K is the midpoint of JL. If: JK = 5x + 1 and KL = 7x - 3. Find JL

The first step to solve this problem is to completely factor the expressions first.

Final Answer:

The quotient in its simplest form is [tex]\(z^2 + 2z - 8\)[/tex].
The restrictions on the variable are [tex]\(z \neq -4\)[/tex] and [tex]\(z \neq 3\)[/tex].

Explanation:

To find the quotient in simplest form when dividing two rational expressions, you need to multiply the first expression by the reciprocal of the second. The given expressions are:

Expression 1: [tex]\(\frac{z^2 - 4}{z - 3}\)[/tex]

Expression 2: [tex]\(\frac{z + 2}{z^2 + z - 12}\)[/tex]
Firstly, let's take the reciprocal of Expression 2, which is:
Reciprocal of Expression 2: [tex]\(\frac{z^2 + z - 12}{z + 2}\)[/tex]

Now, to find the quotient, multiply Expression 1 by the reciprocal of Expression 2:
Quotient: [tex]\(\frac{z^2 - 4}{z - 3} \cdot \frac{z^2 + z - 12}{z + 2}\)[/tex]
Before multiplying, it's helpful to factor where possible to simplify. Let's factor both the numerator and the denominator where applicable:
For the expression [tex]\(z^2 - 4\)[/tex] (the difference of squares), it factors into:
[tex]\(z^2 - 4 = (z - 2)(z + 2)\)[/tex]
For the quadratic expression [tex]\(z^2 + z - 12\)[/tex], we look for two numbers that multiply to -12 and add to +1. These numbers are +4 and -3.

So this expression factors into:
[tex]\(z^2 + z - 12 = (z - 3)(z + 4)\)[/tex]
Now substitute in these factorizations:
[tex]\(\frac{(z - 2)(z + 2)}{z - 3} \cdot \frac{(z - 3)(z + 4)}{z + 2}\)[/tex]
Next, we cancel out the common terms in the numerator and the denominator:
The z + 2 term in the numerator of the first fraction cancels with the z + 2 term in the denominator of the second fraction.
Similarly, the z - 3 term in the denominator of the first fraction cancels with the z - 3 term in the numerator of the second fraction.
What remains is:
Quotient: (z - 2)(z + 4)
Finally, you can expand this to get the simplest form of the quotient:
[tex]\(z^2 + 4z - 2z - 8\)[/tex]
Combine like terms:
[tex]\(z^2 + 2z - 8\)[/tex]
So the simplest form of the quotient is:
[tex]\(\frac{z^2 + 2z - 8}{1}\)[/tex]
or simply:
[tex]\(z^2 + 2z - 8\)[/tex]
Now let's consider the restrictions on the variable z. Before we canceled terms, the original expression had denominators of z - 3 and [tex]\(z^2 + z - 12\)[/tex]. Division by zero is undefined, which means we have restrictions where these denominators equal zero:

For z - 3 = 0, the restriction is [tex]\(z \neq 3\)[/tex].

For [tex]\(z^2 + z - 12 = 0\)[/tex], we had already factored this into (z - 3)(z + 4). From the factored form, we can find the restrictions by setting each factor equal to zero:
z - 3 = 0 gives z = 3 (which we already noted) and z + 4 = 0 gives z = -4.
Therefore, the restrictions on the variable z are [tex]\(z \neq -4\)[/tex] and [tex]\(z \neq 3\)[/tex].

To summarize:
The quotient in its simplest form is [tex]\(z^2 + 2z - 8\)[/tex].
The restrictions on the variable are [tex]\(z \neq -4\)[/tex] and [tex]\(z \neq 3\)[/tex].

The lawn mower can run for approximately 8 hours and 34 minutes on a full tank of gas.

To find out how long the lawn mower can run on a full tank, we can divide the total amount of gas in the tank by the amount of gas used per hour. The lawn mower uses 0.7 gallons of gas every 3 hours. So, it uses 0.7/3 = 0.2333 gallons of gas per hour. The gas tank holds 2 gallons, so the lawn mower can run for 2/0.2333 = 8.57 hours, which is approximately 8 hours and 34 minutes.

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ANSWER

[tex]3 {x}^{2} y \sqrt[4]{y} [/tex]

EXPLANATION

We want to simplify:

[tex] \sqrt[4]{81 {x}^{8} {y}^{5} } [/tex]

We can split the radical sign to obtain:

[tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{5} } [/tex]

Or

[tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4} \times y} [/tex]

[tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y} [/tex]

[tex]\sqrt[4]{ {3}^{4} } \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y} [/tex]

Recall that:

[tex] \sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} } [/tex]

[tex]{3}^{4 \times \frac{1}{4} } \times {x}^{8 \times \frac{1}{4} } \times {y}^{4 \times \frac{1}{4} }\times \sqrt[4]{y} [/tex]

[tex]3 {x}^{2} y \sqrt[4]{y} [/tex]

Answer:

B!!!!!!!!!

Step-by-step explanation:

Answer:

Her total premium would be $1,209.00

Other answer is incorrect.

The formula in computing the maturity value of a savings with a simple interest rate is:

MV = P (1 + rt)

Where: MV = maturity value after certain years

                P = principal amount

                r = interest rate

                t = time in years

If you would manipulate the formula to solve for r in terms of the other variables, you will get this formula:

1 + rt = MV/P

rt = MV/P – 1

r = (MV/P – 1)/t

Substituting the given amounts to the formula:

r = ($896/$800 – 1)/4

r = (1.12 – 1)/4

r = 0.12/4

r = .03 or 3%

Note: The 48 months is equivalent to 4 years (48/12 = 4)

For this case we have the following angle in radians:

[tex] theta = \frac{23\pi}{20} [/tex]

The first thing you should know to answer the question is the following conversion:

π radians = 180 degrees

Applying the conversion to the given angle we have:

[tex] theta = \frac{23\pi}{20}*\frac{180}{\pi} [/tex]

Rewriting we have:

[tex] theta = 207 [/tex]

Answer:

the angle measured in degrees, it is given by:

[tex] theta = 207 [/tex]

Answer:

4.5

Step-by-step explanation:

In similar polygons, the ratios of corresponding sides is equal.

The only two corresponding sides we have measurements for are BC, with a measure of 8, and FG, with a measure of 6.  This makes their ratio 8/6.

The other half of the proportion will be comparing AB, with a measure of 6, to EF, with a measure of y:

8/6= 6/y

Cross multiply:

8(y) = 6(6)

8y = 36

Divide both sides by 8:

8y/8 = 36/8

y = 4.5

The value of y will be 4.5.

What is an expression?

Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

The polygons are similar.

Now,

Since, The polygons are similar.

Hence, The proportional of corresponding sides are equal.

So, We can formulate;

⇒ 6 / y = 8 / 6

⇒ 6×6 / 8 = y

⇒ y = 36 / 8

⇒ y = 4.5

Thus, The value of y will be 4.5.

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the slope of the line is letter B) 1/4....

The slope of the line that contains the points (-1,2) and (3,3) is calculated using a specific formula. After performing the calculation, the result is 1/4.

The slope of a line is calculated using a specific formula based on line's points: (y2 - y1) / (x2 - x1), where (x1,y1) and (x2,y2) are the coordinates of two distinct points on the line. In this case, the points given are (-1,2) and (3,3).

Let's substitute into the formula:

(3 - 2) / (3 - (-1)) = 1 / 4.

Therefore, the slope of the line that contains the points (-1,2) and (3,3) is 1/4, which corresponds to answer choice B.

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The specific name for a regular quadrilateral is a polygon

The dimensions of 5 inches for a side and diagonals of 6 inches and 7 inches for a parallelogram violate the Pythagorean theorem and therefore are not possible for any right-angled triangle, suggesting an error if considered for a parallelogram.

The question is whether parallelogram sides can correspond to the dimensions given, with one side being 5 inches and the possible diagonals being 6 inches and 7 inches respectively. By applying the Pythagorean theorem, we can deduce that a parallelogram with such dimensions may not be possible due to the constraints of the theorem.

Given the Pythagorean theorem, expressed as a² + b² = c², the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. If we consider the diagonals and the side as parts of a right triangle, then 6² + 5² does not equal 7² (36 + 25 = 61, which is not equal to 49).

Therefore, it is not possible for a parallelogram to have side lengths and diagonal lengths as described in the question because the mathematically described conditions violate the rules of the Pythagorean theorem.

The standard form of the given equation is x - 3y = 6.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given is an equation, y = 1/3 x - 2

The given equation is in slope intercept form, i.e. y = mx+ c, where m is slope and c is constant,

Here, slope (m) = 1/3 and constant (c) = -2

Converting the equation in standard form,

y = 1/3 x - 2

3y = x - 6

x - 3y = 6

Hence, the standard form of the equation is x - 3y = 6

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