Answer:
(2x - 3) ^2 - 11x - 6
Step-by-step explanation:
What are the different forms of a quadratic function and what do the variables represent?
Answer:
Quadratic equations of second degree.
[tex]{ \bf{a {x}^{2} + bx + c = 0}}[/tex]
Quadratic equations of third degree.
[tex]{ \bf{a {x}^{3} + {bx}^{2} + cx + d = 0}}[/tex]
What's the answer? Also please tell the steps of the solution.
Answer:
[tex] \rm\displaystyle D) \left (1,3\right)[/tex]
Step-by-step explanation:
well to figure out the point we can consider the following formula:
[tex] \rm\displaystyle \text C(x,y)= \left (\frac{m x_{2} + n x_{1} }{m + n} , \frac{m y_{2} + n y_{1} }{m + n} \right)[/tex]
from the given we acquire that,
[tex](x _{1}, y_{1}) = ( - 1,7)[/tex][tex](x _{2}, y_{2}) = ( 4, - 3)[/tex][tex]m : n = 2 : 3[/tex]therefore substitute:
[tex] \rm\displaystyle \text C(x,y)= \left (\frac{(2) (4)+ 3( - 1) }{2 + 3} , \frac{(2) ( - 3) + (3)(7)}{2 + 3} \right)[/tex]
simplify multiplication:
[tex] \rm\displaystyle \text C(x,y)= \left (\frac{8 - 3 }{2 + 3} , \frac{ - 6+ 21}{2 + 3} \right)[/tex]
simplify:
[tex] \rm\displaystyle \text C(x,y)= \left (\frac{5}{5} , \frac{ 15}{5} \right)[/tex]
simplify division:
[tex] \rm\displaystyle \text C(x,y)= \left (1,3\right)[/tex]
hence our answer is D)
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
Points => (-1, 7) & (4, -3)
Ratio => 2 : 3
(x₁, y₁) = (-1, 7)
(x₂, y₂) = (4, -3)
(m₁, m₂) = (2, 3)
Formula = [tex]\large\left (\frac{m_{1} x_{2} + m_{2} x_{1} }{m_{1} + m_{2}} , \frac{m_{1} y_{2} + m_{2} y_{1} }{m_{1} + m_{2}} \right)[/tex]
Points which divide the line segment
= [tex]( \frac{2 \times 4 + 3 \times - 1}{2 + 3}, \frac{2 \times -3 + 3 \times 7}{2 + 3})[/tex]
[tex] =( \frac{8 - 3}{5} , \frac{ - 6 + 21}{5}) \\ = ( \frac{5}{5} , \frac{15}{5} ) \\ = (1,3)[/tex]
Answer => (1, 3) [option D]
Find the domain of the function. Write the answer in interval notation.
Answer:
(- ∞,∞)
there is no restriction when taking cube roots
Step-by-step explanation:
Which of the following expressions is equivalent to the one shown below? (3/2)8 A 3^8/2^8 B 3^8/2 C 3/2^8 D 8•(3/2)
Answer:
Step-by-step explanation:
Write an equation in point-slope form of the line through point J(-1, 10) with slope -7.
Answer:
y - 10 = -7 (x + 1)
Step-by-step explanation:
pont = (-1,10) slope = -7
y - 10 = -7 (x + 1)
The function g(x) is a transformation of the cube root parent function,
Answer:
I believe that the answer is B as well
Step-by-step explanation:
This might be for Ap3x but not 100% sure
Which of the following is not a function?
O A. {(1,2), (2,2), (3,2), (4,2)}
B. {(1,2), (9,-3), (-3,-1), (8,2)}
C. {(1,2), (2,3), (3,4), (4,5)}
D. {(1,2), (-2,3), (1,3), (-2,2)}
Answer:
D......................
John finds that the sum of two numbers is 24 and their difference is one sixth of the sum. Find the smallest number between the two numbers
Answer:
The smallest number is 10
Step-by-step explanation:
x+y=24---equation 1
x-y=¹/6×24=>x-y=4---equation 2
Add both equations
2x=28
x=14
put x=14 into equation 1
14+y=24
y=24-14=10
Which polynomial function has a leading coefficient of 3 and roots 4, I, and 2, all with multiplicity 1? Of(x) = 3(x + 4)(x - 1)(x - 2) O f(x) = (x - 3)(x + 4)(x - 1)(x - 2) f(x) = (x - 3)(x + 4)(x - 1)(x + 1)(x - 2) O f(x) = 3(x + 4)(x - 1)(x + 1)(x - 2) N
Note: There must be -4 instead of 4 otherwise all options are incorrect.
Given:
A polynomial function has a leading coefficient of 3 and roots -4, 1, and 2, all with multiplicity 1.
To find:
The polynomial function.
Solution:
The general polynomial function is defined as:
[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex]
Where, a is the leading coefficient, [tex]c_1,c_2,...,c_n[/tex] are the zeros with multiplicity [tex]m_1,m_2,...,m_n[/tex] respectively.
It is given that a polynomial function has a leading coefficient of 3 and roots 4, 1, and 2, all with multiplicity 1. So, the polynomial function is defined as:
[tex]P(x)=3(x-(-4))^1(x-1)^1(x-2)^1[/tex]
[tex]P(x)=3(x+4)(x-1)(x-2)[/tex]
Therefore, the correct option is A.
PLEASE HELP MEEEEEEEE ILL MARK YOU BRAINLIEST
A set of 3 pens cost 1.68 at that unit price,how much will 10 pens cost?
Answer:
16.8
Step-by-step explanation:
Answer:
5.60
Step-by-step explanation:
To find what 10 pens cost we have to go down to the cost of 1 pen first.
If 3 pens costs 1.68 then the cost of 1 pen is 1.68 divided by 3.
[tex]\frac{1.68}{3} = 0.56[/tex]
If one pen costs 0.56 then 10 pens cost 0.56 multiplied by 10.
0.56 × 10 = 5.60
You sunk my battleship...The hms petticoat and uss junction are being monitored on a tracking screen where each ship is measured in millimeters from the lower left corner. The linear path of the hms petticoat is given by y=2x+50. If x=3t, express y as a function of t minutes
Answer:
y = f(t) = 6t + 50
Step-by-step explanation:
Given:
y = 2x + 50
Where,
x = 3t
Substitute x = 3t into the equation
y = 2x + 50
y = 2(3t) + 50
Open parenthesis
y = 6t + 50
y = f(t) = 6t + 50
pls help tysm will give brainliest!!
Answer:
% change in perimeter = 43. 44 %
% change in area = 16 %
Step-by-step explanation:
initial perimeter of the rectangle = 2(2p + p)
= 6p
initial area of the rectangle = 2p × p
= 2p²
25% is equal to 0.4therefore,
new length = 2p + (2p × 0.4)= 2p + 0.8p = 2.8 p
new breadth= p - 0.4p
= 0.6 p
new perimeter = 2 ( 2.8 p + 0.6p)= 3.4 p
new area = 2.8p × 0.6p= 1.68 p²
% change in perimeter
[tex] = \frac{6p - 3.4p}{6p} \times 100 \\ = \frac{2.6p}{6p} \times 100 \\ = 43.33\%[/tex]
% change in area
[tex] \frac{2 {p}^{2} - 1.68 {p}^{2} }{2 {p}^{2} } \times 100 \\ = \frac{0.32}{2} \times 100 \\ = 16\%[/tex]
what is the formula for finding the length of a line on the cartesian plane.
Answer:
Step-by-step explanation:
distance = square root [ [tex](x2-x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex] ]
where you have two points on the line
Point 1 = P1 = (x1,y1)
point 2 = P1 =(x2,y2)
Rewrite this function in equivalent forms to identify the key features of the quadratic function it models.
f(x) = 2x2 - 40 - 6
Type the correct answer in each box.
Key features:
y-intercept: 0,
axis of symmetry: z =
vertex: OD
x-intercepts: (-1,0) and ((,)
Answer:
y int = -6
x = 1 axis symmetry
vertex : (1,-8)
x int: (3,0),(-1,0)
Step-by-step explanation:
Help me with the diagram please!!!
Answer:
(B) 30
Step-by-step explanation:
Imagine you drew a line from Point T until it touched Line PR. Let's call that point where it touched Line PR "Point Z".
That line (called Line TZ) would be perpendicular to PR, forming a 90 degree angle.
Now, TZW is a triangle.
To find x, we need to find the angle measurment of Angle ZTW.
This is where we use the hexagon.
A hexagon's interior angle sum is 720, meaning each interior angle is equal to 120 degrees. So Angle UTS would equal 120 degrees.
However, Line TZ bisects that 120 degree angle, so Angle ZTW would equal 60 degrees (because 120/2 = 60).
Now we have two angles of the triangle: 90 & 60.
A triangle's interior angle sum is 180.
Add 90 & 60, which is 150, and subtract 150 from 180.
The result is 30, which is the angle measurement of x.
Hope it helps (●'◡'●)
Please help it’s needed
very easy
[tex]\displaystyle\ (f-g)(x)=f(x)-g(x)=4x^2-5x-3x^2-6x+4=\boxed{x^2-11x+4}[/tex]
[tex]\\ \sf\longmapsto f(x)=4x^2-5x[/tex]
[tex]\\ \sf\longmapsto g(x)=3x^2+6x-4[/tex]
Now
[tex]\\ \sf\longmapsto (f-g)(x)[/tex]
[tex]\\ \sf\longmapsto f(x)-g(x)[/tex]
[tex]\\ \sf\longmapsto 4x^2-5x-(3x^2+6x-4)[/tex]
[tex]\\ \sf\longmapsto 4x^2-5x-3x^2-6x+4[/tex]
[tex]\\ \sf\longmapsto x^2-11x+4[/tex]
Find the area in km2. Round answer to the nearest tenth if necessary
Area of a triangle formula: 1/2 x base x height
Area = 1/2 x 2 x 3.8
Area = 3.8 square km
Answer:
The area of triangle = 3.8km²
Step-by-step explanation:
Given :-
A triangle having length of base is 2km and length of height is 3.8km.
To find :-
Area of triangle.Solution :-
We know that ,
Area of triangle = ½ × Base × height
Substitute the values.Area of triangle = ½ × 2km × 3.8km
Multiply 2km by 3.8km.Area of rectangle = ½ × 7.6km²
Divide by 2 .Area of triangle = 3.8km²
HELLPPPPPPPPPPPP i will give brainliest
Answer:
3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{18}[/tex]
[tex]\sqrt{9}[/tex] [tex]\sqrt{2}[/tex]
3[tex]\sqrt{2}[/tex]
I will mark you the brainliest
What is the opposite polynomial?
Answer:
e t
Step-by-step explanation:
Find slope if a line pass through the original and (3,2)
heyy im not sure if you meant origin instead of original but the origin would be (0,0)
Answer:
2/3
Step-by-step explanation:
the slope form equation is : y2 - y1/ x2-x1 (aka change in y divided by change in x)
so it would be 2-0/ 3-0 = 2/3
the slope is 2/3
Please help!! In class right now, I don’t understand anything
Answer:
x = 2.5
Step-by-step explanation:
Because the triangles are similar, you can divide the sides and equal the results:
24/6 = 10/x
24•x/6 = 10
24•x = 10•6
24•x = 60
x = 60/24
x = 2.5
Answer:
x = 2.5 km
Step-by-step explanation:
In similarity triangles, corresponding sides are in same ratio.
[tex]\frac{DF}{BC}=\frac{EF}{AC}\\\\\frac{10}{24}=\frac{x}{6}\\\\\frac{10}{24}*6=x\\\\x=\frac{10}{4}\\\\x=\frac{5}{2}\\\\x= 2.5[/tex]
Apples are 6 for $1.50 and oranges are 5 for $3.00. How much does it cost to buy 2 apples and 2 oranges Help me solve show me the steps
Answer:
$1.70
Step-by-step explanation:
To figure out how much each apple costs, divide $1.50 by the quantity of apples (6). The answer to that is $0.25, so multiply it by the two apples to get $0.50.
For the oranges, divide $3 by 5. The answer for that is $0.60. Multiply that by the two oranges to get $1.20.
Then, add $0.50 to $1.20 to get a total of $1.70
Answer:
$1.70
Step-by-step explanation:
We know that you can buy 6 apples for $1.50 and 5 oranges for $3.00. So let's look at the cost for one individual apple first.
To find the amount/apple we can divide $1.50 by 6. Here's another way to look at it:
Assume A is cost per apple.
6A = $1.50
6A/6 = $1.50/6
A = $0.25
Now to find the amount for 2 apples, you want to multiply the amount it costs for one apple by 2, because you are multiplying the quantity by 2 as well.
A= $0.25
A *2 = $0.25 * 2
2A = $0.50
So for two apples, it is 50 cents.
We can use a similar process for oranges but with a different price and quantity.
Assume R is cost per orange.
5R = $3.00
5R/5 = $3.00/5
R = $0.60
To find the amount for two oranges we multiply the cost by two.
R = $0.60
R*2 = $0.60*2
2R = $1.20
Finally, we want the total amount for apples AND oranges so we find the sum.
$0.50 + $1.20 = $1.70
The Banker's Rule is another type of simple interest computation that is similar to ordinary simple interest computation. It is based on a 360-day year, but you use the actual number of days in the term when calculating interest. Does this benefit the lender or the borrower? Explain.
Answer:
it would appear tp benefit the borrower. if interest (which is paid by the borrower) is computed on a 360 day year and there are 365 days in a year....
one could consider the "Bankers Rule" to give the borrower 5 "free" days of no interest paid
Step-by-step explanation:
The town of Lakehorn is built on a grid system. Town hall is located downtown at point (0,0). A new school is located 3 miles north and 2 miles east of town hall. Only students who live outside a 5-mile radius from the school are eligible to ride the school bus. Which of the following students are eligible to ride the bus? Select all that apply.
The students eligible to ride the bus are: Marinna, Kaleb and Thomas
What is the distance between two points?The distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex] is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
What is an equation of circle with center at (h, k)?An equation of circle with center at (h, k) and radius 'r' is,
[tex](x-h)^2 + (y-k)^2=r^2[/tex]
For given example,
Town hall is located downtown at point (0,0). A new school is located 3 miles north and 2 miles east of town hall.
Considering positive x-axis = East
negative x-axis = West
positive y-axis = North
negative y-axis =South
Also, locate the position of each student on the graph.
Then the given situation would as shown in following diagram.
We have been given, only students who live outside a 5-mile radius from the school are eligible to ride the school bus.
Using the equation of the circle,
the equation for the area within a circle of 5-mile radius from the school would be,
[tex](x-2)^2+(y-3)^2=5^2[/tex]
From the graph we can observe that, Marinna, Kaleb and Thomas live outside a 5-mile radius from the school.
Therefore, the students eligible to ride the bus are: Marinna, Kaleb and Thomas
Learn more about the equation of circle here:
https://brainly.com/question/10618691
#SPJ2
Miguel can use all or part of his $25 gift card to make a music purchase.Each song costs $1.50, and there is a $1.00 per account activation fee
Answer:
1.5m + 1 ≤ 25
Step-by-step explanation:
Given:
Total amount of gift card Miguel have = $25
Cost of each song = $1.50
Account activation fee = $1
Find:
Inequality
Computation:
Assume;
Number of song Miguel have = m
So,
Total amount of gift card Miguel have ≥ (Cost of each song)(Number of song Miguel have) + Account activation fee
1.5m + 1 ≤ 25
Solve for x. Round your answer to the nearest tenth if necessary.
Answer:
12.6
Step-by-step explanation:
[tex]\frac{84}{87}[/tex] = [tex]\frac{x}{13}[/tex]
cross multiply
87x = 1092
x = 12.6 rounded
Multiply the following rational expressions and simplify the result
Answer:
Step-by-step explanation:
We have to solve the given expression,
[tex]\frac{9y-33y^2-3y^4}{100-49y^2}.\frac{7y^2+17y+10}{14y^2+28y}[/tex]
[tex]\frac{9y-33y^2-3y^4}{100-49y^2}.\frac{7y^2+17y+10}{14y^2+28y}[/tex] = [tex]\frac{-y(-9+33y+3y^3)}{100-49y^2}.\frac{7y^2+17y+10}{14y(y+2)}[/tex]
= [tex]\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{7y^2+10y+7y+10}{14y(y+2)}[/tex]
= [tex]\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{y(7y+10)+1(7y+10)}{14y(y+2)}[/tex]
= [tex]\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{(y+1)(7y+10)}{14y(y+2)}[/tex]
= [tex]\frac{-3y(-3+11y+y^3)}{(10-7y)}.\frac{(y+1)}{14y(y+2)}[/tex]
= [tex]\frac{-3(-3+11y+y^3)}{(10-7y)}.\frac{(y+1)}{14(y+2)}[/tex]
= [tex]\frac{3(3-11y-y^3)(y+1)}{(10-7y)(14(y+2)}[/tex]
x+3/2 + (x-1) = 4/5
Answer:
x = [tex]\frac{3}{20}[/tex]
Step-by-step explanation:
Given
x + [tex]\frac{3}{2}[/tex] + (x - 1) = [tex]\frac{4}{5}[/tex]
Multiply through by 10 ( the LCM of 2 and 5 ) to clear the fractions
10x + 15 + 10(x - 1) = 8
10x + 15 + 10x - 10 = 8
20x + 5 = 8 ( subtract 5 from both sides )
20x = 3 ( divide both sides by 20 )
x = [tex]\frac{3}{20}[/tex]
x + 3/2 + x - 1 = 4/5
Collect the same terms
x + x + 3/2 - 1 = 4/5
2x + 3/2 - 2/2 = 4/5
2x + (3 - 2)/2 = 4/5
2x + 1/2 = 4/5
2x + 0.5 = 0.8
Subtract both sides 0.5
2x + 0.5 - 0.5 = 0.8 - 0.5
2x + 0 = 0.3
2x = 3/10
Divide both sides by 2
2x ÷ 2 = ( 3/10 ) ÷ 2
x = 3/10 × 1/2
x = 3/20
_________________________________
Check :3/20 + 3/2 + ( 3/20 - 1 ) = 4/5
3/20 + 30/20 + ( 3/20 - 20/20 ) = 4/5
(3 + 30)/20 + (3 - 20)/20 = 4/5
33/20 - 17/20 = 4/5
(33 - 17)/20 = 4/5
16/20 = 4/5
4 × 4 / 4 × 5 = 4/5
4/5 = 4/5
Thus we found the correct value of x .
And we're done...
4 is added to two-thirds of d
Answer:
ayan po answer nasa picture po
Step-by-step explanation:
where
x
is the number you are trying to compute the (2/3) rds of
i need this answered soon!! please help!! 20 points and brainliest!!!
Answer:
graph 1
Step-by-step explanation:
if it's all the times BETTER
then it shouldn't include 15
Answer:
Graph 3.
Step-by-step explanation:
.