When two straight lines cross, it is found that the angles opposite each other are the same size. They are known as .............

Answer:

(a) How many are there to select 2 pairs of gloves?

10 ways

(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)

130 ways

Step-by-step explanation:

We solve the above questions using Combination

Combination = C(n, r) = nCr

= n!/n! ×(n - r)!

(a) How many are there to select 2 pairs of gloves?

We have 5 pairs of gloves. Therefore, the number of ways to select 2 gloves =5C2

= 5!/2! × (5 - 2)!

= 5!/2! × 3!

= 5 × 4 × 3 × 2 × 1/(2 × 1) × (3 × 2 × 1)!

= 10 ways.

(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)

We are told to select 4 gloves out of the 10 gloves = 10C4

We have 5 pairs, we need to make sure that two out of the selected 4 make a pair = 5 × 2⁴

= 80

Hence,

10C4 - 5C4

= [10!/4! × (10 - 4)!] - 80

= 210 - 80

= 130 ways

Answer:

thus, the ratios 8 : 16 and 6 : 12 are equal

Step-by-step explanation:

8 : 16 and 6: 12

8 : 16 = 1/2

6: 12= 1/2

Thus, the ratios 8 : 16 and 6 : 12 are equal

Answer: Hi!

So first, I'm going to convert "350 below ground level" to -350, as this is what "below ground level" represents.

Now, we should find the total distance traveled. Take the absolute value of -350 (350) and add it to 10, the metres above ground level. This is 360.

We already know the rate of travel; 6m/min. All we have to do now is divide the total distance (360) by the rate of travel (6)!

360 ÷ 6 = 60

So, it took 60 minutes, or one hour, for the elevator to travel down the shaft!

Hope this helps!

Answer:

y = 5x + 1

Step-by-step explanation:

Lines that are parallel to each other on a graph would have the same slope but different y-intercepts. When option A's equation is graphed along with the line given in the question, the lines appear to be parallel.  

Option A should be the correct answer.

Answer:

or,6x+6=9x-9

or,6+9= 9x-6x

or,15=3x

or,15/3=X

therefore,X=5ans

Answer:

x=3

Step-by-step explanation:

32/24=(6x+6)/(9x-9)

simplify by 8 in the left

4/3=6(x+1)/9(x-1)

simplify by 3 in the right

4/3=2(x+1)/3(x-1)

*3           *3

4=2(x+1)/(x-1)

(x+1)/(x-1)=4/2=2

so x+1=2(x-1)=2x-2

-x                     -x

1=x-2

+2    +2

3=x

so x=3

verify  (6*3+6)/(9*3-9)=32/24

24/18=32/24

simplify by 6  in the left

4/3=32/24

simplify by 8   in the right

4/3=4/3   TRUE

Answer: I'll explore two options here. Your question wasn't entirely clear. If you meant a regular 2 step equation, this would be your answer:

-104(3+1)

-104(4)

   416

However, if you meant -104/(3+1) this would be your answer:

-104 ÷ (3+1)

(3+1) = 4

-104 ÷ 4 = -26

Hope this helped!

Complete Question: Which of the following is an example of the difference of two​ squares?

A x² − 9

B x³ − 9

C (x + 9)²

D (x − 9)²

Answer:

A. [tex] x^2 - 9 [/tex].

Step-by-step explanation:

An easy way to spot an expression that is a difference of two squares is to note that the first term and the second term in the expression are both perfect squares. Both terms usually have the negative sign between them.

Thus, difference of two squares takes the following form: [tex] a^2 - b^2 = (a + b)(a - b) [/tex].

a² and b² are perfect squares. Expanding [tex] (a + b)(a - b) [/tex] will give us [tex] a^2 - b^2 [/tex].

Therefore, an example of the difference of two squares, from the given options, is [tex] x^2 - 9 [/tex].

[tex] x^2 - 9 [/tex] can be factorised as [tex] x^2 - 3^2 = (x + 3)(x - 3) [/tex].

Hello,

First of all, dividing by 0 is not defined we will take x different from 1/3 (because -1+3x= 0 <=> x = 1/3)

Then, dividing this polynomial by (-1+3x) means that you have to have Q(x), a polynomial of degree 1 and R a real number such that

[tex]\dfrac{9x^2-6x+2}{-1+3x}=Q(x)+\dfrac{R}{-1+3x}\\\\\text{We can multiply by (-1+3x)}\\\\9x^2-6x+2=(-1+3x)Q(x)+R[/tex]

Either you do the division and you can select the correct answer or you check the different answer to identify the correct one.

For instance, for the first answer, let's estimate

[tex](-1+3x)(3x-3)+\dfrac{-1+3x}{3x-1}\\\\=-3x+3+9x^2-9x+1\\\\=9x^2-12x+4[/tex]

and this is not equal to our initial polynomial, so this is not the correct answer.

Second Answer.

[tex](-1+3x)(3x-1)+\dfrac{-1+3x}{3x-1}\\\\=-3x+1+9x^2-3x+1\\\\=9x^2-6x+2[/tex]

And this is our initial polynomial. So this is the [tex]\large \boxed{\sf \bf \text{correct answer}}[/tex]

Thank you.

PS: in this example, you can even notice the following (so it makes the division trivial)

[tex](3x-1)^x=9x^2-6x+1 \\\\\text{So}\\\\9x^2-6x+2= (3x-1)^2+1\\\\\text{And, then.}\\\\\dfrac{9x^2-6x+2}{-1+3x}=3x-1+\dfrac{1}{3x-1}[/tex]

Answer:

9000000+20000+20+9

Step-by-step explanation:

Answer:

2 hours.

Step-by-step explanation:

From the question given,

Wade can do the work alone in 6 hours.

Rhonda can do the same work in 3 hours.

Next, we shall determine how much work is done by Wade and Rhonda in 1 hour each. This is illustrated below:

If Wade can do the work alone in 6 hours.

Then Wade can do 1/6 of the work in 1 hour.

If Rhonda can do the same work in 3 hours.

Then Rhonda can do 1/3 of the work in 1 hour.

Next, we shall determine the work done by Wade and Rhonda when they work together. This is illustrated below:

Wade's 1 hour work = 1/6

Rhonda's 1 hour work = 1/3

Therefore, work done by Wade and Rhonda together in 1 hour = 1/6 + 1/3 = 3/6 = 1/2

Since they completed 1/2 of the work in 1 hour, it means they will complete the work in 2 hours.

Answer:

73.437= 74 437/1000

Step-by-step explanation:

73.437 to fraction.

Let's acknowledge the presence of a decimal and how many digit we have after the decimal point.

Actually, the numbers after the decimal point will determine the amount of 10s to be divided with.

What I'm saying is this

73.437= 74 437/1000

In this case, 437 is a prime number

So

73.437= 74 437/1000

Answer:

Step-by-step explanation:

Using the Distributive Property of Multiplication, we get

12

---- - 12x. or 4 - 12x, or 4(1 - 3x)

 3

Answer:

900cm^3

Step-by-step explanation:

1 cm= 10 mm

x=300mm (criss cross)

1cm*300mm/10mm= 10mm*x/10mm

30cm=x

30cm=300mm

1m=100cm

0.2m=x

1m*x/1m=0.2m*100cm/1m

x=0.2*100cm

x=20cm

0.2m=20cm

l=15cm

w=30cm

h=20cm

v=l*w*h

v=15cm*30cm*20cm

v=450cm^2*20cm

v=900cm^3

Answer:

9000cm^3

Step-by-step explanation:

Width:300mm=30cm

Height:15cm=15cm

Depth:0.2m=20cm

V=DxWxH

V= 20x30x15

V=9000cm^3

Answer:

B

Step-by-step explanation:

1 year = 52 weeks. 2 years would be 104 weeks.

$12 per week x 104 weeks = $1248 total.

1248 - 900 = $348

348 /900 = 0.3866 = 38.7%

The answer is B

Answer:

x-3= 4

x= 4+3

Answer: x= 7

Answer:

x=7

Step-by-step explanation:

x-3=4

Adding 4on both sides

x-3+3=4+3

x=7

Hope it will help you :)

Answer:

The answer is 14 :)

Step-by-step explanation:

We have,

Find the measure of ∠ x ?

∠PQR + ∠RQS = ∠PQS

⇒ 76° + x = 90°

⇒ x = 90° - 76°

⇒ x = 14°

Answer:

b

Step-by-step explanation:

The y- intercept is the point on the y- axis where the graph crosses.

On the y- axis the x- coordinate is always zero.

From the table when x = 0 , y = 3, thus

(0, 3 ) is the y- intercept → b

Answer:

4917

Step-by-step explanation:

Given sequence:

This is AP with common difference of 1, the first term of 42 and the last term of 107

Number of terms:

Sum of the terms:

Answer is: 4917

Answer:

the simple multiplier is equal to 4

Step-by-step explanation:

In an economic model,

Y=  C + I + G + (X - M)

the average expenditure Y must be equal  to the totality of the output

If C = 3 + 0.75Y

where;

marginal propensity to consume MPC = 0.75

Then,

Y = 3 + 0.75Y + 2 + 1

Y = 6+0.75 Y

Y - 0.75 Y = 6

0.25 Y = 6

Y = 6/0.25

Y = 24

However,  the simple multiplier can be expressed as:

[tex]=\dfrac{1}{1 - MPC}[/tex]

[tex]=\dfrac{1}{1 - 0.75}[/tex]

[tex]=\dfrac{1}{0.25}[/tex]

= 4

Answer:

The original number is -7.

Step-by-step explanation:

In this section, we are trying to figure out a mysterious number. Let's call this number y. To find the value of y, we need to create an equation. Our equation will be based on clues hidden in the text. So, what do we know?

- A number, aka y, is increased by 3. (y+3)

-That number is doubled. 'That number' refers to the answer of y+3. So, (y+3)x2.

-Finally, the end result is -8.

Great! Now we know our equation: 2(y+3)=-8. We need to figure out what y equals, so let's isolate the y term with some algebra.

2(y+3)=-8; Original formula

2y+6=-8; Distribute the (y+3)

2y=-14; Carry the 6 to the other side of the equation.

y=-7: Divide

Thus, our mysterious number is -7. Hope this helps:)))

Answer:

sinθ = -5/√61

secθ = √61/6

tanθ = -5/6

Step-by-step explanation:

From the given coordinate (6, -5), x = 6 and y = -5. This shows that the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.

Let us get the value of the radius 'r' first before calculating the trigonometry identities.

Using the Pythagoras theorem;

[tex]r^2 = x^2 + y^2\\r^2 = 6^2 + (-5)^2\\r^2 = 36+25\\r^2 = 61\\r = \sqrt{61}[/tex]

Using SOH, CAH, TOA to get the trigonometry identities;

Given x = 6, y =5 and r = √61

[tex]sin \theta = opp/hyp = y/r\\sin \theta = 5/\sqrt{61} \\[/tex]

Since sin θ, is negative in the fourth quadrant, [tex]sin \theta = -5/\sqrt{61} \\[/tex]

[tex]cos \theta = adj/hyp = x/r\\cos \theta = 6/\sqrt{61} \\[/tex]

[tex]sec \theta = \frac{1}{cos \theta} \\sec \theta = \frac{1}{6/\sqrt{61} } \\sec \theta = \frac{\sqrt{61} }{6}[/tex]

For tanθ:

[tex]tan \theta = \frac{opp}{adj} = \frac{y}{x} \\tan \theta = \frac{5}{6}\\[/tex]

Since tan θ, is negative in the fourth quadrant, [tex]tan \theta = -5/6[/tex]

 [tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex],

[tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]  

[tex]TAN\Theta=\frac{-5}{6}[/tex].

Given coordinate of point be (6, -5).

So the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.

Since (6, -5) is on the terminal side that puts us in the fourth quadrant. If we plot that point and draw a diagonal to it from the origin, we will be able to draw a right triangle with that diagonal as the hypotenuse.That means the adjacent side is 6 and opposite side it -5.

By Pythagorean theorem, we find that the hypotenuse

[tex]H=\sqrt{6^{2} +(-5)^{2} }[/tex]

[tex]H=\sqrt{61}[/tex]

We know from trigonometric ratios,

[tex]SIN\Theta=\frac{Perpendicular}{hypotenuse} \\[/tex]

[tex]SIN\Theta=\frac{5}{\sqrt{61} }[/tex]

Since [tex]SIN\Theta[/tex] is negative in 4th quadrant,

so,

[tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex]

Similarly,

[tex]SEC\Theta=\frac{hypotenuse}{base}[/tex]

[tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]

And,

[tex]TAN\Theta=\frac{perpendicular}{base}[/tex]

[tex]TAN\Theta=\frac{-5}{6}[/tex]

Hence,  [tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex], [tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]  and [tex]TAN\Theta=\frac{-5}{6}[/tex].

For more details follow the link:

https://brainly.com/question/1201366

Answer:

Step-by-step explanation:

B:  Above par.  Stock has gained a bit of value since it was purchased.

================================

Explanation:

Answer:

5x^2 -2x +4

Step-by-step explanation:

(8x^2 + 9) - (3x^2 + 2x + 5)

Distribute the minus sign

(8x^2 + 9) - 3x^2 - 2x - 5

Combine like terms

5x^2 -2x +4

Answer:

[tex]-2x-28[/tex]

Step-by-step explanation:

We can apply the distributive property then combine like terms for a simpler equation.

[tex]-4(x+6)+2(x-2)\\\\-4x-24+2x-4\\\\-2x-28[/tex]

Hope this helped!

Answer:

-2x -26

Step-by-step

Answer:

32

Step-by-step explanation:

[tex] 64= 2^6[/tex]

[tex] 96= 2^5\times 3[/tex]

[tex] 64= 2^7[/tex]

Common factor = [tex] 2^5[/tex]

Therefore,

H.C.F OF 64,96,128 = [tex] 2^5[/tex] = 32

Answer:

17

Step-by-step explanation:

first find the value of N