Calculate.

0 = x² + 10x + 16

Enter your answers in the boxes.

The solution of the equation will be x = (ln 3) / 2. Then the correct option is C.

The solution of the equation means the value of the unknown or variable.

The equation is given below.

5e²ˣ – 4 = 11

On simplifying, we have

5e²ˣ = 15

 e²ˣ = 3

Taking log on both sides, then we have

2x ln e = ln3

We know ln e = 1, then we have

2x = ln 3

  x = (ln 3) / 2

Then the correct option is C.

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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]

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].

Answer:

secᎾ=17/8

cotᎾ=8/15

cscᎾ=17/15

Step-by-step explanation:

Answer:

Her total premium would be $1,209.00

Other answer is incorrect.

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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Is the following definition of perpendicular reversible? If yes, write it as a true biconditional.

Two lines that intersect at right angles are perpendicular.

A. The statement is not reversible.  

B. Yes; if two lines intersect at right angles, then they are perpendicular.  

C. Yes; if two lines are perpendicular, then they intersect at right angles.  

D. Yes; two lines intersect at right angles if (and only if) they are perpendicular.

Answer:

Yes; two lines intersect at right angles if (and only if) they are perpendicular.

Step-by-step explanation:

In a biconditional statement, both parts have to be true. In this case, if the two lines intersect at a right angle then they are perpendicular, and if they are perpendicular then they intersect at a right angle

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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Answer:

associative property of multiplication

Step-by-step explanation:

edge 2021

To determine the believability of the Harris Poll's claim that 35% use caffeine to combat drowsiness, a hypothesis test for proportions is needed. The sample proportion of 39.58% from the recent survey would be tested against the null hypothesis of 35% using a z-score calculation. Depending on if the z-score falls within the critical region, we can either reject or fail to reject the null hypothesis.

To determine if the claim of the percentage found in the Harris Poll is believable based on the recent survey, we can conduct a hypothesis test for proportions. The null hypothesis (¿¿H₀) is that the true proportion of people who drink a caffeinated beverage to combat midday drowsiness is 35%, as stated by the Harris Poll. The alternative hypothesis (¿¿H₁) would be that the true proportion is different from 35%.

We use the information that 19 out of 48 randomly selected people stated that they drank a caffeinated beverage for midday drowsiness, which gives us a sample proportion of approximately 39.58%. To test this, we can calculate the z-score for the sample proportion and compare it to the critical value for α = 0.05 (two-tailed test). If the calculated z-score falls within the critical region, we reject the null hypothesis, indicating that the Harris Poll's claim is not believable. However, if the z-score is outside the critical region, we do not have enough evidence to reject the null hypothesis, and thus the claim is considered believable.

To perform this test, we would need to calculate the standard error for the proportion, z-score, and then compare the z-score to the appropriate critical value. Without performing the calculations here, we cannot definitively conclude about the believability of the Harris Poll's percentage claim. However, a statistician would run these numbers to reach a conclusion.

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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