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3 years ago

Write equations for each word problem. You do not need to solve the equations. Make sure to define your variables.

Mathematics

1 answer:

Alenkinab [10]3 years ago

4 0

Answer:

b = quantity of boards purchased

p = quantity of posts purchased

equation: 4b + 6p = 58

Step-by-step explanation:

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Find the measure of AngleJ, the smallest angle in a triangle with sides measuring 11, 13, and 19. Round to the nearest whole deg

Evgen [1.6K]

Answer:

34°

Step-by-step explanation:

The law of cosines is good for finding angles when only sides are known. We'll use the conventional sides a, b, c, and angles A, B, C. Yes, we know the problem statement calls the smallest angle "J". We trust you can make the translation.

a² = b² +c² -2bc·cos(A) . . . . . for sides a, b, c and angle A

Solving for the angle, we get ...

A = arccos((b² +c² -a²)/(2bc))

Filling in the numbers with "a" being the shortest side, we have ...

A = arccos((13² +19² -11²)/(2·13·19)) = arccos(409/494)

A ≈ 34.113°

The smallest angle, ∠J, is about 34°.

8 0

4 years ago

Read 2 more answers

Help please!!!!!!!!!!!!!!

Anika [276]

Answer:

x = 42,33°

Step-by-step explanation:

3x + 1° + 52° = 180° [angles on a straight line]

3x + 53° = 180°

3x = 180° - 53°

3x = 127°

divide both sides by 3

x = 42,33°

4 0

3 years ago

The graph of the function B is shown below. If B(x) = -1, then what is x?

Salsk061 [2.6K]

Answer:

there isnt enough info

Step-by-step explanation:

5 0

4 years ago

If y - 1 = 4x, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs?

abruzzese [7]

Option C

{(0, 1), (1, 5), (2, 9)} represents possible inputs and outputs of the function

Solution:

Given function is:

y -1 = 4x

y = 4x + 1

To find the set which represents possible inputs and outputs of the function. Let's check all the options

<h3>Option A { (1, 4),(2, 8), (3, 12) }</h3>

Let us use the ordered pair (1, 4)

Substitute (x, y) = (1, 4) in given function

4 = 4(1) + 1

4 = 4 + 1

$4\neq 5$

Thus this set is not the required set

<h3>Option B {(4, 1), (8, 2), (12, 3)}</h3>

Let us use the ordered pair (4, 1)

Substitute (x, y) = (4, 1) in given function

1 = 4(4) + 1

1 = 16 + 1

$1\neq 17$

Thus this set is not the required set

<h3>Option C {(0, 1), (1, 5), (2, 9)}</h3>

Let us use the ordered pair (0, 1)

Substitute (x, y) = (0, 1) in given function

1 = 4(0) + 1

1 = 1

Thus this set is the required set represents possible inputs and outputs of the function.

<h3>Option D {(1, 0), (5, 1), (9, 2)}</h3>

Let us use the ordered pair (1, 0)

Substitute (x, y) = (1, 0) in given function

0 = 4(1) + 1

0 = 4 + 1

$0\neq 5$

Thus this set is not the required set

5 0

3 years ago

Each year for 4 years, a farmer increased the number of trees in a certain orchard by of the number of trees in the orchard the

Neko [114]

Answer:

The number of trees at the begging of the 4-year period was 2560.

Step-by-step explanation:

Let’s say that x is number of trees at the begging of the first year, we know that for four years the number of trees were incised by 1/4 of the number of trees of the preceding year, so at the end of the first year the number of trees was $x+\frac{1}{4} x=\frac{5}{4} x$ , and for the next three years we have that

Start End

Second year $\frac{5}{4}x$ -------------- $\frac{5}{4}x+\frac{1}{4}(\frac{5}{4}x) =\frac{5}{4}x+ \frac{5}{16}x=\frac{25}{16}x=(\frac{5}{4} )^{2}x$

Third year $(\frac{5}{4} )^{2}x$ ------------- $(\frac{5}{4})^{2}x+\frac{1}{4}((\frac{5}{4})^{2}x) =(\frac{5}{4})^{2}x+\frac{5^{2} }{4^{3} } x=(\frac{5}{4})^{3}x$

Fourth year $(\frac{5}{4})^{3}x$ -------------- $(\frac{5}{4})^{3}x+\frac{1}{4}((\frac{5}{4})^{3}x) =(\frac{5}{4})^{3}x+\frac{5^{3} }{4^{4} } x=(\frac{5}{4})^{4}x.$

So the formula to calculate the number of trees in the fourth year is

$(\frac{5}{4} )^{4} x,$ we know that all of the trees thrived and there were 6250 at the end of 4 year period, then

$6250=(\frac{5}{4} )^{4}x$ ⇒ $x=\frac{6250*4^{4} }{5^{4} }= \frac{10*5^{4}*4^{4} }{5^{4} }=2560.$

Therefore the number of trees at the begging of the 4-year period was 2560.

7 0

3 years ago