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simplify the radical expression State any restrictions (n^4 -11n^2 +30) / (n^4 -7n^2 +10)

Please show steps!

Answer:the answer is d

Step-by-step explanation:

5x - y ≥ 2

Final answer:

Adjacent angles can be either complementary or supplementary depending on their sum. Complementary angles add up to 90°, while supplementary angles sum to 180°. The term for adjacent angles in terms of their sum is 'supplementary angles', adding up to 180°.

Explanation:

Adjacent angles are two angles that have a common side and vertex, and don't overlap. In terms of their sum, if adjacent angles add up to 90 degrees, they are called complementary angles. If they add up to 180 degrees, they are called supplementary angles. Since the question involves angles ∠2 and ∠3 as adjacent angles but does not provide their specific measures, it's not possible to definitively classify them as complementary or supplementary without additional information. However, the question asks which term describes adjacent angles in terms of their sum. The correct answer is supplementary angles, which have a sum of 180°.

The two consecutive even integers that satisfy the given condition are 6 and 8. When the smaller one (6) is added to three times the larger one (8), the sum is 30.

The student has asked for help in finding two consecutive even integers such that the smaller added to three times the larger gives a sum of 30. To solve this, let's designate the smaller even integer as x. Since the numbers are consecutive even integers, the next integer will be x + 2.

The equation based on the problem statement will look like this:

x + 3(x + 2) = 30

Expanding the equation gives:

x + 3x + 6 = 30

Combining like terms:

4x + 6 = 30

Subtracting 6 from both sides:

4x = 24

And dividing by 4:

x = 6

Now, the two consecutive even integers can be determined:

The smaller integer is 6, and the larger integer is 6 + 2, which equals 8. Therefore, the two integers are 6 and 8, and if we check:

6 + 3(8) = 6 + 24 = 30, which matches the required sum.

Answer:

7092.82

Step-by-step explanation:

i took the quiz

The short-answer question worth of 14 points.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Total points of test =140

and 10 % of those points are from one short-answer question.

So, the points for short-answer question are

=10 % of 140

=10/100 x 140

=1400/100

=14

Hence,  short-answer question worth of 14 points.

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Answer: 17

Step-by-step explanation:

Answer:

30 + 0.15m

Step-by-step explanation:

base rate = 40(1 − 0.25) = 40(0.75) = 30

per mile = 0.15m

thus,

30 + 0.15m

The correct expression represents the situation is,

⇒ 30 + 0.15m

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Eric plans to rent a car for a day from Easy Car Rental.

Here,  He has a coupon for 25% off the daily base rate of $40.

And,  He will also have to pay an additional $0.15 for each mile he drives.

Let m represents the number of miles.

Hence, We can formulate;

⇒ 40 (1 - 0.25) + 0.15m

⇒ 40 × 0.75 + 0.15m

⇒ 30 + 0.15m

Thus, The correct expression represents the situation is,

⇒ 30 + 0.15m

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Answer: A) -4, 3, 10, 17, 24, 31

Step-by-step explanation: To solve the given problem we need to calculate the first six terms of the sequence (starting with a1):

a1=-4

a2=a1+7

a2=-4+7

a2=3

a3=a2+7

a3=3+7

a3=10

a4=a3+7

a4=10+7

a4=17

a5=a4+7

a5=17+7

a5=24

a6=a5+7

a6=24+7

a6=31.

The product of -9(5-2x) is found by multiplying -9 by each term inside the parentheses resulting in -45 + 18x.

The product of -9(5-2x) is found by distributing the -9 to both terms inside the parentheses. Following the rules of multiplication, when a negative number multiplies a positive number, the result is negative, and when a negative number multiplies a negative number, the result is positive. Hence:

-9 x 5 = -45

and

-9 x -2x = 18x.

Combining these results, we get the final expression:

-45 + 18x

Keep in mind that when simplifying expressions or performing multiplication, we need to adhere to the rules for multiplication of numbers with different signs, as described earlier.

Final answer:

The product of -9(5-2x) is calculated by using the distributive property to multiply -9 by each term inside the parentheses, yielding 18x - 45.

Explanation:

The product of -9(5-2x) can be found by applying the distributive property of multiplication over subtraction. This property states that you multiply the term outside the parentheses by each term inside the parentheses. Here are the steps:

Multiply -9 by the first term inside the parentheses (5), which is -45.

Multiply -9 by the second term inside the parentheses (-2x), which gives us +18x (note that a negative multiplied by a negative gives a positive).

Combine these two products to get the final result, -45 + 18x, or 18x - 45.

This demonstrates the rules of multiplication where multiplying two numbers with opposite signs results in a negative product, and multiplying two numbers with the same sign results in a positive product.

Answer:

The answer would be a im sure

Step-by-step explanation:

The true solution to [tex]3 log 2+log8 =2log(4x)[/tex] is [tex]x=2[/tex]. The correct option is b. [tex]x=2[/tex].

[tex]3 \log 2+\log8 =2\log(4x)[/tex].

We have to calculate the value of [tex]x.[/tex]

We know that,  

[tex]n \log m= \log(m)^n[/tex]

and

[tex]\log m + \log n = \log(mn)[/tex]

Solving the equation:

[tex]3 \log 2+\log8 =2\log(4x)[/tex][tex]\log(2)^3+\log8 =\log(4x)^2[/tex]

{using [tex]n \log m= \log (m)^n[/tex]}

[tex]\log8+\log 8= \log 16x^2[/tex]

[tex]\log (8 \times8)=\log16x^2[/tex] {using [tex]log m + log n = log(mn)[/tex]}

Since log is on both sides so it is eliminated from both sides,

[tex]8 \times8=16x^2\\64=16x^2\\[/tex]

[tex]x^{2} =\frac{64}{16}\\x^{2}=4\\x=2[/tex]

Hence the true solution to [tex]3 log 2+log8 =2log(4x)[/tex] is [tex]x=2[/tex].

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The given statement "An equiangular triangle can never be scalene." is true.

An equiangular triangle is a triangle that has three equal angles.

A scalene triangle is a triangle that has three unequal sides.

Therefore, a scalene triangle has three different angles.

Therefore, an equiangular triangle and scalene triangle are two completely different triangles.

Hence, an equiangular triangle can never be a scalene triangle.

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Answer: d) the point of concurrency of the perpendicular bisectors

Step-by-step explanation:

Answer:

13/35

Step-by-step explanation:

gradpoint

Answer:

The answer is 2. hope it helps!

Step-by-step explanation:

Answer:  The area of the shaded portion is [tex](\pi-2)~\textup{sq. units}.[/tex]

Correct option is 2.

Step-by-step explanation:  We are given to find the area of the shaded portion in the figure.

Since, the centre point of each arc is the corresponding central point of the line and the arcs intersect at the centre point of the circle,

so let us divide the figure into four equal parts, one of them is square ABCD as shown in the attached figure.

The area of the square ABCD will be

[tex]A_{ABCD}=\left(\dfrac{1}{2}\times 2\right)^2\\\\\\\Rightarrow A_{ABCD}=1~\textup{sq. units}.[/tex]

Now, area of the shaded portion inside the square ABCD will be

[tex]A_s=2\times \textup{area of the quarter circle with radius 1 unit}}-\textup{area of square ABCD}\\\\\Rightarrow A_s=2\times \left(\pi\times \left(\dfrac{1}{2}\right)^2\right)-A_{ABCD}\\\\\\\Rightarrow A_s=2\times\left(\dfrac{\pi}{4}\right)-1\\\\\\\Rightarrow A_s=\left(\dfrac{\pi}{2}-1\right)~\textup{sq. units}.[/tex]

Since all the four squares are identical in the attached figure, so the required area of the total shaded portion in the figure is

[tex]A=2\times\left(\dfrac{\pi}{2}\right)\\\\\\\Rightarrow A=(\pi-2)~\textup{sq. units}.[/tex]

Thus, the area of the shaded portion is [tex](\pi-2)~\textup{sq. units}.[/tex]

The correct option is 2.

Final answer:

The amount of iodine-123 remaining after t hours can be expressed as I(t) = 52 · 0.945^t, where the constant 0.945 is calculated using the half-life of 13 hours.

Explanation:

The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms to decay. For iodine-123, which has a half-life of approximately 13 hours, we can use an exponential decay model to express the amount of iodine-123 remaining after t hours.

The decay formula is generally given by I(t) = I0e-kt, where I0 is the initial amount, k is the decay constant, and t is time. However, the question asks us to express the equation in the form of I(t) = a · bt, which is another common representation for exponential decay.

To find the value of b, we know that after one half-life, b13 = 1/2. Thus, b = (1/2)1/13.
Let's calculate b: b = (0.5)1/13 ≈ 0.945 (rounded to three decimal places).

Since we start with 52 grams of iodine-123, our initial amount (a) is 52. Therefore, the equation for the amount of iodine-123 remaining after t hours is:

I(t) = 52 · 0.945t

The equation to calculate the amount of iodine-123 remaining after t hours is I(t) = a * b^t, where a is the initial amount of iodine-123, b is the decay constant, and t is the time in hours. The decay constant can be calculated using the formula b = 0.693 / t1/2, where t1/2 is the half-life of iodine-123. In this case, the half-life is 13 hours.

The equation that gives the amount of iodine-123 remaining after t hours can be written as:

I(t) = a * b^t

Where:

To calculate the decay constant b, we can use the formula:

b = 0.693 / t1/2

where t1/2 is the half-life of iodine-123. In this case, the half-life is 13 hours, so:

b = 0.693 / 13 = 0.053

Therefore, the equation becomes:

I(t) = a * 0.053^t

Round the value of b to three decimal places, so b = 0.053.

The area of the frame if the frame is 1 inch thick will be 30 inch².The area of the frame is found as the product of the length and breadth of the frame.

The space filled by a flat form or the surface of an item is known as the area.

If the  frame is 1 inch thick then the total area is found as;

The area of the rectangular picture is;

[tex]\rm A = 5 \times 8 \\\\\rm A =40 \ inch^2 \\\\[/tex]

The total area of the frame is found as;

Area of frame = Total area -  area of the picture

Area of frame =70 -40

Area of frame = 30 inch²

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Answer:

It's 1,3, and 5.

The functions that have  a value of 0 are : [tex]cos(\frac{\pi}{2} ),~sin(0),~tan(\pi)[/tex]

For given question,

We have been given some trigonometric functions.

We need to find the functions that have a value zero.

[tex]i)~cos(\frac{\pi}{2} )=0\\\\ii)~cos(0)=1\\\\iii)~sin(0)=0\\\\iv)sin(\frac{3\pi}{2} )=-1\\\\v)tan(\pi)=0[/tex]

From above, we can observe that functions [tex]cos(\frac{\pi}{2} ),sin(0)[/tex] and [tex]tan(\pi)[/tex] have a value of zero.

Therefore, the functions that have  a value of 0 are : [tex]cos(\frac{\pi}{2} ),~sin(0),~tan(\pi)[/tex]

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There are 5 prime numbers less than 100 that have a units digit of 1.

To determine how many prime numbers less than 100 have a units digit of 1, we need to follow these steps:

The prime numbers less than 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

The primes with a units digit of 1 are: 11, 31, 41, 61, 71.