The equation of the line of best fit of a scatter plot is y = −4x − 6. What is the the y-intercept? −6 −4 4 6

Answers

Answer 1

Answer:

The y-intercept of the equation of the line which best fit of a scatter plot is -6. Option A is the correct option.

What is scatter plot?

Scatter plot is the plot of a graph in which the values of two variables plotted using their coordinates on the graph.

The equation of the lines represents the line by the set of points on which the line lies or passes through in the coordinate system.

$y=mx+c$

Here, (m) is the slope of the line and (c) is the y intercept.

The equation of the line of best fit of a scatter plot is

$y = -4x -6$ .

Comparing it with equation of line, we get,

$m=-4\nc=-6$

Thus, the y-intercept of the equation of the line which best fit of a scatter plot is -6. Option A is the correct option.

Learn more about the scatter plot here;

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Answer 2

Answer:
The equation is in slope-intercept form, and the format for that is y equals slope times x added to the y-intercept. -6 is in the place where the y-intercept should be, so the y-intercept is -6.

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How many inches are in 13 and a half feet

Answers

The best way to work this is out, is to find out how many inches there are in a foot, and half a foot. One foot is equal to 12 inches, and half a foot is equal to 6 inches. It's best to find the whole numbers first. The best way to do this is to simply multiply the length (12in) by the feet (13), 13x12= 156 inches.
You've then got half a foot, which is six inches, so you then have to add this to the 156, giving you 162.
In thirteen and a half feet, there are 162 inches,
Hope this helps :)

Megan draws a triangle on coordinate axes. She reflects the triangle across the y-axis and then translates it 5 units to the right. Which statement is true about the triangle formed from these transformations?A. It will be larger than the original triangle
B. It will be smaller than the original triangle
C. It will be congruent to the original triangle
D. It will be a different shape then the original triangle

Answers

Answer C: It will be congruent to the original triangle. Reflections and translations do not affect the size of a shape, only it’s position and the way it is viewed.

Final answer:

The triangle formed from reflecting the original triangle across the y-axis and then translating it 5 units to the right will be congruent to the original triangle.

Explanation:

The triangle formed from reflecting the original triangle across the y-axis and then translating it 5 units to the right will be congruent to the original triangle.

When a figure is reflected across the y-axis, its shape remains the same, but its orientation is flipped. Then, by translating the reflected triangle 5 units to the right, we are simply shifting it horizontally without changing its size or shape.

Therefore, the statement that is true about the triangle formed from these transformations is C. It will be congruent to the original triangle.

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Solve 2 log2 2 + 2 log2 6 − log2 3x = 3.

Answers

Answer:

x = 6

Step-by-step explanation:

Given : $2\:log_2\:2\:+\:2\:log_26−\:log_2\:3x\:=\:3$

We have to solve the given expression $2\:log_2\:2\:+\:2\:log_26−\:log_2\:3x\:=\:3$

Subtract $2\log _2\left(2\right)+2\log _2\left(6\right)$ both sides , we have,

$2\:log_2\:2\:+\:2\:log_26-\:log_2\:3x-(2\log _2\left(2\right)+2\log _2\left(6\right)):=\:3-(2\log _2\left(2\right)+2\log _2\left(6\right))$

Simplify, we have,

$\log _2\left(3x\right)=3-2\log _2\left(2\right)-2\log _2\left(6\right)$

Divide both side by -1, we have,

$(-\log _2\left(3x\right))/(-1)=(3)/(-1)-(2\log _2\left(2\right))/(-1)-(2\log _2\left(6\right))/(-1)$

Simplify, we have,

$\log _2\left(3x\right)=-3+2\log _2\left(2\right)+2\log _2\left(6\right)$

Apply log rule, $a=\log _b\left(b^a\right)$

$2\log _2\left(6\right)-1=\log _2\left(2^(2\log _2\left(6\right)-1)\right)=\log _2\left(18\right)$

When log have same base,

$\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)$

$\mathrm{For\:}\log _2\left(3x\right)=\log _2\left(18\right)\mathrm{,\:\quad solve\:}3x=18$

3x = 18

x = 6

log(base2)[2² * 6² / 3x] = 3
144 / 3x = 2^3 = 8
144/8 = 3x
18 = 3x
x = 6

F(x) = 4x^2 - 3x + 2kx + 1 What's the value of k for which the function has two zeros??
Can someone show me step by step?

Answers

$f(x)=4x^2-3x+2kx+1=4x^2+(2k-3)x+1\n\na=4;\ b=2k-3;\ c=1\n\nfunction\ has\ two\ zeros\ when\ \Delta=b^2-4ac > 0\n\n\Delta=(2k-3)^2-4\cdot4\cdot1=4k^2-12k+9-16=4k^2-12k-7 > 0\n\na_k=4;\ b_k=-12;\ c_k=-7\n\n\Delta_k=(-12)^2-4\cdot4\cdot(-7)=144+112=256\n\nk_1=(-b_k-√(\Delta_k))/(2a_k);\ k_2=(-b_k+√(\Delta_k))/(2a_k)$

$√(\Delta_k)=√(256)=16\n\nk_1=(12-16)/(2\cdot4)=(-4)/(8)=-(1)/(2);\ k_2=(12+16)/(2\cdot4)=(28)/(8)=(7)/(2)\n\na_k=4 > 0\ (up\ parabola\ arms-see\ the\ picture)\n\nAnswer:k\in(-\infty;-(1)/(2))\ \cup\ ((7)/(2);\ \infty)$

X - 5 > -10. give the solution

Answers

x > -10 + 5
bring the five to the other side of the equation and change the sign in front
x > -5

x-5> -10
means where x minus 5 and more big from 10.

The sum of a geometric series of twelve terms with common ratio 2 is 20,475. What is the first term? Needed help please.

Answers

Answer: the first term is 5

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = (ar^n - 1)/(r - 1)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

S12 = 20475

r = 2

n = 12

Therefore,

20475 = (a × 2^(12) - 1)/2 - 1

20475 = (a × 4095)