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4 years ago

What is the simplest form for 23/30

Mathematics

1 answer:

4vir4ik [10]4 years ago

7 0

23/30 can't be simplified any further because 23 is a prime number.

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Bridget is making greeting cards, which she will sell by the box at an art fair. She paid $30 for a booth at the fair and the ma

LiRa [457]

Answer:

when she sold 10 cards, it will cover all her cost.

Step-by-step explanation:

Profit(without charge of booth)=5x-2x

Profit=3x-30

Calculating:

3x=30

x=10

8 0

4 years ago

Find the center and radius of the circle with the given equation. Then select the correct

8_murik_8 [283]

Answer:

The center of the circle is $(-4, 7)$ .

Its radius is $5$ .

Step-by-step explanation:

Let $(a,\, b)$ represent the center of the circle, and let $r$ represent the radius of this circle. The equation for the circle would be:

$(x - a)^2 + (y - b)^2 = r^2$ .

Expand the left-hand side of this equation using the binomial expansion:

$\left(x^2 - 2\, a\,x + a^2\right) + \left(y^2 - 2\, b\, y + b^2\right) = r^2$ .

$x^2 + (- 2\,a)\, x + y^2 + (-2\, b)\, y + \left(a^2 + b^2 - r^2\right)= 0$ .

Compare this equation with the one given in the question:

$x^2 + 8x + y^2 - 14\, y + 40 = 0$ .

These two equations should represent the same circle. For that to happen, the coefficients should match. That gives a few equations about $a$ , $b$ , and $r$ .

The coefficients for $x$ should match: $(-2\,a ) =8 \implies a = -4$ .
The coefficients for $y$ should match: $(-2\, b) = -14 \implies b = 7$ .
The constant terms should match: $a^2 + b^2 - r^2 = 40$ .

However, it is already determined that $a = -4$ and $b = 7$ . That means $a^2 + b^2 - r^2 = (-4)^2 + 7^2 - r^2 = 65 - r^2$ .

$65 - r^2 = 40 \implies r^2 = 25 \implies r = 5$ .

Hence, the radius of this circle is $r = 5$ . Also, its center is at $(a,\, b) = (-4,\, 7)$ .

7 0

3 years ago

What years are before 1999

NNADVOKAT [17]

X<1999

as it means every year before 1999

7 0

4 years ago

Tatiana wants to give friendship bracelets for 32 classmates. She already has 5 bracelets, and she can buy more bracelets in pac

Natasha2012 [34]

Answer:

b. No she will not have enough bracelets for all 32 classmates if she orders 5 more packages of bracelets

Step-by-step explanation:

write out the equation

p=the number of packages she needs to buy

32=5+4p

subtract five from both sides

32-5=5-5+4p

27=4p

dived both side by 4

27/4=4p/4

6.75=p round to 7

Check your answer:

4 x 7 = 28

add the number of bracelets she already has

28 + 5 = 33 bracelets

33>32

So 7 packages is the minimum number of packages she needs to buy

6 0

4 years ago

Find the area of a circle with radius, r = 6.15m. Give your answer rounded to 2 DP.

suter [353]

Answer: 118.82m²

Hope this helped! Have a nice day :)

Step-by-step explanation:

Area of circle = π x r²

Area = π x 6.15²

= 118.82 (2.d.p)

6 0

3 years ago