Which of the following shows the extraneous solution to the logarithmic equation x = -16
x = -4
x = 4
x = 16

Answers

Answer 1

Answer:

Answer:

The correct answer option is x = 4.

Step-by-step explanation:

We are given the following logarithmic equation and we are to determine whether which of the given options shows its extraneous solution:

$log _ 7 ( 3 x ^ 3 + x ) - log _ 7 ( x ) = 2$

We can rewrite it as:

$log7[(3x^3+x)/(x) ]=2$

But we know that $log_7(49)=2$

So, $log7[(3x^3+x)/(x) ]=log_7(49)$

Cancelling the log to get:

$(3x^3+x)/(x) =49$

Further simplifying it to get:

$3x^2+1=49$

$3x^2=48$

$x^2=(48)/(3)$

$x^2=16$

x = 4

Answer 2

Answer:

Answer:

The extraneous solution to the logarithmic equation is $x=-4$

Step-by-step explanation:

We have the equation:

$Log_(7) (3x^3+x)-Log_7(x)=2$

By properties of logarithms:

$LogA-LogB=Log((A)/(B))$

So, with the equation we have:

$Log_(7) ((3x^3+x))/(x)=2$

$Log_(7)( (3x^3+x)/(x))=2\nLog_(7)( (3x^3)/(x)+(x)/(x))=2\nLog_(7)( (3x^3)/(x)+1)=2\nLog_(7)(3x^2+1)=2$

This logarithm base is 7 and this equation is equal to 2, the number 7 passes as the base on the other side of the equation and the two as an exponent, after that we just to find x:

$7^2=(3x^2+1)\n49=3x^2+1\n49-1=3x^2\n(48)/(3) =x^2\n16=x^2$

Now, we can find x with square root

$16=x^2\n√(16) =√(x^2) \nx_1=4\nx_2=-4$

This equation has two answers because it is a quadratic equation, so with this logic the strange solution is -4

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Luis is doing his math homework. He has 30 problems in all. After an hour, he only has 1/6 of those problems left. How many problems does he have left?

Answers

Answer:

$\huge\boxed{5}$

Step-by-step explanation:

Luis has 30 problems and after one hour, $(1)/(6)$ of those problems are left. This means that the total number of problems left will be $30 \cdot (1)/(6)$ .

Multiplying by a fraction is the same as dividing by a whole. The denominator of $(1)/(6)$ is 6, so we can divide 30 by 6.

$30 / 6 = 5$

Hope this helped!

Answer: 25

Step-by-step explanation: 1/6 of 30 is 5, so 30 minus 5 equals 25.

What is the width of a triangle that has a 15 cm height and hypotenuse of 19 cm

Answers

Answer:

Pythagorean Theorem

Question Answer

Find the width of a triangle that has a 15cm height and a hypotenuse of 19cm. 11.7cm

A helicopter rises straight up 300m then flies west 400m. How far is it from the beginning (if it travels in a straight line back)?

find the least number of sweets that can be packed into polythene bags which contain either 9or 15 or 20 or 24 sweets with none left over

Answers

Answer:

i think 15

Step-by-step explanation:

Find the perimeter of a rectangle whose length is 150 m and the diagonal is 170 m

Answers

Answer:

460 m

Step-by-step explanation:

Use right triangle PSR with right angle S to find the length of PS.

The Pythagorean theorem can be used for this.

a^2 + b^2 = c^2

(PS)^2 + (SR)^2 = (PR)^2

(PS)^2 + (150 m)^2 = (170 m)^2

(PS)^2 = 22500 m^2 = 28900 m^2

(PS)^2 = 6400 m^2

PS = 80 m

PS = 80 m; SR = 150 m

perimeter = 2(length + width)

perimeter = 2(150 m + 80 m)

perimeter = 2(230 m)

perimeter = 460 m

-68 divided (-4)

Help ASAP

Answers

Answer:

Today: Wednesday, 14 October 2020

Hour: 12.58 WIB

______________________________

-68 divinded (-4) is 17

Answer:

Two negatives = positive (17)

Step-by-step explanation:

B. The difference between the cash price and the initial deposit in hire purchase is known as ?

Answers

The difference between the cash price and the initial deposit in hire purchase is known as $_$ \text{Principal} $_$ .

In hire purchase transactions, buyers can acquire goods by making an initial down payment and paying the remaining amount in installments. The difference between the total cost of the item and the initial deposit is a crucial concept known as the $_$ \text{Principal} $_$ in mathematical terms. Let's explore this in detail.

In the context of hire purchase, the total cost of the item is often referred to as the cash price. It represents the actual value of the item without considering any interest or finance charges. On the other hand, the initial deposit, also called the down payment, is the amount paid upfront by the buyer to secure the item.

Now, let's introduce some variables to help us understand this concept mathematically:

- Let CP be the cash price of the item.

- Let D be the initial deposit made by the buyer.

The difference between the cash price and the initial deposit is given by:

$\text{Principal} = CP - D$

The Principal is the amount that remains to be paid off in installments, and it serves as the basis for calculating the subsequent monthly or periodic payments in a hire purchase agreement.

The Principal is critical because it determines the total amount the buyer will end up paying for the item. It also affects the duration of the hire purchase agreement, as the buyer's installments are typically spread over a specific number of months or years.

To know more about Hire purchase here

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