The windows in an old cathedral are made up of 3,744 pieces of stained glass and 5,735 pieces of clear glass. Together, how many pieces of glass make up the windows?

Answer:  the lowest common multiple of 12 and 15 is 60.

Step-by-step explanation: The multiples of 12 are : 12, 24, 36, 48, 60, 72, and 84. The multiples of 15 are: 15, 30, 45, 60, 75, and 90. So, 60 is a common multiple.

Equation of circle G: [tex]\bold{(x-3)^{2} + (y-4)^{2} = 49}[/tex]

"An equation of a circle with center (p, q) and radius r is:[tex](x-p)^{2}+ (y-q)^{2}=r^{2}[/tex] "

"The coordinates of the midpoint M of two points (a, b) and (x, y) :

[tex]M(\frac{a+x}{2} ,\frac{b+y}{2} )[/tex] "

"The distance between two coordinate points (a, b), (m, n):

[tex]d=\sqrt{(n-b)^{2} +(m-a)^{2} }[/tex] "

"A diameter of a circle is the straight line that from one side of a circle to other side and passes through the center."

For given question,

The line segment connecting the two points B(-4,4) and D (10,4) is a diameter of the circle.

This means, the midpoint of the diameter BD would be the center of a circle G.

Let M represents the center of the circle.

First we find the coordinates of the center of the circle.

Using midpoint formula,

⇒ M = [tex](\frac{-4+10}{2} ,\frac{4+4}{2} )[/tex]

⇒ M = (6/2 , 8/2)

⇒ M = [tex](3,4)[/tex]

Now, we find the distance between points B(-4,4) and D (10,4) to determine the diameter of a circle G.

Using distance formula,

⇒ [tex]d=\sqrt{(4-4)^{2} +(10-(-4))^{2} }[/tex]

⇒ [tex]d=\sqrt{0+(14)^{2} }[/tex]

⇒ [tex]d=14[/tex] units

So, the radius of the circle r would be,

r = d/2

⇒ r = 14 / 2

⇒ r = 7 units

Now, we find the equation of circle with center M(3, 4) and radius r = 7 units.

Using center - radius form equation of circle would be,

[tex](x-3)^{2} + (y-4)^{2} = 7^{2}[/tex]

⇒ [tex]\bold{(x-3)^{2} + (y-4)^{2} = 49}[/tex]

Therefore, option (A) is the correct answer.

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Answer:

This is a difficult question

Step-by-step explanation:

is it 3 part?

Answer:

 less=−5

greater=−1

step by step:

/ 3

\begin{aligned} (x + 3)^2 - 4 &= 0 \\\\ (x+3)^2&=4 \\\\ \sqrt{(x+3)^2}&=\sqrt{4} \end{aligned}

(x+3)

2

−4

(x+3)

2

(x+3)

2

​

​

=0

=4

=

4

​

​

Hint #22 / 3

\begin{aligned} x+3&=\pm2 \\\\ x&=\pm2-3 \\ \phantom{(x + 3)^2 - 4}& \\ x=-5&\text{ or }x=-1 \end{aligned}

x+3

x

(x+3)

2

−4

x=−5

​

=±2

=±2−3

or x=−1

​

Hint #33 / 3

In conclusion,

\begin{aligned} \text{lesser }x &= -5 \\\\ \text{greater } x &= -1 \end{aligned}

lesser x

greater x

​

=−5

=−1

​

​

The solutions from least to greatest are lesser x = -2 and greater x = 2/3 for the equation (2x +4)(3x -2)=0

An equation is collection of two or more expressions with an Equal sign

The given equation is (2x +4)(3x -2)=0

To find the solutions, we set each factor equal to zero and solve for x

2x + 4 = 0

Subtract 4 from both sides

2x = -4

Divide both sides by 2

x = -2

Now 3x - 2 = 0

Add 2 on both sides

3x = 2

Divide both sides by 3

x = 2/3

Therefore, the solutions from least to greatest are lesser x = -2 and greater x = 2/3

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Answer: n is greater than or equals to 1, where n is an integer

Step-by-step explanation:

The domain Abraham should use for s so it generates the sequence is n ≥ 1 where n is an integer option (C) is correct.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

Abraham is writing a recursive function for the geometric sequence:

24, 12, 6,3,

The above sequence is a geometric progression.

The first term geometric progression is 24

s(1) = 24

s(n) = s(n-1)(1/2)

The nth term of the geometric progression:

The common ratio = 12/24 = 1/2

s(n) = s(n-1)(1/2)

Here n should be an integer number that is greater than 1

n ≥ 1 where n is an integer.

Thus, the domain Abraham should use for s so it generates the sequence is n ≥ 1 where n is an integer option (C) is correct.

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Answer:

3C + 3D = 12x² -12x + 30

Step-by-step explanation:

Given

To determine

The expression is given by

3C + 3D

substituting C = x² + 7 and D = 3x² - 4x + 3

= 3(x² + 7) + 3(3x² - 4x + 3)

= 3x² + 21 + 9x² - 12x + 9

= 12x² -12x + 30

Thus, the expression in standard form is:

3C + 3D = 12x² -12x + 30

Answer:

m= -[tex]\frac{9}{2}[/tex]

Step-by-step explanation

Answer:

-20=-20

Step-by-step explanation:

Distribute the 4.

(4xp-20)-8=4p-28

get rid of the variables (replace p with 2)

(8-20)-8=8-28

Simplify or combine like terms

-12-8=-20

Simplify or combine like terms

-20=-20

Hope this helps feel free to contact me if you need further help :D

Answer:

-36

Step-by-step explanation:

21, 18, 15, 12....

All you have to do is subtract 3 less on each number you get, until u get to the twentieth term....

21, 18, 15, 12, 9, 6, 3, 0, -3, -6, -9, -12, -15, -18, -21, -24, -27, -30, -33, -36

-36 is the twentieth term of this arithmetic sequence

Hope this helped!

Have a supercalifragilisticexpialidocious day!

Answer:45

Step-by-step explanation:

Answer:

u = 3

Step-by-step explanation:

Subtract 2 on both sides.

8 - 2 = 2u

Add like terms.

6 = 2u

Divide by 2 on both sides.

u = 3

Answer:

The answer is 8 pounds.

Hoped this helped!

Answer:

your pfp please ✋✋✋

9514 1404 393

Answer:

Step-by-step explanation:

Angles opposite congruent sides are congruent, so base angles D and F of this isosceles triangle have the same measure:

  y = 55

__

The sum of angles in the triangle is 180°, so ...

  55° +(11x +4)° +55° = 180°

  11x = 66 . . . . . . . . divide by °, subtract 114

  x = 6 . . . . . . . . . . .divide by 11

The values of x and y are 6 and 55, respectively.

Answer:

HELP FOR HELP?

Step-by-step explanation:

Answer:

Step-by-step explanation:

this is a special triangle, 30-60-90

if you have the hypothenuse =14

one leg will be 14/2=7

the other leg is 7[tex]\sqrt{3}[/tex]=12.12

a=7, b=12.12

Step-by-step explanation: First change the minus inside to plus a negative.

Now we can distribute the -8 through each

of the terms inside the set of parenthses.

So we have -8(2y) + -8(-3) or -16y + 24.

Take a look below.

Answer:

It would take 135 seconds to make 10 sandwiches.

Step-by-step explanation:

108/8 = 13.5

324/24= 13.5

13.5 x 10 = 135

Answer:

135

Step-by-step explanation:

--------------------------------------

ninety four means $94. 36/100 means $0.36. when you put these together you get $94.36

Answer: im not sure

Step-by-step explanation:

Answer: His usual average = 28.

Step-by-step explanation:

Let x = usual average at the basketball game tonight.

As per given,

[tex]\dfrac{x}{2}+10=24[/tex]

Subtract 10 from both sides , we get

[tex]\dfrac{x}{2}+10-10=24-10\\\\\Rightarrow\ \dfrac{x}{2}=14\\\\\Rightarrow\ x=14\times2=28[/tex]

Hence, his usual average = 28.

Answer:

Part D is the correct option as square root of 40 is not greater than 7

Answer: y = 2 √x

Step-by-step explanation:There you go :>

Answer:

2x + 8

Step-by-step explanation:

What we have here is a case of distributive property.

Multiply 2 by x and 4 to get the the equivalent expression.

2(x + 4)

2x + 8 is the equivalent expression.

Answer:

I need Help on this one too.

Step-by-step explanation:

Answer:

1. irrational

2.rational

3. irrational

4. irrational

5. irrational

Step-by-step explanation: