Select all irrational numbers.
√3/16
√4/16
√9/16
√3/4
√9/4

Answer:

new price: $2.9295

Explanation:

original price: 100%

new price: 100% + 5% = 105%

solve:

$2.79 * 105%

$2.9295

Answer:

9,696

Step-by-step explanation:

Answer:

R=50

x=65

x-15=50+2x=180

Answer:  The answer is:  " m∡R = 20° " .

__________________________

Step-by-step explanation:

__________________________

Note that ∡R and ∡Q are "supplementary angles".

In these particular case:

  " m∠R + m∠Q = 180 " ;

We are given (in the picture):

_____________________________

" m∠R = (x - 15) " :

and " m∠Q = 2x " ;

_____________________________

So we plug in these values:

_____________________________

→ m∠R + m∠Q = 180  ;

  → (x - 15) + 2x = 180 ;

  → x - 15 + 2x = 180 ;

  → combine the "like terms" on the "left-hand side of the equation" :

   x + 2x = 1x + 2x = 3x ;

  Rewrite as:  3x - 15 = 180 ;

Now add "15" to each side of the equation:

       3x - 15 + 15 = 180 + 15 ;

 to get:

       3x = 195 ;

Now, divide each side of the equation by "3" ; to isolate "x" on the left-hand side of the equation; and to solve for " x" ;

       3x / 3 = 195/3 ;

    to get:  x = 65 ;

Now, we are to solve for:  m∡R ; which is:  " (x - 15) " ;

 So we substitute "65" ; for "x" ;

→  m∡R = x - 15 = 65 - 15 = 50 ;

The answer is:  " m∡R = 50.°

__________________________________

Note:  Alternate method:

Above; when we have:

 "3x - 15 = 180 " ;

we can divide each side of the equation by "3";

 to get:

   1x - 5 = 60 ;

 → x - 5 = 60 ;

Add "5" to each side of the equation:

     x - 5 + 5 = 60 ;

 → x = 60 ;

and then continue acordingly.

__________________________

Best wishes!

Answer:

-34 - 24i

Step-by-step explanation:

To calculate ( – 2 – 3i)^4, we can use the property that (a + bi)^n = a^n + (n*a^(n-1)b)i + (na^(n-2)*b^2)i^2 + ...

So, ( – 2 – 3i)^4 = (-2 - 3i) * (-2 - 3i) * (-2 - 3i) * (-2 - 3i)

= -2^4 - 2^3 * 3i - 2^2 * 3^2i^2 - 2 * 3^3i^3 - 3^4i^4

= -16 - 24i + 18i^2

= -16 - 24i -18

= -34 - 24i

The solution for the given expression is  7 + 5/12

First we need to write the expression, using fractions, we will get:

(5 + 6/8) + (4 + 4/15) - (2 + 6/10)

We can group like terms, and we will get:

(5 + 6/8) + (4 + 4/15) - (2 + 6/10) = (5 + 4 -2) + (6/8 + 4/15 - 6/10)

Now just simplify that to get.

(5 + 4 -2) + (6/8 + 4/15 - 6/10) =  7 + 3/4 + 4/15 - 3/5

                                                =  7 + 3/4 + 4/15 - 9/15

                                                = 7 + 3/4 - 5/15

                                                = 7 + 9/12 - 4/12

                                                 = 7 + 5/12

That is the answer.

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Answer:

12.87

Step-by-step explanation:

12.00x7%= .87

12.87

Answer:

Step-by-step explanation:

b i think if not it should be a sorry if im wrong

The 6th term of the geometric sequence is 192/243

From the question, we have the following parameters that can be used in our computation:

A geometric sequence is represented as

f(n) = a(r)^(n-1)

Substitute the known values in the above equation, so, we have the following representation

f(6) = 6 * (2/3)^(6-1)

Evaluate

f(6) = 192/243

Hence, the solution is 192/243

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Step-by-step explanation:

Let's call the average speed of the tortoise "t" (in meters per hour) and the average speed of the hare "h" (in meters per hour).

From the problem, we know that:

The tortoise leaves 8 minutes before the hare, so they have a 4-minute head start.

The hare crosses the finish line 4 minutes before the tortoise, so they have a 4-minute lead.

Therefore, the total time it takes for the hare to finish the race is 8 minutes less than the time it takes for the tortoise to finish the race. Let's call this time difference "dt".

The distance the hare runs is 21 meters, and the distance the tortoise runs is also 21 meters, so we have:

h * dt = 21 - t * (dt + 4 minutes)

To solve for the average speeds "t" and "h", we need to convert everything to units of hours. Let's convert 4 minutes to hours:

4 minutes = 4/60 hours = 1/15 hours

So, we can now rewrite the equation in terms of hours:

h * dt = 21 - t * (dt + 1/15 hours)

Rearranging and solving for t, we find:

t = (21 + h * dt) / (dt + 1/15)

Now, the hare runs 0.5 meters per hour faster than the tortoise, so:

h = t + 0.5

Substituting h = t + 0.5 into the equation for t, we get:

t = (21 + (t + 0.5) * dt) / (dt + 1/15)

Solving for t, we find:

t = 40/3 meters per hour

Finally, we can find the average speed of the hare by using h = t + 0.5:

h = 40/3 + 0.5 = 40/3 + 30/60 = 40/3 + 30/3 / 60 = 70/3 meters per hour

So the average speed of the tortoise is 40/3 meters per hour, and the average speed of the hare is 70/3 meters per hour

Angle QNM is =x by alternate angle reason (QU is parallel to MP)

X = 69

Answer:

\(2000 {(1 + \frac{.07}{12}) }^{5 \times 12} = 2835.25\)

The value of x is 1.75 and y is 5. The solution is obtained using properties of congruent triangles.

What is a congruent triangle?

Two triangles that are congruent will have precisely the same three sides and three angles.

The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions.

The triangles are congruent by SAS congruency because

AC = CD (Given)

∠ACB = ∠DCE ( Vertically opposite angles)

BC = CE  (Given)

Thus, Triangle ABC ≅ Triangle DEC

Since, the triangles are congruent, therefore

⇒AC = CD

⇒4y-6 = 2x+6   ...(1)

Also, BC = CE

⇒3y+1 = 4x

⇒(3y+1)/4 = x    ...(2)

Now, substituting the value of x in (1), we get,

⇒4y-6 = 2(3y+1)/4+(6)

⇒4y-6 = (6y+2 +24)/4

⇒16y-24 = 6y+2 +24

⇒10y = 50

⇒y = 5

Now putting the value of y in (2), we get

⇒(3(2)+1)/4 = x

⇒7/4 = x

⇒ x = 1.75

Hence, the value of x is 1.75 and y is 5.

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Answer: y + 7x = -6

Step-by-step explanation:

Standard form: Ax + By = c, where a, b, and c are constants.

Distribute

y - 8 = -7x - 14

Add 8 and 7x to both sides:

y + 7x = -6

Hope it helps :)

The standard form of the equation is y = -7x-14

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given an equation, y-8 = -7(x+2)

We know that standard form of an equation of a line is y = mx+c

Converting into standard form,

y-8 = -7(x+2)

y-8 = -7x-14

y = -7x-14+8

y = -7x-6

Hence, The standard form of the equation is y = -7x-14

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Answer:

9.9 lb of cashews and 23.1 lb of Brazil nuts

Step-by-step explanation:

cashews×$6.80 + Brazil nuts×5.50 = 33 lb × $5.89

C +B = 33lb

C = 33 - B

(33-B)(6.80) + B(5.50) = $194.37

224.4 - 6.80B + 5.50B = 194.37

-1.3B = -30.03

B = 23.1

C = 33 - 23.1

C = 9.9

Answer:

3, 2√2, √7

Step-by-step explanation:

compute the square roots of the next three prime numbers:

√7

√11

√13

Therefore, the next three terms of the sequence are:

{1, √2, √3, 2, √5, √7, √11, √13}

chatgpt

chat

Answer:

-272

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

(12 ÷ 3) 2nd power − (18 ÷ 3 to the 2nd power )) × (4 ÷ 2) →

(12/3)² – (18/3²) × 8 →

16 – 2 × 8 →

16 – 16 →

0

The cost of the molding is given as follows:

$119.30.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The parameters for this problem are given as follows:

d = 9 -> r = 4.5.

(as the radius is half the diameter)

Hence the circumference is given as follows:

C = 2 x π x 4.5

C = 28.27 ft.

The cost is of $4.22 per ft, hence the total cost is given as follows:

4.22 x 28.27 = $119.30.

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The simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.

We can write the simplified form of the given expression using the exponent rule as -

{aˣ/aⁿ} = {aˣ a⁻ⁿ} = {aˣ ⁻ ⁿ}

Given is the expression as -

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\)

We can simplify the expression as -

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (27)^{\frac{1}{2} \times \frac{2}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 27^{\frac{1}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (3)^{3}^{\frac{1}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 3\)

Therefore, the simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.

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Miguel will need to deposit approximately $3,261.25 into the annuity each year for 8 years in order for the annuity to have a total value of $24,000.

What is the annuity?

An annuity is a contract between you and an insurance company that requires the insurer to make payments to you, either immediately or in the future. You buy an annuity by making either a single payment or a series of payments.

We can use the formula for the future value of an annuity:

FV = PMT * \(((1 + r)^n - 1) / r\)

where FV is the future value, PMT is the regular payment, r is the interest rate per compounding period, and n is the number of compounding periods.

In this problem, we want to solve for PMT, given that FV = $24,000, r = 6.6%, n = 8, and payments are made at the end of each year.

First, we need to calculate the interest rate per year, since the annuity is compounded annually:

i = r / 100 = 6.6% / 100 = 0.066

Next, we can plug in the values and solve for PMT:

24000 = PMT *\(((1 + 0.066)^8 - 1) / 0.066\)

24000 = PMT * 7.3605

PMT = 24000 / 7.3605

PMT ≈ $3,261.25

Hence, Miguel will need to deposit approximately $3,261.25 into the annuity each year for 8 years in order for the annuity to have a total value of $24,000.

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The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.

According to the given information:

a. Fourteen more than twice the first integer gives the second integer:

This can be expressed as: 2x + 14 = y

b. The second integer increased by one is the square of the first integer:

This can be expressed as: y + 1 = x^2

Now, we have a system of equations:

1) 2x + 14 = y

2) y + 1 = x^2

To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):

2x + 14 + 1 = x^2

2x + 15 = x^2

Rearranging the equation, we have:

\(x^2 - 2x - 15 = 0\)

Factoring the quadratic equation, we get:

(x - 5)(x + 3) = 0

Setting each factor equal to zero:

x - 5 = 0   -->   x = 5

x + 3 = 0   -->   x = -3

Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':

For x = 5:

2(5) + 14 = y

10 + 14 = y

y = 24

For x = -3:

2(-3) + 14 = y

-6 + 14 = y

y = 8

Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

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The number that belongs to the green box in the triangle shown in the diagram given in the question is 14

From the diagram given in the question, we can see that one side and two angles of the triangle are given.

Thus, we shall use sine rule to obtain the missing side (i.e the green box). Details below:

Sine rule state as follow:

a / Sine A = b / Sine B

Inputting the given parameters, side a can be obtain as follow:

a / Sine 61 = 15 / Sine 70

Cross multiply

a × Sine 70 = 15 × Sine 61

Divide both sides by Sine 70

a = (15 × Sine 61) / Sine 70

a = 14

Thus, we can conclude from the above calculation that the number in the green box is 14

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Answer:

$324.35

Explanation:

Given a $249.50 cell phone with a 30% markup, to determine the selling price of the cell phone we need to first calculate 30% of $249.50 as seen below;

We'll now add $74.85 to $249.50 to finally get the selling price of the cell phone;

Therefore, the selling price of the cell phone is $324.35.

Answer:

\(\boxed{\bf B.\:100^{\frac{6}{7}}}\)

Step-by-step explanation:

\(\tt {\sqrt[7]{100^6}}\)

Apply the radical rule:-

Simplify:-

*6*1/7= 6/7*

Therefore, B. 100^6/7 is our answer.

_________________________

Hope this helps!

The answer for this question is 1/6

Answer:

1/6 and i'm 100% correct ;)

I believe 12 inches because 1 ft is equal to 12 inches.

While we cannot shade the grid because it is not provided, the fraction of the penguins born at the zoo is 2/5.

A fraction is a part or portion of a value or quantity.

A fraction is obtained as the quotient of the numerator divided by the denominator.

The types of fractions include:

The number of penguins born at the Edgewood Zoo = 16

The total number of penguins at the Edgewood Zoo = 40

16/40 = 4/10 = 2/5 or 40%

Thus, we can conclude that 2/5 of the penguins were born at the zoo.

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From the solution;

x = 62.62°

y = 8.9 cm

The sine rule (also known as the law of sines) is a mathematical formula that relates the sides and angles of a triangle. Specifically, it relates the ratios of the lengths of the sides of a triangle to the sine of the opposite angles.

By the use of the sine rule;

a/Sin A = c/Sin C

Sin C = cSin A/a

C = Sin-1(cSin A/a)

C = Sin-1(7.8 * sin 66.4/9.2)

C = 50.98°

B = 180 - (50.98° + 66.4)

B = 62.62°

Then;

a/Sin A = b/Sin B

9.2/Sin66.4 = b/Sin 62.62

b = 9.2 * Sin 62.62/Sin66.4

b = 9.2 * 0.89/0.92

b = 8.9 cm

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Answer: Should be (4,0)

Step-by-step explanation: