Find the second of 3 consecutive integers if the sum of the first and the third is 26

The locations of the given numbers on the number line are needed.

The locations have been shown in the figure attached.

The numbers are [tex]\dfrac{9}{2}[/tex] and [tex]-\dfrac{7}{2}[/tex]

The numbers can be written as

[tex]\dfrac{9}{2}=4.5[/tex]

[tex]-\dfrac{7}{2}=-3.5[/tex]

In the given number line it can be seen that the longer vertical lines are whole numbers which are positive and negative.

The smaller vertical lines are an increment of [tex]0.5[/tex].

As the extreme ends are [tex]+5[/tex] and [tex]-5[/tex] the center longer vertical line will be [tex]0[/tex].

So, [tex]4.5[/tex] will be the smaller vertical line to the left of [tex]+5[/tex].

[tex]-3.5[/tex] will be the smaller vertical line to the right of [tex]-4[/tex].

The locations have been shown in the figure attached.

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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 value of h in the triangle is 6 units.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. Similar triangles are the triangles that are the same in shape, but may not be equal in size.

For the given situation,

The triangles ΔNMP ~ ΔONP.

If two triangles are similar then the ratio of their sides are same.

⇒ [tex]\frac{NP}{MP} =\frac{OP}{NP}[/tex]

⇒ [tex]\frac{h}{12} =\frac{3}{h}[/tex]

⇒ [tex](h)(h)=(3)(12)[/tex]

⇒ [tex]h^{2} =36[/tex]

⇒ [tex]h=\sqrt{36}[/tex]

⇒ [tex]h=6[/tex]

Hence we can conclude that the value of h in the triangle is 6 units.

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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 specific name for a regular quadrilateral is a polygon

Final answer:

Jon can drive 198 kilometers with 22 liters of gas in his car since the car averages 9 kilometers per liter.

Explanation:

The student's question asks how many kiloliters Jon can drive with 22 liters of gas in his car, given that the car averages 9 kilometers per liter of gas. To solve this problem, we will convert liters to kiloliters and then calculate the total distance that Jon can drive.

Firstly, we must recognize that 1 kiloliter (kL) is equal to 1,000 liters (L). Therefore, to convert 22 liters to kiloliters, we simply divide 22 by 1,000, which gives us 0.022 kL.

Now, since Jon's car goes 9 kilometers per liter, to find out how far he can go with 22 liters, we multiply 9 kilometers/liter by 22 liters:

9 km/L × 22 L = 198 km

To express this distance in kiloliters, we once again need to note that 1 kL is the same as 1,000 L. Since the car's consumption is measured per liter, we don't actually need to convert kilometers to kiloliters - the initial conversion of liters to kiloliters was not required to answer this particular problem.

Therefore, Jon can drive a total of 198 kilometers with his 22 liters of gas.

Jon's car with fuel efficiency of 9 km/l can drive 198 kilometers with 22 liters of gas. The distance in volume terms is 0.022 kiloliters, illustrating that 22 liters of gasoline would be used on such a trip.

The student's question is how many kiloliters Jon can drive with 22 liters of gas if his car averages 9 kilometers per liter of gas. To answer this question, we need to perform a simple multiplication. Given that Jon's car has a fuel efficiency of 9 kilometers per liter, we multiply this rate by the amount of fuel he has, which is 22 liters, to determine the distance he can drive:

To convert kilometers to kiloliters (assuming the question intends to ask for the distance in kilometers rather than 'kiloliters'), we note that kiloliters is not a unit of distance, but rather a volume. Therefore, it is likely that the question contains a typo and should ask how many kilometers can Jon drive. To find out how many kiloliters that distance amounts to, we remember that 1 kiloliter equals 1,000 liters, so:

Therefore, Jon can drive 198 kilometers with 22 liters of gas, which equals 0.022 kiloliters of gasoline consumed.

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 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)

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 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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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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