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3 years ago

What are the coordinates of the point (2, −3) after a counterclockwise rotation of 90° about the origin?

2 answers:

7 0

The rule for a 90* counterclockwise rotation around the axis is: (x,y) --> (-y,x) so your answer would be (2,-3) --> (3,-2)

8090 [49]3 years ago

7 0

(3,2) 90* rotation counterclockwise about the origin

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Please help solve for x..

aalyn [17]

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

$x^{100}-4^x \cdot x^{98}-x^2+4^x=0$

Factor out -1:

$\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0$

Divide both sides by -1:

$\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0$

Rearrange the terms:

$\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0$

$\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:$

$\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0$

Factor the first two terms and the last two terms separately:

$\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0$

Factor out the common term $(x^{98}-1)$ :

$\implies (4^x-x^2)(x^{98}-1)=0$

<u>Zero Product Property</u>: If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the <u>Zero Product Property</u>, set each factor equal to zero and solve for x (if possible):

$\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}$

Therefore, the solutions to the given equation are: x = 1 or x = -1

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1 year ago

Sharoda works at Diamond Jewellers. Her basic week of

Novay_Z [31]

52-40 is 12 hours of overtime

4 0

2 years ago

Jan's scores on five quizzes were 2, 8, 8, 9, and 10. Is the mean or median the best measure of center to summarize Jan's scores

Rashid [163]

The mean is the best measure to summarise the scores.

7 0

3 years ago

What is the present value of $6,000 to be received at the end of each of eight periods, assuming the first payment occurs at the

Kipish [7]

Answer: Present value = $7200

Step-by-step explanation: Given Principal that is the original amount is $6000

Rate is 10% every fourth year

But the total period is eight.

So the interest would be paid 8/4 = 2 times.

Therefore,

Simple interest

= {principal * rate * no of times}/100

= {$6000*10*2}/100

Simple interest = $1200

Present value

= principal + Simple interest

= $6000 + $1200

= $7200.

6 0

3 years ago

A furniture company is ordering screws. The company uses 37 screws to make each table and 14 screws to make each chair. The comp

Firdavs [7]

Answer:

1,400 screws

Step-by-step explanation:

You need 1,1116 screws so 1,400 screws is the right amount.

8 0

3 years ago

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