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3 years ago

What is 1/10 (3n+50)=35?

Mathematics

1 answer:

antoniya [11.8K]3 years ago

4 0

Answer:

100

Step-by-step explanation:

1/10(3n+50)=35

3n+50=35*10

3n+50=350

3n=350-50

3n=300

n=300/3

n=100

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Paco buys a total of 15 pencils and markers for $ 11.15. Each pencil costs $ 0.30. Each marker costs $ 1.25

inessss [21]

Answer: Paco bought 7 markers and 8 pencils.

Step-by-step explanation:

Let's define the variables:

P = number of pencils that Paco bought

M = number of markers that Paco bought.

We know that P + M = 15.

We also know that each pencil costs $0.30 and each marker costs $1.25, and the total price for the whole purchase is $11.15

Then:

P*$0.30 + M*$1.25 = $11.15

Then we have the system of equations:

P + M = 15

P*$0.30 + M*$1.25 = $11.15

To solve this, we can start by isolating one of the variables in the first equation, let's isolate P.

P = 15 - M

Now we can replace this in the second equation to get:

(15 - M)*$0.30 + M*$1.25 = $11.15

$4.50 - M*$0.30 + M*$1.25 = $11.15

$4.50 + M*$0.95 = $11.15

M*$0.95 = $11.15 - $4.50 = $6.65

M = $6.65/$0.95 = 7

Then paco bough 7 markers, and we can find the number of pencisl by the equation:

P + M = 15

P = 15 - M = 15 - 7 = 8

Then Paco bought 7 markers and 8 pencils.

4 0

3 years ago

For positive acute angles AA and B,B, it is known that \tan A=\frac{28}{45}tanA= 45 28 and \cos B=\frac{3}{5}.CosB= 5 3 . Fi

MrRa [10]

Answer:

$\cos(A + B) = \frac{23}{265}$

Step-by-step explanation:

Given

$\tan A=\frac{28}{45}$

$\cos B=\frac{3}{5}$

Required

$\cos(A+B)$

In trigonometry:

$\cos(A+B) = \cos\ A\ cosB - sinA\ sinB$

We need to solve for cosA, sinA and sinB

Given that:

$\tan A=\frac{28}{45}$ and the tangent of an angle is a ratio of the opposite side (x) to the adjacent side (y),

So, we have:

$x =28$ and $y = 45$

For this angle A, we need t calculate its hypotenuse (z).

Using Pythagoras,

$z^2 = x^2 + y^2$

$z = \sqrt{x^2 + y^2$

$z = \sqrt{28^2 + 45^2$

$z = \sqrt{2809$

$z = 53$

From here, we can calculate sin and cos A

$\sin A= \frac{opposite}{hypotenuse}$ and $\cos A= \frac{adjacent}{hypotenuse}$

$\sin A= \frac{x}{z}$

$\sin A= \frac{28}{53}$

$\cos A= \frac{y}{z}$

$\cos A= \frac{45}{53}$

To angle B.

Give that

$\cos B=\frac{3}{5}$ and the cosine of an angle is a ratio of the adjacent side (a) to the hypotenuse side (c),

So, we have:

$a = 3$ and $b = 5$

For this angle B, we need to calculate its opposite (b).

Using Pythagoras,

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$5^2 = 3^2 + b^2$

$25 = 9 + b^2$

Collect like terms

$b^2 = 25 - 9$

$b^2 = 16$

$b = \sqrt{16$

$b = 4$

From here, we can calculate sin B

$\sin B= \frac{opposite}{hypotenuse}$

$\sin B = \frac{b}{c}$

$\sin B = \frac{4}{5}$

Recall that:

$\cos(A+B) = \cos\ A\ cosB - sinA\ sinB$

and

$\cos B=\frac{3}{5}$ $\sin B = \frac{4}{5}$ $\sin A= \frac{28}{53}$ $\cos A= \frac{45}{53}$

$\cos(A + B) = \frac{45}{53} * \frac{3}{5} - \frac{28}{53} * \frac{4}{5}$

$\cos(A + B) = \frac{135}{265} - \frac{112}{265}$

$\cos(A + B) = \frac{135-112}{265}$

$\cos(A + B) = \frac{23}{265}$

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A bakery has 245 dozen cupcakes. How many individual cupcakes are there?

balu736 [363]

Answer: 2,940

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3 years ago

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16 quarters and one dime

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3 years ago

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-UIVIT UUNNU INTEREST

Jobisdone [24]

Answer:

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3 years ago

What is 1/10 (3n+50)=35?​

What is 1/10 (3n+50)=35?