What is the opposite and absolute value of -7?​

Answer:

x = 5

Step-by-step explanation:

given 2 secants to a circle from an external point , then

the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant , that is

(x - 1)(x - 1 - 3 + x) = 3(3 + 5)

(x - 1)(2x - 4) = 3(8) ← expand factors on left side using FOIL

2x² - 6x + 4 = 24 ( subtract 24 from both sides )

2x² - 6x - 20 = 0 ( divide through by 2 )

x² - 3x - 10 = 0 ← in standard form

(x - 5)(x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 2 = 0 ⇒ x = - 2

however, x > 0 , then x = 5

The domain of a function is the set of all possible inputs for the function.

Domain: (−∞,∞),{x|x∈R}

Range: (−∞,1],{y|y≤1}

What are the domain and range?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

We have,

f(x) = 1 - x²

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).

f(x) = 1 - x² is defined for all Real values of x and therefore the domain is all Real values (R).

x² has a minimum value of 0 (for x ∈ R)

therefore

−x² has a maximum value of 0

and

−x² + 1 = 1 − x² has a maximum value of 1.

Hence, the domain of a function is the set of all possible inputs for the function,

Domain: (−∞,∞),{x|x∈R}

Range: (−∞,1],{y|y≤1}

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the roots of the auxiliary equation are -1/3 ± i√(8/9), and the general solution of the given second-order differential equation is: y(x) = C1 * e^(-x/3) * cos(√(8/9)x) + C2 * e^(-x/3) * sin(√(8/9)x)

To find the roots of the auxiliary equation and the general solution, follow these steps:

Step 1: Write down the given differential equation:
3y'' + 2y' + y = 0

Step 2: Replace y'' with "m^2", y' with "m", and y with "1" to form the auxiliary equation:
3m^2 + 2m + 1 = 0

Step 3: Solve the auxiliary equation form to find the roots. This is a quadratic equation, so we can use the quadratic formula:
m = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 3, b = 2, and c = 1. Plug in these values and solve for m:
m = (-2 ± √(2^2 - 4*3*1)) / (2*3)
m = (-2 ± √(-8)) / 6
Since the discriminant is negative, we have complex roots:
m = -1/3 ± i√(8/9)

Step 4: Write down the general solution of the given equation using the roots:
y(x) = C1 * e^(-x/3) * cos(√(8/9)x) + C2 * e^(-x/3) * sin(√(8/9)x)

In summary, the roots of the auxiliary equation are -1/3 ± i√(8/9), and the general solution of the given second-order differential equation is:
y(x) = C1 * e^(-x/3) * cos(√(8/9)x) + C2 * e^(-x/3) * sin(√(8/9)x)

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Therefore, the equation of the function h(x) is: h(x) = -f(x) + 2.

A graph is a visual representation of data that shows the relationship between two or more variables. It consists of two axes - the x-axis (horizontal) and the y-axis (vertical) - that intersect at a point called the origin. Each axis is divided into equally spaced intervals or units that represent the range of values for each variable. Data points are plotted on the graph by identifying their corresponding x and y values and locating them on the appropriate axes. The points are then connected by a line or curve that represents the pattern or trend in the data. Graphs are commonly used in various fields such as mathematics, science, economics, and business to help analyze and interpret data. Some common types of graphs include line graphs, bar graphs, scatter plots, pie charts, and histograms.

Here,

Let's assume the equation of the original function f(x) is y = f(x). To obtain the function h(x), we first reflect the graph of f(x) over the x-axis. This means that for any point (x, y) on the graph of f(x), the corresponding point on the graph of h(x) will be (x, -y).

Next, we translate the reflected graph of f(x) two units up. This means that for any point (x, -y) on the reflected graph, the corresponding point on the graph of h(x) will be (x, -y + 2).

Therefore, the equation of the function h(x) is:

h(x) = -f(x) + 2

This equation reflects the graph of f(x) over the x-axis (by negating f(x)) and then translates the reflected graph 2 units up (by adding 2).

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Complete question:

The graph of the function h(x) is the result of reflecting the graph of f(x) over the x-axis and then translating 2 units up. Which equation defines h(x)?​

Answer:

45 and 13…......

Step-by-step explanation:

devide

Answer:

x=-9

Step-by-step explanation:

x=36/-4=-9

Answer:

-9

Step-by-step explanation:

-4x=36

36/-4=-9

x = -9

-4(-9)=36

Answer:

2,3

Step-by-step explanation:

The equation of the tangent(s) to the curve \( y=x^{3}+3 x^{2}+x \) at its inflection point is \( y = 4x + 2 \).

To find the inflection point, we need to find the second derivative of the given curve. Let's start by finding the first derivative \( \frac{dy}{dx} \):

\[ \frac{dy}{dx} = 3x^2 + 6x + 1 \]

Now, let's find the second derivative \( \frac{d^2y}{dx^2} \):

\[ \frac{d^2y}{dx^2} = 6x + 6 \]

To find the x-coordinate of the inflection point, we need to solve the equation \( \frac{d^2y}{dx^2} = 0 \):

\[ 6x + 6 = 0 \]

\[ 6x = -6 \]

\[ x = -1 \]

Now, substitute the value of \( x = -1 \) into the original equation \( y = x^3 + 3x^2 + x \) to find the y-coordinate of the inflection point:

\[ y = (-1)^3 + 3(-1)^2 + (-1) \]

\[ y = -1 + 3 + (-1) \]

\[ y = 1 \]

So, the inflection point is (-1, 1).

To find the equation of the tangent line at this point, we use the point-slope form of the line equation:

\[ y - y_1 = m(x - x_1) \]

where \( (x_1, y_1) \) is the point of tangency and \( m \) is the slope of the tangent line. We can calculate the slope \( m \) by substituting \( x = -1 \) into the first derivative:

\[ m = \frac{dy}{dx}\Bigg|_{x = -1} = 3(-1)^2 + 6(-1) + 1 = 4 \]

Substituting \( x_1 = -1 \), \( y_1 = 1 \), and \( m = 4 \) into the point-slope form, we get:

\[ y - 1 = 4(x + 1) \]

Simplifying the equation, we find the equation of the tangent line:

\[ y = 4x + 2 \]

The equation of the tangent(s) to the curve \( y = x^3 + 3x^2 + x \) at its inflection point is \( y = 4x + 2 \). We found the inflection point by finding the x-coordinate where the second derivative equals zero. Then, we determined the y-coordinate by substituting the x-coordinate into the original equation. Using the point-slope form of the line equation, we calculated the slope of the tangent line and substituted the coordinates of the inflection point to find the equation of the tangent line.

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Answer:

Step-by-step explanation:

4 - 0.4 = 3.6

3.6 - 0.4 = 3.2

2.8 - 0.4 = 2.4

2.4 - 0.4 = 2

2 - 0.4 = 1.6

so the next numbers in the pattern are: 2.4, 2 and 1.6

Answer:

a

Step-by-step explanation:

Answer:

= a⁴

Step-by-step explanation:

(a)(a)(a)(a)

a se multiplica por si misma 4 cuatro veces así que:

(a)(a)(a)(a) = a⁴

Answer:

1 : 4 1/2 :: 8 1/5 : x            proportion

x = (4 1/2)(8 1/5)                product of means/extremes

x = (9/2)(41/5)                   change improper fraction

x = 369/10                         multiply

x = 36.9                              change to decimal

Answer:

3 is the greatest common factor that can go into 9 and 48

The greatest common factor of 9 and 48 is 3.

The greatest common factor (GCF) is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that is a factor of both (or all) of the given numbers.

For example, the GCF of 12 and 18 is 6, beca

To find the greatest common factor (GCF) of 9 and 48, we need to determine the largest number that both 9 and 48 can be divided by evenly.

We can start by listing the factors of each number:

9: 1, 3, 9

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Then we can look for the greatest factor that appears in both lists. In this case, the greatest common factor of 9 and 48 is 3, since it is the largest number that appears in both lists of factors.

Therefore, the GCF of 9 and 48 is 3.

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Answer:

8 / 15

Step-by-step explanation:

By Pythagoras theorem,

OP² + PQ² = OQ²

OP² + 8² = 17²

OP² = 17² - 8²

       = 289- 64

OP² = 225

OP² = 15²

OP = 15

Formula : -

Tan θ = Opposite side / Adjacent side

Here,

θ = Q

Opposite side = PQ = 8

Adjacent side = OP = 15

Tan Q = 8 / 15

Answer: The cost of dress is $20 and belt is $3

Equation's created:

      1) 5d + 4b = 112

      2) 3d + 2b = 66

Here 'd' is dress and 'b' is belt

Make 'd' subject:

  In equation 1:

⇒  5d + 4b = 112

⇒  5d = 112 - 4b

⇒  d = (112 - 4b)/5

  In equation 2:

  ⇒ 3d + 2b = 66

  ⇒ 3d = 66 - 2b

  ⇒ d = (66 - 2b)/3

Solve them simultaneously:

 (66 - 2b)/3 = (112 - 4b)/5

 5(66 - 2b) = 3(112 - 4b)

  330 - 10b = 336 - 12b

   -10b + 12b = 336 - 330

          2b = 6

           b = 3

Now find the value of dress:

d = (66 - 2b)/3

  = (66 - 2(3))/3

  = 20

Answer: it’s 10.0

Step-by-step explanation:

I’m trying to figure it out too

The 80% confidence interval for the population mean is approximately (73.9, 80.5).

To find the 80% confidence interval for a sample of size 43 with a mean of 77.2 and a standard deviation of 16.4, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

The critical value is obtained from the t-distribution table or using statistical software. For an 80% confidence level with 42 degrees of freedom (n-1), the critical value is approximately 1.303.

The standard error is calculated as the sample standard deviation divided by the square root of the sample size:

Standard Error = sample standard deviation / √(sample size)

Plugging in the values, we have:

Standard Error = 16.4 / √43 ≈ 2.50

Now we can calculate the confidence interval:

Confidence Interval = 77.2 ± (1.303 * 2.50)

Confidence Interval = (77.2 - 3.258) to (77.2 + 3.258)

Confidence Interval = (73.9, 80.5).

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Answer:

Vowel= 0.2

Number= 0.5

Step-by-step explanation:

Vowel: There are a total of 5 sample spaces known as A,E,I,O,U. From those 5, there is one randomly selected letter e. This will also be known as 1/5, 20% or 0.2.

Number: There are a total of 2 sample spaces known as 1,2. Out of those two numbers, there will be one random number selected known as 2. This is known to be 1/2, 50% or 0.5

Answer: 19 3/8

Step-by-step explanation:

Add all the fractions and minus it from 28 1/2. So, we have to make all the denominators the same.

1) 3 1/4= 3 2/8

2) 1 3/4= 1 6/8

3) 4 1/8= 4 1/8 ( i multiplied the numerator and denominator by 2 to get number 1 and 2)

Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

Answer:

3

Step-by-step explanation:

Answer:

2 Nights

Step-by-step explanation:

790+93x=932+22x

790+71x=932

71x=142

x=2

Answer: The one on the left.

Step-by-step explanation:

There is no file, but the panda on the left is bigger.

Answer:

This can vary. Are we doing 4 letter words, 5 letter, etc?

Step-by-step explanation:

A sample statistic is is any quantity from the sample of a population.

We can see in the last option, that from the population (total of subjects of study) Kaisa, selected 84 of the total students. This fits in to the definition of sample statistic.

Thus, the correct option is the last one.