7. A shopkeeper sold a pen set for 180 at a profit of 30. To make a profit of 26%, what should be the selling price of the pen set? 1otor​

Step-by-step explanation:

[tex]6 \cos {}^{2} (x) + 4 \sin {}^{2} (x) = 5[/tex]

[tex]6(1 - sin {}^{2} x) + 4 \sin {}^{2} (x) = 5[/tex]

[tex]6 - 6 \sin {}^{2} (x) + 4 \sin {}^{2} (x) = 5[/tex]

[tex]6 - 2 \sin { }^{2} (x) = 5[/tex]

[tex] - 2 \sin {}^{2} (x) = - 1[/tex]

[tex] \sin {}^{2} (x) = \frac{1}{2} [/tex]

[tex] \sin(x) = \frac{1}{ \sqrt{2} } [/tex]

Take the arc Sine of the function

[tex]arcsin( \frac{1}{ \sqrt{2} } ) = \frac{\pi}{4} [/tex]

Finally, Sine is a periodic function so it has two answers within the interval (0, 2 pi)

Use the identity

[tex] \sin(x) = \sin(x + \pi) [/tex]

We know that

[tex] \sin( \frac{\pi}{4} ) = \frac{1}{ \sqrt{2} } [/tex]

so using the identity

[tex] \sin( \frac{\pi}{4} + \pi ) = \sin( \frac{5\pi}{4} ) [/tex]

So we have two answers.

[tex]( \frac{\pi}{4} )[/tex]

[tex]( \frac{5\pi}{4} )[/tex]

x = -7

hope this helps!

Answer:

it is reduction so the answer is B.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Use the formula rise/run. The rise, in this case, was 3 and the run was 1. There for it would be 3/1 which is simplified to 3.

Answer:

0.007

Step-by-step explanation:

0's before other numbers are non-significant. Then you just round your number.

Hope that helps

Answer:

75

Step-by-step explanation:

First divide 2/5 to get 0.4. Then divide 30 by 0.4 to get the answer. A simple way to think about it is how many 0.4 grams are in 30 gram tube.

Answer: See below

Step-by-step explanation:

Isolate x for x-2y+2z=9

3x=9+2y

[tex]x=\frac{9+2y}{3}[/tex]....(1)

Substitute (1) into the 2nd equation

[tex]\begin{bmatrix}-\frac{9+2y}{3}+3y=-4\\ 2\cdot \frac{9+2y}{3}-5y+3z=16\end{bmatrix}[/tex]

[tex]\frac{3\left(-9+7y\right)}{3}=3\left(-4\right)[/tex]

7y=-3

y=-3/7

Substitute y=-3/7

[tex]\begin{bmatrix}3z+\frac{18-11\left(-\frac{3}{7}\right)}{3}=16\end{bmatrix}[/tex]

[tex]\begin{bmatrix}3z+\frac{53}{7}=16\end{bmatrix}[/tex]

Isolate z by substituting it

[tex]3z+\frac{53}{7}=16[/tex]

[tex]\frac{3z}{3}=\frac{\frac{59}{7}}{3}[/tex]

[tex]z=\frac{59}{21}[/tex]

For x =9+2y/3 substitute z=59/21 and y=-3/7

[tex]x=\frac{9+2\left(-\frac{3}{7}\right)}{3}[/tex]

[tex]x=\frac{19}{7}[/tex]

[tex]x=\frac{19}{7},\:z=\frac{59}{21},\:y=-\frac{3}{7}[/tex]

Answer:

(1, - 1, 3 )

Step-by-step explanation:

x - 2y + 2z = 9 → (1)

- x + 3y = - 4 → (2)

2x - 5y + 3z = 16 → (3)

Add (1) and (2) term by term to eliminate x

y + 2z = 5 → (4)

Multiply (2) by 2

- 2x + 6y = - 8 → (5)

Add (3) and (5) term by term to eliminate x

y + 3z = 8 → (6)

Subtract (6) from (4) term by term to eliminate y

- z = - 3 ( multiply both sides by - 1 )

z = 3

Substitute z = 3 into (4)

y + 2(3) = 5

y + 6 = 5 ( subtract 6 from both sides )

y = - 1

Substitute y = - 1, z = 3 into (1) and solve for x

x - 2(- 1) + 2(3) = 9

x + 2 + 6 = 9

x + 8 = 9 ( subtract 8 from both sides )

x = 1

solution is (1, - 1, 3 )

The geometric series that converges from the listed option is [tex]1+\frac{1}{2} + \frac{1}{4} +\frac{1}{8} ,...[/tex] Option B is correct.

The nth term of a geometric sequence is expressed as;

[tex]a_n=ar^{n-1}[/tex]

For a geometric sequence to converge, the modulus of its common ratio must be less than 1 (|r| < 1), otherwise, it diverges.

For the first series given as [tex]\frac{1}{81} + \frac{1}{27} +\frac{1}{9} +\frac{1}{3}+ ,...[/tex]

[tex]r = \frac{1}{27} \div \frac{1}{81}\\r=\frac{1}{27} \times 81\\r=\frac{81}{27} \\r=3 > 1[/tex]

Since the common ratio of the sequence is greater than 1, hence the series diverges.

For the series [tex]1+\frac{1}{2} + \frac{1}{4} +\frac{1}{8} ,...[/tex]

[tex]r=\frac{1/2}{1} =\frac{1/4}{1/2} = \frac{1}{2}[/tex]

Since the common ratio of the sequence is less than 1, hence the series converges.

Learn more on convergence of series here: https://brainly.com/question/14294471

Answer:

3x²-4

Step-by-step explanation:

1 distribute

(-4x²-2x-6)+7x²+2x+2

2 eliminate redudant parentheses

-4x² -2x - 6+7x² +2x+2

3 Add the numbers

-4x²-2x-4+7x²+2x

4 Combine like terms

3x²-2x-4+2x

5 Combine like terms

3x²-4

Answer:

[tex]3x^{2} -4[/tex]

Step-by-step explanation:

Before solving this you have to know that,

( - ) × ( - ) = ( + )

( + ) × ( + ) = ( + )

( - ) × ( + ) = ( - )

Let us solve now.

[tex](-4x^2-2x-6)-(-7x^2-2x-2)[/tex]

[tex](-4x^2-2x-6)+7x^{2} +2x+2[/tex]

[tex]-4x^2-2x-6+7x^{2} +2x+2[/tex]

Now combine like terms

[tex]-4x^{2}+7x^{2} -2x+2x-6+2[/tex]

[tex]3x^{2} -4[/tex]

Hope this helps you .

Let me know if you have any other questions :-)

[tex]\huge \bf༆ Answer ༄[/tex]

Let's solve this using unitary method ~

Therefore , the ostrich will run 105 meters in 5 seconds.

Answer: c

Step-by-step explanation:

Answer: x = 14/23

Step-by-step explanation:

3x-6=4(2-3x)-8x

3x-6=8-12x-8x --> Expand 4(2-3x)

3x-6=8-20x --> Collect like terms

3x-6+6=8-20x+6 --> Add 6 to both sides, to remove it from the right side

3x=-20x+14

3x+20x=-20x+14+20x --> Add 20x to both sides, to remove it from the left side

23x=14

[tex]\frac{23x}{23}=\frac{14}{23}[/tex] --> Divide both sides by 23

x = 14/23

Answer: Friday, 1.25 more per hour

Step-by-step explanation: if we take the inches it snowed and divide it by the hours, we get the rate of snowfall for one hour. 15/6=2.5 and 30/8=3.75

To get how much more we take the bigger snowfall per hour minus the smaller snowfall per hour 3.75-2.5=1.25

Rectangular Poster:

Length = 9

Width = 3

Rectangular Banner:

Length = 10

Width = 2

Hope this is helpful!

Answer:

50%

Step-by-step explanation:

Step-by-step explanation:

x = 2/5 or x = 0 Hope that will help

Step-by-step explanation:

please mark me as brainlest

Answer:

Below in bold.

Step-by-step explanation:

g(12) = √12 + 4

so f(g(12))

= 3(√12 + 4) + 5(√12 + 4)

=  8(√12 + 4)

= 59.71 to nearest hundredth.

Answer:

y^6 z^12

Step-by-step explanation:

When the bases are the same that means that the powers on the inside can be multiplied by whatever is outside.

Hope this helps :)

Answer:

Step-by-step explanation:

1) The slope of line with the coordinate points (10, 7) and (1, 2) is [tex]\frac{5}{9}[/tex].

2) The slope of line with the coordinate points (9, 9) and (1, 16) is [tex]-\frac{7}{8}[/tex].

3) The slope of line with the coordinate points (9, 3) and (2, 1) is [tex]\frac{2}{7}[/tex].

4) The slope of line with the coordinate points (8, 8) and (1, 2) is [tex]\frac{6}{7}[/tex].

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]

From the given table, we have

1) The coordinate points are (10, 7) and (1, 2)

Here, slope [tex]=\frac{(2-7)}{(1-10)}[/tex]

[tex]=\frac{5}{9}[/tex]

2) The coordinate points are (9, 9) and (1, 16)

Here, slope [tex]=\frac{(16-9)}{(1-9)}[/tex]

[tex]=-\frac{7}{8}[/tex]

3) The coordinate points are (9, 3) and (2, 1)

Here, slope [tex]=\frac{(1-3)}{(2-9)}[/tex]

[tex]=\frac{2}{7}[/tex]

4) The coordinate points are (8, 8) and (1, 2)

Here, slope [tex]=\frac{(2-8)}{(1-8)}[/tex]

[tex]=\frac{6}{7}[/tex]

Therefore,

1) The slope of line with the coordinate points (10, 7) and (1, 2) is [tex]\frac{5}{9}[/tex].

2) The slope of line with the coordinate points (9, 9) and (1, 16) is [tex]-\frac{7}{8}[/tex].

3) The slope of line with the coordinate points (9, 3) and (2, 1) is [tex]\frac{2}{7}[/tex].

4) The slope of line with the coordinate points (8, 8) and (1, 2) is [tex]\frac{6}{7}[/tex].

To learn more about the slope of a line visit:

https://brainly.com/question/14511992.

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Answer:

Breeders cross animals of the same species with desirable traits to create desirable offspring.

Step-by-step explanation:

Answer:

I=2t

Step-by-step explanation:

ivan has 2 times t

Answer:

Christmas How many pouds this proportion to solve

Answer:

(12 x 12) - 44 = 100

Step-by-step explanation:

Answer:

Check the picture below

Step-by-step explanation: