Step-by-step explanation:
4/x + 4 = x - 2/x
multiply everything by x
4 + 4x = x² - 2
x² - 4x - 6 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (4 ± sqrt((-4)² - 4×1×-6))/(2×1) =
= (4 ± sqrt(16 + 24))/2 = (4 ± sqrt(40))/2 =
= (4 ± sqrt(4×10))/2 = (4 ± 2×sqrt(10))/2 =
= 2 ± sqrt(10)
x1 = 2 + sqrt(10) = 5.16227766...
x2 = 2 - sqrt(10) = -1.16227766...
A. What are the coordinates of R’ if R (-2, 7) is dilated around the origin with k=3?
B. What are the coordinates of T’ if T (4,-1) is dilated by a scale factor of ½ with R as the center of the dilation?
A: The coordinates of the point R' are (- 6, 21).
B: The coordinates of the point T' are (1, 3).
How to generate new points by definition of dilation
In this question we must make use of rigid transformations to find the location of new points, rigid transformations are transformations used in geometric loci such that Euclidean distance is conserved. In this case, we need to use a kind of rigid transformation known as dilation, which is defined below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)] (1)
Where:
O(x, y) - Center of dilationk - Dilation factorP(x, y) - Original pointP'(x, y) - Resulting pointPart A - If we know that O(x, y) = (0, 0), R(x, y) = (- 2, 7) and k = 3, then the coordinates of point R' are:
R'(x, y) = (0, 0) + 3 · [(- 2, 7) - (0, 0)]
R'(x, y) = (- 6, 21)
Part B - If we know that O(x, y) = (- 2, 7), T(x, y) = (4, - 1) and k = 1/2, then the coordinates of point T' are:
T'(x, y) = (- 2, 7) + (1 / 2) · [(4, - 1) - (- 2, 7)]
T'(x, y) = (- 2, 7) + (1 / 2) · (6, - 8)
T'(x, y) = (- 2, 7) + (3, - 4)
T'(x, y) = (1, 3)
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Jumlah panjang diagonal ruang sebuah kubus adalah 36 cm, maka volume kubus adalah .... cm3
MOHON PAKAI CARA YA TERIMAKASIH
V kubus = s³
= (36 cm)³
= 46.656 cm³
Step-by-step explanation:Kubus adalah sebuah bangun ruang tiga dimensi yang panjang semua rusuknya sama. Dan semua sisinya berbentuk persegi.
SEMOGA MEMBANTU
From the top of a building 30 meters high, the angle of elevation to the top of a monument is found to be equal to the angle of depression to the foot of the monument. Find the height of the monument.
The height of the monument is 30 meters.
We have,
Let's assume the height of the monument is "h" meters.
From the top of the building, the angle of elevation to the top of the monument is equal to the angle of depression to the foot of the monument. This forms a right triangle with the building, the monument, and the ground.
In this triangle, the opposite side of the angle of elevation is the height of the building, which is given as 30 meters.
The opposite side of the angle of depression is the height of the monument, which is "h" meters.
Since the angles of elevation and depression are equal, the triangle is an isosceles triangle.
Therefore, the opposite sides are equal in length.
By setting up the equation:
h = 30
Thus,
The height of the monument is 30 meters.
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2.
(03.01 MC)
Which equation justifies why nine to the one third power equals the cube root of nine? (1 point)
nine to the one third power all raised to the third power equals nine raised to the one third times three power equals nine
nine to the one third power all raised to the third power equals nine raised to the one third plus three power equals nine
nine to the one third power all raised to the third power equals nine raised to the one third minus three power equals nine
nine to the one third power all raised to the third power equals nine raised to the three minus one third power equals nine
The equation "nine to the one-third power, all raised to the third power, equals nine" is the correct justification for why nine to the one-third power equals the cube root of nine.
The equation that justifies why nine to the one-third power equals the cube root of nine is:
"nine to the one-third power, all raised to the third power, equals nine."
To understand why this equation is true, let's break it down:
Start with nine raised to the one-third power: \(9^{(1/3).\)
The exponent of 1/3 indicates the cube root operation.
Now, raise this result to the third power: \((9^{(1/3)})^3\).
When you raise a power to another power, you multiply the exponents.
\((9^{(1/3}))^3 = 9^{(1/3 \times 3)} = 9^1 = 9.\)
By performing these calculations, we see that the value of\((9^{(1/3)})^3\) is equal to 9.
Therefore, the equation "nine to the one-third power, all raised to the third power, equals nine" is the correct justification for why nine to the one-third power equals the cube root of nine.
It's important to note that the other options provided in the question are not correct.
The correct equation emphasizes that the exponentiation and the cube root operation cancel each other out, resulting in the original value of nine.
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You do not need to draw the line of best fit, I just need the answers for the rest. Thanks!
Answer:
c
Step-by-step explanation:
I NEED HELPP Solve for PMR please
The angle PMR in the quadrilateral is 32 degrees.
How to find the angle PMR?The angle PMR can be found as follows;
The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.
∠RPM ≅ ∠WPM
Hence,
∠RPM ≅ ∠WPM = 58 degrees
Therefore,
∠WPM = 58 degrees
∠PWM = 90 degrees
Let's find ∠PMR as follows
∠PMR = 180 - 90 - 58
∠PMR = 90 - 58
∠PMR = 32 degrees
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Select the situation that have a unit rate equivalent to 3 units to 1 unit
Answer:
A gardener harvested 15 tomatoes from 5 plants
find the slope of the line passing through the points (6,-7) and (3,-3) .
Answer:
y2-y1 / x2-x1
-4/3
Step-by-step explanation:
Answer:
-4/3
Step-by-step explanation:
When given two points, the slope is found by
m = (y2-y1)/(x2-x1)
= (-3- -7)/(3 -6)
= (-3+7)/(3-6)
= 4/-3
= -4/3
Blinko’s charges $24.99 to print 100 top-quality single-page resumes. Each additional 50 copies cost $10. Which of the following functions models the cost, r(x), where x is an integer?
Answer:
r (x) ={24.99
{ 24.99 + 10 (x - 2) x < 2
x > 2
Step-by-step explanation:
Not sure if this is what you asked for but this is the best I got sorry.
The function which models the cost will be;
⇒ r (x) = $24.99 + 50 × $10
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Blinko charges $24.99 to print 100 top-quality single-page resumes.
And, Each additional 50 copies cost $10.
Now,
Let the total cost = r(x)
Here, Blinko charges $24.99 to print 100 top-quality single-page resumes.
And, Each additional 50 copies cost $10.
So, We can formulate;
⇒ r (x) = $24.99 + 50 × $10
⇒ r (x) = $24.99 + $500
⇒ r (x) = $529.44
Thus, The function which models the cost will be;
⇒ r (x) = $24.99 + 50 × $10
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What is the answer to c?
Answer:
The answer is 6.5
Step-by-step explanation:
The equation is y=3x-1. Plug in 2.5 as the value for x and solve.
3×2.5=7.5
7.5-1=6.5
Help plz I will give Brainlyest
The questions on a multiple choice test have four answer choices.
Which of the following models could you use to simulate the outcome of guessing the correct answers to a 50-question test?
(HINT: Remember to choose a model with the same number of possible outcomes as each test question.)
Group of answer choices
A. flipping a coin 50 times
B. spinning a spinner with 4 equal sections 50 times
C. rolling a 6-sided die 50 times
D. spinning a spinner with 50 equal sections four times
Answer: spinning a spinner with 4 equal sections 50 times
Step-by-step explanation:
The models that one can use to simulate the outcome of guessing the correct answers to a 50-question test will be to spinn a spinner with 4 equal sections 50 times.
Flipping a coin 50 times is wrong since the coin only has two outcomes which are head and tail. Rolling a 6-sided die 50 times is also wrong.
Therefore, the correct option is B.
What segment is congruent to CD?
Answer:
we need a picture of the problem
Step-by-step explanation:
HELP ME NO RANDOM ANSWERS
Answer: A
Step-by-step explanation:
The answer is letter A..
Question 3 Evaluate. 2|4y+9|=4 Answer A y=7/4 B y=−74,y=11/4 C y=−7/4,y=−11/4 D nosolutio
Answer:
C
Step-by-step explanation:
2|4y+9|/2=4/2
4y+9=2
4y+9=2 or 4y+9=-2
4y=2-9 or 4y=-2-9
4y/4=-7/4 or 4y/4=-11/4
y=-7/4 or y=-11/4
The values of y are -11/4 and -7/4. Therefore, option (C) is correct.
What is an equation ?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
2|4y + 9 | = 4
To find the value of y,
Simplify the equation,
|4y + 9 | = 4 / 2
|4y + 9 | = 2
Use mode property,
-2 ≤ 4y + 9 < 2
Subtract 9 from whole the equation,
-2 - 9 ≤ 4y + 9 - 9 ≤ 2 - 9
-11 ≤ 4y ≤ -7
y = -11/4 and y = -7/4.
The values of y are -11/4 and -7/4.
Hence, option (C) is correct.
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What is the meaning of "if \(\varphi (x)\) has no parameters \(p_{i}\) then the class C is definable"?
The meaning of the statement, "if the function has no parameters, then the class C is definable" is that if there are no parameters given then the class c can be defined with an empty set but if there are no parameters, then the class cannot be defined.
What is the meaning of the statement?The meaning of the above statement is that if no parameters are provided for this function, then the given class represented as c can be defined with an empty set that is enclosed in parameters.
Also, if the parameters are given then the class c is not defined.
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What are two pairs of opposite sides that are parallel and congruent?
Parallelogram have two pairs of opposite sides that are parallel and congruent.
In a parallelogram, two pairs of opposite sides are parallel and congruent. A parallelogram is a quadrilateral with opposite sides that are parallel and congruent. Therefore, any pair of opposite sides in a parallelogram satisfies the criteria of being both parallel and congruent.
For example, let's consider a parallelogram ABCD:
Side AB is parallel and congruent to side CD.Side AD is parallel and congruent to side BC.These two pairs of opposite sides, AB and CD, and AD and BC, are parallel (they never intersect) and congruent (they have the same length).
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Cliff (W-2 wages: $16,228) and Deb (W-2 wages: $2,600) send their daughter Julia (born 10-1-2010) to daycare while they both worked. They paid $250 per month for daycare. They are filing MFJ. They can claim the credit for child and dependent care expenses. What is their eligible amount of work-related daycare expenses?
The eligible amount of work-related daycare expenses will be $2600
What is MFJ?Married filing jointly is a filing status for married couples, allowing them to file joint tax returns. When filing taxes under married filing jointly status, a married couple can record their respective incomes, deductions, credits, and exemptions on the same tax return.
Given here wages of the cliff are $16,228 and if the deb is $2,600
now the mfj is 35% hence cliffs credit is 35% × $16,228 = $5679.8
and daycare yearly expenses are = $250×12
= $3000
but deb's income is $2600 and thus credit cannot exceed deb's wages therefore the revised credit would be $2600
Hence, the eligible amount of work-related daycare expenses will be $2600
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The perimeter of a playing field for a certain sport is 214 ft. The field is a rectangle, and the length is 41 ft longer than the width . Find the dimensions.
Answer:
width: 33 ft
length: 74 ft
Step-by-step explanation:
The perimeter of a rectangle is calculated by adding all of the sides together which includes two lengths and two widths. Since the formula for the length is given (l = 41ft + w) and the perimeter is given, then we can simply use the perimeter formula and substitute the value of length with its formula which would only leave us with one variable in the equation w. Now we must solve for w.
l + l + w + w = 214
(41 + w) + (41 +w) + w + w = 214 ... combine like terms
82 + 4w = 214 ... subtract 82 from both sides
4w = 132 ... divide both sides by 4
w = 33 ft
Finally, we can see that the value of the width is 33 ft . Now we plug this value into the formula for length to calculate its value.
l = 41 + w
l = 41 + 33
l = 74 ft
Noah has 19 bacon pancakes on his plate, and Mackenzie has x less bacon pancakes than Noah. Choose the expression that show how many bacon pancakes Mackenzie has.
Answer:
19-x
the expression that show how many bacon pancakes Mackenzie is 19 - x
On November 1st, Halloween candy is discounted 60%. If the original price of a bag of candy corn was $5, what is the final price of the candy, including the discount and a 10% sales tax?
Answer:
$2.20
Step-by-step explanation:
Original price (before discount and before tax): $5
Discount is 60%.
Amount of discount is: 60% of $5 = 0.6 × $5 = $3
Price after 60% discount: $5 - $3 = $2
Tax is 10%.
Amount of tax is: 10% of $2 = 0.1 × $2 = $0.20
Final price = price after discount + tax = $2.00 + $0.20 = $2.20
A percentage is a way to describe a part of a whole. The final price of the candy, including the discount and a 10% sales tax is $2.2.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given that the cost of the candy is $5 and a 60% discount is given on the candy. Therefore, the price of the candy after the discount will be,
Discounted price = Price - 60% of price
= $5 - 0.60($5)
= $5 - $3
= $2
Now, on the price of the candy 10% sales tax will be added. Therefore, the Price of the candy after adding Tax will be,
Taxed price = Discounted price + 10% of discounted price
= $2 + 0.10($2)
= $2 + $0.2
= $2.02
Hence, the final price of the candy, including the discount and a 10% sales tax is $2.2.
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Pls help with this one I give brainliest thank you! Number 7
Answer:
length x width x height = volume
5.5 x 2 = 11 x 3 = 33
33 ft.
hope this helps
if you have any questions you can ask!
Step-by-step explanation:
What is the surface area of the image below I’ll give b brainliest
Answer:
50(5π + 6) cm²
Step-by-step explanation:
TSA of figure = 1/2 of TSA(Cylinder) + Area of rectangle
= 1/2 of 2πr(h+r) + 20*15
= πr(h+r) + 300
= 10π(15+10) + 300
= 250π + 300 cm²
or 50(5π + 6) cm²
The graph shows the distribution of the lengths (in seconds) of videos on a popular video-streaming site. The distribution is approximately Normal, with a mean of 264 seconds and a standard deviation of 75 seconds.
A graph titled Streaming Videos has length (seconds) on the x-axis, going from negative 36 to 564. The highest point of the curve is at 264.
What percentage of videos on the streaming site are between 264 and 489 seconds?
0.15%
49.85%
95%
99.7%
According to the properties of the standard normal distribution, approximately 99.7% of the values lie within three standard deviations of the mean. Therefore, the answer is 99.7%.
To determine the percentage of videos on the streaming site that are between 264 and 489 seconds, we need to calculate the area under the normal curve within that range. Since the distribution is approximately normal with a mean of 264 seconds and a standard deviation of 75 seconds, we can use the properties of the standard normal distribution to find the desired percentage.
First, we need to convert the values 264 and 489 to z-scores, which represent the number of standard deviations a particular value is away from the mean. The z-score formula is given by:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
z1 = (264 - 264) / 75 = 0
z2 = (489 - 264) / 75 = 3
Next, we can use a standard normal distribution table or a calculator to find the area under the curve between z = 0 and z = 3. The area represents the percentage of videos falling within that range. The answer is 99.7% .
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i need help with this
Answer:
just put any number for the answer if im reading it right they should all answer 0
Step-by-step explanation:
hope i helped ;)
What is the length of the apothem of the regular pentagon shown below? Round to one decimal place
The length of the apothem of the regular pentagon shown is 5.2 meters
How to determine the length of the apothem?Represent the central angle of the regular pentagon using x
The value of the central angle of the regular pentagon is then calculated as:
x = 360/n
Where n represents the number of sides
i.e n = 5
So, we have:
x = 360/5
Evaluate the quotient
x = 72
Represents the apothem with y.
The apothem is then calculated as:
tan(x/2) = (Side length/2)/Apothem
This gives
tan(72/2) = (7.6/2)/y
Evaluate the quotient
tan(36) =3.8/y
Multiply both sides by y
y tan(36) = 3.8
Divide both sides by tan(36)
y = 3.8/tan(36)
Evaluate the quotient
y = 5.2
Hence, the length of the apothem of the regular pentagon shown is 5.2 meters
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Pleaseeeee help I'll give Brainliest urgent!!!!!!!!!!!!!!!
Answer:
2
Step-by-step explanatio: look at the chart
2~~~~~~~~~~~~~~~~~~~~~~~~~~~~
After three exams, Jenny has a mean score of 74. With only one exam remaining in the class, what is the
minimum score she will need on that exam to have an overall mean of 80?
The minimum score Jenny need on that exam to have an overall mean of 80 is 98.
What is mean?In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).
Given that, after three exams, Jenny has a mean score of 74.
Let the minimum score of the one exam remaining be x
Now, (3×74+x)/4 =80
⇒ 222+x=320
⇒ x=320-222
⇒ x=98
Therefore, the minimum score Jenny need on that exam to have an overall mean of 80 is 98.
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Mr. Jay sells a box of 15 seedlings for new trees for $12.84. Mr. Tony sells a box of 18 seedlings for $14.95. What is the cost per seedling for each person? Round your answer to the nearest cent (hundredth). Which is the better buy?
Mr. Jay’s cost $____________ per seed. Mr. Tony’s cost $____________ per seed.
Buying a box of seedlings from _____________________ is the batter buy.
Answer: Mr. Jay’s cost 85 cents and Mr. Tony’s costs 83 cents.
Step-by-step explanation:
you divide the price by how many seeds they sold.
C. A musician had 1.2 x 102
fans at his very first show
ever played. Six years later,
84,000 people were at his
show. How many times more
people were at his most recent
show compared to the very
first show he played?
Answer:
688 people
Step-by-step explanation: