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3 years ago

When the equation 3x + 2y = 7 is expressed in the form ax+by+c=0, indicate the values of a , b and c *

Mathematics

1 answer:

Leviafan [203]3 years ago

4 0

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$3x + 2y = 7$

Subtract sides 7

$3x + 2y - 7 = 7 - 7$

$3x + 2y - 7 = 0$

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Compare :

$ax + by + c = 0$

$3x + 2y - 7 = 0$

Thus ;

$a = 3 \: \: , \: \: b = 2 \: \: , \: \: c = - 7$

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So the correct answer is the third option .

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which of the following best describes the line the arrow is pointing to in the regular pentagon below? A. Leg B. Diagonal C. Bas

Tomtit [17]

It would be B. Diagonal

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4 years ago

6.4f 24 water bottles weigh 30 pounds, how much would a shipment of 150 water bottles weigh?

Marizza181 [45]

Answer:

120 pounds

Step-by-step explanation:

24÷30 =0.8

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7 0

2 years ago

How to solve this trig

n200080 [17]

Hi there!

To find the Trigonometric Equation, we have to isolate sin, cos, tan, etc. We are also given the interval [0,2π).

First Question

What we have to do is to isolate cos first.

$\displaystyle \large{ cos \theta = - \frac{1}{2} }$

Then find the reference angle. As we know cos(π/3) equals 1/2. Therefore π/3 is our reference angle.

Since we know that cos is negative in Q2 and Q3. We will be using π + (ref. angle) for Q3. and π - (ref. angle) for Q2.

Find Q2

$\displaystyle \large{ \pi - \frac{ \pi}{3} = \frac{3 \pi}{3} - \frac{ \pi}{3} } \\ \displaystyle \large \boxed{ \frac{2 \pi}{3} }$

Find Q3

$\displaystyle \large{ \pi + \frac{ \pi}{3} = \frac{3 \pi}{3} + \frac{ \pi}{3} } \\ \displaystyle \large \boxed{ \frac{4 \pi}{3} }$

Both values are apart of the interval. Hence,

$\displaystyle \large \boxed{ \theta = \frac{2 \pi}{3} , \frac{4 \pi}{3} }$

Second Question

Isolate sin(4 theta).

$\displaystyle \large{sin 4 \theta = - \frac{1}{ \sqrt{2} } }$

Rationalize the denominator.

$\displaystyle \large{sin4 \theta = - \frac{ \sqrt{2} }{2} }$

The problem here is 4 beside theta. What we are going to do is to expand the interval.

$\displaystyle \large{0 \leqslant \theta < 2 \pi}$

Multiply whole by 4.

$\displaystyle \large{0 \times 4 \leqslant \theta \times 4 < 2 \pi \times 4} \\ \displaystyle \large \boxed{0 \leqslant 4 \theta < 8 \pi}$

Then find the reference angle.

We know that sin(π/4) = √2/2. Hence π/4 is our reference angle.

sin is negative in Q3 and Q4. We use π + (ref. angle) for Q3 and 2π - (ref. angle for Q4.)

Find Q3

$\displaystyle \large{ \pi + \frac{ \pi}{4} = \frac{ 4 \pi}{4} + \frac{ \pi}{4} } \\ \displaystyle \large \boxed{ \frac{5 \pi}{4} }$

Find Q4

$\displaystyle \large{2 \pi - \frac{ \pi}{4} = \frac{8 \pi}{4} - \frac{ \pi}{4} } \\ \displaystyle \large \boxed{ \frac{7 \pi}{4} }$

Both values are in [0,2π). However, we exceed our interval to < 8π.

We will be using these following:-

$\displaystyle \large{ \theta + 2 \pi k = \theta \: \: \: \: \: \sf{(k \: \: is \: \: integer)}}$

Hence:-

For Q3

$\displaystyle \large{ \frac{5 \pi}{4} + 2 \pi = \frac{13 \pi}{4} } \\ \displaystyle \large{ \frac{5 \pi}{4} + 4\pi = \frac{21 \pi}{4} } \\ \displaystyle \large{ \frac{5 \pi}{4} + 6\pi = \frac{29 \pi}{4} }$

We cannot use any further k-values (or k cannot be 4 or higher) because it'd be +8π and not in the interval.

For Q4

$\displaystyle \large{ \frac{ 7 \pi}{4} + 2 \pi = \frac{15 \pi}{4} } \\ \displaystyle \large{ \frac{ 7 \pi}{4} + 4 \pi = \frac{23\pi}{4} } \\ \displaystyle \large{ \frac{ 7 \pi}{4} + 6 \pi = \frac{31 \pi}{4} }$

Therefore:-

$\displaystyle \large{4 \theta = \frac{5 \pi}{4} , \frac{7 \pi}{4} , \frac{13\pi}{4} , \frac{21\pi}{4} , \frac{29\pi}{4}, \frac{15 \pi}{4} , \frac{23\pi}{4} , \frac{31\pi}{4} }$

Then we divide all these values by 4.

$\displaystyle \large \boxed{\theta = \frac{5 \pi}{16} , \frac{7 \pi}{16} , \frac{13\pi}{16} , \frac{21\pi}{16} , \frac{29\pi}{16}, \frac{15 \pi}{16} , \frac{23\pi}{16} , \frac{31\pi}{16} }$

Let me know if you have any questions!

3 0

3 years ago

Quadrilateral RPQS is a rectangle. Label the missing measures.

Taya2010 [7]

Answer:

Part 1) $PR=9\ units$

Part 2) $PQ=12\ units$

Part 3) $PS=15\ units$

part 4) $QR=15\ units$

Part 5) $RT=7.5\ units$

Step-by-step explanation:

we know that

In a rectangle opposite sides are parallel and congruent

The measure of each interior angle is 90 degrees

The diagonals are congruent and bisect each other

step 1

Find the length of side PR

we know that

$PR=QS$ ----> by opposite sides

we have

$QS=9\ units$

therefore

$PR=9\ units$

step 2

Find the length of side PQ

we know that

$PQ=RS$ ----> by opposite sides

we have

$RS=12\ units$

therefore

$PQ=12\ units$

step 3

Find the length of diagonal PS

we know that

$PS=2PT$ ---> the diagonals bisect each other

we have

$PT=7.5\ units$ ---> given problem

therefore

$PS=2(7.5)=15\ units$

step 4

Find the length of diagonal QR

we know that

$QR=PS$ ---> the diagonals are congruent

we have

$PS=15\ units$

therefore

$QR=15\ units$

step 5

Find the length of RT

we know that

$QR=2RT$ ---> the diagonals bisect each other

we have

$QR=15\ units$

substitute

$15=2RT\\RT=7.5\ units$

7 0

3 years ago

Find lim h->0 f(9+h)-f(9)/h if f(x)=x^4 a. 23 b. -2916 c. 2916 d. 2925

Svetach [21]

$\displaystyle\lim_{h\to0}\frac{f(9+h)-f(9)}h = \lim_{h\to0}\frac{(9+h)^4-9^4}h$

Carry out the binomial expansion in the numerator:

$(9+h)^4 = 9^4+4\times9^3h+6\times9^2h^2+4\times9h^3+h^4$

Then the 9⁴ terms cancel each other, so in the limit we have

$\displaystyle \lim_{h\to0}\frac{4\times9^3h+6\times9^2h^2+4\times9h^3+h^4}h$

Since h is approaching 0, that means h ≠ 0, so we can cancel the common factor of h in both numerator and denominator:

$\displaystyle \lim_{h\to0}(4\times9^3+6\times9^2h+4\times9h^2+h^3)$

Then when h converges to 0, each remaining term containing h goes to 0, leaving you with

$\displaystyle\lim_{h\to0}\frac{f(9+h)-f(9)}h = 4\times9^3 = \boxed{2916}$

or choice C.

Alternatively, you can recognize the given limit as the derivative of f(x) at x = 9:

$f'(x) = \displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h \implies f'(9) = \lim_{h\to0}\frac{f(9+h)-f(9)}h$

We have f(x) = x ⁴, so f '(x) = 4x ³, and evaluating this at x = 9 gives the same result, 2916.

8 0

3 years ago