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3 years ago

A certain shade of pink is created by adding 3 cups of white paint to 2 cups

Mathematics

1 answer:

Julli [10]3 years ago

3 0

Answer:

22.5

Step-by-step explanation:

red : white

2 : 3

1 : 3/2

15 : 3/2 ×15

15 : 22.5

the answer is first opition , 22.5

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Can someone help me plz .. Use these lengths to find cos B, tan B, and sin B.

lara [203]

Answer:

cos B = $\frac{7}{25}$

tan B = $\frac{24}{7}$

sin B = $\frac{24}{25}$

Step-by-step explanation:

In the right triangle, there are three sides and 2 acute angles

Hypotenuse ⇒ the opposite side of the right angle

Leg1 and Leg 2 ⇒ the sides of the right angle

The trigonometry functions of one of the acute angles Ф are

sin Ф = opposite leg/hypotenuse

cos Ф = adjacent leg/hypotenuse

tan Ф = opposite leg/adjacent leg

In Δ ACB

∵ ∠C is the right angle

∴ AB is the hypotenuse

∵ AC is the opposite side of ∠B ⇒ leg1

∵ CB is the adjacent side of ∠B ⇒ leg2

→ By using the ratios above

∴ cos B = $\frac{CB}{AB}$ , tan B = $\frac{AC}{CB}$ , sin B = $\frac{AC}{AB}$

∵ CB = 7, AB = 25, AC = 24

∴ cos B = $\frac{7}{25}$

∴ tan B = $\frac{24}{7}$

∴ sin B = $\frac{24}{25}$

6 0

3 years ago

The function f is linear. If f(2) = 2 and f(-6)=6 find f(6)

lina2011 [118]

$The\ slope-intercept\ form:y=mx+b\\\\f(2)=2\to for\ x=2\to y=2\\f(-6)=6\to for x=-6\to y=6\\\\put\ in\ equation\ of\ the\ line:\\\\ -\left\{\begin{array}{ccc}2=2m+b\\6=-6m+b\end{array}\right\ \ \ |subtract\ sides\ of\ the\ equations\\----------\\.\ \ \ -4=8m\ \ \ \ \ |divide\ both\ sides\ by\ 8\\.\ \ \ \ \boxed{m=-\frac{1}{2}}\\\\put\ m=-\frac{1}{2}\ to\ equation\ 2=2m+b:\\\\2=2\cdot(-\frac{1}{2})+b\\2=-1+b\ \ \ \ |add\ 1\ to\ both\ sides\\\boxed{b=3}\\\\\boxed{\boxed{y=-\frac{1}{2}x+3}}$

$therefore:f(x)=-\frac{1}{2}x+3\Rightarrow f(6)=-\frac{1}{2}\cdot6+3=-3+3=0\\\\Answer:\boxed{f(6)=0}$

5 0

3 years ago

You go shopping at a local department store with your friend and cousin. You buy one pair of jeans, four pairs of shorts, and tw

VashaNatasha [74]

Answer: Cost per pair of jeans = $ 20

Cost per pair of shorts = $12

Cost per shirt = $8

Step-by-step explanation:

Let x= cost per pair of jeans

y = Cost per pair of shorts

z= cost per shirt.

For you, total cost = x+4y+2z= 84

For your friend, total cost = 2x+y+3z=76

For cousin, total cost = x+2y+z= 52

Required system:

$x+4y+2z=84\ (i)\\ 2x+y+3z=76\ (ii)\\ x+2y+z=52\ (iii)$

from (i), $x=84-4y-2z$ (*)

put this in (ii) and (iii) we get

$2\left(84-4y-2z\right)+y+3z=76\\\Rightarrow\ -7y-z+168=76\ (iv)\\\\ 84-4y-2z+2y+z=52\\\Rightarrow\ -2y-z+84=52 \ (v)$

from (iv), $y=-\frac{z-92}{7}\ (vi)$

$\mathrm{Subsititute\:}y=-\frac{z-92}{7}\ \text{in}\ (v)$

$-2\left(-\frac{z-92}{7}\right)-z+84=52\\\\\Rightarrow\ -2\left(-\frac{z-92}{7}\right)-z=-32\\\\\Rightarrow\ -\frac{5z}{7}-\frac{184}{7}=-32\\\\\Rightarrow\ -5z-184=-224\\\\\Rightarrow\ -5z=-40\\\\\Rightarrow\ z=8$