Answer:
The equation of the hyperbola in standard form is [tex]\frac{(x - 4)^2 }{ 9} - \frac{(y +2)^2}{2.25} = 1[/tex]
Step-by-step explanation:
Given:
Centre of the hyperbola=(−2,4)
one vertex of the hyperbola= (−2,7) .
slope of the asymptote = 12
To Find:
The equation of the hyperbola in standard form=?
Solution:
W know that the standard form of hyper bola is
[tex]\frac{(x - h)^2 }{ a^2} - \frac{(y - k)^2}{ b^2} = 1[/tex]............................(1)
where
(h,k) is the centre
(x,y) is the vertex of the parabola
a is the length between the centre and the vertices of the hyperbola
b is the distance perpendicular to the transverse axis from the vertex to the asymptotic line
Now the length of a is given by
a=|k-y|
a=|4-7|
a=|-3|
a=3
Also we know that,
Slope =[tex]\frac{a}{b}[/tex]= 2
=>[tex]\frac{3}{b}=2[/tex]
=>[tex]\frac{3}{2}=b[/tex]
=>b=1.5
Now substituting the known values in equation(1)
[tex]\frac{(x - 4)^2 }{ 3^2} - \frac{(y - (-2)^2}{ 1.5^2} = 1[/tex]
[tex]\frac{(x - 4)^2 }{ 9} - \frac{(y +2)^2}{2.25} = 1[/tex]
Answer:
[tex]\frac{(x+2)^{2}}{1296} - \frac{(y-4)^{2}}{9} = 1[/tex]
Step-by-step explanation:
The standard form of a hyperbola centered at a point distinct from origin has the following form:
[tex]\frac{(x-h)^{2}}{a^{2}} - \frac{(y-k)^{2}}{b^{2}} = 1[/tex]
The distance between the center and the vertex is:
[tex]b = \sqrt{[(-2)-(-2)]^{2}+(7-4)^{2}}[/tex]
[tex]b = 3[/tex]
The value of the other semiaxis is:
[tex]\frac{a}{b} = 12[/tex]
[tex]a = 12\cdot b[/tex]
[tex]a = 36[/tex]
The standard equation of the hyperbola is:
[tex]\frac{(x+2)^{2}}{1296} - \frac{(y-4)^{2}}{9} = 1[/tex]
Laura drew the triangle shown below. Side A is 7.8 cm in length. Side C is 9.5 cm in length. What is the measure of angle x, in degrees?
Answer:
55.19 degrees
Step-by-step explanation:
See the given diagram of the triangle attached to this question.
This is a right triangle and one of its angles other than 90° is x degrees.
Now, if we assume c is the hypotenuse and a is the perpendicular, then we can write that
[tex]\sin x = \frac{\textrm{Perpendicular}}{\textrm {Hypotenuse}} = \frac{a}{c}[/tex]
Now, it is given that a = 7.8 cm and c = 9.5 cm.
Therefore, [tex]\sin x = \frac{7.8}{9.5} = 0.821[/tex]
⇒ [tex]x = \sin^{-1} (0.821) = 55.19[/tex] degrees. (Answer)
All computers are on sale for 10% off the original price.If x is the original price of the computer,then the function that represents the price after only a 10% discount is
P(x)=x - 0.1x
P(x)=0.9x
The function that gives the price,C,if only a $150 coupon is used is: C(x)=x-150
All computers are on sale for 10% off the original price. If x is the original price of the computer, then the function that represents the price after only a 10% discount is: P(x) = x - 0.1x P(x) = 0.9x The function that gives the price, C, if only a $150 coupon is used is: C(x) = x - 150 Choose the composition function that gives the final sale price after a 10% discount is followed by a $150 coupon
Answer:The final price of the computer after both discounts is T(x) = 0.9x - 150
Solution:We have been given that all computers are on sale for 10% off the original price. If x is the original price of the computer, then the function that represents the price after only a 10% discount is:
P(x) = x - 0.1x
P(x) = 0.9x
The function that gives the price, C, if only a $150 coupon is used is:
C(x) = x - 150
We need to choose the composition function that gives the final sale price after a 10% discount is followed by a $150 coupon.
So, we have to formulate a function to combine both the discounts.
The price after 10% discount is 0.9x and the price after $150 coupon is x-150.
So, the composite function that gives the final sale price after 10% discount followed by $150 is given as follows:
Let the final price be denoted as T(x)
Therefore,
T(x) = original price - 10% discount - $150 coupon
T(x) = x - 10% of x -150
T(x) = x - 0.1x - 150
T(x) = 0.9x -150
Hence the final price of the computer after both discounts is T(x) = 0.9x-150
Answer:
A
570
Step-by-step explanation:
got it correct
David’s age is four times Alisa’s age. In eight years, David will be twice as old as Alisa. How old is each now?
David is 16 years old.
Alisa is 4 years old.
Find the sum of the first 5 terms of the series.
7 - 14 + 28 - 56+...
Answer:
The sum of the first 5 terms of the series is 77.
Step-by-step explanation:
1. Let's review the information provided to us for solving the sum of the first 5 terms of the series:
1st term = 7
2nd term = - 14
3rd term = 28
4th term = - 56
2. Let's solve the sum of the first 5 terms of the series:
Aₙ = Aₙ₋₁ * -2 ; A₁ = 7
A₁ = 7
A₂ = A₁ * -2 = 7 * - 2 = - 14
A₃ = A₂ * - 2 = -14 * - 2 = 28
A₄ = A₃ * - 2 = 28 * - 2 = - 56
A₅ = A₄ * - 2 = -56 * - 2 = 112
Sum of the first 5 terms of the series = 7 - 14 + 28 - 56 + 112
Sum of the first 5 terms of the series = 77
A company rents two storage units. Both units are cube-shaped. what is the difference in volume of the two storage units? note that the volume of a cube is s cubed where s is the side length explained
The question is missing the figure. So, the figure is attached below.
Answer:
237.375 ft³
Step-by-step explanation:
Given:
Side length of bigger cube is, [tex]S_1=8\ ft[/tex]
Side length of smaller cube is, [tex]S_2=6.5\ ft[/tex]
Now, volume of the bigger storage unit is given as:
[tex]V_1=S_1^3\\V_1=S_1\times S_1\times S_1\\V_1=8\times 8\times 8=512\ ft^3[/tex]
Volume of the smaller storage unit is given as:
[tex]V_2=S_2^3\\V_2=S_2\times S_2\times S_2\\V_2=6.5\times 6.5\times 6.5=274.625\ ft^3[/tex]
Now, difference in the volume of the two storage units is given as:
[tex]V_1-V_2=512-274.625=237.375\ ft^3[/tex]
Therefore, the difference in their volumes is 237.375 ft³.
To find the difference in volume between two cube-shaped storage units, determine the length of one side for each cube, calculate their volumes with the formula 'Volume = side length cubed', and subtract one volume from the other.
Explanation:To calculate the difference in volume between the two cube-shaped storage units, follow these steps:
Obtain the side length (s) of each cube.Calculate the volume (V) of each cube using the formula V = s^3. This equation is derived from the standard SI unit of volume which is a cubic meter (m³). This means that the volume of a cube is equal to the length of one side cubed.Subtract one volume from the other to find the difference.For example, let's assume the side length of cube 1 is 2 meters and the side length of cube 2 is 3 meters. The volume of cube 1 will be 2^3 or 8 m³ and the volume of cube 2 will be 3^3 or 27 m³. The difference in volume between the two cubes would be 27 m³ - 8 m³ = 19 m³.
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_ 4. How many roots does the following equation have: 2x^4 – x^3 – 12x^2 – 25x + 5 = 0
A. 5
B. 4
C. 3
D. 2.
Answer:
B. 4
Step-by-step explanation:
The degree of the polynomial (the exponent of the highest term) is the total number of roots (including imaginary roots).
The degree of this polynomial is 4, so there are 4 roots.
Find the distance between the points given. (-3, -4) and (0, 0) -5 √(22) 5
Distance between the points (-3, -4) is 5
Step-by-step explanation:
Given
points =(-3,-4) and (0,0)
To Find:
The Distance between the two given points =?
Solution:
[tex]Distance =\sqrt{(x2-x1)^2+(y2-y1)^2 }[/tex]
where
[tex](x_1, y_1)[/tex] = coordinates of the first point
[tex](x_2, y_2)[/tex] = coordinates of the second point
So here, we have
[tex]x_1[/tex] = -3
[tex]y_1[/tex] = -4
[tex]x_2[/tex] = 0
[tex]y_2[/tex] = 0
So, after putting the values of [tex]x_1[/tex] , [tex]y_1[/tex] , [tex]x_2[/tex] [tex]y_2[/tex] in the above equation, we have
[tex]Distance=\sqrt{(0+3)^2+(0+4)^2 }[/tex]
[tex]Distance=\sqrt{(3)^2+(4)^2 }[/tex]
[tex]Distance=\sqrt{(9)+(16) }[/tex]
[tex]Distance=\sqrt{(25)}[/tex]
Distance = 5
for two weeks the highest temperature each day was recorded in four different cities lines l,m,n, and p are graphs of the temperature over time in Lubbock, Memphis, New Orleans, and phoenix which statement is true
As per the graphical diagram, the largest temperature for each day was recorded in four different cities shows n in lines 1 and m
The temperature in four different cities such as Lubbock, New Orleans, Phoenix, and Memphis is shown where Memphis is the only city that has the highest temperature. As the initial temperature of Lubbock is lower than Memphis the initial temperature is the on Y-axis. The line of Memphis slopes downward which shows a decrease in temperature while the line of other cities is loping upwards.Hence the option B is correct.
Learn more about the weeks the highest temperature recorded in four different cities lines l,m,n p.
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i need help on this plZ
Answer:
1. See the attached figure to this answer.
2. Lines A and B are parallel to each other.
3. Line Z is the transversal.
4. The same side interior angles are ∠ 4, ∠ 6 & ∠ 3, ∠ 5.
5. The alternate interior angles are ∠ 3, ∠ 6 & ∠ 4, ∠5
6. Corresponding angles are ∠ 1, ∠ 6 & ∠ 2, ∠ 5 & ∠ 3, ∠ 7 & ∠ 4, ∠ 8.
7. Alternate interior angles are ∠ 4, ∠ 5 & ∠ 3, ∠ 6 (Answer)
Step-by-step explanation:
1. See the attached figure to this answer.
2. Lines A and B are parallel to each other.
3. Line Z is the transversal.
4. The same side interior angles are ∠ 4, ∠ 6 & ∠ 3, ∠ 5.
5. The alternate interior angles are ∠ 3, ∠ 6 & ∠ 4, ∠5
6. Corresponding angles are ∠ 1, ∠ 6 & ∠ 2, ∠ 5 & ∠ 3, ∠ 7 & ∠ 4, ∠ 8.
7. Alternate interior angles are ∠ 4, ∠ 5 & ∠ 3, ∠ 6 (Answer)
Answer:
The answers are below:
Step-by-step explanation:
Answer 1: Attachment.
Answer 2: Line A is parallel to line B.
Answer 3: Line Z is a Traversal.
Answer 4:
[tex]\angle 3 \ and \ \angle 5\ and\\ \angle 4 \ and \ \angle 6\\[/tex] are the same side interior angles.
Answer 5:
[tex]\angle 3 \ and \ \angle 6\ and\\ \angle 4 \ and \ \angle 5\\[/tex] are the alternate interior angles.
Answer 6:
[tex]\angle 3 \ and \ \angle 7\ and\\ \angle 4 \ and \ \angle 8\\[/tex][tex]\angle 6 \ and \ \angle 1\ and\\ \angle 5 \ and \ \angle 2\\[/tex] are corresponding pair angles.
Answer 7:
[tex]\angle 8 \ and \ \angle 2\ and\\ \angle 7 \ and \ \angle 1\\[/tex]are the alternate exterior pair angles.
In which number does the digit 2 have a value that is 1/10 times as great as the digit 2 in the number 6,257.11
Answer:
7,326.64
Step-by-step explanation:
20 is 1/10 times as great as 200.
A number that satisfies this equation is 26
What is a decimal number?A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32 etc.
Given here the number 6,257.11 , here the digit 2 is in the 100th place hence it is equivalent to 200 and 1/10 th of 200 is 20 . Thus any number with its tenth place with digit 2 is acceptable and 26 is one such number.
Hence, the number is 26
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Angle Cis an inscribed angle of circle P. Angle C measures (3x+5)^arc AB measures (16x)^arc. Find X.
Answer:
x=1
Step-by-step explanation:
we know that
The inscribed angle is half that of the arc it comprises
so
In this problem
m∠C=(1/2)arc AB
we have
m∠C=(3x+5)°
arc AB=(16x)°
substitute the values
[tex](3x+5)\°=(1/2)(16x)\°[/tex]
solve for x
[tex]3x+5=8x\\8x-3x=5\\5x=5\\x=1[/tex]
PLZZZ HELP ME.I WOULD RLLY APPRECIATE IT
this is alegbra 1 so if your rlly good at that please help me, the problem is about systems of linear equations
question: Jack and Julio each improved their yards by planting daylilies and geraniums. They bought their supplies from the same store.
Jack spent $22 on 1 daylily and 5 geraniums. Julio spent $30 on 13 daylilies and 1 geranium. Find the cost of one daylily.
Answer:
$2
Step-by-step explanation:
x = daylily
y = geranium
1x + 5y = 22
13x + 1y = 30
Multiply second equation by 5 and subtract the two equations.
1x + 5y = 22
- (65x + 5y = 150)
-64x = -128
x = 2
So one daylily costs 2 dollars
The length of a rectangle is 3 more inches than its width. The area of
the rectangle is 54 square inches. What is the width of the rectangle
in inches?
Answer:
9
Step-by-step explanation:
Length: a
Width: b
ab = 54
a = b + 3
=> (b + 3)b = 54
=> b^2 + 3b = 54
=> b^2 + 3b - 54= 0
=> (b - 6)(b + 9)
=> b = 6 AND b = -9
Rectangular's sides > 0 => b = 6
Hope it's helpful :)
write (1/5) as a percentage?
Answer: 20%
Step-by-step explanation: if u want it on a decimal, here :0.2
hope this helps u :)
PPPPPPPPPPLLLLLLLLLLLLZZZZZZZZ HHHHEEELLLPPP 3(9 - 7)² + 5 × 2
Answer:
22
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
9g - 6> 12g + 1 or 4 >
+ 8
Answer: The second one is not clarified give us the full clarification please....
Step-by-step explanation:
Let's evaluate the two inequalities:
1. 9g - 6 > 12g + 1
Subtracting 9g from both sides gives:
-6 > 3g + 1
Subtracting 1 from both sides gives:
-7 > 3g
Dividing both sides by -3 (and flipping the inequality sign) gives:
g < 7/3
1. 4 > + 8
This inequality is not correct, as it is missing a term on the right-hand side. It should be something like:
4 > x + 8
Subtracting 8 from both sides gives:
-4 > x
Without more information, we can't determine the value of x.
Please clarify or provide more context for the second inequality!
Solve: -7(3+6x)=9(-5x+7)
Answer:
x=28
Step-by-step explanation:
-7(3+6x)=9(-5x+7)
-21-42x=-45x+63
-21-42x-(-45x)=63
-21-42x+45x=63
-21+3x=63
3x=63-(-21)
3x=63+21
3x=84
x=84/3
x=28
Answer:
x=28
Step-by-step explanation:
-7(3+6x) = 9(-5x+7)
-21-42x=-45x+63
-42x=-45x+84
3x=84
x=28
Please, I need help in this ??
Answer:
[tex]\int\frac{x^{4}}{x^{4} -1}dx = x + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1)-\frac{1}{2} arctanx + c[/tex]
Step-by-step explanation:
[tex]\int\frac{x^{4}}{x^{4} -1}dx[/tex]
Adding and Subtracting 1 to the Numerator
[tex]\int\frac{x^{4} - 1 + 1}{x^{4} -1}dx[/tex]
Dividing Numerator seperately by [tex]x^{4} - 1[/tex]
[tex]\int 1 + \frac{1}{x^{4}-1 }\, dx[/tex]
Here integral of 1 is x +c1 (where c1 is constant of integration
[tex]x + c1 + \int\frac{1}{(x-1)(x+1)(x^{2}+1)}\, dx[/tex]----------------------------------(1)
We apply method of partial fractions to perform the integral
[tex]\frac{1}{(x-1)(x+1)(x^{2}+1)}[/tex] = [tex]\frac{A}{x-1} + \frac{B}{x+1} + \frac{C}{x^{2} + 1}[/tex]------------------------------------------(2)
[tex]\frac{1}{(x-1)(x+1)(x^{2}+1)} = \frac{A(x+1)(x^{2} +1) + B(x-1)(x^{2} +1) + C(x-1)(x+1)}{(x-1)(x+1)(x^{2} +1)}[/tex]
1 = [tex]A(x+1)(x^{2} +1) + B(x-1)(x^{2} +1) + C(x-1)(x+1)[/tex]-------------------------(3)
Substitute x= 1 , -1 , i in equation (3)
1 = A(1+1)(1+1)
A = [tex]\frac{1}{4}[/tex]
1 = B(-1-1)(1+1)
B = [tex]-\frac{1}{4}[/tex]
1 = C(i-1)(i+1)
C = [tex]-\frac{1}{2}[/tex]
Substituting A, B, C in equation (2)
[tex]\int\frac{x^{4}}{x^{4} -1}dx[/tex] = [tex]\int\frac{1}{4(x-1)} - \frac{1}{4(x+1)} -\frac{1}{2(x^{2}+1) }[/tex]
On integration
Here [tex]\int \frac{1}{x}dx = lnx and \int\frac{1}{x^{2}+1 } dx = arctanx[/tex]
[tex]\int\frac{x^{4}}{x^{4} -1}dx[/tex] = [tex]\frac{1}{4} ln(x-1)[/tex] - [tex]\frac{1}{4} ln(x+1)[/tex] - [tex]\frac{1}{2} arctanx[/tex] + c2---------------------------------------(4)
Substitute equation (4) back in equation (1) we get
[tex]x + c1 + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1) - \frac{1}{2} arctanx + c2[/tex]
Here c1 + c2 can be added to another and written as c
Therefore,
[tex]\int\frac{x^{4}}{x^{4} -1}dx = x + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1)-\frac{1}{2} arctanx + c[/tex]
If a truck holds 200 cubic feet of asphalt, how many truckloads do you need for covering a road that is 500 feet long by 20 feet wide, with a 6-inch-thick layer of asphalt?
Answer:
1
Step-by-step explanation:
There are 5 bacteria in a petri dish at the start of an experiment. This type of bacteria doubles every 20 minutes.
Find the number of bacteria after 4 hours.
40
10,240
20,480
40,960
Answer:
The next answer is 3 hours
Step-by-step explanation:
I just did it on edge 2021 :)
Answer:
the first answer is c
Step-by-step explanation:
Ed stein paid $40.00 interes tonaloan
OF $2,000 for 3 months
what's the rate of interest hepaid?
Answer:
The rate of interest paid on the principal amount is 8%.
Step-by-step explanation:
Here, Principal Amount = $2,000
Time = 3 months = (3/ 12 ) Years = 0.25 years
Rate = R
Interest Amount = $40
Now, as we know :
Simple Interest = [tex]\frac{P \times R \times T}{100}[/tex]
⇒[tex]40 = \frac{2,000 \times R \times 0.25}{100}\\\implies R = \frac{40 \times 100}{2000 \times 0.25} =8[/tex]
or, R = 8%
Hence, the rate of interest paid is 8%.
Question # 4
1) Brett is 18 years younger than Mark Carl is 10 years younger
than Mark. The sum of the ages of Brett, Mark, and Carl is 212
How old are each of the 3 men? explain in your own words of how u get the answer
Ages of Mark, Brett and Carl are 80 years, 60 years and 70 years respectively.
Solution:
Given that
Brett is 18 years younger than Mark.
Carl is 10 years younger than Mark.
The sum of the ages of Brett, Mark, and Carl is 212
Need to determine age of Brett, Mark, and Carl.
Let assume age of mark in years be represented by variable x
As it is given that Brett is 18 years younger than Mark , so if we subtract 18 from the age of Mark we will get age of Brett ,
=> Age of Brett = x – 18
Also given that Carl is 10 years younger than Mark , so if we subtract 10 from the age of Mark we will get age of Carl ,
=> Age of Carl = x – 10
Given sum of ages of Brett, Mark, and Carl is 212
=> Age of Mark + Age of Brett + Age of Carl = 212
=> x + ( x – 18 ) + ( x – 10) = 212
=> 3x – 28 = 212
=> 3x = 212 + 28
Age of Mark = x = 80 years
Age of Brett = x – 18 = 80 – 18 = 62 years
Age of Carl = x – 10 = 80 – 10 = 70 years
Hence Ages of Mark , Brett and Carl are 80 years, 60 years and 70 years respectively.
5. 20 is what percent of 50?
O A. 40%
O B. 250%
O C. 10%
O D. 30%
Answer:
Step-by-step explanation:
A 40 percent
Answer: (A)
(40%)
Step-by-step explanation:
By making an equation, we can get this answer. Let's say "what percent" is wp.
20 is wp of 50
20=wp(50)
20=50wp
wp=2/5
wp=40% (A)
The measure of an angle is three times the measure of its supplementary angle. What is the measure of each angle?
Answer:
Angle = 135°
Supplement of the Angle = 45°
Step-by-step explanation:
The complement of an angle, say "x", would be 90 minus that angle:
90 - x
The supplement of an angle, say "y", would be 180 minus that angle:
180 - y
Since we have 1 angle, let it be "x", and that angle is 3 TIMES the SUPPLEMENT of that angle, we can write:
x = 3(180 - x)
Now, we solve for the angle x:
[tex]x = 3(180 - x)\\x = 540 - 3x\\x + 3x = 540\\4x = 540\\x = \frac{540}{4}\\x=135[/tex]
So, the angle is 135°
The supplement of the angle is 180 - 135 = 45°
The measure of the smaller angle is 45 degrees, and the larger angle, which is three times the size of the smaller one, measures 135 degrees.
Explanation:The subject of this question falls under the branch of Mathematics, specifically geometry. The question deals with supplementary angles, which are pairs of angles that add up to 180 degrees.
Let's denote the smaller angle as 'x.' According to the problem, the larger angle is three times the size of the smaller, thus it is 3x. Because these are supplementary angles, they add up to form 180 degrees. So, we can create this equation: x + 3x = 180.
By simplifying and solving for x, we get: 4x = 180, hence x = 45 degrees. Therefore, the larger angle, which is three times the smaller, is 3*45 = 135 degrees.
Result
In conclusion, the measure of the smaller angle is 45 degrees while the larger angle measures 135 degrees.
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-1/3=j/4-10/3 solve for j
How do you find the value of each variable if y=3x-6 and x=2x+1
Answer:
x=-1, y=-9. (-1, -9).
Step-by-step explanation:
y=3x-6
x=2x+1
----------
x-2x=1
-x=1
x=-1
--------
y=3(-1)-6=-3-6=-9
In Dale's cooler there are 9 bottles of soda and 6 bottles of water.
Dale is going to choose 8 bottles at random from the cooler to give to his friends.
What is the probability that he will choose 5 sodas and 3 waters? Round your answer to three decimal places.
Answer:
5/18??? might be wrong
Step-by-step explanation:
The probability that Dale will choose 5 sodas and 3 water is 0.391 and this can be determined by using the concept of probability.
Given :
In Dale's cooler, there are 9 bottles of soda and 6 bottles of water. Dale is going to choose 8 bottles at random from the cooler to give to his friends.The following steps can be used in order to determine the probability that he will choose 5 sodas and 3 water:
Step 1 - The concept of probability is used in order to determine the probability that he will choose 5 sodas and 3 water.
Step 2 - First, determine the total number of bottles.
Total Bottles = 9 + 6
= 15
Step 3 - So, the probability that he will choose 5 sodas and 3 water is:
[tex]\rm P = \dfrac{\;^9C_5 \times ^6C_3}{\;^{15}C_8}[/tex]
Step 4 - Simplify the above expression.
[tex]\rm P = \dfrac{126 \times 20}{6435}[/tex]
P = 0.391
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A metalworker has a metal alloy that is 20% copper and another alloy that is 70% copper. How many kilograms of each alloy should the metalworker combine to create 60 kg of a 50% copper alloy? The metal worker should use (blank) kilograms of the metal alloy that is 20% copper and (blank) kilograms of the metal alloy that is 70% copper.
X+Y=60kg
X=60-Y
X*0.2+Y*0.7=60*0.5
(60-Y)*0.2+Y*0.7=30
12-0.2*Y+0.7*Y=30
0.5*Y=18
Y=36 kg
X=60-36
X=24 kg
The metal worker should use 24 kilograms of the metal alloy that is 20% copper and 36 kilograms of the metal alloy that is 70% copper.
Answer:
36kg 24kg
Step-by-step explanation:
The graph shows g(x), which is a translation of f(x) = x^2. Write the function rule for g(x). Show step by step.
Points on nonlinear graph are (9,10) (5,10) (7,6).
Using the given points, solve for a, h, k in g(x) = [tex]a(x - h)^2[/tex] + k . The function rule is g(x) = [tex]a(x - h)^2[/tex] + k .
To find the function rule for g(x), which is a translation of the quadratic function[tex]\( f(x) = x^2 \)[/tex], we need to determine the horizontal and vertical shifts based on the given points on the graph. The general form for a translated quadratic function is [tex]\( g(x) = a(x - h)^2 + k \)[/tex], where (h, k) represents the vertex of the parabola.
Let's use the given points (9,10), (5,10), and (7,6) to find the translation values.
1. Vertex Form of Quadratic Function:
The vertex form of a quadratic function is [tex]\( f(x) = a(x - h)^2 + k \)[/tex], where (h, k) is the vertex. Let's find the vertex using the given points.
For (9,10):
[tex]\[ 10 = a(9 - h)^2 + k \][/tex]
For (5,10):
[tex]\[ 10 = a(5 - h)^2 + k \][/tex]
For (7,6):
[tex]\[ 6 = a(7 - h)^2 + k \][/tex]
2. Solve the System of Equations:
Solve the system of equations to find the values of a , h , and k .
3. Substitute into Vertex Form:
Once you find the values of a , h , and k , substitute them into the vertex form g(x) = [tex]a(x - h)^2[/tex] + k.
By following these steps, you'll obtain the function rule for g(x), which is a translation of [tex]f(x) = x^2[/tex] based on the given points on the graph.
Which equation is equivalent to 2 4x = 8x-3
Answer:
x = -9
Step-by-step explanation:
the equation is 2^4x = 8^x - 3.
therefore 2^4x = 2^3(x-3)
since both have powers of 2
therefore
4x = 3(x-3)
4x = 3x - 9
4x -3x = -9
x = -9
Answer:
D) 2^4x=2^3x-9
Step-by-step explanation:
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