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3 years ago

What is the value of this expression? 27+4×(8−4) Enter your answer in the box.

Mathematics

1 answer:

marta [7]3 years ago

3 0

Answer:

43.

Step-by-step explanation:

Follow PEMDAS (Parentheses, exponents, multiply, divide, add, subtract). First you do 8-4 which is 4, then you multiply 4 by 4 which is 16 since you multiply next, then you add 27 to 16 which then gets you to 43.

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Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Ro

Ugo [173]

Answer:

$Side\ B = 6.0$

$\alpha = 56.3$

$\theta = 93.7$

Step-by-step explanation:

Given

Let the three sides be represented with A, B, C

Let the angles be represented with $\alpha, \beta, \theta$

[See Attachment for Triangle]

$A = 10cm$

$C = 12cm$

$\beta = 30$

What the question is to calculate the third length (Side B) and the other 2 angles ( $\alpha\ and\ \theta$ )

Solving for Side B;

When two angles of a triangle are known, the third side is calculated as thus;

$B^2 = A^2 + C^2 - 2ABCos\beta$

Substitute: $A = 10$ , $C =12$ ; $\beta = 30$

$B^2 = 10^2 + 12^2 - 2 * 10 * 12 *Cos30$

$B^2 = 100 + 144 - 240*0.86602540378$

$B^2 = 100 + 144 - 207.846096907$

$B^2 = 36.153903093$

Take Square root of both sides

$\sqrt{B^2} = \sqrt{36.153903093}$

$B = \sqrt{36.153903093}$

$B = 6.0128115797$

$B = 6.0$ (Approximated)

Calculating Angle $\alpha$

$A^2 = B^2 + C^2 - 2BCCos\alpha$

Substitute: $A = 10$ , $C =12$ ; $B = 6$

$10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

$100 = 180 - 144 *Cos\alpha$

Subtract 180 from both sides

$100 - 180 = 180 - 180 - 144 *Cos\alpha$

$-80 = - 144 *Cos\alpha$

Divide both sides by -144

$\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}$

$\frac{-80}{-144} = Cos\alpha$

$0.5555556 = Cos\alpha$

Take arccos of both sides

$Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)$

$Cos^{-1}(0.5555556) = \alpha$

$56.25098078 = \alpha$

$\alpha = 56.3$ (Approximated)

Calculating $\theta$

Sum of angles in a triangle = 180

Hence;

$\alpha + \beta + \theta = 180$

$30 + 56.3 + \theta = 180$

$86.3 + \theta = 180$

Make $\theta$ the subject of formula

$\theta = 180 - 86.3$

$\theta = 93.7$

5 0

3 years ago

Sarah's craft project uses pieces of yarn that are 1/8 yard long. She has a piece of yarn that is 3 yards long. How many 1/8 yar

Verdich [7]

If she used all of her yarn, she'd have 24 pieces. If she wanted 1.25 left, she'd have ten less because 24 • .125 = 8, and 1/4 of eight = 2, and 2 + 8 = 10.

So she'd have 14 pieces.

5 0

3 years ago

What is the height of the tree show all work

poizon [28]

Answer:

x=32.91

Step-by-step explanation:

Given: Triangle

Find: x

_______

Tan(35°)=x/47

x=tan(35)×47

x=0.7×47

x=32.91

Hope it helps!

3 0

3 years ago

Read 2 more answers

A study has indicated that the sample size necessary to estimate the average electricity use by residential customers of a large

Zanzabum

Answer:

$\sigma=547.1125$

Step-by-step explanation:

-The margin of error is calculated using the formula:

$ME=z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}\\\\$

-We substitute the values, n=900 and ME=30 in the formula to solve for standard deviation:

$ME=z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}\\\\\\30=1.645\times\frac{\sigma}{\sqrt{900}}\\\\\sigma=\frac{30^2}{1.645}\\\\=547.1125$

Hence, the population standard deviation is 547.1125

7 0

4 years ago

Solve the system by elimination. (Please explain how to do it)

Naddika [18.5K]

Apply to Row 2 : Row 2 + Row 1

2x + 2y + 3z = 0

y + 4z = -3

2x + 3y + 3z = 5

Apply to Row 3: Row 3 - Row 1

2x + 2y + 3z = 0

y + 4z = -3

y = 5

Apply to Row 3: Row 3 - Row 2

2x + 2y + 3z = 0

y + 4z = -3

-4z = 8

Simplify rows

2x + 2y + 3z = 0

y + 4z = -3

z = -2

Note that the matrix is in echelon form now. The next steps are for back substitution.

Apply to Row 2: Row 2 - 4 Row 3

2x + 2y + 3z = 0

y = 5

z = -2

Apply to Row 1: Row 1 - 3 Row 3

2x + 2y = 6

y = 5

z = -2

Apply to Row 1: Row 1 - 2 Row 2

2x = -4

y = 5

z = 2

Simplify the rows

x = -2

y = 5

z = -2

3 0

3 years ago