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3 years ago

Calculate the distance between the points P=(-1, -1) and L=(6, -9) in the coordinate plane.

Mathematics

1 answer:

Over [174]3 years ago

6 0

Answer:

≈ 10.63

Step-by-step explanation:

Calculate the distance d using the distance formula

d = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = P(- 1, - 1) and (x₂, y₂ ) = L(6, - 9)

d = $\sqrt{(6-(-1))^2+(-9-(-1))^2}$

= $\sqrt{(6+1)^2+(-9+1)^2}$

= $\sqrt{7^2+(-8)^2}$

= $\sqrt{49+64}$

= $\sqrt{113}$ ≈ 10.63 ( to the nearest hundredth )

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7a-4b=2b-5a solve for a

uysha [10]

Step-by-step explanation:

7a - 4b = 2b - 5a

7a + 5a = 2b + 4b

12a = 6b

a = 6b/12

a = b/2

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3 years ago

A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 12, length of BC is 11.5. A similar right trian

expeople1 [14]

Answer:

Option D is correct.

Length of PQ is 36 unit.

Explanation:

If the measures of two sides in one triangle are proportional to the corresponding sides in the another triangle and their including angles are congruent, then the triangles are similar.

Given: Right angle triangle ABC at B , Length of AB = 12 unit and length of BC = 11.5 unit and in right angle triangle PQR at Q , length of QR = 34.5 unit.

Also it is given that Angle A is congruent to angle P and angle C is congruent to angle R.

To find the length of QR:

It is given that ΔABC and ΔPQR are Similar triangle

then, by the definition of similar triangle:

$\frac{PQ}{AB} = \frac{QR}{BC}$

Substitute the value of AB, QR and BC to solve for PQ;

$\frac{PQ}{12}=\frac{34.5}{11.5}$ or

$PQ = \frac{34.5 \times 12}{11.5}$

On simplify:

$PQ = 3 \times 12 = 36$

Therefore, the length of side PQ is 36 units.

8 0

3 years ago

Read 2 more answers

Solve the system of inequalities and indicate all the integers which are in the solution set:

elena-s [515]

1.) a>10
2.) a<3.5
How I got it: 1.) Subtract 3 from both sides, leaving -2a<10.
2.) Divide by -2 from both sides, remember to flip the inequality sign when dealing with negatives. This leaves you with a>10.
For number 2.) I divided both sides by 5, leaving a<3.5, though this answer may be wrong.

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3 years ago

Please help me with this question.

Rufina [12.5K]

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3 0

3 years ago

After breaking your penny bank, you notice that you have $4.87 in quarters ($0.25), dimes ($0.10), nickels ($0.05), and pennies

ira [324]

Answer: Option 'c' is correct.

Step-by-step explanation:

Let the number of dimes be 'x'.

Let the number of nickels be ' $\dfrac{3}{2}x$ '.

Let the number of pennies be $\dfrac{3}{2}\times 2x=3x$

Let the number of quarters be '3x-34'.

As we know that

1 quarter = $0.25

1 dime = $0.10

1 nickel = $0.05

1 penny = $0.01

According to question, we get that

$0.10x+0.05\times \dfrac{3x}{2}+0.01\times 3x+0.25(3x-34)=4.87\\\\0.10x+0.075x+0.03x+0.75x-8.5=4.87\\\\\\0.955x=4.87+8.5\\\\0.955x=13.37\\\\x=\dfrac{13.37}{0.955}\\\\x=14$

So, the number of pennies is given by

$3x=3\times 14=42$

Hence, Option 'c' is correct.

3 0

3 years ago