What are the digits of pii?

Answer:

[tex]\large\boxed{x=\dfrac{5\pi}{4}\ \vee\ x=\dfrac{7\pi}{4}}[/tex]

Step-by-step explanation:

The first step in attachment.

[tex]\sin(x)=-\dfrac{\sqrt2}{2}\to x=-\dfrac{\pi}{4}+2k\pi\ \vee\ x=\dfrac{5\pi}{4}+2k\pi\\\\x\in[0,\ 2\pi)\\\\\text{Therefore}\\\\x=-\dfrac{\pi}{4}+2\pi=\dfrac{7\pi}{4}\ \vee\ x=\dfrac{5\pi}{4}[/tex]

Answer:

The length of side j is 11.85cm

Step-by-step explanation:

Given that

In triangle JKL,

[tex]\angle k=15[/tex]

[tex]\angle l=41[/tex]

Side k=LJ=3.7cm

To find side j=KL:

By using sine rule,

We can write as

[tex]\frac{SinK}{LJ} = \frac{SinL}{JK} = \frac{SinJ}{KL} \\\frac{Sin15}{3.7} = \frac{Sin41}{JK} = \frac{SinJ}{KL}[/tex]

Using property of triangle,

[tex]\angle k+\angle l+\angle j=180[/tex]

[tex]15+41+\angle j=180[/tex]

[tex]\angle j=124[/tex]

[tex]\frac{Sin15}{3.7} = \frac{Sin41}{JK} = \frac{Sin124}{KL}\\\frac{Sin15}{3.7} = \frac{Sin124}{KL}\\KL=3.7\frac{Sin124}{Sin15}\\KL=3.7\frac{0.8290}{0.2588}\\KL=11.85cm[/tex]

Thus,

The length of side j is 11.85cm

Answer: 11.9

Step-by-step explanation:

nearest 10th you have to round it

Answer:

yes

what grade

Step-by-step explanation:

Answer:

  d)  1/6 + (-3/8) + 1/2

Step-by-step explanation:

For equivalence, the sign of each term must match the original. Here's how the answer choices stack up:

  a) wrong sign for -3/8

  b) wrong sign for -3/8 and for 1/2

  c) wrong sign for 1/2

  d) correct choice

Final answer:

Option (c) 1/6 + (-3/8) + (-1/2) is equivalent to the original expression 1/6 - 3/8 + 1/2 because it accurately reflects the original values and operations without any alterations.

Explanation:

The student's question asks to find an expression equivalent to the arithmetic operation 1/6 - 3/8 + 1/2. To find the equivalent expression, we should look for an option that represents the same operation without any alteration to the values or their signs.

Upon review, option (c) 1/6 + (-3/8) + (-1/2) is the correct equivalent expression because it maintains the original values and their associated signs. The negative signs in front of the fractions in this option simply denote subtraction, which matches the original expression given.

The use of parentheses in the alternative expression is typical in algebra to emphasize operations, but it does not change the value of the expression. Thus, the correct option is c.

Answer:

I thinks its r = 11

Step-by-step explanation:

So you just need to take the number to the r and multipliy it by r So,

9x2=18

then minus it by the other number which would Be 7 so.

18-7=11

Answer:

11

Step-by-step explanation:

(-9 times 2) - 7

18 - 7

11

Answer:

t = 3h

Step-by-step explanation:

Given

h = [tex]\frac{1}{3}[/tex] t

Multiply both sides by 3 to clear the fraction

3h = t

Picture 1: The amount of tax for Veena's meal is $1.02

Picture 2: Christian reads [tex]\frac{3}{8}[/tex] books per week.

Picture 3: 80% is equal to [tex]\frac{4}{5}[/tex].

Step-by-step explanation:

Picture 1: Veena ate lunch at a deli. She ordered turkey sandwich for $9.25 and a salad for $4.35. The tax was 7.5%. What is the amount of tax for Veena's meal.

Given,

Price of turkey sandwich = $9.25

Price of salad = $4.35

Total amount = 9.25+4.35 = $13.60

Tax = 7.5%

Amount of tax = 7.5% of total cost

Amount of tax = [tex]\frac{7.5}{100}*13.60[/tex]

Amount of tax = [tex]\frac{102}{100} = \$1.02[/tex]

The amount of tax for Veena's meal is $1.02

Picture 2: Christian reads 1/4 book every 2/3 week.  How many books does Christian read per week?

Given,

Books read every 2/3 weeks = 1/4 books

[tex]\frac{2}{3}\ weeks=\frac{1}{4}\ books\\[/tex]

For determining the number of books read per week, we will multiply both sides by [tex]\frac{3}{2}[/tex]

[tex]\frac{3}{2}*\frac{2}{3}\ week=\frac{1}{4}*\frac{3}{2}\ books\\\\1\ week = \frac{3}{8}\ books\\\\[/tex]

Christian reads [tex]\frac{3}{8}[/tex] books per week.

Picture 3: What percent is equivalent to [tex]\frac{4}{5}[/tex]?

We will multiply the given fraction with hundred for calculating the percentage.

[tex]\frac{4}{5}*100\\\\\frac{400}{5}\\\\80\%[/tex]

Therefore,

80% is equal to [tex]\frac{4}{5}[/tex].

Keywords: percentage, division

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To prove congruence by SSS, two statements are needed about equal sides: AC―――― ≅ ED―――― and DE―――― ≅ BC――――. A third unlisted statement equating the other sides is also required.

To prove two triangles are congruent using the Side-Side-Side (SSS) Postulate, we need to establish that all three corresponding sides of the triangles are equal in length. Statement B indicates that AC―――― ≅ ED――――, which provides one pair of corresponding sides. Statement C suggests that DE―――― ≅ BC――――, providing a second pair of corresponding sides. Lastly, if we had information that AB―――― = DF――――, not provided in the options but necessary to complete the SSS congruence, then we could establish the congruence of the two triangles. Therefore, the statements needed for SSS congruence proof are options B and C, along with an unlisted statement that equates the third pair of corresponding sides.

Answer:

see explanation

Step-by-step explanation:

(1)

Given the perimeter then the third side is the perimeter subtract the sum of the 2 given sides, that is

third side

= 4x + 3y - (x - y + x + y)

= 4x + 3y - 2x ← collect like terms

= 2x + 3y

(2)

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

Here b = 2x + 6 and h = x - 2, thus

A = [tex]\frac{1}{2}[/tex](2x + 6)(x - 2) ← expand factors using FOIL

   = [tex]\frac{1}{2}[/tex](2x² + 2x - 12) ← distribute

   = x² + x - 6 ← in standard form

Answer:

x=11

Step-by-step explanation:

7(x)-7(3)=56

7x-21=56

7x-21+21=56+21

7x=77

7x/7=77/7

x=11

Answer:

1915 miles more to drive to complete their trip.

Step-by-step explanation:

Given:-

Total distance to travel (D) = 2598 miles.

Distance travelled (d) = 683 miles.

To calculate = remaining distance (r) to complete trip.

Remaining distance = Total distance minus Distance travelled

i.e.  [tex]r=D-d[/tex]

[tex]r=2598-683[/tex]

[tex]r=1915\ miles[/tex]

Therefore kalsbeeks have to travel 1915 miles more to complete their trip.

Answer:

11

Step-by-step explanation:

- 7 + 8 = 11 and the absolute value of 11 is 11

Answer:

(12-7x)

Step-by-step explanation:

144 − 49x²

by observation, we can see that 144 = 12² and 49 = 7²

hence we can rewrite the equation

144 − 49x²

= 12² - 7²x²

= 12² - (7x)²

recall that the expression x² - y² = (x+y)(x-y)

hence,

12² - (7x)²

= (12 + 7x)(12-7x)

(12-7x) appears in the expression above, hence 12 -7x is a factor

Answer:

Answer is C

Step-by-step explanation:

Option A

The equation [tex]4x^2 - 3x + 1 = 0[/tex] has two imaginary solutions

Solution:

Given that we have to determine the type and number of solutions of given quadratic equation

[tex]4x^2 - 3x + 1 = 0[/tex]

[tex]\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

In a quadratic equation, the discriminant helps tell you the number of real solutions to a quadratic equation

In the case of a quadratic equation [tex]ax^2 + bx + c = 0[/tex], the discriminant is [tex]b^2 -4ac[/tex]

[tex]\text{If } b^{2}-4 a c=0 ;$ then the given quadratic equation has one real root\\\\If b^{2}-4 a c>0,$ then the given quadratic equation has two real roots[/tex]

If [tex]b^2-4ac<0[/tex], then the given quadratic equation has two imaginal roots which are complex conjugates

Given quadratic equation is:

[tex]4x^2 - 3x + 1 = 0[/tex]

Here a = 4 and b = -3 and c = 1

The discriminant is given as:

[tex]b^2 - 4ac = (-3)^2 - 4(4)(1) = 9 - 16 = -7\\\\b^2 - 4ac = -7\\\\b^2-4ac < 0[/tex]

Therefore the given equation has two imaginary solutions

Answer:

two imaginary solutions

Step-by-step explanation:

Answer:

[tex]3a^4[/tex]

Step-by-step explanation:

What is the cube root of  [tex]27a^{12}[/tex]? This is the question.

We can write:

[tex]\sqrt[3]{27a^{12}}[/tex]

We will use the below property to simplify:

[tex]\sqrt[n]{a*b}=\sqrt[n]{a}  \sqrt[n]{b}[/tex]

So, we have:

[tex]\sqrt[3]{27a^{12}} =\sqrt[3]{27} \sqrt[3]{a^{12}}[/tex]

We will now use below property to further simplify:

[tex]\sqrt[n]{x} =x^{\frac{1}{n}}[/tex]

Thus, we have:

[tex]\sqrt[3]{27} \sqrt[3]{a^{12}} =3*(a^{12})^{\frac{1}{3}}[/tex]

We know power to the power rule:  [tex](a^z)^b=a^{zb}[/tex]

Now, we have:

[tex]3*(a^{12})^{\frac{1}{3}}\\=3*a^{\frac{12}{3}}\\=3a^4[/tex]

This is the correct answer:  [tex]3a^4[/tex]

Answer:

Italy Time is in the Central European Time Zone . Central European Standard Time ( CET ) is 1 hours ahead of Greenwich Mean Time ( GMT+1 ).

Step-by-step explanation:

Central European Time Zone

Italy's time zone is one hour ahead of GMT (Greenwich Mean Time), so if it is 1 PM GMT, it would be 2 PM in Italy. This reflects the Time Zone Difference concept.

If Italy's time zone is GMT + 1, and it is currently 1 PM GMT, then the time in Italy would be 2 PM. This is due to the fact that Italy is one hour ahead of GMT (Greenwich Mean Time). Therefore, to convert from GMT to Italy's time zone, one simply needs to add one hour. For example, if it was 5 PM in GMT, it would be 6 PM in Italy, and so on. This concept is referred to as Time Zone Difference.

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Answer:

Arc VU = 44°

Step-by-step explanation:

Given:

Arc SV means ∠SOV = 120°

Arc VU means ∠VOU = ?

We know that, from central angle theorem, central angle made by arc is twice the angle made the same arc at the circumference.

∴ ∠SOU = 2 × ∠STU

⇒ ∠SOU = 2(82°)

⇒ ∠SOU = 164°

Now, from angle addition theorem,

∠SOU = ∠SOV + ∠VOU

⇒ 164° = 120° + ∠VOU

⇒ 164° - 120° = ∠VOU

⇒ ∠VOU = 44°

Therefore, the measure of the arc VU is 44°.

Answer:

The actual length in feet of the car is 48 feet.

Step-by-step explanation:

Given:

Tiffany sketched a picture of a car she used the scale 2 inches : 12 feet.

In her sketch the car is 8 inches long.

Now, to find the length in feet of the actual car.

Let the actual length of car in feet be [tex]x\ feet.[/tex]

And the length of car in her sketch is 8 inches.

Thus, 8 inches is equivalent to [tex]x\ feet[/tex].

So, the ratio of the scale used by Tiffany as given is 2 inches : 12 feet.

Thus, 2 inches is equivalent to 12 feet.

Now, to get the actual length of car by using cross multiplication method:

[tex]\frac{2}{12} =\frac{8}{x}[/tex]

By cross multiplying we get:

⇒  [tex]2x=96[/tex]

Dividing both sides by 2 we get:

⇒  [tex]x=48[/tex]

⇒  [tex]x=48\ feet.[/tex]

Therefore, the actual length in feet of the car is 48 feet.

Answer:-18

Step-by-step explanation: if f(x)= -9x

And x =2

-9(2)

= -18

Answer:

f(-2)=-18

Step-by-step explanation:

given f(x)=9x...........(1)

put x=-2 in equation (1)

f(-2)=[tex]9\times(-2)[/tex]

f(-2)=-18 answer

Answer: OPTION C

Step-by-step explanation:

There are some transformations for a function f(x). Some of them are shown below:

1. If [tex]f(x)+k[/tex], the function is shifted up "k" units.

2. If [tex]f(x)-k[/tex], the function is shifted down "k" units.

3. If [tex]f(x+k)[/tex], the function is shifted left "k" units.

4. If [tex]f(x-k)[/tex], the function is shifted right "k" units.

In this case you know that the function "g" is the transformation of the function "f".

Observe that the function "f" intersects the y-axis at:

[tex]y=2[/tex]

And the function "g" intersects the y-axis at:

[tex]y=-2[/tex]

Therefore, since both functions are 4 units apart, you can conclude that the function "f" was shifted down 4 units to get the function "g".

Then, the rule that shows that transformation is:

[tex]g(x)=f(x)-4[/tex]

Answer:

36

Step-by-step explanation:

since a fair die has 6 sides (i.e 6 possible outcomes),

P (rolls a 4 on 1 roll) = 1/6

hence if he rolls the die 216 times, we would expect to roll a 4 for 1/6 of the time. I.e.

expected number of times to roll a 4

= (1/6) x 216 = 36 times.

Answer:

Answer:

36

Step-by-step explanation:

since a fair die has 6 sides (i.e 6 possible outcomes),

P (rolls a 4 on 1 roll) = 1/6

hence if he rolls the die 216 times, we would expect to roll a 4 for 1/6 of the time. I.e.

expected number of times to roll a 4

= (1/6) x 216 = 36 times.

Step-by-step explanation:

Answer:

(1/4) ^3 = 0.0833333333

Answer:

12

Step-by-step explanation:

28/2=14

16+14=30

30-6=24

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

4*2=8

10-8=2

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

24/2=12

Answer:

[tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex] can be written in power notation as [tex]a^{4}\times 13^{2}[/tex]

Step-by-step explanation:

The given expression

[tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex]

Writing a\times (-a)\times 13\times a\times (-a)\times 13 in power notation:

Let

[tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex]

= [tex][13\times13][(a\times (-a)\times a\times (-a)][/tex]

As

[tex]13\times13 = 13^{2}[/tex] , [tex]a\times a = a^{2}[/tex] , [tex](-a)\times (-a) = (-a)^{2}[/tex]

So,

[tex]=[13^{2}][a^2\times (-a)^2][/tex]

As

[tex](-a)^2 = a^{2}[/tex]

So,

[tex]=[13^{2}][a^2\times a^2][/tex]

As ∵[tex]a^{m} \times a^{n}=a^{m+n}[/tex]

[tex]=[13^{2}][a^{2+2}][/tex]

As ∵[tex]a^{m} \times a^{n}=a^{m+n}[/tex]

[tex]=13^{2}\times a^{4}[/tex]

[tex]=a^{4}\times 13^{2}[/tex]

Therefore, [tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex] can be written in power notation as [tex]a^{4}\times 13^{2}[/tex]

Keywords: power notation

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Answer:

The correct option is E. 8

The value of h is 8 unit.

Step-by-step explanation:

Given:

Δ BAD ~ Δ CBD

AC = 20

DC = 4

∴ [tex]AD = AC - DC=20-4=16[/tex]

To Find:

h = ?

Solution:

Δ BAD ~ Δ CBD      ................Given

If two triangles are similar then their sides are in proportion.

[tex]\frac{BD}{CD} =\frac{AD}{BD} =\frac{BA}{CB}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]  

On substituting the given values we get

[tex]\dfrac{BD}{CD} =\dfrac{AD}{BD}[/tex]

[tex]\dfrac{h}{4} =\dfrac{16}{h}\\\therefore h^{2}=64\\\therefore h=8\ unit[/tex]

The value of h is 8 unit.

Answer:

8

Step-by-step explanation:

Answer:

440 pounds

Step-by-step explanation:

Ratio is basically "parts".

We have ratio of 4:3:4, that is a total of 4 + 3 + 4 = 11 parts

The apple is 4 parts and total amount is 160 pounds. So each "part" is:

160/4 = 40 pounds

The total pounds of all 3 fruits is 11 parts * 40 pounds per part = 11 * 40 = 440 pounds

hence,

Truckload of fruits weigh at 440 pounds

with an expression like 3x6 you can separate parts of the expression using parentheses like: 3(2+4)

you can find ways to separate a variable (like 6) into a sum of two addends

ex 1+5

0+6

3+3

so a distributive version of 3x6 is 3(2+4) = (3x2) + (3x4)

Answer:

e) Shamika= 224 balloon, Crystal= 112 balloon, Aliya= 114 Balloon.

f)  We know,Crystal sold "b" balloon

           Aliya sold (b+2) balloon

          Shamika sold 2b balloon.

As per data given in question part c that each balloon cost $2 and Total cost of balloon is $900.

Now, solving to find how much each student sold balloon at school´s winter dance.

As we know total cost is $900 and each balloon cost is $2.

∴ Total cost= [tex]Total\ quantity \times cost\ of\ each\ unit[/tex]

Total quantity= [tex]{b+(2+b)+2b}[/tex]

∴ [tex]\$ 900= {b+(2+b)+2b}\times \$ 2[/tex]

Once we solve, we will get the value of b as 112 balloon, which is the number of balloon sold by Crystal.

Substituting the value of b in the equation of Aliya and Shamika, we will get the number of balloon sold by them.

Which is 114 and 224 respectively.

Step-by-step explanation:

Given: Crystal sold "b" balloon

           Aliya sold (b+2) balloon

          Shamika sold 2b balloon.

As per data given in question part c that each balloon cost $2 and Total cost of balloon is $900.

Now, solving to find how much each student sold balloon at school´s winter dance.

As we know total cost is $900 and each balloon cost is $2.

∴ Total cost= [tex]Total\ quantity \times cost\ of\ each\ unit[/tex]

Total quantity= [tex]{b+(2+b)+2b}[/tex]

∴ [tex]\$ 900= {b+(2+b)+2b}\times \$ 2[/tex]

Opening the parenthesis.

⇒[tex]\$ 900= (b+2+b+2b)\times \$ 2[/tex]

⇒[tex]\$ 900= 2+4b \times 2[/tex]

Dividing both side by 2

⇒ [tex]\$ 450= 2+4b[/tex]

Subtracting both side by 2

⇒ [tex]\$ 448= 4b[/tex]

Cross multiplying

∴[tex]b= \frac{448}{4} = 112[/tex]

∴ b= 112.

Hence, we can say Crystal have sold 112 balloons.

Next subtituting the  value of "b" in the equation for Aliya and Shamika to get number of balloon they have sold.

We know, Aliya sold b+2 balloons

∴ Aliya sold= [tex]112+2= 114\ balloon[/tex]

Aliya sold 114 balloon.

We know, Shamika sold 2b balloons

∴[tex]2\times 112= 224 balloon.[/tex]

Shamika sold 224 balloon.

Answer:

24 hours in first week and 29 hours in second week.

Step-by-step explanation:

Given: Orlando work at $6/h in first week and at $7/h in second week.

           Total earning is $347 in both weeks.

Let the number of hours Orlando work in first week be`x` hours

∴ working hours in second week is (x+5) hours

Now, solving to find the number of working hours.

⇒ Total earning= earning in first week+earning in second week.

⇒ [tex]\$ 347= x\times 6+(x+5)\times 7[/tex]

Opening the parenthesis and solving it.

⇒ [tex]\$ 347= 6x+7x+35[/tex]

Subtracting both side by 35

⇒ [tex]312= 13x[/tex]

∴ x= [tex]\frac{312}{13} = 24\ h[/tex]

∴ Working hours in first week is 24 hours

   Working hours in second week is [tex]24+5= 29\ h[/tex]