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2 years ago

7

lani used 2 3s cup of raisins,3 8s cup of cranberries, and 3 4s cup of oatmeal to bake cookies. Which ingredient did lani use le

ast amount of?

1 answer:

Alex Ar [27]2 years ago

3 0

Answer:

Step-by-step explanation:

To compare the fractions, give them a common denominator.

⅔ = 16/24

⅜ = 9/24

¾ = 18/24

⅜ < ⅔ < ¾

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Let f(x)=x^4-3x^3+5x-3, f(-2)

BabaBlast [244]

$f(-2)=(-2)^4-3(-2)^3+5(-2)-3
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3 years ago

In ∆MNP, m∠N = 90º, NH – altitude, m∠P = 21º, PM = 4 cm. Find MH.

Sveta_85 [38]

Answer:

0.51 cm

Step-by-step explanation:

In right triangle MNP, MP = 4 cm, m∠N = 90°, m∠P = 21°

By the sine definition,

$\sin \angle P=\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}=\dfrac{MN}{MP}\\ \\MN=MP\sin \angle P\\ \\MN=4\sin 21^{\circ}\approx 1.43\ cm$

Now, consider right triangle HMN (it is right because NH is an altitude). By the cosine definition,

$\cos \angle M=\dfrac{\text{Adjacent leg}}{\text{Hypotenuse}}=\dfrac{MH}{MN}\\ \\MH=MN\cos \angle M$

In the right triangle, two acute angles are always complementary, so

$m\angle M=90^{\circ}-m\angle P=90^{\circ}-21^{\circ}=69^{\circ}$

Thus,

$MH=1.43\cos 69^{\circ}\approx 0.51\ cm$

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