3 inches
3 cubic inches
8 cubic inches
8 inches
Answer:
8 cubic inches
Step-by-step explanation:
The problem mentions that the box has a volume, which is a measure of the amount of space that the box occupies. Volume is typically measured in cubic units, such as cubic inches, cubic feet, or cubic meters.
Lily is practicing multiplying complex numbers using the complex number (2+i).
To determine the value of (2+i)²,Lily performs the following operations:
Step 1: (2+i)²= 4+i²
Step 2: 4+i² = 4+ (−1)
Step 3: 4+(-1)=3
Lily made an error.
Explain Lily's error and correct the step which contains the error.
Bonus:
Lily is continuing to explore different ways in which complex numbers can be multiplied so the
answer is not a complex number. Lily multiplies (2+i) and (a+bi), where a and b are real
numbers, and finds that her answer is not a complex number.
A. Write an equation that expresses the relationship between a and b.
Lily's error is in the first step, (2+i)^2 ≠ 4 + i^2.
(2+i)^2 = (2+i)(2+i) and you need to FOIL.
(2+i)^2 = (2+i)(2+i)
= 4 + 2i + 2i + i^2
= 4 + 4i + (-1)
= 3 + 4i
Bonus:
If you want to multipy (2+i) by (a+bi) and not end up with a complex number, you'd first FOIL
(2+i)(a+bi) = 2a + 2bi + ai + bi^2
We know i^2 = -1, so this becomes
= 2a + 2bi + ai + b(-1)
= 2a + 2bi + ai - b
= 2a - b + 2bi + ai
Now, for this not to be complex, we need the imaginary pieces to cancel each other out. In other words 2bi+ai=0. For that to happen, 2b + a = 0, or
2b = -a or a = -2b
So it would seem that if we pick any b-value and make a = -2b, then we'll end up with a non-complex number.
Let's try b=5, making a = -10
(2+i)(-10+5i) = -20 + 10i - 10i + 5i^2
The 10i's cancel and 5i^2 = -5, so we're left just with -25.
how to find volume of a prism
Answer:
- HOW TO FIND VOLUME OF PRISM -
1st step - Write the formula for finding the volume of a regular pentagonal prism. The formula is V = [1/2 x 5 x side x apothem] x height of the prism.
2nd step - Find the area of the pentagonal base face. Let's say the length of a side is 6 cm and the length of the apothem is 7 cm.
3rd step - Find the height. Let's say the height of the shape is 10 cm.
4th step - Multiply the area of the pentagonal base face times the height. ...
and last step - State your answer in cubic units.
Step-by-step explanation:
:):):)
the slide part of a water slide is 89 feet long and makes a 42 angle of depression with the ground, how high up in the air do you start your ride?
In a case whereby the slide part of a water slide is 89 feet long and makes a 42 angle of depression with the ground, the lenght or how high up in the air is 73.6 feet
How can the height ber calculated?We know that the length of the slide AB is 89 feet, and the angle of depression from A to B is 42 degrees. We want to find the height h of point A above the ground.
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is h (the height we're looking for), and the adjacent side is AB (the length of the slide). So we can write base on trigonometery as ;
tan(42) = h / 89
h = 89 * tan(42)
h ≈ 73.6 feet
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PLEASE I NEED THE ANSWER WITH THE EXPLANATION DON'T IGNORE MY QUESTION!!!
The
mean of six numbers is 12.five of the numbers
are 11,7,21,14 and 9. calculate the sixth number.
The answer is attached. I hope this helps answer your question!
Answer:
10
Step-by-step explanation:
data=11,7,21,14,9,x
mean=sum of data/no of data
12=11+7+21+14+9+x/6
12*6=62+x
72-62=x
10=x
therefore sixth number is 10.
The state of Colorado covers about 1.04 x 10^5 square miles. The Indian Ocean covers about 2.808 x 10^7 square miles. How many times bigger is the Indian Ocean than Colorado?
Answer:
27976000
Step-by-step explanation:
1.04 x 10^5=104000, and 2.808 x 10^7=28080000
28080000-104000=27976000
that's what I think, did this help
what would you buy if you had $125,000?
I would buy my mom a house :)
Find the perimeter.
7 1/2 + 7 1/2 + 6 + 6
Answer:
Perimeter- The distance around the figure.
Perimeter- 7.5 + 7.5 + 6 + 6
Perimeter- 15 + 6 + 6
Perimeter- 21 + 6
Perimeter- 27 m
Let me know if this helps!
A researcher claims that the percentage of infants who receive immunizations is less than 80%. They select a sample of size 900 infants and 693 have received immunizations. a. State the null and alternative hypotheses. b. Compute the test statistic (z value). c. Compute the P-value. d. What conclusion should be made at a 5% significance level?
The results of given question's parts based on hypothesis testing.
a) Null and Alternative hypothesis
H₀ : p = 0.8
H₀ : p = 0.8 Hₐ : p < 0.8
b) test statistic (z value ) is Z = -2.25.
c) P- value ( Z꜀ ) is - 1.64
d) Rejected the null hypothesis.
We have given that
Sample size, n = 900
Hypothesis population proportion, p₀ = 0.80
Sample proportion , p-hat = 0.77
favourable cases, X = 693
significance level, α = 0.05
a) The following null and alternative hypothesis for population proportion needs to be tested :
H₀ : p = 0.8
Hₐ : p < 0.8
This is corresponding to a left tailed test for a z test for one population will used .
c) we have given that, Significance level is α=0.05 and the critical value for a left tailed test is Z꜀ = - 1.64
so, the rejection region for left tailed test R = { Z Z<- 1.64 }
b) Z- statistic value :
Z = (p-hat - p₀)/√p₀(1-p₀)/n
=> Z = ( 0.77 - 0.8 )/√0.8×0.2/900
=> Z = -2.25
d) Decision about Null hypothesis,
Since, it is observed that Z = - 2.25 < Z꜀ = - 1.645 it is then concluded that the null hypothesis is rejected. Reject the null hypothesis. There is not enough evidence to conclude that the percentage of infants who receive immunization s is less than 80%.
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Please help me on this question!
Based on the information presented, one cup measures a total of 14 centimeters.
How to know the measure of one cup?To discover this, let's start by analyzing the information provided:
2 cups = 16 centimeters4 cups = 20 centimetersThis means that by adding 2 cups, the total height increases by 4 centimeters, and therefore if you add one cup this will increase by 1 centimeter.
Based on this idea, if two cups are 16 cm, let's calculate the height of one cup:
\(16 centimeters -2 centimeters = 14 centimeters\)
Based on the previous information one cup is 14 centimeters.
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Which of the following is equal to the number sentence listed below?
(21 × 25) + (21 × 12)
21 + 25 = 46
21 + 12 = 33
46 + 33 = 79
therefore the answer is 79
Step-by-step explanation: thank you for listening
Please show your work.
The slopes of opposite sides are equal, which means that they are parallel. Therefore, JKLM is a parallelogram.
Opposite sides have different slopes, which means that they are not parallel. Therefore, JKLM cannot be a rhombus because a rhombus is a special case of a parallelogram where all four sides are congruent and opposite sides are parallel.
What are parallelograms and rhombus?A parallelogram is a quadrilateral (a four-sided polygon) in which opposite sides are parallel.
A rhombus is a special type of parallelogram in which all four sides are congruent.
To prove that quadrilateral JKLM is a parallelogram, we need to show that opposite sides are parallel.
We can find the slope of each side by using the formula:
\(m = \dfrac{y_2-y_1}{x_2-x_1}\)
The slope of JK:
(-5 - 1) / (1 - (-3)) = -6/4 = -3/2
The slope of LM:
(4 - (-2)) / (3 - 7) = 6/-4 = -3/2
The slope of KL:
(-2 - (-5)) / (7 - 1) = 3/6 = 1/2
The slope of MJ:
(1 - (-5)) / (-3 - 1) = 6/-4 = -3/2
We can see that the slopes of opposite sides are equal, which means that they are parallel. Therefore, JKLM is a parallelogram.
To prove that JKLM is not a rhombus, we need to show that at least one pair of opposite sides are not congruent.
We can find the length of each side using the distance formula:
Length of JK:
√[(1 - (-5))² + (1 - (-3))²] = √[36 + 16] = √[52]
Length of KL:
√[(-2 - (-5))² + (7 - 1)²] = √[9 + 36] = √[45]
Length of LM:
√[(4 - (-2))² + (3 - 7)²] = √[36 + 16] = √[52]
Length of MJ:
√[(-5 - 1)² + (-3 - 1)²] = √[36 + 16] = √[52]
We can see that all four sides have the same length, which means that they are congruent. Therefore, JKLM is a rhombus.
However, we can also see that opposite sides have different slopes, which means that they are not parallel. Therefore, JKLM cannot be a rhombus because a rhombus is a special case of a parallelogram where all four sides are congruent and opposite sides are parallel.
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a doctor knows that the disease meningitis causes the patient to have a stiff neck 50 % of the time. the doctor also knows that the probability that the patient has meningitis is 1 in 50,000. and the probability that any patient has stiff neck is 1 in 20. find the probability that a patient with the stiff neck has meningitis.
The probability that a patient with a stiff neck has meningitis is very low at 0.002%.
To find the probability that a patient with a stiff neck has meningitis, we can use Bayes' theorem.
Let A be the event that the patient has meningitis and B be the event that the patient has a stiff neck.
We know that P(B|A) = 0.5, meaning that if a patient has meningitis, there is a 50% chance they will have a stiff neck. We also know that P(A) = 1/50,000, meaning that the probability that any patient has meningitis is 1 in 50,000. Additionally, we know that P(B) = 1/20, meaning that the probability that any patient has a stiff neck is 1 in 20.
Using Bayes' theorem, we can find the probability that a patient with a stiff neck has meningitis:
P(A|B) = P(B|A) * P(A) / P(B)
P(A|B) = 0.5 * (1/50,000) / (1/20)
P(A|B) = 0.00002 or 0.002%
Therefore, the probability that a patient with a stiff neck has meningitis is very low at 0.002%.
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The radius of a circle is 8 millimeters. What is the circle's area?
Use 3.14 for PI
HELP!!
Also introduce each terms provided in option!
The error expression of |A - N| in the given problem is: Absolute Error
How to identify the mathematical error?The absolute error is gotten by subtracting the true value from the measured value. The answer is normally expressed as ± or with an absolute value sign. The absolute error equation is expressed as: Absolute error = |measured value - true value|
Relative error is defined as a measurement of error that depends on the absolute error of a measuring tool as well as a measured value. Relative error can thus be defined as a decimal or as a percentage.
Now, we are told that
A is an actual value.
N is near the value,
From the definition of absolute error, we can clearly state that |A - N| is known as absolute error.
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Find the length of the side of the square whose perimeter is 540 mm
Answer:
Step-by-step explanation By verified ✔️
So The answer for this question is 6cm
If the circle radius is 27yd, how do I find the circumference without using pi?
Circumference of a circle having radius of 27 yard can be found using the formula, π = 2(Area of Circle)/r, which is C = 169.6 yd
What is the Circumference of a Circle?Circumference of a circle is the distance round the circle.Circumference = Perimeter Circumference of a circle without using π = 2(Area of Circle)/r.Given:
radius of circle = 27 yd
Thus:
Area = πr² = π(27)²
Area = 2,290.2 yd²
Circumference of a circle without using π = 2(2,290.2)/27
= 169.6 yd.
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The Pythagorean Theorem is
a2 + b2 = c2
a + b = c
c² + a²=b²
Answer:
a² + b² = c²
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
We use the Pythagorean Theorem to help us solve for missing right triangle side lengths. It is wise to remember this formula.
Find the missing factor
Answer:
\((x^4y^5)(x^2y^4)\)
Step-by-step explanation:
Keep these things in mind:
\(x^3\times x^3=x^{3+3}=x^6\\\\(x^3)^3=x^{3\times3}=x^9\)
Using those, simplify the left side of this equation:
\((x^2y^3)^3\\x^6y^9\)
Now we know what the exponents need to become, so we can find the difference between those and what we have on the right:
\(6-4=2\\9-5=4\)
We need to add a 2 to the x, and add a 4 to the y.
\((x^4y^5)(x^2y^4)\)
Write the fraction as a decimal
Round to the nearest hundredth
8
11
[?] is i think 0.73 or 0.73/1. or 73/100
Answer: It is 0.73 my friend. Very good work.
Step-by-step explanation:
90-4x=80-3.5x what’s the value of x (hint: it’s not 1 1/3 or -1 1/3)
Answer:
11/3
Step-by-step explanation: