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Alecsey [184]
2 years ago
14

The equations -6x + 3y = 6 and x² + y = 10 intersect at the

Mathematics
1 answer:
eimsori [14]2 years ago
5 0

The values of the letters in coordinates (a, b) and (c,d) are;

<u><em>a = -4</em></u>

<u><em>b = -6</em></u>

<u><em>c = 2</em></u>

<u><em>d = 6</em></u>

<u><em /></u>

We are given two equations;

-6x + 3y = 6  ---(eq 1)

x² + y = 10 ---(eq 2)

  • We are told that they intersect at coordinates; (a, b) and (c, d).

Let us make y the subject in eq 2 to get;

y = 10 - x²  --(eq 3)

  • Let us put 10 - x² into eq 1 to get;

-6x + 3(10 - x²) = 6

expanding further gives;

-6x + 30 - 3x² = 6

rearranging gives;

3x² + 6x - 24 = 0

Using online quadratic equation <em>solver</em>, we have;

x = -4 and x = 2

Putting x = -4 into eq 3 gives;

y = 10 - (-4)²

y = 10 - 16

y = -6

Putting x = 2 into eq 3 gives;

y = 10 - (2)²

y = 10 - 4

y = 6

  • Thus, the coordinates are; (-4, -6) and (2, 6)

Comparing with (a, b) and (c,d), we have;

a = -4

b = -6

c = 2

d = 6

Read more at; brainly.com/question/15165519

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Answer:

No trees and just buildings.

Step-by-step explanation:

In the future, it is most likely to have some tall, bulky buildings.

Some scientists say that the future will be more about buildings and work spaces and less about trees.

So it is MORE likely for the future to have at least... 20 trees in the park. Also, less land. The land will be used to build buildings.

7 0
3 years ago
Simplify. 54+4(3/4−1/2)2
Effectus [21]

Answer:

56

Step-by-step explanation:

54 + 4(3/4 − 1/2)2

=> 54 + 4(1/4)2

=> 54 + (1)2

=> 54 + 2

=> 56

Therefore, 56 is our answer.

Hoped this helped.

7 0
3 years ago
Martin deposits $700 into a savings account that gains interest at a rate of 5.5% annually. If he waits 7 years to withdraw the
Travka [436]

。☆✼★ ━━━━━━━━━━━━━━  ☾  

Use the multiplier 1.055

final = original x multiplier^n

where 'n' is the number of years

Sub the values in

final = 700 x 1.055^7

final = 1018.27

Subtract the values:

1018.27 - 700 = 318.27

Thus, he earns more than $275

He earns $43.27 more

Have A Nice Day ❤    

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4 0
3 years ago
Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity. In the given triangle ABC, angle A
lana66690 [7]

The relationship between the lengths of the sides of a right triangle are

given by Pythagoras theorem.

  • Part A: <u>ΔABC is similar to ΔADC</u>
  • Part B: ΔABC and ΔADC are similar according <u>AA similarity postulate</u>
  • Part C: <u>DA = 6</u>

Reasons:

Part A:

∠A = 90°

Segment AD ⊥ Segment BC

Location of point D = Side BC

Part A: In triangle ΔABC, we have;

∠A = 90°, ∠B = 90° - ∠C

In triangle ΔADC, we have;

∠ADC = 90°, ∠DAC = 90° - ∠C

∴ <u>ΔABC is similar to ΔADC</u> by Angle-Angle, AA, Similarity Postulate

Part B: The triangles are similar according to <u>AA similarity postulate</u>,

because two angles in one triangle are equal to two angles in the other

triangle and therefore, by subtraction property of equality, the third angle

in both triangles are also equal.

Part C: The length of DB = 9

The length of DC = 4

Required: Length of segment DA

In triangle ΔABD, we have;

∠BDA = 90°= ∠ADC

∠DAC ≅ ∠B by Congruent Parts of Congruent Triangles are Congruent

Therefore;

ΔABD ~ ΔADC by AA similarity, which gives;

\displaystyle \frac{\overline{DA}}{\overline{DC}}  = \frac{\overline{BD}}{\overline{DA}}

\overline{DA}^2 = \overline{DC} \times \overline{BD}

Which gives;

\overline{DA}^2 = 4 × 9 = 36

\overline{DA} = √(36) = 6

\overline{DA}<u> = 6</u>

Learn more here:

brainly.com/question/2269451

3 0
2 years ago
What is the derivative of w=(t^2+1)^100<br><br> How is it 200t(t^2+1)^99?
GuDViN [60]
(t^2+1)^100

USE CHAIN RULE

Outside first (using power rule)

100*(t^2+1)^99 * derivative of the inside

100(t^2+1)^99 * d(t^2+1)

100(t^2+1)^99 * 2t

200t(t^2+1)^99
6 0
3 years ago
Read 2 more answers
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