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ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

The product of 9 and Jenny's age 15 is 135.

So, let the missing value be 'x'.

Then,

Therefore, the product of 9 and 15 is 135.

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The answer is:

( - 179 – 78 ) + 41 - ( - 165 )

=-51

Answer:

(-257) +41+165

-257+206

-51

Answer: A

Step-by-step explanation: The dot is a filled-in circle, meaning it has to be A, B, or E. Then, B is saying that the arrow is going left, so that's wrong. E is saying that it is just 6 instead of -6, which leaves us with A.

hope this helps!

please give brainliest!

Answer:

91°

Step-by-step explanation:

180° in a triangle; so

31+58=89

180-89=91

BC=91°

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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No, it is not a regular polygon.

A hexagon is a six sided polygon. And a convex hexagon means, the hexagon's vertices are pointed outwards.

And no interior angle has an angle measure more than 180°.

Given:

A polygon.

To be a regular polygon:

Given Hexagon,

should have equal sides and equal angles.

We have no information about the angles and sides.

Therefore, it is not a regular polygon.

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answer: Equation of line is : Y = mx +b

 Y intercept is origin ( 0,0)

Therefore :

  Y = 6/5 X

All lines passing through origin have equation:

 Y = mX

Answer: y= 2x/5 -2

Step-by-step explanation:

y=mx+b

y=2/5x + (-2)

y=2x/5 -2

Given:

Answer:

Step-by-step explanation:

5x + 9 = 3x + 11 ( Alternate angles )

5x - 3x = 11 - 9

2x = 2

x = 2/2

x = 1

Hope this helps

plz mark as brainliest!!!!!

Answer:

$12.40

subtract 12.80 from 50 to get 37.20 then divide by 3

Answer:

A

Step-by-step explanation:

The relation is not a function. All you need to solve this problem is the following: Relations are NOT functions when the domain values repeat!

Note: The domain is the set of input values. The domain is x, the first number in the pair. For example, in the pair (0, 2), the domain is 0.

In the relation {(0,2),(2,4),(1,7),(2,5)}, 2 is repeated two times, which, by definition, means that the relation is not a function.

Answer: (-10,4) and (0,4)

Step-by-step explanation:

the endpoints need to be equidistant from the midpoint (-5,4).

(-10,4) is 5 spaces to the left

(0,4) is 5 spaces to the right

5=5 so equidistant

The length of the side of the square is given as follows:

20 cm.

In the figure, there are two expressions used to give the side length to each square, as follows:

In a square, all the four side lengths have the same length, hence the value of x is obtained as follows:

6x - 1 = 4x + 6

2x = 7

x = 3.5 cm.

Then the side length of the square is obtained as follows:

6(3.5) - 1 = 20 cm.

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Answer:

2/3 divided by 4 = .16

Step-by-step explanation:

This problem is pretty simple. Since we cannot divide this we can change the division sign into a multiplication, but to do this we need to also take the reciprocal of 2/3, which means we flip th number so it becomes 3/2. Now we can simply multiply. (1/4)*(3/2) which should give you 3/8

Answer:

x > -3

Step-by-step explanation:

-3x + 6 < 15

-3x < 15 - 6

-3x < 9

-x < 3

x > -3

A. x > -3

Step-by-step explanation:

Step 1: Subtract 6 from both sides.

−3x + 6 − 6 < 15 − 6

−3x < 9

Step 2: Divide both sides by -3.

−3x/−3 < 9/−3

x > −3

Answer:84

Step-by-step explanation:

Answer:

84 hamburgers were sold

EXPLANATION

Given the expression 2y -3x = 18

Adding +3x to both sides:

2y = 3x + 18

Dividing both sides by 2:

y = (3/2)x + 18/2

Simplifying:

y = (3/2)x + 9 [SLOPE-INTERCEPT FORM]

Hence, we have the slope-intercept form :

where m=slope=(3/2) and b=y-intercept=9

Answer:

B. 15

Step-by-step explanation:

The first quartile of a box plot is indicated at the first point of the main box. Hope it helps!

The first quartile in the box plot is 15

Option B is the correct answer.

An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.

W can find the values of the upper and lower quartile and median from a box plot.

The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.

The formula used is Upper quartile - Lower quartile.

We have,

From the box plot,

Median = 20

First quartile = 15

Third quartile = 35

Now,

The first quartile, denoted as Q1, is a measure of central tendency that divides a dataset into four equal parts.

It is the value that separates the lowest 25% of the data from the rest of the data.

Thus,

The first quartile is 15

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The volume of the slick would be 25 cubic feet after 60 mins/

Consider the volume of the slick is roughly given as:

V(r) = 0.08\(\pi r^2\)

r is the radius of the slick in feet

And r(t) = 0.5t

V(r(t)) = V(0.5t)

= 0.08\(\pi\)(0.5t)^2

= 0.02\(\pi t^2\)

Recall the volume is 225ft^3

225 =  0.02\(\pi t^2\)

Make t subject formula

t = 60 mins.

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Answer:

Step-by-step explanation:

Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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(1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

Given are the polynomials,

1) x² - 2 x - 8

Factors = (x+2)(x-4)

2) x² + 2 x - 8

Factors = (x-2)(x+4)

3) x²-2x-4 = There will be no integral root.

4) x²+2x-4 = There will be no integral root.

Hence the (1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

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After answering the presented questiοn, we can cοnclude that The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape

An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpοse οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.

The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape. Here are sοme cοmmοn fοrmulas:

1. Rectangle:

• Area: A = length x width

• Perimeter: P = 2(length + width)

2. Square:

• Area: A = side x side (οr A = side²)

• Perimeter: P = 4 x side

3. Circle:

• Area: A = π x radius²

• Circumference (perimeter): C = 2π x radius (οr C = π x diameter)

4. Triangle:

• Area: A = (base x height) / 2

• Perimeter: P = side1 + side2 + side3

5. Trapezοid:

• Area: A = ((base1 + base2) x height) / 2

• Perimeter: P = side1 + side2 + side3 + side4

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The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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The values of x that make the expression undefined are 0 and 2

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

Volume = 5 - x

Width = x - 2

Height = 5 - x/x(x -2)

Introduce brackets to the height expression to differentiate between the numerator and the denominator

So, we have

Height = (5 - x)/x(x -2)

The question implies that we calculate the domain

Set the denominator to 0

This gives

x(x - 2) = 0

So, we have

x = 0 or x - 2 = 0

Solve for x

x = 0 or x = 2

This means that the undefined height value of x are 0 and 2

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I assume you're asking what this expression is to the second power.

(8*100)^2=(8*10)^2

Simplify

8 squared = 64

100 squared = 10000

8 squared = 64

10 squared = 100

Result:

64 + 10000 = 64 + 100

8x100=8x10 is false

Answer:

how many cans?

Step-by-step explanation:

Answer:

Hope this helps ;)

Step-by-step explanation:

To find the time it takes the T-shirt to reach its maximum height, we need to find the value of t when the velocity of the T-shirt is zero, because at this point the T-shirt has reached its maximum height and starts falling back down. We can find the velocity of the T-shirt by taking the derivative of the height equation with respect to time:

v(t) = h'(t) = 72

The velocity of the T-shirt is a constant 72 feet per second, so it will never reach a velocity of zero and will never reach its maximum height. The T-shirt will keep going up indefinitely.

If the problem had specified that the T-shirt was launched with an initial upward velocity of -72 feet per second (meaning it was launched downward), then we could have found the time it takes the T-shirt to reach its maximum height by setting v(t) = 0 and solving for t. In this case, we would find that t = 1, so it would take the T-shirt 1 second to reach its maximum height. The maximum height would be h(1) = -16 + 72(1) + 6 = 62 feet.