Use the properties of logarithms to evaluate each expression. 3log₉ 3- 1/4 log₉ 81

The sum of the given series is 50

The summation notation or sigma notation is used to simplify the writing of long summation into a single formula.

The given series in sum notation is:

       [tex]\sum\limits^5_{n=1} {(3n+1)}[/tex]

Substitute n = 1 ...5 into the nth term formula inside the sum notation:

a(1) = 3 . (1) + 1 = 4

a(2) = 3. (2) +1 = 7

a(3) = 3. (3) +1 = 10

a(4) = 3. (4) +1 = 13

a(5) = 3. (5) +1 = 16

Hence, the series:

    4 + 7 + 10 + 13 + 16

We can evaluate the sum directly by adding all the terms:

S(5) = 4 + 7 + 10 + 13 + 16 = 50

Or we can also use the sum formula of an arithmetic series:

S(n) = n/2 [a(1) + a(n)]

For n = 5

S(5) = 5/2 (4 + 16)

S(5) = 5/2 . 20 = 50

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Answer: 1/10

Step-by-step explanation: -2/5+1/2=0.1

If we convert 0.1 into a fraction, it becomes 1/10.

Answer:

1/10 is the answer

Answer:

1.48

Step-by-step explanation:

Redefined the logarithm into its decimal form within the base.

Hope this helps.

Answer:

9/28 of the lawn is left

Step-by-step explanation:

Make 3/7 and 1/4 have the same denominator

3/7 becomes 12/28 and 1/4 becomes 7/28

added together is 19/28

The amount of gas he would have in the tank after 3 hours is 8 gallons.

The gas left after tt hours is 11 - tt.

In order to determine the amount of gas that would be left in the tank, the amount of gas used would have to be subtracted from the initial amount of gas in the car.

Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign that is used to represent subtraction is -.

Amount of gas left = initial amount of gas - (gas used per hour x number of hours travelled)

11 - tt

11 - 3 = 8 gallons

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Answer:

let 3A5A be equal to 15

3A5A=15

A=1

Answer:

a = 5

Step-by-step explanation:

3555/15 is 237 which means it is divisible

Answer:

2;3, that is the ratio =)

Step-by-step explanation:

Answer:The answer would be 4 to 6 or 4:6

Answer:

  see attached

Step-by-step explanation:

You want the height drawn on each triangle corresponding to the base shown.

The height of a triangle is the perpendicular distance from the base to the opposite vertex. The point at which the height segment meets the base may or may not lie on the triangle.

The height segments for the two given triangles are shown in the attachment.

__

Additional comment

As this problem suggests, any side of a triangle may be designated the "base."

The height segment is also called an altitude. When all three altitudes are extended until they coincide, the point at which they meet is called the "orthocenter" of the triangle.

The orthocenter of an acute triangle lies inside the triangle. For a right triangle, it lies at the right-angle vertex. For an obtuse triangle, the orthocenter is outside the triangle.

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By substitution, the solution of the system of equations, 3u + 8 = 4v and 24v = 6 - 3u, is (u , v) = (-2 , 1/2).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in u and v,

3u + 8 = 4v     (equation 1)

24v = 6 - 3u     (equation 2)

Using the first equation, find the value of one variable, lets say u, in terms of the other.

3u + 8 = 4v     (equation 1)

3u = 4v - 8

u = (4v - 8)/3

Substitute the value of u to the second equation.

24v = 6 - 3u     (equation 2)

24v = 6 - 3[(4v - 8)/3]

24v = 6 - (4v - 8)

24v = 6 - 4v + 8

Combining all terms containing the variable v on one side and the constants on the other side of the equality, and solve for v.

24v = 6 - 4v + 8

24v + 4v = 6 + 8

28v = 14

v = 1/2

Substitute the value of v in the equation for u and solve for u.

u = (4v - 8)/3

u = [4(1/2) - 8]/3

u = (2 - 8)/3

u = -6/3

u = -2

Hence, the solution of the given system of equations is (u , v) = (-2 , 1/2).

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Step-by-step explanation:

the first answer is -3 the second answer is -2/3 outside -1

The quotient of the decimal number 89.904 divided by 34 will be 2.65.

In mathematics, the sum obtained by diluting two numbers is known as a quotient. In mathematics, the word "quotient" is widely used, and it is sometimes referred to as the integer part of a division, a fraction, or a ratio.

The decimal numeral system is widely used to express both integer and non-integer numbers.

Given numbers are 89.904 and 34. The quotient will be calculated as below:-

Quotient = 89.904 / 34

Quotient = 2.65

Therefore, the quotient of the decimal number 89.904 divided by 34 will be 2.65.

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The width of the frame is 8 inches.

We are given that:

The measures of the rectangular painting are:

Length = 13 inches

width = 20 inches

Now, the frame is of uniform with around the corner.

Let it be x inches.

So the new dimensions will be:

Length = 13 + x inches

Width = 20 + x inches.

Also, we are given that:

Perimeter = 98 inches

So, we get that:

P = 2(l + b)

Substituting the values, we get that:

98 = 2 (13 + x + 20 + x)

98 = 2( 33 + 2 x)

98 = 66 + 4 x

4 x = 98 - 66

4 x = 32

x = 32 / 4

x = 8 inches.

Therefore, the width of the frame is 8 inches.

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the correct statement is the first one.

The inverse of 6^2 is 6^(1/2), then 6^(1/2) is the square root of 6.

Well, this is just a notation thing.

We know the following property for exponents:

(a^n)^m = a^(n*m)

And we know that the square rooth is the inverse of the square power (exponent equal to 2) such that:

√x^2 = 2

Then if we define the square root as an exponent, let's say that is an exponent "a" we will have:

√x = x^a

Rewritting the above relation again, we can write:

√(x^2) = (x^2)^a = x^(2*a)

And we know that it must be equal to x, so we get:

x^(2*a) = x

This means that 2*a = 1

then a = 1/2

√x = x(1/2)

Then the correct statement is the first one.

The inverse of 6^2 is 6^(1/2), then 6^(1/2) is the square root of 6.

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Answer:8

Step-by-step explanation:

1

The number of units manufactured at a cost of $8900 will be 104 units.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

If the cost, C(x), for manufacturing x units of a certain product is given by

C(x) = x² - 19x + 60

The number of units manufactured at a cost of $8900 will be given by factorization.

x² - 19x + 60 = 8900

x² - 19x - 8840 = 0

x² - 104x + 85x - 8840 = 0

x(x - 104) + 85(x - 104) = 0

(x - 104)(x + 85) = 0

x = 104, -85

The number of units manufactured at a cost of $8900 will be 104 units.

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Answer:

x = 5

Step-by-step explanation:

Change "minus a negative" to "plus a positive"

x - (-3) = 8

x + 3 = 8

Next, subtract 3 from both sides.

x + 3 - 3 = 8 - 3

x = 5

Check it!

x - (-3) = 8

5 - (-3) = 8

5 + 3 = 8

8 = 8 Check!

Answer:

x= negative goes on the out side of it 15 over 4

The size of angle is X=13

y + 98 =180(LP)

Y =180-98

Y=82

<AOB + <OAB + <OBA=180(Sum of all angles of triangles)

85 + X + 82 =180

167 + X =180

X = 180-167

X=13

In Euclidean geometry, any three points that are not collinear produce a singular triangle  angle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle angle is contained in a plane, and there is only one plane that contains that triangle. All triangles  angle are enclosed in a single plane if all of the geometry is the Euclidean plane, however, this is no longer true in higher-dimensional Euclidean spaces.

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The linear functions that model the positions of the Python and of the Anaconda are given as follows:

A linear function is modeled by the following rule:

y = mx + b

In which:

For the functions in this problem, we have that:

Considering their velocities, and that when the Anaconda leaves the Python has already traveled half a mile, the functions are given as follows:

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The equation in slope-intercept form for the line that passes through (-12,3), perpendicular to y = -(2/3)x-11 is y = (3/2)x + 21.

The slope intercept form of a line is:-

y = mx + b

Where:-

m represents the slope of a line

b represents the y-intercept of a line

x and y represent the ordered pairs (x,y) throughout a line

We are given the line y = - (2/3)x-11 is perpendicular to the line whose equation we have to find.

Hence,

slope of the line*(-2/3) = -1

slope of the line, m = 3/2

Also, (-12,3) passes through the line,

Hence,

3 = (3/2)*(-12) + b

3 = -18 + b

b = 21

Hence, the equation of the line in slope intercept form is y = (3/2)x + 21.

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The volume of the larger cylindrical can of tuna with radius 5.2 centimeters is 419.6 cubic centimeters.

Solids of the same type that have proportional corresponding linear measures are similar solids. In the case of similar cylinder:

height of A / height of B = radius of A / radius of B

Using this scale, if the larger and similar can of tuna has a radius of 5.2 centimeters, and the small cylindrical can of tuna has a radius of 4 centimeters and a height of 3.8 centimeters, then:

radius of larger cylinder / radius of smaller cylinder = 5.2 cm/4cm = 13/10

height of larger cylinder / height of smaller cylinder = 13/10

height of larger cylinder = 13/10 (3.8 cm)

height of larger cylinder = 4.94 cm

Solving for the volume of the larger can using the formula for the volume of cylinder:

V = πr^2h

V = π(5.2 cm)^2(4.94 cm)

V = 419.6464068 cubic centimeters

Rounding off to the nearest tenth.

V = 419.6 cubic centimeters

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Answer:

Yes, 3 + (-4) is the same as -4 + 3.

Step-by-step explanation:

When doing addition problems such as this, the order of the numbers does not matter, even when negative numbers are included.
For example, 1 + 2 or 2 + 1 would equal 3.

3 + (-4) = -1
-4 + 3 = -1

Hope this helped you! Let me know if you need more clarification. :)

Answer:

if I can't explain in one line, then I will include the steps in the explanation.

Step-by-step explanation(Q3):

[tex]3^2-\left(5-3\right)^3+6\\5-3=2\\3^2-2^3+6\\3^2=9\\9-2^3+6\\2^3=8\\9-8+6\\9-8=1\\1+6\\1+6=7\\=7[/tex]

Hope it helps!

Answer:

c=0/0

Step-by-step explanation:

Let's solve for c.

x−c

c−x

=−1

Step 1: Multiply both sides by c-x.

−c+x=−c+x

Step 2: Add c to both sides.

−c+x+c=−c+x+c

x=x

Step 3: Add -x to both sides.

x+−x=x+−x

0=0

Step 4: Divide both sides by 0.

0

0

=0/0

c= 0/0

Answer:

Step-by-step explanation:

False for all value of x, because "x" should not be equal "c"

The  radius of the new sphere of dough is 5.3368

In the given statement is :

Two spherical pieces of cookie dough have radii of 3 centimeters and 5 centimeters, respectively. The pieces are combined to form one large spherical piece of dough.

To find the approximate radius of the new sphere of dough

V 1 = 4/2 · 3³ π = 108/3 π

V 2 = 4/3 · 5³ π = 500/3 π

The new sphere:  V = V 1 + V 2 = 608/3 π

4/3 r³ π = 608/3 π  / : π/3

4 r³ = 608

r³ = 608 : 4 = 152

r = ∛152

r = 5.3368 cm

Hence, The  radius of the new sphere of dough is 5.3368

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10.50+1.50x=total cost

since they wanted 3 topings it would be x=3

10.50+(1.50*3)

simplify

10.50+4.50=15

I hope this helps