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Slav-nsk [51]
3 years ago
7

2. Apples cost $0.99 per pound. Aaliyah has a

Mathematics
1 answer:
UkoKoshka [18]3 years ago
4 0

Answer:

a= about 2.7 pounds of apples

Step-by-step explanation:

2.14=0.99a-0.50

2.64=0.99a

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Find a solution to the following system of equations.<br><br> −2x + y = −3<br> −x + 2y = 3
exis [7]
Multiply the first equation by -2 to give 

4x - 2y = 6
-x + 2y = 3     Adding:-
3x = 9
x = 3
Plug x = 3 into second equation:-
-3 + 2y = 3
2y = 6
y = 3


Answer is x=3, y = 3
5 0
3 years ago
Read 2 more answers
Hii! I need some help, would anyone mind helping me?
Kisachek [45]

Step-by-step explanation:

{x}^{2}  - 14x  - 25 {y}^{2}  + 100y = 76

Factor by grouping,

( {x}^{2}  - 14x)   - (25 {y}^{2}  - 100y) = 76

Complete the square, with the x variables,

( {x}^{2}  - 14x + 49)  - (25 {y}^{2}  - 100y) = 125

Factor out 25 for the y variables

( {x}^{2}  - 14x + 49) - 25( {y}^{2}  - 4y) = 125

Complete the square

( {x}^{2}  - 14x + 49) - 25( {y}^{2}  - 4y + 4) = 25

Simplify the perfect square trinomial

(x - 7) {}^{2}  - 25(y - 2) {}^{2}  = 25

Make the right side be 1 so divide everything by 25.

\frac{(x - 7) {}^{2} }{25}  -  (y - 2) {}^{2}  = 1

Here our center is (7,2).

8 0
2 years ago
Urgent!! Will mark brainliest!!
anastassius [24]

Answer:

1) tanФ = 0.8392 ⇒ 2nd answer

2) cosФ = 20/29 ⇒ 3rd answer

3) cosФ = -√2/2 , cotФ = -1 ⇒ first answer

Step-by-step explanation:

* At first check the quadrant of the angle

∵ 180° < Ф < 270°

∴ Ф lies on the third quadrant

* Remember in the 3rd quadrant tanФ and cotФ only positive

∵ sinФ ≅ -0.7660

∵ tan²Ф = sec²Ф - 1

∵ secФ = 1/sinФ

∵ secФ = 1/-0.7660

∴ sec²Ф = (1/-0.7660)²

* Substitute this value in the equation

∴ tan²Ф = (1/-0.7660)² - 1 = 0.70428594 ⇒ take √ for both sides

∴ tanФ ≅ ± 0.8392

∵ Ф lies on the 3rd quadrant

∴ tanФ = 0.8392

* At first check the quadrant of the angle

∵ 0° < Ф < 90°

∴ Ф lies on the first quadrant

* Remember in the 1st quadrant all are positive

∵ sinФ = 21/29

∵ sin²Ф + cos²Ф = 1

∴ (21/29)² + cos²Ф = 1 ⇒ subtract (21/29)² from both sides

∴ cos²Ф = 1 - (21/29)² = 400/841 ⇒ take √ in both sides

∴ cosФ = ± 20/29

* Because Ф lies in the 1st quadrant

∴ cosФ = 20/29

* Remember that when the point is at the terminal side of angle Ф

∴ Its x-coordinate is cosФ

∴ Its y-coordinate is sinФ

* The point is (-√2/2 , √2/2)

∵ x-coordinate is negative ad y-coordinate is positive

∴ the point is on the 2nd quadrant

∴ 90° < Ф < 180°

∴ The values of sinФ and cscФ only positive

* From previous we know that:

∴ cosФ = -√2/2

∴ sinФ = √2/2

∵ cotФ = cosФ/sinФ

∴ cotФ = -√2/2 ÷ √2/2 = -√2/2 × 2/√2 = -√2/√2 = -1

* cosФ = -√2/2 , cotФ = -1

3 0
3 years ago
What is the average (arithmetic mean) of the first 90 measurements in a certain list of 92 measurements? (1) the average of the
marishachu [46]
The sum of all the measurements is just the average times the number.

\bar x = \frac{1}{n} \sum_{i=1}^n x_i

\sum_{i=1}^n x_i = n \bar x

So if the average of all 92 is 7 the sum of those is 92 \times 7

The average of the last two is 7.2 so their sum is 2 \times 7.2

That means the sum of the first 90 is 92 \times 7 - 2 \times 7.2

so the average of the first 90 is

 \dfrac{92 \times 7 - 2 \times 7.2}{90} = 6.99556 cm



7 0
3 years ago
A pizza pan is removed at 9:00 PM from an oven whose temperature is fixed at 450°F into a room that is a constant 70°F. After 5​
gladu [14]

Answer:

A) It will get to a temperature of 125°F at 9:19 PM

B) It will get to a temperature of 150°F at 9:16 PM

C) as time passes temperature approaches the initial temperature of 450°F

Step-by-step explanation:

We are given;

Initial temperature; T_i = 450°F

Room temperature; T_r = 70°F

From Newton's law of cooling, temperature after time (t) is given as;

T(t) = T_r + (T_i - T_r)e^(-kt)

Where k is cooling rate and t is time after the initial temperature.

Now, we are told that After 5​ minutes, the temperature is 300°F.

Thus;

300 = 70 + (450 - 70)e^(-5k)

300 - 70 = 380e^(-5k)

230/380 = e^(-5k)

e^(-5k) = 0.6053

-5k = In 0.6053

-5k = -0.502

k = 0.502/5

k = 0.1004 /min

A) Thus, at temperature of 125°F, we can find the time from;

125 = 70 + (450 - 70)e^(-0.1004t)

125 - 70 = 380e^(-0.1004t)

55/380 = e^(-0.1004t)

In (55/380) = -0.1004t

-0.1004t = -1.9328

t = 1.9328/0.1018

t ≈ 19 minutes

Thus, it will get to a temperature of 125°F at 9:19 PM

B) Thus, at temperature of 150°F, we can find the time from;

150 = 70 + (450 - 70)e^(-0.1004t)

150 - 70 = 380e^(-0.1004t)

80/380 = e^(-0.1004t)

In (80/380) = -0.1004t

-0.1004t = -1.5581

t = 1.5581/0.1004

t ≈ 16 minutes.

Thus, it will get to a temperature of 150°F at 9:16 PM

C) As time passes which means as it approaches to infinity, it means that e^(-kt) gets to 1.

Thus,we have;

T(t) = T_r + (T_i - T_r)

T_r will cancel out to give;

T(t) = T_i

Thus, as time passes temperature approaches the initial temperature of 450°F

6 0
3 years ago
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