If there are 6 family members in your family and they are all going to skate
4 hours each, it would cost $

Therefore, the equation x^3 - 15x + c = 0 has at most one root in the interval (-2, 2).

To show that the equation x^3 - 15x + c = 0 has at most one root in the interval (-2, 2), we can use the concept of the Intermediate Value Theorem and Rolle's Theorem.

Let's assume that the equation has two distinct roots, denoted as a and b, in the interval (-2, 2). Without loss of generality, we assume a < b.

Since the function is continuous on the closed interval [-2, 2] and differentiable on the open interval (-2, 2), we can apply Rolle's Theorem. According to Rolle's Theorem, there exists a point c in the open interval (a, b) such that the derivative of the function at c is zero.

Consider the derivative of the function f(x) = x^3 - 15x + c:

f'(x) = 3x^2 - 15

Setting f'(c) = 0, we have:

3c^2 - 15 = 0

c^2 - 5 = 0

c^2 = 5

Taking the square root of both sides, we get:

c = ±√5

Now, let's consider the function values at the endpoints of the interval (-2, 2):

f(-2) = (-2)^3 - 15(-2) + c = -8 + 30 + c = 22 + c

f(2) = (2)^3 - 15(2) + c = 8 - 30 + c = -22 + c

If c = √5, then f(-2) = 22 + √5 and f(2) = -22 + √5.

If c = -√5, then f(-2) = 22 - √5 and f(2) = -22 - √5.

In either case, the function values at the endpoints have different signs. This implies that there exists at least one value, say k, in the interval (-2, 2) such that f(k) = 0, according to the Intermediate Value Theorem.

However, we assumed at the beginning that there are two distinct roots in the interval (-2, 2), denoted as a and b. This contradicts our finding that there is at most one root in the interval. Hence, our assumption of having two distinct roots is false.

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If every dimension of a triangular prism is quadrupled, then the surface area will increase by a factor of 16.

Given that,

every dimension of a triangular prism is quadrupled.

We have to find by what factor does the surface area of the prism increase.

Consider a triangular prism.

It consists of two triangular bases and three rectangular faces joining each of the corresponding sides of triangular bases.

Surface area of a triangular prism = area of the triangular bases + Area of the rectangular faces.

Surface area = (bh) + 3(lw)

Here there are 4 dimensions using.

If each of these dimensions are quadrupled,

New surface area = (4b . 4h) + 3 (4l . 4w)

                              = 16 (bh) + 3 (16 lw)

                              = 16 [bh + 3(lw)]

                              = 16 (Area of original prism)

So the surface area increased by a factor of 16.

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Answer:

2

Step-by-step explanation:

Answer: I think it's 9 days.

Step-by-step explanation:

Answer & tep-by-step explanation:

To solve the system of equations using the substitution method, we can solve one of the equations for one variable and substitute that expression into the other equation. We'll solve the first equation for y:

y - 2x = 8

y = 2x + 8

Now we substitute this expression for y into the second equation:

16 + 4x = 2y

16 + 4x = 2(2x + 8)

16 + 4x = 4x + 16

Simplifying, we get:

4x = 0

x = 0

Now we can substitute this value for x into either of the original equations to solve for y. Let's use the first equation:

y - 2x = 8

y - 2(0) = 8

y = 8

Therefore, the solution to the system of equations is (0, 8).

The answer choices given do not match this solution, so there is no correct answer among them.

The statement is false given in the question pointing to the ratio of a pair of corresponding sides is 9/16, under the condition that two similar hexagons have areas 36 sq. inches and 64 sq.inches

Now the ratio of the areas of two given similar polygons is equal to the square of the ratio of their corresponding sides .

Then, if two similar hexagons have areas of 36 square inches and 64 square inches,

Therefore, the ratio of their corresponding sides is

√(64/36) = 4/3

But, the problem gives the ratio of a pair of corresponding sides is 9/16 .

Then,

9/16 ≠ 4/3,

The statement is false given in the question pointing to the ratio of a pair of corresponding sides is 9/16.

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y=6x+6 is the equation of the tangent line to the curve at point (0,6)

In order to fing the equation of tangent of any graph we need 2 things.

i . A point on the graph at which tangent need to be drawn.

ii . Slope a line on that point.

solpe of line = \(y^'\)  =\(\frac{d(y)}{dx}\)

=> d(6\(e^xcosx\))/dx

in order to differentiate the above equation we have to use by parts

=> 6(\(e^xcox-e^xsinx\))

finding the slope at point(0,6)

\(y^'\) = 6*(1*1-1*0)

=>6

so slope is 6

now equation of line with slope 6 and point (0,6)

=> y-6 = 6(x-0)

=> y = 6x+6

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The proportion of a normal distribution that is located in the tail when z = 1.50 is 0.0668. So, the correct option is a.

Here's how to solve the problem:

We are given that z = 1.50.

To find the proportion of a normal distribution that is located in the tail when z = 1.50, we need to use a standard normal distribution table (also known as a z-score table). The table provides the area under the standard normal distribution curve to the left of a given z-score.

Since z = 1.50 is positive, we are interested in the area in the right tail of the standard normal distribution curve. The standard normal distribution table provides the area to the left of a given z-score. Therefore, to find the area in the right tail, we subtract the area in the left tail from 1 (the total area under the curve).

Using the standard normal distribution table, we find that the area to the left of z = 1.50 is 0.9332. Therefore, the area to the right of z = 1.50 (in the right tail) is: 1 - 0.9332 = 0.0668

Thus, the proportion of a normal distribution that is located in the tail when z = 1.50 is 0.0668, which is option (a).

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Answer:

Step-by-step explanation:

i think the answer could be one certain number in particularly advance. ur welcome

The second derivative of v with respect to t, denoted as d²v/dt², is equal to 4

The second derivative of v with respect to t, we will differentiate v twice.

v = 2t² + 7t + 11

First, let's find the first derivative of v with respect to t (dv/dt):

dv/dt = d/dt (2t² + 7t + 11)

Using the power rule of differentiation, we differentiate each term separately:

dv/dt = 2(2t) + 7(1) + 0

dv/dt = 4t + 7

Now, let's find the second derivative of v with respect to t (d²v/dt²):

d²v/dt² = d/dt (4t + 7)

Again, using the power rule of differentiation, we differentiate each term separately:

d²v/dt² = 4(1) + 0

d²v/dt² = 4

Therefore, the second derivative of v with respect to t, denoted as d²v/dt², is equal to 4.

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(A) Circular orbits of stable particles are possible at radii greater than three times the Schwarzschild radius for the non-rotating spherically symmetric mass.

This represents the radius of a black hole's event horizon, within which nothing can escape. The Schwarzschild radius is the event horizon radius of a black hole with mass M.

M can be calculated using the formula: r+ = 2Mwhere r+ is the radius of the event horizon.

(B)  1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ R. This is the required expression.

Tau is the proper time of the particle moving around a circular orbit. Hence, by making use of the formula given above:1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ dt.

(C) Time passes differently in different gravitational fields, and it follows that the period as measured at infinity should be larger than that measured by the particle.

The principle of equivalence can be defined as the connection between gravitational forces and the forces we observe in non-inertial frames of reference. It's basically the idea that an accelerating reference frame feels identical to a gravitational force.

(D) The period of the orbit as measured by an observer at infinity is 16π M^(1/2) and the period of the orbit as measured by the particle is 16π M^(1/2)(1 + 9/64 M²).

The period of orbit as measured by an observer at infinity can be calculated using the formula: T = 2π R³/2/√(M). Substitute the given values in the above formula: T = 2π (8M)³/2/√(M)= 16π M^(1/2).The period of the orbit as measured by the particle can be calculated using the formula: T = 2π R/√(1-3M/R).

Substitute the given values in the above formula: T = 2π (8M)/√(1-3M/(8M))= 16π M^(1/2)(1 + 9/64 M²).

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Answer:

I think it's -4418

Answer:

i think 58, but if not, go to khan academy and watch a video!

Step-by-step explanation:

The scale factor used to create the travel version of the piece is 1: 0.16

0.6 is the scale factor used to reduce the dimensions of the original piece having sides measuring 3 inches each.

Scale factor is calculated by dividing the new reduced scale by original scale. Hence:

0.5/3 = 0.166

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Scale Factor = New Shape Dimension / Original Shape Dimension

Enlarging a small form into a huge one is known as scaling up. Upscaling always uses a scale factor greater than 1. A scale factor 2 means the figure is enlarged twice the original figure's size.

A large number gets scaled down in order to become a smaller one. Scaling down always results in a scale factor less than 1.

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Answer:

\(E =\) \((-3,3)\)

Step-by-step explanation:

Given

Parallelogram: DEFG

\(D(x_1,y_1) = (-2,-4)\)

\(F(x_3,y_3) = (0,7)\)

\(G(x_3,y_4) = (1,0)\)

Required

Find the coordinates of \(E(x_2,y_2)\)

To do this, we make use of mid-point formula which is:

\(M = (\frac{x_1+x_3}{2},\frac{y_1+y_3}{2})= (\frac{x_2+x_4}{2},\frac{y_2+y_4}{2})\)

This gives:

\((\frac{-2+0}{2},\frac{-4+7}{2})= (\frac{x_2+1}{2},\frac{y_2+0}{2})\)

\((\frac{-2}{2},\frac{3}{2})= (\frac{x_2+1}{2},\frac{y_2+0}{2})\)

Multiply through by 2

\(2 * (\frac{-2}{2},\frac{3}{2})= (\frac{x_2+1}{2},\frac{y_2+0}{2})*2\)

\((-2,3) = (x_2+1,y_2+0)\)

\((-2,3) = (x_2+1,y_2)\)

By comparison:

\(-2 = x_2 + 1\) and \(3= y_2\)

So, we have:

\(-2-1=x_2\) and \(3= y_2\)

\(-3 = x_2\) and \(3 = y_2\)

This gives:

\(x_2 = -3\) and \(y_2 =3\)

Hence, the 4th coordinate is: \((-3,3)\)

Answer:

12 skittles are red

Step-by-step explanation:

and easy way to do this on the calculator is 40*0.3 which will give you the number that is the 30%.

Answer:

30

Step-by-step explanation:

because there is 40% and 30% are red so 30

not a 100% sure just trying to help

Answer:

38miles/hour

Step-by-step explanation:

Speed = Distance/Time

According to the question:

Time = 0.75hr

Distance = 28.5

Hence,

Speed = 28.5/0.75

= 38 miles/hr

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the correct option would be b (-2,5/3)

Answer:

y=4x-2

Step-by-step explanation:

Answer:

third expression

Step-by-step explanation:

the surface area (SA) is the area of the 6 faces.

Note that opposite faces are congruent.

the surface area is the the area of each face multiplied by 2 , since they are congruent.

SA = 2(front area ) + 2(side area ) + 2(area of base)

   = 2(5 × 7 ) + 2(4 × 7 ) + 2(4 × 5 ) ← third option

  = 2(35) + 2(28) + 2(20)

 = 70 + 56 + 40

= 166 cm²

Answer:  A. 2 17 /21

Step-by-step explanation:you divide them.You change both mixed number to improper fraction.which is 236  /9  divide  28 /3.You do kcf which stand for KEEP CHANGE FLIP.YOU KEEP 236/9 and change Divide to mulipction sign and flip 28/3 to 3/28.You multiply236  /9  and  28/3 which gives u 708  /252.After that u simply it to 59 /21 .Lastly change back to mix number which is 2 17/21.

Hope it helps bye ;)

The triangle QRS with points Q(8, -4), R(-1, 2), and S(3, 7). After the triangle is reflected across Y axis, then the coordinates of vertex Q are (-8, -4).

How to determine reflection coordinates?

These are the specified parameters:

Q(8, -4), R(-1, 2), and S(3, 7)

Determine the reflected of Q(8, -4) across Y-axis

A(a, b) ⇔ A' (-a, b)

Q(8, -4) ⇔ Q' (-8, -4)

Determine the reflected of R(-1, 2) across Y-axis

A(a, b) ⇔ A' (-a, b)

R(-1, 2) ⇔ R' (1, 2)

Determine the reflected of S(3, 7) across Y-axis

A(a, b) ⇔ A' (-a, b)

S(3, 7) ⇔ S' (-3, 7)

The coordinates of vertex Q after the triangle is reflected across the y-axi are (-8, -4).

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Answer:

8

Step-by-step explanation:

Using the Heron's formula we can find that the total area of the triangle is 84 inches.

Then, to find the height of the triangle, you have to multiply the area by 2 since the formula for the area of a triangle is (h*b)/2

Now, when we multiply 84 and 2 we get 168, so you have to divide 168 by 21 to find 8.

In triangle def, if m∠d is (2x)°, m∠e is (3x − 2)°, and m∠f is (x + 8)°, then the value of x is 29.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Triangle is DEF

if m∠d is (2x)°, m∠e is (3x − 2)°, and m∠f is (x 8)°

We need to find the value of x.

We know that the sum of three angles of triangle is 180 degrees

m∠d + m∠e + m∠f=180°

2x+3x-2+x+8= 180°

6x+6=180

Subtract 6 on both sides

6x=174

Divide by 6 on both sides.

x=174/6

x=29

Hence, the value of x is 29.

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Answer:

:) i have no idea have a good day hope u get it

Step-by-step explanation:

In the equation y = mx + b, the meaning of the m and the b is

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + b

Information gotten from the question include

In the equation y = mx + b

m = ? and b = ?

y = mx + b

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

b = y intercept

therefore m and b are the slope and y intercept respectively

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Answer:

x=20 degrees

Step-by-step explanation:

Line y is a perpendicular bisector making a 90 degree angle with the base of the triangle. The Interior Angle Sum Theorem states that the sum of the interior angles of a triangle is always equal to 180 degrees. Add 70 to 90

70+90=160 degrees

Subtract the sum from 180

180-160=20 degrees

One x is equal to 20 degrees. Both x's are equal to 40 degrees.

Hope this helps. Have a nice day. May it be filled with joy and happiness. Please, stay safe and wash your hands. Happy Holidays.

Answer:

x=20 degrees

Step-by-step explanation:

Tbh I just copied from the other guy I just wanted points thanks :)

slope (m) = 1/2

y-intercept (b) = -3

You use the y-intercept first to find the first point of (0, -3). From there you can use the slope to find the other points.

Age will be 40 years old.

R, in beats per minute, can be approximated by the formulas, where a represents the person's age.

where R= 143 - 0.65a for women.... (1)

and R= 165 - 0.75a for men,..... (2)

So by implementing these two equation we get a = 40

If the sum of ages is X and Y, and the ratio of their ages is p:q, then the age of Y can be calculated using the formula shown below: Y's age = Y's ratio/Sum of ratios x sum of ages The age dependency ratio is the ratio of dependents (people under the age of 15 or over the age of 64) to the working-age population (people between the ages of 15 and 64). The proportion of dependents per 100 working-age population is shown in the data.

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The lighter pumpkin weighs 3.12 kg, and the heavier pumpkin weighs 6.24 kg.

To solve this, we'll use the given information to set up an equation and then solve for the weight of each pumpkin.
Let the weight of the lighter pumpkin be x kg.

Since the heavier pumpkin is twice the weight of the lighter one, its weight would be 2x kg.
The combined weight of both pumpkins is 9.36 kg, so we can write an equation as follows:
x + 2x = 9.36
Now, we'll solve for x:
3x = 9.36
x = 9.36 / 3
x = 3.12 kg
Now that we have the weight of the lighter pumpkin (x = 3.12 kg), we can find the weight of the heavier pumpkin:
2x = 2(3.12) = 6.24 kg.

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