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mafiozo [28]
2 years ago
6

Are these expressions equivalent? Explain why or why not. 42 + 35 7(6 + 5)

Mathematics
2 answers:
cricket20 [7]2 years ago
8 0
You use pemdas and they both equal to 77. So yes they are equivalent.
snow_tiger [21]2 years ago
5 0

Yes, the expressions are equivalent. If you sum 42 + 35, you get 77. If you simplify 7(6 + 5), you also get 77

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Find all points of intersection of the given curves. (Assume 0 ≤ θ ≤ 2π and r ≥ 0. Order your answers from smallest to largest θ
DerKrebs [107]

Answer:

∅1=15°,∅2=75°,∅3=105°,∅4=165°,∅5=195°,∅6=255°,∅7=285°,

∅8=345°

Step-by-step explanation:

Data

r = 8 sin(2θ), r = 4 and r=4

iqualiting; 8.sin(2∅)=4; sin(2∅)=1/2, 2∅=asin(1/2), 2∅=30°, ∅=15°

according the graph 2, the cut points are:

I quadrant:

0+15° = 15°

90°-15°=75°

II quadrant:

90°+15°=105°

180°-15°=165°

III quadrant:

180°+15°=195°

270°-15°=255°

IV quadrant:

270°+15°=285°

360°-15°=345°

No intersection whit the pole (0)

7 0
2 years ago
Find the GCF of the expression.<br> 3a²+9<br> A. 3<br> B. a<br> C. a+3<br> D. 3a
elixir [45]

Answer:

3

Step-by-step explanation:

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4 0
1 year ago
Read 2 more answers
Ramona's backyard is fenced and represented by parallelogram YARD with measures in meters. She installed a 12-meters fence to se
Alisiya [41]
The fencing line x is the height of a rectangle triangle of base = y, hypothenuse of 9 m, so we use Pythagoras theorem to solve:

hyp^2 = height^2 + base^2
9^2 = x^2 + y^2
x^2 = 81 - y^2


we can see that x is also the height of another rectangle triangle of base = 15 - y, hypothenuse of 12 m, so we use Pythagoras theorem to solve:
hyp^2 = height^2 + base^2
12^2 = x^2 + (15 - y)^2

lets expand:
144 = x^2 + 225 - 30y + y^2

substitute x^2 from the first equation in the last:
144 = 81 - y^2 + 225 - 30y + y^2
144 = 81 + 225 - 30y
30y = -144 + 81 + 225
y = 5.4 m

substitute in the fence equation:
x^2 = 81 - y^2
x^2 = 81 - 5.4^2
x = 7.2 m that is the length of the fence



3 0
2 years ago
Melinda works at a cafe. Each day that she works, she records x, the total dollar amount of her customers’ bills and then y, her
Anna35 [415]

Answer:

$26

Step-by-step explanation:

In the picture attached, the table, the plot and the line of best fit are shown. There we can see the next equation:

y = 0.177x + 25.936

where x is the total dollar amount of her customers’ bills and then y is her total daily wages.

This means that even if she serves no customers (x = 0) she will earn $26  ($25.936 rounded to the nearest dollar)  for each day of work.

5 0
2 years ago
Milton spilled some ink on his homework paper. He can't read the coefficient of $x$, but he knows that the equation has two dist
Lera25 [3.4K]

Answer:

Sum = -81

Step-by-step explanation:

See the comment for complete question.

Given

c = 36 ----- Constant

No coefficient of x^2

Required:

Determine the sum of all distinct positive integers of the coefficient of x

Reading through the complete question, we can see that the question has 3 terms which are:

x^2 ---- with no coefficient

x ---- with an unknown coefficient

36 ---- constant

So, the equation can be represented as:

x^2 + ax + 36 = 0

Where a is the unknown coefficient

From the question, we understand that the equation has two negative integer solution. This can be represented as:

x = -\alpha and x = -\beta

Using the above roots, the equation can be represented as:

(x + \alpha)(x + \beta) = 0

Open brackets

x^2 + (\alpha + \beta)x + \alpha \beta = 0

To compare the above equation to x^2 + ax + 36 = 0, we have:

a = \alpha + \beta

\alpha \beta = 36

Where: \alpha, \beta and \alpha \ne \beta

The values of \alpha and \beta that satisfy \alpha \beta = 36 are:

\alpha = -1 and \beta = -36

\alpha = -2 and \beta = -18

\alpha = -3 and \beta = -12

\alpha = -4 and \beta = -9

So, the possible values of a are:

a = \alpha + \beta

When \alpha = -1 and \beta = -36

a = -1 - 36 = -37

When \alpha = -2 and \beta = -18

a = -2 - 18 = -20

When \alpha = -3 and \beta = -12

a = -3 - 12 = -15

When \alpha = -4 and \beta = -9

a = -4 - 9 = -13

At this point, we have established that the possible values of a are: -37, -20, -15 and -9.

The required sum is:

Sum = -37 -20 -15 - 9

Sum = -81

7 0
2 years ago
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