Write an equation in slope-intercept form for the line that passes through
(–1, –2) and (3, 4).

Answer:

it depends on what you're doing

what's the name of the topic

Answer:

Step-by-step explanation:

See the attached file .

Answer: one senior ticket is $8 and one student ticket is $14

Hope this helps a little

The value of t₄ in the arithmetic sequence is 103/8.To determine the value of t₄ in an arithmetic sequence, we need to use the given information that t₁ = 11 (the first term of the sequence) and S₉ = 243 (the sum of the first 9 terms of the sequence).

We know that the formula for the sum of an arithmetic sequence is Sₙ = (n/2)(2a + (n-1)d), where Sₙ is the sum, a is the first term, n is the number of terms, and d is the common difference.

From the given information, we have S₉ = 243, a = 11, and n = 9. Plugging these values into the sum formula, we can solve for d:

243 = (9/2)(2(11) + (9-1)d)

243 = 9(22 + 8d)

243 = 198 + 72d

45 = 72d

d = 45/72 = 5/8

Now that we have the common difference, we can find t₄ using the formula for the nth term of an arithmetic sequence:

tₙ = a + (n-1)d

t₄ = 11 + (4-1)(5/8)

t₄ = 11 + 3(5/8)

t₄ = 11 + 15/8

t₄ = 88/8 + 15/8

t₄ = 103/8

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the solutions to the equation \(2x^2 - x - 3 = 0\) are x = 1.5 or x = -0.5.

The square root of 25 can be expressed simply as 5:

x = (1 ± 5) / 4

This provides us with two potential answers:

x = (1 + 5) / 4 = 1.5

or

x = (1 - 5) / 4 = -0.5

The square root of a negative number is not a real number, so this equation does not have a real solution using geometric mean.

By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.

Based on the provided data set, the fundamental formula to determine the mean is calculated. When calculating the mean, every term in the data set is taken into account. The ratio between the total number of terms and the sum of all the terms provides the general formula for the mean. Hence, we may state;

Mean is equal to the product of the given data and the total amount of data.

from the question:

The following formula can be used to find x using geometric mean:

\(x = \sqrt{(ab)}\)

where a and b are the two numbers whose geometric means we're interested in finding.

The two roots of the quadratic equation \(ax^2 + bx + c = 0\) in standard form can be used here as a and b. Applying the previous solutions, we obtain:

\(x = \sqrt{(1.5 (-0.5)}\)

\(x = \sqrt{(-0.75)}\)

As the square root of a negative number is not a real number, the geometric mean method cannot find a real solution to this problem.

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Here, lots of questions are asking.

The study of shapes, sizes, locations, and qualities of objects in space is referred to as geometry. It covers the examination of points, lines, angles, planes, and solid figures as well as their interrelationships. In areas including architecture, engineering, physics, and computer graphics, among others, geometry is used in real-world settings. It is frequently taught to kids starting at a young age and is a crucial component of mathematics education.

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Answer:

..........................................

Answer:

34

Step-by-step explanation:

Answer:

82

Step-by-step explanation:

1000% sure this is correct

For the function \(f(x) = \frac{2x -1 }{x+3}\),

Domain: (-∞, -3) U (-3, ∞)

Holes: None

Vertical asymptote: x = -3

Horizontal asymptote: y = 2

x-intercept: (1/2, 0)

y-intercept: (0, -1/3)

Domain:

All real numbers, with the exception of those that would make the denominator to equal zero, are included in the domain of a rational function. We must eliminate x = -3 from the domain in this situation since x + 3 cannot equal zero. With the exception of x = -3, all real numbers fall under the domain.

Domain: (-∞, -3) U (-3, ∞)

Holes:

When a factor in the numerator and denominator cancels out, a hole appears in the graph of a rational function. In this function, there are no gaps in the graph because there are no factors that cancel one another.

No holes in the graph.

Vertical Asymptote:

When the denominator of a rational function becomes zero while the numerator does not, this is known as vertical asymptotes. The vertical asymptote in this case is at x = -3, which is associated with the value that is excluded from the domain.

Vertical asymptote: x = -3

Horizontal Asymptote:

We must look at the degrees of the numerator and denominator in order to get the horizontal asymptote. The numerator and denominator of this function have degrees of 1, and vice versa. Dividing the leading coefficients of the numerator and denominator gives the horizontal asymptote when the degrees are equal.

The leading coefficients of the numerator and denominator are 2 and 1, respectively. As a result, y = 2/1, which may be written as y = 2, is the horizontal asymptote.

Horizontal asymptote: y = 2

x-intercept:

Setting the numerator equal to zero and solve for x to find the x-intercept. In this case, we have:

2x - 1 = 0

2x = 1

\(x = \frac{1}{2}\)

So the x-intercept is at \(x = \frac{1}{2}\).

x-intercept: ( \(\frac{1}{2}, 0\) )

y-intercept:

Setting x equal to zero and evaluate the function to find the y-intercept.

\(f(0) = \frac{(2(0) - 1)}{(0 + 3)}\)

\(f(0) = \frac{-1}{\ 3}\)

So the y-intercept is at y = -1/3.

y-intercept: (0, -1/3)

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Answer:

33

Step-by-step explanation:

Answer:

4 miles in 1 min

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

Answer:

B. Add two -1 counters to each side

Step-by-step explanation:

If you were to do this problem normally you would subtract 2 from each side so B just makes sense.

Using confidence interval concepts, it is found that the reasonable estimate for the proportion of all American adults who believe that regular exercise is important is of 0.753.

It is the range in which a parameter is expected to be given a confidence level, has format (a,b), and the point estimate of the parameter is the mean between a and b.

In this problem, the interval is [0.726, 0.780], hence, the estimate is of:

(0.726 + 0.78)/2 = 0.753

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Hello there!

Answer:

16

Step-by-step explanation:

\( |x| = x \: \: \: if \: \: x \: \geqslant 0 \\ |x| = - x \: \: \: if \: \: \: x \: \leqslant 0\)

-12 < 0 so |-12| = -(-12) = 12

4 > 0 so |4| = 4

|-12| + |4| = 12 + 4 = 16

Answer:

16

Step-by-step explanation:

Hello! This question is looking for the absolute value of integers. The absolute value is the distance the number has from zero. For example, -12 as twelve numbers away from zero, twelve away in the negative direction. The absolute value of -12, then, is just twelve. An easy way to remember this is to take away the negative sign when taking the absolute value, since an absolute value can never be negative. The absolute value sign is represented by a squarish bracket [ and ].

This question says to find the absolute value of each integer and then add the two. First we have [-12]. This is 12 away from zero, and we can take away the - sign from the asked integer and we get 12.

The second integer given is 4, and when we take the absolute value of 4, [+4], we get positive four. This is because four is four spaces away from zero on the number line.

Thus, we have +12 and +4 as are values to add since they are the absolute values and we can form this equation

12+4=16

Thus, the answer is 16.

Hope this helps! Remember the hint, when something has brackets like that or asks for the absolute value, take away a negative sign and make it positive! Have a great day!

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Given

number 89.396668...

Find

Determine if the number is rationa or irrational

Explanation

As the number 89.396668... is a rational number as it is a non terminating decimal because it is keep on continuing after decimal point .

It can be represented in the form of p/q where q is not equal to 0.

Final Answer

The number 89.396668...is a rational number

Hi!!!

B. the point lies directly on the regression line.

Hope this helped!

Have a good day:)

The point lies directly on the regression line.

Option B is the correct answer.

A regression line is a straight line that represents the relationship between two variables in a scatter plot.

In other words, it is a line that best fits the data points in a scatter plot by minimizing the difference between the actual data points and the predicted values on the line.

We have,

When we talk about the residual of a data point in the context of regression analysis, we are referring to the difference between the actual value of the response variable (dependent variable) for that data point and the predicted value of the response variable based on the regression equation.

If a data point has a residual of 0, it means that the predicted value for that data point is exactly equal to the actual value of the response variable.

This can occur when the data point falls directly on the regression line, as in option B.

Thus,

The point lies directly on the regression line.

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Answer:

A picture that you can see

Step-by-step explanation:

The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.

Let x be the hotel charge before tax in the first city, and y be the hotel charge before tax in the second city. Then we have:
y = x + 1500   (the hotel charge before tax in the second city was $1500 higher than in the first)
0.075x + 0.05y = 825   (the total hotel tax paid for the two cities was $825)
We can use the first equation to solve for y in terms of x:
y = x + 1500
Then we can substitute this expression for y into the second equation:
0.075x + 0.05(x + 1500) = 825
Simplifying this equation, we get:
0.075x + 0.05x + 75 = 825
0.125x = 750
x = 6000
So the hotel charge before tax in the first city was $6000. Using the first equation, we can find the hotel charge before tax in the second city:
y = x + 1500
y = 6000 + 1500
y = 7500
So the hotel charge before tax in the second city was $7500.
Therefore, the answer is: The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.

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The equation of the circle is x² + (y + 8)² = 13.

What is a circle?

All points in a plane that are at a specific distance from a specific point, the centre, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

We know that the standard equation of a circle is

(x - h)² + (y - k)² = r²

where (h,k) represents the center and r is the radius.

We are given the center of the circle to be (0, -8) and that the circle passes through the point (2,-5).

In order to find the radius, we will use the distance formula.

Using this, we get

⇒r = √ (2 - 0)² + (-5 - (-8))²

⇒r = √13

So, we get the equation as

⇒(x - 0)² + (y - (-8))² = √13²

⇒x² + (y + 8)² = 13

Hence, the equation of the circle is x² + (y + 8)² = 13.

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Answer:

Grogg's dad is 22

Step-by-step explanation:

Let D = dad's current age

Let g = Grogg's current age

6(d - 7) = g - 7 → 6d - 42 = g - 7 → 6d -35 = g

4(d - 3) = g - 3 → 4d -12 = g - 3 → 4d -9 = g

Set the two equations equal to each other and solve for d

6d - 35 = 4d - 9  Subtract 4d from both sides

2d -35 = -9  Add 35 to both sides

2d = 44  Divide both sides by 2

d = 22

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

d = current dad age

g = current grogg age

d-7 = 6(g-7)

d-3 = 4(g-3)

Let's solve the first equation first:

Add 7 to both sides: d - 7 +7 = 6g - 42 + 7 so d = 6g - 35

Substitude d = 6g - 35 for d in d - 3 = 4g - 12

(6g-35)-3 = 4g-12 = 6g-38 = 4g-12

Subtract 4g from both sides: 2g - 38 = -12

Add 38 to both sides: 2g = 26

Easy: g = 13

And now substitude g in for any equations.

d-3 = 52-12

d = 43

Given :

Required :

Recall from the properties of a rectangle that

Hence :

The given focal points and the lengths of the minor and major axis of 16 and 20 gives the equation of the ellipse as the option;

\( B. \: \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 \)

The equation of an ellipse is presented as follows;

\( \mathbf{ \frac{(x - h)^{2}}{ {a}^{2} } + \frac{(y - k)^{2}}{ {b}^{2} } } = 1 \)

Where;

(x, y) = Coordinates of the center of the ellipse

a = Semi major axis

b = Semi minor axis

Length of minor axis = 16 units

Length of major axis = 20 units

By observation of the coordinates of the focal point, we have;

y-value of the center of the ellipse, k = 2

x-value of the center, h = (-9 + (3 - (-9))/2 = -3

The equation of the ellipse is therefore;

\( \frac{(x - ( - 3))^{2}}{ {10}^{2} } + \frac{(y - 2)^{2}}{ {8}^{2} } = 1 \)

\( \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 \)

The equation that represents the ellipse is the option;

\( B. \: \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 \)

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Answer:

About 86 situps or if being really accurate 86.25

Step-by-step explanation:

Answer:

1/8 is marked on a ruler

Step-by-step explanation:

Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

Answer:

<1 = 100

<2 = 80

Step-by-step explanation:

Angle 1 and angle 2 are supplementary

Supplementary angles add to 180 degrees

<1 + <2 = 180

The angles are in a ratio of 5 to 4

Multiply by x to get the measure of each angle

<1 = 5x  <2 = 4x

5x+4x = 180

Combine like terms

9x = 180

Divide by 9

9x/9 =180/9

x =20

<1 = 5x = 5*20 = 100

<2 = 4x = 4*20 = 80

Answer:

m1 = 122

m2 = 58

m5 = 68

Step-by-step explanation:

m2 = 180 - 54 - 68 = 58

m1 = 180 - m2 = 180 - 58 = 122

m5 = 180 - 58 - 54 = 68

Answer:

x = 0

Step-by-step explanation:

The distributive property of multiplication states that a(b - c) = a(b) - a(c). We can apply that to the given equation.

3(2 - x) = 6

3(2) - 3(x) = 6 (Apply distributive property on LHS)

6 - 3x = 6 (Simplify LHS)

6 - 6 - 3x = 6 - 6 (Subtract 6 from both sides)

-3x = 0 (Simplify both sides)

\(\frac{-3x}{-3} =\frac{0}{-3}\) (Divide both sides by -3)

x = 0 (Simplify)

Hope this helps!

Let f(x) = lnx and g(x) = log₂x. for all 0 < x < 1, f(x) < g(x): True.

In this scenario and exercise, we would determine the corresponding output value for the functions f(x) and g(x) under the given mathematical operation and independent variables.

When x = 1, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(1) = ln(1).

f(1) = 0.

When x = 2, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(2) = ln(2).

f(2) = 0.69314718

When x = 1, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(1) = log₂(1)

g(1) = 0.

When x = 2, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(2) = log₂(2)

g(2) = 1.

In this context, we can logically deduce that the function f(x) is less than function g(x) for all 0 < x < 1.

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