Answer: (A) The image of JKL after a 90° counterclockwise about the origin is shown in figure 1. (B) The image of JKL after a reflection across the y-axis is shown in figure 2.

Explanation:

(A)

From the given figure it is noticed that the coordinate points are J(-4,1), K(-4,-2) and L(-3,-1).

If a shape rotate 90 degree counterclockwise about the origin, then,

$(x,y)\rightarrow (-y,x)$

$J(-4,1)\rightarrow J'(-1,-4)$

$K(-4,-2)\rightarrow K'(2,-4)$

$L(-3,-1)\rightarrow L'(1,-3)$

Therefore, the vertex of imare are J'(-1,-4), K'(2,-4) and L'(1,-3). The graph is shown in figure (1).

(B)

If a figure reflect across the y-axis then,

$(x,y)\rightarrow (-x,y)$

$J(-4,1)\rightarrow J''(4,1)$

$K(-4,-2)\rightarrow K''(2,-4)$

$L(-3,-1)\rightarrow L''(3,-1)$

Therefore, the vertex of imare are J''(4,1), K''(2,-4) and L''(3,-1). The graph is shown in figure (2).

8 0

3 years ago

b is the midpoint of AC and E is the midpoint of BD if A(-9,-4) C(-1,6) and E(-4,-3) find the coirdinates of D

natima [27]

To find the coordinate of the point D, we can use the Midpoint point of a line Segment formula. Calculation of the formula are as follows,

Given two points A(x1,y1) and C(x2,y2), we need to locate the midpoint coordinate of this line denoted as B(x,y).

To solve for the value of x and y, we get,

x=(x1+x2)/2 and y=(y1+y2)/2

For the given problem, we need to solve first the midpoint coordinate of AC which is B.

So, A(-9,-4)=A(x1,y1) and C(-1,6)=C(x2,y2)

Hence,

B(x,y)=B((-9+(-1))/2, (-4+6)/2)=B(-10/2,2/2)=B(-5,1)

Now, since the midpoint is given but one point in the line is missing. To solve for the missing point D(x2,y2), we need to use the Midpoint Segment Formula.

That is, B(-5,1)=B(x,y) and E(-4,-3)=E(x1,y1)

So,

x=(x1+x2)/2 and y=(y1+y2)/2

-5=(-4+x2)/2 and 1=(-3+y2)/2

By Cross Multiplication and Transposing method,

-5(2)=-4+x2 and 1(2)=-3+y2

x2=-10+4=-6 and y2=3+2=5

Thus, the coordinate of D is D(-6,5).

5 0

3 years ago

The difference of number p and 2 is at least 5

hichkok12 [17]

Step-by-step explanation:

The difference of number p and 2 is at least 5

means

p - 2 ≥ 5

then

p ≥ 7

6 0

3 years ago

You are testing the claim that the proportion of men who own cats is significantly different than the proportion of women who ow

Nadya [2.5K]

Answer:

Test statistic =1.30

Step-by-step explanation:

Given that you are testing the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats.

Men Women Difference

Sample size n 60 120

Proportion p_1, p_2 0.45 0.35 0.10

60 120 180

0.45 0.35 0.383333333

27 42 69

p = 0.3833

Std error for proportion difference = $\bar p (1-\bar p)(\frac{1}{n_1}+\frac{1}{n_2})\\=0.3833(0.6167)(\frac{1}{60}+\frac{1}{120})\\=0.0769$

Test statistic = $\frac{p_1-p_2}{\bar p (1-\bar p)(\frac{1}{n_1}+\frac{1}{n_2}) }$

= $1.3008$

=1.30

4 0

3 years ago