Which of the following demonstrates the distributive property?
A. (r + s)t = (s+r)t
B. (r + s)t=r + (st)
C. (r + s)t = t(r + s)
D. (r + s)t = rt + st

Answer: (1, -2)

Concept:

There are three general ways to solve the system of equations:

Here, we are going to use the elimination method to solve.

Solve:

Given

[tex]\left \{ {{y=-5x+3} \atop {2x-3y=8}} \right.[/tex]

Convert the first equation's arrangement to correlate with the second equation

[tex]\left \{ {{5x + y=3} \atop {2x-3y=8}} \right.[/tex]

Multiply 3 on both sides in the first equation

[tex]\left \{ {{15x + 3y=9} \atop {2x-3y=8}} \right.[/tex]

Eliminate [y] by adding the two equations

[tex]17x = 17[/tex]

Divide both sides by 17

[tex]17x / 17=17/17[/tex]

[tex]x=1[/tex]

[tex]y=-5x+3=-5(1)+3=-5+3=-2[/tex]

[tex](1, -2)[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:560

Step-by-step explanation:

Step-by-step explanation:

f(0)=-2(0)-9=0-9=-9

f(1/2)=-(1/2)-9=-1/2 -9=-19/2

f(-2)=-2(-2)-9=4-9=-5

Answer:

Concept:

Here, we need to understand the idea of evaluation.  

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Question One. Identify the value of f(0)

f(x) = -2x - 9

f(0) = -2(0) - 9

f(0) = 0 - 9

f(0) = -9

Question Two. Identify the value of f(1/2)

f(x) = -2x - 9

f(1/2) = -2(1/2) - 9

f(1/2) = -1 - 9

f(1/2) = -10

Question Three. Identify the value of f(-2)

f(x) = -2x - 9

f(-2) = -2(-2) - 9

f(-2) = 4 - 9

f(-2) = -5

Hope this helps!! :)

Please let me know if you have any questions

Answer:

17

Step-by-step explanation:

17 is the only prime number present.

Answer:

17 does not belong

Step-by-step explanation:

In this image (and problem), 17 is the only prime number there.

Hopefully this helped you out!

Answer:

[tex]x+17[/tex]

Step-by-step explanation:

Hi there!

Let [tex]x[/tex] represent "the number".

The sum of a number and seventeen

⇒ [tex]x+17[/tex]

I hope this helps!

Answer:

Angle + the Complementary angle = 90 degrees. Let x be the measure of the angle under the question. Then the measure of the Complementary angle is (x+46) degrees, and you have this equation x + (x+46) = 90, or 2x+ 46 = 90, or 2x = 90 - 46 = 44. Then x =  = 22. The given angle has the measure of 22 degrees. The complementary angle is 90-22 = 68 degrees. Check. 68 - 22 = 44 degrees. Correct !!

Answer:

Cheetah

Step-by-step explanation:

American Antelope's speed = 94980 meters per hour

                                           = 59 miles per hour

The Cheetah is faster than the American Antelope

Answer:

Step-by-step explanation:

The American Antelope is going at a rate of 1583 meters / minute

1583 m [ 1 km / 1000 m ] = 1.583 km / minutes

In an hour, the Antelope will go 1.583 km / minute * 60 min / hour

1.583 * 60 = 94.98 km / hour

The cheetah is going 61 miles / hour * 1.6 km / mile  = 97.6 km/hour

The Cheetah is  not going to go hungry tonight.

Answer:

It turns out that knowing all four sides of two quadrilaterals are congruent is not enough to conclude that the quadrilaterals are congruent. Unlike with triangles, some information about angles is needed in order to conclude that two quadrilaterals are congruent. I will give you the video that might be helpful. I dont own the video but i hope it helps you . <3

Step-by-step explanation:

https://www.khanacademy.org/math/cc-fifth-grade-math/properties-of-shapes/imp-quadrilaterals-2/v/quadrilateral-types-exercise

Answer:

Step-by-step explanation:

P=(2,-3)

Q=(a,a²-2a-3)

[tex]\Delta y=a^2-2a-3-(-3)=a^2-2a\\\Delta x=a-2\\\\\displaystyle \lim_{a \to 2} \dfrac{a^2-2a-3-(-3)}{a-2} \\\\=\lim_{a \to 2} \dfrac{a^2-2a}{a-2} \\\\=\lim_{a \to 2} \dfrac{a(a-2)}{a-2} \\\\=\lim_{a \to 2} \dfrac{a}{1} \\\\=\lim_{a \to 2} a \\\\=2\\[/tex]

Proof:

y'=(x²-2x-3)'=2x-2

y'(2)=2*2-2=2

Answer: JK = 234

Concept:

Here, we need to know the idea of the segment addition postulate.

The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.

Solve:

Given information

JL = 8x - 3

LK = 4x + 57

Given expression deducted from the given figure

JL = LK

Substitute values into the expression

8x - 3 = 4x + 57

Add 3 on both sides

8x - 3 + 3 = 4x + 57 + 3

8x = 4x + 60

Subtract 4x on both sides

8x - 4x = 4x + 60 - 4x

4x = 60

Divide 4 on both sides

4x / 4 = 60 / 4

x = 15

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

Given information

JL = 8x - 3

LK = 4x + 57

x = 15

Given expression deducted from the segment addition postulate

JK = JL + LK

Substitute values into the expression

JK = 8x - 3 + 4x + 57

JK = 8(15) - 3 + 4(15) + 57

Simplify by multiplication

JK = 120 - 3 + 60 + 57

Simplify by simple operation (addition/subtraction)

JK = 117 + 60 + 57

JK = 177 + 57

[tex]\boxed{JK=234}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

10 is whole number .......

yes ten is natural,whole, integers,rational

Step-by-step explanation:

because natural contains all numbers wiThout 0 and whole contains all numbers with 0 so 10 is both of them.Integers are the number which is not a fraction,it is a whole number.And 10 is a rational number because all integers are rational.But it is not irrational.

Answer:

3.49410504

It is the answer hope it helps.

Mark me as Brainliest plz

Answer:

3.49410503751

Step-by-step explanation:

But as a smaller version it is

3.494

Hi! I'm happy to help!

To  solve this, we first need to find our what could give us 1/3. WE realize that the sequence is descending, so we must be dividing. We can then, from here, multiply our top number by 1/3, because that is our end number, and could possibly work for our common ratio. From this, we can check if this fits in our equation. (dividing by 3)

243×1/3=81

81×1/3=27

27×1/3=9

9×1/3=3

3×1/3=1

1×1/3=1/3

We can check if this is the correct amount of numbers that would fit into the geometric sequence. Let's see if this fits in:

243, 81, 27, 9, 3, 1, 1/3

This does fit into our geometric sequence. Our middle terms are underlined. (missing numbers)

Our common ratio is the number we multiply the previous number by to get our next, so our common ratio is 1/3.

So, our geometric sequence is 243, 81, 27, 9, 3, 1, 1/3, our middle terms are 81, 27, 9, 3, and 1. Our common ratio is 1/3.

I hope this was helpful, keep learning!

Answer:

Step-by-step explanation:

Given:

To find the terms in between.

Find the common ratio first:

The terms in between are:

Answer:

9/79/169%, 523.2, 458 (to 3sf)

Step-by-step explanation:

Example 1:

16/169×100%=9/79/169% of the students

Example 2:

87.2%×600=523.2 students

Example 3:

27.3%=125 students

100%=458 students (to 3sf)

Answer:

2 1/8 as a decimal is 2.125

Step-by-step explanation:

Answer:

2.125

Step-by-step explanation:

To find the decimal version of the fraction number, you need to divide 1/8, which is .125; combining that with the original whole number, you get 2.125.

Answer:

62.9

Step-by-step explanation:

Answer:

√40 = √ ( 2× 2 ×2 ×5) = 2√10

.........

Answer:

the first option is the answer. I am sure of this

Answer:

the first option is the answer

Answer:

80001235152

Step-by-step explanation:

hope this helped!

Answer:

1538.6cm^3

Step-by-step explanation:

See the image for solution

Hope it helps

Have a great day

Answer:

y=4x+1

Step-by-step explanation:

First the slope of the line is 4. The equation of the line is y-1=4x, y=4x+1

Answer:

-i

Step-by-step explanation:

'i' is the square root of -1, so i^2 would be -1. so now:

[tex]i^3 = (i^2)i = (-1)i = -i[/tex]

Answer:

none of these

Step-by-step explanation:

5.04*100=524.16

Answer:

none of these

Step-by-step explanation:

5.04 x 104 = 524.16

there is no option with 524.16

so none of these

Answer:

Step-by-step explanation:

a= 12 mm ; b = 16 mm  ; c = 18 mm

s = (a + b+c)/2

[tex]=\dfrac{12 + 16 + 8}{2}\\\\= \dfrac{36}{2}\\\\= 18\\\\[/tex]

s -a =  18 -  12 = 6 mm

s  -b = 18 - 16 = 2 mm

s  -c = 18 - 8 = 10 mm

[tex]area = \sqrt{s(s -a)(s-b)(s-c)}[/tex]

       [tex]= \sqrt{18*6*2*10}\\\\= \sqrt{2160 }\\\\=46.47\\\\=46 \ mm^{2}\\[/tex]

[tex]\dfrac{1}{2}* \ base * \ height = 46\\\\\dfrac{1}{2}*16* \ height = 46\\\\height = \dfrac{46*2}{16}\\\\[/tex]

  = 5.75

Height = 5.8 mm

Answer:

A. 5.8mm

Step-by-step explanation:

[tex]area \: of \: triangle = \sqrt{s(s - a) \times (s - b) \times (s - c)} \\ s = \frac{a + b + c}{2} \\ s = \frac{12 + 8 + 16}{2} \\ s = 18 \\ area \: of \: triangle \: = \sqrt{18(18 - 12) \times (18 - 8) \times (18 - 16)} \\ = \sqrt{2160} \\ = 46.47 {m}^{2} \\ area \: of \: triangle \: = \frac{1}{2} \times base \times height \\ 46.47 = \frac{1}{2} \times 16 \times h \\ h = \frac{46.47}{8} \\ h = 5.8mm[/tex]

Answer:

∠ ABC = 48°

Step-by-step explanation:

∠ ABC + ∠ DBC = ∠ ABD , that is

6x - 6 + 3x + 8 =  83

9x + 2 = 83 ( subtract 2 from both sides )

9x = 81 ( divide both sides by 9 )

x = 9

Then

∠ ABC = 6x - 6 = 6(9) - 6 = 54 - 6 = 48°

Answer:

Step-by-step explanation: