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3 years ago

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Graph the line that goes through point (5, 6) with slope 1/2.

1 answer:

rjkz [21]3 years ago

7 0

$(5, 6), \ slope : \ m=\frac{1}{2} \\ \\ x=5, \ y = 6 , \ m = \frac{1}{2} \\ \\the \ slope \ intercept \ form \ is : \\ \\ y= mx +b \\ \\ 6=\frac{1}{2}\cdot 5+b$

$6=\frac{5}{2} +b \\ \\b=6-\frac{5}{2}=6-2\frac{1}{2}=3\frac{1}{2}\\ \\ y=\frac{1}{2}x + 3\frac{1}{2}$

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Analyze the diagram below and complete the instructions that follow.

lora16 [44]

Answer:

$\displaystyle y=2\sqrt{6}$

$\displaystyle x=2\sqrt{2}$

Step-by-step explanation:

<u>Trigonometric Ratios </u>

The ratios of the sides of a right triangle are called trigonometric ratios.

The longest side of the right triangle is called the hypotenuse and the other two sides are the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

The image provided shows a right triangle whose hypotenuse is given. We are required to find the value of both legs.

Let's pick the angle of 30°. Its adjacent side is y. We can use the cosine ration, which is defined as follows:

$\displaystyle \cos 30^\circ=\frac{\text{adjacent leg}}{\text{hypotenuse}}$

$\displaystyle \cos 30^\circ=\frac{y}{4\sqrt{2}}$

Solving for y:

$y=4\sqrt{2}\cos 30^\circ$

Since:

$\cos 30^\circ=\frac{\sqrt{3}}{2}$

$\displaystyle y=4\sqrt{2}\frac{\sqrt{3}}{2}$

Simplifying:

$\displaystyle y=2\sqrt{6}$

Now we use the sine ratio:

$\displaystyle \sin 30^\circ=\frac{\text{opposite leg}}{\text{hypotenuse}}$

$\displaystyle \sin 30^\circ=\frac{x}{4\sqrt{2}}$

Solving for x:

$x=4\sqrt{2}\sin 30^\circ$

Since:

$\sin 30^\circ=\frac{1}{2}:$

$\displaystyle x=4\sqrt{2}\frac{1}{2}$

Simplifying:

$\displaystyle x=2\sqrt{2}$

The choices are not clear, but it seems like the correct answer is C.

$\boxed{\displaystyle y=2\sqrt{6}}$

$\boxed{\displaystyle x=2\sqrt{2}}$

6 0

3 years ago

Central Market sells 5 jars of jam for $3.00. Valley Market sells jars of jam at 59 cents per jar. Yasmin bought 10 jars from Ce

tamaranim1 [39]

Answer:

Yasmin will spend $6

Nadia will spend $5.9

Step-by-step explanation:

Step one:

the cost of 5 jars at Central market is $3

the cost of 1 jar = 3/5= $0.6

60 cents per jar

we are told that Valley Market sells jars of jam at 59 cents per jar.

$0.59

Step two:

If Yasmin buys 10 jars from Central Market,

Yasmin will spend = 10*0.6= $6

If Nadia buys 10 jars from Valley Market.

Nadia will spend = 10*0.59= $5.9

The market difference is 6-5.9= $0.1

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How do I simplify this in exponential expression

r-ruslan [8.4K]

It is d because you add the exponents

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y = -4x + 80

f(x) = -4x + 80

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