Answer number 1 please. Thank you.

The  two numbers are 8 and 13 and the system of equations are x + y = 21 and xy = 104

Let the two unknown numbers be x and y

If the sum of the numbers is 21, hence;

x + y = 21

x = 21 - y

If the product is 104, then;

xy = 104
(21-y)y = 104

21y - y^2 = 104
y^2-21y + 104 = 0

Factorize the result

y^2-8y - 13y+ 104 = 0
y(y-8) - 13()y-8) = 0
y = 13 and 8

Hence the two numbers are 8 and 13 and the system of equations are x + y = 21 and xy = 104

Learn more on system of equation here:  https://brainly.com/question/847634

Step-by-step explanation:

[tex]the \: length \: of \: the \: ladder \: becomes \: the \: hypotenuse \: [/tex]

[tex]the \: base \: becomes \\ = \sin( \alpha ) \times hypotenuse \\ = \sin(12) \times 15 \\ = 3.119ft[/tex]

Answer:

3.

Step-by-step explanation:

remember, when we multiply the same basic term, we add the exponents.

so,

x⁴×x² = x⁶

now, when there are other factors, we need to multiply them in too.

so,

(6x⁴)(3x²) = 6×3×x⁴×x² = 18x⁶ or simply (6×3)x^(4+2)

Answer:

1: Side-Side-Side theorem

2: Side-Angle-Side theorem

3: Angle-Side-Angle theorum

4: Side-Angle-Angle theorum

Step-by-step explanation:

Look at the order of the sides and/or angles of the triangles. Because both of the triangles have the same sides/angles based off either the side-side-side, side-angle-side, angle-side-angle, or side-angle-angle theorem, they are congruent.

Hope this helps! :)

Answer:

The circumference of a circle with diameter 4 is 12.57.

Answer:

[tex]\frac{5\pi }{3} = 0.5[/tex]

Step-by-step explanation:

5π/3 radians = 5π/3 × (180°/π) = 300°

⇒ cos 5π/3 = cos 5π/3 = cos(300°) = 1/2 or 0.5

Answer:

Roy eat 4 sweets

Step-by-step explanation:

Roy =R

Mike= (R-2)

Leen= 3(R+ R-2)

R + (R-2) + 6R-6 = 24

8R-8=24

8R=32

R=4

     Mike  4-2 = 2

     Leen 3(4+2) = 18

4+2+18=24

Answer:

104

Step-by-step explanation:

There are two ways to do it, though we need to know how it is affected.

20+6=26

26+6=32

32+6=38

38+6=44

Thus, you are adding 6 for each term.

1. You do it manually...(yes.)

I'll number it one by one

1.20

2.26

3.32

4.38

5.44

6.50

7.56

8.62

9.68

10.74

11.80

12.86

13.92

14.98

15.104

The 15th term is 104.

2. This method is easier. As shown above, there is a pattern. We can apply it using this formula:
20+6(n-1)

You can get this formula from the facts that:
-you start off with an additional added 8

-you add 6 every time

-if we do it 6n then it would be incorrect, with an extra 6 for each

-the formula is correct; you can test it for terms 2,3,4,5 like this:

20+6=26

20+2x6=32

20+3x6=38

20+4x6=44

To find the 15th term, you can:

20+14x6=20+84=104.

Answer:

not similar

Step-by-step explanation:

4/3 = 1.3333...

10/8 = 1.25

The ratios are not equal, so the triangles are not similar.

Work Shown:

[tex]a^2 + b^2 = c^2\\\\a^2 + 5^2 = 8^2\\\\a^2 + 25 = 64\\\\a^2 = 64-25\\\\a^2 = 39\\\\a = \sqrt{39}\\\\a \approx 6.244998\\\\a \approx 6.2[/tex]

answer: FALSE

Step-by-step explanation:

V=Bh

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm. The area A of a rectangle with length l and width w is A=lw .

Step-by-step explanation:

i¹ = i

i² = i×i = -1

i³ = -1 × i = -i

i⁴ = -i×i = - -1 = 1

i⁵ = 1×i = i

...

so, when the exponent of i modulo 4 (the remainder when dividing by 4) = 0, then the result is 1.

= 1, then the result is i

= 2, then the result is -1

= 3, then the result is -i

233 modulo 4 = 1 (233/4 = 58, remainder 1).

so, the result is i (the third answer option).

The height of the shot starts to increase when x is -5 feet, It continues to increase until x = 10 feet and then the height decreases until x = 25 feet

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h(x) represent the height of the shot put, when the horizontal distance is x feet.

h(x)= -0.05x² + x + 6

From the graph of h(x):

The height of the shot starts to increase when x is -5 feet, It continues to increase until x = 10 feet and then the height decreases until x = 25 feet

Find out more on equation at: https://brainly.com/question/2972832

ANSWER: p^2 - 2p + 2

Step-by-step explanation:

Total age of three = p + p-2 + (p-2)^2

= 2p-2 + p^2-4p+4

= p^2 - 2p + 2

Answer:

4, 4, 4, 4, and 4

Step-by-step explanation:

mode = 4

median = 4

so we know two of the five numbers are 4;

[tex](x+x+x+4+4)/5 =4[/tex]

[tex](3x+8x)/5 = 4[/tex]

multiply both sides by 5

[tex]3x+8=20\\3x=20-8\\3x=12\\x=4\\[/tex]

therefore; the numbers are all 4

2600 pens.

the remaining pens Ali have after giving 1547 away.

2600 - 1547

= 1053

so, Ali has 1053 pens with him.

Ali has 2600 pens.

the amount of pens Ali has left after he gave away 1547 pens.

subtract 2600 from 1547.

[tex]2600 - 1547[/tex]

[tex] = 1053 \: pens[/tex]

hence, Ali has 1053 pens left with him after giving 1547 pens away.

Answer:

4/3

Step-by-step explanation:

f(2) = (-2*2)^2 / (7(2))-4)

f(2) = (-4)^2 / 14-4

f(2) = 16 / 12

f(2) = 4 / 3

Answer:

Subtract 3 from both sides.

Step-by-step explanation:

x + 3 = 5

x = 5 - 3

x = 2

I know I`m late sorry, still wanted to answer

. _ .

Answer:

1/52.

Step-by-step explanation:

The suit AND the number must be correct.

When you see AND in a probability question think 'multiply'.

That would be 13/52 * 4/52

= 52/(52)^2

= 1/52.

In the equation, 1/6 represents the constant of proportionality.

If a person weighs 60 kg on earth, the person would weigh 10kg ont he moon.

The equation that represents inverse proportion is: m = ke

Where:

If k is 1/6 and e is 60kg,

m = 1/6 x 60 = 10kg

To learn more about inverse proportion, please check: https://brainly.com/question/20391784

Answer: ✨So I divided. 120 by 15 and got 8. I then multiplied it by 20 and got 160 bouquets✨

Step-by-step explanation: Still stuck? Get 1-on-1 help from an expert tutor now.

Step-by-step explanation:

so, the garden seems to be rectangular.

it has a length.

and width = length - 2

I assume the fence should go all around the rectangular garden.

that means it has to cover 2 lengths and 2 widths.

fence = 2×length + 2×(length - 2) =

= 2×length + 2×length - 4 = 4×length - 4 =

= 4×(length - 1)

length = 7.5 m

so, he will need

4×(7.5 - 1) = 4×6.5 = 26 meter of fencing.

Answer: c = -28

Step-by-step explanation:

substitue x for 2

2(2^2) + 10(2) + c = 0

8 + 20 + c = 0

28 + c = 0

c = -28

The value of coefficient c of the quadratic equation 2x^2+10x+c=0  is -28.

One of the roots of the quadratic equation 2x^2+10x+c=0 is equal to 2.

The roots of a quadratic equation are the values of the variable that satisfy the equation.

They are also known as the solutions or zeros

The equation is 2x^2+10x+c=0.

a=2, b=10 and c=?

To substitute x for 2

2(2^2) + 10(2) + c = 0

8 + 20 + c = 0

28 + c = 0

c = -28

To learn more about the quadratic equation visit:

https://brainly.com/question/1214333

Step-by-step explanation:

By the secant-secant theorem, (AC)(BC)=(DC)(x+DC)

Substituting in the given values, (21)(9)=(8)(8+x)

So, 189=64+8x, meaning x = 15.625, or about 15.63.

Answer:

16 and 25

Step-by-step explanation:

they are square numbers

1^2 = 1 .. etc.

this is a I

There is an error 2*2 is 4 lol realised I wrote tht whoops