Which equation below represents the Exponent Property of Logs?

The exact value of Cosθ is -1/√10 .

In the question ,

it is given that ,

the value of tanθ = 3/1 ,

that means the perpendicular = 3x

and the base of the triangle is = 1x,

So ,By Pythagoras Theorem

hypotnuse² = perpendicular² + base²

hypotnuse² = (3x)² + (1x)²

hypotnuse² = 9x² + 1x²

hypotnuse² = 10x²

hypotnuse = (√10)x

So , Cosθ = base / hypotnuse

Cosθ = 1x/(√10)x

Cosθ = 1/√10

Since , [tex]\theta[/tex] lies in the second quadrant ,

and in second quadrant Cos is negative ,

So , Cosθ = -1/√10

Therefore , The exact value of Cosθ is  -1/√10  .

The given question is incomplete , the complete question is

If Tanθ = 3 , θ lies in the second quadrant. Use a Pythagorean identity to find the exact value of Cosθ ?

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Answer: Rise is 5 and run is 1 and now that is equal 5

Step-by-step explanation:

The root of the quadratic equation is 2x² + 7x + 6 is x = -2 and x = -3 / 2.

The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.

The equation to find the roots, is a quadratic equation.

Hence,

2x² + 7x + 6

2x² + 3x + 4x + 6

x(2x + 3) + 2(2x + 3)

Hence,

(x + 2)(2x + 3) = 0

Therefore,

x + 2 = 0    or 2x + 3 = 0

x = -2 or x = -3 / 2

The roots of the equation is x = -2 and x = -3 / 2

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The coordinates of the point which divide the lines joining the pairs of points (5,8) and (-1,3) in the given ratio  2:3 is  (8,4).

Using the section formula, if a point (x,y) divides the line joining the points (x₁, y₁) and (x₂, y₂) in the ratio m:n, then

(x,y)=( (mx₂+nx₁)/m+n ,  (my₂+ny₁)/m+n )

Let the points be A(5,8) and B(-1, 3). Let a point P(x,y) divides AB in the ratio 2:3

Therefore, we have

P(x,y)=((2(-1) + 3x5)/(2+3) , (2(3) + 3x8)/(2+3))

P(x,y)=(2.6,6)

Hence,the coordinates of the point which divide the lines joining the pairs of points (5,8) and (-1,3) in the given ratio  2:3 is  (8,4).

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Answer:

The height of the flagpole is about 25.6 feet.

Step-by-step explanation:

The figure is omitted--please sketch it.

Put your calculator in degree mode.

Let h be the height of the flagpole.

[tex] \tan(52) = \frac{h}{20} [/tex]

[tex]h = 20 \tan(52) = 25.6[/tex]

The value of the exponent given as 24 - (5 + 3)^2 + 4 × 2^3 is -8.

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the value given will be expressed thus:

= 24 - (5 + 3)^2 + 4 × 2^3

= 24 - (8)² + 4 × 8

= 24 - 64 + 32

= -8

The value is -8.

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Answer:Answer: SAS

Step-by-step explanation:

The average monthly increase in net worth for the 6-month period is $1832.16.

Given:

A business started the year with a net worth of $4,873. During the first six months of the year, the business recovered and increased its net worth to a value of $15,866.

Six months net worth = 15,866 - 4873

= 10,993

Average monthly increase in net worth =  six month net worth / 6

= 10,993/6

= $1832.16.

Therefore The average monthly increase in net worth for the 6-month period is $1832.16.

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Answer:

A,C,D

Step-by-step explanation:

Answer:

L = 6 feet ; W = 4 feet

Step-by-step explanation:

l = 2 + w

perimeter/2 = 8

l + w > 8

2 + w + w > 8

2 + 2w > 8

2w > 8-2

2w > 6

2/2 w > 6/2

w > 3

smallest integer > 3 = 4

W= 4

L = 4 + 2 = 6

60% of the fruit punch is orange juice.

In this question, we have been given 3/5 of a fruit punch is orange juice.

We need to find the percentage of the fruit punch is orange juice.

3/5 of a fruit punch is orange juice, means 3 of 5 fruit punch is orange juice.

Using the percentage formula,

3/5 * 100

= 0.6 * 100

= 60%

Therefore, 60% of the fruit punch is orange juice.

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For the given ratio of orange juice , the percentage of the orange juice from the given fruit juice is equal to 60%.

As given in the question,

Ratio of orange juice in the given fruit juice = 3/5

From the given ratio it indicates out of 5 fruits 3 are orange

Percentage of fruit punch is orange juice in the given juice is equal to

= ( 3 / 5 ) × 100

= ( 3 × 100 ) / 5

= 300 / 5

= 60%

60% of the fruit punch is orange juice.

Therefore,  for the given ratio of orange juice , the percentage of the orange juice from the given fruit juice is equal to 60%.

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Answer:

2/3

Step-by-step explanation:

The gradient is found by doing rise/run. If you go to a point on the line you can then rise 2 squares and run 3 to the right. This means that the gradient is 2/3. It is not negative as the line is going up.

Answer:

21%

Step-by-step explanation:

126 out of 600=126/600

=0.21 *100 for

21%

Answer in multiple forms depending on what needed

Answer:

c = 3

Step-by-step explanation:

48- (3c+4)=4(c+5)+3

48-3c-4=4(c+5)+3 Distributed the - sign

48 -3c -4= 4c+20 +3 Distributed the 4

44-3c =4c+23 Combined like terms

21-3c=4c Subtract 23 from both sides

21=7c Add 3c to both sides

3=c

The largest multiple of 30 that is less than the number, 520, can be found to be 510.

To find the largest multiple that 30 has, which is also less than 520, first find the number of times that 30 can go into 520:

= 520 / 30

= 17.333

Then use this number to find the largest multiple below 520 by rounding 17.33 downwards to 17.

The multiple of 30 that is the largest and below 520 is then:

= 30 x Rounded down result of division of 520

= 30 x 17

= 510

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Answer:

the answer for x when h(x) is 2.9

By taking some simple quotients, we will see that the cost per student is:

$26.36

First, we know that the school spends $643.34 on passes for 38 people, then the cost of each pass is given by the quotient:

p = $643.34/38 = $16.93

Then there is also lunch for the 36 students, which costed $339.48, then the cost in lunch per student is.

l = $339.48/36 = $9.43

The total cost per student is:

$16.93 + $9.43 = $26.36

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There are 855 cockroaches crawling on the front of the building

An equation is an expression showing the relationship between two or more numbers and variables.

The population density is given as:

Population density = total animals / area occupied

Given that, the population density of the cockroaches is 5 cockroaches per square meter.

The area of the building = area of triangle + area of square

Area of building = (1/2) * (24 - 9)(12) + (9 * 9) = 90 + 81 = 171 m²

Population density = total animals / area occupied

5 cockroaches per square meter = Total cockroaches / 171 m²

Total cockroaches = 855

There are 855 cockroaches

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The diameter of a semicircle is 4 yards. The perimeter for a semicircle having a diameter of 4 yards is 10.28 yards.

The perimeter of a shape is the distance of the path or boundary that surrounds the shape.

The formula for the perimeter of a semicircle is πr + 2r

π(pie)=3.14

r(radius)=2 yards (∴ radius=1/2diameter)

∴ the perimeter of a semicircle = πr + 2r

                                                    = 3.14×2+2×2

                                                    =10.28 yards.

∴ The perimeter of a semicircle with a diameter of 4 yards is 10.28 yards.

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Answer:

y=3x+25

Step-by-step explanation:

we need start by making slope intercept form

lets move the 12x after moving it we get

-4y=-12x+4 we need to remove the - 4 from the y so we need to divide the whole equation by - 4

we get y=3x-1

now we can create an equation to get the parallel line

y+2=3(x+9) now distribute

y+2=3x+27 and subtract the two

y=3x+25

Answer:

x³ - 8

Step-by-step explanation:

Order of operation to simplify this expression as follows:

   [tex]((1\div4+7\div 8)\times 1)\div 2[/tex]

⇒ [tex]((0.25+7\div 8)\times 1)\div 2[/tex]

⇒ [tex]((0.25+0.875)\times 1)\div2[/tex]

⇒ [tex](1.125\times 1)\div2[/tex]

⇒ [tex]1.125\div 2[/tex]

⇒ [tex]0.5625[/tex]

What is order of operation?

The best way to solve an expression is from left to right if all the operations are the same (for instance, only addition, only subtraction, only multiplication, or only division). However, we must adhere to the order of operations for expressions including several operations.

The rule that dictates how to solve an expression involving numerous operations is known as the order of operations.

PEMDAS can help you remember that sequence. In PEMDAS, each letter denotes a mathematical operation.

Given Expression is ; [tex]((1\div4+7\div 8)\times 1)\div 2[/tex]

Firstly we calculate the highest priority between(+,-, x, and [tex]\div[/tex])

Here, division is the highest priority ,

[tex]((0.25+7\div 8)\times 1)\div 2[/tex]

[tex]((0.25+0.875)\times 1)\div2[/tex]

and then we solve parathesis,

[tex](1.125\times 1)\div2[/tex]

now we do multiply,

[tex]1.125\div 2[/tex]

and the final answer will be [tex]0.5625[/tex]

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Answer:

y=8 x=-19.5

Step-by-step explanation:

Start from the bottom equation and work your way upSolve the fourth equation for w-5w=-15-5w/(-5)=-15/(-5)w = 3 Then use that value of w to plug into the third equation. Notice we're going backwards or up the chain of equations. After w is replaced, solve for zz+w = 2z+3 = 2z+3-3 = 2-3z = -1 Now use z = -1 and w = 3 to plug into the second equation. Solve for y-2y-12z-4w = -16-2y-12(-1)-4(3) = -16-2y+12-12 = -16-2y = -16-2y/(-2) = -16/(-2)y = 8 

Use y = 8, z = -1, w = 3 to plug into the first equation. Solve for x:

2x+4y+z+3w=12x+4(8)+(-1)+3(3)=12x+32-1+9=12x+40=12x+40-40=1-402x=-392x/2=-39/2x = -39/2 The value of x as a fraction is x = -39/2The value of x in decimal form is x = -19.5 

Answer:  The correct answer is x = 50

Step-by-step explanation:

The sum of angles in a triangle = 180 degrees

This is a right-angled triangle, so one of the angles is 90 degrees + x +y

Therefore: 90 + y + x = 180

Substitute the variables:

90 + 40 + x = 180

130 + x =180

Subtract 130 from each side:

(-130) 130 + x =180 (-130)

x = 50

Answer:

5^4

Step-by-step explanation:

5^3x5

5x5x5x5

5^4

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The simplified form of the expression, 5³.5 will be 625.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that the expression is, 5³.5

=5³.5

The base should remain constant and the exponents added when multiplying like bases. Keep the base constant when raising a base with power to another power, and multiply the exponents instead. Keep the base constant and deduct the exponents in the denominator and numerator when dividing like bases.

Apply the law of exponent as

xᵃ × xᵇ = xᵃ⁺ᵇ

=5³⁺¹

=5⁴

=5x5x5x5

=625

Thus, the simplified form of the expression, 5³.5 will be 625.

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The required change in height of the missile is 16100 feet.

Given that,
A missile was fired from a submarine from 200 feet below sea level. If the missile reached a height of 15900 feet before exploding, the change in the altitude of the missile is to be determined.

Change in defined as when the object is in one state but after a certain period of time, the state of the object changes is called change of the state.

here,
The height attained by the missile above sea level is 15900 feet.
The height attained by the missile below the seal level is 200 feet.
Change in height = 15900- (-200) = 15900 + 200 = 16100.

Thus, the required a change in height of the missile is 16100 feet.

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Answer:

-5/4

Step-by-step explanation:

slope

[tex]\frac{y2-y1}{x2-x1}\\\\ \frac{2-(-3)}{-4-0}=\frac{5}{-4}\\ \\slope = \frac{-5}{4}[/tex]