Have you ever seen rational exponents? Rational exponents are designed to fit within the properties of exponents. That is, (31/2)2 is equal to 31, or 3. What operation does the power 1/2 represent? Can you think of operations that other fractional powers represent, such as 1/3, 1/4 and 2/3?

Answer:

The area of a triangle is base * height / 2. In this case that is:

3 * (2x - 4) / 2 = 3 * 2(x - 2) / 2 = 3 * (x - 2) = 3x - 6 in²

Answer:

3x-6 inches^2

Step-by-step explanation:

[tex]A =\frac{ (a \times b)}{2} \\A =\frac{(3(2x-4))}{2} \\A = \frac{(6x -12)}{2} \\\\Area = (3x-6)^2 inches[/tex]

Answer:

The cross-section of the rectangular prism is a:

Step-by-step explanation:

When you take a cross-section of a rectangular prism, regularly you will obtain a rectangle because this was the base or the two-dimension figure that was used to form the three-dimension figure, in this case, the rectangular prism, the form of obtaining other figure is using how reference the square face, in that case, the cross-section would be a square, this happens because the cross-section is bind with the reference face. Possibly you think the cross-section in the figure doesn´t appear a rectangle, this happens by the perspective because we are looking at the rectangular prism with an inclination of 45°, but if the inclination was 90°, you would see a blue rectangle.

Answer:

-9ab3a3b-52

Step-by-step explanation:

-8a3b+3a2b2-52+5a2b3a3b+7-9a2b2

-8a3b-6a-52+5a2b3a3b

-14a3b-52+5a2b3a3b

-9ab3a3b-52

Answer:

0.1875

Step-by-step explanation:

The geometric sequence is going down by 3/4 so just continue it on down

Hope this helps, though put some thought into it

Answer:170

Step-by-step explanation:

122+24+24=170

Answer:

True

Step-by-step explanation:

A chord of a circle is a straight line segment whose endpoints both lie on the circle.

Vertical Angles are the angles opposite each other when two lines cross.

Any intersecting segments (chords or not) form a pair of congruent, vertical angles.

Answer:

Option C, i.e., point B.

Step-by-step explanation:

The given system of inequalities is

[tex]y>-2x+10[/tex]     ...(1)

[tex]y>\dfrac{1}{2}x-2[/tex]     ...(2)

If a point is a solution of given system of inequalities, then the both inequalities must be satisfy by the point.  

From the given graph it is clear that coordinates of point E are (4,-2).

Put x=4 and y=-2 in (1).

[tex]-2>-2(4)+10\Rightarrow -2>2[/tex] False.

From the given graph it is clear that coordinates of point K are (2,3).

Put x=2 and y=3 in (1).

[tex]3>-2(2)+10\Rightarrow 3>6[/tex] False.

From the given graph it is clear that coordinates of point B are (4,7).

Put x=4 and y=7 in (1).

[tex]7>-2(4)+10\Rightarrow 7>2[/tex] True.

Put x=4 and y=7 in (2).

[tex]7>\dfrac{1}{2}(4)-2\Rightarrow 7>0[/tex] True.

Since both inequalities are true for B(4,7), therefore point B is the solution.

From the given graph it is clear that coordinates of point D are (-7,1).

Put x=-7 and y=1 in (1).

[tex]1>-2(-7)+10\Rightarrow 1>24[/tex] False.

Since the given inequalities are false for points E, K and D, therefore they are not the solution.

Answer:

y = 3/4x + 17/4

Step-by-step explanation:

Step 1: Find slope m

m = (5 - 2)/(1 + 3)

m = 3/4

y = 3/4x + b

Step 2: Find b

5 = 3/4(1) + b

5 = 3/4 + b

b = 17/4

Step 3: Rewrite equation

y = 3/4x + 17/4

Answer:

y = 3/4x + 17/9

Step-by-step explanation:

Find the slope:

5 - 2/ 1 - (- 3)

3/ 1 + 4

3/4

Find the y-intercept:

2 = 3/4(-3) + b

2 = -9/4 + b

17/4 = b

Put it in an equation:

y = 3/4x + 17/9

Answer:

3) (x – 2)^2 + (y + 1)^2 = 16

Step-by-step explanation:

Equation of circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center, and r is the radius.

From the graph, we see the center is at (2, -1), so h = 2, and h = -1.

The radius is 4, so r = 4.

The equation is

(x - 2)^2 + (h - (-1))^2 = 4^2

(x - 2)^2 + (h + 1)^2 = 16

Answer:

Step-by-step explanation:

Given,

R = 8 m

H = 15 m

Slant height :

[tex] = \sqrt{ {r}^{2} + {h}^{2} } [/tex]

[tex] = \sqrt{ {(8)}^{2} + {(15)}^{2} } [/tex]

[tex] = \sqrt{64 + 225} [/tex]

[tex] = \sqrt{289} [/tex]

[tex] = \sqrt{ {(17)}^{2} } [/tex]

[tex] = 17 \: m[/tex]

Now, Finding the surface area of the cone:

[tex]\pi \: r(r + s)[/tex]

Plugging the values:

[tex] = \pi \: \times 8(8 + 17)[/tex]

[tex] = 8\pi \: \times 25[/tex]

[tex] = 200 \: \pi[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

money invested at 3% is $4000

Step-by-step explanation:

let the money invested in 3% account be x

then money invested in 5% account = 6000 - x

we know interest = p*r*t/100

p is the principle amount invested

here t = 1 year

interest on 3% money

interest= x*3*1/100 = 3x/100

interest on 5% money

interest= (6000-x)*5*1/100

Total interest earned on both the account

3x/100 + 5(6000-x)/100 = (3x + 30,000 - 5x)/100 =( 30000-2x)/100

given that total interest earned = $220

thus

( 30000-2x)/100 = 220

=> 30000-2x = 220*100= 22,000

=> -2x = 22,000- 30,000

=> x = -8000/-2 = 4000

Thus, money invested at 3% = x = $4000

Answer:)

$4000

Step-by-step explanation:

Answer:

y ≥ x - 2

Step-by-step explanation:

I'm pretty sure this will be the answer, a thanks a rating of a 5 star would be helpful :)

The inequality shown by the shaded region in the graph with the boundary line y = x-2 is y ≥  x - 2

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given is an inequality, with the boundary line y = x-2

A solid line, and the shaded part is above the line.

y ≥  x - 2

Hence, The inequality shown by the shaded region in the graph with the boundary line y = x-2 is y ≥  x - 2

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Answer:

Option (2)

Step-by-step explanation:

This question is incomplete; find the picture attached which makes this question complete.

Vertices of the given triangle are A(-2, -4), B(2, -1) and C(3, -4).

Length of AB = [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]

AB = [tex]\sqrt{(2+2)^2+(-1+4)^2}[/tex]

     = [tex]\sqrt{16+9}[/tex]

     = 5 units

Since AB = AC

AC = 5 units

Similarly, BC = [tex]\sqrt{(3-2)^2+(-4+1)^2}[/tex]

BC = [tex]\sqrt{10}[/tex] units

Therefore, perimeter of the given triangle = AB + AC + BC

                                                                      = 5 + 5 + √10

                                                                      = (10 + √10) units

Option (2) will be the answer.

Answer:

b

Step-by-step explanation:

Answer:

24.

Step-by-step explanation:

To solve this question, you might need to do a little math. So, there are four digits, correct? And they cannot be repeated? Well, you can solve this problem by creating the numbers. Here are the ones I came up with:

1234

1324

1432

1342

1243

1423

See? There are 6. You can do the same with these:

2341

2413

2314

2143

2134

2134

These are only half of the expressions. Hopefully this helps you come up with the rest. Best of luck.

Hey there! :)

Answer:

21 minutes.

Step-by-step explanation:

Begin by calculating the number of 12 hour periods in a week.

Each day contains two 12 hour periods. (24 hours/12 = 2)

There are 7 days in a week, therefore:

2 × 7 = 14 times the watch will lose minutes.

Multiply to find the total number of minutes lost:

14 × 1.5 = 21 minutes.

Answer:

21 minutes

Step-by-step explanation:

There are 24 hours in one day, and 7 days per week.  Thus there are

(24)(7), or 168, hours in one week, or 14 - 12-hour periods.

Thus, we multiply 14 - 12-hr periods to answer this question:

1.5 minutes / 14 - 12-hour periods)= 21 minutes will be lost in one week.

Answer:

Step-by-step explanation:

Answer:

1. B

2.B

3. B

4. B

Step-by-step explanation:

Answer:

t

Step-by-step explanation:

The letter that comes next in the given sequence is K.

The given sequence is F H K N Z.

We need to find which letter comes next in the given sequence.

The pattern followed by the given sequence is they are letters of sounding board consonants.

Therefore, the letter that comes next in the given sequence is K.

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It will be a negative.

for an example: -20 for x would mqke 2x + 1 into -39 and 8x + 5 into -155. that's 116 apart, so maybe -2(8) + 5 = -11

-2(2) + 1 = -3

but that's only 8 apart, so it'd be higher.

-4(2) + 1 = -7

-4(8) + 5 = -27

BOOM

Tadaaaa,

You probably thought positive, but sometimes it's negative, you know what I mean?

Answer:

y = -4

Step-by-step explanation:

x = 3 is a vertical line.

The perpendicular line passes through (0, -4) (x, y)

y = -4

The line is perpendicular, so the line should be also horizontal.

Answer:

y = -4

Step-by-step explanation:

The line x = 3 is a vertical one; any line perpendicular to x = 3 is a horizontal line (which has a zero slope).  

Thus, the desired line is a horizontal one that passes through (0, -4) and is represented by y = -4.

We can find roots by setting f(x) = 0 --> x^4 - x^3 - 13x^2 + x + 12 = 0.

Factoring f(x) to make things easier for us gives us (x - 1)(x + 1)(x - 4)(x + 3), which, equal to 0, gives us the ability to set each set of parentheses = 0.

x - 1 = 0 gives us x = 1.

x + 1 = 0 --> x = -1.

x - 4 = 0 --> x = 4.

x + 3 = 0 --> x = -3.

our roots are x = 1, -1, 4, and -3.

Answer:

The answer is 19

Step-by-step explanation:

I am not good at explainig at all and im not sure how to explain but I had this question

Cecilia is 19 m behind the Arman.

Arman, Babken, and Cecilia decided to compete in a 100m run.
When Arman crossed the finish line, Babken was 10m behind him.
When Babken crossed the finish line, Cecilia was 10m behind him.

percentage is the ratio of composition of matter to the overall composition of matter multiplied by 100.

Here,
When Babken is 10m behind the Arman, distance covered by babken is 90 m. Cecilia is 10 m behind when Babken cross the finish line implies Cecilia cover 90% of Babken covered distance.
So Cecilia covers 90% of Babken covered distance when Arman crossed finish line.

As arman crossed finish line Cecilia is at  = 90% of run covered by babken, 
= 90 * 90/100
= 81
Now, Cecilia behind Arman when he crossed the finish line = 100-81
=19

Thus, Cecilia is 19 m behind the Arman.

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Answer:

The total number of books is 1020.

Step-by-step explanation:

Denote the books by their first letter.

From the provided information:

Compute the expression of T as follows:

[tex]H = A-80\\\\\frac{1}{5}T=A-80\\\\T=5A-400...(i)[/tex]

Compute the value of C in terms of A:

[tex]C=\frac{1}{4}T\\\\C=\frac{1}{4}\times {5A-400}\\\\C=\frac{5}{4}A-100...(ii)[/tex]

Compute the value of A as follows:

Use expressions (i) and (ii):

[tex]T=S+C+H+A\\\\5A-400=\frac{3}{4}A+\frac{5}{4}A-100+A-80+A\\\\5A-400=4A-180\\\\A=220[/tex]

Compute the value of T as follows:

[tex]T=5A-80\\\\T=(5\times 220)-80\\\\T=1100-80\\\\T=1020[/tex]

Thus, the total number of books is 1020.

Answer:

L: y= -4x + 17

Step-by-step explanation:

For a line L to pass through two points, we use the slope formula to calculate the slope, m, where

m = (y2-y1) / (x2-x1)

= (9-1) / (2-4)

= 8 / -2

= -4

Next we use the point slope form to find the line equation:

L: (y-y1) = m (x-x1)

substitute (x1,y1) = (4,1)

L: y-1 = -4 (x-4)

Simplify:

L: y = -4x + 16 + 1

L: y= -4x + 17

Check: substitute (4,1)

y = -4(4)+17 = 1  checks

substitute (2,9)

y = -4(2)+17 = 9 checks

so

L: y= -4x + 17

Answer:

y is equal to 5 and x is equal to 11

Answer:

The independent variable is the depth below the surface of the lake the dependent is the tempeature of the water

Step-by-step explanation:

Tempeture = depth x

Answer:  

1.) The sum of 12 and x   12 + x   or   x + 12

2.) The product of 25 and p     25 × p    or  25p

3.) 24 increased by twice a number z    24 + 2z     or  2z + 24

4.) The quotient of a number x and 4   x ÷ 4 .  or   x/4

5.) 6 less than a number x     x - 6

6.) One-half of n squared       n² ÷ 2     or    n²/2    

Step-by-step explanation:  In most cases, the first expression uses symbols that are commonly used in arithmetic or elementary math.  As you advance into Algebra, the ÷ and × are rarely used in favor of  /  or fraction form like   [tex]\frac{x}{4}[/tex] and  [tex]\frac{x^{2} }{2}[/tex]  for division.  Parentheses replace × for multiplication, for example  (25)(p)=25p   to avoid confusion with x, commonly used as an unknown or variable.

Answer:

2) 49.5°

Step-by-step explanation:

From the above diagram, we are asked to calculate the measure of ∠C.

The formula to be used for this calculation is given as:

∠C = 1/2 (Far Arc - Near Arc)

∠BAD = 127° = Far Arc

∠EAF = 28° = Near Arc

The measure of ∠C = 1/2 (BAD - EAF)

= 1/2 ( 127° - 28°)

= 1/2 × 99°

measure of ∠C = 49.5°

Answer:

49.5

Step-by-step explanation:I took the test