Ask question

Ask question

All categories

3 years ago

15

Juila brought 6note books for $ 2.35 each and 6 packs of dividers for $ 1.25 each. Write an equation using the distributive prop

erty that can be used to find the total cost ,c,of the note books and dividers .

1 answer:

snow_lady [41]3 years ago

8 0

($2.35+$1.25)×6=6($2.35)+6($1.25)

You might be interested in

Kelly practiced her flute for 30 minutes a day for 9 days. How many total minutes did she practice?

Lesechka [4]

she practice 270 minutes

7 0

3 years ago

Read 2 more answers

In the triangle pictured, let A, B, C be the angles at the three vertices, and let a,b,c be the sides opposite those angles. Acc

Troyanec [42]

Answer:

Step-by-step explanation:

(a)

Consider the following:

$A=\frac{\pi}{4}=45°\\\\B=\frac{\pi}{3}=60°$

Use sine rule,

$\frac{b}{a}=\frac{\sinB}{\sin A}
\\\\=\frac{\sin{\frac{\pi}{3}}
}{\sin{\frac{\pi}{4}}}\\\\=\frac{[\frac{\sqrt{3}}{2}]}{\frac{1}{\sqrt{2}}}\\\\=\frac{\sqrt{2}}{2}\times \frac{\sqrt{2}}{1}=\sqrt{\frac{3}{2}}$

Again consider,

$\frac{b}{a}=\frac{\sin{B}}{\sin{A}}
\\\\\sin{B}=\frac{b}{a}\times \sin{A}\\\\\sin{B}=\sqrt{\frac{3}{2}}\sin {A}\\\\B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

Thus, the angle B is function of A is, $B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

Now find $\frac{dB}{dA}$

Differentiate implicitly the function $\sin{B}=\sqrt{\frac{3}{2}}\sin{A}$ with respect to A to get,

$\cos {B}.\frac{dB}{dA}=\sqrt{\frac{3}{2}}\cos A\\\\\frac{dB}{dA}=\sqrt{\frac{3}{2}}.\frac{\cos A}{\cos B}$

b)

When $A=\frac{\pi}{4},B=\frac{\pi}{3}$ , the value of $\frac{dB}{dA}$ is,

$\frac{dB}{dA}=\sqrt{\frac{3}{2}}.\frac{\cos {\frac{\pi}{4}}}{\cos {\frac{\pi}{3}}}\\\\=\sqrt{\frac{3}{2}}.\frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}\\\\=\sqrt{3}$

c)

In general, the linear approximation at x= a is,

$f(x)=f'(x).(x-a)+f(a)$

Here the function $f(A)=B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

At $A=\frac{\pi}{4}$

$f(\frac{\pi}{4})=B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{\frac{\pi}{4}}]\\\\=\sin^{-1}[\sqrt{\frac{3}{2}}.\frac{1}{\sqrt{2}}]\\\\\=\sin^{-1}(\frac{\sqrt{2}}{2})\\\\=\frac{\pi}{3}$

And,

$f'(A)=\frac{dB}{dA}=\sqrt{3}$ from part b

Therefore, the linear approximation at $A=\frac{\pi}{4}$ is,

$f(x)=f'(A).(x-A)+f(A)\\\\=f'(\frac{\pi}{4}).(x-\frac{\pi}{4})+f(\frac{\pi}{4})\\\\=\sqrt{3}.[x-\frac{\pi}{4}]+\frac{\pi}{3}$

d)

Use part (c), when $A=46°$ , B is approximately,

$B=f(46°)=\sqrt{3}[46°-\frac{\pi}{4}]+\frac{\pi}{3}\\\\=\sqrt{3}(1°)+\frac{\pi}{3}\\\\=61.732°$

8 0

3 years ago

During a business trip, an individual stopped at two rest stops. In the parking lot of the first rest stop, they counted 20 cars

olganol [36]

Answer

given,

on first stop

number of car = 20 and number of trucks = 18

on second stop

number of car = 18 and number of trucks = 10

we need to calculate which rest stop has higher ratio of car to truck.

Rest Stop 1

ratio= r₁ = $\dfrac{cars}{trucks}$

r₁ = $\dfrac{20}{18}$

r₁ = $\dfrac{10}{9}$

Rest Stop 2

ratio= r₂ = $\dfrac{cars}{trucks}$

r₂ = $\dfrac{18}{10}$

r₂= $\dfrac{9}{5}$

hence, r₂ > r₁

rest stop 2 has more car to truck ratio than rest stop 1

3 0

3 years ago

Choose the problem modeled by the picture. A) 1 3 × 3 2 = 3 6 B) 1 4 × 3 6 = 3 24 C) 3 4 × 1 6 = 3 24 D) 1 3 × 3 4 = 3 12

Morgarella [4.7K]

Answer: The answer is (C) 3 4 × 1 6 = 3 24

Step-by-step explanation: We are given a rectangular picture made of square boxes and we are to find among the given options which is modelled by the given picture.

In the diagram, there are 6 boxes lengthwise and 4 boxes breadthwise. Also, 3 × 4 boxes are painted yellow and 1 × 6 boxes are painted blue. The common boxes will be 3.

Therefore, the correct choice is 3 4 × 1 6 = 3 24

Hence, (C) is the correct option.

3 0

4 years ago

Read 2 more answers

5. What is the greatest common factor<br> of 12 and 16?<br> A 2<br> C 12<br> B 4<br> D 48

telo118 [61]

The answer for the greatest common factor of 12 and 16 is 4

4 0

3 years ago

Read 2 more answers