Find the equation of the line tangent to the graph of x(t)=t²+1 and y(t)=
\( \sqrt{1 + t} \)at point t=3​

Answer:

The assembly line manufactures 13 riding lawn mowers per hour of operation. And the graph that the line is vertical but slightly tilted.

Step-by-step explanation:

the events A and B as follows: A = { x | x < 72.5] and B = { x | x > 52.5].

From the question given above, the following data were obtained:

Angle θ = 71°

Hypothenus = 25

Adjacent = x

Thus, we can obtain the x component of the vector by using the cosine ratio as illustrated below:

Cos θ = Adjacent /Hypothenus

Cos 71 = x/25

Cross multiply for events

x = 25 × Cos 71

x = 25 × 0.3256

x = 8.1

Therefore, the x component of the vector is 8.1

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Answer:

a= 5

Step-by-step explanation:

3 (a-7)= 14-4a -Remove Parentheses

3a-21=14-4a -Move the terms

3a+4a=14+21 -Collect like terms

7a=35 -Divide both sides

a=5 - Solution

Answer:

Cost of Washer = $696

Cost of Dryer = $232

Step-by-step explanation:

Start by making and equation, put a variable for the missing prices, let's say the cost of the dryer is 'x' and since the cost of the washer is three times, it will be '3x'.

Put the equation together, so we can add the x variables together.

3x + x = 4x

The total cost will be what the '4x' is equal to.

4x = 928

Going back to algebra, we solve the equation by dividing both sides by 4.

x = 232

Remember x is the variable we gave to the dryer, so now we must find the cost of the washer. In order to do this, we will have to multiply it by 3.

3x

3(232) = 696.

To check the answer, we can add them together to make sure we get the total cost.

696 + 232 = 928

Answer:

\(x=2\\y=3\)

Step-by-step explanation:

Solve by substitution method

\(y=4x-5\\y=3x-3\)

First, solve \(y=4x-5\) for \(y\):

Substitute \(4x-5\) for \(y\) in \(y=3x-3\)

\(y=3x-3\)

\(4x-5=3x-3\)

\(4x-3x=5-3\)

\(x=2\)

Now that we have the value of x

substitute \(2\) for \(x\) in \(y=4x-5\)

\(y=4x-5\)

\(y=4(2)-5\)

\(y=8-5\)

\(y=3\)

∴ The value of \(x\) is \(2\) and the value of \(y\) is \(3\)

Answer:

On a plane

Step-by-step explanation:

Answer:

A plane

Step-by-step explanation:

Answer:

.05

Step-by-step explanation:

Khan

Using the normal distribution and the central limit theorem, it is found that the probability that the mean of these 100 sleep times is farther than 0.4 hours away from the population mean is:

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

We want the probability that the mean is farther than 0.4 hours away from the population mean, hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{0.4}{s}\)

\(Z = \frac{0.4}{0.2}\)

\(Z = 2\)

The probability is P(|Z| > 2), which is 2 multiplied by the p-value of Z = -2.

Hence, option A is correct.

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The center of the ellipse defined by the equation 9x^2 + 4y^2 + 18z - 23 = 0 is (0, 0, 0).

9x^2 + 4y^2 + 18z - 23 = 0 must be rearranged to its standard form in order to determine the location of the ellipse's centre. The ellipse equation has the following standard form:

(x - h)^2/a^2 + (y - k)^2/b^2 + (z - l)^2/c^2 = 1,

where (h, k, l) represents the center of the ellipse, and a, b, and c are the semi-major, semi-minor, and semi-vertical axes, respectively.

Let's rearrange the given equation to match the standard form:

9x^2 + 4y^2 + 18z - 23 = 0

Dividing by 23 to simplify the equation:

(9x^2)/23 + (4y^2)/23 + 18z/23 - 1 = 0

Now, we can rewrite the equation as:

(9x^2)/23 + (4y^2)/23 + 18z/23 = 1

Comparing this with the standard form, we can identify the values of a, b, and c:

a^2 = 23/9

b^2 = 23/4

c^2 = 23/18

Taking the square roots of these values:

a ≈ √(23/9) ≈ 1.53

b ≈ √(23/4) ≈ 1.92

c ≈ √(23/18) ≈ 1.23

Therefore, the semi-major axis (a) is approximately 1.53, the semi-minor axis (b) is approximately 1.92, and the semi-vertical axis (c) is approximately 1.23.

The center of the ellipse is represented by the values (h, k, l). Since the equation does not involve any shifts or translations, the center is located at the origin (0, 0, 0).

As a result, (0, 0, 0) is the centre of the ellipse formed by the equation (9x2 + 4y2 + 18z - 23 = 0).

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Answer:

Center: (-3, 1)

Step-by-step explanation:

The center of an ellipse is always the point that is equidistant from the two foci and the two vertices.

In order to find the center of the ellipse, we can complete the square in both the x and y terms.

First, we move the constant term to the right side of the equation:

\(9x^2+18x + 4y^2-8y = 23\)

The coefficient of x is 18, so half of it is 9, and squaring that gives us 81. Adding 81 to both sides of the equation gives us:

\(9x^2+18x + 81 = 23 + 81\)

which combines the terms in x into a squared term:

\((9x+9)^2 = 104\)

Similarly:

\(4y^2-8y + 4 = 23 + 4\)

which combines the terms in y into a squared term:

\((2y-2)^2 = 27\)

Now that we have completed the square in both x and y, we can write the equation in standard form for an ellipse:

\(\frac{(x+3)^2}{11^2} + \frac{(y-1)^2}{3^2} = 1\)

The standard form for an ellipse is:

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

where (h, k) is the center of the ellipse, a is the radius in the x-direction, and b is the radius in the y-direction.

In the equation for our ellipse, (h, k) = (-3, 1).

So the center of the ellipse is at the point (-3, 1).

In the nearest tenth, this is (-3.0, 1.0).

Answer : 8$

you have 1$ left

Answer:

Step-by-step explanation:

multiply and divide your equation then subtarct it and you get your answer

Answer:

yesss???

Step-by-step explanation:

Answer:yes

Step-by-step explanation:

Answer:

(x-3) is the correct expression

Step-by-step explanation:

To factor you split the expression apart -

x² + 2x – 15

This breaks up to (x+5)(x-3)

If you multiply (FOIL) these you get your expression x² + 2x – 15

Your answer choices do not include (x+5) so it must be (x-3)

I hope this helps!

The area of the figure ABDECA, and the coordinates of the points on the quadrilateral are;

1. The area is about 15.16 units²

2. The coordinates of the points are;

(i) B(5, 8)

(ii) C(8.58, 4)

(ii) D(8,58, 1.21)

A quadrilateral is a four sided polygon.

1. The coordinate of the point C can be found as follows;

Let (x, y) represent the coordinates of the C, we get;

(x + 8)/2 = 5

x = 2 × 5 - 8 = 2

(y + 8)/2 = 6

y = 2 × 6 - 8 = 4

The coordinates ot the point C (2, 4)

The length of the segment BC = √((8 - 2)² + (8 - 4)²) = 2·√(13)

Length of the side AB = √((8 - 6)² + (8 - 11)²) = √(4 + 9) = √(13)

The area of the triangle ABC = (1/2) × 2·√(13) × √(13) = 13

CE is perpendicular to DE, let (a, b), represent the coordinates of the point E, therefore;

(4 - y)/(2 - x) = -(5 - x)/(6 - y)

y - 4 = (-4/7)(x - 2)

y - 6 = (7/4)(x - 5)

(-4/7)(x - 2) + 4 = (7/4)(x - 5) + 6

x = (17/5) = 3.4

y = (7/4)((17/5) - 5) + 6 = 3.2

The coordinates of the point E is (3.4, 3.2)

The length of the side DE = √((5 - 3.4)² + (6 - 3.2)²) = √(10.4)

Length of the side CE = √((3.2 - 2)² + (3.4 - 4)²) = √(1.8)

Area of the triangle ΔCDE = (1/2) × √(10.4) × √(1.8)

Area of the figure is therefore;

2. The equation of the line AB is; y - 6 = (1/3)·(x - (-1))

y - 6 = (1/3)·(x + 1)

y = (1/3)·(x + 1) + 6

The slope of the segment AE = (4 - 6)/(3 - (-1)) = -1/2

Slope of the segment BE = -1/(-1/2) = 2

Equation of BE is; y - 4 = 2·(x - 3)

y = 2·(x - 3) + 4 = (1/3)·(x + 1) + 6

Therefore, x = 5

y = (1/3)·(5 + 1) + 6 = 8

(ii) Area of the triangle EBC = 24 unit²

EB = (1/2) × √((5 - 3)² + (8 - 4)²) = √20

Therefore;

BC = 24/(√20) = 12/√5 = 12·√5/5 = √(28.8)

(x - 5)² + (y - 8)² = 28.8

y = 4, therefore;

(x - 5)² + (4 - 8)² = 28.8

(x - 5)² = 28.8 - (4 - 8)² = 12.8

x = √(12.8) + 5

(iii) The equation of the segment AD is; y - 4 = (-1/2)(x - 3)

x = √(12.8) + 5

Therefore;

y - 4 = (-1/2)((√(12.8) + 5) - 3)

y = (-1/2)((√(12.8) + 5) - 3) + 4 ≈ 1.21

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Answer:

Actually their difference depends on some factors : Both x and y have to express same nature of phenomenon. The value of x and y. Unit of the values ( say x is a variable represents distance in kilometer, and y represents distance in meter , then mere |x-y| will not work until both the distances are in the same unit) .

Step-by-step explanation:

solve  -6x2-3x+12 dived by 3x-3 using pemdas

Step-by-step explanation:

The question is how to divide this this is how to solve it

The recursive formula will be

\(a_n = (-1)^{n+1\) [3 times difference + previous term]

When objects are defined in terms of other objects of the same type, the process is said to be recursive. The full class of objects can then be constructed from a few beginning values and a handful of rules using some kind of recurrence relation.

Given:

4,-17,46,…

Now, as the difference is

s= -17- 4= -21

and, d= 46 - (-17)= 63

Then, the recursive formula will be

\(a_n = (-1)^{n+1\) [3 times difference + previous term]

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Answer:

You cannot add two numbers that have different variables.

Step-by-step explanation:

You can multiply them, but since 3 is multiplied by "a" or a different number than "b" then the answer would be incorrect.

Answer:

because 3a and 3b have different variables. You can't add "unlike terms" to each other because the variables have different values. by writing 3a+2b as 5ab, you're completely changing the meaning of the problem. You would get a totally different answer than you would by just adding the two terms together.

(1) +8,+4,0,+2,+3 = 0 , 2 , 3 , 4 , 8

(2) -1,-11,-5,-0,-12 = -12 , -11 , -5 , -1 , -0

The following that are possible units for measuring mass in the metric system include the following below:

B. Kilogram

D. Gram.

This is a quantitative measure of inertia and it is referred to as the amount of matter which is present in a given body.

Options B and D both have the suffix "gram" which represents a metric system and are used in measuring mass unlike anagram which isn't a form of measurement which was why they were chosen as the correct set of options.

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Answer:

Step-by-step explanation:

pix

The calculated volume of the prism is 702 cubic cm

From the question, we have the following parameters that can be used in our computation

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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The equation of the circles are x² + y² = 1 and (x - 4)² + (y + 1)² = 25

What is the equation of the circle?

The standard equation of a circle is:

(x - h)² + (y - k)² = r²

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

a) Since the center of the circle is (0,0), the equation of the circle is of the form:

(x - 0)²+ (y - 0)² = r²

Since a point on the circle is (1,0), we substitute these values in the equation:

(1 - 0)² + (0 - 0)² = r²

1 + 0 = r²

r² = 1

Therefore, the equation of the circle is:

x² + y² = 1

b) Since the center of the circle is (4,-1), the equation of the circle is of the form:

(x - 4)² + (y - (-1))² = r²

Simplifying the equation, we get:

(x - 4)² + (y + 1)² = r²

Since a point on the circle is (-1,-1), we substitute these values in the equation:

(-1 - 4)² + (-1 + 1)² = r²

(-5)² + 0 = r²

25 = r²

Therefore, the equation of the circle is:

(x - 4)² + (y + 1)² = 25

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The data set is approximately periodic with a period of 3 and an amplitude of about 7.5.

The period is the length of time it takes for the data to repeat itself. In this case, the data repeats itself every 3 hours. The amplitude is the distance between the highest and lowest values in the data set. In this case, the amplitude is about 7.5 cars.

Hour | Number of cars

------- | --------

1     | 90

2     | 52

3     | 76

4     | 75

5     | 91

6     | 104

7     | 89

8     | 105

9     | 119

10    | 103

11    | 121

12    | 135

As you can see, the data repeats itself every 3 hours. The highest value in the data set is 135 cars, and the lowest value is 52 cars. The difference between these two values is 83 cars, which is about 7.5 times the average number of cars (90 cars). Therefore, the amplitude of the data set is about 7.5 cars.

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The wheelchair access ramp must be 216.09 inches long.

To find the length of the wheelchair access ramp, we can use trigonometry.

The tangent function relates the angle of elevation to the ratio of the opposite side (height) to the adjacent side (length of the ramp).

Let's denote the length of the ramp as "x".

The height of the ramp is given as 18 inches.

Using the tangent function:

tan(angle of elevation) = height/length of the ramp

tan(4.8 degrees) = 18/x

To solve for x, we can rearrange the equation:

x = 18 / tan(4.8 degrees)

Using a calculator to evaluate the tangent of 4.8 degrees:

x = 18 / 0.08331

x= 216.09

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We can be performed Multiplication on algebraic expressions in the same way as it can be performed on two whole numbers or fractions.

Multiplication of algebraic expressions or variable expressions involves multiplying two expressions combined with various arithmetic operations like addition, subtraction, multiplication, and division and contains constants, variables, terms, and coefficients.

Multiplying the algebraic equation involves the following steps.

1. Multiply the coefficients of the terms, add the powers of the variables with the same base, and obtain the algebraic sum of the like and unlike terms before learning about the multiplication of algebraic expression.

The multiplication of two terms with the same signs is positive, and two terms with different signs are negative.

Example:

−a×−b=ab

a×−b=−ab

We can add the exponents of the same bases in case of multiplication as a^m×a^n=a^m+n

Example:

a^2×a^3=a^2+3=a^5

b^5×b^8=b^5+8=b^13

Algebraic Expression: An algebraic expression is the collection of the constants and the variables connected by fundamental operators like addition (+), subtraction (−), etc.

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Answer:B

Step-by-step explanation:the answers B because the closed circle is greater that or equal too, and because the inequality is greater than the arrow points to the left. B, the dot is on 7 which if we add that to 18 is 25 which is the greatest number that can work for this inequality making this answer correct.

Hope this helps you understand it!

The value of x from the equation 3x + 4 = 31 and x + 4 = 13 is 9.

3x + 4 = 31

x + 4 = 13

From equation (2)

x + 4 = 13

subtract 4 from both sides

x = 13 - 4

x = 9

Substitute x = 9 into (1)

3x + 4 = 31

3(9) + 4 = 31

27 + 4 = 31

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Answer:

The answer is 245.7

Step-by-step explanation:

7 days in a week. 9 weeks. 9 x 7 = 63.

63 x 3.9 = 245.7