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3 years ago

The image of the point (1, -2) after a rotation of 180° about the origin is

Mathematics

2 answers:

Reika [66]3 years ago

8 0

Answer:

(-1,2)

Step-by-step explanation:

In this problem, the signs are switched because there is a rule to 180 rotation that is (x,y) to (-x,-y).

(1,-2)×(-1x, -1y)= (-1,2) .

if both points were negative, the points would be positive. if they were positive, they would be negative.

Harlamova29_29 [7]3 years ago

4 0

Answer:

(-1,2)

Step-by-step explanation:

Found answer on brainly.

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Through: (-3,0), perp. to y = 3x - 1

Marrrta [24]

Answer:

$y=-\dfrac{1}{3}x-1$

Step-by-step explanation:

Given:

line y=3x-1

point (-3,0)

Write: equation of the line that is perpendicular to the given and passes through the point (-3,0)

Solution:

The slope of the given line is $m=3$

If $m_1$ is the slope of perpendicular line, then

$m\cdot m_1=-1\\ \\3m_1=-1\\ \\m_1=-\dfrac{1}{3}$

So, the equation of the needed line is $y=-\dfrac{1}{3}x+b.$

Find b. This line passes through the point (-3,0), so its coordinates satisfy the equation:

$0=-\dfrac{1}{3}\cdot (-3)+b\\ \\0=1+b\\ \\b=-1\\ \\y=-\dfrac{1}{3}x-1$

7 0

3 years ago

What is the area of the following trapezoid? 13.5 yd 2 3.38 yd 2 6.75 yd 2 8.25 yd 2

Neporo4naja [7]

Answer:

$area = \frac{a + b}{2} h \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2 + 7}{2} \times 1.5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 6.75 {yd}^{2}$

8 0

3 years ago

Martin was given this expression to simplify: 23x + xy – y + 3y + 5 – 20x + 6xy He simplified the expression to: 43x + 7xy −3y W

tensa zangetsu [6.8K]

Answer:

Step-by-step explanation:

23x + xy - y + 3y + 5 - 20x + 6xy = 23x - 20x + xy + 6xy -y + 3y + 5

= 3x + 7xy + 2y + 5

Errors:1) The combined coefficients of the x terms should be 3x, not 43x

2) The coefficients of the y terms have been multiplied.

3) The constant was left off.

3 0

3 years ago

Read 2 more answers

Chase consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Chase's body

PIT_PIT [208]

Answer:

(a) The 5-hour decay factor is 0.5042.

(b) The 1-hour decay factor is 0.8720.

Step-by-step explanation:

The amount of caffeine in Chase's body decreases exponentially.

The 10-hour decay factor for the number of mg of caffeine is 0.2542.

The 1-hour decay factor is:

$1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720$

(a)

Compute the 5-hour decay factor as follows:

$5-hour\ decay\ factor=(0.8720)^{5}\\=0.504176\\\approx0.5042$

Thus, the 5-hour decay factor is 0.5042.

(b)

The 1-hour decay factor is:

$1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720$

Thus, the 1-hour decay factor is 0.8720.

(c)

The equation to compute the amount of caffeine in Chase's body is:

A = Initial amount × (0.8720)ⁿ

It is provided that initially Chase had 171 mg of caffeine, 1.39 hours after consuming the drink.

Compute the amount of caffeine in Chase's body 2.39 hours after consuming the drink as follows:

$A = Initial\ amount \times (0.8720)^{2.39} \\=[Initial\ amount \times (0.8720)^{1.39}] \times(0.8720)\\=171\times 0.8720\\=149.112$

Thus, the amount of caffeine in Chase's body 2.39 hours after consuming the drink is 149.112 mg.

4 0

3 years ago

Evaluate 15/5 + 40 . 7 - 3 to the power of 4.

Lina20 [59]

15/5 + 40.7 -3^4
= 3 + 40.7 - 81
= -37.3

hope this helps! :)))

4 0

3 years ago