Answer:
(1, 2 ) and ([tex]\frac{8}{3}[/tex], [tex]\frac{3}{4}[/tex] )
Step-by-step explanation:
3x + 4y = 11 → (1)
xy = 2 ( divide both sides by y , y ≠ 0 )
x = [tex]\frac{2}{y}[/tex] → (2)
Substitute x = [tex]\frac{2}{y}[/tex] into (1)
3([tex]\frac{2}{y}[/tex] ) + 4y = 11
[tex]\frac{6}{y}[/tex] + 4y = 11 ( multiply through by y )
6 + 4y² = 11y ( subtract 11y from both sides )
4y² - 11y + 6 = 0
Consider the factors of the product of the y² term and the constant term which sum to give the coefficient of the y- term
product = 4 × 6 = 24 and sum = - 11
The factors are - 8 and - 3
Use these factors to split the y- term
4y² - 8y - 3y + 6 = 0 ( factor first/second and third/fourth terms )
4y(y - 2) - 3(y - 2) = 0 ← factor out (y - 2) from each term
(y - 2)(4y - 3) = 0
Equate each factor to zero and solve for y
4y - 3 = 0 ⇒ 4y = 3 ⇒ y = [tex]\frac{3}{4}[/tex]
y - 2 = 0 ⇒ y = 2
Substitute these values into (2)
y = 2 : x = [tex]\frac{2}{2}[/tex] = 1 ⇒ (1, 2 )
y = [tex]\frac{3}{4}[/tex] : x = [tex]\frac{2}{\frac{3}{4} }[/tex] = 2 × [tex]\frac{4}{3}[/tex] = [tex]\frac{8}{3}[/tex] ⇒ ( [tex]\frac{8}{3}[/tex], [tex]\frac{3}{4}[/tex] )
find the slope and y intercept
(0,1) and (2,-3)
whats the slope M=
whats the y intercept b=
Answer:
y = -2x + 1
Step-by-step explanation:
Y2 - Y1 / X2 - X1
-3 - 1 / 2 - 0
-4 / 2
= -2
y = -2x + b
-3 = -2(2) + b
-3 = -4 + b
1 = b
y = -2x + 1
Identify the shapes in the picture
Answer:
we're are the images pls
prove that: (sinθ/1+cosθ) + (1+cosθ/sinθ) = 2cosecθ
[tex] \: prove \: that: \frac{ sinθ}{1+cosθ}+ \frac{1+cosθ}{sinθ} = 2 \: cosec \: θ [/tex]
Consider LHS
(sinθ/1+cosθ) + (1+cosθ/sinθ) =
= [sinθ(sinθ)+(1+cosθ)+(1+cosθ)]/[(1+cosθ)(sinθ)]
= [sin²θ+(1+cosθ)²]/[(1+cosθ)sinθ]
= [sin²θ+1+cos²θ+2cosθ]/[(1+cosθ)sinθ]
[°.° (a+b)² = a²+2ab+b²]
Here, a = 1, b = cosθ
= [(sin²θ+cos²θ)+1+2cosθ]/[(1+cosθ)sinθ]
= [1+1+2cosθ]/[(1+cosθ)sinθ]
[°.° sin²θ+cos²θ = 1]
= [2+2cosθ]/[1+cosθ)sinθ]
= [2(1+cosθ)]/[(1+cosθ)sinθ]
= 2/(sinθ)
[°.° 2/sinθ = cosecθ]
= 2cosecθ = RHS.
Hence, Proved.
Read more:
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BrainlyCPT~
Brainly Team
Find the slope. simplify if needed.
(-10,5) and (2, -3)
What’s the answer to 2(x+3)
Hello there!
This isn't an equation, but here are some options for what you may be looking for!
Product, Multiplying, Evaluating, and Simplified Form: 2x + 6
Factor: 2(x+3)
Hope I helped,
Brainliest is always appreciated.
Happy Holidays.
Please help- It's due this week.
100x + 150y = 3,050
x + y = 23
Graph the system of equations and plot the intersection point
Find the time it takes for a rocket following the path, h(x) = -2x2 + 18, to hit the ground. 2 sec 3 sec 8 sec 9 sec
The time it takes for a rocket to hit the ground is 3 seconds
Step-by-step explanation:
We are given equation for height as
where
x is the time in seconds
When object hits the ground
then height becomes 0
so, we can set h(x)=0
and then we can solve for x
Subtract both sides by 18
So,
the time it takes for a rocket to hit the ground is 3 seconds
plz help look at the pic below
Answer:
You can use the exponential rule where
[tex](n^x)^y=n^{xy}[/tex]
Therefore,
[tex](a^3)^{-2}=a^{3*(-2)}=a^{-6}[/tex]
[tex]\\ \rm\leadsto (a^3)^{-2}[/tex]
(a^m)^n=a^mn[tex]\\ \rm\leadsto a^{-6}[/tex]
[tex]\\ \rm\leadsto \dfrac{1}{a^6}[/tex]
can someone help me please
Answer:
3: 55 degrees
4: 128 degrees
Step-by-step explanation:
A straight line is 180 degrees and so you do 180-125 to get 55 degrees
180-58 is 128 degrees
It took 5 days for a committee of 7 pupils to clean the auditorium for the school program. How many days would have taken the committe of 10 pupils to do the same work?
Answer:
3.5 days
Step-by-step explanation:
If it takes 7 pupils 5 days, then it would take 1 pupil 7 times as long, or 35 days.
1 pupil alone cleans the auditorium is 35 days.
10 pupils work 10 times faster than 1 pupil, so 10 pupils take 3.5 days.
(Pythagorean theorem) find the missing side length. Round to the nearest hundredth (show steps)
Answer:
5.39
Step-by-step explanation:
To find the third side (let's call it x) you plug the side lengths given into the Pythagorean theorem to get:
5² + 2² = x²
Which, simplified, is:
25 + 4 = x²
And to get x, you do:
x=√(29)
So, if you want it to the nearest hundredth, it is 5.39.
square root of 29.00
Step-by-step explanation:
5square +2square=29 to the nearest hundredth 29.00 .but there is no square root of 29
Is - 1/2 equivalent to 1/-2
YES
- 1/2 is equivalent to 1/-2
The detailed answer is in the image attached.
Hope it helps you.....
Please mark as Brainlliest!!!
20 decreased by the product of 5 and a number x
miggy ask to solved the given quadratic equation x²+8x-20=0 using the quadratic formula,Help miggy to determine the following
roots of the quadratic 3
discriminant
nature of roots
sum of the roots
product of the roots
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
roots of the quadratic equation ~
[tex]2 \: \: \: \:a nd \: \: - 10[/tex]discriminant ~
[tex]144[/tex]nature of roots ~
[tex]real[/tex]sum of the roots ~
[tex] - 8[/tex]product of the roots ~
[tex] - 20[/tex][tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
Let's solve he given quadratic equation using quadratic formula ~
Let's consider the following values ~
b (Coefficient of x) = 8 a (Coefficient of x²) = 1 c (Constant term) = -20According to quadratic formula, the roots are ~
[tex] \dfrac{ - b \pm \sqrt{b {}^{2} - 4ac } }{2a} [/tex]where, ( b² - 4ac ) is known as it's discriminant ~
that is equal to ~
[tex](8) {}^{2} - (4 \times 1 \times - 20)[/tex][tex]64 - ( - 80)[/tex][tex]64 + 80[/tex][tex]144[/tex]Hence, Discriminant = 144
And since discriminant is positive, then the roots of the quadratic polynomial are real .
Let's find the roots now ~
[tex] \dfrac{ - b \pm \sqrt{b {}^{2} - 4ac} }{2a} [/tex][tex] \dfrac{ - 8 \pm \sqrt{144} }{2 \times 1}[/tex][tex] \dfrac{ - 8 \pm12}{2} [/tex][tex] \dfrac{ 2( - 4 \pm6)}{2} [/tex][tex] - 4 \pm6[/tex]So, the two roots are ~
[tex] - 4 + 6[/tex][tex]2[/tex]and
[tex] - 4 - 6[/tex][tex] - 10[/tex]Sum of roots ~
[tex] - 10 + 2[/tex][tex] -8[/tex]product of roots ~
[tex] - 10 \times 2[/tex][tex] - 20[/tex]Which of the following sets here the closure property w.r.t. Addition
(A) {0}
(B) {0, -1)
(C) (0, 1)
)
(D) {1,V3.
Answer:
the answer is number 1 make my answer brainlist answer
Which graph is a quadratic graph? A. graph A B. graph B C. graph C D. graph D
Answer:
graph ab
Step-by-step explanation:
Step-by-step explanation:I just did it and got it right...
solve pls brainliest
Answer:
$18.15
Step-by-step explanation:
45% of $33 = $14.85
$33 - $14.85 = $18.15
If the area of a rectangle is x^2+5x+6, and x represents 15 cm, what is the perimeter of the rectangle?
Answer:
To calculate the length and width of a rectangle first, calculate the value of width 'w' by using the area of rectangle formula that is, 'w = A/l'.
Step-by-step explanation:
Help me with this question please!! Show all work
Which expression is equivalent to 4(6 - 2x) ?
Answer:
Option A
Step-by-step explanation:
[tex]4(6-2x)\\\rule{150}{0.5}\\\rightarrow ((6 * 4) ( -2x*4)) \leftarrow \text{Distribute the '4' into the content in the parenthesis.}\\\\\\\\\rightarrow 6 * 4 = 24\\\\\rightarrow -2x * 4 = -8x\\\\\\\\\rightarrow 4(6-2x) = \boxed{24 - 8x}[/tex]
Hope this helps.
Find the integer value of x that satisfies both the inequalities
x + 5 > 8 and 2x - 3<7 il edmun er
Answer:
x = 4 is the solution
Step-by-step explanation:
Solving the inequalities
x + 5 > 8 ( subtract 5 from both sides )
x > 3
-------------
2x - 3 < 7 ( add 3 to both sides )
2x < 10 ( divide both sides by 2 )
x < 5
The only integer value of x > 3 and < 5 is 4
Are the ratios 2:3 and 8:12 equivalent? Justify you answer.
Answer:Yes
Step-by-step explanation:You are multiplying the ratios by 4
Find x. please help me!!
Answer:
I want to say B.
Step-by-step explanation:
What is the value of x
Answer:
16
Step-by-step explanation:
(3x +3) + (5x-2) + (3x+3) =180
3x +3 + 5x-2 + 3x+3 =180
11x +4=180
11x =180-4
11x=176
x=176/11
x= 16
the coordinates of the point of intersection of lines px + y = 3 and x + 2y = q are (2, -3). find the value of p and q
Answer:
p = 3 and q = - 4
Step-by-step explanation:
Substitute the coordinates of the solution (2, - 3 ) into the equations and solve for p and q
px + y = 3 , then
2p - 3 = 3 ( add 3 to both sides )
2p = 6 ( divide both sides by 2 )
p = 3
and
x + 2y = q , then
2 + 2(- 3) = q
2 - 6 = q , so
q = - 4
Ryan earned $2400 a month. He recieved a raise, which increased his monthly pay to $2700. Did Ryan's pay increase or decrease? By how much?
Answer:
Ryan's pay increased by $300.
Step-by-step explanation:
Answer:
His pay increased by $300
Step-by-step explanation:
2,700-2,400
=300
Find the slope of the line y=-1/4x+1
Answer:
slope is -1/4 the number before the x is the slope
Step-by-step explanation:
Answer:
The slope is -1/4
Step-by-step explanation:
The equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = -1/4x +1
The slope is -1/4 and the y intercept is 1
Demonstrate your knowledge by giving clear, concise solutions to each problem. Be sure to include all relevant drawings and justify your answers (show all your work). You may show your solution in more than one way to investigate beyond the requirements of the problem. 1. Some important formulas are given below Area of a circle is A=πR^2 where r is the radius of the circle.
A)Write a formula for the area of the figure below. (5pts)
Answer:
A = 8a + [tex]\frac{1}{2}[/tex]πa²
Step-by-step explanation:
The figure consists of a rectangle and a semi- circle
area of rectangle = 4 × 2a = 8a
area of semi- circle = [tex]\frac{1}{2}[/tex]πr² ( r is the radius = a )
= [tex]\frac{1}{2}[/tex]πa²
Then area (A ) of figure is
A = 8a + [tex]\frac{1}{2}[/tex]πa² ← factor out [tex]\frac{1}{2}[/tex] a from each term
= [tex]\frac{1}{2}[/tex] a(16 + aπ)
The sum of the ages of a woman and her
son is 64 years. In 4 years time the woman
will be three and half times as old as her
son. How old were they three years ago?
Step-by-step explanation:
sorry for my ugly handwriting, hope it helps
HELP PLEASE AHH I WILL GIVE BRAINLIEST
Answer:
140 Minutes
Step-by-step explanation:
Y = 0.125x ---> Corinne every 1 minute
Y = 3.5 + .1x ----> Aretha
0.125x = 3.5 + .1x
-.1x - .1x
0.025x = 3.5
0.025x/.025 = 3.5/.025
x = 140 minutes