Suppose that a and b are positive numbers for which log, (a) = log15(b) = log25 (a + 2b). What is the value of a​

H 48 feet could be the perimeter of Rebecca's garage door.

We know,

Perimeter is the distance around a two-dimensional shape. It is measured in units of length, such as feet or inches.

Rebecca found the length and width of the garage door, which are both measurements of length. Let's say she found that the length was 8 feet and the width was 6 feet.

To find the perimeter, she would add up the lengths of all four sides of the rectangle:

Perimeter = 2(length) + 2(width)

Perimeter = 2(8 feet) + 2(6 feet)

Perimeter = 16 feet + 12 feet

Perimeter = 28 feet

So the perimeter of Rebecca's garage door is 28 feet. None of the answer choices given match this value exactly, but H 48 feet is a possible perimeter if the garage door was much larger than the example given above. However, it is important to note that the term "cubic feet" (answer choice J) does not apply to perimeter, as cubic feet is a unit of volume and not length.

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The surface area of the triangular prism is 672 square millimeters.

what is surface area ?

Surface area is a metric used to determine how much overall space an object occupies. the total volume of the area of surface of a three-dimensional shape. The term "surface area" refers to a three-dimensional shape's entire surface area.

The triangular base has a height of 7 mm and a base of 24 mm, so its area is:

[tex]1/2 * base * height = 1/2 * 24 \ mm * 7\ mm = 84 \ mm^2[/tex]

There are two identical triangular faces, so their combined area is:

[tex]2 * 84 \ mm^2 = 168\ mm^2[/tex]

The three rectangular faces are all the same size, with a length of 24 mm and a height of 7 mm, so the area of each is:

[tex]length * height = 24 \ mm * 7 \ mm = 168 \ mm^2[/tex]

There are three rectangular faces, so their combined area is:

[tex]3 * 168\ mm^2 = 504\ mm^2[/tex]

To find the total surface area, we add the area of the two triangular faces to the area of the three rectangular faces:

[tex]168 \ mm^2 + 504 \ mm^2 = 672 \ mm^2[/tex]

Therefore, the surface area of the triangular prism is 672 square millimeters.

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Answer:

[tex]x=\pm\sqrt{\frac{2}{7}} \text{ and }x=\pm i\sqrt{\frac{2}{7}}[/tex]

(real solution)       (imaginary solution)

Step-by-step explanation:

For these type of questions, where the exponent is even, it helps to try to rewrite the equation into a quadratic equation as we have a closed formula (quadratic formula) to solve for the zeroes, and it's also just easier to deal with in general.

Let's say that: [tex]u=x^2[/tex], now if we square both sides, [tex]u^2=x^4[/tex], so from here we can substitute in u squared as x to the power of four.

This results in our following equation: [tex]49u^2-4[/tex], from here we could use the quadratic formula, but you may notice a pattern here. We have a difference of squares: [tex]a^2-b^2=(a-b)(a+b)[/tex]

[tex]49u^2[/tex] can be written as [tex](7u)^2[/tex] and [tex]4[/tex] can be written as [tex]2^2[/tex], this gives us our equation: [tex](7u)^2-2^2\implies (7u-2)(7u+2)[/tex]. If we use this definition of the equation on the left side, it gives us: [tex](7u-2)(7u+2)=0[/tex] and this is very convenient as we can solve both of them individually.

Whenever we multiply any number (assuming it's defined) by zero, we should get.... zero. This intuitively makes sense as no matter how many times we add zero up (multiplication is repeated addition), we're always just going to have zero.

So when we have the equation: [tex]a*b=0[/tex], if "a" is zero then regardless of what "b" is (assuming it's defined), then the product will be zero. If "b" is zero then regardless of what "a" is (assuming it's defined), then the product will be zero.

Now if we look back at our equation: [tex](7u-2)(7u+2)=0[/tex], if [tex]7u-2=0[/tex], then regardless of what [tex]7u+2[/tex] is equal to, the product will be zero. Likewise, if [tex]7u+2=0[/tex] then regardless of what [tex]7u-2[/tex] is equal to, the product will be zero, thus making the equation true.

So to find the solutions to this, we find what makes [tex]7u-2=0 \text{ and }7u+2=0[/tex] true. If we work them both out individually we

get:

[tex]7u-2=0\\7u=2\\u=\frac{2}{7}\\\\7u+2=0\\7u=-2\\u=-\frac{2}{7}[/tex]

So now we have our two solutions right? Well remember we started off with a "x" variable, and the "u" is merely a substitution. If you recall, the "u" value is set equal to "x^2", so we can just plug that back in, so we can find the solutions in terms of x.

[tex]x^2=\frac{2}{7} \text{ and } x^2=-\frac{2}{7}[/tex]

If we take the square root of both sides, we get:

[tex]x=\pm\sqrt{\frac{2}{7}} \text{ and }x=\pm\sqrt{-\frac{2}{7}}[/tex]

you'll notice in one of them, we're taking the square root of a negative number. This will result in imaginary solutions, if we factor out a "-1" and take the square root of that, we'll just get an "i" infront, giving us the solutions of: [tex]x=\pm\sqrt{\frac{2}{7}} \text{ and }x=\pm i\sqrt{\frac{2}{7}}[/tex].

Out of the following minerals hornblende is made up of more than one element. Therefore, option D is the correct answer.

Solid, naturally occurring materials known as minerals have a particular chemical makeup and crystal structure. They can be discovered in rocks, soil, and water and are primarily created by geological processes. Minerals are crucial for our bodies' nutritional needs as well as for the construction of structures and the manufacture of electronics, among other facets of our daily life.

Hornblende is a mineral made up of multiple elements, including calcium, magnesium, iron, aluminum, silicon, and sometimes sodium and potassium. The other minerals listed, copper, silver, and gold, are each made up of a single element.

Therefore, the correct option is d. Hornblende

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The geometric means of the pairs of numbers are approximately:

14.85 for 7.16 and 27

13.42 for 5 and 36

22.94 for 10.8 and 48.

It should be noted that to find the geometric mean of two numbers, we multiply them together and then take the square root of the result. So, for each pair of numbers, we can follow these steps:

Multiply the two numbers together.

Take the square root of the product.

Using this formula, we get:

7.16 and 27:

Geometric mean = √(7.16 × 27) ≈ 14.85

5 and 36:

Geometric mean = √(5 × 36) = √180 ≈ 13.42

10.8 and 48:

Geometric mean = √(10.8 × 48) ≈ 22.94

Therefore, the geometric means of the pairs of numbers are approximately:

14.85 for 7.16 and 27

13.42 for 5 and 36

22.94 for 10.8 and 48.

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The new mixture contains 34% peanuts.

The correct option is A

We have,

Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts.

First, Total weight = 4 kg + 12 kg = 16 kg

Now, Total weight in kilograms is =  (4 kg) (0.16) + (12 kg) (0.40)

= 0.64 kg + 4.80 kg

= 5.44 kg.

Now, the Percent of peanuts

= (Total amount of peanuts / Total weight) x 100%

= (5.44 kg / 16 kg) x 100

= 34%

Thus, the new mixture contains 34% peanuts.

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1/(x-2)². The correct option is C

The quotient rule is a formula used in calculus to find the derivative of a function that is the quotient of two other functions. Specifically, it gives the formula for finding the derivative of a function of the form f(x) = g(x) / h(x), where g(x) and h(x) are both functions of x.

We can use the quotient rule to find the derivative of h(x):

h(x) = (x+2)/(x-2)

h'(x) = [ (x-2)(1) - (x+2)(1) ] / (x-2)^2 (apply quotient rule)

Simplifying the numerator, we get:

h'(x) = [ x-2 - x-2 ] / (x-2)^2

h'(x) = -4 / (x-2)^2

Therefore, the answer is (C) 1/(x-2)².

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Answer:

Step-by-step explanation:

Answer: B

Step-by-step explanation:

The word that would indicate that the cat was afraid of the veterinarian is "cowered." "Cowered" means to crouch down in fear or shame. So, the sentence would be: "The cat cowered under the table when the veterinarian came into the examining room."

Answer:

Step-by-step explanation:

The area of the triangle LMN is A = ( 1/2 ) x base x height

Given data ,

Let the triangle be represented as ΔLMN

Now , the base of the triangle be , b = MN

Let the height of the triangle be = h

Now , the area of the triangle is A = b x h

On simplifying , we get

A = LM x MN

Therefore , the value of A = base x height

Hence , the area of triangle is solved

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Answer:

7 ÷ 2 = 3.5, so 2:7 = 1:3.5 (1 to 3.5).

Answer:

1 : 3.5

Step-by-step explanation:

2: 7 written in the ratio 1 : n...

2:7

1:n

To get to 1 from 2 you have to divide by 2.

So do the same for 7.

Therefore the answer is 1: 3.5

Answer:

x = 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then

x² + 4² = 8²

x² + 16 = 64 ( subtract 16 from both sides )

x² = 48 ( take square root of both sides )

x = [tex]\sqrt{48}[/tex] = [tex]\sqrt{16(3)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex]

Answer:

  D.  9 clubs

Step-by-step explanation:

Given a stem-and-leaf plot of the number of members in clubs, you want to know the number of clubs with 30 or more members.

The plot shows the club membership to be ...

  {10, 13, 15, 24, 26, 30, 36, 39, 50, 55, 59, 61, 66, 78}

The 9 clubs whose member numbers are in bold have at least 30 members.

The number of clubs with at least 30 members is ...

  D.  9 clubs

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Answer: (440-308) ÷ 22 = The cost of each tool kit is 6 dollars

Step-by-step explanation:

The original price of the field trip was $308 after the price fof each tool kit was added the price was $440.

The total costs of all the tool kits was 132

440-308=132

the total cost of the tool kits divided by the number of kids will get the price of each tool kit

132÷22 =

K=

The correct option is (D) A, B, C, E, G, I

What is the cube?

A cube is a three-dimensional solid shape that has six square faces of equal size. It has twelve edges and eight vertices, and all angles between the faces are right angles. The cube is a regular polyhedron, which means that all its faces are congruent and all its edges have the same length.

The net of a cube is the one that has the faces arranged in such a way that it makes a complete cubic structure

A) In the given figure, the net cannot be folded into a cube by folding the six faces of the net. Therefore, it is not a cube net.

B)  In the given figure, the net cannot be folded into a cube by folding the six faces of the net. Therefore, it is not a cube net.

C) In the given figure, the net cannot be folded into a cube by folding the six faces of the net. Therefore, it is not a cube net.

D) In the given figure, the net can be folded into a cube when its faces are folded one over the other. Therefore, it is a cube net.

Hence, The correct option is (D) A, B, C, E, G, I.

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Answer:t = 9.6.

Step-by-step explanation:

From the calculation, g increases on the interval [-3, 6) and for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)^2.

To determine where g is increasing, we need to find where its derivative, g'(x), is positive. We can find g'(x) by differentiating g(x) with respect to x:

g'(x) = f(x)

Since f(x) is a piecewise-defined function, we need to consider each interval separately.

Therefore, g is increasing on the interval [-3, 6).

To justify this, note that g'(x) = 0 at x = 0 and x = 6, where g has local maxima. This means that g is increasing on the intervals (-3, 0) and (0, 6) and decreasing on (6, 9]. Since g is continuous, it cannot have any jumps, so it must be increasing or decreasing on each of these intervals. Since g(-3) = 0 and g(6) = 9, we know that g is increasing on the interval [-3, 6).

We can evaluate g(x) on the interval [0, 6] by integrating f(x) with respect to t from -2 to x:

g(x) = ∫_{-2}^{x} f(t) dt

On the interval [-3, 0), f(t) = 3, so we have:

g(x) = ∫_{-2}^{0} 3 dt + ∫_{0}^{x} (-t + 3) dt

Simplifying the integrals, we get:

g(x) = 6 - 1/2(x-2)^2, for 0 ≤ x ≤ 6

(Note that we can drop the "+C" since it's being evaluated at the limits of integration.)

Therefore, for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)^2.

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The supplied value of 4 is a solution to the equation m + 2(m + 1) = 14.

Given the equation in the question;

m + 2(m + 1) = 14

And supplied value = 4

To substitute the value of 4 into the equation, we replace every occurrence of the variable "m" with 4:

m + 2(m + 1) = 14

Plug in m = 4 by replace m with 4 and simplify both sides

4 + 2(4 + 1) = 14

4 + 2(5) = 14

4 + 10 = 14

14 = 14

We can see that both sides of the equation simplify to 14, which means that the value of 4 is a solution.

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The inequalities for the given word problems are:

g) p/q ≤ 6

h) 1/w ≥ 9

Inequality word problems are statements or words used to describe specific inequalities.

g) We are told that the quotient of p and q is at most 6. Thus, it is a maximum of 6. Therefore, we can write the inequality as:

p/q ≤ 6

h) We are told that the reciprocal of w is at least 9. Thus, the inequality is expressed as:

1/w ≥ 9

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Answer:

The answer for Probability is 1/2

Step-by-step explanation:

7,6,8,1,54,23

Probability of spinning an odd number greater than 3=1,7,23

P=3/6

P=1/2

Answer:

Work smartly not hard.

Step-by-step explanation:

AI

Answer: 300

Step-by-step explanation:

10*8*6=480-6*6*5=180=300

The solution to the given composite function is; C: 4x² - 4x - 2

From the question, we are given the individual functions as;

f(x) = x² - 3

g(x) = 2x - 1

Now when it comes to composite functions, we know that;

(f ° g)(x) = f[g(x)]

Substitute the known values in the above equation, so, we have the following representation

(f ° g)(x) = f(2x - 1) = (2x - 1)² - 3 = 4x² - 2x - 2x + 1 - 3 = 4x² - 4x - 2

This is the final solution of the composite function expression.

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The solution to the given composite function is; Option D: 2x² - 7

Composite functions are defined as functions where the output of one function is used as the input of another. Wheb we have a function f and another function g, then the function fg(x), said as “ f of g of x”, is the composition of the two functions.

The given functions are:

f(x) = x² - 3

g(x) = 2x - 1

We want to find (g ° f)(x) . We know that:

(g ° f)(x) = g[f(x)]

Thus:

(g ° f)(x) = g(x² - 3)

= 2(x² - 3) - 1

= 2x² - 6 - 1

= 2x² - 7

This is the final result of the composite function expression.

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The data that appears to have a consistent rate of change over time or with respect to another variable often appears to be linear.

The data that has a clear trend or pattern that can be represented by a straight line is best modeled using a line.

Linear graphs are useful because they allow us to easily visualize and analyze trends or patterns in data. The equation of a line can also be used to make predictions or forecasts based on the data. Linear graphs can be used to identify correlations between variables and to assess the strength and direction of those correlations.

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The surface area of the figure is 344 m².

Area is the region bounded by a plane shape.

To calculate the surface area of the figure, we use the formula below.

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 2

Hence, the area is 344 m².

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Answer:

yes it is if you bisect 5m on a 12m line

To find the LCM of 24 and 6, we can use the prime factorization method.

First, we find the prime factorization of each number:

24 = 2 x 2 x 2 x 3

6 = 2 x 3

Then, we identify the highest power of each prime factor that appears in either number.

The prime factor 2 appears three times in 24, but only once in 6. Therefore, we take the highest power of 2, which is 2 x 2 x 2 = 8.

The prime factor 3 appears once in both numbers, so we take the highest power of 3, which is 3.

Finally, we multiply these together to get the LCM:

LCM(24, 6) = 8 x 3 = 24

Therefore, the LCM of 24 and 6 is 24.

~~~Harsha~~~

Answer: LCM of  24 and 6 is 24

Step-by-step explanation:

The angle AOB is approximately 98 degrees.

The measure of the angle AOB of the sector can be found as follows:

AOB is the central angle.

Therefore,

length of an arc = ∅ / 360 × 2πr

where

Therefore,

12 = ∅ / 360 × 2 × 3.14 × 7

12 = 43.96∅ / 360

cross multiply

360 × 12 =  43.96∅

4320 = 43.96∅

divide both sides by 43.96

∅ = 4320 / 43.96

∅ = 98.271155596

Therefore,

∅ = 98 degrees

AOB = 98 degrees

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