Evaluate each logarithm.
log₆₄ 4

Step-by-step explanation:

a) Imagine folding the net into the shape. In this case, Net A can have both triangles fold up, and both rectangles fold in to make the above shape.

b) Side AB on this net is the height of the triangle, 3 inches.

   Side BC is the same as the hypotenuse (diagonal) on the triangle, which       .   is 5 inches.

   Side CD is the same as the length of the shape, which is 8.6 inches.

c) Surface area = area of all sides

Triangle = 1/2 bh

              = 2*3

              = 6 inches squared

There are two triangles, so that adds to 12 inches squared.

Now all of the rectangles:

Left most = 3*8.6

                = 25.8 inches squared

Middle = 4*8.6

            = 34.4

Right most = 5*8.6

                  = 43

Now we can add all of this:

43 + 34.4 + 25.8 + 12

= 115.2 inches squared.

This is the surface area of the prism.

The coordinates of four points on each of the lines are:

6. (1, 4), (2, 9), (3, 14), (4, 19)

7. (1, 7), (2, 6), (3, 5), (4, 4)

8. (1, 0.5), (2, 0.7), (3, 0.9), (4, 1.1)

9. (1, -1.5), (2, 0), (3, 1.5), (4, 3)

10. (1, 4.5), (2, 5), (3, 5.5), (4, 6)

11. (0, -5), (3, -3), (6, -1), (9, 1)

12. (0.1, 34), (0.2, 38), (0.3, 42), (0.4, 46)

The equation of a line in slope-intercept form where m = slope and b = y-intercept is written as:

y = mx + b.

To find the coordinates, plug in x-values to find the corresponding y-values the equation of the line would give.

6. Slope (m) = 5

y-intercept (b) = -1

Equation of the line: y = 5x - 1

Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:

y = 5(1) - 1

y = 4

y = 5(2) - 1

y = 9

y = 5(3) - 1

y = 14

y = 5(4) - 1

y = 19

The coordinates of four points on the line are:

(1, 4), (2, 9), (3, 14), (4, 19)

7. Slope (m) = -1

y-intercept (b) = 8

Equation of the line: y = -x + 8

Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:

y = -(1) + 8

y = 7

y = -2 + 8

y = 6

y = -3 + 8

y = 5

y = -4 + 8

y = 4

The coordinates of four points on the line are:

(1, 7), (2, 6), (3, 5), (4, 4)

8. Slope (m) = 0.2

y-intercept (b) = 0.3

Equation of the line: y = 0.2x + 0.3

Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:

y = 0.2(1) + 0.3

y = 0.5

y = 0.2(2) + 0.3

y = 0.7

y = 0.2(3) + 0.3

y = 0.9

y = 0.2(4) + 0.3

y = 1.1

The coordinates of four points on the line are:

(1, 0.5), (2, 0.7), (3, 0.9), (4, 1.1)

9. Slope (m) = 1.5

y-intercept (b) = -3

Equation of the line: y = 1.5x - 3

Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:

y = 1.5(1) - 3

y = -1.5

y = 1.5(2) - 3

y = 0

y = 1.5(3) - 3

y = 1.5

y = 1.5(4) - 3

y = 3

The coordinates of four points on the line are:

(1, -1.5), (2, 0), (3, 1.5), (4, 3)

10. Slope (m) = 1/2

y-intercept (b) = 4

Equation of the line: y = 1/2x + 4

Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:

y = 1/2(1) + 4

y = 4.5

y = 1/2(2) + 4

y = 5

y = 1/2(3) + 4

y = 5.5

y = 1/2(4) + 4

y = 6

The coordinates of four points on the line are:

(1, 4.5), (2, 5), (3, 5.5), (4, 6)

11. Slope (m) = 2/3

y-intercept (b) = -5

Equation of the line: y = 2/3x - 5

Substitute x = 0, 3, 6, and 9, into the equation to find their corresponding y-values:

y = 2/3(0) - 5

y = -5

y = 2/3(3) - 5

y = -3

y = 2/3(6) - 5

y = -1

y = 2/3(9) - 5

y = 1

The coordinates of four points on the line are:

(0, -5), (3, -3), (6, -1), (9, 1)

12. Equation of the line: y = 40x + 30

Substitute x = 0.1, 0.2, 0.3, and 0.4, into the equation to find their corresponding y-values:

y = 40(0.1) + 30

y = 34

y = 40(0.2) + 30

y = 38

y = 40(0.3) + 30

y = 42

y = 40(0.4) + 30

y = 46

The coordinates of four points on the line are:

(0.1, 34), (0.2, 38), (0.3, 42), (0.4, 46)

Learn more about equation of a line on:

https://brainly.com/question/13763238

#SPJ1

The length of the rectangular pool is 50 meters

The formula for perimeter of a rectangle is expressed as;

Perimeter = 2 ( l + w)

Where:

From the information given, we have;

Perimeter = 160 meters

Length = 20 + w

Substitute into the formula

160 = 2( 20 + w+ w)

expand the bracket

160 = 2(20 + 2w )

160 = 40 + 4w

collect like terms

160 - 40 = 4w

4w = 120

w = 120/ 4

w = 30 meters

But length = 20 + w = 20 + 30 = 50 meters

Thus, the length of the rectangular pool is 50 meters

Learn more about rectangles here:

https://brainly.com/question/25292087

#SPJ1

Paying monthly premium, at the end of 12 months Colin pays $1,155.36

Colin pays $95.36 more monthly than he would annually.

Colin pays (to the nearest percent) 8.99 % more by paying monthly premium than he would paying annually.

Premium is the amount of money one has to pay to insurance companies so that they provide us coverage at the time of need.

If we make payments monthly, the the premium is monthly.

If we pay the amount at the end of the year, then the premium is annual.

Given that Edmond has a $60,000 term life policy. The annual premium is $1,060. Colin pays $96.28 monthly.

Monthly premium of Edmond = $96.28

If he pays monthly, then total payment at the end of 12 months

= 12 *$96.28 = $1155.36

Then total payment at the end of 12 months is greater than the annual premium by = 1,156.36 - 1,060 = 95.36

Percentage of extra amount paid  when colin paid monthly

    = (extra payment made/ annual payment ) *100 = (95.36/1,060)*100             =8.99 %

Therefore, Colin pays 8.99 % more by paying monthly than he would paying annually.

Also, learn more about the premiums from the link below:

https://brainly.com/question/7511249

#SPJ1

Step-by-step explanation:

the common number of 4 and 8 is 8. You multiply 1/4 by 2 and it is equal to 2/8. 2/8+ 5/8= 7/8. 8-7=1. 1/8 of the houses are gray.

The ticket for a crab meal costs $44 and a ticket for a vegetarian meal costs $27

From the question, we are to solve the system of equations.

First, we will form the system of equations

Let x represent the ticket for a crab meal and y represent the ticket for a vegetarian meal

From the given information,

"One troop member sold tickets for 23 crab meals and 34 vegetarian meals, with total receipts of $1,930"

That is,

23x + 34y = 1930            -------------- (1)

Also,

"Another sold tickets for 20 crab meals and 38 vegetarian meals, bringing in a total of $1,906"

20x + 38y = 1906           -------------- (2)

Now, solve the equations simultaneously

Multiply equation (1) 20 and equation (2) by 23

20 × [23x + 34y = 1930

23 × [20x + 38y = 1906

460x + 680y = 38600

460x + 874y = 43838

Subtracting the resulting equations, we get

-194y = -5238

y = -5238/-194

y = 27

Substitute the value of y into equation (1)

23x + 34y = 1930

23x + 34(27) = 1930

23x + 918 = 1930

23x = 1930 - 918

23x = 1012

x = 1012/23

x = 44

Hence, the ticket for a crab meal costs $44 and a ticket for a vegetarian meal costs $27

Learn more on Solving system of equations here: https://brainly.com/question/13729904

#SPJ1

After five months, the percentage decrease in the daylight is 51.815%

As per the question, On the first day of June, there was 16.81 hours of daylight in a city and five months later, there was 8.10 hours of daylight. We are supposed to find the percent decrease in the daylight.

Percentage increases or decreases are calculated by setting the problem up proportionally.

We are trying to calculate at what percentage of 16.81 is 8.10 first

Let "x" be the percentage required percentage

therefore [tex]\frac{x}{100} =\frac{8.10}{16.81}[/tex]

[tex]x = \frac{8.10*100}{16.81} \\x=\frac{810}{16.81} \\x=48.185%[/tex]

8.10 is approximately 48.185% of 16.81.

So the percentage decrease is [tex]100 - 48.185=51.815[/tex]%

Hence the percentage decrease is 51.815%

To learn more about percentage, click on the link given below:

https://brainly.com/question/23469589

#SPJ9

Answer:

Im pretty sure its A

Step-by-step explanation:

According to the given figure, option (A) and option (F) are correct options which better shows ∠4 ≅ ∠6 respectively.

Let's procced to solve this question.

∠4 ≅ ∠8 by the corresponding angle postulate because two parallel lines is cut by a transversal and ∠4 ≅ ∠8 by the corresponding angle postulate. It's true.

∠6 ≅ ∠8 by the definition of vertical angles. It's true.

and by using the transitive property of congruence that ∠A ≅ ∠B and ∠B  ≅ ∠C then ∠A ≅ ∠C.

⇒ ∠4 ≅ ∠6 by the transitive property of congruence.

Hence, option (A) is correct.

Now,

∠2 ≅ ∠6 by the corresponding angle postulate because two parallel lines is cut by a transversal and ∠2 ≅ ∠6 by the corresponding angle postulate. It's true.

∠2 ≅ ∠4 by the definition of vertical angles. It's true.

and by using the transitive property of congruence that ∠A ≅ ∠B and ∠B  ≅ ∠C then ∠A ≅ ∠C.

⇒ ∠4 ≅ ∠6 by the transitive property of congruence.

Hence, option (F) is correct.

Therefore, option (A) and option (F) are correct option.

Learn more in depth about lines and angles at https://brainly.com/question/25716982

#SPJ1

Answer: 2.6 or 2 2/3

Step-by-step explanation:

3 1/4 = 3.25

3.25/5 = 0.65

0.65 x 4 = 2.6 or 2 2/3

Based on the number of cups of flour and the number of teaspoons of cooking oil, if 1 cup of flour is used, the number of teaspoons of cooking oil needed is 2 / 5 teaspoons of cooking oil

When 5 cups of flour are used, then 2 teaspoons of cooking oil are needed by the recipe.

If there is only 1 cup of flour being used therefore, the number of teaspoons of cooking oil needed will be:

= Number of teaspoons needed for 5 cups / Number of cups of flour needed
= 2 / 5 teaspoons of cooking oil

First part of question is:
A recipe calls for 5 cups of four and 2 teaspoons of cooking oil.

Find out more on fraction form at https://brainly.com/question/28570858

#SPJ1

Answer:

An equivalent expression for 4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power is 2d⁻³/11d⁻⁹

What is an expression?

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

What is an exponent?

An exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.

Translating the word problem into an algebraic expression, we have;

4 times d raised to the negative third power = (4 × d)⁻³ = 4d⁻³

22 times d raised to the ninth power = (22 × d)⁻⁹ = 22d⁻⁹

Next, we would write the equation as a quotient:

Expression = 4d⁻³/22d⁻⁹

Expression = 2d⁻³/11d⁻⁹

Expression as a single natural logarithm of -2 ln 2 is -1.386.

-2 ln 2

[tex]ln 2^{-2}[/tex] = - 1.386

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

To learn more about natural logarithm from the given link:

brainly.com/question/20785664

#SPJ4

Answer:

Im letting yall know rn that the answer actually 19 other guys wildn with 14

Step-by-step explanation:

The appropriate choice of ratio  will be given by

Polly got £30, Andy got £60, Phoebe got £180

What is ratio?

Ratio determines the comparision among many quantities with the same unit.

Here,

Let Polly got £x

So Andy got £2x and Phoebe got £3(2x) = £6x

Total Amount = £(x + 2x + 6x)

                       = £9x

By the problem,

                         9x = 270

                           x = [tex]\frac{270}{9}[/tex]

                           x = 30

So Polly got £30,

Andy got £(2 * 30) = £60

Phoebe got £(6 * 30) = £180

To learn more about ratio, refer to the link:

https://brainly.com/question/25927869

#SPJ9

Answer:

X=-5 :)

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

14+5=19, so -14+ -5= -19

Answer:

x = 152°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle , then

x = 79° + 73° = 152°

If two quantities are proportional, the true statements about the graph showing the relationship between them are-

D. The points of the graph form a straight line.

E. The points of the graph must include the origin.

F. The points must all form equivalent ratios.

In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant.

Now let us suppose there are two quantities x and y.

A graph between two quantities is plotted.

Suppose x is directly proportional to y.

Thus, these Two variable quantities have a constant ratio

So, we can write

y ∝ x

Applying constant of proportionality,

y = kx

Where k is the constant of proportionality.

It represents a straight line.

Now,the value of x = 0 then the value of y must be equal zero, then the line which represented the direct variation must be passes through the origin

Now  If two variable quantities have a constant ratio and since y = kx is a straight line and passes through origin therefore from the given options the correct answer are-

D. The points of the graph form a straight line.

E. The points of the graph must include the origin.

F. The points must all form equivalent ratios.

Thus, If two quantities are proportional, the true statements about the graph showing the relationship between them are-

D. The points of the graph form a straight line.

E. The points of the graph must include the origin.

F. The points must all form equivalent ratios.

To learn more about proportionality :

brainly.com/question/10159347

#SPJ1

If a 42-inch string is to be cut so that one piece is 7 inches longer than the other, then the shorter piece has a length of 17.5 inches

The length of the shorter piece can be determined by using an algebraic expression.

Any expression consisting of both numbers and letters is considered to be an algebraic expression.

Considering, x to be the length of the shorter piece

As the longer piece is 7 inches longer than the shorter piece, an algebraic expression can be given as,

x + (x + 7) = 42

x + x + 7 = 42

2x + 7 = 42

2x = 42 - 7

2x = 35

x = 35 ÷ 2

x = 17.5

Hence, the length of the shorter piece is calculated to be 17.5 inches.

To learn more about algebraic expressions, click here:

https://brainly.com/question/4344214

#SPJ4

The amount in a continuously compounded account is $ 565.2 .

If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach.

The amount in the continuously compounded account is given as:

[tex]A=Pe^{rt}[/tex]

Where P is the principal amount, r is the interest rate, and t is the time period in years.

Now, we have

The principal amount, P = $500

Annual interest rate, r = 4.9 % = 4.9 / 100 = 0.049

Time = 2.5 years

Therefore, the amount in a continuously compounded account is:

[tex]\[A=Pe^{rt}\][/tex]

[tex]A = $500 \times e^{0.049 \times 2.5}[/tex]

[tex]A = $500 \times e^{0.049 \times 2.5}[/tex]

[tex]A = $500 \times e^{0.1225}[/tex]

A = $500 × 1.13031912007

A = $ 565.159

A = $ 565.2

Learn more about principal amount here:

https://brainly.com/question/13033578

#SPJ4

Answer: 10

Step-by-step explanation:

x = 2

y = 4

equation :

7x - y

after putting the values to the equation :

7(2x) - (4)

7*2 = 14

14 - 4 = 10

The answer is 10.

After solving the given inequality the answer is logx+log₁₀(x+1)<3.

So,

Then,

Therefore, after solving the given inequality the answer is logx+log₁₀(x+1)<3.

Know more about inequality here:

brainly.com/question/24372553

#SPJ4

Answer:

After 4 minutes

Step-by-step explanation:

After 1 min: Ant 1 is 9.75 mm underground. Ant 2 is 14.5 mm underground.

After 2 min: Ant 1 is 9.5 mm under. Ant 2 is at 14 mm under.

After 3 min: Ant 1 is 9.25 mm under.

After 4 min: Ant 1 is 9 mm under. Ant 2 is 13.5 mm under.

Ant 2 is now closer to the surface than Ant 1.

The function rule after the given transformation is g(x) = -3x

A function is defined as a relation between a set of inputs having one output each.

We have,

f(x) = 9x

Vertical compression = 1/3

Reflection in x-axis.

We know that when we compress a function f(x) by scale factor m

The new compress function is represented:

F(x) = m(f(x))

Reflection across the x-axis changes the sign of the new function.

Now,

With the vertical compression:

F(x) = 1/3 (f(x))

F(x) = 1/3(9x) = 3x

With the reflection in the x-axis:

g(x) = - F(x)

g(x) = -3x

Thus the function rule after the given transformation is g(x) = -3x

Learn more about function here:

https://brainly.com/question/5340022

#SPJ1

Total estimated cost for advertising= 30 +12x

The initial fees for ad is given= $30

And the fixed amount per click = 8 cents

Total number of click ad per day= 150

We know that,

$1= 100 cents

So 8 cents= $0.08

Now we will find the total estimated cost of advertising in dollars for x days.

Total estimated cost= The initial fees + charge per click ×total clicks ×total days

⇒ $30 + 0.08×150×x

⇒ 30+ 12x

Hence the answer is option( I) 30+12x.

https://brainly.com/question/25109150

#SPJ4

Reason:

The counting numbers, aka the set of natural numbers, is the set {1, 2, 3, 4, 5, ...} which is the set of positive integers

A value like 5 is the same as 5/1, which shows it is rational.

A rational number is any fraction of two whole numbers (eg: 2/3 and 4/7). The denominator cannot be zero.

Since we can rewrite the 5 as 5/1, it can be done with any counting number to show the natural numbers is a subset of the rational numbers.

Any counting number is rational, but not the other way around.

Left-Skewed is the answer.

Histograms are a very common method of visualizing data, and that means that understanding how to interpret histograms is a valuable and important skill in virtually any career. There are a number of things to pay particular attention to when reading a histogram.

Bell-Shaped: A histogram with a prominent ‘mound’ in the center and similar tapering to the left and right. One indication of this shape is that the data is unimodal – meaning that the data has a single mode, identified by the ‘peak’ of the curve.

Uniform: A uniform-shaped histogram indicates data that is very consistent; the frequency of each class is very similar to that of the others.

Right-Skewed: A right-skewed histogram has a peak that is left of the center and a more gradual tapering to the right side of the graph.

Left-Skewed: A left-skewed histogram has a peak to the right of the center, more gradually tapering to the left side. It is unimodal, with the mode closer to the right and greater than either mean or median.

Undefined Bimodal: This shape is not specifically defined, but we can note regardless that it is bi-modal, having two separate classes or intervals equally representing the maximum frequency of the distribution.

For more information on histograms click on the link below:

https://brainly.com/question/2962546

#SPJ4

Answer: 2= -8+x

Step-by-step explanation:

Add eight to both sides to get

10=x

CHECK

then plug it in to get

2=-8+10

simplify

2=2

Answer:

Step-by-step explanation:

flip 3/4 since we are dividing so we get 4/5 times 4/3 to get 16/15

So we get 1 1/15

Let me know if this was helpful