Step-by-step explanation:
The two equation will intersect each other at the point which will be the solution of the given two equations , and the given equations are ,
[tex]\implies 2x -y +6=0\\\\\implies 2x + 3y -6=0[/tex]
On subtracting the given equations we have,
[tex]\implies -y - 3y +6 -(-6) = 0 \\\\\implies -4y = -12 \\\\\implies y = -12/-4\\\\\implies y = 3 [/tex]
Put this value in any equation , we have ,
[tex]\implies 2x -3 +6 =0\\\\\implies 2x = -3 \\\\\implies x =\dfrac{-3}{2} \\\\\implies x =-1.5 [/tex]
Hence the lines will Intersect at ,
[tex]\implies\underline{\underline{ Point=(-1.5, 3)}}[/tex]
for the first one x = 1/2 y-3" and y = 2 x + 6 and for the other one is x = − 3 /2 y+ 3 and y= − 2 /3 x + 2
how i did this Step 1: Add -3y to both sides.
Step 2: Add 6 to both sides.
Step 3: Divide both sides by 2.
Are the two triangles similar. If so, State how
Answer:
Yes by AAA
Step-by-step explanation:
Angle A is the same for both triangles. Angle D is congruent to Angle A since BC and DE are parallel lines and same with angle E. So by AAA the triangles are similar
If 4/3 . sin42⁰ = x then 4/3 . cos48⁰ = ?
Step-by-step explanation:
If 4/3 . sin42⁰ = x then 4/3 . cos48⁰ = ?
so it's that
Find the value of x in x + y= 9 and x - y= 3.
6
-6
3
-3
x + y= 9 and x - y= 3
rearrange the second equation:
x - y= 3
x = 3 + y
x -3 = y
substitute y with "x-3" in the first equation and solve
x + y= 9
x + (x-3)= 9
2x -3 = 9
2x = 12
x = 6
you could also start with the first equation and substitute y in the second.
graphically speaking, it's the intersection point of to lines, at least the six-part of the point.
HELP PLEASE (CIRCLES) (40 points)
the line 3y - x = 5 is the tangent to a circle at the point A(1,2). (1) Find the equation of the line passing through A and the centre of the circle. The equation of another line passing through the centre of the circle is x + 3y = 15. (2) Find the equation of the circle.
Answer:
x² + (y - 5)² = 10Step-by-step explanation:
Tangent line is:
3y - x = 5 ⇒ 3y = x + 5 ⇒ y = 1/3 x + 5/3, the slope is 1/3Perpendicular line to this has a slope of -3 and passes through point (1, 2).
Its equation is:
y - 2 = -3(x - 1) ⇒ y = -3x + 3 + 2 ⇒ y = -3x + 5Using the second line passing through the center, find the coordinates of the center:
x + 3y = 15 ⇒ 3y = -x + 15 ⇒ y = -1/3x + 5Solve the system by elimination:
-3x + 5 = -1/3x + 5 ⇒ x = 0Then
y = 5The center is (0, 5) and radius is the distance from center to point (1, 2):
r² = (0 - 1)² + (5 - 2)² = 1 + 9 = 10The equation of circle:
(x - h)² + (y - k)² = r²(x - 0)² + (y - 5)² = 10 ⇒ x² + (y - 5)² = 10In AJKL, mZJ = (8x + 6)", mZK = (2x + 2)°, and młL = (4x + 4)º. Find m_L.
Answer:
Step-by-step explanation:
∠J + ∠K + ∠L = 180 {Angle sum property of triangle}
8x + 6 + 2x + 2 + 4x + 4 = 180
8x + 2x + 8x + 6 + 2 + 4 = 180
Combine like terms.
14x + 12 = 180
Subtract 12 form both sides
14x = 180 - 12
14x = 168
Divide both sides by 14
x = 168/14
x = 12
∠L = 4x + 4
= 4*12 + 4
= 48 + 4
∠L = 52
18
Select the correct answer.
Which function is a horizontal translation of the parent quadratic function, f(x)=x^2
A. j(x)= x^2- 4
B. g(x)= (x-4)^2
C. k(x)= -x^2
D. h(x)= 4x^2
Answer:
B
Step-by-step explanation:
When we have a horizontal translation on the x-axis, it means the translation in question would be affecting only the x component of our function
With respect to the question, what we have here is that we are going to take out some values from x (or add some values) to it
Thus;
f(x) = x^2 would be;
g(x) = (x-4)^2
Corresponding to a shift to the right of upto 4 units on the x axis
Answer:
g(x)= (x-4)^2
Step-by-step explanation:
Plato/Edmentum
A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters.
Answer:
[tex]Height = 12cm[/tex]
Step-by-step explanation:
Given
[tex]Volume = 1200cm^3[/tex]
The dimension of the base is:
[tex]Base =10cm[/tex]
[tex]Sides = 13cm[/tex]
See comment for complete question
Required
The height of the base
To do this, we make use of Pythagoras theorem where:
[tex]Sides^2 = (Base/2)^2 + Height^2[/tex]
So, we have:
[tex]13^2 = (10/2)^2 + Height^2[/tex]
[tex]13^2 = 5^2 + Height^2[/tex]
[tex]169 = 25 + Height^2[/tex]
Collect like terms
[tex]Height^2 = 169 - 25[/tex]
[tex]Height^2 = 144[/tex]
Take square roots of both sides
[tex]Height = 12cm[/tex]
Given f(x) = 19x + 12 , find f(3)
F(3)= ?
Answer:
69
Step-by-step explanation:
to find f(3), we'll have to substitute x with 3
therefore,
f(3) = 19 × 3 + 12
= 57 + 12
= 69
Answer:
f ( 3 ) = 69
Step-by-step explanation:
Given :-
f ( x ) = 19x + 12.
To find :- f ( 3 ) = ?
Solution :-
f ( x ) = 19x + 12.
Substitute as the 3 as x
f ( 3 ) = 19 ( 3 ) + 12
Multiply ; 19 × 3
f ( 3 ) = 57 + 12
Add 57 and 12
f ( 3 ) = 69
IM BEGGING PLEASE I NEED THE ANSWER TO THIS :C
Answer:
The answer is D.
Step-by-step explanation:
I will mark you the brainliest
What is the opposite polynomial?
Answer:
e t
Step-by-step explanation:
nate and laura picked 20 apples laura picked 1/2 of what nate picked
how many did nate pick?
Answer:
10
Step-by-step explanation:
20÷2=10 the half of 20 is 10 simple as that
Answer:
ok so together they picked 20 apples so
20=y+1/2y
y=40/3 or 13 1/3
thats how many nate picked and we divide by 2
6 2/3
Hope This Helps!!!
Use the quadratic formula to find both solutions to the quadratic equation
given below.
3x2 - x + 4 = 0
Answer:
[tex]x = \dfrac{1 + i\sqrt{47}}{6}[/tex] or [tex]x = \dfrac{1 - i\sqrt{47}}{6}[/tex]
Step-by-step explanation:
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
We have a = 3; b = -1; c = 4.
[tex] x = \dfrac{-(-1) \pm \sqrt{(-1)^2 - 4(3)(4)}}{2(3)} [/tex]
[tex]x = \dfrac{1 \pm \sqrt{1 - 48}}{6}[/tex]
[tex]x = \dfrac{1 \pm \sqrt{-47}}{6}[/tex]
[tex]x = \dfrac{1 + i\sqrt{47}}{6}[/tex] or [tex]x = \dfrac{1 - i\sqrt{47}}{6}[/tex]
5/8 divided by 8 please help man I will give the brainly thing \y
Answer:
5/64
Step-by-step explanation:
5/8 : 8 = 5/8 * 1/8 = 5/64
Answer:
12 4/5
Step-by-step explanation:
simplified
PLEASE ANSWER HURRY!!
What is 2.16 (6 is repeating) to a fraction??
Answer:
[tex]2\frac{1}{6}[/tex]
Step-by-step explanation:
let x=2.16666...
10 x=21.666...(1)
100 x=216.666...(2)
(2)-(1) gives
90x=195
6x=13
x=13/6
x=2 1/6
Find the area of the triangle bounded by the lines y=x y=-x and y=6.
The area of the triangle bounded by the lines y=x y=-x and y=6 is 36 units.
What is area of triangle?The formula for finding area could be represented in the form of determinants as given below.
[tex]A = \frac{1}{2} \left[\begin{array}{ccc}x1&y1&1\\x2&y2&1\\x3&y3&1\end{array}\right][/tex]
First, we need to find the coordinates of the point of intersection of these lines.
y = x
y = -x
Adding the two equations,
2y = 0
y = 0
x = 0
coordinate: (0, 0)
y = x
y = 6
Subtracting the two equations,
0 = x - 6
x = 6
coordinate: (6, 6)
y = -x
y = 6
Subtracting the two equations,
- x - 6 = 0
x = -6
coordinate: (-6, 6)
Calculating area of triangle bounded by the given line:
Area of triangle =
[tex]\frac{1}{2}\left[\begin{array}{ccc}0&0&1\\6&6&1\\-6&6&1\end{array}\right][/tex] = [tex]\frac{1}{2} (36 + 36) = \frac{72}{2} = 36[/tex]
Learn more about area of triangle here
https://brainly.com/question/19305981
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You have job were you are paid (p) $1,000 a month plus $15.00 for every hour (h) you work. You work 150 hrs (h), how much money did you make?
Answer:
15 x 150 = 2250
2250 + 1000 = 3250
you make $3250,00
Someone please answer this
Answer:
(x - 1)(5x - 6)
Step-by-step explanation:
Given
5x² - 11x + 6
Consider the factors of the product of the coefficient of the x² term and the constant term (ac) which sum to give the coefficient of the x- term (b)
ac = 5 × 6 = 30 and b = - 11
The factors are - 5 and - 6
Use these factors to split the x- term
5x² - 5x - 6x + 6 ( factor the first/second and third/fourth terms )
= 5x(x - 1) - 6(x - 1) ← factor out (x - 1) from each term
= (x - 1)(5x - 6)
Jin completed 8 pages in his math workbook and
12 pages in his science workbook. This is 25% of the
total number of pages in both workbooks together.
If there are 32 pages in his math workbook, how
many pages are there in his science workbook?
A. 20
B.
48
C. 80
D. 128
How do i solve this help me
Answer:
-24
Step-by-step explanation:
First substitute
(6x8)/-2
Then solve
48/-2=-24
-24
Answer:
[tex]-24[/tex]
Step-by-step explanation:
The value of y is given as 8
The value of z is given as -2
The expression given is [tex]\frac{6y}{z}[/tex]
Substitute the value of y as 8 & z as -2 in the brackets:
[tex]=\frac{6(8)}{-2}[/tex]
[tex]=\frac{48}{-2}[/tex]
[tex]=-24[/tex]
hope this helps....
PLS HELP (algebra 1)
solve -6 + 8(16 - 19z)
Answer:
122-152z
Step-by-step explanation:
-6+ 8(16 - 19z)
= -6 + 128 - 152z
= 122 - 152z
I hope this helps!
Find the measure of DA
Answer:
15
Step-by-step explanation:
First, find x
set your formula up as 3x+5=6x-10, since AB and DC are the same length.
This means x = 5
Now substitute 5 for x in the line DA
4x-5
4 * 5 - 5 = 15
On vacation, Tim plans to spend less than $30 a day. If he spends $12 for food, what is the greatest number of dollars he can spend per day on other things? (Express in whole dollars.) Write an inequality and solve.
Answer:
So, Tim spent maximum $ 18 dollars on other things
Step-by-step explanation:
Total spent per day is less than $ 30.
Money spent on food= $ 12
So, the maximum amount amount spent on the things is
= $ 30 - $ 12 = $ 18
So, Tim spent maximum $ 18 dollars on other things.
series calcular s=1+2+3+....+86
Answer:
S = 3741
Step-by-step explanation:
Here, we want to calculate the sum of the first 86 numbers (starting from 1)
Mathematically, we can use the formula;
Sn = n/2[ a + L]
Where n is the number of terms (86 here)
a is the first term which is 1 and L is the last term which is 86
So, we have the sum as;
Sn = 86/2(1 + 86) = 43 * 87 = 3741
I need help in these questions please !
Answer:
b,b.a
Step-by-step explanation:
6. Write two rational numbers which are their own reciprocals ?
1 and -1 are the only rational numbers which are their own reciprocal.[tex] \: [/tex]
Find the value of x that makes A || B
HELPPPPP
Answer:
x = 90
Step-by-step explanation:
If lines A and B were parallel , then
∠ 1 and ∠ 4 are corresponding angles and congruent, so
3x - 160 = x + 20 ( subtract x from both sides )
2x - 160 = 20 ( add 160 to both sides )
2x = 180 ( divide both sides by 2 )
x = 90
In ΔVWX, the measure of ∠X=90°, XW = 20, WV = 29, and VX = 21. What ratio represents the cosine of ∠W?
Drag each expression to the correct category.
Apply the produc rules to determine the sign of each expression.
[tex]( - \frac{4}{9} )( \frac{7}{4} ) = \: \: negative [/tex]
[tex]( - 2 \frac{3}{4} )( - 1 \frac{1}{5} ) = \: \: positive[/tex]
[tex](3)( - 3)( - 3)( - 3)( - 3) = \: \: positive[/tex]
[tex]( - \frac{1}{6} )( - 2)( - \frac{3}{5} )( - 9) = \: \: positive[/tex]
[tex]( - \frac{4}{7} )( - \frac{3}{5} )( - 9) = \: \: negative[/tex]
[tex]( - \frac{10}{7} )( \frac{8}{3} ) = \: \: negative[/tex]
helppppppppppppp plzzzzz
the answer is in the picture
which of the following numbers has the least number of positive divisors if a=50^(100) . choose: 1)25a 2)4a 3)3a 4)26a 5)10a
Answer:
the answer would have to be B
Step-by-step explanation:
