How many points of intersection will the following system of linear equations have? y = 9x, 3y = -3x - 5 a) 0 b) 1 c) 2 d) Infinite
Answers
Answer:
b
Step-by-step explanation:
given the system of equations
y = 9x → (1)
3y = - 3x - 5 → (2)
substitute y = 9x into (2)
3(9x) = - 3x - 5
27x = - 3x - 5 ( add 3x to both sides )
30x = - 5 (divide both sides by 30 )
x = - = -
substitute x = - into (1) and solve for y
y = 9x = 9 × - = -
= -
point of intersection = ( - , -
)
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b. Find the length of side a to two decimal places in three different ways.
2. Solve the triangles below.
Answers
A) b = 10.57
B) a = 22.66
#2)
A) a = 1.35 (across from the 15° angle)
∠C = 50.07° (the angle at the top of the triangle)
∠B = 114.93°
B) ∠A = 83°
b = 10.77 (across from angle B)
a = 15.11 (across from angle A)
Explanation
#1)
A) Since b is across from the 25° angle and we have the hypotenuse, we have the information for the sine ratio (opposite/hypotenuse):
sin 25 = b/25
Multiply both sides by 25:
25*sin 25 = (b/25)*25
25*sin 25 = b
10.57 = b
B) We will first use the cosine ratio. Side a is the side adjacent to the angle and we have the hypotenuse, and the cosine ratio is adjacent/hypotenuse:
cos 25 = a/25
Multiply both sides by 25:
25*cos 25 = (a/25)*25
25*cos 25 = a
22.66 = a
Now we will use the Pythagorean theorem. We know from part a that side b = 10.57, and the figure has a hypotenuse of 25:
a²+(10.57)² = 25²
a² + 111.7249 = 625
Subtract 111.7249 from both sides:
a²+111.7249-111.7249=625-111.7249
a² = 513.2751
Take the square root of both sides:
√a² = √513.2751
a = 22.66
#2)
A) Let A be the 15° angle, B be the angle to the right and C be the angle at the top of the triangle. This means side a is across from angle A, side B is across from angle B, and side c is across from angle C.
Using the law of cosines,
a²=3²+4²-2(3)(4)cos(15)
a²=9+16-24cos(15)
a²=25-24cos(15)
a²=1.8178
Take the square root of both sides:
√a² = √1.8178
a = 1.3483≈1.35
Now we can use the Law of Sines to find angle C:
sin 15/1.35 = sin C/4
Cross multiply:
4*sin 15 = 1.35* sin C
Divide both sides by 1.35:
(4*sin 15)/1.35 = (1.35*sin C)/1.35
(4*sin 15)/1.35 = sin C
Take the inverse sine of both sides:
sin⁻¹((4*sin 15)/1.35) = sin⁻¹(sin C)
sin⁻¹((4*sin 15)/1.35) = C
50.07 = C
To find angle B, add angle A and angle C together and subtract from 180:
B=180-(50.07+15) = 180-65.07 = 114.93
B) To find angle A, add angle B and angle C together and subtract from 180:
180-(52+45) = 180-97 = 83
Now use the Law of Sines to find side b (across from angle B):
sin 52/12 = sin 45/b
Cross multiply:
b*sin 52 = 12*sin 45
Divide both sides by sin 52:
(b*sin 52)/(sin 52) = (12*sin 45)/(sin 52)
b = 10.77
Find side a using the Law of Sines:
sin 83/a = sin 52/12
Cross multiply:
12*sin 83 = a*sin 52
Divide both sides by sin 52:
(12*sin 83)/(sin 52) = (a*sin 52)/(sin 52)
15.11 = a
b. -3.236 or 1.236
c. 04 or 9
d. 2.487 or -5.859
e. None of these
Answers
Answer:
a.) 3.236 or -1.236
Step-by-step explanation:
Used an online calculator for this answer...
Using the Quadratic Formula where
The discriminant b^2−4ac > 0
so, there are two real roots.
Simplify the radical...
This simplifies to...
Answers
y=kx where k is constant
y=40
x=16
find k
40=k16
divide both sides by 16
5/2=k
y=5/2x
y=-5 find x
-5=5/2x
times 2/5 both sides to cancle fraciton (5/2 times 2/5=10/10=1)
-10/5=x
-2=x
x=-2
(°C) Distance
(inches)
0 10
2 12
4 12
5 15
9 10
9 8
10 6
10 9
10 8
12 7
12 7
13 5
14 4
16 2
18 2
19 2
19 2
19 1
19 1
20 0
21 4
21 0
The chart shows the damage index to a head gasket on trucks according to ambient temperature. Draw a scatterplot of the data.
Which equation is closest to the line of best fit?
A) y = 14 x - 2/3
B) y = -14 x + 2/3
C) y = -2/3 x + 14
D) y = 2/3 x - 14
Answers
If we take a look at the data presented in the chart we can see the damage that the head gasket on truck suffers according to the ambient temperature. The correct answer is letter C) because there is a negative slope that is less than one and the y-intercept begins 14 units up the y-axis.
I hope this helps, Regards.
Answer:
C. I would recommend that he does not go as lower temperatures have a strong negative correlation, therefore the lower the temperature the more damage is caused
Step-by-step explanation:
The correct answer is I would recommend that he does not go as lower temperatures have a strong negative correlation, therefore the lower the temperature the more damage is caused. For temperatures below 19 degrees Celsius the scatterplot forms a negative correlation.
Answers
Answer: X=216
Step-by-step explanation:
18×12=216
Now, to find the number x times 18 times 12, you can multiply 216 by x:
X x 216
Answers
Answer 10x8=80+3
Step-by-step explanation:
i.d.k 83?????