without using tables solve for x in: Log10(x²+4)=2+Log10x-Log10 20​

Answer:

[tex]g(x) = (x-4)^2\; and \;h(x)= x^2-4 \;are\;\bold{not}\;equivalent[/tex]

Step-by-step explanation:

For two functions g(x) and h(x)  to be equivalent, they must have the same domain and range.

Domain is the set of all values of x(inputs)  that result in a real and defined value for the function

Range is the set of all values of the function that it can take given the values of x in the domain

[tex]g(x)=(x-4)^2=16-8x+x^2\\[/tex]

Can be rewritten as
[tex]g(x) = x^2 -8x + 16[/tex]  The domain of g is unrestricted, g can be any value so the

Domain of g: [tex]-\infty < x < \infty[/tex]
Range of g: Since [tex](x-4)^2[/tex] is always positive including 0, the range of g(x) is g(x) ≥ 0

[tex]h(x) = x^2 - 4[/tex]

Domain of h : [tex]-\infty < x < \infty[/tex] since x can be any value and we will still get a real number as function output

However x² is always zero or a positive number so we have the restriction
x² ≥ 0

Subtract 4 on both sides

x²-4 >= -4

But the above is nothing but the outputs of h(x)

So h(x) >= -4 and can be written as -4 ≤ x ≤ ∞

So we can see that, while the domains of the two functions are the same, their ranges are different

Hence the two functions g(x) and h(x) are not equivalent

Tip
If you have difficulty determining domain and range, take a specific value of x for both functions and check if the function output values are the same. It may not always be easy choosing an appropriate x value depending on the function

For x = 0

g(0) = (0-4)² = (-4)² = 16

h(0) = 0^2 -4 = 0-4 = -4

So we get different output values for the same input value for both functions and therefore they are not equivalent

You can this latter explanation to the above explanation

Hope that helps and is understandable :)

The journal entry will be:

Date            General           Debit      Credit

                                                $             $

Dec 31        Equipment        10000  

                  Cash                                 10000

We know that:

1) The $10,000 will be posted to the debit side of the Equipment Account as the equipment is an asset and it is being bought in the company. So, purchasing an asset is being debited in the account.

2) The $10,000 will be posted to the credit side of the Cash Account as cash is also an asset which is being given. Since, the asset is going out from the company, it is being credited in the company's account.

The journal entry then will become as:

Date            General           Debit      Credit

                                                $             $

Dec 31        Equipment        10000  

                  Cash                                 10000

Therefore, the journal entry will be:

Date            General           Debit      Credit

                                                $             $

Dec 31        Equipment        10000  

                  Cash                                 10000

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Your question was incomplete. Please refer the content below:

On December 31, the company purchases equipment for $10,000 and pays cash of $10,000. Complete the necessary journal entry by selecting the account names from the pull-down menus and entering dollar amounts in the debit and credit columns.

The function of cost is C(x) = 3.50x + 2000 and revenue is R(x) = 6x and 800 t-shirts must be sold to break even.

The cost is differently of touching on the slope of the value perform. this suggests that

m = 3.50 and b = 2000 swing this into the value perform, we have

C(x) = 3.50x + 2000

Revenue function = selling price × number of shirt

        R(x) = 6x

The break-even purpose is found by setting the value perform C(x) adequate to the revenue perform R(x) .

 C(x) =  R(x)

3.50x + 2000 = 6x

      2000 = 2.5x

      800 = x

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Answer:

4915

Step-by-step explanation:

y= 983 so multiply 983 by 5

5x983 = 4915

Answer: 4915

Step-by-step explanation: Pls brainliest.

Answer: x = -20

▬▬▬▬▬▬▬

[tex]7-7(x)-7=147-7\\-7(x)=140\\= \frac{-7x}{-7}=\frac{140}{-7}\\=-20\\= x = -20[/tex]

▬▬▬▬▬▬▬

Answer Explained:

Using phrases such as subtracted, times, a number, we make an equation using the integers in the equation, and make a variable for the unknown number, x. We then subtracted 7 from both sides, and for the division, substituted 7 as absolute number, |-7|.

Therefore,

7 - 7 × -20 = 147

Answer:

x = 22.5

∠ADE = 67.5

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180° and the given is a right triangle so we can find the value of x easily:

90 + x + 3x = 180 add like terms

90 + 4x = 180 subtract 90 from both sides

4x = 90 divide both sides by 4

x = 22.5

To find the measure of angle ADE we use the same equation:

90 + 22.5 + ∠ADE = 180 add like terms

112.5 + ∠ADE = 180 subtract 112.5 from both sides

∠ADE = 67.5

Answer:

y = 5x -4x

y = x

The method that will not give the correct number of inches is that the total length of the plant in a week is 19/4 inches.

Length of the small plant = 2 1/2 = 5/2 inches

Rate of growth = 3/4 inches

Increase in length in 3 weeks will be:

= 3 × 3/4 = 4

Total length = 5/2 + 9/4

= 19/4 inches.

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Answer:

Step-by-step explanation:

1.

Only the graph on the left is a function, due to the one on the right failing the vertical line test.

2.

This is asking for a positive x-value of the two functions, we can find that by setting them equal to a common value and then equal to each other.

Lets set them both equal to x.

First equation:

[tex]y=x^2\\\sqrt{y}=x[/tex]

Second equation:

[tex]y^2=x[/tex]

Now we set them equal to each other:

[tex]y^2=\sqrt{y}[/tex]

Then solve for y by squaring both sides:

[tex]y^4=y[/tex]

Now we solve by factoring:

[tex]y^4=y\\y^4-y=0\\y(y^3-1)=0\\y^3-1=0\\y^3=1\\y=\sqrt[3]{1}\\ y=1[/tex]

Answer:

(A)  -24 × 1/4 ft

(B)  -6 ft

A negative times a positive is a negative

Step-by-step explanation:

 Sea level is 0, therefore the elevation of city (A) is -96 , and the elevation of city (C) is -24 . The elevation of city (D) is  1/4 of city (C).

Expression = - 24 × 1/4

Part (B)

-24 × 1/4 = -6

Explanation A negative times a positive gives a negative product.

The equation for L in terms of W is ( 1 + 2w) where length and width of the rectangle is 35 cm and 17 cm respectively

Perimeter of rectangle = 2(L + W)

104 = 2{(1 + 2w) + w}

104 = 2(1 + 2w + w)

104 = 2(1 + 3w)

104 = 2 + 6w

104 - 2 = 6w

102 = 6w

w = 102 / 6

w = 17 cm

Recall,

Length of the rectangle, l = 1 + 2w

= 1 + 2(17)

= 1 + 34

= 35 cm

Therefore, the equation for L in terms of W is ( 1 + 2w) where length and width of the rectangle is 35 cm and 17 cm respectively

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Answer: 6x-5

5 less is just subtract 5 from whatever follows

Answer:

1 = 34°

2 = 52°

3 = 38°

4 = 94°

5 = 56°

6 = 38°

The rectangular equivalence to the parametric equations is;

(x - 2)²/9 + (y + 1)²/4 = 1

We want to find the rectangular equivalence to the parametric equations;

x(θ) = 3cosθ + 2

y(θ) = 2sinθ − 1

where 0 ≤ θ < 2π .

Making the trigonometric ratio the subject gives us;

cosθ = (x - 2)/3

sinθ = (y + 1)/2

Now, from trigonometric identities, we know that;

cos²θ + sin²θ = 1

Thus;

((x - 2)/3)² + ((y + 1)/2)² = 1²

(x - 2)²/9 + (y + 1)²/4 = 1

Thus, the rectangular equivalence to the parametric equations is;

(x - 2)²/9 + (y + 1)²/4 = 1

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Answer:

y=1x-1

Step-by-step explanation:

Answer:4 X 8 =32

Step-by-step explanation:4 groups of 4 is 32

32 divied by 4 is 8 so 8 boxes

The equation has one solution.

A value of x that makes the equation true is -3, which when substituted into the equation will turn the equation into: 18 = 18.

A value of x that makes the equation false can be 4, which when substituted into the equation will turn the equation into: -24 = 18.

Given the equation, -6x = 18, the value of x that makes the solution true would be determined as shown below:

-6x/-6 = 18/-6

x = -3

Therefore, we can conclude the following:

A value of x that makes the equation true is -3, which when substituted into the equation will turn the equation into:

-6(-3) = 18

18 = 18.

A value of x that makes the equation false can be 4, which when substituted into the equation will turn the equation into:

-6(4) = 18

-24 = 18.

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Answer:

The equation has one solution.

A value of x that makes the equation true is -3, which when substituted into the equation and simplified makes the equation turn into 18=18.

A value of x that makes the equation false is 0, which when substituted into the equation and simplified makes the equation turn into 0=18.

Step-by-step explanation:

Hope this helped! :)

Answer:

Step-by-step explanation:

um first add 7+11 u get 18 and so yeah

the orders served by Laura are 22, the orders served by Aldo are 29 and the orders served by Juan are 44.

Total number of orders served on Monday at the school cafeteria = 95

Juan served 2 times as many orders as Laura and Aldo served 7 more orders than Laura.

Let the orders served by Laura be x

Orders served by Juan = 2 x

Orders served by Aldo = x + 7

So, we get the equation as:

x + 2 x + x + 7 = 95

4 x + 7 = 95

4 x = 95 - 7

4 x = 88

x = 88 / 4

x = 22

x + 7 = 22 + 7 = 29

2 x = 2 (22) = 44

Therefore, we get that, the orders served by Laura are 22, the orders served by Aldo are 29 and the orders served by Juan are 44.

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Answer:

3.  (d) y = 2x + 2

4.  (c) 10

5.  See attachment.

Step-by-step explanation:

Slope formula

[tex]\boxed{\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

where (x₁, y₁) and (x₂, y₂) are points on the line.

Slope-intercept form of a linear equation

[tex]\boxed{y=mx+b}[/tex]

where m is the slope and b is the y-intercept.

Given points on the line:

Substitute the given points into the slope formula to find the slope, m:

[tex]\implies \textsf{slope}\:(m)=\dfrac{-2-4}{-2-1}=\dfrac{-6}{-3}=2[/tex]

Substitute the found slope and one of the points into the slope-intercept equation and solve for b:

[tex]\implies 4=2(1)+b[/tex]

[tex]\implies b=2[/tex]

Therefore, the equation of the line is:

[tex]\boxed{y=2x+2}[/tex]

Given equation:

[tex]y=10x-6[/tex]

Upon comparing the given equation with the slope-intercept formula, the slope of the given line is:  [tex]\boxed{10}[/tex]

The equation y = 2 means that y is 2 for all values of x.

Therefore, to graph y = 2, draw a straight, horizontal line at y = 2.

(See attached graph).

From the graph of a function over the interval [-4,4]. the following are found for each function

The domain of a function refers to the input variables, often times the domain comprises of the x axis. for the given graph the domain is -4 ≤ x ≤ 4.

This would be through the points in the function. We are given  [-4,4]

-4 is the negative side while 4 is the positive. We have to write this out as

-4 ≤ x ≤ 4.

The positive part part of the function is at 4. This is because we can assume a +4 sign.

The negative part is the point -4.

Hence we can say that the domain is -4 ≤ x ≤ 4 with the positive and negative at 4 and -4 respectively

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Answer:

I can help you.

Step-by-step explanation:

so, you have to write in a)

2•5=10, 4÷2=2, 6+10=16, 16+2=18, 18-3=15. so answer is 15

And then, u have to write in b) 6+2=8, 8•5=40, 40+4=44, 44÷2=22, 22-3=19. so answer is 19.

Using an exponential function, it is found that 0.6% of the original carbon 14 in the charcoal was present.

The exponential function for the amount of the substance after t years is given by:

[tex]A(t) = A(0)e^{-kt}[/tex]

k is the exponential decay rate, given by:

k = ln(2)/5600 = 0.00012377628.

Hence:

[tex]A(t) = A(0)e^{-0.00012377628t}[/tex]

The amount after 41,000 years is given as follows:

[tex]A(41000) = A(0)e^{-0.00012377628 \times 41000}[/tex]

A(41000) = 0.006A(0).

Hence:

0.6% of the original carbon 14 in the charcoal was present.

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The required solution is 5,14,15,12,14,10,6,16 respectively.

It is required to find round to the nearest tenth.

A number that is easily multiplied, divided, etc., and especially a number that ends in zero.

Given:

The tenth number is the first digit after decimal point. If the second digit is greater than or equal to 5 add 1 to calculate rounding to nearest tenth.

Rounding to the nearest tenth means adjusting the given number to an approximate value without changing the whole part of the number.

5.0 the nearest tenth is 5.

14.0 the nearest tenth is 14.

15.0 the nearest tenth is 15.

12.0 the nearest tenth is 12.

14.0 the nearest tenth is 14.

10.0 the nearest tenth is 10.

6.0 the nearest tenth is  6.

16.0  the nearest tenth is  16.

Therefore, the required solution is 5,14,15,12,14,10,6,16 respectively.

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According to the chart, homes in the United States have fluctuated between $90,000 and $130,000 most of the time between 1890 and 2010 and then rise to more than $200,000.

The graph shows the changes in the value of homes in the United States from the year 1890 to the year 2010. An important aspect of this graph is the influence that international events such as the world wars, the great depression, the boom of the 70s and 80s and the great boom.

According to the graph, the price of houses varies as follows:

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Lindsay has the greater balance after one year and also had the greater balance in investment account after 12 years

What does monthly compounding mean?

The monthly compounding means that the interest is computed every month , 12 months a year rather than once a  year.

Monthly compounding?

FV=PV*(1+r)^N

FV=future worth

PV=initial investment=$80

r=monthly interest rate=1%/12=0.000833333333333333

N=number of months in one year=12

FV(1 year)=$80*(1+0.000833333333333333)^12

FV(1 year)=$80.80

FV(year 12)=$80*(1+0.000833333333333333)^(12*12)

FV(year 12)=$90.20

Weekly compounding:

weekly interest rate=2%/52=0.000384615384615385

FV(1 year)=$60*(1+0.000384615384615385)^52

FV(1 year)=$61.21

FV( year 12)=$60*(1+0.000384615384615385)^(52*12)

FV(year 12)=$76.27

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Concluding part of the question:

a. Whose balance is greater after one year?

b. Whose balance is greater after twelve years?

Answer:

d

Step-by-step explanation:

as x→-∞ , y→+∞

as x→∞ , y→-∞

The value of the expression when c = 5 and d = 42  is 12

The given parameters are:

c = 5 and d = 42

The expression is given as:

d - 6c

To evaluate the expression when c = 5 and d = 42, we substitute c = 5 and d = 42 in expression d - 6c

This is represented as

d - 6c = 42 - 6 * 5

Evaluate the product in the above expression

So, we have

d - 6c = 42 - 30

Evaluate the difference in the above expression

So, we have

d - 6c = 12

Hence, the value of the expression when c = 5 and d = 42  is 12

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The total cost of 3 one scoop sundaes and 2 two scoop sundaes by evaluating an expression  2.75(3)+ 4.25(2)  is 16.75.

An expression in two variables is a combination of  numbers and two variables using mathematical operation +,-,/,*. It will a linear expression when the maximum power of variables is only one in the expression.

Let x and y are two variables and a, b, c are some numbers. Then a linear two expression can be given by ax+ by+ c

Given the cost of one scoop sundae is 2.75 and a cost of a two scoop sundae is 4.25

Let the number of sundaes of one scoop sundae be x and the numbers of sundaes be y

Then the total cost of these sundaes is given as by expression 2.75x + 4.25y

Given that there are 3 one scoop sundaes and 2 two scoop sundaes

Thus, x= 3 and y = 2

Total cost  is given by expression= 2.75(3)+ 4.25(2)= 16.75

Therefore, he total cost of 3 one scoop sundaes and 2 two scoop sundaes    is 16.75

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