The equation sec^2x-1=tan^2x is an identity true or false

best answer is b = it has exactly 1 x intercept

Answer:

B.

Step-by-step explanation:

We know that for x-intercept the graph crosses x-axis i.e the value of y = 0.

As in the table, the value of y is changing from negative to positive, so it will obtain the value y = 0 for some vale of x.

Therefore, this function will have only one x-intercept.

Hence, option A, C, D are discarded and option B is correct.

Answer:

Rate of interest = 6%

Step-by-step explanation:

Alexis put $2000 in a savings account. After 4 years, she had $2543 in the account.

Use the formula,

[tex]A=Pe^{rt}[/tex]

[tex]P\rightarrow \$2000[/tex]

[tex]r\rightarrow ?[/tex]

[tex]A\rightarrow \$2543[/tex]

[tex]t\rightarrow 4\text{ years}[/tex]

Substitute the value into formula and solve r

[tex]2543=2000e^{4r}[/tex]

[tex]e^{4r}=1.2715[/tex]

Apply ln both sides

[tex]4r\ln(e)=\ln(1.2715)[/tex]

[tex]r=0.06[/tex]

Rate of interest = 6%

Hence, The rate of interest is 6%

area of a circle = pi x r^2

using 3.14 for pi

 radius = 36/2 =18

area = 3.14 x 18^2 = 1017.36 square inches

1 sq ft = 144"

1017.36/144 = 7.065 sq ft

7.065*3.50 = $24.73 to the nearest dollar = $25

The answer is 14 inches and 28 inches:

Total length of stick = 42 inches.

Let the shorter piece be x inches.

Thus, the longer piece is 2x.

2x + x = 42

3x = 42

x = 14

Therefore, the length of the two pieces are 14 inches and 28 inches.

Answer:

$234.39

Step-by-step explanation:

The slope of the line passing through the points (12, -18) and (11, 12) is calculated using the formula for slope (y2 - y1) / (x2 - x1). The result is -30.

The subject of this question is Mathematics, more specifically the topic of 'Slope of a Line'. The grade level appears to be High School.

To answer the question 'Find the slope for the given coordinates (12,-18) and (11,12)', we use the formula to calculate the slope between two points which is (y2 - y1) / (x2 - x1). Let's take (12, -18) as (x1, y1) and (11, 12) as (x2, y2). Now we just input the values into the formula:

Slope (m) = (12 - (-18)) / (11 - 12).

This simplifies to Slope (m) = 30 / -1 = -30.

So, the slope of the line passing through the points (12, -18) and (11, 12) is -30.

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To find the value of a in the ordered pair (a,b), we can solve the given equations. Substituting ab^4 with 12 in the second equation, we get a^5 (12)^5 = 7776. Solving for a gives a = 0.03125^(1/5) = 0.5.

To find the value of a in the ordered pair (a,b), we can solve the given equations.

From the first equation, ab^4 = 12, we can substitute ab^4 with 12 in the second equation:
a^5 b^5 = 7776

This gives us:
a^5 (12)^5 = 7776
12^5 = 12 * 12 * 12 * 12 * 12 = 248,832

Dividing both sides of the equation by (12^5) gives:
a^5 = 7776 / (12^5) = 7776 / 248,832 = 0.03125

Taking the fifth root of both sides gives:
a = 0.03125^(1/5) = 0.5

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Answer: The correct option is

(B) Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.

Step-by-step explanation: Given that Aiden calculated the area of triangle QRS by finding half the product of 1.5 and 1.1.

We are to select the correct option which states the error made by Aiden.

The AREA of a triangle is given by

[tex]A=\dfrac{1}{2}\times \textup{base}\times \textup{altitude},[/tex]

where the altitude is perpendicular to the base.

In ΔQRS, the length of the base is given by

b = QS = 0.9 + 4.5 = 5.4 units

and

the length of the altitude is given by

h = 1.1 units.

So, the area of the triangle QRS will be

[tex]A=\dfrac{1}{2}\times b\times h=\dfrac{1}{2}\times 5.4\times 1.1[/tex]

Therefore, the area of ΔQRS will be calculated by finding half the product of 1.1 and 5.4.

So, Aiden made the error by finding half the product of 1.5 and 1.1, because 1.5 line is not perpendicular to 1.1 line.

Thus, Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.

Option (B) is correct.

Answer:

The option A.) 2007 is correct

Step-by-step explanation:

The formula which is to be used is given :

[tex]P(t) = 1.1\cdot e^{0.047t}[/tex]

where P(t) is the function of time t and t is the time in years after January 1 , 1980

Now, we need to find the year when the price will reach $4

So, substituting P(t) = 4 and finding the value of t from the given equation.

[tex]\implies 4=1.1\cdot e^{0.047t}\\\\\implies 3.64=e^{0.047t}\\\\\text{Taking natural log ln on both the sides}\\\\\implies \ln 3.64=\ln e^{0.047t}\\\\\implies 1.29=0.047\cdot t\\\\\implies t = 27.49[/tex]

So, t = 27.49 which is approximately equals to 27.5 years

So, 27.5 years after January 1, 1980 is the year 2007

Hence, The price will reach $4 in the year 2007

Therefore, The option A.) 2007 is correct

Answer:

d on edge

Step-by-step explanation:

Since no two different ordered pairs have the same x -coordinate, relations D given by the following sets of ordered pairs is a function.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The relation might be put up as a table of ordered pairs. The next step is to determine if each element in the domain matches precisely one element in the range.

A function is a collection of ordered pairs where no two ordered pairs are the same in terms of x-coordinate. A function is defined by an equation that yields such a collection of paired objects.

The relations given by the following sets of ordered pairs is a function is,

d. {(8,1),(−4,1),(3,5),(0,4),(−1,2)(8,1),(−4,1),(3,5),(0,4),(−1,2)}

Thus, no two different ordered pairs have the same x -coordinate, relations D given by the following sets of ordered pairs is a function.

Learn more about the function here:

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divide 111 in half

111/2 = 55.5

 take the whole number above and below 55.5

 so you get 55 and 56

55 + 56 = 111

56 is the larger one