BROOO HELP what is the slope of the line through (-3,3) and (-1,-1)?

A. 1/2
B. -1/2
C. -2
D. 2

Explanation:

The period of a function measures how long a cycle takes. Think of tides on a beach. There's a regular pattern that can be predicted whether its high tide or low tide. Time is often the critical component with the period. Since choice D mentions time and the key term "repeat", this is why it's the answer.

The other values, while useful elsewhere, aren't going to tell us anything about the period. The initial value being 5 doesn't tell us when y = 5 shows up again, and if the function is repeating itself at this point or not. So info about choice A is not sufficient to determine the period. The same goes for choices B and C as well.

The required frequencies are 9, 8, 5, 2, 1, 2.

The quantity of times a specific data value happens is known as its frequency. For instance, the score of 80 is said to have a frequency of four if four pupils receive an overall math score of 80.

The frequency of 0 is 9.

The frequency of 1 is 8.

The frequency of 2 is 5.

The frequency of 3 is 2.

The frequency of 4 is 1.

The frequency of 5 is 2

Thus, required frequencies are 9, 8, 5, 2, 1, 2.

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Answer:ANS: (3,4)

(x,y) (x,y)

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

3x² + 8 = 83

3x² = 83 - 8

3x² = 75

x² = 75/3

x² = 25

x = √25

x = 5

-TheUnknownScientist

Answer:

x =5

Step-by-step explanation:

3x²+8=83

3x²=83-8

3x²=75

x²=75

3

x²=25

x=√25

x=5

hope it help u.

Answer:

(i) x ≤ 1

(ii) ℝ except 0, -1

(iii) x > -1

(iv) ℝ except π/2 + nπ, n ∈ ℤ

Step-by-step explanation:

(i) The number inside a square root must be positive or zero to give the expression a real value. Therefore, to solve for the domain of the function, we can set the value inside the square root greater or equal to 0, then solve for x:

\(1-x \ge 0\)

\(1 \ge x\)

\(\boxed{x \le 1}\)

(ii) The denominator of a fraction cannot be zero, or else the fraction is undefined. Therefore, we can solve for the values of x that are NOT in the domain of the function by setting the expression in the denominator to 0, then solving for x.

\(0 = x^2+x\)

\(0 = x(x + 1)\)

\(x = 0\)     OR     \(x = -1\)

So, the domain of the function is:

\(R \text{ except } 0, -1\)

(ℝ stands for "all real numbers")

(iii) We know that the value inside a logarithmic function must be positive, or else the expression is undefined. So, we can set the value inside the log greater than 0 and solve for x:

\(x+ 1 > 0\)

\(\boxed{x > -1}\)

(iv) The domain of the trigonometric function tangent is all real numbers, except multiples of π/2, when the denominator of the value it outputs is zero.

\(\boxed{R \text{ except } \frac{\pi}2 + n\pi} \ \text{where} \ \text{n} \in Z\)

(ℤ stands for "all integers")

Answer:

(i)  x ≤ 1

(ii)  All real numbers except x = 0 and x = -1.

(iii)  x > -1

(iv)  All real numbers except x = π/2 + πn, where n is an integer.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

\(\hrulefill\)

\(\textsf{(i)} \quad f(x)=\sqrt{1-x}\)

For a square root function, the expression inside the square root must be non-negative. Therefore, for function f(x), 1 - x ≥ 0.

Solve the inequality:

\(\begin{aligned}1 - x &\geq 0\\\\1 - x -1 &\geq 0-1\\\\-x &\geq -1\\\\\dfrac{-x}{-1} &\geq \dfrac{-1}{-1}\\\\x &\leq 1\end{aligned}\)

(Note that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign).

Hence, the domain of f(x) is all real numbers less than or equal to -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x \leq 1\\\textsf{Interval notation:} \quad &(-\infty, 1]\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \leq 1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(ii)} \quad g(x) = \dfrac{1}{x^2 + x}\)

To find the domain of g(x), we need to identify any values of x that would make the denominator equal to zero, since division by zero is undefined.

Set the denominator to zero and solve for x:

\(\begin{aligned}x^2 + x &= 0\\x(x + 1) &= 0\\\\\implies x &= 0\\\implies x &= -1\end{aligned}\)

Therefore, the domain of g(x) is all real numbers except x = 0 and x = -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x < -1 \;\;\textsf{or}\;\; -1 < x < 0 \;\;\textsf{or}\;\; x > 0\\\textsf{Interval notation:} \quad &(-\infty, -1) \cup (-1, 0) \cup (0, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq 0,x \neq -1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iii)}\quad h(x) = \log_7(x + 1)\)

For a logarithmic function, the argument (the expression inside the logarithm), must be greater than zero.

Therefore, for function h(x), x + 1 > 0.

Solve the inequality:

\(\begin{aligned}x + 1 & > 0\\x+1-1& > 0-1\\x & > -1\end{aligned}\)

Therefore, the domain of h(x) is all real numbers greater than -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x > -1\\\textsf{Interval notation:} \quad &(-1, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x > -1\right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iv)} \quad k(x) = \tan x\)

The tangent function can also be expressed as the ratio of the sine and cosine functions:

\(\tan x = \dfrac{\sin x}{\cos x}\)

Therefore, the tangent function is defined for all real numbers except the values where the cosine of the function is zero, since division by zero is undefined.

From inspection of the unit circle, cos(x) = 0 when x = π/2 and x = 3π/2.

The tangent function is periodic with a period of π. This means that the graph of the tangent function repeats itself at intervals of π units along the x-axis.

Therefore, if we combine the period and the undefined points, the domain of k(x) is all real numbers except x = π/2 + πn, where n is an integer.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &\pi n\le \:x < \dfrac{\pi }{2}+\pi n\quad \textsf{or}\quad \dfrac{\pi }{2}+\pi n < x < \pi +\pi n\\\textsf{Interval notation:} \quad &\left[\pi n ,\dfrac{\pi }{2}+\pi n\right) \cup \left(\dfrac{\pi }{2}+\pi n,\pi +\pi n\right)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq \dfrac{\pi}{2}+\pi n\;\; (n \in\mathbb{Z}) \right\}\\\textsf{(where $n$ is an integer)}\end{aligned}}\)

The measurement that is closest to the volume of the sphere is given as follows:

1,767.1 in³.

The volume of an sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:

\(V = \frac{4\pi r^3}{3}\)

From the image given at the end of the answer, we have that the diameter is of 15 units, hence the radius of the sphere, which is half the diameter, is given as follows:

r = 0.5 x 15

r = 7.5 units.

Then the volume of the sphere is given as follows:

V = 4/3 x π x 7.5³

V = 1,767.1 in³.

The sphere is given by the image presented at the end of the answer.

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Answer:

x = (v - u) / a

Step-by-step explanation:

v = u + ax.

subtract u from both sides:

v - u = ax.

divide both sides by a:

(v - u) / a = x.

so x = (v - u) / a.

this can also be written v/a - u/a

The 1/2, 5/12, and 1/2 hour duration it takes Tiffany, Gary, and Noland to walk round the park provides the following;

1) The time in minutes it takes Tiffany to walk round the park is 30 minutes

Gary takes 25 minutes and Noland takes 20 minutes to walk round the park

2) Tiffany will go round 12 times, Gary will go round 12 times and Noland will go round the park 15 times before all three will meet again.

3) The solution to question 2 is arrived at by dividing the least common multiple of 30, 25, and 20, which is 300 by 30, 25, and 20 respectively

The least common multiple also known as the L.C.M. is the least number two or more numbers have as their multiples.

The time it takes Tiffany to walk around the track = 1/2 hour

The time it takes Gary to walk round the park = 5/12 hour

The time it takes Noland to walk round the park  = 1/3 hour

1) The duration in minutes it takes each person to walk round the park are found using the conversion factor for minutes and hours as follows;

60 minutes = 1 hour

Therefore;

1/2 hour = 30 minutes

It takes Tiffany 30 minutes to walk around the track

5/12 hour = 25 minutes

It takes Gary 25 minutes to walk around the track

1/3 hours = 20 minutes

It takes Noland 20 minutes to walk round the park

2) The number of times each person will go round the track before all three meet again is given by the least common multiple of 30, 25, and 20, which is 300

Therefore;

The number of times Tiffany would walk round the park before all three meet again is 300 ÷ 30 = 10

The number of times Gary would walk round the park = 300 ÷ 25 = 12

The number of times Noland walks round the park = 300 ÷ 20 = 15

When all three meet again, Tiffany will halve walked 10 times, Gary would have walked 12 times and Noland would have walked 15 times round the park.

3) The solution for question 2 was arrived at by looking for the lowest common multiple of the durations it takes each of the three persons to walk round the park. The least common multiple provides the time at which all three will have made complete cycles simultaneously.

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Answer:

Pls can u type it out ur self so I can help u out

Answer:

21 and 22 are the integers.

Step-by-step explanation:

Let's say the lower number is x. This means that the bigger number would be x+1

x+x+1=43

Simplify

2x+1=43

Subtract 1 on each side of the equation to isolate 2x:

2x=42

Divide

x=21

Let's put this to the test! The lower number(x) is 21, and the bigger number(x+1) would be 22. The total is 43.

Happy learning!

--Applepi101

Answer:

x=\(-\frac{6}{85}\)

Step-by-step explanation:

Answer:

x = -6/85

Step-by-step explanation:

2/3x - 4(2x-3) = 7(3x+2)

2/3x - 8x + 12 = 21x + 14

28 1/3x = -2

x = -2 ÷ 28 1/3

x = -2 ÷ 85/3

x = -2 x 3/85

x = -6/85

Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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Answer:

C.

Step-by-step explanation:

Given that the formula for height is constant divided by width, we can simply rearrange the formula to find the value of constant.

Thus, the formula would be constant = height x width. We will just multiply the x and y coordinates to get the constant.

Hope it helps!

(s+12)^3

I am wasting space here as you can tell but no fr the answer is (s+12)^3

Answer:

A - x < 8,,,,,,,,,,,,,,,,,

=6

The answer for it is diagram B because it does not cross or have parallel lines

The solution is the area of the figure is 53.17.

The area of a trapezoid is found using the formula, A = ½ (a + b) h,

where 'a' and 'b' are the bases (parallel sides) and 'h' is the height .

here, we have,

from the given figure we get,

a = 10,

b = 6

h = 8

so, A = 64

again, the cut triangle is a equilateral triangle with side = 5

then, area of triangle = √3/4 * 5^2

                                   = 10.82

so, required area = 53.17

Hence, The solution is the area of the figure is 53.17.

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Answer:

Y equals 12 when X equals 4

There are X automobiles, with a mean of 12.5 cars. The standard deviation for X is also SD = 12.0.

First, a data set's mean and standard deviation convey distinct information. The average (center) of a data collection is provided by mean (it is a measure of central tendency). You may learn about the range (dispersion) of data around the mean by looking at the standard deviation. We may investigate a data set's characteristics and characterize it using both the mean and standard deviation. To provide confidence intervals for data that has a normal distribution, they are frequently combined. If two or more data sets need to be compared:

The mean reveals whether data set is, on average, greater or lower (or better or worse). We can determine whether data set has a wider dispersion using the standard deviation (higher standard deviation means data is more spread out from the mean). Second, there are variations in how each metric is calculated. In particular, we utilize squaring to get the standard deviation but not the mean. We completely avoid using squaring when determining the mean of a data collection. Simply multiplying the total number of data points in the set by the sum of all the values in the data set yields the answer.

The mean is calculated as follows:

Mean = (all data values added together) / (number of data values)

However, when calculating standard deviation, we do employ squaring. We take the square of the deviation between each data point and the mean in particular.

The standard deviation equation is as follows:

Finally, when we add the identical value to each data point in the data set, the mean and standard deviation "respond" differently. If we multiply every value in a data collection by the constant "K":

No of the size of the data collection, the mean rises by precisely K.

No matter how many observations are in the data collection, the standard deviation does not vary. The identical value is then added.

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Answer:

\(f(x)=\sqrt{x+2}-2\)

Step-by-step explanation:

So for the graph as shown in your image, it either appears to be logarithmic or a radical function.

Considering how it doesn't have a long tail at the end going towards negative infinity, it's most likely a radical. I attached an image of a square root, and a logarithmic function to really demonstrate the difference (notice the long "tail" at the end of the logarithmic function)

Generally whenever you have a square root, you have it in the form: \(f(x)=a\sqrt[n]{x-h}+k\)

where (h, k) will be the minimum point (only if degree is even, since odd degrees are defined for all values of x, so there is no "minimum" value)

In your graph you provided, it appears that the minimum point is (-2, -2), so h=-2, and k=-2

Plugging this into the equation, you get: \(f(x)=a\sqrt{x-(-2)}-2=a\sqrt{x+2}-2\)

Now to make sure there isn't some value in front of the radical we can calculate some values (besides the minimum, sqrt(2-2) = 0, so any value of a will result in a * 0 - 2 = 0 - 2 = -2, thus all values of a work specifically at the minimum, so we can't use that point)

So by looking at the graph we see the point: (-1, -1)

Using the equation, plug in the values to get: \(-1=a\sqrt{-1+2}-2\\-1=a\sqrt{1}-2\\-1=a-2\\1=a\)

So we know a is just 1, thus we don't have to explicitly write it in our equation: \(f(x)=\sqrt{x+2}-2\)

The required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.

Given,
To determine the value of the unknowns in the matrix,

A matrix is a collection of numbers that are arranged in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.

Here,
\(2\left[\begin{array}{ccc}w&2\\5&z\end{array}\right] +3\left[\begin{array}{ccc}2&x\\-2&-6\end{array}\right] = 4\left[\begin{array}{ccc}4&7\\y&3\end{array}\right]\)
From the above matrix,
Equation formed,
2w + 6 = 16,
w = 5,

2z -18 = 12
z = 15

10 - 6 = 4y
y = 1

Thus,  the required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.

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Answer:

$660.

Step-by-step explanation:

So when we apply a discount to a product we multiply the price of the product (let's all is x) for the percentage of the discount (let's apply 90% as the probnlem says) so then we have the following operation:

x ⋅ (1-0.9) = y

Variable y is the price at which you bought the product, it's $66, on this case. Therefore, this is the expression we have:

x ⋅ (1-0.9) = $66

Now, to get the original value of the product (x), we solve the equation for x:

x ⋅ (1-0.9) = $66

x= $66 / (1-0.9)

x= $66 / (0.1)

x= $660

• Why did we multiply by 1-0.9?

This is because we were looking for the 10% of the original price, since it's a 90% discount. A simple way to solve the problem would've been to just divide the price by 0.1 (10%), because that's what remains after you discount 90% of the price.

-------------------------------------------------------------------------------------------

A different example would be the following:

What was the original price of a product bought for $48 if it has a 60% discount?

x is original price.

Since a 60% discount was applied, 40% of the price remains at full price. Therefore, we multiply the original price (x) by 40%:

x ⋅ 40%= $48

x= $48 / 40%

x= $48 / 0.4

x= 120

$120 was the original price.

Answer:

90% of 300 = .90 × 300 = 270 high- definition televisions on order.

Our assumption that 3-2√5 is a rational number is false, and hence it is an irrational number.

Let's prove that 3-2√5 is irrational. Let's suppose that 3-2√5 is a rational number, it means it can be represented as a ratio of two integers. Thus, we can write

3-2√5 = p/q, where p and q are integers with no common factors. Assume q≠0. Rearranging, we get:

3 = (2√5)q + p

Now, squaring both sides we get:

9 = 20q2 + 2pq√5 + p2(5)

Since p and q are integers, we have that 5q2 and p2(5) are both multiples of 5, and hence their difference is also a multiple of 5. Thus, 5 divides 9-p2(5) which means that 5 also divides (3-p)(3+p). Since 5 is prime and it divides the product of (3-p)(3+p), it must divide 3-p or 3+p (or both).

Hence, either 3-p or 3+p is divisible by 5. However, the possible values of p are ...,-3,-2,-1,0,1,2,3,... and thus p+3 is also in this set. Since 5 divides p+3, it must be the case that p+3 = 5n for some integer n. Hence p = 5n - 3. Now we have:

3 = (2√5)q + p = (2√5)q + (5n - 3)

Rearranging, we get:

(2√5)q = 6 - 5n

Since 2√5 is irrational, we have a contradiction because we have found that 2√5 is a rational number which is impossible.

Therefore, our assumption that 3-2√5 is a rational number is false, and hence it is an irrational number.

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The table that represents a linear equation is the first one, and the line can be:

y = -4x - 1

A general linear function can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Now, notice that if we evaluate the line in x + 1, we will get:

y = a*(x + 1) + b

y = a*x + a + b

So, for an increase of one unit on the variable x, we have a constant increase in the y value.

Now, if you look at the first table, you can see that for each increase of 1 unit on the value of x, the value of y decreases by 4.

So that is the table that can represent a linear function.

And the line is:

y = -4x - 1

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Answer:

\(\sqrt{97} \\ \sqrt{9^{2}+4^{2} }\)

Step-by-step explanation: