Can you show me the steps that you took to get the answer for this question?

The distance between the coordinate point (3, 2) and line y = ¹/₄x - 9 is; 10.25 units

We want to find the distance between the coordinate point (3, 2) and line y = ¹/₄x - 9.

Thus, we will plug in 3 for x in the line equation given to get;

y = ¹/₄(3) - 9

y = 0.75 - 9

y = -8.25

Thus, we can say that point on the line is (3, -8.25)

The difference in y-values would give us the required distance;

Required distance = -8.25 - 2

Required distance = -10.25

However distance cannot be negative and so we will take the absolute value as 10.25 units.

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Answer: 19

Step-by-step explanation:

Using the sum of an arithmetic series formula,

[tex]\sum^{30}_{n=2} (an+b)=2407 \implies 29(16a+b)=2407 \implies 16a+b=83\\\\\sum^{40}_{n=1} (an+b)=4220 \implies 20(41a+2b)=4220 \implies 41a+2b=211[/tex]

Multiplying the second equation by 2 gives us [tex]32a+2b=166[/tex].

Subtracting this from the second equation, we get that [tex]9a=45 \implies a=5[/tex].

Substituting this back into the first equation, we get that [tex]b=3[/tex].

Therefore, [tex]2a+3b=2(5)+3(3)=19[/tex]

The expression that can be used to determine the slope of the line is (1 + 4)/(-3 - 2)

The slope of a line is the gradient  or the average rate of change of the line or a line equation

Note that linear equations are equations that have constant average rates of change, slope or gradient

The two points are given as

(2,-4);(-3,1)

The slope of a line is calculated using

m = (y2 - y1)/(x2 - x1)

Substitute the coordinates of the points in the above equation

m = (1 + 4)/(-3 - 2)

Evaluate the numerator

m = 5/(-3 - 2)

Evaluate the denominator

m = 5/-5

Rewrite the quotient as

m = -5/5

Evaluate the quotient

m = -1

Hence, the expression that can be used to determine the slope of the line is (1 + 4)/(-3 - 2)

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Sofia will order 7 more rolls of sushi (84 pieces) and pay $56St

Step-by-step explanation: im right

Answer:

[tex]\mathrm{pK}_{\mathrm{a}}+\mathrm{pK}_{\mathrm{b}}=\mathrm{pK}_{\mathrm{w}}[/tex] for [tex]\mathrm{HCl}[/tex] \& [tex]\mathrm{ClOH}[/tex]

Answer:

f(x):  Amplitude = 2, Period = 2

g(x):  Amplitude = ¹/₂, Period = π

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

Standard form of a cosine function:

f(x) = A cos(B(x + C)) + D

where:

Function f(x)

[tex]f(x)=2 \cos (\pi x)[/tex]

Comparing this with the standard form of a cosine function:

Function g(x)

[tex]g(x)=\dfrac{1}{2} \cos (2x)[/tex]

Comparing this with the standard form of a cosine function:

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Answer:

9.8 is the final anwser

Step-by-step explanation so easy

Answer:

A) 39

Step-by-step explanation:

If you calculate the volume of the cube which is the V=a^3 you get 27, then calculating the pyramid, the Length is 3, and the Width is also 3. Then the height is 4. so you put that into the formula to calculate the volume which is V=L*W*H
    --------

        3

you get 12. Now its simple, you just add the 2 volumes, so you do 27+12 and its 39.

39 is the answer by calculating the volume using formula!

Answer:

16 chairs

Step-by-step explanation:

800 - 300 = 500

500/30 = 16.6 since it's money you can only afford 16

The fraction of students that play basketball is  [tex]\mathbf{= \dfrac{1}{10}}[/tex].

The fraction of students that play basketball from the given information can be determined by assuming that the whole number of students in the middle school is whole i.e. (1)

Let us first determine the number of students that participate in sports, we have:

[tex]\mathbf{=1- \dfrac{3}{5}}[/tex]

[tex]\mathbf{= \dfrac{2}{5}}[/tex]

If 1/4 of these students play basketball, then we have:

[tex]\mathbf{= \dfrac{1}{4}\times (\dfrac{2}{5})}[/tex]

[tex]\mathbf{= \dfrac{1}{10}}[/tex] students play basketball.

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The number of bacteria when t = 8 is approximately 66 bacterias

Given the function that gives the number of bacteria in a population as a function of time in hour expressed as:

P=48∙e^((0.045t))

If the value of t is 8, hence;

P=48∙e^((0.045(8))

P = 48e^0.36

P = 65.933

Hence the number of bacteria when t = 8 is approximately 66 bacterias

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The median age of your customer base = 45

The median is the value that divides a data sample, a population, or even a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set. The fundamental difference between the mean and the median when describing data is that the median is more representative of the "typical" value because it is not skewed by the a small proportion of extremely large or small values. Due to the fact that income distribution can be highly skewed, the median income, for instance, might be a better indicator of what is considered a "typical" income.

Mean = middle term

          = 6th term

          = 45

Hence, Median of age = 45.

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The measure of angle A and C will be 94.5° and 85.5°.

(5y - 3) + (3y + 27) = 180

Collect like terms

5y + 3y - 3 + 27 = 180

8y = 180 - 27 + 3

8y = 156

y = 156/8 = 19.5

(5y - 3) = (5 × 19.5) - 3 = 94.5

(3y + 27) = (3 × 19.5) + 27 = 85.5

Therefore, the measure of angle A and C will be 94.5° and 85.5°.

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Evaluating the function from the given graph, g(-9) = 1.

To find the value of a function for a given x-value using a given graph, trace the x-value against the corresponding y-value on the y-axis.

To evaluate the function from the graph given, for g(-9), find the y-value that corresponds to the x-value of -9.

The graph shows that when x = -9, the corresponding y-value is 1.

Therefore, g(-9) = 1.

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Answer:

The first one, you cannot factor because the two values do not share any common factors. Hence, the answer would just be:

a. 51x-25

The other one, we can factorise to:

b. 3x(4-x)

Step-by-step explanation:

For the second option:

Common factor between 12x and 3x^2 is 3x.

Take this out to the front, we are left with:

3x(4-x)

A website I recommend you use (math calculator with some instructions) is Symbolab.

https://www.symbolab.com/solver/factor-calculator/factor%2012x-3x%5E%7B2%7D?or=input

Answer:

Step-by-step explanation:

his function will be an exponential function, because the number of rabbits double each year

the basic form for exponential functions is

where s is the starting number, c i s the constant (rate of change like double, triple, etc.) and x is the number repeats (in this case, years)

so in this case, the starting number (year 0) is 8, and the rate of change is 2

therefore, the equation is:

f(X) =8 times 2

hope this helps!

p.s. can i have brainliest?

The equation, in point-slope from, of the line that is perpendicular to the given line and passes through the point (-4,-3) is  y + 3 = 1/4(x + 4)

The complete question is added as an attachment

The points on the line are given as:

(-1, 1) and (0, -3)

Start by calculating the slope of the line using

m = (y2 - y1)/(x2 - x1)

The slope of the perpendicular line is

m2 = -(x2 - x1)/(y2 - y1)

So, we have:

m2 = -(0 + 1)/(-3 - 1)

This gives:

m2 = 1/4

The equation of the line is then calculated as

y - y1 = m(x - x1)

This gives

y + 3 = 1/4(x + 4)

Hence, the equation, in point-slope from, of the line that is perpendicular to the given line and passes through the point (-4,-3) is  y + 3 = 1/4(x + 4)

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Answer:

2x-3/7x

Step-by-step explanation:

Answer: $350

Step-by-step explanation:

$700 divided by 2 is 350

The interest rate needed to double the investment in 18 years is  6%.

Interest earned is a function of the amount invested, interest rate and time. The future value of the investment is to be $6000 (3000 x 2). Interest earned would be $3000 (6000 - 3000)

Interest rate = interest earned / (amount invested x time )

$3000 / ($3000 x 18) = 6%

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Since the x-coordinates are equal, hence the equation of the line will be x =4

The equation of a line in slope-intercept form is expressed as:

y = mx + b

where

m is the slope

b is the intercept

From the given coordinate points (four, three) and (four, negative two), we can see that the x-coordinates are equal, hence the equation of the line will be x =4

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Since the multiplication between two matrices is not commutative, then [tex]\vec A\, \times\,\vec I \ne \vec I \,\times \,\vec A[/tex], regardless of the dimensions of [tex]\vec A[/tex].

In linear algebra, we define the product of two matrices as follows:

[tex]\vec C = \vec A \,\times \vec B[/tex], where [tex]\vec A \in \mathbb{R}_{m\times p}[/tex], [tex]\vec B \in \mathbb{R}_{p\times n}[/tex] and [tex]\vec C \in \mathbb{R}_{m \times n}[/tex]     (1)

Where each element of the matrix is equal to the following dot product:

[tex]c_{ij} = \left[\begin{array}{cccc}a_{i1}&a_{i2}&\ldots&a_{ip}\end{array}\right]\,\bullet\,\left[\begin{array}{ccc}b_{1j}\\b_{2j}\\\vdots\\b_{pj}\end{array}\right][/tex], where 1 ≤ i ≤ m and 1 ≤ j ≤ n.     (2)

Because of (2), we can infer that the product of two matrices, no matter what dimensions each matrix may have, is not commutative because of the nature and characteristics of the definition itself, which implies operating on a row of the former matrix and a column of the latter matrix.

Such "arbitrariness" means that resulting value for [tex]c_{ij}[/tex] will be different if the order between [tex]\vec A[/tex] and [tex]\vec B[/tex] is changed and even the dimensions of [tex]\vec C[/tex] may be different. Therefore, the proposition is false.

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Answer:

[tex]-\frac{4}{3}[/tex](Your answer choices were really confusing, so I just put the plain answer)

Step-by-step explanation:

To find the slope of a line with just two points, we can use the formula [tex]\frac{y2-y1}{x2-x1}[/tex]. In this case, [tex]\frac{5-(-3)}{2-8}[/tex]. This is [tex]\frac{8}{-6}[/tex]. This reduces to [tex]-\frac{4}{3}[/tex]

The 2 x 2 matrices of the transformations are

[tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex], [tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex], [tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right][/tex] and [tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right][/tex]

The rule of reflection in the y-axis is

(x, y) ⇒ (-x, y)

This is represented as:

[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]

When solved using a graphing calculator, we have:

[tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]

Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex]

The rule of reflection in the line y = x is

(x, y) ⇒ (y, x)

This is represented as:

[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}y&x\end{array}\right][/tex]

When solved using a graphing calculator, we have:

[tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}y&x\end{array}\right][/tex]

Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex]

The rule of rotation through 180◦ about the origin is

(x, y) ⇒ (-x, -y)

This is represented as:

[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&-y\end{array}\right][/tex]

When solved using a graphing calculator, we have:

[tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]

Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right][/tex]

The rule of the enlargement from the origin with scale factor λ.

(x, y) ⇒ (λx, λy)

This is represented as:

[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}\lambda x&\lambda y\end{array}\right][/tex]

When solved using a graphing calculator, we have:

[tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}\lambda x&\lambda y\end{array}\right][/tex]

Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right][/tex]

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A patient should be given 8 and a half tablets and Approx. 8 days should the patient stay on the medication.

Given:

To find:

Solution:

If each tablet contains 7 mg and the doctor orders 60 mg of Benadryl.

Then the patient should be given 60/7 tablets i.e., 8 and a half tablets.

If the patient is only to take 1 tablet per day, then approx 8 days the patient we stay on the medication.

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Part (a)

[tex]\frac{1}{10}+\frac{3}{10}=\frac{4}{10}=\boxed{\frac{2}{5}}[/tex]

Part (b)

[tex]200\left(\frac{2}{5} \right)=\boxed{80}[/tex]

The value of x in 2^x - 2 when x = 0, x = 1 and x = 2 are -1, 0 and 2 respectively. option A

2^x - 2

when x = 0

2^x - 2

= 2^0 - 2

= 1 - 2

= -1

when x = 1

2^x - 2

=2^1 - 2

= 2 - 2

= 0

when x = 2

2^x - 2

= 2^2 - 2

= 4 - 2

= 2

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There are 1024 outcomes in the event

The given parameters are:

Device = coin

Number of flips = 10

A coin has 2 faces.

So, the number of outcomes is

Outcome = Faces^Flip

This gives

Outcome = 2^10

Evaluate

Outcome = 1024

Hence, there are 1024 outcomes in the event

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Answer:

[tex]1024[/tex]

Step-by-step explanation:

Each and every flip of our coin has two possible outcomes on the whole: it is either the heads or the tails. Besides, it resembles the bit in computing, right? Indeed, it has two options likewise: it can be either [tex]0[/tex] or [tex]1[/tex]. For now on I suggest thinking neither in heads nor in tails, but in bits. Suppose the heads is [tex]0[/tex], the tails is [tex]1[/tex]. Let us slightly simplify the condition, namely: suppose that the number of flips is [tex]3[/tex]. Then, our possible outcomes:

[tex]000 \\ 001 \\ 010 \\ 011 \\ 100 \\ 101 \\ 110\\ 111[/tex]

Take a look at the first number. In case it is [tex]0[/tex], we have [tex]4[/tex] outcomes because we can put either [tex]0[/tex] or [tex]1[/tex] not only on the second place, yet also on the third one. Abiding by the same logic, we also have [tex]4[/tex] outcomes when the first one is [tex]1[/tex]. In mathematics: [tex]2 * 2 * 2 = 2^3 = 8[/tex] outcomes.
As for the initial condition, it does not globally differ from our simplification, it just has more flips, hence it is not just a walk in the park to list all the possible outcomes anymore in this case, it is time-consuming otherwise. Even though, it is still not a big deal to count it: [tex]2 * ... * 2 = 2^{10} = 1024[/tex] outcomes.

Term life insurance has the lower premium because term life insurance pays the face value to your beneficiary if you die within a certain set period of time, whereas whole life insurance covers you your entire life. (Option A)

Insurance is when a third-party (the insurer) promises to indemnify another party (the insured) for losses they might suffer in the future in exchange for agreed upon payments.

Permanent life insurance is a type of insurance that provides a coverage that never expires. The person with a permanent life insurance is covered until he or she passes on. Whole life insurance is a type of permanent life insurance that has a fixed and guaranteed premium and a fixed death benefit.

Term life insurance is a type of insurance that provides coverage to a person only for a scheduled period of time. For example, a person who buys a 10 year term life insurance, the person's insurance only lasts for 10 years. If the person passes on within the 10 years, his beneficiary receives payments. If the person passes on after 10 years, his beneficiary does not receive any payments.

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Part A

[tex]f(x)=(x-1)(2x-3)[/tex]

Part B

[tex](x-1)(2x-3)=0\\\\x=1, \frac{3}{2}[/tex]

So, the x-intercepts are [tex](1,0)[/tex] and [tex]\left(\frac{3}{2}, 0 \right)[/tex]

Part C

As [tex]x \to \infty[/tex], [tex]f(x) \to \infty[/tex] because the leading coefficient is positive.

As [tex]x \to -\infty[/tex], [tex]f(x) \to \infty[/tex] because the degree is even and the leading coefficient is positive.

Part D

Plot the x-intercepts on the graph, and then find the value of [tex]f(x)[/tex] at [tex]x=\frac{5}{4}[/tex] (the midpoint of the two roots) to plot the vertex. Then, draw a curve through these three points that approaches infinity as [tex]x \to \pm \infty[/tex]

The factored polynomial is given as follows:

(5x - 1)(6x² + 1)

Polynomials are factored placing the common factor in evidence, then dividing all terms by the common factor.

The polynomial is:

6x²(5x - 1) + (5x - 1).

The common factor is (5x - 1), hence:

[tex](5x - 1)\left(\frac{6x^2(5x - 1)}{5x - 1} + \frac{5x - 1}{5x - 1}\right) = (5x - 1)(6x^2 + 1)[/tex]

Hence the factored polynomial is given as follows:

(5x - 1)(6x² + 1)

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