Rachel can walk 2.5 miles in 40 minutes at this rate how far can she walk in one hour

Answer:

the ant would have traveled 2.045 miles

The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

1. Start with the given equation: 2-3cos(x) = 5+3cos(x).

2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.

3. Combine like terms: 2-6cos(x) = 5.

4. Subtract 2 from both sides: -6cos(x) = 3.

5. Divide both sides by -6: cos(x) = -1/2.

6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.

7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.

8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.

9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

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Answer:

Find the graph that has (2,0)

Step-by-step explanation:

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

+ x          +x

\(\frac{3}{2}x - 1 = 2\)

\(2(\frac{3}{2}x - 1 = 2)\)

3x - 2 = 4

    + 2   + 2

3x = 6

/3   /3

x = 2

Your image is blurry, but the point that has (2,0)

Hope that helps!

Not all linear transformations have a matrix representation. A counter-example is a linear transformation that changes the dimension of the vector space.

What is Linear transformation?

The function g(x) is a linear transformation if each term of each component of g(x) is a number times one of the variables.

For example, consider the linear transformation T: R^2 -> R^3 defined by:

T(x, y) = (x, y, 0)

This transformation maps each point in the xy-plane to a point in the x,y,z-space with z-coordinate 0. It is a linear transformation, since it preserves addition and scalar multiplication. However, it cannot be represented by a matrix, since it changes the dimension of the vector space.

The theorem that establishes the existence of a matrix representation for every linear transformation is known as the matrix representation theorem. It states that every linear transformation from a finite-dimensional vector space to another finite-dimensional vector space can be represented by a matrix with respect to suitable bases of the vector spaces. However, it does not apply to linear transformations that change the dimension of the vector space.

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Answer:

A

Step-by-step explanation:

\(f(x) ~ \mathsf{has ~(1,1)~ in ~it, ~so ~the ~answer~ is ~ \boxed{A}}\).

Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

A sample is only a small portion of the population.

Let's imagine you were interested in determining the average income for all Americans in your population.

Instead of knocking on every door in America because of time and money constraints, you decide to ask 1,000 random people. Your sample consists of these a thousand persons.

Given, A gardener wants to determine which of two brands of fertilizer is best for the plants.

And the gardener decides to conduct an experiment using 28 individual plants.

Plan A will be a biased sampling and the experiment would not yield

desired results.

Therefore, The gardener should choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

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Step-by-step explanation:

"Determine the number and type of roots for the equation using one of the given roots. Then find each root. (inclusive of imaginary roots.)"

Given one of the roots, we can use either long division or grouping to factor each cubic equation into a binomial and a quadratic.  I'll use grouping.

Then, we can either factor or use the quadratic equation to find the remaining two roots.

1. x³ − 7x + 6 = 0; 1

x³ − x − 6x + 6 = 0

x (x² − 1) − 6 (x − 1) = 0

x (x + 1) (x − 1) − 6 (x − 1) = 0

(x² + x − 6) (x − 1) = 0

(x + 3) (x − 2) (x − 1) = 0

The remaining two roots are both real: -3 and +2.

2. x³ − 3x² + 25x + 29 = 0; -1

x³ − 3x² + 25x + 29 = 0

x³ − 3x² − 4x + 29x + 29 = 0

x (x² − 3x − 4) + 29 (x + 1) = 0

x (x − 4) (x + 1) + 29 (x + 1) = 0

(x² − 4x + 29) (x + 1) = 0

x = [ 4 ± √(16 − 4(1)(29)) ] / 2

x = (4 ± 10i) / 2

x = 2 ± 5i

The remaining two roots are both imaginary: 2 − 5i and 2 + 5i.

3. x³ − 4x² − 3x + 18 = 0; 3

x³ − 4x² − 3x + 18 = 0

x³ − 4x² + 3x − 6x + 18 = 0

x (x² − 4x + 3) − 6 (x − 3) = 0

x (x − 1)(x − 3) − 6 (x − 3) = 0

(x² − x − 6) (x − 3) = 0

(x − 3) (x + 2) (x − 3) = 0

The remaining two roots are both real: -2 and +3.

"Find all the zeros of the function"

For quadratics, we can factor using either AC method or quadratic formula.  For cubics, we can use the rational root test to check for possible rational roots.

4. f(x) = x² + 4x − 12

0 = (x + 6) (x − 2)

x = -6 or +2

5. f(x) = x³ − 3x² + x + 5

Possible rational roots: ±1/1, ±5/1

f(-1) = 0

-1 is a root, so use grouping to factor.

f(x) = x³ − 3x² − 4x + 5x + 5

f(x) = x (x² − 3x − 4) + 5 (x + 1)

f(x) = x (x − 4) (x + 1) + 5 (x + 1)

f(x) = (x² − 4x + 5) (x + 1)

x = [ 4 ± √(16 − 4(1)(5)) ] / 2

x = (4 ± 2i) / 2

x = 2 ± i

The three roots are x = -1, x = 2 − i, x = 2 + i.

6. f(x) = x³ − 4x² − 7x + 10

Possible rational roots: ±1/1, ±2/1, ±5/1, ±10/1

f(-2) = 0, f(1) = 0, f(5) = 0

The three roots are x = -2, x = 1, and x = 5.

"Write the simplest polynomial function with integral coefficients that has the given zeros."

A polynomial with roots a, b, c, is f(x) = (x − a) (x − b) (x − c).  Remember that imaginary roots come in conjugate pairs.

7. -5, -1, 3, 7

f(x) = (x + 5) (x + 1) (x − 3) (x − 7)

f(x) = (x² + 6x + 5) (x² − 10x + 21)

f(x) = x² (x² − 10x + 21) + 6x (x² − 10x + 21) + 5 (x² − 10x + 21)

f(x) = x⁴ − 10x³ + 21x² + 6x³ − 60x² + 126x + 5x² − 50x + 105

f(x) = x⁴ − 4x³ − 34x² + 76x − 50x + 105

8. 4, 2+3i

If 2 + 3i is a root, then 2 − 3i is also a root.

f(x) = (x − 4) (x − (2+3i)) (x − (2−3i))

f(x) = (x − 4) (x² − (2+3i) x − (2−3i) x + (2+3i)(2−3i))

f(x) = (x − 4) (x² − (2+3i+2−3i) x + (4+9))

f(x) = (x − 4) (x² − 4x + 13)

f(x) = x (x² − 4x + 13) − 4 (x² − 4x + 13)

f(x) = x³ − 4x² + 13x − 4x² + 16x − 52

f(x) = x³ − 8x² + 29x − 52

Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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Answer:

for x is 8 and for y is 20

Step-by-step explanation:

because i subtitute and then you multiply and you divide and thats how you get your answer i hope it helps:)

Answer:

0 ≤ < 2

Step-by-step explanation:

Answer:1.02 5.27 are correct

Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):

3u^2 + 6u - 4 = 0

Now we can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 3, b = 6, and c = -4. Substituting these values, we get:

u = (-6 ± sqrt(6^2 - 4(3)(-4))) / 2(3)

u = (-6 ± sqrt(84)) / 6

u = (-3 ± sqrt(21)) / 3

Therefore, either:

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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The mean is approximately 1.67 units of rainfall. The median is 2 units of rainfall.

In statistics, the median is a measure of central tendency that represents the middle value of a set of data. Specifically, it is the value that separates the upper half of the data from the lower half when the data is arranged in order from smallest to largest (or vice versa).

Looking at the line plot, we can see that there are two values marked with a single asterisk and four values marked with two asterisks. Since each asterisk represents a certain amount of rainfall, we can interpret this as follows:

The two values marked with a single asterisk are each 1 unit of rainfall.

The four values marked with two asterisks are each 2 units of rainfall.

Therefore, the data represented in this line plot is as follows:

1, 1, 2, 2, 2, 2

To find the center of this data, we can calculate the mean and median.

The mean is calculated by adding up all the values and dividing by the total number of values. In this case, we have:

(1 + 1 + 2 + 2 + 2 + 2) / 6 = 10 / 6 = 1.67

So the mean is approximately 1.67 units of rainfall.

The median is the middle value when the data is arranged in order. In this case, the data is already in order, so we just need to find the middle value:

The middle value is the average of the two middle numbers:

(2 + 2) / 2 = 2

So the median is 2 units of rainfall.

Based on these calculations, we can conclude that the BEST way to describe the center of the data represented in this line plot is by the median, which is 2 units of rainfall. Therefore, the correct option to complete the statement is:

"The median is 2 inches."

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Answer:

x<_-5

Step-by-step explanation:

-4(x+3)<_-2-2x

-4x-12<_-2-2x

-4x+2x<_-2+12

-2x<_10

-2x/-2<_10/-2

x<_-5

Answer:

i think that $19980 is the answer

Step-by-step explanation:

i hope it will help u

Answer:

0.72% per month

Step-by-step explanation:

I looked it up!

Answer:

Direct materials

Step-by-step explanation:

In this case we must bear in mind that as more products are sold, more material is needed to manufacture those additional final products

.

Therefore, in this case the cost would be related mainly to the materials, mainly the direct materials, since they are essential in the production of the product.

Answer:

hi! once you link the picture I will answer the problem.

Step-by-step explanation:

Answer: The distance between the library and the florist’s shop is the length of C⁢D¯. The endpoints of this line segment are C(3, 4) and D(3, -3). Because the x-coordinates of both points are the same (3), the length of C⁢D¯ can be found by subtracting the smaller y-coordinate from the greater y-coordinate: CD = 4 – (-3) = 4 + 3 = 7 units. The distance between the library and the florist’s shop is 7 blocks.

Step-by-step explanation: sample answer

Liu will earn $472 on an investment of $1298.

Given, Liu earned $316 on an investment of $869.

We have to find how much he would earned if he invest $1298 in the same investment.

Now, $869 investment = $316 earned

$1 investment = 316/869 earned

$1298 investment = 316/869 × 1298 earned

$1298 investment = $472 earned

Hence, Liu will earn $472 on an investment of $1298.

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The solution to the system of equation is dependent and x = 20, y = -15 and z = -3

x+y+ z= 2

3x+4y- z=3

3x + 4y -2z = 6

Multiply (1) by -1 and subtract (1) from (2) to eliminate z

-x - y - z = -2

3x+4y- z=3

4x + 5y = 5

Then multiply (2) by 2 and subtract (3) from it to eliminate z

6x + 8y - 2z = 6

3x + 4y -2z = 6

3x + 4y = 0

4x + 5y = 5

3x + 4y = 0

Multiply 4x + 5y = 5 and 3x + 4y = 0 by 3 and 4 respectively

12x + 15y = 15

12x + 16y = 0

Subtract

16y - 15y = 0 - 15

y = -15

Substitute y = 15 into

12x + 16y = 0

12x + 16(-15) = 0

12x - 240 = 0

12x = 240

divide both sides by 12

x = 20

From (1)

x+y+ z= 2

20 + (-15) + z = 2

20 - 15 + z = 2

5 + z = 2

z = 2 - 5

z = -3

Therefore, x = 20, y = -15 and z = -3.

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Answer: line segment ab

Step-by-step explanation:ye

9514 1404 393

Answer:

  (-16, -12), (16, -12)

Step-by-step explanation:

The given values (side length and hypotenuse) have the ratio ...

  12 : 20 = 3 : 5

This suggests that the triangle formed by the axes and the point 20 units from the origin is a 3-4-5 triangle, and the remaining side is 16 units from the y-axis. That means the points of interest are ...

  (-16, -12) and (16, -12)

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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Answer:

Yes, it is realistic to have 3 owners that spend 720$ a year on their pets

Step-by-step explanation:

See graph

Answer:

  XY is tangent to circle Z

Step-by-step explanation:

You want to know if segment XY, measuring 3.6 units, is tangent to circle Z at point X. Segment YZ has length 1.8 units outside the circle, which has radius 2.7 units.

If the triangle XYZ is a right triangle, then we have ...

  XY² +XZ² = YZ²

  3.6² +2.7² = (1.8 +2.7)²

  12.96 +7.29 = 20.25 . . . . . true

Segment XY is a tangent.

If segment YZ is extended across the circle, the lengths of the segments from Y to the circle intersection points are 1.8 and (1.8 +2·2.7) = 7.2. The relation between the secant and the "tangent" will be ...

  3.6² = (1.8)(7.2) . . . . . true

This means XY is a tangent.

Answer:

6

Step-by-step explanation:

The function N(t)=t2−8t−1, for evaluating N(6) will be -13.

A function is the rule which assigns a unique output value for each input value. The input values are typically called the domain of the function, and the output values are called the range of the function.

To evaluate means to find the value of an expression or a function at a particular point or set of points. This typically involves substituting given values for any variables in the expression or function and then simplifying or solving the resulting equation to obtain a numerical result.

To evaluate N(6), we substitute t = 6 into the expression for N(t);

N(6) = 6² - 8(6) - 1

Simplifying;

N(6) = 36 - 48 - 1

N(6) = -13

Therefore, N(6) = -13.

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The equation of the line is: y + 3 = -6(x + 2) [point-slope form] or y = -6x - 15 [slope-intercept form].

Given a point (-2, -3) and a slope (m) of -6, you can write the equation of the line in point-slope form by substituting (a, b) = (-2, -3) and m = -6 into y - b = m(x - a):

y - (-3) = -6(x - (-2))

y + 3 = -6(x + 2) [point-slope form]

Rewrite in slope-intercept form as:

y + 3 = -6(x + 2)

y + 3 = -6x - 12

y = -6x - 12 - 3

y = -6x - 15 [slope-intercept form]

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Answer:

1 real root   2 imaginary roots

Step-by-step explanation:

f(x) = x^3 + 5x^2 + x + 5

Set equal to zero to find the zeros

0  = x^3 + 5x^2 + x + 5

Factor by grouping

0 = x^2( x+5)  + 1( x+5)

0 = (x+5) ( x^2+1)

Using the zero product property

x+5 =0    x^2+1 =0

x=-5    x^2 = -1

x=-5    x = ±i

1 real root   2 imaginary roots

Answer:

1 real root   2 imaginary roots

Step-by-step explanation:

f(x) = x^3 + 5x^2 + x + 5

Set equal to zero to find the zeros

0  = x^3 + 5x^2 + x + 5

Factor by grouping

0 = x^2( x+5)  + 1( x+5)

0 = (x+5) ( x^2+1)

Using the zero product property

x+5 =0    x^2+1 =0

x=-5    x^2 = -1

x=-5    x = ±i

1 real root   2 imaginary roots

Answer:

(6,4)

Step-by-step explanation:

slope (rise over run) is 4/1

go up 4 and right 1

2 (x) + 4 = 6

3 (y) + 1 + 4