Answer:
Step-by-step explanation:
If you're tasked to do this mathematically, you have to complete the square to get it into vertex, or work, form. Do that by first setting the equation equal to 0 then moving over the constant:
[tex]3x^2+2x=8[/tex] Next you have to have a +1 as the leading coefficient, and ours is a 3, so we factor it out:
[tex]3(x^2+\frac{2}{3}x)=8[/tex]. Now take half the linear term, square it, and add it in to both sides. Our linear term is 2/3. Half of 2/3 is 2/6 which reduces to 1/3. Squaring 1/3 gives us 1/9, so that's what we add in.
[tex]3(x^2+\frac{2}{3}x+\frac{1}{9})=8+\frac{1}{3}[/tex] to the right of the equals sign we added in 3*1/9 which is 3/9, which reduces to 1/3. Now we clean up both sides. The right side is easy; the left side, not so much. The reason we do this (complete the square) is to get a perfect square binomial on the left. When we re-write the left side into that perfect square binomial, we get
[tex]3(x+\frac{1}{3})^2=\frac{25}{3}[/tex] Now we move the constant back over and set the parabola back equal to y:
[tex]y=3(x+\frac{1}{3})^2-\frac{25}{3}[/tex] which shows us that the vertex is
[tex](-\frac{1}{3},-\frac{25}{3})[/tex]
Simplify......................
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \frac{( {a}^{2} + {b}^{2} )}{a} }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{ {a}^{4} - {b}^{4} }{ {a}^{3} - a {b}^{2} } [/tex]
[tex] \\= \frac{ ({ {a}^{2} })^{2} - { ({b}^{2} })^{2} }{a( {a}^{2} - {b}^{2} )} [/tex]
[ ∵ (a²)² = [tex]{a}^{4}[/tex] ]
[tex] \\= \frac{( {a}^{2} + {b}^{2} )( {a}^{2} - {b}^{2}) }{a( {a}^{2} - {b}^{2}) } [/tex]
[tex] \\= \frac{( {a}^{2} + {b}^{2} )}{a} [/tex]
Note:[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{ヅ}}}}}[/tex]
EG is the angle bisector of
Answer:
the remaining angle will be 32
cz angle bisector cuts an angle in two equal parts hooe it may help u
A bus completed a journey of 98 km in 140 minutes. Calculate the average speed, in kilometres per hour, for this journey.
Answer:
hope you like it
Step-by-step explanation:
at first change minutes to hour and calculate by dividing 98 to specific hour
If α and β are the zeroes of the polynomial ax^2 + bx + c, find the value of α^2 + β^2
Answer:
Step-by-step explanation:
α + β = -b/a
αβ = c/a
α² + β² = (α + β)² - 2αβ
[tex]= (\frac{-b}{a})^{2}-2\frac{c}{a}\\\\= \frac{b^{2}}{a^{2}}-\frac{2c}{a}\\\\=\frac{b^{2}}{a^{2}}-\frac{2c*a}{a*a}\\\\=\frac{b^{2}-2ca}{a^{2}}[/tex]
AC and DG are parallel. Find the value of x, show CLEARLY how you got your answers with reasons
Answer:
x = 79°
Step-by-step explanation:
∠ABE = ∠BEF = 41° [Alternate angle ]
Now sum of angles of a triangle = 180°
Therefore,
∠EBF + ∠BEF + ∠BFE = 180°
60° + 41° + x = 180°
x = 180° - 60° - 41°
x = 79°
what is 11010^2 - 1101^2
Answer:
-120,007,899
Step-by-step explanation:
Given :
[tex]11010^{2} -1101^{2}[/tex]
It can be solved as :
[tex]11010^{2} -1101^{2}[/tex]
121,220,100-1212201
-120,007,899
Therefore, answer will be -120,007,899
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{11,010^2 - 1,101^2}[/tex]
[tex]\mathsf{11,010^2}[/tex]
[tex]\mathsf{= 11,010 \times 11,010}[/tex]
[tex]\mathsf{= \boxed{\bf 121,220,100}}[/tex]
[tex]\mathsf{\bold{121,220,100} - 1,101^2}[/tex]
[tex]\mathsf{1,101^2}[/tex]
[tex]\mathsf{= 1,101 \times 1,101}[/tex]
[tex]\mathsf{= \boxed{\bf 1,212,201}}[/tex]
[tex]\mathsf{121,220,100 - \bf 1,212,201}[/tex]
[tex]\mathsf{= \boxed{\underline{\bf 120,007,899}}}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \underline{\bf 120,007,899}}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Question 7 of 10 Classify the following triangle. Check all that apply. 6 D A. Scalene D B. Right C. Obtuse D. Isosceles E. Acute F. Equilateral
Answer:
Right angle triangle
Acute
Step-by-step explanation
1 right angle/90 degrees
2 acute angles
A 3 by 3cm grid shows nine 1 by 1 cm squares and uses 24cm of wire.
What length would the wire be for a similar 20 by 20cm sqaure
Answer:
840 cm
Step-by-step explanation:
Given that in the question we have, : 9, 1 cm × 1 cm squares setting a 3 × 3 grid.
Therefore wire required in 3 x 3 grid is
3(3+1) + 3(3+1)
= 3 × 4 + 3 × 4
= 24 I'm
Similarly, the length of the wire required in 20 by 20 grid will be
=> 20(20+1) + 20(20+1)
=> 20 × 21 + 20 × 21
=> 420 + 420
= 840cm
The seventh term of an arithmetic series is 29 and the sum of the first seventeen terms is 629. Find the sum of the first 100 terms of the series.
Step-by-step explanation:
everything can be found in the picture
please complete the table.
Answer:
my answer in this picture.......
I need help!!! Parallel lines p and q are cut by two non parallel lines m and n as shown in the figure the value of x is degrees and the value of y is degrees
Answer:
x = 78° , y = 115°
Step-by-step explanation:
The angle adjacent to x on the left side is corresponding to 102° , then
x = 180° - 102° = 78°
----------------------------------------
y and 115° are corresponding angles and congruent, then
y = 115°
There is 28 kg 750 g of sugar in a sack. How many tins of 500 g sugar can be filled using the sugar in the sack?
Answer:
Step-by-step explanation:
28 kg + 750 g = 28*1000 + 750
28000 + 750
= 28750 g
Number of sack = Total quantity of sugar ÷ quantity of sugar in a sack
= 28750 ÷ 500
= 57 sacks
Answer:
57 sacks
Step-by-step explanation:
28750 ÷ 500 =
57 sacks
Glad to help! :)
Help pleaseeeeeeeeeeeeeeeeeeeeee
Answer: x= -7/8
Step-by-step explanation:
Hope it helps you
A bag contains 26 letters and 10 numerals. Robin draws two cards from the
bag. What is the probability that she draws 2 numerals?
Answer:
10C2 / (36C2)
Step-by-step explanation:
Which of the following is a geometric sequence?
O A. -2, 6, 14, 22, ...
O B. 6, 13, 19, 24, ...
O c. 11, 16, 21, 26, ...
O D. -3,3, -3, 3, ...
Answer:
O B. 6, 13, 19, 24,
Step-by-step explanation:
because this is the correct answer
a bicycle was sold for $285 at a discount of 5% calculate the cost price of that bicycle
Answer:
Cost price = $300
Step-by-step explanation:
Let the cost price be = x
Discount % = 5%
Price after discount = $285
Find Cost price .
[tex]Price \ after \ discount = x - (5 \% \ of \ x)\\\\285 = x - \frac{5}{100}x\\\\285 = \frac{100 - 5 }{100} x\\\\95x = 285 \times 100\\\\x = \frac{28500}{95} = \$ 300[/tex]
i cant do this lollllllll
Answer:
12
Step-by-step explanation:
first, do the question in parenthesis
then do the questions in the exponent
then do the question with division
then do addition part
(7-4)^2 = (3)^2
9/3 = 3
9+3 = 12
consider the system of equations given below
Y=2/3x+2
Y=5/2x+7/2
which of the following is true about the solution set of the system?
A. The solution is a point on the x-axis.
B. The solution is all the points on the line y=2/3x+3.
C. The solution is a point in the coordinate plane.
D. The solution is the region in the coordinate plane above y=5/2x+7/2.
Answer:
its A or C
Step-by-step explanation:
please helpppp its due nowwwww
Answer:
Step-by-step explanation:
instead of (2x - 60 ) there should be (60 - 2x) because since they are parallel lines corresponding sides must be equal . It is contradictory because the size of the corresponding angles is different.
Note : Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).
April is randomly choosing five CDs to bring in her car from the following: 6 pop CDs, 8 rock CDs, and 10 R&B CDs.
What is the complement of April choosing five pop CDs?
choosing five CDs where none of them are pop
choosing five CDs where not all of them are pop
choosing five CDs where at least one of them is pop
choosing five CDs where all of them are pop
Answer:
Choosing five CDs where not all of them are pop.
Step-by-step explanation:
Answer:
B) choosing five CDs where not all of them are pop
Step-by-step explanation:
E2020
14. A polygon ABCD is inscribed in a circle. Find angle ABC
15. A polygon GHIJ is inscribed in a circle if GHI=76 and HIJ=66 what is IJG
Answer:
m<ABC = 100degrees
m<IJG = 104degrees
Step-by-step explanation:
14. The sum of the opposite angle of the quadrilateral is 180degrees. Hence;
m<ADC + m<ABC = 180
3y+8+4y+4 = 180
7y + 12 = 180
7y = 180 - 12
7y = 168
y = 168/7
y = 24
Get <ABC
m<ABC = 4y+4
m<ABC = 4(24) + 4
m<ABC = 96 + 4
m<ABC = 100degrees
15. Similarly for this;
GHI + IJG = 180
76 + m<IJG = 180
m<IJG = 180 - 76
m<IJG = 104degrees
Which is equivalent to 80
?
80
4
V80*
O 809
80
o
what is equivalent to 80 1/4?
Which table shows a proportional relationship between a and b?
A.
a b
3 9
4 12
5 20
B.
a b
20 25
24 30
32 40
C.
a b
4 12
5 15
6 24
D.
a b
3 4
6 9
12 16
Help me plssss? Thanks
Answer:
B
Step-by-step explanation:
The manned is a powerful force in a free market and 3 to 4 cents and fling some of the factors that cause changes in demand and why it is important for consumer standards and the changes
Answer:
The description as per the given question is provided below.
Step-by-step explanation:
Demand reflects a shareholder's intent to attract consumers as well as works as a gauge of such a buyer's ability to collect a particular preference for a particular commodity.
The factors that change the demand are as follows:
User needs as well as requirements.Changes affecting associated commodity prices.Peoples' political revenues.The general economy's proportion of participants.what is the value of the expression below?
Answer:
C
Step-by-step explanation:
Using the rule of exponents/ radicals
[tex]a^{\frac{1}{2} }[/tex] = [tex]\sqrt{a}[/tex] , then
[tex]121^{\frac{1}{2} }[/tex] = [tex]\sqrt{121}[/tex] = 11 → C
I need help with this plz
Answer:
[tex]x^{15}[/tex]
Step-by-step explanation:
Distribute the ^3 on top
(27 [tex]x^{6}[/tex] [tex]y^{-9}[/tex])
distribute the ^ -9 on bottom, only to what is in the parenthesis
(27 [tex]x^{-9}[/tex] [tex]y^{-9}[/tex])
the 27's cross out, the [tex]y^{-9}[/tex] 's cross out
[tex]x^{6}[/tex]/ [tex]x^{-9}[/tex] is left
move the [tex]x^{-9}[/tex] to the top of fraction to change its sign
[tex]x^{6}[/tex] · [tex]x^{9}[/tex] = [tex]x^{15}[/tex]
Consider the system of equations: Equation 1: -2x + 3y=9 Equation 2 : -8.1 – 7y = 10 Before adding the equations together, which would not result in the elimination of the variables in this system? Multiply the first equation by 8 and the second equation by 2. O Multiply the first equation by 7 and the second equation by 3. O Multiply the first equation by 4 and the second equation by -1. o Multiply the first equation by 14 and the second equation by 6.
The first option :
Multiply the first equation by 8 and the second equation by 2
would not result in the elimination of the variables in this system
35 into binary number
Answer:
35 in binary is 100011.
Step-by-step explanation:
To find decimal to binary equivalent, divide 35 successively by 2 until the quotient becomes 0.
Please help me with this question.
Answer:
[tex]80\text{ square miles}[/tex]
Step-by-step explanation:
Since the map is using a scale of 1 inch : 5 miles, to find the scale of square inches to square miles, square the ratio:
[tex]\implies 1\text{ square inch}:25\text{ square miles}[/tex]
Since the section of land has an area of 3.2 square inches, the actual area of the section of land must be [tex]3.2\cdot 25=\boxed{80\text{ square miles}}[/tex]