MATH HELP!!! 100PTS!!!

Suppose that u=log10(3) and v=log10(5). Find possible formulas for the following expressions in terms of u and/or v. Your answers should NOT involve any log 's.

a) log10(0.6)=
u-v


b) log10(0.25)=



c) log10(27000)=
3+3u


d) log10(sqrt10)=

Answer:

         (8b − 1)b = 8b*b - 1*b

                        = 8b2 - b

Step-by-step explanation:

Hence the expression (8b − 1)b=8b2 - b.

This shows that if s is doubled and h tripled, then V multiplied by 12

Given the formula below expressed as:

V = s²h

If s is doubled and h tripled, the new volume will ne:

V1 = (2s)² * 3h

V2 = 4s² * 3h

V2 = 12s²h

V2 = 12V

This shows that if s is doubled and h tripled, then V multiplied by 12

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Nicolai would get worth of 13958.62 in five years for an 8% rate of return.

The net gain or loss of an investment over a given period stated as a percentage of the investment's starting cost is known as a rate of return (RoR).

Any type of investment instrument, including real estate, bonds, equities, and fine art, can be subject to a rate of return.

You determine the percentage change from the start of the period to the end when computing the rate of return.

Initial amount=9500

Rate of return=8%

Amount after 5 years=[tex]9500*(1+\frac{8}{100}) ^{5}[/tex]

                                    [tex]=9500*(\frac{108}{100} )^{5}[/tex]

                                   [tex]\\=13958.62[/tex]

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The inverse of the given function is y = (12-x)/6

Given the following function expressed as:

f(x) = -6x +1/2

Replace y with x

x = -6y + 1/2

Make y the subject of the formula

6y = -x + 12

y = (12-x)/6

Hence the inverse of the given function is y = (12-x)/6

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The decay factor of the equation given in the task content is; 0.87.

According to the task content; the equation given is; y = 453(0.87)^4.

By comparison with exponential decay functions, it follows that the decay factor from the equation given is; 0.87 which insinuates that the factor of change after each decay is 0.87.

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Step-by-step explanation:

the area of a parallelogram is

baseline × height

which is in our case

9 × 7 = 63 m²

Answer:

ayo give the other guy brainilest

Step-by-step explanation:

Answer: 60°

Step-by-step explanation:

- the two angles created by CD and EF are vertical angles so they are equal

- one angle is 30° so the other one is 30° and it splits an existing 90° angle so 90-30 = 60 so x is 60°

hope this helps :)

Answer:

∠x=60°

Step-by-step explanation:

Add 90° and 30° then subtract by 180 to find ∠x.

How I got 30 degrees is because of the vertical angle. Vertical angles are always equal.

I got the 90 degrees from the left top side.

180 degrees is the degrees of a straight angle.

90+30=120

180-120=60

Hope this helps!

If not, I am sorry.

By summing the areas of minor rectangles and triangles, the area of the irregular polygon whose vertices are (- 3, 4), (2, 4), (4, 2), (2, - 3) and (- 3, - 3) is equal to 42 square units.

In this problem we have to determine the area of a irregular polygon, whose calculation is defined as a sum of the areas of triangles and rectangles. To determine the combination of squares and triangles, we need first to plot the vertices and construct the figure on a Cartesian plane.

The area of the irregular figure is:

A = (5) · (7) + 0.5 · 2² + 0.5 · (2) · (5)

A = 35 + 2 + 5

A = 42

By summing the areas of minor rectangles and triangles, the area of the irregular polygon whose vertices are (- 3, 4), (2, 4), (4, 2), (2, - 3) and (- 3, - 3) is equal to 42 square units.

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Answer:

Answer:

yes , y = - 3.3x

Step-by-step explanation:

if y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation , then

k = [tex]\frac{y}{x}[/tex]

checking k for each ordered pair in the table

[tex]\frac{-6.6}{2}[/tex] = - 3.3

[tex]\frac{-9.9}{3}[/tex] = - 3.3

[tex]\frac{-13.2}{4}[/tex] = - 3.3

[tex]\frac{-16.5}{5}[/tex] = - 3.3

thus k = - 3.3

so y varies directly with x and the equation of direct variation is

y = - 3.3x

Based on the number of coins in the jar, the probability that Nina would not pick a penny or dime is a. 0.36.

The cost of the entire trip to the Cross family should they use the two cars is c. $107.07.

This can be found as:

= Number of quarters, and nickels) / (Number of quarters, nickels, dimes, and pennies)

= (13 + 18) / (13 + 25 + 18 + 30)

= 0.36

= Cost of gas to first car + Cost of gas to second car

= (450/18 x 2.49) + (450 / 25 x 2.49)

= 62.25 + 44.82

= $107.07

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Answer:

See proof below

Step-by-step explanation:

Given [tex]\triangle ADE \cong \triangle CBD[/tex]

Then, [tex]\angle AED \cong \angle CFB[/tex] because corresponding parts of congruent triangles are congruent.

Since [tex]\angle AED \text{ and } \angle DEB \text{ form a linear pair}[/tex], by the linear pair postulate, [tex]\angle AED \text{ and } \angle DEB \text{ are supplementary}[/tex].

Similarly, [tex]\angle CFB \text{ and } \angle BFD \text{ form a linear pair}[/tex], so by the linear pair postulate,  [tex]\angle CFB \text{ and } \angle BFD \text{ are supplementary}[/tex].

By the Congruent supplements theorem, since [tex]\angle AED \text{ and } \angle DEB \text{ are supplementary}[/tex], [tex]\angle CFB \text{ and } \angle BFD \text{ are supplementary}[/tex], and [tex]\angle AED \cong \angle CFB[/tex] , then [tex]\angle DEB \cong \angle BFD[/tex]. (note, this is one pair of opposite angles inside quadrilateral DFBE)

Recalling that [tex]\overline {ED} \text{ bisects } \angle ADC, \text{ and } \overline {FB} \text{ bisects } \angle ABC[/tex], then, [tex]\angle ADE \cong \angle CDE[/tex], and [tex]\angle CBF \cong \angle FBA[/tex] by definition of angle bisector.

Note that [tex]\angle ADE \cong \angle CBF[/tex] because corresponding parts of congruent triangles are congruent.

Also, note that [tex]\angle EDF \cong \angle EDC[/tex] and [tex]\angle FBA \cong \angle FBE[/tex] because B, E, A are colinear, and D, F, C are colinear.

So, by the transitive property of angle congruence, [tex]\angle EDF \cong \angle FBE[/tex]  (This is the other pair of opposite angles inside quadrilateral DFBE)

So, since both pairs of opposite angles are congruent, quadrilateral DFBE is a parallelogram, by a theorem about quadrilateral properties (your book may or may not have a name for it.  It may just have a number).

The number of cube that can be packed in the rectangular prism is 30 cubes

Volume of the rectangular prism in terms of small cube and unit cube = 30(1 / 8) ft³

volume of rectangular prism = lwh

where

Therefore,

volume of rectangular prism = 3 / 2 × 1 × 5 / 2  = 15 / 4 ft³

volume of cube = 1 / 2 × 1 / 2 × 1 / 2  = 1 / 8 ft³

number of cube that can be packed in the rectangular prism = 15 / 4 × 8 =  30 cubes

Volume of the rectangular prism in terms of small cube and unit cube = 30(1 / 8) ft³

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The First graph does not have an initial Value

The second graph's solution is (3, -4)

A quadratic graph is a pictorial representation of quadratic functions.

It shows the relationship between a variable on the x-axis and a variable on the y-axis.

Analysis:

The First graph did not either start from the x or y-axis so it does not have an initial value.

The second graph each mark is 0.5 on both axes so the point of intersection of the two graphs is the solution of the graphs which the x- value is 3 and the y-value is -4.

Therefore (3, -4) is the solution of the graph.

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See below for the description of changes when the dependent and the independent variables are switched

The table of values

When the dependent and the independent variables are switched, the values also become switched on the table.

This means that the table becomes an inverse table of the function

The scatter plot

Switching the variables implies that the original function is being reflected across the line y = x

The description in words

This description is an inverse relation of the original function

The equation

This description is an inverse equation of the original function.

If the initial equation is y = ax + c, the new equation becomes x = ay + c

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Answer:

C

Step-by-step explanation:

let f(x)=y and g(x)=x

so y=x²

if y-2=(x-2)

y=x

Answer:

24 km/h and 17 km/h

Step-by-step explanation:

We know that when two cyclists are traveling together, they will meet in the same time as if one cyclist with the combined speed of the two cyclists travelled the whole length. We don't know the speeds of the cyclists, so let's assign the one with the slower speed "x", and the one with the faster speed "x+7" the combined speeds is "2x+7"

Since the speed = distance / time, we can plug in the values

2x+7=205/5
2x+7=41
2x=34
x=17
We substitute x into the equation for the speed of the cyclists

Cyclist 1's speed: x, so their speed is 17 km/h
Cyclist 2's speed: x+7, so their speed is 17 + 7, or 24 km/h

Answer:

Step-by-step explanation:

Note : I am assuming that the question is asking for all no. of total pens.

If 5 red pens were 25% of the total quantity, we can say that 1/4th of the pens were red.

If 5 pens = 1/4, we multiply 5 * 4 to find the total quantity. 5*4 = 20

So, Ms. Sullivan bought 20 pens.

Hope this helps!

Answer:

The area of the shape is 68 cm².

Step-by-step explanation:

We have to calculate the areas of the rectangle and triangle separately, and then add them together.

• Area of rectangle = length × breadth

                                = 30 cm × 2 cm

                                = 60 cm²

• Area of triangle = [tex]\frac{1}{2}[/tex] × base × perpendicular height

                             = [tex]\frac{1}{2}[/tex] × 2 cm × 8 cm

                             = 8 cm²

Adding the areas together = 60 cm² + 8 cm²

                                             = 68 cm²

There is a significant value in the difference in the value of the car after nine years

The table of values is given as:

Years     1     2     3

Car 1 17,390 16,346.60 15,365.80

Car 2 17,500 16,500 15,500

The values of car 1 have a common ratio of 0.94; this is calculated by dividing the terms of the function

The common ratio implies that the function of car 1 is a geometric function.

The values of car 2 have a common difference of -1000.

The common difference implies that the function of car 2 is a linear function.

Car 1

In (a), we have:

Common ratio, r = 0.94

The initial value is given as:

a = 18,500

So, the function of car 1 is

f(x) = 18500 * 0.94^x

Car 2

In (a), we have:

Common difference, d = -1000

The initial value is given as:

a = 18,500

So, the function of car 2 is

f(x) = 18500 - 1000x

This means that

x = 9

So, we have:

Car 1

f(9) = 18500 * 0.94^9

f(9) = 10600

Car 2

f(9) = 18500 - 1000 *9

f(9) = 9500

10600 is greater than 9500

Hence, there is a significant value in the difference in the value of the car after nine years

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Answer:

C

Step-by-step explanation:

Given y = amount of money spend for the long distance plan per month

and x = minutes used each month

Note these 2 plans are in per month basis.

Plan A: Flat $5 + $0.99 Per min used (variable cost)

transform into an equation:

y = 0.99x + 5

Plan B: Flat $10 + $0.79 per min used (variable cost)

transform into equation:

y = 0.79x + 10

Put these 2 equations together, will give you the answer as C.

The value of A and B are -10x and -4 respectively.

Division involves gathering a number of expressions into smaller forms.

The quotient is represented by the expression

Quotient= Dividend /Divisor

We have the value of the Dividend from the division table given in the question

Dividend of the Operation= A

Divisor of the Operation=2

Quotient of the Operation= -5x

As we know Quotient= Dividend /Divisor

So, -5x= A/2

multiplying 2 on both sides

⇒(-5x)2= A/2*2

⇒ A= -10x

Similarly, We have the value of the Dividend from the division table given in the question

Dividend of the Operation= B

Divisor of the Operation=2

Quotient of the Operation = -2

As we know Quotient= Dividend /Divisor

So, -2= B/2

multiplying 2 on both sides

⇒(-2)2= AB2*2

⇒ B= -4

Therefore the value of A and B are -10x and -4 respectively.

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Answer:

D: 4(2a+3)=8a+3

Step-by-step explanation:

4x2a = 8a and 4x3 = 12

Answer:

just saying this so other can get brainliest

Step-by-step explanation:

d

LM=XY, then LM-GH= XY - GH and this illustrates the subtraction property of equality.

It should be noted that the subtraction property of equality simply implies that when the same number is subtracted form both sides, then the two sides will still remain equal.

In this case, when LM=XY, then LM-GH= XY - GH. This illustrates the subtraction property.

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A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. An isosceles triangle is one with two equal-length sides.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.

In ΔBAD and ΔBDC,

m∠ADB = m∠CDB {Given}

BD = BD {Common side in two triangles}

AD ≅ DC {Given}

Using the ASA postulate the two triangles are congruent. Therefore,

m∠BAD= m∠BCD.........equation 1

m∠ABD= m∠CBD

In ΔADC, AD ≅ DC {Given}, therefore, the triangle is an isosceles triangle. Thus,

m∠DAE = m∠DCE.......equation 2

Adding two of the equation 1 and 2,

m∠BAD + m∠DAE = m∠DCE + m∠BCD

∠BAC = ∠BCA

Since in ΔABC, ∠BAC = ∠BCA therefore, the triangle is an isosceles triangle, thus, AB = BC,

BE is the common side between ΔAEB and ΔCEB

Also, m∠ABD= m∠CBD

Therefore, ΔAEB ≅ ΔCEB

Now as ΔAEB ≅ ΔCEB, therefore, AE=EC,

Thus, BE is the median of the isosceles triangle ABC, and for an isosceles triangle, the median opposite to the non-common sides is the perpendicular bisector to the opposite side.

Hence, BD⊥AC.

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Answer: 50,001²-49,999²=0,2.

Step-by-step explanation:

[tex]50,001^2-49,999^2=(50,001+49,999)*(50,001-49,999)=100*0,002=0,2.[/tex]

Answer:

[tex]f(x) = (x-12)(x-1)[/tex]

Step-by-step explanation:

So when you have a quadratic equation it can usually be expressed as: [tex]a(x-b)(x-c)[/tex] where b and x are the roots of the equation. Since it's just asking for a function whose zeroes are 12 and 1, I'm assuming it doesn't care about the stretch/compression (value of a determines that), so I'll just assume a=1. if 12 and 1 are zeroes, that means it makes one of the factors equal to 0 because is x-b = 0 then no matter the value of x-c the value of y is 0 because 0 * (x-c) will be 0. So the equation becomes [tex]f(x) = (x-12)(x-1)[/tex] plugging in 12 or 1 as x will make one of the factors 0 thus making f(x) equal to 0

The probability that a randomly selected cable repair visit will take at least 43 minutes will be 88%.

Given: The times required for a cable company to fix cable problems in its customers' homes are uniformly distributed between 40 minutes and 65 minutes.

It can be deduced that the probability that a randomly selected cable repair visit will take at least 43 minutes will be calculated thus:

= 1 - [(43 - 40)/(65 - 40)

= 1 - 0.12

= 0.88

Hence, The probability that a randomly selected cable repair visit will take at least 43 minutes will be 88%.

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Answer:

The initial value in the word problem is the output value when input value is set to zero.

Step-by-step explanation: