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3 years ago

(-5,-4) rotated 270° counterclockwise

Mathematics

1 answer:

stepladder [879]3 years ago

6 0

Answer:

(4, - 5 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 270°

a point (x, y ) → (- y, x ) , thus

(- 5, - 4 ) → (4, - 5 )

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Please help me with this!

ivanzaharov [21]

1. The first equation is - 2x + 5y = 0

Second equation is $y = \frac{2}{5} x$

5y = 2x

- 2x + 5y = 0

Hence, the two equations are equivalent.

2. $a_{1} = 2, a_{2} = - 2$

$b_{1} = -1, b_{2} = -1$

$\frac{a_{1} }{a_{2}} =\frac{2}{-2} = -1$

$\frac{b_{1} }{b_{2}} = \frac{-1}{-1} = 1$

$\frac{a_{1} }{a_{2}} \neq \frac{b_{1} }{b_{2}}$

Hence, the equations are consistent.

3. $a_{1} = 4, a_{2} = 6$

$b_{1} = -1, b_{2} = -1$

$\frac{a_{1} }{a_{2}} =\frac{4}{6} = \frac{2 }{3}$

$\frac{b_{1} }{b_{2}} = \frac{-1}{-1} = 1$

$\frac{a_{1} }{a_{2}} \neq \frac{b_{1} }{b_{2}}$

Hence, the equations are consistent.

4. Equations can be re-arranged as:

x + y - 4 = 0 and

x + y + 6 = 0

$a_{1} = 1, a_{2} = 1$

$b_{1} = 1, b_{2} = 1$

$c_{1} = -4, c_{2} = 6$

$\frac{a_{1} }{a_{2}} =\frac{1}{1} = 1$

$\frac{b_{1} }{b_{2}} =\frac{1}{1} = 1$

$\frac{c_{1} }{c_{2}} =\frac{-4}{6} = \frac{-2}{3}$

$\frac{a_{1} }{a_{2}} = \frac{b_{1} }{b_{2}} \neq \frac{c_{1} }{c_{2}}$

Hence, the equations are inconsistent.

5. If we multiply the first equation by 4, we will get,

2y = -4x + 20 which is the second equation.

Hence, the equations are equivalent.

4 0

4 years ago

fire work a travels at the speed 300 ft/s firework b travels 240 ft/s. firework b is launched 0.25s before firework a. how many

storchak [24]

Answer:

Both fireworks will explode after 1 seconds after firework b launches.

Step-by-step explanation:

Given:

Speed of fire work A= 300 ft/s

Speed of Firework B=240 ft/s

Time before which fire work b is launched =0.25s

To Find:

How many seconds after firework b launches will both fireworks explode=?

Solution:

Let t be the time(seconds) after which both the fireworks explode.

By the time the firework a has been launched, Firework B has been launch 0.25 s, So we can treat them as two separate equation

Firework A= 330(t)

Firework B=240(t)+240(0.25)

Since we need to know the same time after which they explode, we can equate both the equations

330(t) = 240(t)+240(0.25)

300(t)= 240(t)+60

300(t)-240(t)= 60

60(t)=60

$t=\frac{60}{60}$

t=1

7 0

3 years ago

Please answer the question in the picture

lorasvet [3.4K]

A loan of $50,000 is taken out for six years at 9% interest compounded annually. If the loan is paid off in full at the end of that time period, $50433 must be returned.

<h3>What is Compound interest?</h3>

Compound interest is calculated by multiplying the initial loan amount, or principal, by one plus the annual interest rate multiplied by the number of compound periods multiplied by one.

Compound interest is when you earn interest on both your savings and your interest earnings. When you compound interest, you add the interest you've earned back into your principal balance, which earns you even more interest, compounding your returns.

Assume you have $1,000 in a savings account earning 5% interest per year. You'd earn $50 in year one, giving you a new balance of $1,050. Compound interest occurs when interest earned on savings begins to earn interest on itself.

To learn more about Compound interest, refer to:

brainly.com/question/24924853

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5 0

1 year ago

A display case of hat pins are marked 5 for $3. If Patty has $21, how many hat pins can Patty get? (assume no other taxes and fe

Nonamiya [84]

Answer: 35

Explanation: If patty has $21, and $3 is the price for 5 hat pins, then: 21/3=7, so she can buy 7 packages which cost $3 and contain 5 pins, and because the question asked the number of pins, we will multiply 7 • 5 and that equals 35

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2 years ago

While on a road trip, Steve drove 300 miles in 5 hours. After stopping for gas, he drove an additional 120 miles in 2 hours. Doe

lawyer [7]

Answer:

B. Yes, this is direct variation. Time is the independent variable, and miles driven is the dependent variable.

Step-by-step explanation:

In a direct variation, when the independent variable increase the dependent variable also increases. In this case, the independent variable is the time (time is always independent) and the miles driven by Steve is the dependent variable. This means, the miles driven increase as time pass.

3 0

3 years ago