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AleksAgata [21]
2 years ago
14

5 Find the slope of the line that contains points (1,-3) and (-4,5).

Mathematics
1 answer:
ch4aika [34]2 years ago
3 0

Answer:

gradient = m

    m=\frac{rise}{run}

m=\frac{1-(-4)}{-3-5}

m=\frac{5}{-8}

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Find exact values for sin θ, cos θ and tan θ if csc θ = 3/2 and cos θ &lt; 0.
kumpel [21]

Answer:

Part 1) sin(\theta)=\frac{2}{3}

Par 2) cos(\theta)=-\frac{\sqrt{5}}{3}

Part 3) tan(\theta)=-\frac{2\sqrt{5}}{5}

Step-by-step explanation:

step 1

Find the sin(\theta)

we have

csc(\theta)=\frac{3}{2}

Remember that

csc(\theta)=\frac{1}{sin(\theta)}

therefore

sin(\theta)=\frac{2}{3}

step 2

Find the cos(\theta)

we know that

sin^{2}(\theta) +cos^{2}(\theta)=1

we have

sin(\theta)=\frac{2}{3}

substitute

(\frac{2}{3})^{2} +cos^{2}(\theta)=1

\frac{4}{9} +cos^{2}(\theta)=1

cos^{2}(\theta)=1-\frac{4}{9}

cos^{2}(\theta)=\frac{5}{9}

square root both sides

cos(\theta)=\pm\frac{\sqrt{5}}{3}

we have that

cos(\theta) < 0 ---> given problem

so

cos(\theta)=-\frac{\sqrt{5}}{3}

step 3

Find the tan(\theta)

we know that

tan(\theta)=\frac{sin(\theta)}{cos(\theta)}

we have

sin(\theta)=\frac{2}{3}

cos(\theta)=-\frac{\sqrt{5}}{3}

substitute

tan(\theta)=\frac{2}{3}:-\frac{\sqrt{5}}{3}=-\frac{2}{\sqrt{5}}

Simplify

tan(\theta)=-\frac{2\sqrt{5}}{5}

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2 years ago
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ladessa [460]

Answer:

she can purchase 5 cheesecakes

Step-by-step explanation:

15.99*5=79.95

if we add 9.99 for the shipping of thw whole order

79.95+9.99=89.94

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2 years ago
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