Express log2 6+ log2 7 as a single logarithm

Answer:

x > 3

Step-by-step explanation:

Given

2(4 + 2x) < 5x + 5 ← distribute left side

8 + 4x < 5x + 5 ( subtract 5 from both sides )

3 + 4x < 5x ( subtract 4x from both sides )

3 < x ⇒ x > 3

Answer:

Option C. 1,493

Step-by-step explanation:

If the deer population in a region is expected to decline 1.1% from 2010 to 2020. Assuming this continued, we can say that the deer population decreases 1.1% each ten years.

From 2010 to 2060 there are 50 years. If the deer population decreases 1.1% each ten years, then it will decrease 5.5% in 50 years.

If the population in 2010 was 1,578. Then, the population in 2060 is going to be:

Using the rule of three:

If 1578 ----------------> Represents 100%

    X       <-----------------       5.5%

X = (5.5%x1578)/100% = 86.79 ≈ 87

Then the total population in 2060 is: 1578 - 87 = 1491

None of the answers equal to 1491. That's why I assume the correct answer must be Option C. 1,493. Given that it's the closest answer!

Answer:

The population would be 1,493.

Step-by-step explanation:

Given,

The initial population, P = 1,578, (  In 2010 )

Also, the decline rate per 10 years, r = 1.1 %,

And, the number of the periods of 10 years since, 2010 to 2060, n = 5,

Hence, the population in 2060 would be,

[tex]A=P(1-\frac{r}{100})^n[/tex]

[tex]=1578(1-\frac{1.1}{100})^5[/tex]

[tex]=1493.09849208\approx 1493[/tex]

Option third is correct.

from 76 down to 60 is a 16 difference.

if we take 76 to be the 100%, what is 16 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 76&100\\ 16&x \end{array}\implies \cfrac{76}{16}=\cfrac{100}{x}\implies \cfrac{19}{4}=\cfrac{100}{x} \\\\\\ 19x=400\implies x=\cfrac{400}{19}\implies x\approx 21.05[/tex]

Answer

The price reduced by 21.05%

Explanation

•To determine the price decrease in dollars, subtract:

76 - 60 = 16

•The price decreased by 16 dollars as shown above.

•16 is what percent of 76?

So, to find that, set up an equation:

76x = 16

•Divide both sides by 76.

[tex]\frac{76x}{76} = x[/tex]

[tex]\frac{16}{76} = .21 or 21%[/tex]

x = .2105 or 21.05%

the equation of the graph should be

f(x)= 1/2x -1

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = [tex]\frac{0+1}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]

Note the line crosses the y- axis at (0, - 1) ⇒ c = - 1

y = [tex]\frac{1}{2}[/tex] x - 1 ← in slope- intercept form

f(x) = [tex]\frac{1}{2}[/tex] x - 1 ← in functional notation

Answer:

SY=34, SK=21 and KY=13

Step-by-step explanation:

we have that

SY=SK+KY

substitute the given values

(36-x)=(13x-5)+(2x+9)

solve for x

36-x=15x+4

15x+x=36-4

16x=32

x=2

Find the value of SY

SY=(36-x)=36-2=34

Find the value of SK

SK=(13x-5)=13(2)-5=21

Find the value of KY

KY=(2x+9)=2(2)+9=13

To find the values of SK, KY, and SY, substitute the given expressions for x into the equations.

To find the values of SK, KY, and SY, we need to substitute the given expressions for x into the equations.

Therefore, SK = 86, KY = 23, and SY = 29.

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Answer:

The answer is y = 6/x ⇒ answer A

Step-by-step explanation:

* Lets revise what is the meaning of the inverse variation

- It is a mathematical relationship between two variables

- It can be expressed by an equation in which the product of two

 variables is equal to a constant

- If y is in inverse variation with x

∴ y ∝ 1/x

- Change this relation to equation

∴ y = k/x, where k is the constant of the variation

- We can write it by another way

∵ y ∝ 1/x

∴ y = k/x ⇒ by using cross multiplication

∴ yx = k

* Now lets solve the problem

∵ There is an inverse variation between the two variables x and y

∴ y ∝ 1/x

∴ y = k/x

- Look to the answer

# We will chose A because

∵ y = 6/x  ⇒ use the cross multiplication

∴ yx = 6 ⇒ and 6 is a constant

∴ k = 6

* The answer is y = 6/x

Answer:

See graph below for answer

Step-by-step explanation:

Step 1) Change to y-intercept form

6y = 2x - 12

y = 1/3x - 2

Step 2) Graph.

See graph below for answer

Answer:

B

Step-by-step explanation:

Adjusting entries for prepaid expenses are classified as a (D) deferral. They gradually recognize the cost as expense over the period of benefit. This involves decreasing the prepaid asset account and increasing the corresponding expense account.

Prepaid expenses are costs that have been paid in advance for services or goods that will be received in the future. In accounting, prepaid expenses are considered assets because they provide future economic benefits to the company. When adjusting entries for prepaid expenses, the necessary adjusting entry is a ( D) deferral.

This means that the initial payment is recorded in a prepaid asset account, and then as the expense is incurred over time, it is gradually recognized as an expense on the income statement. For example, if a company pays a year's worth of rent in advance, each month, a portion of that prepaid rent would be moved from the prepaid asset account to the rent expense account, reflecting the usage of the space.

An adjusting entry for a deferral decreases the prepaid asset account and increases the expense account. The goal of this type of entry is to apportion the expense to the periods in which the benefits from the prepaid cost are actually realized.

Answer: [tex]x=\frac{23}{22}[/tex]≈[tex]1.04[/tex]

Step-by-step explanation:

You need to solve for the variable "x" to find its value.

To solve for "x" you need to apply the Division property of equality. This  states that:

[tex]If\ a=b\ then\ \frac{a}{c}=\frac{b}{c}[/tex]

Then, knowing this, you can divide both sides of the equation by 22. Therefore, you get that the value of "x" is the following:

[tex]\frac{22x}{22}=\frac{23}{22}[/tex]

[tex]x=\frac{23}{22}[/tex]

[tex]x[/tex]≈[tex]1.04[/tex]

Answer:

The value that best approximates the correlation coefficient is r=0.50

Step-by-step explanation:

we know that

The correlation coefficient r measures the strength and direction of a linear relationship between two variables. Are expressed as values between +1 and -1

Using a Excel tool (Correl function)

see the attached table

the correlation coefficient  is r=0.45

so

The value that best approximates the correlation coefficient is r=0.50

Answer: its called an image

Step-by-step explanation:

This is because it the result of the reflection

The reflection of a figure is called an image.

A reflection is a transformation representing a flip of a figure.

An image formed by mirrors is due to the reflection of light originating from an object.

Image may be real or virtual, upright or inverted, and diminished or enlarged.

When we place an object in front of the mirror, we see the same object in the mirror. This image that appears to be behind the mirror is called the image.

Image is a visual or other representation of a real object; a graphic; a picture while reflection is the act of reflecting or the state of being reflected.

Whereas, The pre-image is the original appearance of a figure in a transformation operation.

The definition of a reflection is a thought or writing about something, particular in the past, or what one sees when looking into a mirror or body of water. An example of reflection is an article written by an author discussing how he feels he has grown in the past year in his writing style.

When a ray of light approaches a smooth polished surface and the light ray bounces back, it is called the reflection of light. The incident light ray that land on the surface is reflected off the surface. The ray that bounces back is called the reflected ray.

Hence, the reflection of a figure is called an image.

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Answer:

T > -9/28

Step-by-step explanation:

A quadratic has two real solutions when the discriminant (b² - 4ac) is positive.

b² - 4ac > 0

3² - 4(T)(-7) > 0

9 + 28T > 0

28T > -9

T > -9/28

Answer:

A number line with an open circle on −2, a closed circle on 5, and shading in between

Step-by-step explanation:

solve it you get x>-2

and 3x <=15

x<=5

so its close on 5 and open on -2

Answer:

64

Step-by-step explanation:

We are dividing by 2 each time

1024 /2 = 512

512/2 = 256

256/2 =128

128/2 = 64

Answer:

C) none

Step-by-step explanation:

The two lines are parallel (have the same slope (x-coefficient), but different y-intercepts). They have no point in common, hence there is no solution to the system of equations.

___

Another way to think about this: subtract the first equation from the second. You get ...

0 = 1

There are no values of the variables that will make this be true, hence no solutions.

Answer:

Step-by-step explanation:

[tex]\text{The sum of cubes:}\\\\a^3+b^3=(a+b)(a^2-ab+b^2)\\\\\text{Therefore}\\\\\text{for}\ a=6\ \text{and}\ b=s:\\\\6^3+s^3=(6+s)(6^2-6s+s^2)=(6+s)(36-6s+s^2)[/tex]

Answer: (6 + s)(s^2 – 6s + 36)

Step-by-step explanation:

Answer:

91 campers can swim

Step-by-step explanation:

step 1

Find the number of campers

we know that

The ratio of counselors to campers at a camp is 1 : 9

so

by proportion

Find the number of campers if there are 13 counselors

Let

x-----> the number of campers

1/9=13/x

x=9*13=117 campers

step 2

How many campers can swim?

we know that

The ratio of campers who can swim to campers who cannot swim is 7 : 2

so

The ratio of total campers  to campers who can swim is 9 : 7

by proportion

Find how many campers can swim for a total of 117 campers

Let

x----> the number of campers that can swim

9/7=117/x

x=117*7/9

x=91 campers can swim

Answer:

The maximum value of the equation is 1 less than the maximum value of the graph

Step-by-step explanation:

We have the equation [tex]y=-x^2+4x-8[/tex].

We can know that this graph will have a maximum value as this is a negative parabola.

In order to find the maximum value, we can use the equation [tex]x=\frac{-b}{2a}[/tex]

In our given equation:

a=-1

b=4

c=-8

Now we can plug in these values to the equation

[tex]x=\frac{-4}{-2} \\\\x=2[/tex]

Now we can plug the x value where the maximum occurs to find the max value of the equation

[tex]y=-(2)^2+4(2)-8\\\\y=-4+8-8\\\\y=-4[/tex]

This means that the maximum of this equation is -4.

The maximum of the graph is shown to be -3

This means that the maximum value of the equation is 1 less than the maximum value of the graph

Answer:

The maximum value of the equation is 1 less than the maximum value of the graph

Step-by-step explanation:

Answer:

7 + (-2) is equivalent to 5

Step-by-step explanation:

Answer:

A)

62/3 = 20.67 hours

B)

60 hours

C)

2074.29 miles

Step-by-step explanation:

If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.

A)

In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;

(24/360) = (x/310)

solving for x;

x = (24/360) * 310 = 62/3 = 20.67 hours

B)

In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;

(24/2π radians) = (x/5π radians)

Solving for x;

x = (24/2π radians)*5π radians = 60 hours

C)

If the diameter of the earth is 7920 miles, then in 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle we have;

circumference = 2*π*R = π*D

                         = 7920π miles

Therefore, the speed of the earth is approximately;

(7920π miles)/(24 hours) = 330π miles/hr

The distance covered by a point in 2 hours will thus be;

330π * 2 = 660π miles = 2074.29 miles

Answer:

Part A). In 20 hr 24 minutes earth rotate 310°.

Part B). In 19 hr 6 minutes earth rotate 5 radians

Part C). 2072.4 miles point on equator rotates in 2 hours.

Step-by-step explanation:

Degree that earth rotate in 24 hour = 360°

Number of radian that earth rotate in 24 hour = 2π radian

Part A).

Time taken to rotate 360° = 24 hours

Time taken to rotate 1° = [tex]\frac{24}{360}=\frac{1}{15}\,hours[/tex]

Time taken to rotate 310° = [tex]310\times\frac{1}{15}=20\frac{2}{5}=20\,hr\:24\,minutes[/tex]

Part B).

Time taken to rotate 2π radian = 24 hours

Time taken to rotate 1 radian = [tex]\frac{24}{2\pi}=\frac{12}{\pi}\,hours[/tex]

Time taken to rotate 5 radian = [tex]5\times\frac{12}{\pi}=\frac{60}{\pi}=19.1\.hr=19\,hr\:6\,minutes[/tex]

Part C).

Diameter of Earth = 7920 miles

Radius of earth, r = 3960 miles

Degree of rotation in 1 hours = [tex]\frac{360}{24}=15^{\circ}[/tex]

Degree of rotation in 2 hours , [tex\theta[/tex] = 15 × 2 = 30°

Length of the arc for angle 30° of circle with radius 3960 miles = Distance covered by point in 2 hours.

Length of the arc = [tex]\frac{\theta}{360^{\circ}}\times2\pi r=\frac{30}{360}\times2\times3.14\times3960=2072.4\:miles[/tex]

Therefore, Part A). In 20 hr 24 minutes earth rotate 310°.

                  Part B). In 19 hr 6 minutes earth rotate 5 radians

                  Part C). 2072.4 miles point on equator rotates in 2 hours.

Answer:

y = 90°

Step-by-step explanation:

The left side base angle of the triangle and the angle of 110° form a straight angle and are supplementary, thus

base angle = 180° - 110° = 70°

The right base angle is also 70° , thus the triangle is isosceles

The line segment from the vertex is a perpendicular bisector, hence

y = 90°

Answer:

3

Step-by-step explanation:

The leading coefficient is the number in front of the highest power term.

We only have one term, so the leading coefficient is 3

ANSWER

[tex]p + q= 7[/tex]

EXPLANATION

We determine the slope of each line using the slope formula;

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

The slope of BC is

[tex] = \frac{ q - 1}{9 - 6} [/tex]

[tex] \frac{ q - 1}{3} [/tex]

The slope of AB is

[tex] = \frac{1 - 4}{6 - p} [/tex]

[tex] = - \frac{3}{6 - p} [/tex]

The two lines are perpendicular so the product of their slopes is -1.

[tex] - \frac{3}{6 - p} \times \frac{ q - 1}{3} = - 1[/tex]

This implies that,

[tex]\frac{q - 1}{6 - p} = 1[/tex]

[tex]q - 1=6 - p[/tex]

[tex]q + p = 6 + 1[/tex]

[tex]p + q= 7[/tex]

.

Answer:

Its subtract 12.

Step-by-step explanation:

The first question mark is positive 6.

6-12= -6

The second question mark is  -22.

Negative 10 minus 12 equals negative 22

Once you understand integers, it will be really easy. I was in 6th grade last year.

T*4 just go step by step

To find the answer for one cup of flour, divide the cups of sugar by the cups of flour. Here’s how it works.

Since we want the proportion for 1 cup of flour, we divide it by itself to get 1.

Thus, we need to have equal sides, so we divide the number of cups of sugar by the amount the cups of flour divided by.

So: 2.5/7.5=1/3

1 cup of flour is proportional to 1/3 cups of sugar.

Hope this helps!

The amount of sugar for 1 cup of flour can be determined through setting up and solving a proportion based on the given proportional relationship, though specific values are required. For example, if 3 cups of sugar are needed for 2 cups of flour, then 1.5 cups of sugar would be needed for 1 cup of flour.

Unfortunately, the specific values are not given in the question, but we can still explain how you would find the answer. In a proportional relationship, the ratios between the two quantities (in this case, sugar and flour) is constant. This means that if we know the amount of sugar used for a certain amount of flour, we can determine the amount of sugar used for 1 cup of flour by setting up an equation and solving for the unknown variable, provided we have the necessary data.

For example, if the relationship was such that for every 2 cups of flour, you used 3 cups of sugar, then the ratio of sugar to flour would be 3/2. To find out how much sugar you need for 1 cup of flour, you can create a proportion that reads 3/2 = x/1 and solve for x. In this case, x is the equivalent amount of sugar needed for 1 cup of flour.

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Answer:

We need to simplify the following expressio:

[tex]\frac{1}{2} x^{2}- 4x-\frac{2}{x}[/tex]

Multiply the whole expression by '2x':

[tex]x^{3}-8x^{2}-4[/tex]

The expression can't be more simplified.

Answer:

can you make it more specific please?

Step-by-step explanation:

I honestly don't get what you're saying in what subject this is?

Answer:

The radius of the silo should be [tex]16\ ft[/tex]

Step-by-step explanation:

we know that

The volume of the grain silo is equal to the volume of the cylinder plus the volume of a hemisphere

[tex]V=\pi r^{2} h+\frac{4}{6}\pi r^{3}[/tex]

we have

[tex]V=35,500\pi\ ft^{3}[/tex]

[tex]h=4D=8r[/tex]

substitute the values and solve for r

[tex]35,500\pi=\pi r^{2} (8r)+\frac{4}{6}\pi r^{3}[/tex]

Simplify

[tex]35,500=r^{2} (8r)+\frac{4}{6}r^{3}[/tex]

[tex]35,500=8r^{3}+\frac{2}{3}r^{3}[/tex]

[tex]35,500=\frac{26}{3}r^{3}[/tex]

[tex]r^{3}=35,500*(3)/26[/tex]

[tex]r=16\ ft[/tex]

To find the radius of the silo, we need to calculate the volume of the cylinder and hemisphere components of the silo, and then set their sum equal to the desired volume of grain. By substituting the given relationship between the height and radius, we can express the volumes in terms of the radius, and solve for the value of r that satisfies the equation.

To find the radius of the silo, we can start by calculating the volume of the cylinder. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height. In this case, we are given that the height of the cylinder is 4 times the diameter of the base, so we can write h = 4r. The volume of the cylinder portion would then be V_cylinder = πr²(4r) = 4πr³.

The volume of the hemisphere on top can be calculated using the formula for the volume of a sphere, which is V = (4/3)πr³. Since the radius of the hemisphere is the same as the radius of the base of the cylinder, this volume would be V_hemisphere = (4/3)πr³.

The total volume of the silo is the sum of the cylinder volume and the hemisphere volume. So we have the equation V_total = V_cylinder + V_hemisphere = 4πr³ + (4/3)πr³ = (16/3)πr³. We know that the silo is to hold 35,500π cubic feet of grain, so we can set up the equation (16/3)πr³ = 35,500π and solve for r. Dividing both sides by (16/3)π, we get r³ = 35,500/((16/3)π), and taking the cube root of both sides, we find r = ∛(35,500/((16/3)π)). Evaluating this expression, we find that r ≈ 5.02 feet.

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Step-by-step explanation:

The area is

[tex] {x}^{2} - 110x + 2800 \\ = {x}^{2} - 40x - 70x + 2800 \\ = x(x - 40) - 70(x - 40) \\ = (x - 40)(x - 70)[/tex]

Since the width is

[tex]x - 40 \: (feet)[/tex]

Then, the length will be

[tex]x - 70 \: (feet)[/tex]