Simplify the following without a calculator ( a) √3 × √3 (b)( 2√7)² (c) 3√6 × 4√6

Answer:

[tex]y=\displaystyle\frac{2}{3}x[/tex]

Step-by-step explanation:

Hi there!

The given linear equations are organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope of the line and b is the y-intercept (the value of y when x=0)

First, we can determine the slope using the following formula:

[tex]m=\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in any two points from the graph that falls on the line (you can see below that I've used (3,2) and (0,0):

[tex]m=\displaystyle\frac{2-0}{3-0}\\\\m=\displaystyle\frac{2}{3}[/tex]

Therefore, the slope of the line is [tex]\displaystyle\frac{2}{3}[/tex]. Plug this into [tex]y=mx+b[/tex] as m:

[tex]y=\displaystyle\frac{2}{3}x+b[/tex]

We know that the point (0,0) falls on the line. Because y=0 when x=0, we know that the y-intercept (b) is 0:

[tex]y=\displaystyle\frac{2}{3}x+0\\\\y=\displaystyle\frac{2}{3}x[/tex]

I hope this helps!

Answer:

8/3

Step-by-step explanation:

To make this function be continuous, we need to make the one-sided limits of the function at x=3 equal.

this means that 3c+8=9c-8

8=6c-8

16=6c

c=16/6 = 8/3

The value of constant c that makes the given function continuous at (-∞ , ∞) is 6.

What do you mean by continuity of a function ?

Continuity of a function meant all the points in the given interval satisfy the function.

We know that the conditions for which a function is continuous at b = x is :

a) f(x) exists

b) [tex]\lim_{ b\to x}[/tex] or f(b) exists.

c) [tex]\lim_{b \to x}[/tex] f(b) = f(x)

We know that for any value of c , for b ∈ ( - ∞ , 3] the function is continuous and for b ∈ ( 3 , ∞) the function is continuous. So , for any value of c, the first two conditions are satisfied.

Now we need to check for the continuity of the function at b = 3.

or

[tex]\lim_{b \to 2}[/tex] f(b) = c × 3 + 8

or

[tex]\lim_{b \to 2}[/tex] f(b) = 3c + 8

Now , check for the continuity of the function for other interval at b = 3.

[tex]\lim_{b \to 2}[/tex] f(b) = c × 9 - 8

or

[tex]\lim_{b \to 2}[/tex] f(b) = 9c - 8

To be continuous both values should be equal.

i.e.,

3c + 8 = 9c - 8

The value of constant c will be :

6c = 18

or

c = 6

Therefore , the value of constant c that makes the given function continuous at (-∞ , ∞) is 6.

Learn more about continuity of a function here :

https://brainly.com/question/27896299

#SPJ2

Answer:

c. 18%

e. 46%

Step-by-step explanation:

c. Since the time given is 5.9, it is easiest to just calculate for every 0.1 second. So, there are 50 0.1 seconds in 5 seconds. If you divide 100/50 you get 2. So that is your percentage for each 0.1 seconds. It says less than 5.9 so theres 10 0.1 seconds. If you multiply 9x2 you get 18%.

e. based on 2% for every 0.1 seconds, there are 5 0.1 seconds between 5 and 5.5 and 18 0.1 seconds between 7.2 ad 10. 23x2= 46%

I would like to note that this question is incorrectly asked as it says less than which means the time given wouldnt count. It would have made much more sense to say 5.9 minutes or less.

Im pretty sure this is the right answer but it could be c. 20% and e. 50%

Hope this helps!

Suppose the time it takes Lizzie to eat an apple is uniformly distributed:

a. The distribution of X is Uniform, denoted as X ~ U(5, 10).

b. To find the probability that it takes Lizzie more than 11 minutes to finish the next apple, find the area of the distribution curve to the right of 11. Since the distribution is uniform, the probability is the ratio of the length of the interval [11, 10] to the total length of the interval [5, 10].

Probability (X > 11) = (10 - 11) / (10 - 5) = -1 / 5 = 0 (rounded to 4 decimal places)

c. Probability (X < 5.9) = (5.9 - 5) / (10 - 5) = 0.18

d. Probability (5.5 < X < 7.2) = (7.2 - 5.5) / (10 - 5) = 0.34

e. To find the probability that it takes Lizzie fewer than 5.5 minutes or more than 7.2 minutes to finish the next apple, find the sum of the probabilities of these two disjoint events:

Probability (X < 5.5 or X > 7.2) = Probability (X < 5.5) + Probability (X > 7.2)

= (5.5 - 5) / (10 - 5) + (10 - 7.2) / (10 - 5)

= 0.1 + 0.36

= 0.46

Find out more on probability here: https://brainly.com/question/30390037

#SPJ3

Answer:

60 in²

Step-by-step explanation:

Area of parallelogram = base x height

= 10 in x 6 in

= 60 in²

The area of the parallelogram is 60in².

Answer: 5

Step-by-step explanation:

V = lwh = 20 * 12 * ? = 1200

240 * ? = 1200

? = 5

Answer:

60 divided by 2 = 30

We half it because Angle E halfs Angle D

Step-by-step explanation:

As with all quadrilaterals, the sum of the interior angles of a rhombus is 360 degrees; as with a parallelogram, the angles of opposite pairs of vertices are equal, and the sum of the angles of two adjacent vertices is 180 degrees.

Step-by-step explanation:

area of ∆ = .5*b*h

b= x+5

h= x-5/2

let's do (x+5) * (x-5/2)

x^2+5x-5/2x-25/2

x^2+5/2x-25/2

area = .5x^2+5/4x-25/4

The polynomial expression that represents the area of wall space covered by the display case is (1/2)x² + (5/4)x - 25/4.

A polynomial is a mathematical expression made up of two or more algebraic terms that have been added, subtracted, or multiplied (no division). Polynomial expressions generally comprise at least one variable, as well as constants and non-negative exponents.

The area of a triangle is calculated using the formula: (1/2)*base*height.

We find the area of the triangle-shaped display case. We can see the base of this triangle is x+5 and its height is x - 5/2.

∴ Area of the display case = (1/2)*(x+5)*(x-5/2)

or, area = (1/2)*(x+5)*(2x-5)/2

or, area = (1/4)(2x² + 5x - 25)

or, area = (1/2)x² + (5/4)x - 25/4.

∴ The polynomial expression that represents the area of wall space covered by the display case is (1/2)x² + (5/4)x - 25/4.

Learn more about polynomials and areas of triangles at

https://brainly.com/question/2833285

https://brainly.com/question/17335144

#SPJ2

Answer:

1/12

Step-by-step explanation:

Since these are dependent events, the fractions will vary on the second trial.

First trial 3 green marbles out of a total of 9 marbles. That's a 3/9 chances of the marble being green.

Second trial if you already pulled out a green. 2 green marbles are left with 6 other colors. That makes it a 2/8 odds.

Multiply the fractions and you get 6/72, which simplifies to 1/12.

Answer:

3/9

Step-by-step explanation:

Simply add up the marbles the total being 9 and the 3 green marbles.  

Answer: $29.10

Step-by-step explanation:

Shoes:

10% of 24 is 2.4

The shoes cost 21.60  with the 10% discount and before tax.

Belt:

25% of 10 is 2.5

The belt cost $7.50 with the 25% discount and before tax.

Total:

You still owe 29.10 for the belt and shoes before tax.

You saved $2.4 on the shoes and $2.5 on the belt (total of $4.90)

Answer: m < 1 or m > 7

The correct answer is m < 1 or m > 7.

Step-by-step explanation:

Hope this helps =)

Answer:

A≈3.14m²

Step-by-step explanation:

Answer:

Area of Circle =

\begin{gathered}\pi {r}^{2} \\ = \pi( {1}^{2} ) \\ = 1\pi \\ = \pi {m}^{2} \end{gathered}

πr

2

=π(1

2

)

=1π

=πm

2

Answer:

40

Step-by-step explanation:

[tex]15 \times 2 \frac { 2 } { 3 }\\= 15\times \left(\frac{6+2}{3}\right) \\= 15\times \left(\frac{8}{3}\right) \\= \frac{15\times 8}{3} \\= \frac{120}{3} \\\Longrightarrow \boxed{40}[/tex]

Hope it helps ⚜

The answer is:   " x – (x + 8) " .

{Note:  The simplified form is:  " -8 ."}.
_______
Step-by-step explanation:
We are given:  

→  " A number decreased by the sum of the number and eight."
_______

Let "x" represent the number referred to as "a number."

_______

"{A number} decreased by {the sum of the (number and eight).}"  ;

        ↑                 ↑                                       ↑

       "x"              "(minus)"                       " (x + 8) "          ;
_______

So; we can write this as:
_______
   →    "   x – (x + 8) "  ;
_______

Edit—Addendum:

{Now, if are then asked to simply this expression}:
     →    "   x – (x + 8) "  ;
_______

Then: Rewrite as:
     →    "   x – 1(x + 8) "  ;
_______
Take note of the distributive property of multiplication:
      →  " a(b + c) = ab + ac " ;

_______
Likewise:
     →    "   x – 1(x + 8) "  ;

→ Note the:  " -1(x + 8) ";
_______

 →   -1(x + 8) = (-1*x) + (-1*8) ;

                    = (-1x) + (-8) ;
                    = (-1x – 8) ;
Now, bring down the " ⁺x " :
         →  " x – 1x – 8 " ;  
  Rewrite as:
         →  " 1x – 1x – 8 " ;
      Simplify:
     →  " 1x – 1x – 8 " ;

                      = " (1x – 1x) – 8 " ;

                       = " (0 – 8) " ;

                       =  " -8 " ; which is the simplified form of the
                                          given algebraic expression.
_______

Hope this explanation is helpful to you!
________

Hi!

I can help you with joy! :)

First of all, "the sum of" means we add.

Let the number be r.

So, we add r and 8:

r+8

Now, "decreased" means we subtract, so we subtract

r-(r+8) (Final Answer)

Simplified Form:

r-(r+8)

r-r+8

[tex]\fbox{8}\checkmark[/tex]

Hope it helps!

Enjoy your day!

Feel free to ask if you have any doubts.

~Misty~

Answer:

58

Step-by-step explanation:

(360 - 122 -122)/2= 58

please brainliest

Answer:

58°

Step-by-step explanation:

well first we know that the total degrees all the way around are 360° so the total number must add up to 360°.

vertical angles are the angles across from each other when two lines intersect and we know that vertical angles are congruent (the same) so 122° equals d. Next we look at the angles e and c. It might seem difficult but we remember that vertical angles are congruent so e and c are equal. the sum the first angle(122°) and d(which we already found equals 122°) equals 122+122=244. we learned at the beginning that all the angles must be 360 so 360-244=116. 116 is the sum of e and c but we know e and c are equal so 116/2=58. e=58 and c=58 so there is our answer

d=122°

e=58°

c=58°

I hope this helps!

1) 4x + 5y

→ 4*6 + 5*1

→ 24 +5 = 29

2) 2x (20-y)

→ 2*6 (20-1)

→ 12 *19 = 228

3) x ÷ 3 + y

→ 6 ÷ 3 + 1

→ 2 +1 = 3

4) 4y ÷ 2 + (8x + 10)

→ 4*1 ÷ 2 +(8*6+10)

→ 2 + (48+10)

→ 2 + 58

→ 60

5 ) 5. Patty made $34 baby sitting on each of 3 weekends. If she spent $50 on gifts for her family, how much money does she have left?

Money made each weekend = $34

Money made in 3 weekend = $34*3 =$102

Money spent = $50

Therefore ,

→Money left = Money made in 3 weekends - Money spent

→ Money left = $102 - $50 = $52

6.Carlos solved 20-(2x6) + 8 divide 4 = 29. Is this the correct answer? ( In attachment it's written 29 and not 28 .)

Given equation is ,

→ 20 - (2 × 6) + 8 ÷ 4 = 29

Solve inside the brackets ,

→ 20 - 12 + 8 ÷ 4

Perform division ,

→ 20 -12 + 2

Perform addition ,

→ 22 - 12

Perform subtraction,

→ 10

No , he is wrong the answer should have been 10 but he got 29 .

I hope this helps .

Answer:16feet

Step-by-step explanation:

The explanation is in the attached file

Answer:

a) -0.6

b) 8.1

c) -6.5

d) 5.2¯9. The little line on top of the 9 is "bar notation".

Step-by-step explanation:

Hope this helps =)

Answer:

Robert should put $32 in his wallet.

Step-by-step explanation:

18 + x > 50

-18      -18

x > 32

Hope this helps!

Answer:

What are you referring to?

Step-by-step explanation:

Let ∠1 be x

Let ∠2 be x+84

[tex]\rm\:x+x+84= 180 \degree[/tex]

[tex] \rm \: 2x + 84 = 180[/tex]

[tex] \rm \: 2x = 180 - 84[/tex]

[tex] \rm \: 2x = 96[/tex]

[tex]\boxed{ \bf \: x=48 \degree}[/tex]

[tex]\begin{gathered} \sf \: ∠1 = x \\ \sf \: = 48 \degree\end{gathered}[/tex]

[tex]\begin{gathered} \sf \: ∠2 = x+84 \\ \sf = \: 48+84 \\ \sf∠2 = 132 \degree\end{gathered}[/tex]

Answer:

48°

132°

Step-by-step explanation:

Let the measure of one angle be x°

So, Measure of supplementary angle = (x + 84)°

x° +(x +84)° = 180°

(2x + 84)° = 180°

2x + 84 = 180

2x = 96

x = 96/2

x = 48°

(x + 84)° = 48 + 84 = 132°

Answer:

0.003*10=0.03

0.3*10=3

30x10=300

300x10=3000

Step-by-step explanation:

Multiply each by 10

Answer:

0.03 , 3, 300, 3,000

Step-by-step explanation:

every time you multiply a decimal by 10 you move the decimal to the right once , on a whole number you just add another zero

Answer:

e=26

Step-by-step explanation:

e= 8 + 18 = 26

Answer:

21.748 mph

Step-by-step explanation:

Answer: See below

Step-by-step explanation:

Event 1:

When the aces and twos (8 cards in total) are removed:
52 - 8 = 44 total cards

Since 2 cards (an ace and a two) were removed there are a total of 11 hearts

Probability: 11/44

P = 1/4 or 25%

Event 2:

Since 4 cards (2 aces and 2 two's) were removed there are a total of 22 blacks

Probability: 22/44

P = 1/2 or 50%

Event 3:

There are 12 face cards in the deck

Probability: 12/44

P = 3/11 or 27.27%

Event 4:

Probability of a heart + Probability of not a heart = 1 --> 100%

P(not a heart) = 1 - P(heart)

P = 1 - 1/4

P = 3/4 or 75%

Answer:

y = -2

Step-by-step explanation:

The midline is the horizontal line that passes exactly in the middle between the graph's maximum and minimum points.

From inspection, curve has a maximum at y = 1 and a minimum at y = -5

The midline between these is [tex]y=\frac{1-5}{2}=-2[/tex]

So the equation for the midline of this graph is y = -2  (shown in red on the attached graph)

Answer:

D) 3 1/3 hours

Step-by-step explanation:

10÷3=3.3=3 1/3

Answer:

$321.6915

Step-by-step explanation:

original price= $399.00

20% off $399 is $319.2

$319.2-$15.00=$304.2

0.75% of 304.2 is 2.2815

5% of 304.2 is 15.21+2.2815=17.4915+304.2=321.6915

hope this helps

A percentage is a way to describe a part of a whole. The final cost of the television is $321.69.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that a 55" flat screen television is regularly priced at $399.00. Now, It is on sale for 20% off. Therefore, the cost of the flat screen is,

Cost after discount = $399 - 20% of $399

= $399 - 0.20($399)

= $319.2

The cost after the application of the coupon of $15.00 off on any purchase over $100.00. Therefore, the new cost will be,

New Cost = $319.20 - $15.00

                 = $304.2

Since the tax on the cost is 5.75%, therefore, the cost after the application of the tax is,

Cost after the tax = $304.2 + 5.75% of $304.2

                             = $304.2 + 0.00575($304.2)

                             = $321.69

Hence, the final cost of the television is $321.69.

Learn more about Percentages:

https://brainly.com/question/6972121

#SPJ5

Answer:

15

Step-by-step explanation:

Given the following question:

ABC = 2, 4, and 5
DEF = 6, and 12

We know the two triangles are similar, so we can use the given information to find the hypotenuse for the second triangle.

[tex]2\times3=6[/tex]
[tex]4\times3=12[/tex]
[tex]5\times3=15[/tex]

DEF is three times larger than ABC

? = 15

Hope this helps.

Here is your answer

I hope this answer is ok

Answer:

Carlo is 12 and Daniel is 16.

Step-by-step explanation:

There is probably a formula for this but I just used guess and check. Im assuming that carlo is the 3 and daniel is the 5.