let y = x^2
4y^2 -21y + 20 = 0
solve for y
then substitute back in to get x
Answer:
4y^2 - 21y + 20 = 0
Step-by-step explanation:
As (4x^4 - 21x^2 + 20=0) being a biquadratic equation, meaning it is a 4-degree equation without the terms of degree 1 and 3.
To solve this particular case you only need to replace the variables of degree 4 and 2 for a new variable of degree 2 and 1 and solve it as regular quadratic equation and then undo the change.
* Using a new variable we can rewrite the equation:
Let y be the new variable;
y= x^2, then y^2= x^4
Then we have;
4y^2- 21y+20=0
Solve for y and then find X which will be the roots for the biquadratic equation.
if axb=0, then a=0 or b=0
3x=0
Answer:
The given equation is
ax b= 0,
As we see that, it is a linear equation in one variable containing two constant.
So , a≠ 0 [then equation has no meaning.If a=0 , then [tex]0 \times x=0[/tex], which is meaningless]. ∴ a=0 is incorrect.
Similarly , b≠ 0 [ Reason same as above]. ∴b=0 is incorrect.
⇒3 x=0
⇒x=0 is the correct response.
Let me explain by this giving an example
⇒5 x=0
⇒ x=0 but 5≠0
So, x=0 or 3 x=0 is correct response.
the product of two rational number is 19/27. if one of the number be 38/9 ,find the other
[tex]\frac{38}{9} x = \frac{19}{27}[/tex]
[tex](27)\frac{38}{9} x = \frac{19}{27}(27)[/tex]
3(38)x = 19
[tex]x = \frac{19}{3(38)}[/tex]
[tex]x = \frac{1}{3(2)}[/tex]
[tex]x = \frac{1}{6}[/tex]
Answer: [tex]x = \frac{1}{6}[/tex]
One of the stamps in Evelyn's stamp collection is 19.51 mm wide and 24.4 mm long. How much longer is the length of the stamp than the width of the stamp? Enter your answer in the box.
24.4-19.51= 4.89
Answer: 4.89 mm
Examine the worked problem and solve the equation.
The solution is x =
Answer:
x = 7
Step-by-step explanation:
Edginuity, got le question correct humans
Based on the expression given, the for x will be 7.
From the diagram given, we can see that the last expression that's given is 4x/3 = 28/3. The next thing that will be done in this case is to cross multiply and this will be:
4x/3 = 28/3.
Cross multiply
4x × 3 = 28 × 3
12x = 84
x = 84/12.
x = 7
Therefore, the value of x will be 7.
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what are 3 equivalent ratios for 14/2
The answer is:
28/4
42/6
56/8
What is the value of f(x) = 3x - 5 when x = 6
Plug in 6 for x in the equation:
f(6) = 3(6) - 5
Remember to follow PEMDAS. First, multiply
f(6) = 3(6) - 5
f(6) = 18 - 5
Finally, subtract
f(6) = 18 - 5
f(6) = 13
f(6) = 13 is your answer
hope this helps
twelve is the same as two-thirds a number diminished by two.
12 = 2/3(x - 3)
Distributive property.
12 = 2/3x - 2
Add 2 to both sides.
14 = 2/3x
Multiply both sides by 3.
42 = 2x
Divide both sides by 2.
21 = x
The value of x is equal to 21.
The equation, twelve is the same as two-thirds a number diminished by two - True
Explanation:To determine if twelve is the same as two-thirds of a number diminished by two, we can set up an equation. Let's represent the number as 'x.' According to the statement, twelve is equal to two-thirds of x diminished by two. Mathematically, this can be written as:
12 = (2/3)x - 2
To solve for x, we need to isolate it on one side of the equation. First, we can add 2 to both sides:
14 = (2/3)x
Next, we can multiply both sides by 3/2 to eliminate the fraction:
14 * (3/2) = x
21 = x
Therefore, the number in question is 21. To confirm, we can substitute x back into the original equation:
12 = (2/3)(21) - 2
12 = 14 - 2
12 = 12
Since the equation is true, we can conclude that the statement is True.
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Complete Question:
Twelve is the same as two-thirds a number diminished by two. True or False ?
can someone give me an example on how to graoh and equation like these plz asap thanks
to graph you have to look ate the first number and move forward or backwards on the x axis if it is negative move backward if it is normal move forward
for the y axis(second number) go up or down again if it is posative move up
if it is negative move down
P.S. move from ''0''
find x if a =13 and C = 47 need help
So you're using the Pythagorean theorem which is a^2 + b^2 = c^2... so if you dont have b you can manipulate the equation. That equation is c^2 - a^2= b^2, so you square 47 which is 2209 and then square 13 which is 169... you do 2209-169 and that equals 2040, then you do the square root of that which is 45.166359 that can be simplified to 45 or two decimal points 45.167. Hope that Helped! :)
Leeann works 20 hours per week and makes $15 per hour. What is her yearly pay?! SOME ONE PLEASE HELP ME PLATO
(20 hrs/1 wk)*(15 dollars/1 hr) = 20*15 = 300 dollars per week
There are 52 weeks in a year. If Leeann works all 52 weeks (ie no sick days, vacations, etc) then,
(52 weeks/1 yr)*(300 dollars/1 week) = 52*300 = 15600
Her yearly pay is $15,600
Answer:
$15,600
Step-by-step explanation:
Leeann works 20 hours per week and makes $15 per hour
Her weekly income = 20 × 15 = $300
In one year = 52 weeks
Therefore, her yearly pay = 300 × 52
= $15,600
Leeann's yearly pay is $15,600
A piece of candy weighs 30 grams. All of the candy in a bag weighs 750 grams. How many pieces of candy are in the bag? A) 15 B) 21 C) 25 D) 35
21 (c) pieces of candy
Answer:
c
Step-by-step explanation:
Jeremy surveyed students in his class about their spending habits in the school cafeteria. He used the data to create a scatterplot.
Answer:
Step-by-step explanation:
From the graph, you can first see that there is a positive slope, and a negative y intercept. That should automatically rule out the first option.next, find the slop...
To do this take the two points that are given (2,5.5) and (5,15.25) and do rise over run. This would be (15.25-5.5)/(5-2). I just put this in a calculator and found the slope to be 3.25. You automatically know the answer because the only equation with the slope 3.25 is the third one.
The scatterplot shows the distribution of the students' spending habit
The equation of the trend line is: [tex]\mathbf{y = 3.25x -1}[/tex]
From the scatter plot (see attachment), we have the following points:
[tex]\mathbf{(x,y) = (2,5.5)\ (5,15.25)}[/tex]
So, the slope (m) of the trend line is:
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
This gives
[tex]\mathbf{m = \frac{15.25 - 5.5}{5- 2}}[/tex]
[tex]\mathbf{m = \frac{9.75}{3}}[/tex]
[tex]\mathbf{m = 3.25}[/tex]
The equation of the trend line is then calculated as:
[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]
This gives
[tex]\mathbf{y = 3.25(x - 2) + 5.5}[/tex]
[tex]\mathbf{y = 3.25x - 6.5 + 5.5}[/tex]
[tex]\mathbf{y = 3.25x -1}[/tex]
Hence, the equation of the trend line is: [tex]\mathbf{y = 3.25x -1}[/tex]
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How are the absolute values of opposite intergers related ?? Help me 16 points give me a good answer plz and THX
Opposite integers are pairs of opposite sign, so the opposite integer to 2 is -2, 3 is opposite to -3, and so on.
Absolute value make any integer non-negative by removing its negative sign if there is any.
Absolute values of opposite integers are related in that they are *identical*
Any pair of opposite integers shares the same absolute value.
Lmk if you have questions.
I need help with Math please
Brianna is graphing the function f(x) = x2 + 6x + 5. What x-intercepts should Brianna use to graph f(x)?
to find t he x intercepts factor the quadratic and set them = to 0
x^2 +6x+5 = 0
(x+5) (x+1)=0
x+5 = 0 x+1=0
x=-5 x=-1
the x intercepts are -5, x=-1
Answer:
-5 -1
Step-by-step explanation:
Ten years ago in Louisiana, schools average 182 pupils for every 10 teachers what is the ratio?
I think the ratio is 182:10
182/10 so every teacher will have about 18 students.
Hope this helps,im very sorry if it dont!!
Is -6.809 more or less than -6.812
it is more because of the negative.
In mathematics, when dealing with negative numbers, the number closer to zero is greater. Thus, -6.809 is greater than -6.812 because it's closer to zero.
Explanation:In the field of mathematics, when you're dealing with negative numbers, the number that is closer to zero is always greater. Here, we have the numbers -6.809 and -6.812. Looking carefully, -6.809 is closer to zero than -6.812. Hence, -6.809 is greater than -6.812.
Let's understand it with a simpler example. If we have -3 and -5, even though 5 is greater than 3, -5 is lesser than -3 because it's further away from zero.
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What is 1 2/4 plus 9 5/10
First we find the fraction in decimal form,
so they it will equal to 1.5 because 2/4 is 0.5 and 9.5 because 5/10 is .5 as well
Then we add and get a whole number which is 11
Answer,
11
Hope this helps :-)
If y = 7x, what happens to x when y is increased by 5 times its original value?
A) x decreases 5 times its original value
B) x increases to 11/5 its original value
C) x also increases 5 times its original value
D) x decrease to 4/5 of its original value
B) Because to find the value of x and y you have to divide x by 7 to make it x and the multiply 7 by y because you divided by the opposite side, which is x.
the height h increased by 6 inches
"Height h increased by 6" can be displayed as:
h + 6
Complete the mapping of the vertices of ΔDEF. D(2, –4) → D' E(1, –1) → E' F(5, 1) → F' What is the rule that describes a reflection across the line y = x? rx = y(x, y) →
D(2, –4) → D' = (-4, 2)
E(1, –1) → E'= (-1, 1)
F(5, 1) → F'=(1, 5)
What is the rule that describes a reflection across the line y = x?
rx = y(x, y)= (y, x)
The rule which describes a reflection across the line is y(x, y) --> (y, x) and the mapping of the vertices of ΔDEF is (-4, 2)D', (-1, 1)E' , (1, 5)F'.
What is reflection?The reflection of a plane or shape is flipping the original figure with respect to a reference line.
The following steps are used to for reflecting a shape-
Select the shape which has to be reflected.Select a base line or reference line over which the shape has to be reflected.Mark the corners of the shape at the equidistant from the reference line as the original shape has, but in the opposite direction.The reflected shape is now is facing the opposite direction.The rule that describes a reflection across the line says that when your reflect a point across the line say y=x. Then the coordinates of x and y are interchanged as,
y(x, y) → (y, x)
Now let's complete the mapping of the vertices of ΔDEF using the above rule. For this, change the places of x and y coordinate as,
D(2, –4) → (-4, 2)D'
E(1, –1) → (-1, 1)E'
F(5, 1) → (1, 5)F'
Thus, the rule which describes a reflection across the line is y(x, y) --> (y, x) and the mapping of the vertices of ΔDEF is (-4, 2)D', (-1, 1)E' , (1, 5)F'.
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as improper fraction 2 1/2
5/2 because its 2 times 2 plus one for the numerator and the denominator stays 2
how do write 3 to 4 2 other ways?
The ratio "3 to 4" can also be written as "3:4". Typically, though, we write it as "3/4" like a fraction. Those are the three main ways to write out ratios ( a to b, a:b, or a/b).
the 8th grade class planned a trip to kings dominion and 120 students went. Ten students rode with their parents. The rest rode on two charter busses. How many stidents were on each bus
120-10=110/2=55 students per bus
Step one: 120-10= 110
Step two: 110÷2=55
Answer: 55 students per bus
Reflectional symmetry is the quality a design has if it maintains _____ when it is reflected across an axis or line of symmetry. A. some characteristics B. all characteristics C. no characteristics
The correct answer would be B, all characteristics. Reflectional Symmetry is when an object is divided into halve in which to completely identical pieces are left.
(B) All characteristics.
Reflection symmetry:In mathematics, symmetry with regard to a reflection is known as reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry. In other words, a figure with reflectional symmetry does not alter when it is reflected.There is a symmetry line or axis in 2D and a symmetry plane in 3D. A mirror-symmetric object or figure is one that is identical to its changed counterpart. In conclusion, the shape is divided in two by a line of symmetry, and both parts should be the same.Therefore, the correct option to fill the blank is (B) All characteristics.
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Solve for ?
F(x)=3x-1
F(x)+4=?
Answer:
F(x) + 4 = 3x + 3
Step-by-step explanation:
F(x) = 3x - 1 |add 4 to both sides
F(x) + 4 = 3x + 3
What is the product in simplest form?
−8/9⋅5/6
The answer is 20/27. 8/9x5/6=20/27.
which expression correctly shows the sum of 20 and 8minus the product of 3 and 5
It would be 20+8-(3x5).
Audrey is trying to find the equation of a line parallel to y = 2 over 3 x −5 in slope-intercept form that passes through the point (−6, −1). Which of the following equations will she use
Final answer:
To find the parallel line's equation, Audrey used the slope of 2/3 from the given line and the point (-6, -1) to write the equation in point-slope form, eventually simplifying it to y = 2/3x + 3.
Explanation:
Audrey is looking to find the equation of a line that is parallel to the line with the equation y = 2/3x - 5 and that passes through the point (-6, -1). Since parallel lines have the same slope, our new line will keep the slope of 2/3. Using the point-slope form of the equation of a line, we set up y - y1 = m(x - x1). Plugging in the known slope m and point (x1, y1), we get y - (-1) = 2/3(x - (-6)). After simplifying, we have y + 1 = 2/3x + 4. Finally, we solve for y by subtracting 1 from both sides, yielding the equation y = 2/3x + 3 as the line that is parallel to the original line and passes through the given point.
Solve the equation. Check your solution, if possible
[tex]4(3q - 2) = 16q[/tex]
Hey there!!
Given equation :
... 4 ( 3q - 2 ) = 16q
... 12q - 8 = 16q
Subtract by 12q on both sides
... -8 = 4q
Divide by 4 on both sides
... -8 / 4 = q
... q = -2
Given equation :
4 ( 3q - 2 ) = 16q
Substitute the value of -2 in place of q
... 4 ( -6 -2 ) = 16 × -2
... 4 ( -8 ) = -32
... -32 = -32
∴ Hence proved
Hope my answer helps!!