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2 years ago

Hello! Please Help Its just one simple Question ^^

Mathematics

1 answer:

Flura [38]2 years ago

4 0

$\\ \sf\longmapsto f(x)=112-kx$

f(-3)=121

Put -3 in f(x)

$\\ \sf\longmapsto f(-3)=121$

$\\ \sf\longmapsto 112-k(-3)=121$

$\\ \sf\longmapsto 112+3k=121$

$\\ \sf\longmapsto 3k=9$

$\\ \sf\longmapsto k=3$

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Verify that [tan(theta) + cot(theta)]^2 = sec^2(theta) + csc^2(theta)

Wittaler [7]

(tanθ + cotθ)² = sec²θ + csc²θ

Expand left side: tan²θ + 2tanθcotθ + cot²θ

Evaluate middle term: 2tanθcotθ = $2*\frac{sin\theta}{cos\theta}*\frac{cos\theta}{sin\theta}$ = 2

⇒ tan²θ + 2+ cot²θ

= tan²θ + 1 + 1 + cot²θ

Apply trig identity: tan²θ + 1 = sec²θ

⇒ sec²θ + 1 + cot²θ

Apply trig identity: 1 + cot²θ = csc²θ

⇒ sec²θ + csc²θ

Left side equals Right side so equation is verified

7 0

3 years ago

Luke's bill for breakfast at a restaurant was $80. He left a 20% tip. What was the amount of

Alexandra [31]

Answer:

$16

Step-by-step explanation:

Multiply $80 dollars by 20% or .2.

You should get $16.

A tip for the future is to move the decimal point to the left twice.

ie. 60%=0.6, 175%=1.75, 3%=0.03

6 0

2 years ago

Martine’s town is building a volleyball court based on a scale drawing that is 40cm to 80cm and uses the scale 1cm:22.5cm write

never [62]

Answer:

$y=22.5x$

Step-by-step explanation:

we have that

The scale drawing is

$\frac{1}{22.5}\frac{cm}{cm}$

we know that

Using proportion find out the actual dimensions of the volleyball court

Let

x -----> drawing court lengths in cm

y ----> court lengths in cm

For x=40 cm

$\frac{1}{22.5}\frac{cm}{cm}=\frac{40}{y}\frac{cm}{cm}\\\\y=40*22.5\\\\y=900\ cm$

For x=80 cm

$\frac{1}{22.5}\frac{cm}{cm}=\frac{80}{y}\frac{cm}{cm}\\\\y=80*22.5\\\\y=1,800\ cm$

Find the equation for the proportional relation ship between drawing court lengths x in centimeters and court lengths in y centimeters

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

For x=40 cm, y=900

substitute

$k=y/x$ -----> $k=900/40=22.5$

The equation is

$y=22.5x$

5 0

3 years ago

A patient is instructed to take three 50-mcg tablets of pergolide mesylate (Permax) daily. How many milligrams of the drug would

Black_prince [1.1K]

Answer:

The patient would receive 1.05mg of the drug weekly.

Step-by-step explanation:

First step: How many mcg of the drug would the patient receive daily?

The problem states that he takes three doses of 50-mcg a day. So

1 dose - 50mcg

3 doses - x mcg

x = 50*3

x = 150 mcg.

He takes 150mcg of the drug a day.

Second step: How many mcg of the drug would the patient receive weekly?

A week has 7 days. He takes 150mcg of the drug a day. So:

1 day - 150mcg

7 days - x mcg

x = 150*7

x = 1050mcg

He takes 1050mcg of the drug a week.

Final step: Conversion of 1050 mcg to mg

Each mg has 1000 mcg. How many mg are there in 1050 mcg? So

1mg - 1000 mcg

xmg - 1050mcg

1000x = 1050

$x = \frac{1050}{1000}$

x = 1.05mg

The patient would receive 1.05mg of the drug weekly.

6 0

3 years ago

Mrs. Taylor bought a water tube to pull behind her boat. The tube cost $87.00 and 9% sales tax was added at the register. Mrs, T

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... cost $87.00 and 9% sales tax was added at the register. ms.taylor gave the cashier five $20 bills. how much change should she have received ...

6 0

3 years ago