A ski club rents cross-country skis. The table below shows the cost of rentals for two and four days. Number 1 2 3 of Days Rented Rental Cost ($) 12 17 22 27 Which explicit formula models the cost of renting skis from the club? o an . = 12 + 5n O an . 10n An = 5 + 5n O an an = 7+5n​

A dilation or combination of stiff movements and dilations constitutes a similarity transformation.

Similar figures don't always have to have the same size but share the same form.

A transition called a dilation keeps shape but not size. So a dilatation is a motion that is not rigid. A dilation or combination of stiff movements and dilations constitutes a similarity transformation. If and only if a similarity transformation translates one of the geometric figures onto the other, then two figures are said to be similar. Similar figures don't always have to have the same size but share the same form.

Similarity transformations include translation, reflection, rotation, and dilation. Rotation, reflection, and translation retain both size and form since they are rigid movements, whereas dilation just makes sure that the shape is preserved.

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Answer:

In mathematics, a linear equation is an equation that may be put in the form {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}+b=0, } where x_{1}, \ldots, x_{n} are the variables, and {\displaystyle b, a_{1}, \ldots, a_{n}} are the coefficients, which are often real numbers.

Step-by-step explanation:

Answer:

8411.67 m³

Step-by-step explanation:

The volume of a pyramid is one third its height times the area of its base. The Louvre pyramid has a height of 20.6 meters and a square base with sides of 35 meters. Find its volume, rounded to the nearest hundredth. Include units in your answer.

Volume of a pyramid is given as:

1/3 × Height × Area of it's base

= 1/3 × 20.6m × (35 m)²

= 8411.6666667 m³

Approximately = 8411.67 m³

Therefore, the volume of the pyramid = 8411.67 m³

The geometric mean radius of the unconventional conductors in terms of the radius r of an individual strand is 1.583r.

To find the geometric mean radius of the unconventional conductors, we need to understand the concept of geometric mean. The geometric mean of two numbers is the square root of their product. In this case, we are looking for the geometric mean radius of multiple strands.

First, we need to determine the number of strands in the unconventional conductors. The question does not provide this information explicitly, so we assume there are at least two strands.

We know that the geometric mean radius is the square root of the product of the individual strand radii. Let's assume there are n strands, and the radius of each strand is r. Therefore, the product of the individual strand radii would be r^n.

Now, we can calculate the geometric mean radius by taking the square root of r^n. Mathematically, it can be expressed as (r^n)^(1/n) = r^((n/n)^(1/n)) = r^1 = r.

Therefore, the geometric mean radius in terms of the radius r of an individual strand is 1.583r.

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Answer:

x = 12 and x = -6

Step-by-step explanation:

First subtract 6x on both sides to get a 2nd degree polynomial equal to zero:

\(x^2-6x-72=0\)

To complete the square, the formula is to divide 'b' by 2 and square the result. The general form for a 2nd degree polynomial of the variable 'x' is as follows:

\(ax^2+bx+c=0\)

For your case, b = 6. Therefore, the term that must be added and subtracted to our equation is:

\((6/2)^2=3^2=9\)

Add and subtract 9 to our equation to get:

\(x^2-6x+9-9-72=0\)

The first three terms form a perfect square, we have:

\((x^2-6x+9)-9-72=0\)

\((x^2-6x+9)-81=0\)

What multiplies to equal 9 but adds to equal -6? That would be -3 and -3. Therefore:

\((x-3)^2-81=0\)

Add 81 to both sides to get:

\((x-3)^2=81\)

We want to take the square root, but recall a square root has a positive and negative branch. Therefore we have two solutions:

\(x-3=9\)

\(x-3=-9\)

\(x=12\)

\(x=-6\)

Answer:

D

Step-by-step explanation:

dfjhygcftujnnbiijjhfsrfhhhuu

The vector parameterization for the line passing through the points (1, 1, -1) and (6, -9, 4) is:

x = 1 + 5t

y = 1 - 10t

z = -1 + 5t

To find a vector parameterization for the line passing through the points (1, 1, -1) and (6, -9, 4), we can use the vector equation of a line:

r = a + t * d

where r is the position vector of any point on the line, a is a known point on the line, t is a parameter, and d is the direction vector of the line.

First, let's find the direction vector d. We can subtract the coordinates of the two points to obtain the direction vector:

d = (6, -9, 4) - (1, 1, -1)

= (5, -10, 5)

Now, we can choose one of the given points, say (1, 1, -1), as our known point a.

Substituting these values into the vector equation, we have:

r = (1, 1, -1) + t * (5, -10, 5)

So, the vector parameterization for the line passing through the points (1, 1, -1) and (6, -9, 4) is:

x = 1 + 5t

y = 1 - 10t

z = -1 + 5t

where t is a real number that can vary to give different points along the line.

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Answer:

x=94

y=86

Step-by-step explanation:

A parallelogram has opposite angles that are congruent.  Originally our equation would look like this:
360=y+2x+86

Because opposite angles are congruent, we know that y and 86 degrees have to be equal, so:

y=86

meaning:

360=86+86+2x

simplify

360=172+2x

subtract 172 from both sides

188=2x

divide both sides by 2

94=x

So, x=94 and y=86.

Hope this helps! :)

Answer:

x=94°, y=86°, z=94°

Step-by-step explanation:

1) Since you know that consecutive angles are supplementary angles to each other, which means that they add up to 180°, you can come up with the equation x+86°=180°.

2) We can solve the equation by subtracting 86 on both sides to isolate x, and therefore solve for it. x=94°.

3) We can use the same theorem we used above to create an equation to find the value of y. y+94°=180°.

4) We can solve the equation for y by subtracting 94 on both sides. y=86°.

5) We can create another equation using this theorem, z+86°=180°.

6) We can solve the equation by subtracting 86 on both sides to isolate z. z=86°.

7) We can double-check this by adding all the values together, 86+94+86+94=360. This is the right answer!

Answer:

x=70

Step-by-step explanation:

The angle type is a verticle angle as such they are congruent.

Answer:

The answer is 70

Step-by-step explanation:

70 is across from X and because of this it equals 70. Ignore line I and thing of a 180 degree straight line if you have 70 then the other side is going to equal 110 so its the same for below the line.

(a) The z-score corresponding to x = 25 is -1. (b)The z-score corresponding to x = 42 is 2.4.(c) The raw score corresponding to z = -3 is 15. (d)  The raw score corresponding to z = 1.5 is 37.5.

For a normal distribution with mean μ = 30 and standard deviation σ = 5:

(a) To find the z-score corresponding to x = 25, we use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (25 - 30) / 5 = -1

Therefore, the z-score corresponding to x = 25 is -1.

(b) To find the z-score corresponding to x = 42, we again use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (42 - 30) / 5 = 2.4

Therefore, the z-score corresponding to x = 42 is 2.4.

(c) To find the raw score (x) corresponding to z = -3, we use the formula:

z = (x - μ) / σ

Rearranging the formula, we get:

x = μ + zσ

Substituting the values, we get:

x = 30 + (-3) x 5 = 15

Therefore, the raw score corresponding to z = -3 is 15.

(d) To find the raw score (x) corresponding to z = 1.5, we use the same formula:

x = μ + zσ

Substituting the values, we get:

x = 30 + 1.5 x 5 = 37.5

Therefore, the raw score corresponding to z = 1.5 is 37.5.

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Assuming you meant to say triangle ABC is congruent to triangle DEF, then the corresponding pieces AB and DE are the same length.

In short AB = DE.

Since DE = 10, this makes AB = 10 also.

Answer:

(x+1)2+(y−2)2=5

Explanation:

The general form for a circle with center  

(a,b) and radius r is XXX(x−a)2+(y−b)2=r2

With center  (−1,2) and given that  (0,0) is a solution (i.e. a point on the circle),according to the Pythagorean Theorem: XXX r 2=(−1−0)2+(2−0)2=5

and since the center is  (a,b)=(−1,2)by applying the general formula we get:XXX(x+1)+(y−2)2=5

Step-by-step explanation:

its already in the answer

Answer:

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

(8+1/8) = 8.125

(2.5+3/4) = 2.5 + 0.75 = 3.25

8.125 / 3.25 = 2.5

During evaluation, Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.

Given the expression, a³ - b³ / 5, where:

a = 2

b = -3

Substitute the values into the expression

Step 1: (2)³ - (-3)³ / 5

Evaluate

Step 2: 8 - (-27) / 5 (this is where Raya made a mistake, she had -9 instead of -27)

Step 3: 8 + 27/5

Step 4: 35/5 [addition]

Simplify

Step 5: 35/5 = 5 [division]

Thus, we can state that Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.

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Using the function f(x) defined here, f(-20). f(x)={(3x+5,x<=0),(7x-1,x>0):} is -55.

To find the value of f(-20), we need to determine which part of the function definition applies to the input -20.

Given the function f(x) = {(3x+5, x ≤ 0), (7x-1, x > 0)}, we can see that for x ≤ 0, the expression 3x + 5 applies.

Substituting x = -20 into this expression, we get:

f(-20) = 3(-20) + 5 = -60 + 5 = -55

Therefore, function f(x) defined here, f(-20). f(x)={(3x+5,x<=0),(7x-1,x>0):} the value of f(-20) is -55.

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Answer:

x > 10.4

Step-by-step explanation:

Isolate X by adding 3.5 to each side of the inequality

That leaves you with x > 6.9 + 3.5

Answer:

a) 3/1 that is 3

b) 8/7

c) the mixed fraction is converted into simple fraction: 3*2+2/3 = 8/3

therefore the reciprocal is 3/8

d) 1/5

e) the mixed fraction is converted into simple fraction: 6*6+1/6 = 37/6

therefore the reciprocal is 6/37.

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Answer:

a. \(3\)

b. \( \frac{8}{7} \)

c. \( \frac{3}{8} \)

d. \( \frac{1}{5} \)

e. \( \frac{6}{37} \)

Step-by-step explanation:

a. \( \frac{1}{3} \)

Just flip the fraction , you will get:

\( = \frac{3}{1} \)

\( = 3\)

b. \( \frac{7}{8} \)

flip the fraction

\( = \frac{8}{7} \)

c. \(2 \frac{2}{3} \)

The first thing you have to do is that convert mixed fraction into improper fraction

\( \frac{8}{3} \)

Flip the fraction

\( = \frac{3}{8} \)

d. \(5\)

flip the fraction

\( = \frac{1}{5} \)

e. \(6 \frac{1}{6} \)

Convert mixed fraction into improper fraction

\( = \frac{37}{6} \)

Flip the fraction in order to get reciprocal

\( = \frac{6}{37} \)

Hope this helps...

Best regards!!

Work Shown:

x = number of hours she babysits

1 hour = 7 dollars

x hours = 7x dollars (multiply both sides by x)

She earns 7x dollars after babysitting x hours if we ignore the $10 base fee. Add on the $10 base fee to get 7x+10 dollars total.

Therefore y = 7x+10 is the equation we want.

Answer:

I thought it would be y=10x+7 because the base fee which is the starting fee is 10 and your adding 7 every hour so that would be +7.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The smaller one is divided by 2 and is reflected around the y-axis

(i'm not good at explaining)

Answer:

a) acute

the triangle is acute

Answer: 104.65%

Step-by-step explanation: 45/43=1.0465 so you just move the decimal to the right 2 places to make it a percent. It’s over 100% because 45 is higher than the total of 43.

The inequality that represents the solution of -2(3x + 6) ≥ 4(x + 7) is  x ≤ -4, the correct option is B.

An inequality is a statement that is formed when two expressions are joined using an inequality operator.

The inequality is -2(3x + 6) ≥ 4(x + 7)

To find the solutions, the inequality has to be simplified.

Solving the inequality by using Distributive Property,

-6x -12 ≥ 4x +28

Adding (+12) on both sides of the inequality

-6x ≥ 4x +28 +12

Adding (-4x) on both the sides of the inequality

-6x + (-4x) ≥ 40

-10x ≥ 40

Dividing 10 on both the sides

-x ≥ 4

Reversing the sign of the inequality to remove the negative sign of x

x ≤ -4

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Answer:

45

Step-by-step explanation:

15% of 100 = 15

15 x 3 = 45

The correct answer for the carrying capacity of the population in the logistic model with the equation dp/dt = p(12-3p) is 4.

In the logistic model, the carrying capacity represents the maximum population size that an environment can sustain in the long term. In the equation dp/dt = p(12-3p), the carrying capacity is represented by the value at which the growth rate of the population is zero.

To find this value, we set the right-hand side of the equation to zero and solve for p:

0 = p(12-3p)

0 = p(4-p)

This equation has two solutions: p = 0 and p = 4. The solution p = 0 represents the population size when the growth rate is zero, but it is not the carrying capacity since the population would not survive at this size.

The solution p = 4 represents the carrying capacity, which is the maximum population size that the environment can support in the long term.

Therefore, the carrying capacity of the population in the logistic model with the equation dp/dt = p(12-3p) is 4.

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Answer:

C, 42 degrees

Step-by-step explanation:

Considering  angle BAD is 60 degrees, that makes angle BCD also 60 degrees. Since parallelograms have 360 degrees in total, we're still missing 240 degrees. Since angles BAD and BCD are congruent (equal), that means that angles ABC and ADC also have to be congruent. To find their angles, we do 240 divided by 2, which equals 120. Now that we know all of the angles, lets focus on angle ADC. Since angle 1 has been given to us, all we need to do is subtract 78 from 120 which turns out to be 42 degrees, which is the answer.

Answer:

19 + 21 = 40.

Step-by-step explanation:

Step-by-step explanation:

V epual to L x W x H

9.6cm x 0.8cm

9.6

x 0.8

46

Answer:

12 cm

Step-by-step explanation:

\(v_{eraser} = area \: of \: base \times height \\ \\ \therefore \: area \: of \: base = \frac{v_{eraser}}{height} \\ \\ = \frac{9.6}{0.8} \\ \\ = 12 \: cm\)

Answer:

Step-by-step explanation:

Assuming an additive relation, we have ...

  BC +CD = BD

Substituting the given relations, we can find x:

  (4x -2.9) +(5x -0.9) = 7x -1

  2x = 2.8 . . . . . . . . . add 3.8-7x to both sides

  x = 1.4

Then the segment values are ...

  BD = 7(1.4) -1 = 8.8

 BC = 4(1.4) -2.9 = 2.7

  CD = 5(1.4) -0.9 = 6.1