Add the following: (i) 2a+b+c, a - b -c, 3a + b
What is the equation of the line that passes through the point (-4,-3)(−4,−3) and has a slope of \frac{3}{4}
Answer:
y = 3/4x
Step-by-step explanation:
Given:
x1 = -4
y1 = -3
slope (m) = 3/4
Solution:
y - y1 = m ( x - x1 )
y - (-3) = 3/4 ( x - (-4) )
y + 3 = 3/4 ( x + 4 )
y + 3 = 3/4x + 3
y = 3/4x + 3 - 3
y = 3/4x
[tex] \sf \huge{ question \hookleftarrow}[/tex]
If [tex] \alpha \: and \: \beta [/tex] are roots of a equation " ax² + by + c ", then find the value of the following in terms of a , b and c ~
[tex] \boxed{ \boxed{ \sf \sqrt{ \alpha} + \sqrt{ \beta } = \: ?}}[/tex]
[tex]\underline{\bf{Given \:equation:-}}[/tex]
[tex]\\ \sf{:}\dashrightarrow ax^2+by+c=0[/tex]
[tex]\sf Let\:roots\;of\:the\: equation\:be\:\alpha\:and\beta.[/tex]
[tex]\sf We\:know,[/tex]
[tex]\boxed{\sf sum\:of\:roots=\alpha+\beta=\dfrac{-b}{a}}[/tex]
[tex]\boxed{\sf Product\:of\:roots=\alpha\beta=\dfrac{c}{a}}[/tex]
[tex]\underline{\large{\bf Identities\:used:-}}[/tex]
[tex]\boxed{\sf (a+b)^2=a^2+2ab+b^2}[/tex]
[tex]\boxed{\sf (√a)^2=a}[/tex]
[tex]\boxed{\sf \sqrt{a}\sqrt{b}=\sqrt{ab}}[/tex]
[tex]\boxed{\sf \sqrt{\sqrt{a}}=a}[/tex]
[tex]\underline{\bf Final\: Solution:-}[/tex]
[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}[/tex]
[tex]\bull\sf Apply\: Squares[/tex]
[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2= (\sqrt{\alpha})^2+2\sqrt{\alpha}\sqrt{\beta}+(\sqrt{\beta})^2[/tex]
[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2 \alpha+\beta+2\sqrt{\alpha\beta}[/tex]
[tex]\bull\sf Put\:values[/tex]
[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2=\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}[/tex]
[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\sqrt{\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}}[/tex]
[tex]\bull\sf Simplify[/tex]
[tex]\\ \sf{:}\dashrightarrow \underline{\boxed{\bf {\sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\sqrt{\dfrac{-b}{a}}+\sqrt{2}\dfrac{c}{a}}}}[/tex]
[tex]\underline{\bf More\: simplification:-}[/tex]
[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{-b}}{\sqrt{a}}+\dfrac{c\sqrt{2}}{a}[/tex]
[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{a}\sqrt{-b}+c\sqrt{2}}{a}[/tex]
[tex]\underline{\Large{\bf Simplified\: Answer:-}}[/tex]
[tex]\\ \sf{:}\dashrightarrow\underline{\boxed{\bf{ \sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\dfrac{\sqrt{-ab}+c\sqrt{2}}{a}}}}[/tex]
The value [tex]\sqrt{\alpha } +\sqrt{\beta }[/tex] in terms of a, b and c is [tex]\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]
Roots of a quadratic equation
Given the quadratic equation ax² + bx + c, the sum and product of the roots are expressed as:
[tex]\alpha +\beta =-\frac{b}{a} [/tex][tex]\alpha \beta =\frac{c}{a} [/tex]Get the value of the radical expression [tex]\sqrt{\alpha } +\sqrt{\beta } [/tex]
Taking the square of the expression will give:
[tex](\sqrt{\alpha } +\sqrt{\beta } )^2=(\sqrt{\alpha } )^2+(\sqrt{\beta } )^2+2\sqrt{\alpha \beta} [/tex]Take the square root of both sides:
[tex]\sqrt{(\sqrt{\alpha } +\sqrt{\beta } )^2} =\sqrt{(\sqrt{\alpha } )^2+(\sqrt{\beta } )^2+2\sqrt{\alpha \beta} } \\ \sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(\alpha }+{\beta} )+2\sqrt{\alpha \beta} } \\[/tex]
Substitute the product and the sum values into the expression to have:
[tex]\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(-\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]
Hence the value [tex]\sqrt{\alpha } +\sqrt{\beta }[/tex] in terms of a, b and c is [tex]\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]
Learn more on the roots of equation here: https://brainly.com/question/25841119
Yaniq has these two spinners
Answer it all right NO wrong
Answer:
b should be 2/11
c should be 2/11 as well
Step-by-step explanation:
Used The Graph info
total spins 11
both are 2over9
Step-by-step explanation:
9 results 2 only
Pablo has $5,483 in a savings account. The interest rate is 5%, compounded annually.
To the nearest cent, how much will he have in 3 years?
(compound interest formu)
Answer:
$6347.26Step-by-step explanation:
Given:
Initial amount P = 5483Interest rate r = 5% or 0.05Compound number n = 1Time t = 3 yearsFind the total amount in 3 years:
[tex]A = P(1+r/n)^{nt}[/tex][tex]A = 5483*(1+0.05/1)^{1*3}=5483*(1.05)^3 = 6347.26[/tex]Here we've been given,
Principal amount (p) = $5843 Compound number (n) = 1 Rate of Interest (r) = 5% = 5 × 1/100 = 0.05 Time (t) = 3 years A = ?The standard formula for Compound interest (C.P) is given by,
[tex]:\implies\tt{A = p( { \frac{1 + r}{n} )}^{n \times t} } \\ \\ \\ :\implies\tt{A = 5483( { \frac{1 + 0.05}{1}) }^{1 \times 3} } \\ \\ \\ :\implies\tt{A = 5483 \times {1.05}^{3} } \\ \\ \\ :\implies\tt{A = 6347.26}[/tex]
The price of a pair of shoes increases from $54 to $68. What is the percent increase to the nearest percent? [The percent increase is ___%]
Answer:
25.93%
Step-by-step explanation:
Percent change formula is [tex]\frac{(V_2-V_1)}{|V_1|}[/tex]x 100
v2 = value 2
v1 = Value 1
now you substitute in.
[tex]\frac{68-54}{|54|}[/tex]x 100
[tex]\frac{14}{54}[/tex]x100
0.259259x100
= 25.9259% or 25.93%
Which number is greater than 555,621,000? A. 5.0 x 10 B. 6.2 x 10 C. 5.55621 x 10 D. 9.99 x 10
Answer:
None of these
Step-by-step explanation:
None of these are correct because you would need to multiply 5 x 10 to a certain power. 5.55621 x 10 to the 8th power would do it.
Answer: I believe D is correct
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST
Answer:
S (2, - 15 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
Using (x₁, y₁ ) = T (0, 3 ) and (x₂, y₂ ) = S (x, y )
Calculate the midpoint using above and equate to coordinates of (1, - 6 )
[tex]\frac{x+0}{2}[/tex] = 1 ( multiply both sides by 2 )
x = 2
[tex]\frac{y+3}{2}[/tex] = - 6 ( multiply both sides by 2 )
y + 3 = - 12 ( subtract 3 from both sides )
y = - 15
S has coordinates (x, y ) = (2, - 15 )
Answer:
Point S is at the ordered pair (2,-15)
Step-by-step explanation:
midpoint formula : midpoint ordered pair (x,y) = ( [tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])
midpoint x = [tex]\frac{x1+x2}{2}[/tex] ; midpoint y = [tex]\frac{y1+y2}{2}[/tex]
midpoint x = 1 x1 = 0 midpoint y = -6 y1=3
Solve each equation for x2 and y2 to get the points for S.
x = [tex]\frac{x1+x2}{2}[/tex]
1 = (0) +x2 / 2
2 = x2
y = [tex]\frac{y1+y2}{2}[/tex]
-6 = 3 + y2 / 2
-12 = 3 + y2
-15 = y2
(2,-15) are the coordinates to point S.
PLEASE ANSWER ASAP
Please give an answer i can copy paste into the answer box, please nothing extra
Using the following 3 equations, answer the questions:
11x + y = 4x + y = -2x - 2y = 18
How can you determine which equations can be graphed more easily using x- and y-intercepts, rewriting in slope-intercept form, or using a table of values?
Which method works best for you personally? When does it not work as well?
Answer:
Step-by-step explanation:
I'll assume these are the equations:
11x + y = 18
4x + y = 18
-2x - 2y = 18
=======
The easiest approach to graphing, for me, is to rearrange each to y=mx+b (slope-intercept) format:
y = -11x+18 y-intercept of 18 (0,18)y = -4x + 18 y-intercept of 18 (0,18)y = - x -9 y-intercept of -9 (0,-9)It seems to me that all three can be graphed easily from simply reading the slope and y-intercept values. Since these are straight lines, all we need is two points for each line, and one is standing out in plain view, the y-intercept: (0,y-intercept). The second point can be determined by using whatever value of x makes the calculation easy
An example: y = - x -9. Plot (0,-9) for the y intercept, and then calculate one additional point (e.g., for x = - 9). (-9,0) Then connect a straight line between these two points and presto (metric term for magic), a graph. For the first equation, I picked 20 for x. For x = 20, y = -29. That was easy, and we have the second point: (1,-10)
See the attachment for how this was done. The first points are all for the y-intercept (0,[18 or 9]). All of the second points were calculated in my head by using a convenient value for x.
This approach doesn't work well for non-linear equations. There, I find it easier to set up a table of values - a spreadsheet such as Excel is my tool for the calculations.
The attachment also demonstrates the Really Easy Way to graph functions. DESMOS, a free, and excellent, online calculator.
Two trains, Train A and Train B, weigh a total of 378 tons. Train A is heavier than Train B. The difference of their weights is 210 tons. What is the weight of each train?
Answer:
Train A is 294 tons and Train B is 84 tons
Step-by-step explanation:
You can create a system of equations
A+B=378
A-B=210
Adding both would get
2A=588
2A/2=588/2
A=294
Now plug that in to the second equation (either is fine)
294-B=210
B=84
Check
294+84=378
Step-by-step explanation:
Let,
Weight of train A = x
Weight of train B = y
x + y = 378 (1)
x - y = 210 (2)
Now,
On adding 1 and 2
x + y + x - y = 378 + 210
2x = 588
x = 588/2
x = 294 tons
From 1
294 + y = 378
y = 378 - 294
y = 84 tons
What do the following two equations represent?
9-3 = 2(x – 3)
y+5 2(+ 1)
Choose 1 answer:
The same line
ons
Distinct parallel lines
Perpendicular lines
Intersecting, but not perpendicular lines
HELP
Answer:
Intersecting but not perpendicular
Step-by-step explanation:
Assuming you forgot to add the = between y+5 and 2(1)
Since there is a opposite single variable in either equation the lines will intersect but not be perpendicular
Solve the system by graphing. Y=2x-9 y=-2x-1
Answer:
(2,-5)
Step-by-step explanation:
See attachment
One can also solve this by calculation:
y=2x-9
y=-2x-1
-
Rearrange either equation to find x. I'll use the first:
y=2x-9
2x = y+9
x = (y+9)/2
Now use this value of x in the second equation:
y = -2x-1
y =-2((y+9)/2)-1
y = (-2y-18)/2)-1
y = -y -9 - 1
2y = -10
y = -5
Now use -5 for y in the rearranged equation:
y = -2x-1
-5 = -2x-1
-2x = -4
x = 2
Solution is (2,-5)
But the question wants a graph solution, which is also fun when you use DESMOS.
the ratio of boys and girs at rotterdam high school is 3:5. there are 160 students at the school calculate the number of boys and the number of girls at rotterdam high school
Answer:
There are 60 boys and 100 girls at Rotterdam High SchoolStep 1: Add the ratios
=> 3 + 5=> 8Step 2: Divide 160 by 8.
=> 160 ÷ 8=> 20Step 3: Multiply.
=> Total students of boys: 20 x 3 = 60 students=> Total students of girls: 20 x 5 = 100 studentsTherefore, there are 60 boys and 100 girls at Rotterdam High School
Hoped this helped.
[tex]BrainiacUser1357[/tex]
1. Edna bought an RTW dress for Php575.00 at 20% discount. What was
the original price?
Answer:
i think original price Php656.25
Step-by-step explanation:
original price Php x
80%x = 575
x = 575×100/80
x = 656.25
original price Php656.25
HELP ASAP PLEASEEEEEEEEEEE HELP MEEE
Answer:
5x 24 = 120 pulus degreece so that = a 120 digree angle
Step-by-step explanation:
can someone help me with this
Answer:
what is that i dont answering this sorry
Which functions are invertible? Select each correct answer. A coordinate graph with both horizontal and vertical axes ranging from negative 10 to 10 in increments of 2. A line is graphed with one end is in the first quadrant and the other end is in the third quadrant. The line passes through the x axis between 0 and negative 2 and it passes the y axis between 0 and 2. A coordinate graph with both x and y axes are ranging from negative 10 to 10 in increments of 2. A parabola is drawn facing down whose vertex is in the first quadrant and the parabola crosses the x axis at begin ordered pair 0 comma 0 end ordered pair and begin ordered pair 2 comma 0 end ordered pair. Parabola has arrows on both ends. An absolute value function graphed on a coordinate plane. The x and y axes range from negative 10 to 10 in increments of 2. The vertex is at begin ordered pair 0 comma negative 2 end ordered pair. The graph opens up and passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 2 comma 0 end ordered pair. Graph has arrows on both ends. Graph of a square root function on a coordinate plane. Both axes range from negative 10 to 10 in increments of 2. The curve begins at begin ordered pair 0 comma 0 end ordered pair. It increases from left to right and passes through begin ordered pair 4 comma 2 end ordered pair. Curve has an arrow on one end.
Using function concepts, it is found that:
Graph 1 (Left-top) is invertible.Graph 4(Bottom-right) is invertible.A function f(x) has an inverse if, and only if:
[tex]f(a) = f(b) \leftrightarrow a = b[/tex]
That is, each value of the output y is associated with only one value of the input x.In this problem:
In graphs 1(left-top) and 4(bottom-right), these conditions are respected, hence, they are invertible. In the parabola of graph 2(top-right), for example, y = 0 is associated with both x = 0 and x = 2, so it is not invertible.In the absolute value function is graph 3(bottom-left), for example, y = 0 is associated with both x = -2 and x = 2, so it is also not invertible.To learn more about the use of graphs to verify if a function is invertible, you can take a look at https://brainly.com/question/13160937
Which equation is equivalent to the formula r = st? t equals s over r t = rs s equals r over t s = rt.
Answer:
Step-by-step explanation:
r = st------------Other correct expressions:
t = r/s
s = r/t
------------------
Choices
1) t = s/r No
2) t = rs No
3) s =r/t Yes
4) s = rt No
The equation that is equivalent to the given equation is [tex]s = r/t[/tex] and this can be determined by using the arithmetic operations.
Given :
Equation is [tex](r = st)[/tex].
The following steps can be used in order to determine the equation that is equivalent to the given equation:
Step 1 - Write the given equation.
[tex]r = st[/tex] --- (1)
Step 2 - The arithmetic operations can be used in order to determine the equation that is equivalent to the given equation.
Step 3 - Now, divide 't' on both sides in the equation (1).
[tex]\dfrac{r}{t} = \dfrac{st}{t}\\\\\\dfrac{r}{t}=s[/tex]
Therefore, the correct option is C).
For more information, refer to the link given below:
https://brainly.com/question/11897796
help pls, i will give brainliest :)
Need help Please due soon help I beg
Answer:
the variables mean (1)
Step-by-step explanation:
you need to divide
Answer:
equals y<5?
Step-by-step explanation:
i dont think this will help but i hope it does help
Gerry purchases 12 hamburgers at a fast food restaurant for $2.25 each. For half the amount of money, he could purchase 5 buffalo chicken sandwiches. What is the “half” amount?
For #8 and #9, fill in the missing information for the following trapezoids. SHOW YOUR WORK to solve for the missing value.
9.
height = ________
b1 = 20 cm
b2 = 21 cm
area = 205 cm2
Applying the equation for the area of the trapezoid, it is found that the height is of 10 cm.
The area of a trapezoid is half the multiplication of the sum of the bases and the height, that is:
[tex]A = \frac{h}{2}(b_1 + b_2)[/tex]
For this problem, we have that: [tex]A = 205, b_1 = 20, b_2 = 21[/tex], hence:
[tex]A = \frac{h}{2}(b_1 + b_2)[/tex]
[tex]205 = \frac{h}{2}(20 + 21)[/tex]
[tex]20.5h = 205[/tex]
[tex]h = \frac{205}{20.5}[/tex]
[tex]h = 10[/tex]
The height is of 10 cm.
To learn more about area of a trapezoid, https://brainly.com/question/9918120
Answer:
The height of trapezoid is 10 cm.
Step-by-step explanation:
Given :
»» [tex]\rm{b_1}[/tex] = 20 cm»» [tex]\rm{b_2}[/tex] = 21 cm»» [tex]\rm{area}[/tex] = 205 cm²To Find :
»» Height of trapezoidUsing Formula :
[tex]{\star{\small{\underline{\boxed{\sf{\red{Area_{(Trapezoid)} = \dfrac{1}{2} \Big(b_1 + b_2\Big)h}}}}}}}[/tex]
✧ [tex]\rm{b_1}[/tex] = 20 cm✧ [tex]\rm{b_2}[/tex] = 21 cm✧ [tex]\rm{area}[/tex] = 205 cm²Solution :
Substituting all the given values in the formula to find height of trapezoid :
[tex]{\dashrightarrow{\small{\sf{Area_{(Trapezoid)} = \dfrac{1}{2} \Big(b_1 + b_2\Big)h}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{205 = \dfrac{1}{2} \Big(20 + 21\Big)h}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{205 = \dfrac{1}{2} \Big( \: 41 \: \Big)h}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{205 = \dfrac{1}{2} \times 41 \times h}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{205 = \dfrac{ 41}{2}\times h}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{h = 205 \times \dfrac{2}{41}}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{h = \cancel{205} \times \dfrac{2}{\cancel{41}}}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{h =5 \times 2}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{h =10 \: cm}}}}[/tex]
[tex]{\star{\small{\underline{\boxed{\frak{\pink{h =10 \: cm}}}}}}}[/tex]
Hence, the height of trapezoid is 10 cm.
[tex]\rule{300}{1.5}[/tex]
Peter has 100$. The price of a watch is 60$. If Peter gets 25% discount,can he buy 2 watches?
yes.
25 percent discount means that the price of one watch is 45 dollars.
45 plus 45 is less than 100.
Answer:
The answer is yes.
Step-by-step explanation:
25% = divide by 4
25% of 60$ = 60$ divided by 4 = 25$
So then we need to do 60$ - 25$ which equals to 45$.
45$ + 45$ = $90.
Hope that helps. x
last one… someone help please.
Answer:
32 degrees
a triangle is = to 180 degrees
Find an equivalent ratio in simplest terms:
64 : 24
Submit Answer
Answer:
64/24
32/12
16/6
8/3
8:3
Hope This Helps!!!
how to sovle
(x+1/x)^2
[tex] (\frac{x + 1}{x} ) ^{2} \\ = \frac{ {(x + 1)}^{2} }{ {x}^{2} } \\ = \frac{ (x + 1)(x + 1) }{ {x}^{2} } \\ = \frac{ {x}^{2} + 2x + 1}{ {x}^{2} } [/tex]
Hope you could get an idea from here.
Doubt clarification- use comment section.
Please I need help!!
1. Complete the gaps:
α) 2,3dm² = …......mm²
β) 4.670 mm² = m²
γ) 0,0054km² =................dm²
δ) 307,3 acre= km²
2. Complete the gaps:
a) 0,3m² =..........dm² =..............cm² = mm²
β) 0,056dm² =.............cm² = mm²
γ) 7,31 cm² = mm²
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no spams
Report useless answers
BRAINLIEST ANSWER
Answer:
1a 2dm²= 20000mm² 3dm²=30000mm²
b 18898.8194926 m²
c 0.0054 km²= 540000 dm²
d 1.21931784007 km²
2a 30dm²=3000cm²=300000mm²
b 560cm²=56000mm²
c 7.31cm²=731mm²
Please help me solve this
Answer:
i think 2²m² is answer. you are correct, my sweetie !
Answer:
c)
[tex] {2}^{2} {m}^{2} [/tex]
Step-by-step explanation:
2 × 2 =4 it can also be written as 2^2( 2 squared) which also equals 4
same with m
find 3 solutions that satisfy the equation -5x=10+2y
Answer:
(2, -10)
(4, -15)
(6, -20)
Step-by-step explanation:
First you should simplify the equation.
-5x=10+2y
-5x-10=2y
-2.5x-5=y
Then put in any number in for x. since we have a decimal I'll make the numbers I put in even the keep the solution whole numbers.
Putting in 2 gives you -10 so (2, -10) is a solution.
Putting in 4 gives you -15 so (4, -15) is a solution.
Putting in 6 gives you -20 so (6, -20) is a solution.
Suppose Earth’s axis was not tilted. What would be the effect of this on temperature variation?
Step-by-step explanation:
If earth did not tilt and orbited in an upright position around the sun, there would be minor variations in temperatures and precipitation throughout each year as Earth moves slightly closer and farther away from the sun. Basically, we would not have any seasons.
Answer:
Assuming you're saying the earth is flat in hence scenerio it would be hotter or. Colder depending how far the sun's placement is from the earth
Step-by-step explanation:
Closer to sun warmer you are
Shift in moon causes water drought or water rise