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]
The graphs below have the same shape. What is the equation of the red
graph?
F(x) =
A. F(x) = (2 - x)
B. F(x) = (3-X)
C. F(x) = 3 - X2
D. F(x) = 2 - x?
The equation of red graph is [tex]F(x) = 2 -x^{2}[/tex].
What is the general equation of parabola?The general equation of parabola is [tex]y = a(x-h)^{2} + k[/tex].
Where,
(h, k) are the vertices of the parabola.
According to the given question.
We have two graph.
The blue and red graph both represents the equation of downward parabola.
Since, blue graph represents the equation of downward parabola.
Whose equation is given
[tex]G(x) = 5 - x^{2}..(i)[/tex]
The general equation of a parabola is [tex]y = a(x-h)^{2} + k..(ii)[/tex]
Where, (h, k) are the vertices of the parabola.
Compare the equation (i) with (ii)
We get
(h, k) = (0, 5) and a = -1.
Now, the red graph which also represents the downward parabola whose vertices are (0, 2)
Therefore, the equation red graph is given by
[tex]F(x) = a(x-0)^{2} + 2[/tex]
⇒ [tex]F(x) = -1(x-0)^{2} + 2[/tex]
⇒ [tex]F(x) = 2 - x^{2}[/tex]
Hence, the equation of red graph is [tex]F(x) = 2 -x^{2}[/tex].
Find out more information about equation of parabola here:
https://brainly.com/question/4074088
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Check whether (0, -2) is solution of the equation x - 2y = 4 or not
Answer:
Step-by-step explanation:
Plugin x = 0 & y = -2 in the LHS of the equation. After substituting, if you get the RHS, then this point is the solution of the equation.
x - 2y = 0 - 2*(-2)
= 0 + 4
= 4 = RHS.
(0,-2) is solution of the equation.
can somebody help me with these questions
Answer:
The first one is B. 11.75
The second one is A. 4
Step-by-step explanation:
In order to find how many liters (L) of paint he used you need to do 2.5*5.5=13.75 Then to find out how much he has left you do 25-13.75=11.75 So your answer is 11.75.
The second one you have to do the reverse. So since it says 4*_=48, you do 48÷4=_=12. Then since it says 12*1/3=_ You can do 12÷3=_=4 So your answer is 4.
Given The following right triangle, what is the ratio of Cos(b)
A) 5/13
B) 5/12
C) 13/5
D) 12/13
Answer:
A. 5/13
Step-by-step explanation:
Cos = Adjacent/Hypotenuse
Adjacent of B = 5
Hypotenuse = 13
Hence CosB = 5/13
simplify ( √ 5 ) ( 3 √ 5 )
Answer:
[tex]5^\frac{5}{6}[/tex]
Step-by-step explanation:
[tex]\sqrt{5}[/tex] can be represented as [tex]5^{\frac{1}{2}}[/tex] and [tex]\sqrt[3]5}[/tex] can be represented as [tex]5^{\frac{1}{3}}[/tex]. Therefore, the expression can be rewritten as:
[tex]5^{\frac{1}{2}}*5^{\frac{1}{3}}[/tex]
The rule for multiplying two exponents with the same base is you add the exponents. For example: [tex]x^m*x^k=x^{m+k}[/tex]
We can use the same property to get:
[tex]5^{\frac{1}{2} +\frac{1}{3}}[/tex]
which is just [tex]5^\frac{5}{6}[/tex] after you add the fractions
9: A rectangular room is 14m long and 8m wide. Jessica is going to carpet the room with carpet that costs £17.50 per square metre. Work out the cost of carpeting the room.
Answer:
£1,960
Step-by-step explanation:
Find the area of the room using the formula, A = lw
Plug in the length and width, and solve:
A = lw
A = 14(8)
A = 112
So, the area of the room is 112 square meters. Find the cost of carpeting the room by multiplying this by the price, £17.50
112(17.5)
= 1960
So, the price will be £1,960
Select all the correct answers.
Cineplex operates two movie theaters in a city. The profits from one theater can be represented by the expression t^3 - t^2 + 2t - 100, where
t is the number of tickets sold. The profits from the second theater can be represented by the expression t^2 - 2t - 300.
which statements are true about the expression representing Cineplex's total profits in that city?
Answers:
The total profit expression is a binomial.
The total profit expression is a polynomial.
The total profit expression has a constant term.
The total profit expression is a polynomial
The total profit expression is a binomial
The total profit expression has a constant term
The first step to determining which type of function it is, is to add the profits in both theatres together
(t³ - t² + 2t - 100) + (t² - 2t - 300) = t³ - 400
A polynomial function is a mathematical expression that is made up of different types of variables. They include non-zero coefficients, positive exponents, and constants.
Types of polynomials include :
1. Linear polynomial function : a linear function is a function that has a single variable raised to the power of 1.
An example is x + 2
The variable x is raised to the power of 1. 2 is the constant terms
2. Quadratic polynomial function - A quadratic function is a function that usually has a single variable and it is raised to the power of 2.
An example is 2x² + 10x + 25
3. Cubic polynomial function : this is a function that usually has a single variable raised to the power of 3.
An example is 5y³ + y²
4. Binominal function: this is a function that contains only two terms.
An example is t³ - 400
t³ - 400
The above equation of the total profit has a constant term which is -400
The above equation is a polynomial. This is because it has different types of variables.
The above equation is a binomial equation because it has only two terms t³ and 400
In order to determine the type of expression the total profit is, the first step is to add the two profit expressions provided in the question. Based on the expression derived, the type of expression it is can then be deduced.
To learn more about polynomials, please check: https://brainly.com/question/17822016?referrer=searchResults
Help me with this one plz
Answer:
-1 is the only number there that is an integer as all the rest of them are mixed fractions.
Answer:
- 1
Step-by-step explanation:
Find the exact value of x.
Answer:
24
Step-by-step explanation:
4 times 4
8 times 8
Subtract the 2 #'s
Then divide your answer by 2.
Step-by-step explanation:
use Pythagoras theorem
hypotenuse² = base² + height²
8²=base²+4²
64-16=B²
√48=B
√2×3×2×2×2=B
2×2√3
4√3 = B
hope it helps
Craig threw a handful of identically shaped buttons into the air then collected 14 bottoms that landed on the carpet. Is this sample of the buttons likely to be biased yes or no
Answer:
possible?? but I think that there is a typo, and that there would not be a bias
Step-by-step explanation:
can we assume that there are no typos in the question
he threw BUTTONS in the air, and look at buttons that landed with the BOTTOMS facing up ??? in that case the weight might bias the orientation of the landing... I think that you have a typo and it just says that he collected 14 BUTTONS, in that case given that they are "IDENTICAL" we most likely can assume that there would be no bias (size color, texture are all the same)
I need helpppppp cause I’ll make ur bra list of however u spell it
Answer:
DBH
Step-by-step explanation:
#1
Initial Price = 100% = 18
Discount = 15% = x
0.15 ( 18 ) = 0.15 * 18 = 2.7
Discount = $2.7 or $2.70
Letter = D
#2
Initial Price = 100% = 450
Markup = 20% = x
0.20 ( 450 ) = 1/5 of 450 = 90
Markup = $90
Letter = B
#3
Initial Payment = 100% = 37.60
Tip = 15% = x
0.15 ( 37.60 ) = 0.15 * 37.60 = 5.64
Tip = $5.64
Letter = H
Your Code = DBH
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Hey guys I need help real quick it’s question number 6 pls :)
Select all the expressions that
are equivalent to 23. (22)
Answer: 2 to the 8th power
Step-by-step explanation:
In a wildlife park, there were 18 gray wolves. After three years, there were 27 gray wolves. What is the percent gain?
Answer:
50%.
Step-by-step explanation:
Gain as a fraction is (27-18) /18
= 9/18
= 1/2.
Percent gain = 1/2 * 100 = 50%.
Find 3v - 4w if v = -3i and w=-i + 5j. Use < > for
vector notation.
Answer:
[tex]<-5, 20>[/tex]
Step-by-step explanation:
What we're given:
[tex]\vec{v}=-3i[/tex] [tex]\vec{w}=-i+5j[/tex]The vector [tex]3v-4w[/tex] is then [tex]3(-3i)-4(-i+5j)=-9i+4i-20j=-5i+20j\implies \boxed{<-5, 20>}[/tex]
What is the equation of the line that is parallel to the line y = -1/3 x + 4 and passes through the point (6, 5)?
y = -1/3 x + 3
y = -1/3x + 7
y = 3x – 13
y = 3x + 5
Answer:
[tex]5)8 \sqrt[6]{?} [/tex]
allá paosgesusussj siisveveu días dbd dusv
Solve for x:
4x + 1 = 7x - 5
Answer:
x = 2
Step-by-step explanation:
First, subtract 4x from both sides:
4x + 1 = 7x - 5
1 = 3x - 5
Add 5 to both sides:
6 = 3x
Divide each side by 2:
2 = x
So, the answer is x = 2
Answer:
2 =x
Step-by-step explanation:
4x + 1 = 7x - 5
Subtract 4x from each side
4x-4x + 1 = 7x-4x - 5
1 = 3x-5
Add 5 to each side
1+5 = 3x-5+5
6 = 3x
Divide each side by 3
6/3 = 3x/3
2 =x
What is the inverse of the statement below?
x →y
A. -X
B. y = x
C. y = x
O D. -x=y
Help plz
Answer:
d -x=y the awnssr may not be correct but I tried so
What is the x-value of point A?
1
6
4
ТА
2
-6
-4
-2
-8
х
-2
-4
-6
please help and hurry!!
Factorx^2 + x - 6, asappp
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: ( \: x - 2 \: )( \: x + 3 \: )}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] {x}^{2} + x - 6[/tex]
➼[tex] \: {x}^{2} + 3x - 2x - 6[/tex]
Taking [tex]x[/tex] as common from first two terms and 2 from last two terms, we have
➼[tex] \: x \: ( \: x + 3 \: ) - 2 \: ( \: x + 3 \: )[/tex]
Taking the factor [tex](x+3)[/tex] as common,
➼[tex] \: ( \: x - 2 \: )( \: x + 3 \: )[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
Write cos 29° in terms of sine.
Help pls :(
Answer:
0.48480962
Step-by-step explanation:
1. Take the sine of 29 ° .
sin ( 29 ° )
2. Evaluate sin ( 29 ° ) .
0.48480962
Will give brainliest but Please hurry got until tmrw
A train is traveling at a constant
speed, and its distance over time is
shownin the graph. What is the speed
of the train?
Answer:
It looks like 35 miles per hour
Step-by-step explanation:
if you look at the vertical line between 0 and 2 (which is the one hour mark) on the horizontal axis of the graph you can see the line of the graph crossed under the 40 mi. Therefore the train traveled about 35 miles in one hour (or 35 mph) because there are no other answers under 40.
I need help with this one
Answer:
Step-by-step explanation:
Convert fractions to decimals. Then compare the whole part of the decimal numbers. The decimal having the highest whole part is the greatest number.
If whole part of the decimals are same, compare the tenth place ....
[tex]68 \frac{1}{2}= \frac{137}{2}=68.5[/tex]
[tex]\frac{336}{5}=67.2[/tex]
67.59
67.22
Greatest to least: 68.5 , 67.59 , 67.22 , 67.2
68 1/2 , 67.59 , 67.22 , 336/5
Which graphs are inverses of one another?
Graph A and B
Graph A and C
Graph B and C
none of the graphs shown
Well... kinda need those graphs to be shown.
Answer:
A and C
Step-by-step explanation:
3. Round off the following numbers to three decimal places:
a) 31,1104
b) 0,10989
Answer:
311.104
010.989
Step-by-step explanation:
hi, last thing !! awarding 30 points here !! answer asap thank you so much !!
Answer:[tex]\color{yellow}{}[/tex]
[tex]\color{iron}{{-1, 0, 4}}[/tex]
[tex]\color{iron}{{-3, 1, 2}}[/tex]
Domain is 5 and the range is 4 so the Function is 1.25
Which of the following expressions is equivalent to the one shown below? (-11/14)^5
help----------------------------
Answer:
One solution;
[tex]x=-1\frac{2}{7}[/tex]
[tex]y=-5\frac{3}{7}[/tex]
Step-by-step explanation:
The method of elimination is a way of solving a system of equations. There are many steps involved in this process. First, one must manipulate one of the equations in the system by multiplying each term in it by a certain number such that one of the variables is the inverse of the other like the variable in the other equation. Then one must add the two equations. This will eliminate one of the variables in the equations. After doing so, one has to use inverse operations to solve for the other variable. Finally, one will back solve, substitute the value of the solved variable into one of the equations and solve for the remaining unknown variable.
[tex]\left \{ {{y=5x+1} \atop {y=-2x-8}} \right.[/tex]
Manipulate the system;
[tex]\left \{ {{y=5x+1*(-1)} \atop {y=-2x-8}} \right.[/tex]
Simplify,
[tex]\left \{ {{-y=-5x-1} \atop {y=-2x-8}} \right.[/tex]
Add the equations,
[tex]\left \{ {{-y=-5x-1} \atop {y=-2x-8}} \right.[/tex]
[tex]0=-7x-9[/tex]
Inverse operations,
[tex]0=-7x-9[/tex]
[tex]7x=-9[/tex]
[tex]x=-\frac{9}{7}[/tex]
[tex]x=-1\frac{2}{7}[/tex]
Backsolve,
[tex]y=-2x-8[/tex]
Substitute
[tex]y=-2(-\frac{9}{7})-8[/tex]
Simplify,
[tex]y=-2(-\frac{9}{7})-8[/tex]
[tex]y=\frac{18}{7}-8[/tex]
[tex]y=\frac{18}{7}-8\\y=-\frac{38}{7}[/tex]
[tex]y=-5\frac{3}{7}[/tex]
Anthony is building a rectangular shaped swimming pool with a perimeter of 80 feet. Determine a function A(w) that models the area of the top surface of the swimming pool in terms of width W. A(w)= For w>0
Answer:
[tex]A(w) = 40w - w^2[/tex]
Step-by-step explanation:
Given
[tex]P = 80[/tex] --- perimeter
Required
Define the area in terms of width
The perimeter of the pool is:
[tex]P =2(l + w)[/tex]
Where:
[tex]l\to length[/tex]
[tex]w\to width[/tex]
So:
[tex]80 =2(l + w)[/tex]
Divide by 2
[tex]40 =l + w[/tex]
Make l the subject
[tex]l = 40-w[/tex]
The area is then calculated as;
[tex]A(w) = l * w[/tex]
Substitute: [tex]l = 40-w[/tex]
[tex]A(w) = (40 - w) * w[/tex]
[tex]A(w) = 40w - w^2[/tex]
i need help with this
Answer:
[tex]y = - \frac{1}{2} x + 4[/tex]
Step-by-step explanation:
Let us consider two points through which the line passes through
[tex](x_1 , y _ 1 ) = ( 0 , 4 ) \ and \ (x_ 2 , y _ 2 ) = ( 4, 2 )[/tex]
Step 1 : Find slope of the line
[tex]Slope, m_1 = \frac{rise}{run} \\\\That \ is \ m_1 \ = \frac{y_2 - y _ 1}{x_2 - x_1}[/tex]
[tex]= \frac{2 - 4}{4-0} \\\\=-\frac{2}{4}\\\\= - \frac{1}{2}[/tex]
Step 2 : Find equation of the line.
[tex](y - y _ 1) = m_ 1 (x - x_1)\\\\( y - 4) = - \frac{1}{2}(x - 0)\\\\y = -\frac{1}{2}x + 4[/tex]
can somebody help me with this question !
Answer:
No please! Mr excuse me I am not your type bye