Answer:
Step-by-step explanation:
4x + 3y = -1 --------------(i)
3x - 9y = 33 -------------(ii)
multiply equation (i) by 3
(i)* 3 12x + 9y = -3
(ii) <u> 3x - 9y = 33</u>
add, 15x = 30
x = 30/15
x = 2
Put x =2 in Equation (i)
4*2 + 3y = -1
8 +3y = -1
3y = -1-8
3y = -9
y = -9/3
y= -3
Look at this video: https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-fractions-topic/cc-5th-multiplying-fraction-whole-number-product
Answer:
540 m
Step-by-step explanation:
The building of the Blue Museum of Barcelona is triangular and each side of the building is 180 m.
This means the building is shaped as an equilateral triangle.
We need to find the total distance traveled if we go round the building, that is, its perimeter.
The perimeter of an equilateral triangle is given as:
P = 3L
where L = length of the side of the building = 180 m
The total distance traveled if we go round the building will be:
P = 3 * 180 = 540 m
We would need to go 540 m to travel around the building completely.
Answer:
sin-¹(10/11)
Step-by-step explanation:
The height of the building is 100 ft and the ladder is 110ft long .We can imagine this situation as a right angled ∆. For figure refer to the attachment .
- We can use ratio sine here. Let the angle of elevation be theta.
<u>In </u><u>∆</u><u> </u><u>ABC </u><u>:</u><u>-</u><u> </u>
=> sinθ = p/h
=> sinθ = 100ft / 110 ft
=> sinθ = 10/11
=> θ = sin -¹ ( 10/11) .
<h3><u>Hence </u><u>the</u><u> </u><u>angle</u><u> of</u><u> elevation</u><u> </u><u>is </u><u>sin </u><u>-</u><u>¹</u><u> </u><u>(</u><u> </u><u>1</u><u>0</u><u>/</u><u>1</u><u>1</u><u>)</u><u>. </u><u> </u></h3>
Answer:
Equation is: y = 0.5x² + 0.5x - 3
Explanation:
general form of the parabola is:
y = ax² + bx + c
Now, we will need to solve for a, b and c.
To do this, we will simply get points from the graph, substitute in the general equation and solve for the missing coefficients.
First point that we will use is (0,-3).
y = y = ax² + bx + c
-3 = a(0)² + b(0) + c
c = -3
The equation now becomes:
y = ax² + bx - 3
The second point that we will use is (2,0):
y = ax² + bx - 3
0 = a(2)² + b(2) - 3
0 = 4a + 2b -3
4a + 2b = 3
This means that:
2b = 3 - 4a
b = 1.5 - 2a ...........> I
The third point that we will use is (-3,0):
y = ax² + bx - 3
0 = a(-3)² + b(-3) - 3
0 = 9a - 3b - 3
9a - 3b = 3 ...........> II
Substitute with I in II and solve for a as follows:
9a - 3b = 3
9a - 3(1.5 - 2a) = 3
9a - 4.5 + 6a = 3
15a = 7.5
a = 7.5 / 15
a = 0.5
Substitute with the value of a in equation I to get b as follows:
b = 1.5 - 2a
b = 1.5 - 2(0.5)
b = 0.5
Substitute with a and b in the equation as follows:
y = 0.5x² + 0.5x - 3
Hope this helps :)
