Dylan had $42 in his savings account. Each week, he takes $7 out of the account and doesn’t make any deposits. How much money does he have in his savings account after 13 weeks? How much money does Dylan have after 13 weeks?

According to the question, the logarithmic function can be simplified with the help of the concept of indices as well as logarithmic laws.

Expression = [tex]log_{3} \sqrt[n]{9x}[/tex]

Using logarithmic laws, it can be written as:

Expression = [tex]log_{3} \sqrt[n]{9x}= log_{3} 3\sqrt[n]{x}=log_{3}3 +log_{3}x^{1/2}[/tex]

                       [tex]1+\frac{1}{2}log_{3}x[/tex]

Therefore, the final answer of the given logarithmic function is:[tex]1+\frac{1}{2}log_{3}x[/tex]

What is logarithmic function?

In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.

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Answer:

I think its 93

Based on the alternate exterior angles theorem, the equation is: 15x - 3 = 14x + 2

The value of x = 5.

The angles, (15x - 3) and (14x + 2) are alternate exterior angles. Based on the alternate exterior angles theorem/postulate, they are congruent to each other.

Thus, the equation to create in solving for the value of x would be:

15x - 3 = 14x + 2

Subtract 14x from both sides of the equation

15x - 3 - 14x = 14x + 2 - 14x [subtraction property of equality]

x - 3 = 2

Add 3 to both sides

x - 3 + 3 = 2 + 3 [addition property of equality]

x = 5

In summary, based on the alternate exterior angles theorem, the equation is: 15x - 3 = 14x + 2

The value of x = 5.

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The size of each plot is 3630 square feet to plant six vegetables.

Given, Susan is using 0.5 acres of land.

we know that 1 acre = 43,560 square feet

0.5 acre = 1/2 acre = 1/2 × 43,560

= 21780 square feet.

we need to divide the land into 6 equal sized plots.

divide 21780 into six equal parts.

= 21780/6

= 3630 square feet

the land is being divided into 3630 square feet to plant 6 equal sized plots.

Hence susan plants six vegetables in 3630 square feet each.

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The simplification of √x / √6 y³ after rationalizing all denominators is

[tex]\sqrt{6x}[/tex] [tex]y^{-3}[/tex]/ 6

Given; [tex]\frac{\sqrt{x} }{\sqrt{6} y^{3} }[/tex] , we are to simplify and also rationalize the denominators

[tex]\frac{\sqrt{x} }{\sqrt{6} y^{3} }[/tex]  *  [tex]\frac{{\sqrt{6} y^{3} }}{{\sqrt{6} y^{3} }}[/tex]

= [tex]{\sqrt{6} y^{3} }[/tex] * [tex]\sqrt{x}[/tex] / [tex]{\sqrt{6} y^{3} }[/tex]*  [tex]{\sqrt{6} y^{3} }[/tex]

=[tex]\sqrt{6x}[/tex] * [tex]y^{3}[/tex] / [tex]\sqrt{36}[/tex]* [tex]y^{6}[/tex]

= [tex]\sqrt{6x}[/tex] *  [tex]y^{3}[/tex] / 6 * [tex]y^{6}[/tex]

=[tex]\sqrt{6x}[/tex] * [tex]y^{3-6}[/tex]  / 6

= [tex]\sqrt{6x}[/tex] [tex]y^{-3}[/tex] /6

The final answer to this question, is, [tex]\sqrt{6x}[/tex] [tex]y^{-3}[/tex] /6

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Applying the midpoint formula, the endpoints for the midsegment are (-0.5, 0.5) and (-5/2, -7/2).

The midsegment of a trapezoid is the line segment that intersects the two legs of the trapezoid at their midpoints.

Hence, to find the endpoint for the midsegment of the other leg of the trapezoid, apply the midpoint formula, M[(x2 + x1)/2, (y2 + y1)/2].

Find the midpoint between A(-2, -5) and B(-3, -2):

A(-2, -5) = (x1, y1)

B(-3, -2) = (x2, y2)

Plug in the values

M[(-3 + (-2))/2, (-2 + (-5))/2]

M(-5/2, -7/2)

Therefore, using the midpoint formula, the endpoints for the midsegment are (-0.5, 0.5) and (-5/2, -7/2).

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Answer:

-2.5,-3.5

Step-by-step explanation:

Answer:

Segment VU (or u can say UV)

Step-by-step explanation:

A line segment has two endpoints. It contains these endpoints and all the points of the line between them. You can measure the length of a segment, but not of a line.

There are 75% of red cars and blue cars if you add them together.

Hope this helps, please give me brainliest if I'm correct. ;)

Answer:y x

Step-by-step explanation:

calculator

Answer:

36

Step-by-step explanation:

Fine I wont

Answer:

x=36

Step-by-step explanation:

20+2x=x+56

-20         -20

2x=x+36

-x  -x

x=36

20+2(36)=(36)+56

20+72=36+56

92=92

Hope this helps.

Answer:

504 ways fr

Step-by-step explanation:

Answer:

81?

Step-by-step explanation:

-

frac

5

4

t

= -4 ×

5

×

xt =

frac

(5

4

t)=-4

x 5 x x t

→ -

9×9

=

81

From unitary method calculations, we have found that the large jar is the best value for money because a penny buys more honey.

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

We need to determine which has the best value for money using the quantity a pound can purchase.  

So, first for the large jar.

£4.10 will be purchase 540g of honey then,

£1.00 will be purchase xg

Then cross multiplying for x will be;

x = 1.00 (540g )/4.10

x = 131.7g

Hence for the large jar a penny will buy 131.7g of honey.

Now second for the small jar

£2.81 will be purchase 360g of honey then,

£1.00 will purchase xg

Now cross multiplying

x = 1.00 (360g )/ 2.81

x = 128.1g  

Hence for the small jar a penny will buy 128.1g of honey.

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Answer:

log₇(xy/z)

Step-by-step explanation:

We know that

[tex]\log_ax = b \implies a^b = x[/tex]

we also know that:

[tex]a^b \cdot a^c = a^{b + c}[/tex]

so it follows that

[tex]\log_ax + log_ay = log_a(xy)[/tex]

from:

[tex]\frac{a^b}{a^c} = a^{b - c}[/tex]

follows that

[tex]\log_ax - log_ay = log_a(\frac{x}{y})[/tex]

so

[tex]\log_7x + \log_7y - \log_7z = \log_7(xy) - \log_7z = \log_7(\frac{xy}{z})[/tex]

The table in question shows a proportional relationship between x and y, this shows that there is an independent and a dependent variable and their value compliments each other

This is further explained below.

Generally, The table in question demonstrates that there is a proportionate connection between x and y.

This indicates that there is both an independent and a dependent variable and that the values of both variables complement one another.

In conclusion, Relationships between two variables that are proportional occur when their ratios are equal.

Another way to consider them is that in a proportionate connection, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.

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Answer:

8q + 32 that is the answer to the problem using the distributive property

The frequency of the red light is 4.6 × 10⁵ Hz

From the question, we are to determine the frequency of the red light with the given wavelength

From the given information,

Wavelength = 650 nm

c = 3.0 × 10⁸ m/s

From the formula,

c = fλ

∴ f = c/λ

Where c is the speed of light

f is the frequency

λ is the wavelength

Thus,

f = 3.0 × 10⁸/650

f = 4.6 × 10⁵ Hz

Hence, the frequency of the red light is 4.6 × 10⁵ Hz

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1. The slope-intercept equation of the line is: y = x - 3.

2. The equation of the line in standard form is: -1/5x + y = 5

3. The equation in point-slope form is: y + 7 = 14(x + 2)

4. The value of x ≈ 5.94

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

There are three ways too write the equation of a line, they include:

1. find the slope (m) of the line that passes through (8, 5) and (7, 4):

Slope (m) = (5 - 4)/(8 - 7)

Slope (m) = 1/1

Slope (m) = 1

Substitute m = 1 and (a, b) = (8, 5) into y - b = m(x - a):

y - 5 = 1(x - 8)

y - 5 = x - 8

y = x - 8 + 5

y = x - 3

The slope-intercept equation is: y = x - 3.

2. The slope of perpendicular lines are negative reciprocals, therefore, the slope of the line perpendicular to the line that has a slope of -5 would be, m = 1/5.

Substitute m = 1/5 and (a, b) = (-15, 2) into y - b = m(x - a):

y - 2 = 1/5(x - (-15))

y - 2 = 1/5(x + 15)

y - 2 = 1/5x + 3

y = 1/5x + 3 + 2

y = 1/5x + 5

-1/5x + y = 5 [standard form]

3. Parallel lines have the same slope. The slope of y = 14x - 3 is 14. The line that is parallel to y = 14x -3 would also be, m = 14.

Substitute m = 14 and (a, b) = (-2, -7) into y - b = m(x - a):

y - (-7) = 14(x - (-2))

y + 7 = 14(x + 2) [point-slope equation]

4. y = kx

1.4 = k3.2

1.4/3.2 = k

The equation would be: y = 1.4/3.2x

Substitute y = 2.6 to find x:

2.6 = 1.4/3.2x

(2.6)(3.2) = 1.4x

8.32 = 1.4x

8.32/1.4 = x

5.94 ≈ x

x ≈ 5.94

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Answer:

64

Step-by-step explanation:

first compute the bracket 2 cubed which is 8

then square the contents of the bracket which results in 64

Answer:

x < - 5

Step-by-step explanation:

4x + 1 < 3x - 4 ( subtract 3x from both sides )

x + 1 < - 4 ( subtract 1 from both sides )

x < - 5

the graph is the number line with an open circle at - 5 and arrow pointing to the left.

Answer: x<-5

Step-by-step explanation: i did it on OW

Answer:

1/2

Step-by-step explanation:

1. LCD = 10

2. [tex]-\frac{1}{5} * \frac{2}{2} + \frac{7}{10}[/tex]

3.[tex]-\frac{2}{10} + \frac{7}{10}[/tex]

4. [tex]-\frac{2+7}{10}[/tex]

5. 5/10

6. Simplify : 1/2

Hope this helps!
--Blu

Answer:

65,209

Step-by-step explanation:

I got it write

Answer:

65209

the answer is 65209

Answer:

-a²,a, a²,2a²,a³,2ab

Step-by-step explanation:

-------

Using laws of indices, we can easily find the values of expressions below.

To solve this given problem, we have to apply different laws of indices.

12.

[tex](x^4 * x^-8)^3 = x^-^1^2=\frac{1}{x^1^2}[/tex]

13.

[tex](a^5b^2)^-^3* (a^-^2)^-^3 = \frac{1}{a^9b^6}[/tex]

14.

[tex]\frac{(m^-^3n^-^4)^8}{(m^2n^5)^-^7}=\frac{n^3}{m^1^0}[/tex]

15.

[tex]\frac{(p^-^2^0^0q^1^7^0)^-^3^0}{(p^4^0q^5^0)^9^0} =\frac{p^2^4^0^0}{q^9^6^0^0}[/tex]

16.

[tex]\frac{[(x^2y^8)^-^1]^3*(y^-^1^2)^6}{(x^-4y^5)^2*x^6(y^-^1)^3}=\frac{1}{x^4y^1^0^3}[/tex]

17.

[tex]\frac{(2m^-^7n^8)^6}{4m^9n^-^5)^-^3}*\frac{(8m^-5n)^6}{(2mn^3)^-5} = \frac{134217728n^7^4}{m^7^6}[/tex]

From the above calculation, we can solve the respective given expression using indices.

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The proportionality constant for the above equation y = 2.35x is 2.35.

An equation can be defined in several ways. Algebraically speaking, an equation is a statement that shows the equivalence of two mathematical expressions.

A linear equation could have more than one variable. If a variable's maximum power constantly equals one, an equation is considered to be linear.

Let us x ∝ y.

Following that, x = ky, where k is a constant or proportional.

When two variables that were in proportion are split, it will result in a constant proportional because k = x/y.

The constant of proportionality for the above equation y = 2.35x will be y/x = 2.35.

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Answer:

x = 120°

Step-by-step explanation:

Since s and t are parallel and are on a supplementary line, that means that the interior angle and the exterior angle (60°) will equal 180° (supplementary)

So to find the angle of x, you have to minus 60 from 180, and you get x, which is 120°

I hope this helps! :)

Answer:

A city hospital tracked how many patients visited its ER over 9 days.

Using the data below, write out the five number summary and make a box and whisker plot.

4, 16, 24, 21, 7, 22, 8, 9, 14

Minimum: ________4______ Maximum: ______24________

Q1 is 8.5

: _______14___ Q2

: ______23____ Q3

: __________

Step-by-step explanation:

The area of the rectangle with a base of 5ft and a height of 2 inches is: 120 square inches.

The area of a rectangle is the product of the length of its base and its height.

Area of rectangle = (base)(height)

Given the parameters:

Length of the base of the rectangle = 5 ft

[Note: 1 ft = 12 inches]

Convert 5 feet to inches

5 feet = (5)(12) = 60 inches

Height of the rectangle = 2 inches

Substitute

Area of the rectangle = (60)(2)

Area of the rectangle = 120 square inches

In conclusion, the area of the rectangle with a base of 5ft and a height of 2 inches is: 120 square inches.

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Answer:

4|−12| = 48 dollars.

Step-by-step explanation:

The question asks for the total decrease after 4 weeks. Since there is no such thing as negative weeks, A and C are disqualified. Since D is simply wrong math (-4x12=-48), it is also wrong.