The answer is
x = 7, -7, √2, -√2
Add the two equations to get
x2 + y2 = 74
Eliminate y from the first by solving for y and using that result:
(x2 − 14) = x√74 - x2
square both sides, then condense:
x4 − 51x2 + 98 = 0
These ready factors:
(x−7)(x+7)(x−√2)(x+√2)=0
I'll let you handle it from there, but keep in mind that if we square all sides, we might find roots that need to be pulled out afterward.
Therefore,
x = 7, -7, √2, -√2
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Paige has 5/6 of a cake to divide evenly among 4 people. What fraction of the cake does each person get?
Each person will get a 5/24 portion of the available cake with Paige
Cake available with Paige = 5/6
Number of people = 4 people
Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
Fraction of cake each person gets:
Cake available with Paige/Number of people with whom the cake is to share equally
= (5/6)/(4)
= (5/6)*(1/4)
= 5/24
The fraction of cake each person will get is 5/24
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x 8 x 7 x 5 x 6 a planned building was going to be 100 feet long, 75 feet deep, and 30 feet high. the owner decides to increase the volume of the building by 10% without changing the dimensions of the depth and the height. what will be the new length of this building?
The new length of the building will be 110 feet.
Volume of Cuboid:
Volume of cuboid is
V = length x breadth x height cubic unit
Given,
The building was going to be 100 feet long, 75 feet deep, and 30 feet high.
Therefore, the volume will be:
= 75 × 100 × 30 ft³
= 225000 ft³
Now owner decided increase the volume of the building by 10% without changing the dimensions of the depth and the height.
There was an increase by 10%,
New volume will be,
V' = 225000 + (10% × 225000)
= 247500 ft³
Therefore, the new length will be:
as,
Volume = length x breadth x height
length = Volume/ (breadth x height)
New length will be
= 247500/(30 × 75)
= 110 feet
Thus the new length of the building will be 110 feet.
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Mai is filling her fish tank. Water flows into the tank at a constant rate complete the table you answer the questions. 1. How many gallons of water will be in the fish tank after 3 minutes? Explain your reasoning. 2. How long will it take to fill the tank with 40 gallons of water. Explain your reasoning. 3. What is the constant of proportionality?
Table:
0.5 : 0.8
1 : ?
3 : ?
? : 40
1. Based on the proportional relationship table created, 4.8 gallons of water will be in the fish tank after 3 mins.
2. 25 minutes.
3. The Constant of proportionality is: 1.6.
How to Determine the Constant of Proportionality?In a proportional relationship between variables x and y, the Constant of proportionality, k, is determined using any pair of values from the table as:
k = y/x.
The relationship is modelled as y = kx.
Constant of proportionality = k = y/x = 0.8/0.5
Constant of proportionality = k = 1.6
The equation for the relationship would be: y = 1.6x. Use the equation to complete the table:
For x = 1:
y = 1.6(1) = 1
For x = 3:
y = 1.6(3) = 4.8
For y = 40:
40 = 1.6x
40/1.6 = x
x = 25
The complete table is:
x y
0.5 0.8
1 1.6
3 4.8
25 40
1. Using the proportional relationship table, we can conclude that, 4.8 gallons of water will be in the fish tank after 3 mins.
2. Using the proportional relationship table, the time it would take to fill the tank with 40 gallons of water is: 25 mins.
3. Constant of proportionality = k = 1.6.
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Help for trigonometry class please
The most appropriate choice for matrix and multiplicative inverse of matrix will be given by
B is the multiplicative inverse of A
What is a matrix and multiplicative inverse of matrix?
Matrix is a rectangular representation of numbers or symbols arranged in the form of rows and column. Matrix is a very important tool in mathematics.
To learn about multiplicative inverse, it is important to know about identity matrix
[tex]\begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}[/tex] is a 2 x 2 identity matrix denoted by I.
Let A and B be two matrices
A is said to be a multiplicative inverse of B if AB = BA = I
Here,
A= [tex]\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}[/tex] B = [tex]\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}[/tex]
AB =
[tex]\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}[/tex]
[tex]\begin{bmatrix} 2\times 1 + 1 \times -1& 2 \times -1 + 1\times 2\\1 \times 1+1\times-1 & 1 \times -1 + 1 \times 2\end{bmatrix}\\\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]
BA =
[tex]\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}[/tex]
[tex]\begin{bmatrix} 1\times 2 + -1 \times 1& 1 \times 1 + -1\times 1\\-1 \times 2+2\times 1 & -1 \times 1+ 2 \times 1\end{bmatrix}\\\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]
AB = BA = [tex]\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]
So B is the multiplicative inverse of A
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Trigonometry question with show work
a)I WILL USE THE THEOREM OF PYTHAGORAS IN TRIANGLE BCD
[tex] {y}^{2} = {(5.3)}^{2} - {(4.4)}^{2} \\ {y}^{2} = 28.9 - 19.36 \\ {y}^{2} = 9.54 \\ y = \sqrt{9.54} \\ y = 3.09[/tex]
y=3.90cm
b)
[tex] \sin(x) = \frac{cb}{ac} \\ \sin(x) = \frac{5.3}{8.2} \\ x = sin^{ - 1} ( \frac{5.3}{8.2} ) \\ x =40.27[/tex]
x=40,27 cm
GOODLUCK.
Write the following ratio using two other notations. 7/3 use only the numbers above
notation one: ?
notation two: ?
7/3 in notation one can be written as 7 : 3 and 7/3 in notation two can be written as 0.7 and 0.3.
What is a ratio?The ratio is a comparison between two similar quantities in the simplest fraction form. We can write ratios in fractions and in decimals also.
We know we can write a : b as a/b in fraction form and a/(a+b) and b/(a+b) in decimal form.
∴ 7/3 in decimal form can be written as 7 : 3 and 7/3 can also be written as 7/(7+3) = 7/10 = 0.7 and 3/(7+3) = 3/10 = 0.3.
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Use the Segment Addition Postulate to find the unknown variables/lengths:
X, Y, and Z are collinear. If Y is between X and Z, XY = (5x-5) feet, YZ = (3x + 3) feet, and XZ = (3x + 8) feet, then x =
feet.
feet, and XZ =
Blank 1:
Blank 2:
Blank 3
PLEASE HURRY
On a tour of a old gold mine, you find a nugget containing 0.82 ounce of gold. Gold is worth $1323.80 per ounce. How much is your nugget worth
For the gold worth $1323.80 per ounce ,the nugget containing 0.82 ounce of gold is worth of $1085.516.
As given in the question,
On a tour of a gold mine,
Ounce of gold contained by nuggets found in the mine = 0.82 ounce
Worth of gold per ounce = $1323.80 per ounce
Worth of nuggets containing 0.82 ounce of gold
Worth of 1 ounce of gold = $1323.80
⇒ Worth of nuggets containing 0.82 ounce of gold =$( 1323.80 ×0.82 )
= $1085.516
Therefore, for the gold worth $1323.80 per ounce ,the nugget containing 0.82 ounce of gold is worth of $1085.516.
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One factor of the function f(x) = x3 − 9x2 + 20x − 12 is (x − 6). Describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technology. Show your work and include all intercepts in your answer.
For the given function f(x), x-intercepts are 1,2 and 6 and the y-intercept is -12
Given :
[tex]f(x) = x^{3} -9x^{2} +20x -12 \\[/tex]
One of the factors of f(x) is (x-6)
Dividing f(x) by (x-6), we get :
[tex]\frac{x^{3} -9x^{2} +20x -12 \\}{x-6} = x^{2} -3x +2[/tex]
Now expanding, [tex]x^{2} -3x +2[/tex]
[tex]x^{2} -3x +2 = x^{2} -2x -x +2 =x(x-2) -(x-2) = (x-2)(x-1)[/tex]
Hence, [tex]x^{3} -9x^{2} +20x -12 = (x-6)(x-1)(x-2)[/tex]
For x-intercept, f(x) = 0 . Then
(x-6)(x-1)(x-2) =0
x = 1,2 and 6
For y-intercept, x=0 in f(x)
f(0) = -12
Hence, the x-intercepts are 1,2, and 6 and the y-intercept is -12.
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"Complete the table" can someone help on thi thank you!
Answer:
2000 pounds is 1 ton
6 tons is 12,000
7 tons is 14,000
16,000 pounds is 8 tons
Write a polynomial P(x) of degree 4 and with zeros 1, 3/2, (which of multiplicity one) and 0 (of multiplicity 2).
Answer
The polynomial is
P(x) = 2x⁴ - 5x³ + 3x²
Explanation
We are told to write a polynomial of degree 4 with zeros (roots)
x = 1
x = (3/2) = 1.5
x = 0
x = 0 (multiplicity of 2 means it appears twice)
So, we can piece together the polynomial
P(x) = (x - 1) (x - 1.5) (x) (x)
We can write this as
P(x) = x² (x - 1) (x - 1.5)
= (x³ - x²) (x - 1.5)
We can multiply through by 2 to turn the 1.5 into a whole number
P(x) = (x³ - x²) (2x - 3)
= x³ (2x - 3) - x² (2x - 3)
= 2x⁴ - 3³ - 2³ + 3x²
= 2x⁴ - 5x³ + 3x²
Hope this Helps!!!
what is the distributive property of 24+40
For a given recipe, 24 cups of flour are mixed with 12 cups of sugar. How many cups of sugar should be used if 8 cups of flour are used?
Answer:
First, 24 divided by 8 equals 3. this means you divide 12 by 3. you get 4. 4 cups of sugar will be used when 8 cups of flour are used.
(20 points) i need help with this asap (the x is -20)
Answer:
119º and 61º
Step-by-step explanation:
2x-15 and 3x+5 are supplementary because the angles corresponding to 2x-15 is supplementary with 3x+5
2x-15+3x+5=180
5x-10=180
5x=190
x=38
fill in x
2(38)-15
=76-15
=61
angle is 61
fill in x for angle 2
3(38)+5
=114+5
=119
angle 2 is 119
Ava took a taxi from her house to the airport. The taxi company charged a pick-up fee
of $1.10 plus $3.75 per mile. The total fare was $19.85, not including the tip. Which
tape diagram could be used to represent the context if a represents the number of
miles in the taxi ride?
A
B
1.1
3.75
1.1
1.1X
3.75
19.85
1.1
19.85
3.75...
3-75
1.1
Using a linear function, it is found that her taxi ride was of 5 miles.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).For the cost function, we have that:
The slope is the cost per mile, hence m = 3.75.The intercept is the flat fee, hence b = 1.10.Thus the cost for a ride of x miles is of:
C(x) = 3.75x + 1.10.
Her total fee was of $19.85, hence the mileage is found as follows:
19.85 = 3.75x + 1.10
x = (19.85 - 1.10)/3.75
x = 5 miles.
Which was the length of her taxi ride.
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What is the difference between a union and an intersection in math?Select one:a. The union of two sets contains only the elements that are in both sets. The intersection of two sets all the elements contained in either set (or both sets).b. The union of two sets contains all the elements contained in either set (or both sets). The intersection of two sets contains only the elements that are in both setsc. The union and intersection are exactly the same.
The union of two sets contains all the elements contained in either set (or both sets). The intersection of two sets contains only the elements that are in both sets
Therefore the answer is B.
What is the missing height?
Answer:
h = 6.36619772 cm
Step-by-step explanation:
h = (3 * v) / (πr2)
Answer:
h = 20 cm
Step-by-step explanation:
the volume (V) of a cone is calculated as
V = [tex]\frac{1}{3}[/tex] πr²h ( where r is the radius )
given r = 9 and V = 540π , then
[tex]\frac{1}{3}[/tex] π × 9² × h = 540π
[tex]\frac{1}{3}[/tex] × π × 81h = 540π
27πh = 540π ( divide both sides by 27π )
h = [tex]\frac{540\pi }{27\pi }[/tex] = 20 cm
solve for x: square root of 3x-4 = 2 times the square root of x-5
The solution of x for the equation [tex]\sqrt{3x - 4} = 2\sqrt{x-5}[/tex] is x = 16.
Given,
The equation; [tex]\sqrt{3x-4} =2\sqrt{x-5}[/tex]
We have to solve this equation to get the value of x.
That is,
[tex]\sqrt{3x-4} =2\sqrt{x-5}[/tex]
Square both sides to remove square root.
[tex]\sqrt{3x-4} ^{2} = (2\sqrt{x-5} )^{2}[/tex]
We get,
3x - 4 = 4 (x - 5)
That is,
3x - 4 = 4x - 20
Here,
20 - 4 = 4x - 3x
Then,
x = 16
That is,
The solution of x for the equation [tex]\sqrt{3x - 4} = 2\sqrt{x-5}[/tex] is x = 16.
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Expand and simplify (x -5)(x- 4).
Answer: x^2-9x+20
Step-by-step explanation: you have to distribute (x-5) (x-4)
which would be x^2-4x -5x +20 when you simplify that you get x^2-9x+20
What is 1000 x 9.2 ?
Write an expression that represents the total owed for 3 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $25?
2(25) + c
25c + 3
3(c) + 25
3(c + 25)
Answer:
3(c) + 25
Step-by-step explanation:
Write an expression that represents the total owed for 3 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $25?
2(25) + c
25c + 3
3(c) + 25
3(c + 25)
Find x of the triangle
Answer:
x=65
Step-by-step explanation:
47+68+x=180
x=65
:]
Answer: 65 = x
Step-by-step explanation:
1) First find the mini triangles, left and right angles
We will be calling the left one A and the right one B.
2) Next use triangle sum to find B.
62 + 50 + b = 180
b=68
3) Use triangle sum again to find A.
53 + 80 + a = 180
a = 47
4) Use triangle sum to find the top mini angle.
47 + 68 + c = 180
c = 65
5) Since x is in the vertical angle of c, they are equal
c = x
65 = x
Graph the image of the figure using the transformation given.
Answer:
D
Step-by-step explanation:
(2x^2+4x-7)(3x-1) use a table
The solution for the given binomial multiplication is 6x³ + 10x² - 17x - 7
Given,
The binomials; (2x² + 4x - 7) (3x - 1)
We can use FOIL method to solve this;
FOIL method;
Binomials are multiplied using the FOIL Method. An acronym is FOIL FOIL. First, Outside, Inside, and Last are the letters that stand for the order of multiplying terms. To get your answer, multiply the first term, then the outside term, then the inside term, then the last term, and then combine terms that are similar.
Here,
(2x² + 4x - 7) (3x - 1)
= (3x × 2x²) + (3x × 4x) - (3x × 7) - 2x² + 4x - 7
= 6x³ + 12x² - 21x - 2x² + 4x - 7
= 6x³ + 10x² - 17x - 7
That is,
The solution for the given binomial multiplication is 6x³ + 10x² - 17x - 7
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16c+4(-5)=220
Just solve
Answer:
15
Step-by-step explanation:
16c+4(-5)=220
16c-20=220
16c=240
C=15
Find x of the triangle
Answer: x = 22
Step-by-step explanation:
We will use the exterior angle theorem to solve. First, we will write an equation, then we will solve by combing like terms are using inverse operations.
(6x - 7) = (2x) + (103 - x)
6x - 7 = 2x + 103 - x
6x - 7 = x + 103
5x = 110
x = 22
A private university has a endowment fund that currently has 49 million dollars in it. if she invested in a one year cd that pays 5.12% interest compounded continuously, how much interest will it earn
If the university invest in a one year CD at 5.12% interest compounded continuously, the interest it will earn is determined by calculating as: Interest = Future value – Present value which would be $2.54 million
Continuously compounded interest means that a principal amount is constantly earning interest with infinite compounding periods for a certain time period. There are no increment compounding periods as with monthly or annually compounding.
The continuously compounding formula:
FV = PV* e^rt
Where FV is the future amount, PV is the initial amount, e is a mathematical constant (2.7183), r is the rate and t is the time period.
Hence,
FV = 49* 2.7183^(0.0512*1) =51.57
Interest earned= 51.57-49=2.54
Hence, the university will earn an interest of $2.54 million.
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What is the area of a triangle whose vertices are J(−2, 1), K(0, 3), and L(4, −4)?
area of triangle with vertices (x1,y1) ; (x2,y2) and (x3,y3) is
(x1 (y2 - y3 ) + x2 ( y3 - y1 )+ x3 ( y1 - y2))/2
hence, substituting the points (x1, y1)= (-2, 1);
( x2, y2)= (0,3) ; and (x3, y3)= (4,-4) in the area formula ,we get
area of triangle =
( -2(3-(-4)) + 0( -4 - 1) + 4(1-3))/2
(-14+0-8)\2
22\2
11 sq unit
a rectngular piece of paper measures 96 cm by 84 cm. it is cut into square pieces of equal lenght such that no paper is wasted. what is the maximum lenght of a square?
89 squares will be present.
Given that the rectangle has the following dimensions: length = 96 cm, breadth = 84 cm, and
its total area is 8064 square centimeters, we may deduce that the maximum square area
[tex]\sqrt[2]{8064}[/tex]
that can be removed from the rectangle with its total area of 8064 square centimeters is equal to 89.8 square centimeters.
In order to determine the total number of squares, divide 8064 by 89.8 to arrive at 89.
How do square roots work?Taking an integer's square root is the opposite of squaring an integer. A number's square value is obtained by multiplying it by itself, whereas the square root value is obtained by finding a number that, when squared, produces the original value of the number.
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Help!!! With this math question
Answer:
QPR SAS
Step-by-step explanation:
As you can see. Hope it can help