6h=2k+9. 3h+4k=12 use elimination please help me
Answer:
h = 2 and k = 1.5
Step-by-step explanation:
The solution is, Solve of the system of equations. using elimination,
6h=2k+9 & 3h+4k=12 is, h = 2 & k=3/2.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
given that, the system of equations.
6h-2k=9.......(1)
3h+4k=12 ...........(2)
now, for solving, multiply (1) by 2 & add with (2),
we get,
12h - 4k = 18
3h + 4k = 12
---------------------
15h = 30
i.e. h = 2
from (1), we get, k = 3/2
Hence, The solution is, Solve of the system of equations. using elimination,
6h=2k+9 & 3h+4k=12 is, h = 2 & k=3/2.
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Which equation can be used to determine the reference angle
Answer:
2nd option
Step-by-step explanation:
[tex]\frac{7\pi }{12}[/tex] is an angle in the second quadrant
Thus to find the reference angle, subtract from π , that is
r = π - θ
help please!! first answer gets marked brainliest!
Answer:
Answer 30
Step-by-step explanation:
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Consider the line y=7x-8.
Find the equation of the line that is parallel to this line and passes through the point (6, – 4).
Find the equation of the line that is perpendicular to this line and passes through the point (6, - 4).
Answer:
a). y = 7x - 46 b). y = -1/7x - 22/7
Step-by-step explanation:
a). y = 7x + b
-4 = 7(6) + b
-4 = 42 + b
-46 = b
y = 7x - 46
b). y = -1/7x + b
-4 = -1/7(6) + b
-4 = -6/7 + b
-22/7 = b
y = -1/7x - 22/7
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Answer:
The simple answer is we round the square root of the number of data points. For example: 25 data points = 5 bars. 100 data points = 10 bars
Miguel is trying to find the height of a radio antenna on the roof of a local building. He stands at a horizontal distance of 22 meters from the building. The angle of elevation from his eyes to the roof (point A) is 26 degrees , and the angle of elevation from his eyes to the top of the antenna ( oint B) is 31 degrees If his eyes are 1.53 meters from the ground, find the height of the antenna (the distance from point A to point B). Round your answer to the nearest tenth of a meter if necessary.
Given the 22 m. horizontal distance and the angles of elevation of 26°
and 31° gives the height of the building as approximately 2.49 meters.
How can the height of the building be found?Horizontal distance from the building = 22 m
Angle of elevation to the top of the roof = 26°
Angle of elevation to the top of the antenna = 31°
Height of his eyes from the ground = 1.53 m
Required:
The height of the antenna.
Solution:
In a right triangle, we have relative to an angle of the triangle, we have;
Opposite side = Adjacent side
Height of the building + Height of antenna = [tex]1.53 + 22 \times tan \left(31^{\circ} \right)[/tex] ≈ 14.75
Which gives;
Height of the building = [tex]1.53 + 22 \times tan \left(26^{\circ} \right)[/tex] ≈ 12.26
Height of antenna = Height of the building + Height of antenna - Height of the buildingTherefore;
Height of the antenna ≈ 14.75 - 12.26 ≈ 2.49
Height of the antenna ≈ 2.49 mLearn more about trigonometric tangent ratio here:
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heya kitties. graph y−5=43(x−5)
coordinates plz
Given:
The equation is:
[tex]y-5=\dfrac{4}{3}(x-5)[/tex]
To find:
The graph of the given equation.
Solution:
Point slope form of a line is:
[tex]y-y_1=m(x-x_1)[/tex] ...(i)
We have,
[tex]y-5=\dfrac{4}{3}(x-5)[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]x_1=5,y_1=5,m=\dfrac{4}{3}[/tex]
It means, slope of the line is [tex]\dfrac{4}{3}[/tex] and it passes through the point (5,5).
Putting x=2 in the given equation, we get
[tex]y-5=\dfrac{4}{3}(2-5)[/tex]
[tex]y=\dfrac{4}{3}(-3)+5[/tex]
[tex]y=-4+5[/tex]
[tex]y=1[/tex]
The line passes through the point (2,1). Plot the points (2,1) and (5,5) on a coordinate plane and connect them by a free hand curve as shown below.
The equation px²+px+3q=1+2x has roots 1/p and q
(a) Find the values of p and of q
Answer:
p = 2/3
q = 1/2
Step-by-step explanation:
The given equation is ,
[tex]\sf\to px^2 + px + 3q = 1 + 2x [/tex]
We can write it as ,
[tex]\sf\to px^2 + px + 3q - 1 -2x=0 [/tex]
Rearrange the terms ,
[tex]\sf\to px^2 - 2x + px + (3q -1)=0 [/tex]
This can be written as ,
[tex]\sf\to px^2 + x ( p - 2) + (3q -1) =0[/tex]
Now wrt Standard form of a quadratic equation ,
[tex]\bf \implies ax^2+bx + c = 0 [/tex]
we have ,
a = p b = p - 2 c = 3q - 1We know that product of zeroes :-
[tex]\to \sf q \times \dfrac{1}{p} = \dfrac{3q-1}{p } \\\\\sf\to 3q - 1 = q \\\\\sf\to 2q = 1 \\\\\sf\to \boxed{ q =\dfrac{1}{2}}[/tex]
Sum of roots :-
[tex]\to \sf q + \dfrac{1}{p} = \dfrac{2-p}{p} \\\\\sf\to \dfrac{ qp + 1}{p}= \dfrac{2-p}{p} \\\\\sf\to qp + 1 = 2 - p \\\\\sf\to p/2 + p = 1 \\\\\sf\to 3p/2 = 1 \\\\\sf\to \boxed{ p =\dfrac{2}{3}}[/tex]
Using the table below, what is the rate of change? Don't forget to include your units.
Number of sodas 24
28
32
36
Total Cost ($)
18
21
24
27
Answer:
0.75
Step-by-step explanation:
Given the table :
Number of sodas 24
28
32
36
Total Cost ($)
18
21
24
27
The rate of change :
Rate of change = Rise / Run
Rise = y2 - y1 ; Run = x2 - x1
From the table :
Take number of sodas as X - axis
Total cost as Y - axis
Taking the points :
(24, 18) ;(36, 27)
x1 = 24 ; x2 = 36
y1 = 18 ; y2 = 27
Rise = (y2 - y1) = (27 - 18) = 9
Run = (x2 - x1) = (36 - 24) = 12
Rate of change = 9 / 12 = 0.75
the solution of the quadratic equation x square - 4 x + 4
Answer:
[tex]\rm x = 2 , 2 [/tex]
Step-by-step explanation:
A quadratic equation is given to us and we need to find the solution of the equation. The given equation is ,
[tex]\implies x^2 -4x + 4 = 0 [/tex]
Now for finding the roots of the equation , let's use the quadratic formula , or by factorising out the equation . Here I would be using the factorization method , as ,
[tex]\implies x^2 -4x + 4 = 0\\\\\implies x^2-2x-2x+4 = 0 \\\\\implies x(x-2) -2(x-2) = 0 \\\\\implies (x-2)(x-2) = 0 \\\\\implies x = 2, 2 [/tex]
Hence the Solution of the equation is 2,2.
Answer:
Step-by-step explanation:
x² - 4x +4 = 0
Factorization method:
Sum = -4
Product = 4
Factor = (-2) ; (-2) {-2 * -2 = 4 & (-2) + (-2) = -4}
x² -4x + 4 = 0
x² - 2x - 2x + (-2)*(-2) = 0
x(x - 2) - 2 (x - 2) = 0
(x - 2) (x - 2) = 0
x - 2 = 0 or x -2 = 0
x = 2 or x = 2
x = 2 , 2
Susanna deposits $400 in a savings account with an interest rate of 3% compounded annually. What equation could Susanna use to calculate how many years it will take for the value of the account to reach $600?
Fill in the values of A, b, and c to write the equation modeling this situation.
Answer:
So, you have $400savings, 3%intrest rate, you'll need to have $400 and a 10%intrest rate.
I hope this helps
Step-by-step explanation:
The equation of line r is y = 1/2 * x + 1 line runs parallel to line r and passes through (2, 5) what would be the equation of line 8 ?help please
Answer:
x - 2y + 8 = 0
Step-by-step explanation:
that is the procedure above
Evaluate the expression 42 +6.52 – 33 = 32,
please help guys !!!
Answer:
[tex] \frac{1}{4} \: \: \: \frac{1}{3} \: \: \: \frac{1}{2} \: \: \: \frac{7}{12} \: \: \: \frac{3}{4} [/tex]
Step-by-step explanation:
To arrange in ascending order, first make the denominators of all the fractions the same.
LCM of 2, 3, 4 and 12 is 12.
Now,
[tex] \frac{1}{3} = \frac{4}{12} [/tex]
[tex] \frac{3}{4} = \frac{9}{12} [/tex]
[tex] \frac{1}{4} = \frac{3}{12} [/tex]
[tex] \frac{7}{12} \: \: will \: be \: \: \frac{7}{12} [/tex]
[tex] \frac{1}{2} = \frac{6}{12} [/tex]
Arranging these in ascending order:
[tex] \frac{3}{12} \: \: \: \frac{4}{12} \: \: \: \frac{6}{12} \: \: \: \frac{7}{12} \: \: \: \frac{9}{12} [/tex]
Work out the area of this circle.
Give your answer in terms ofand state its units.
units:
Submit ANSWEI
6 mm
Plss help due in very soon
Answer:
36π mm²
Step-by-step explanation:
Formula: πr²
r=radius
r=6
π6²=36π
helpppppppppppppppp//////////////////////////////////////////
Answer:
m(x)
Step-by-step explanation:
environment is not ___ uniform all form
environment is not natural uniform all from
What is the frequency of the graph of y = 1/3 sin(2x)?
Given:
The sine function is:
[tex]y=\dfrac{1}{3}\sin (2x)[/tex]
To find:
The frequency of the graph of given function.
Solution:
If a sine function is defined as:
[tex]y=A\sin(Bx+C)+D[/tex]
Then, the frequency of the sine function is:
[tex]f=\dfrac{B}{2\pi}[/tex]
We have,
[tex]y=\dfrac{1}{3}\sin (2x)[/tex]
Here, [tex]B=2[/tex]. So, the frequency of the given function is:
[tex]f=\dfrac{2}{2\pi}[/tex]
[tex]f=\dfrac{1}{\pi}[/tex]
Therefore, the correct option is D.
Tegan is checking her tax bill for the last year.
The tax rates were as follows:
• No tax on the first £11 000 of earnings
• Earnings in excess of £11 000 and up to £43 000 taxed at a rate of 20%
• Earnings in excess of £43000 and up to £150 000 taxed at a rate of 40%
• Earnings over £150 000 taxed at a rate of 45%
Last year, Tegan earned £48 300 before tax.
How much tax did she pay in total?
Answer:
£8520
43000-11000=32000
20/100×32000
£6400
48300-43000=5300
40/100×5300=2120
£8520
PLS HELP (algebra 1)
solve 4( -15x - 2) + 8
Answer:
-60x
Step-by-step explanation:
A petting zoo gives out large buckets of healthy popcorn snacks for visitors to feed to the animals. what fraction of the snack is left in the bucket after a cow eats 1/3, a goose eats 1/12, and a goat eats 2/9?
Answer:
13/36 is left
Step-by-step explanation:
cow- 1/3 = 12/36
goose- 1/12 = 3/36
goat= 2/9 = 8/36
12 + 3 + 8 = 23/36
23/36 is consumed...
13/36 is left
The fraction of the snack left in the bucket will be 13/36.
What is a fraction?The fraction is defined as the division of the whole part into an equal number of parts.
Given that:
cow- 1/3 = 12/36goose- 1/12 = 3/36goat= 2/9 = 8/36The amount consumed is:-
( 12/ 36 )+ (3 / 36 ) +( 8 / 36 ) = 23/36
So the amount left will be calculated as:-
Amount left = 1 - ( 23 / 36 )
Amount left = ( 36 - 23 ) / 36
Amount left = 13 / 36
Therefore fraction of the snack left in the bucket will be 13/36.
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Mr. Harris earns $12 per hour for 40 hours of work. He earns $18 per hour for hours worked over 40. How many hours did he work if he earned $642?
Answer:
$49 hours
Step-by-step explanation:
12*40=$480
642-480= $162
$162/18= 9 hours more than 40
40+9=49 hours
Tommy went to the shop where there was a 20% off sale taking place
The shirt he wanted to buy was originally £20
How much money does he save in the sale?
Answer:
4 pounds
Step-by-step explanation:
take 20% off the original price. 20(0.20)= 4
So that's a discount of 4 pounds and the sale price is 16 pounds.
The savings is 4 pounds on 1 shirt.
write an expression for 8 less than 2 times a number
show your work
Answer:
Step-by-step explanation:
Let's call the number x. The statement "...2 times a number" if the number is x looks like this:
2x
"8 less than" that looks like this:
... - 8
Putting the whole thing together:
2x - 8
Find the value of x. Write it as a decimal.
Answer:
68.5
Step-by-step explanation:
Arc ABE = 360 - 2x
Arc AE = 2x
half the difference between the two arcs is 43
43 = [tex]\frac{1}{2}[/tex] [360 -2x - (2x)]
Thank you very much you can help me with the others that I am uploading to my profile and there is more in case you can please
Answer: y = 2x + 20; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.
Step-by-step explanation:
Because it's time, it don't have to be just integers. Seconds are fractions of minutes.(0,20) is the y-intercept and there will be no smaller y-values because x(time) cannot go negative.He goes at a rate of a problem per 2 minutes, so 2 is his slope.Answer:
The second one is the answer.
Step-by-step explanation:
Objective: Linear Equation Problems.
Let model the equation given to us.
Vlad spent 20 minutes on his homework already and he complete x math problems every 2 minutes so we represent this as
[tex]y = 2x + 20[/tex]
X can be any real number greater than or equal zero because time isnt negative so anything below zero is wrong.
Y can be any real number but however since Vlad spent 20 mins on his homework already, he must spend over or equal to 20 minutes completing the total homework.
The second one is the answer
6. The coordinates of the vertices of triangle CDE are C(3, - 2), D(5, 2) , and E(7, 0) The figure is rotated 90about the origin . What are the vertices of the resulting image, Figure C'D'E?
Answer:
Step-by-step explanation:
if it is rotated in clockwise direction then C'(-2,-3),D'(2,-5),E'(0,-7)
if rotated in anticlockwise direction C'(2,3),D'(-2,5),E'(0,7)
What is –70 divided by 700
PLZ HELP ME!!!
Answer: -0.1
Step-by-step explanation: Calculator
Hello!
-70 : 700 = -0,1 → answer
Good luck! :)
find missing side of triangle, help!
Answer:
2√10 km
Step-by-step explanation:
By Pythagoras theorem,
x^2 + 9^2 = 11^2
x^2 + 81 = 121
x^2 = 121 - 81
x^2 = 40
= 4 x 10
x^2 = 2^2 x 10
x = 2√10 km
What is the area of this figure? Enter your answer in the box.
Answer:
Step-by-step explanation:
33
