Solve -(6)^x-1 +5=(2/3)^2-x

Answer:

6π,0.3636

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a fraction for any integers.

So 6π and 0.3636 are irrational numbers

Answer: no solution

Step-by-step explanation:

In a system of equations, if the final equation simplifies to a statement that is always true, like 5=5, this indicates the system has in fact an infinity of solutions, not no solutions.

The question given pertains to the solution of a system of equations. In a system of equations, if you simplify to a point where you end up with a statement that is always true, such as 5=5, this indicates that the system has an infinite number of solutions, not no solutions as suggested.

Let's imagine we have a system of two linear equations representing two lines on a graph. If the lines overlap perfectly (one is exactly the same as the other), every point on the line is a point of intersection, meaning it is a solution to the system. When we simplify such a system algebraically, we get an identity like 5=5 which is true no matter what values the variables may take, directly indicating that there are an infinite number of solutions.

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The answer is B.)

1. Find the area of the rectangle = L x W

- 5 x 6 = 30

2. Find the area of the triangle = bh/2

- 4*3/2 = 6

3. Add the areas of the figures.

- 30 + 6 = 36 cm^2

To prove that:

[tex]$\frac{1}{\sin ^{2}A}-\frac{1}{\tan ^{2}A}=1[/tex]

LHS = [tex]\frac{1}{\sin ^{2}A}-\frac{1}{\tan ^{2}A}[/tex]

Using basic trigonometric identity, [tex]\tan (x)=\frac{\sin (x)}{\cos (x)}[/tex]

       [tex]$=\frac{1}{\sin ^{2}A}-\frac{1}{\left(\frac{\sin A}{\cos A}\right)^{2}}[/tex]

      [tex]$=\frac{1}{\sin ^{2}A}-\frac{1}{\frac{\sin^2A}{\cos^2 A}}[/tex]

      [tex]$=\frac{1}{\sin ^{2}A}-\frac{\cos^2 A}{\sin^2A}[/tex]

      [tex]$=\frac{1-{\cos^2 A}}{\sin ^{2}A}[/tex]

Using trigonometric identity: [tex]1-\cos ^{2}(x)=\sin ^{2}(x)[/tex]

      [tex]$=\frac{\sin ^{2}A}{\sin ^{2}A}[/tex]

      = 1

      = RHS

LHS = RHS

[tex]$\frac{1}{\sin ^{2}A}-\frac{1}{\tan ^{2}A}=1[/tex]

Hence proved.

61.23 square inches of metal is needed to create a cylindrical can.

Solution:

Diameter of the base = 3 in

Radius of the base = 3 ÷ 2 = 1.5 in

Height of the cylinder = 5 in

The value of π = 3.14

To find the surface area of the cylinder:

Surface area of the cylinder = [tex]2 \pi r^{2}+2 \pi r h[/tex]

                                               = 2 × 3.14 × (1.5)² + 2 × 3.14 × 1.5 × 5

                                               = 14.13 + 47.1

Surface area of the cylinder = 61.23 sq. in

Hence 61.23 square inches of metal is needed to create a cylindrical can.

9514 1404 393

Answer:

  5.3 m

Step-by-step explanation:

The angle opposite the given side is ...

  180° -105° -40° = 35°

Then the law of sines tells us the unknown distance (d) is ...

  d/sin(40°) = 4.7 m/sin(35°)

  d = (4.7 m)sin(40°)/sin(35°) ≈ 5.267 m

Denis will need to jump about 5.3 m to reach the neighboring roof.

_____

Additional comment

Denis will need a running start. The world record for a standing broad jump is less than 4 m.

Answer:

B. reflection, then translation

Step-by-step explanation:

Hope this helps :)

Triangle ABC can be mapped onto triangle FED through reflection, then translation

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Triangle ABC can be mapped onto triangle FED through reflection, then translation

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Answer:

[tex]a_n= - 1( - 2)^{n-1}[/tex]

Step-by-step explanation:

The given geometric sequence is :

-1,2,-4,8,...

The first term is

[tex]a_1=-1[/tex]

The common ratio is

[tex]r = \frac{2}{ - 1} = - 2[/tex]

The nth term is given by;

[tex]a_n=a_1(r^{n-1})[/tex]

We substitute the values of the first term and common ratio to get:

[tex]a_n= - 1( - 2)^{n-1}[/tex]

This is called the explicit formula.

Answer:

1/4=0.25

Step-by-step explanation:

The required answer is 0.25.

Given that, 1.6 ÷ 6.4.

To divide a decimal by another decimal:

Now, 1.6/6.4=0.25

Therefore, the required answer is 0.25.

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Answer:

11

Step-by-step explanation:

3 + 38 - 63 + 33 = 11

Answer:

11

Step-by-step explanation:

I found the answer simply by doing trial-and-error, but here are the steps:

11 - 33 = -22

-22 +  63 = 41

41 + (-38) = 3

To find out how many tiles they would need for the border of a 3 x 3 swimming pool, you would need to add 3 tiles on the top, 3 tiles on the bottom, and 2 tiles on the left and right sides, resulting in a total of 10 tiles.

The student wants to find out how many orange tiles they will need for the border of the Nguyens' 3 x 3 swimming pool. To do this, we can visualize the 3 x 3 square and count the tiles around the border, but we want to find a way to do it without counting them one-by-one.

The pool is 3 tiles by 3 tiles, which is a total of 9 tiles. However, the border tiles are only the tiles around the edges. Moreover, corners are shared by two sides. So, for a 3 x 3 square, there are 3 tiles on the top, 3 tiles on the bottom, 2 tiles on the left, and 2 tiles on the right. So, in total, we would need 3 + 3 + 2 + 2 = 10 tiles for the border of the pool.

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Final answer:

To find the number of orange tiles needed for the border of the Nguyens' 3 x 3 swimming pool, we need to calculate the perimeter of the pool and divide by the length covered by each tile.

Explanation:

To find the number of orange tiles needed for the border of the Nguyens' 3 x 3 swimming pool, we need to calculate the perimeter of the pool. The perimeter is the sum of all the sides of the pool.

In a 3 x 3 pool, each side has a length of 3 units. Since there are 4 sides, the total perimeter is 4 x 3 = 12 units.

Each tile covers a length of 1 unit, so to find the number of tiles needed, we divide the perimeter by the length covered by each tile: 12 ÷ 1 = 12 tiles.

Answer:

3

Step-by-step explanation:

51 divided by 17 equals 3

Answer:

The answer

x=3

y=4

Step-by-step explanation:

You use substitution to solve it:

x+1=-2x+10

3x+1=10

3x=9

x=3

y=4

plug in the solution to the equation to verify your answer.

Answer:

  look for places where the derivative is zero or undefined

Step-by-step explanation:

Find the derivative. Critical points are where the derivative is zero, and where it is undefined.

__

A polynomial function may or may not have points where the derivative is zero. It will never have points where the derivative is undefined (tangent lines are vertical).

A rational function, or one involving fractional exponents may have critical points where the derivative is undefined.

__

For example, the function ...

  y = √(1 -x^2)

has the derivative ...

  y' = -x/√(1 -x^2)

This has a zero at x=0 (tangent is horizontal). It is undefined at x = ±1, where the denominator is zero (tangent is vertical). Those values of x tell you the critical points are (-1, 0), (0, 1), (1, 0).

Critical points in a mathematical function are found by deriving the function, setting the derivative equal to zero, and solving for x. The x-values obtained are the x-coordinates of the critical points. An example is provided for the function f(x) = x3 - 3x2.

To find the critical points in a function, you first need to identify the derivative of the function. Once you have obtained the derivative, you set it equal to zero and solve for x. The x-values you get are the x-coordinates of your critical points.

Let's illustrate with an example, using the function f(x) = x3 - 3x2.

First, let's find the derivative, f'(x) = 3x2 - 6x. Then set f'(x) = 0 and solve for x. This gives us x = 0 and x = 2. Therefore, (0, f(0)) and (2, f(2)) are the critical points of the function.

Please note, critical points are also the points where the derivative is undefined. However, in this case the derivative exists for all real numbers, so we do not have any such critical points here.

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Answer:

x = -14

Step-by-step explanation:

Step 1:  Distribute

1336 = 8(-14x - 29)

1336 = -112x - 232

Step 2:  Add 232 to both sides

1336 + 232 = -112x - 232 + 232

1568 = -112x

Step 3:  Divide both sides by -112

1568 / -112 = -112x / -112

-14 = x

Answer:  x = -14

Answer:

The solution is x = -14

Step-by-step explanation:

To solve for x, first perform the indicated multiplication.  We get:

1336 = 8(-14x - 29) => 1336 = -112x - 232

Adding 232 to both sides isolates -112x:

1336 + 232 = -112x, or

1568 = -112x

Next, x = -1568/112 = -14

The solution is x = -14.

Answer:

32f+72

Step-by-step explanation:

Distribute the -8

Answer:

32f + 72

Step-by-step explanation:

-8(-4f-9)

Distribute

(-8)(-4f) + (-8)(-9)

Multiply

32f + 72

Hope this helps :)

Answer:

600 meters

Step-by-step explanation:

1 kilometer= 1000 meters

0.6/1=x/100

Which makes x=600

Answer:

146.67 dollars

Step-by-step explanation:

9.36*15.67

Answer:

$146.67

Step-by-step explanation:

$9.36 per hour

15.67 hours

Multiply

$146.67

Hope this helps :)

Answer:

47

Step-by-step explanation:

32+[4×(15÷3)]−5

At first we have to apply "BODMAS" rule. According to the rule, we will work 1st bracket.

Hence,

32+[4×5]−5

Then, we will take 3rd bracket into consideration,

32+20−5

Then, we will use addition from the BODMAS rule-

52 - 5

Finally, subtracting 5 from 52, we can get

= 47

The value of the expression is 47.

Final answer:

The value of the expression 32+[4×(15÷3)]−5 is calculated using the order of operations to be 47.

Explanation:

The value of the expression 32+[4×(15÷3)]−5 can be calculated by following the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). Let's solve it step by step:

Solve the expression inside the parentheses: (15÷3) = 5.

Multiply this result by 4: 4×5 = 20.

Add this result to 32: 32 + 20 = 52.

Finally, subtract 5 from this sum: 52 − 5 = 47.

Therefore, the value of the expression is 47.

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h }{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r = 11\\ h = 15 \end{cases}\implies V=\cfrac{\pi (11)^2(15)}{3} \\\\\\ V=605\pi \implies V \approx 1900.664\implies \stackrel{\textit{rounded up}}{V = 1901}[/tex]

Final answer:

To simplify the expression 3,500÷(34+8×2)−4, first simplify the expression inside the parentheses, then divide and subtract to get the final answer of 66.

Explanation:

To simplify the expression 3,500÷(34+8×2)−4, we need to follow the order of operations which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In this case, we first simplify the expression inside the parentheses, which is (34+8×2). We perform the multiplication first, then the addition, resulting in 34+16. Next, we divide 3,500 by the sum of 34 and 16. Finally, we subtract 4 from the quotient.

Step-by-step:
1. Simplify (34+8×2) = 34+16 = 50
2. Divide 3,500 by 50 = 70
3. Subtract 4 from 70 = 66

Answer:

165

Step-by-step explanation:

525-360=165

Answer:

The easiest way of calculating discount is, in this case, to multiply the normal price $3200 by 12 then divide it by one hundred. So, the discount is equal to $384. To calculate the sales price, simply deduct the discount of $384 from the original price $3200 then get $2816 as the sales price.

Answer: 0.153 is the largest

Step-by-step explanation:

1/7=0.14, 1/12=0.08, and 15%= 0.150

Answer:

65 miles every 1 hour

Step-by-step explanation:

Unit rate is found once one of the units is 1. In this case we need to reduce the ratio so that it is 1 hour and we get a unit rate. We can do this by dividing both sided by 2 so that the hours are reduced to 1.

130=2

130/2=65                2/2=1

65=1

65 miles every hour

The unit rate of 130 miles per 2 hours is 65 miles per hour. This is calculated by dividing the number of miles (130) by the number of hours (2).

In Mathematics, the term unit rate refers to the ratio of two measurements, in which the denominator is 1. In this situation, you are given the rate of 130 miles per 2 hours and need to reduce it to a unit rate. To do this, you divide the number of miles (130) by the number of hours (2).

The calculation would be 130 miles ÷ 2 hours = 65 miles per hour. Hence, the unit rate of 130 miles per 2 hours is 65 miles per hour. This means that if you travel at this rate, you would cover 65 miles in one hour.

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Answer: Y= 6/7 or Y=0.86

Step-by-step explanation:

-3=7(y-9/7)

-3=7y-9

+9     +9

6=7y

divide both sides to get y by it self

6/7=y

Answer:

Y=6/7

Step-by-step explanation:

You have to isolate the variable by doing the opposite of PEMDAS to both sides of the equation.

Answer:

19 units.

Step-by-step explanation:

Consider the below figure attached with this question.

From the below figure it is given that MN=PQ.

It is given that MP = 6x – 5, QR = 3x + 1, and RN = 6.

Since non parallel sides are equal, therefore it is an isosceles trapezoid.

The diagonals of an isosceles trapezoid are equal.

[tex]MP=QN[/tex]

[tex]MP=QR+RN[/tex]

Substitute the given values.

[tex]6x-5=3x+1+6[/tex]

[tex]6x-5=3x+7[/tex]

[tex]6x-3x=5+7[/tex]

[tex]3x=12[/tex]

[tex]x=4[/tex]

The value of x is 4.

[tex]QN=MP=6x-5=6(4)-5=24-5=19[/tex]

Hence, the measure of QN is 19 units.

To find QN,  RN from the value of QR which is 3x - 5

The value can be found using Algebraic expressions.

To find QN, we need to find the value of QR and subtract RN from it.

Given that QR = 3x + 1 and RN = 6, we can substitute these values into the equation.

So, QN = (3x + 1) - 6.

Simplifying further, QN

= 3x + 1 - 6

= 3x - 5.

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Answer:

1)

A. m arc QRS = 100°

B. m arc QRT = 255°

C. m arc UTS = 180°

D. m arc UTR = 205°

2)

1] The major arc CA = 255°

2] The minor arc AB = 90°

Step-by-step explanation:

In a circle:

1)

In circle O

A.

∵ m∠QOR = 75°

∵ ∠QOR subtended by arc QR

- By using the 1st note above

∴ m of arc QR = m∠QOR

∴ m of arc QR = 75°

∵ m∠ROS = 25°

∵ ∠ROS subtended by arc RS

∴ m of arc RS = m∠ROS

∴ m of arc RS = 25°

The measure of arc QRS is the sum of the measures of arcs QR and RS

∴ m arc QRS = 75° + 25° = 100°

B.

∵ m∠SOT = 155°

∵ ∠SOT subtended by arc ST

∴ m of arc ST = m∠SOT

∴ m of arc ST = 155°

The measure of arc QRT is the sum of the measures of arcs QR, RS and ST

∴ m arc QRT = 75° + 25° + 155 °= 255°

C.

∵ m∠UOT = 25°

∵ ∠UOT subtended by arc UT

∴ m of arc UT = m∠UOT

∴ m of arc RUT = 25°

The measure of arc UTS is the sum of the measures of arcs UT and TS

∴ m arc UTS = 25° + 155° = 180°

D.

The measure of arc UTR is the sum of the measures of arcs UT, TS and SR

∴ m arc UTR = 25° + 155° + 25 = 205°

2)

1]

∵ The sum of the measures of the minor and major arcs is 360°

∵ m of minor arc AC = 105°

- Subtract 105 from 360° to find the measure of the major arc CA

∴ m of major arc CA = 360° - 105°

∴ m of major arc CA = 255°

2]

∵ m of major arc AB = 270°

- Subtract 270° from 360° to find the measure of the minor arc AB

∴ m of minor arc AB = 360° - 270°

∴ m of minor arc AB = 90°

Answer:

A - y - 5= 4(x - 2)

Step-by-step explanation:

First find slope with the two points given

( -1 , -7) and ( 2 , 5)

Using

m = y_2 - y_1 / x_2 - x_1

m - slope

x_1 = -1

y_1 = -7

x_2 = 2

ÿ_2 = 5

Inserting the values

m = 5 - (-7) / 2 - (-1)

= 5 + 7 / 2 + 1

= 12 / 3

= 4

Slope is 4

Then let's proceed

y - y_1 = m ( x - x_1)

using ( 2 , 5) as x_1 and y_1 respectively

x_1 = 2

y_1 = 5

m = 4

y - 5 = m ( x - 2)

m = 4

y - 5 = 4 ( x - 2)

We are asked to give the answer in point slope form

The word OF means to multiply in math.

So, 3/4 of m becomes (3/4)m, which means 3/4 TIMES m.

We can also write the expression

this way: (3m)/4.

They both mean the same thing.

The requried 3/4 of m is represented by the algebraic expression (3/4)m, and its value depends on the specific value assigned to m.

To express 3/4 of a quantity, m, as an algebraic expression, we can multiply 3/4 by m.

The algebraic expression for 3/4 of m is (3/4)m.

To evaluate this expression, we simply multiply 3/4 by the value of m.

For example, if m = 10, we substitute m = 10 into the expression to find (3/4)(10) = (3/4) * 10 = 30/4 = 7.5.

Therefore, 3/4 of m is represented by the algebraic expression (3/4)m, and its value depends on the specific value assigned to m.

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