Determine the rate of change from the graph.
On a coordinate plane, a line with positive slope goes through points (negative 3, 0) and (negative 1, 4).
The rate of change shown in the graph is .

Answer:

x = -10

Step-by-step explanation:

5 (x + 8) = -10

5x + 40 = -10

5x = -50

x= -10

Answer:

x= -10

Step-by-step explanation:

5(x+8)=-10

5x+40=-10

move the 40 to the other side

5x=-10-40

5x= -50

divide 5 by both sides to get rid of the x.

x=-10

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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The midsegment is equal to the average of the lengths of the bases, so:

Where:

and

Therefore:

Answer:

i hope 67° is the answer .

Answer:

The number line is attached below.

Step-by-step explanation:

The number to be plotted on the number line is:

\(x=-1\frac{7}{8}\)

The value of x lies between -2 and 0.

Draw a number line from -2 to 0 with intervals at every one-eight value.

Mark the point at \(x=-1\frac{7}{8}\).

The number line is attached below.

The total surface area of the prism is 204 cm²

Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross-sections. The faces of the prism are parallelograms or rectangles without the bases.

Given here: A prism with triangular base with three of its faces as rectangle and its bases triangles.

Thus total surface area is the sum of areas of all these 5 faces

TSA= Sum of the area of the two slanted rectangles + Sum of the two bases + the sum of the rectangle the prism is resting on in the figure

Now dimensions of the slanted rectangles are given by length =12 and breadth =5 and the dimensions of the last rectangle are length =12 and breadth = 6

∴ TSA= 2×12×5 +1/2 ×6×4 +12×6

         = 120+12+72

        =204 cm²

Hence, The total surface area of the prism is 204 cm²

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Answer:

1+6v

Step-by-step explanation:

1+5v+v

1+6v add the 5v and v

Answer:

C. 31 kilometers north of its starting location

Step-by-step explanation:

Please see attached a rough sketch of the situation for your reference.

Step one:

Displacement North= 57km

Displacement South= 26km

Required

The  final displacement

The current position is attained by subtracting 26km from 57km

=57-26= 31km

Therefore the current position is

C. 31 kilometers north of its starting location

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

The 22 degree angle is opposite to the 10 m side of the right triangle.

We need to find the length x of the hypotenuse.

Use trigonometry:

Answer:

PLEASE HELP!!!!! 100 points!!!

The angle of elevation from an anchor to the top of a flag pole is 22 If the pole is

10 meters high, how long does the wire connecting the anchor to the pole must be?

(Round answer to the 1st decimal place.)

Answer:

a ≈ 3.009075116

Step-by-step explanation:

cos(α) = adj/hyp

cos(53°) = a/5

a = 5 * cos(53°)

a ≈ 3.009075116

Milliliters can be converted into milligrams by a specific formula: Milliliters x Density = Milligrams. Density of a substance vary with different temperature and other factors.

Milliliters and milligrams are two different units of measurement used for different types of substances. Milliliters measure volume, while milligrams measure weight. To convert milliliters to milligrams, you need to know the density of the substance in question. The formula for this conversion is as follows:

Milliliters x Density = Milligrams

It is important to note that the density of a substance can vary depending on its temperature and other factors, so it is always best to double-check the density before making any conversions.

For example, if you have 10 milliliters of a substance with a density of 2 grams per milliliter, the calculation would be:

10 ml x 2 g/ml = 20 mg

In other words, the conversion of  10 milliliters of this substance would weigh 20 milligrams.

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Answer:

524.30

Step-by-step explanation:

No, it is not required to be accurate. The growth rates of the two functions can vary.

It's not necessary for log f(n) to equal log g(n). Depending on the equation's constants and the inputs to the two functions, the growth rates of the two functions may differ. For instance, log f(n) = 2 log n and log

g(n) = 3 log n,

which are not equal, if

f(n) = n2 and g(n) = n3.

In this instance, log f(n) is equal to (log n) and log g(n) to (log n3), indicating that the two functions grow at various rates. Likely not equal are log f(n) and log g(n) if

f(n) = n and g(n) = n2,

respectively. Log f(n) is defined as (log n) and log Therefore, the statement "log f(n) = (log g(n)" is not necessarily true.

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Answer:

98

Step-by-step explanation:

97 is prime, so its only factors are 1 and 97, which add to 98.

Answer:

5 ^15

Step-by-step explanation:

(5 ^3)^5 =5 ^(3×5)=5 ^15

The rule used is (a^b)^c = a^(b*c)

If you raise some exponential expression to another exponent, then you multiply the exponents. You keep the base the same.

In this case, a = 5, b = 3, c = 5.

Using a calculator,

5^15 = 30,517,578,125

But it's likely your teacher will want you to keep the answer in exponential form since it's easier to work with.

Answer:

c. 5

Step-by-step explanation:

1.5m = 1.5*100 cm = 150 cm

Divide 150 cm by 30 cm,

150/30 = 5

Answer: 7 Inches left

Step-by-step explanation:

1 foot is 12 inches

12 inches minus 5 = 7

subtract the 2 feet from 3

7 inches left

(0,0) is a saddle point and (1,1) is a local minimum.

From the contour map, the level curves intersect at (0,0) . Hence (0,0) is a saddle point.

and the center of level curve 3.2 (1,1) is a local minimum.

Hence (0,0) is a saddle point and (1,1) is a local minimum.

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Answer:

3/4

or

0.75

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

The expression to represent the new area of the garden after changes will be  N = x² + 20x + 84

A rectangular garden with the dimensions in terms of x is mentioned.

Dimensions length and width have a relation between them.

Taking Width as 'x', It is said that the length of the original garden is 8 feet more than its width. Length = x +8. To calculate the area of the original garden we have the formula for the Area of the rectangle: Length * Width

for the original dimensional garden, the Expression for Area will be :

                 => A = L * W    => A = (x+8)*x

                 =>  A = x² + 8x

Now when the Dimensions of the garden are extended by 6 feet :

L = (x+8+6)  =>  L = x + 14

W = (x+6)

Expression for the modified Area of the Garden will be :

                   =>  N = (x+14)*(x+6)  =>  x² + (14+6)x + 14*6   {using identity}

                   =>  N = x² + 20x +84

Hence, the expression for the new Area will be N = x² + 20x +84

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Answer:

Scale drawing is Larger

Step-by-step explanation:

There are 10mm in one cm, so scale drawing is larger than original by factor of 10.

Answer:

$55.58

Step-by-step explanation:

First off turn your percent to decimals then times it by 45 like this

45 x 0.18 = 8.10

45 x 0.055 = 2.475 - 2.48 (round this one up)

Now add them all together

45 + 8.10 + 2.48 = 55. 58

ANSWER: $55.58

The change in profit (ΔP) when the number of units (Δx) increases by 5, based on the given marginal profit function, is -18331.50

To find the change in profit (ΔP) when the number of units (Δx) increases by 5.

we need to evaluate the marginal profit function and multiply it by Δx.

The marginal profit function is given by dP/dx = 12.1(60 - 3x).

We are given the value of x as 121, so we can substitute it into the marginal profit function to find the marginal profit at that point.

dP/dx = 12.1(60 - 3(121))

= 12.1(60 - 363)

= 12.1(-303)

= -3666.3

Now, we can calculate the change in profit (ΔP) by multiplying the marginal profit by Δx, which is 5 in this case.

ΔP = dP/dx×Δx

= -3666.3 × 5

= -18331.5

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The correct option that is logically equivalent to the statement "It is necessary for me to have a driver's license in order to drive to work" is "If I don't have a driver's license, then I won't drive to work."Explanation: Logically equivalent statements are statements that mean the same thing. Given the statement "It is necessary for me to have a driver's license in order to drive to work," the statement that is logically equivalent to it is "If I don't have a driver's license, then I won't drive to work. "The statement "If I don't drive to work, I don't have a driver's license" is not logically equivalent to the given statement. This statement is a converse of the conditional statement. The converse is not necessarily true, so it is not equivalent to the original statement. The statement "If I have a driver's license, I will drive to work" is also not logically equivalent to the given statement. This statement is the converse of the inverse of the conditional statement. The inverse is not necessarily true, so it is not equivalent to the original statement.

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So, the basketball player needs to shoot the ball with a velocity of u so that the maximum height attained by the ball is 10.0625 feet.

Given, A basketball player shoots a foul shot, releasing the ball at a 45-degree angle from a position 6 feet above the floor, then the path of the ball can be modeled by the quadratic function,

h(x) = -0.005x² + 0.45x + 6

Here, the ball has released at an angle of 45 degrees, then the vertical velocity (v) and horizontal velocity (u) can be given as:

v = usinθ = ucosθ = gt...

As the projectile motion is a 2-D motion]where t is the time, g is the acceleration due to gravity.

As the maximum height is attained at the mid of the total time taken, thus the time taken to attain the maximum height (H) can be given as:

H = u sin(θ)/g

So, H = u/g [Here, sin(θ) = 1/root2]

Also, The total time (T) of flight can be given as:

T = 2u sinθ/g

We can calculate the value of T using the formula above.

T = 2u sinθ/g

= 2u(1/root2)/g

= u/g√2

Now, Let's put the value of T in the quadratic equation of the path of the ball,h(x)

= -0.005x² + 0.45x + 6h(x)

= -0.005(x² - 90x) + 6h(x)

= -0.005(x²- 90x + 2025 - 2025) + 6h(x)

= -0.005((x - 45)²- 1012.5) + 6h(x)

= -0.005(x - 45)² + 10.0625

As the vertex of the parabola represents the maximum height, thus the maximum height (H) can be given as, H

= 10.0625 feet

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Answer:

Step-by-step explanation:

diagonal  = 32 cm

Area of square = \(\dfrac{d^{2}}{2}\)

                        \(=\dfrac{32*32}{2}\\\\=512 \ cm^{2}\)

Diagonal separate the square into two equal triangles.

Area of upper triangle that is shaded black = area of lower triangle = 512/2

= 256 cm²

Isosceles triangle:

a = 6 cm  ; b = 6 cm c = 8cm

\(s = \dfrac{a+b+c}{2}\\\\=\dfrac{6+6+8}{2}\\\\=\dfrac{20}{2}\\\\=10\\\\s-a = 10 - 6 = 4 \ cm\\\\s-b = 10-6 = 4 \ cm\\\\c - c = 10 - 8 = 2 \ cm\\\\Area = \sqrt{s*(s-a)(s-b)(s-c)}\\\\=\sqrt{10*4*4*2}\\\\=\sqrt{2 * 2 * 4 * 4 * 5}\\\\=4*2\sqrt{5}\\\\=8\sqrt{5}\\\\=8*2.24\\\\=17.92 \ cm^{2}\)

Area of black shade paper = 256 + 17.92 =  273.92 cm²

Area of white shade paper = 256 cm²

Area of the isosceles triangle = s(s-a)(s-b)(s-c)

Answer:

Step-by-step explanation:

Number of boys = g - 7.

g - 7 + g = 23

2g = 30

g = 15.

The are 15 girls in the class.

Answer: g-7

Step-by-step explanation:

g = number of girls in the club

b = number of boys in the club.

There are 7 more girls than boys in the club, therefore

g = b + 7            

Subtract 7 from each side.

g - 7 = b + 7 - 7

g - 7 = b

That is,

b = g - 7

Answer:  g - 7

Answer:

diagram B

Step-by-step explanation:

all complementary angles have one right angle in it.

Answer:

12 mph

Step-by-step explanation:

Given that:

Total distance traveled = 78 miles

Time taken, t = 6 hours

Average speed for first 30 miles = 15 mph

Time taken = distance / speed

Time taken = 30 / 15

Time taken = 2 hours

Average speed for last 48 miles = x

Time taken to travel last 48 miles = (6 - 2) = 4 hours

Average speed for last 48 miles :

Distance traveled / time taken

48 miles / 4 hours

= 12 mph

If in  triangle ABC, EG = x inches and BG = (5x - 12) inches, the length of EB is 7x - 12 inches.

In triangle ABC, the centroid G is the point of intersection of the three medians AD, BE, and CF. We are given that EG = x inches and BG = (5x - 12) inches. We need to find the length of EB.

We can use the fact that the centroid G divides each median in the ratio of 2:1. Let M be the midpoint of AC, and let N be the midpoint of BC. Then, we have:

BE/EN = 2/1

Using this proportion, we can solve for EB as follows:

BE/EN = 2/1

BE/(BN + EN) = 2/1

BE/((5x - 12)/2 + x) = 2/1 (substituting BN = (5x - 12)/2 and EN = x)

BE/(7x/2 - 6) = 2/1

BE = 2(7x/2 - 6)

BE = 7x - 12

In conclusion, we can use the fact that the centroid divides each median in the ratio of 2:1 to find the length of EB in triangle ABC. We can solve for the unknown using a proportion and the lengths of the medians that pass through it.

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Complete question is:

Answer:

12

Step-by-step explanation:

i got it right