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3 years ago

A number is three times another number. The difference of these two numbers is 10. Find these number.

Mathematics

2 answers:

Katyanochek1 [597]3 years ago

5 0

Answer:

$\Large \boxed{\sf 15 \ and \ 5}$

Step-by-step explanation:

Let the first number be x.

Let the second number be y.

x is 3 times y.

Difference of x and y is 10.

$x=3y$

$x-y=10$

Put x as 3y in the second equation.

$3y-y=10$

Combine like terms.

$2y=10$

Divide both sides by 2.

$y=5$

Plug y as 5 in the first equation.

$x=3(5)$

Multiply.

$x=15$

The two numbers are 15 and 5.

kow [346]3 years ago

3 0

Answer:

5,15

Step-by-step explanation:

let the numbers be x and y

but y = 3x

3x - x = 10

2x = 10

x = 5

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Please provide more information. You need to add the sides of the polygon to find the perimeter.

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3 years ago

There are 8employees on The Game Shop's sales team. Last month, they sold a total of g games. One of the sales team members, Chr

Anuta_ua [19.1K]

Answer:

(g/8) - 17

Step-by-step explanation:

Given that:

Number of employees = 8

Employees sold a total of g games

Chris sale = 17 fewer than team Average

Number of games Chris sold :

Team average :

Total sales made / number of employees

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7 0

3 years ago

The straight line with equation y=3/4x makes an acute angle theta with the x-axis.

yanalaym [24]

The angle is arctan(3/4) => sin(2t) = sin(2arctan(3/4)) =
2sin(arctan(3/4))cos(arctan(3/4))

Let z = arctan(3/4) => tan(z) = 3/4

2sin(arctan(3/4))cos(arctan(3/4)) = 2sin(z)cos(z) = 2(3/5)(4/5) = 24/25

<span>cos(2t) = cos^2(t) - sin^2(t) = cos^2(z) - sin^2(z) = (4/5)^2 - (3/5)^2 = (16 - 9)/25

= 7/25

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
</span>

7 0

3 years ago

1 The prism-shaped roof has equilateral triangular bases. Use the model you created in question #1 to calculate the height of th

Diano4ka-milaya [45]

Answer:

Step-by-step explanation:

Step-by-step explanation: As shown in the attached figure, the prism-shaped roof has equilateral triangular bases, one of which is ΔABC. We need to create an equation that models the height of one of the roof's triangular bases in terms of its sides. Let ii be AD.

See the figure attached herewith, ΔABC forms an equilateral triangle, in which AD is the height. So, D will be the mid-point of BC and ∠ADB = ∠ADC = 90°.

Now, in ΔADB, we have

AD^2=AB^2-BD^2

AD^2=AB^2-(1/2AB^2)^2

AD=√3/4AB^2

we can find the height of any one of the roof's triangular bases.

2.1. Check picture 1. Let the one side of the triangle be a, drop one perpendicular, CD. Then triangle ADB is a right triangle, with hypothenuse a and one side equal to 1/2a. By the Pythagorean theorem, as shown in the picture, the height is √3/2a

2. if a=25 ft, then the height is √3/2a=√3/2*25=1.732/2*25=21.7(ft)

3. consider picture 2. Let the length of the roof be l feet.

one side of the prism (the roof) is a rectangle with dimensions a and l, so the area of one side is a*l

the lateral Area of the roof is 3a*l

the area of the equilateral surfaces is 2*(1/2*a*√3/2a)=√3/2a^2

so the total area of the roof is

4. The total area was the 2 triangular surfaces + the 3 equal lateral rectangular surfaces. Now instead of 3 lateral triangular surfaces, we have 2.

So the total area found previously will be decreased by al

5. so the area now is √3/2a^2 + 2al

6. now a=25 and l=2a=50

Area= √3/2a^2+2al=√3/2*25^2+2*25*50=25^2(√3/2+4)=625*4.866

=3041.3 (ft squared)

6 0

3 years ago

For integers a, b, and c, consider the linear Diophantine equation ax C by D c: Suppose integers x0 and y0 satisfy the equation;

Dmitrij [34]

Answer:

$x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )$

b. x = -8 and y = 4

Step-by-step explanation:

This question is incomplete. I will type the complete question below before giving my solution.

For integers a, b, c, consider the linear Diophantine equation

$ax+by=c$

Suppose integers x0 and yo satisfy the equation; that is,

$ax_0+by_0 = c$

what other values

$x = x_0+h$ and $y=y_0+k$

also satisfy ax + by = c? Formulate a conjecture that answers this question.

Devise some numerical examples to ground your exploration. For example, 6(-3) + 15*2 = 12.

Can you find other integers x and y such that 6x + 15y = 12?

How many other pairs of integers x and y can you find ?

Can you find infinitely many other solutions?

From the Extended Euclidean Algorithm, given any integers a and b, integers s and t can be found such that

$as+bt=gcd(a,b)$

the numbers s and t are not unique, but you only need one pair. Once s and t are found, since we are assuming that gcd(a,b) divides c, there exists an integer k such that gcd(a,b)k = c.

Multiplying as + bt = gcd(a,b) through by k you get

$a(sk) + b(tk) = gcd(a,b)k = c$

So this gives one solution, with x = sk and y = tk.

Now assuming that ax1 + by1 = c is a solution, and ax + by = c is some other solution. Taking the difference between the two, we get

$a(x_1-x) + b(y_1-y)=0$

Therefore,

$a(x_1-x) = b(y-y_1)$

This means that a divides b(y−y1), and therefore a/gcd(a,b) divides y−y1. Hence,

$y = y_1+r(\frac{a}{gcd(a, b)})$ for some integer r. Substituting into the equation

$a(x_1-x)=rb(\frac{a}{gcd(a, b)} )\\gcd(a, b)*a(x_1-x)=rba$

$x = x_1-r(\frac{b}{gcd(a, b)} )$

Thus if ax1 + by1 = c is any solution, then all solutions are of the form

$x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )$

In order to find all integer solutions to 6x + 15y = 12

we first use the Euclidean algorithm to find gcd(15,6); the parenthetical equation is how we will use this equality after we complete the computation.

$15 = 6*2+3\\6=3*2+0$