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3 years ago

The sum of two numbers is 52. One number is 3 times as large as the other. What are the numbers?

2 answers:

8 0

Let b>a

b+a=52

b=52-a, we are also told that the larger number, b, is 3 times the smaller a:

b=3a, since b=b we can say:

3a=52-a

4a=52

a=13, and since b=3a

b=39

So the numbers are 13 and 39

JulsSmile [24]3 years ago

3 0

Let x be the smaller number.
Then 3x is the larger number.
We also know that the smaller added to the larger is 52, or:
x + 3x = 52
4x =52
x = 13
Therefore the smaller is 13, the larger is 3(13)=39.

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If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all 4 cards are diamonds

diamong [38]

Probability=13/52*12/51*11/50*10/49=11/4165

4 0

3 years ago

Find an equation of the line passing through the pair of points. Write the equation in the form Ax +By = C.

Alexxandr [17]

9514 1404 393

Answer:

5x -y = -37

Step-by-step explanation:

One way to find the coefficients A and B is to use the differences of the x- and y-coordinates:

A = Δy = y2 -y1 = 2 -(-3) = 5

B = -Δx = -(x2 -x1) = -(-7 -(-8)) = -1

Then the constant C can be found using either point.

5x -y = 5(-7) -2 = -37

The equation of the line is ...

5x -y = -37

_____

Additional comment

This approach comes from the fact that the slope of a line is the same everywhere.

$\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{\Delta y}{\Delta x}\\\\\Delta x(y-y_1)=\Delta y(x-x_1)\qquad\text{cross multiply}\\\\\Delta y(x-x_1)-\Delta x(y-y_1)=0\qquad\text{subtract y term}\\\\\Delta y(x) -\Delta x(y) = \Delta y(x_1)-\Delta x(y_1)\qquad\text{Ax+By=C form}$

The "standard form" requires that A be positive, so we chose point 1 and point 2 to make sure that was the case.

5 0

2 years ago

A triangle has angles measuring 15° and 45°. What is the measurement of the triangle’s third angle?

nexus9112 [7]

First you need to know that the internal angles of a triangle always equals 180°. Therefore:

15+45= 90°

Then since the angles should equal 180, you do:

180-90=90

So the missing angle equals 90°

6 0

3 years ago

Read 2 more answers

an earthquake measures 3.6 on the richter scale. what is the amount of energy (ergs) released by the earthquake? give an exact a

Alisiya [41]

We have that

log10 E = 4.4 + 1.5M
E=the released energy in Joules (J)
M= earthquake measures---------- > 3.6
log10 E = 4.4 + 1.5*3.6
log10 E = 9.8----------> E=10^(9.8)= 6.309573444 x10^9 J

the answer is 6.309573444 x10^9 J

5 0

3 years ago

Write an algebraic expression for the given quantity. Let x represent the unknown value.

Lelechka [254]

Answer:

Step-by-step explanation:

There is no equal sign.

1/2 x - 5*x

is all there is.

7 0

3 years ago