A personal trainer offers two different plans. Plan A costs $25 per session and Plan
B costs $50 per session. If the trainer coaches 18 sessions this week and earns $625
dollars, how many sessions of each type did he coach?

Answer:

 65 pairs

Step-by-step explanation:

Black makes up 5/(5+8) = 5/13 of the total order, so ...

 (5/13)(169 pairs) = 65 pairs

Vinny will order 65 pairs of black high tops.

Step 1

Given;

Required; To factor it out into products of prime factors.

Step 2

A prime factor is a factor that is a prime number. In other words: any of the prime numbers that can be multiplied to give the original number is a prime factor. Examples of prime factors are; 1,2,3,5 etc. When a composite number is written as a product of all of its prime factors, we have the prime factorization of the number.

Step 3

Find the prime factor of 540

Therefore, the prime pr

Let x represent the number of pounds of coffee that she bought.

From the information given,

cost per pound of coffee = $8.73

Cost of x pounds of coffee = 8.73 * x = 8.73x

Initial amount that she had = $90

After spencing $8.73x, the amount left is $63.81. This means that

90 - 8.73x = 63.81

8.73x = 90 - 63.81

8.73x = 26.19

x = 26.19/8.73

x = 3

She bought 3 pounds of coffee

The graph of the figure is attached below.

Given equation of line:-

y = (-3/2)x - 1

First we will find the x and y intercepts of the line to plot in the line.

Putting x = 0 to find the y-intercept, we get,

y = (-3/2)(0) - 1

y = -1

Hence, the coordinates of the point are (0,-1).

Putting y = 0 to find the x-intercept, we get,

0 = (-3/2)x - 1

1 = (-3/2)x

x = -2/3

Hence, the coordinates of the point are (-2/3,0).

We can find another point on the line.

Putting x = 2, we get,

y = (-3/2)(2) - 1

y = -3 - 1

y = -4

Hence, the coordinates of the point are (2,-4).

Plotting these in a graph, we can get a straight line.

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Answer: [tex]y < \frac{1}{3}x+2, y < -2x+2[/tex]

Step-by-step explanation:

The equations of the lines are [tex]y=\frac{1}{3}x+2[/tex] and [tex]y=2-2x[/tex].

Since the line [tex]y=\frac{1}{3}x+2[/tex] has a dotted boundary and is shaded below, it represents the inequality [tex]y < \frac{1}{3}x+2[/tex].

Since the line [tex]y=2-2x[/tex] has a dotted boundary and is shaded below, it represents the inequality [tex]y < 2-2x[/tex].

Given:

• AD = 3

• DC = 27

• BD = x + 3

Let's solve for x.

To solve for x, apply the altitude formula:

Where BD is the altitude.

Cross multiply:

Plug in the values and solve for x:

Take the square root of both sides:

Therefore, the value of x is 6 .

ANSWER:

d. 6

Answer:

$194.69

Step-by-step explanation:

The best way to predict the amount of tips is using this formula:

[tex]100(\frac{Tips(total)}{Customers(total)} )[/tex]

This finds the average tip per customer with all of the data, and multiplies it by 100 to get the predicted amount of tips for 100 customers.

Plugging in the data from the table gives you this equation:

[tex]100(\frac{1174}{603} )[/tex]

This equals $194.69.

A perpendicular bisector is a segment which intersects another segment on its midpoint and with a right angle.

First, we have to find the midpoint between X(-9,1) and Y(3,5), as follows

This means the perpendicular bisector must pass through (-3,3). Now, with the given points we find the slope of XY

Then, we apply the rule of perpendicularity to find the slope of the perpendicular bisector.

Now, we use the slope-point formula to find the equation for the perpendicular bisector.

Where we replace the slope -3 and the point (-3,3).

Answer: x < -4

Step-by-step explanation:

➜ First thing we notice is the open circle. This means we will use either < or >

➜ The next thing we notice is that the values are pointing to the left of the circle, this means we will be using <

➜ The last part we notice is that the dot is on -4. This is the value we'll use to write our inequtliy.

    The last thing to do is to write the inequality using the parts we pointed out above:

x < -4

Let t be the time, in hours, elapsed till the buses are 791 miles apart, then we can set the following equation:

Solving the above equation for t we get:

Answer: 7 hours.

Answer:

the probability is 2/8

Step-by-step explanation:

Answer:

This is an isosceles right triangle, so

x = 45°.

The cost of Sneakers, pair of pants, Jacket and T-shirt are $95, $50, $100 and $290 respectively.

This can be solved by forming linear equations. A linear equation is the one which can be represented in the form ax + b = 0 where a, b are coefficients and x is the independent variable. Let us assume the cost of Sneakers be 's', cost of Pants be 'p', cost of Jacket be 'j' and cost of t-shirt be 't'.

The cost of all the items is equal to $535

s + p + j + t = $535                 ......(1)

Sneakers cost $5 less than the jacket

s = j - $5                                 ......(2)

Pants cost $50 less than the jacket

p = j - $50                              ......(3)

T-shirt cost $10 less than three times the jacket

t = 3j - $10                              ......(4)

Putting the values of equation (2), (3) and (4) in equation (1)

j - $5 + j - $50 + j + 3j - $10 = $535

6j = $535 + $65

=> 6j = $600

=> j = $100 which is the cost Jacket.

Now, s = $100 - $5 = $95 which is the cost of Sneakers.

p = $100 - $50 = $50 which is the cost of pair of pants.

t = $300 - $10 = $290 which is the cost of t-shirt.

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Answer:  600,000 + 70,000 + 5,000 + 400 + 30 + 2

Explanation:

Each digit forms a different number depending on its place value.

The 6 is in the hundred thousands place value, so the 6 in 675,432 corresponds to 600,000. Similar ideas apply for the other digits as well

Given the expression;

Step 1:

Step 2:

Step 3:

The solution is;

Answer: 40000

+ 5000

+ 800

+ 3

Step-by-step explanation:

The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.

The given algebraic expression would be equivalent to the expression [tex]\dfrac{1}{4(x)^\frac{2}{9} }[/tex] which is the correct answer would be an option (B)

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The given algebraic expression is:

[tex](64x^{\frac{2}{3} })^{-\frac{1}{3} }[/tex]

Apply the property of a⁻ˣ = 1/aˣ in the above term,

[tex]\dfrac{1}{ (64x^{\frac{2}{3} })^{\frac{1}{3} }}[/tex]

Here 64 = 4×4×4 = 4³

[tex]\dfrac{1}{ (4^3x^{\frac{2}{3} })^{\frac{1}{3} }}[/tex]

Apply the cube root property and Multiply the exponent of the variable x to 1/3

[tex]\dfrac{1}{ 4x^{\frac{2}{3} }^\times^{\frac{1}{3} }}[/tex]

Apply the multiplication operation to the exponent of the variable x to get the solution.

[tex]\dfrac{1}{4(x)^\frac{2}{9} }[/tex]

Hence, the correct answer would be an option (B)

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Equation for the line in point-slope form is 5x + 6y = 6.

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.

Given Data

P(6, -3)

y =1/2 x + 2

When the equation has been solved for y, the line in slope intercept form with slope = m = 1/2 = the coefficient of the x term is represented by the equation y= (1/2)x + 2. 2 represents the y coordinate of the location (0, 2) where the line intersects the y axis as the y intercept.

So, the points are (6,-3) and (0,2)

Formula

y₂ - y₁ = m(x₂ - x₁)

slope of the line (m) = [tex]\frac{x-x}{y-y}[/tex]₁¹

m= [tex]\frac{2-(-3)}{0-6}[/tex]

m = -[tex]\frac{5}{6}[/tex]

Equation

y- (-3) = -[tex]\frac{5}{6}[/tex](x- 6)

y +5 = -[tex]\frac{5}{6}[/tex]x + 6

y + 5 = -[tex]\frac{5+36 }{6}[/tex]

6y + 30 = -5x + 36

5x + 6y = 6

Equation for the line in point-slope form is 5x + 6y = 6.

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Answer: Linear

Step-by-step explanation:

Each time [tex]x[/tex] increases by [tex]1[/tex], [tex]y[/tex] decreases by [tex]8[/tex]. Since the value of y changes at a constant rate, the relationship is linear.

Answer:

You were right. The answer is (C)

Step-by-step explanation:

Remember, the line always goes up in the top right corner, also the first dot is 2,20, to 4,40, to 6,60, and last 8,80 which is the number of the same total amount and number of hours.

The lengths of the major and minor axis of the ellipse, are;  4√6 and 4√3 respectively.

An ellipse describes the locus of a point on a curve, such that the sum of the distance between two focal points from the points on the curve is a constant.

The function of the ellipse can be calculated as follows;

[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]

Where (h, k) = The coordinates of the center of the ellipse

a = The length of the semi-major axis

b = The length of the semi-minor axis

Now,

[tex]\dfrac{(x-3)^2}{12} + \dfrac{(y+ 4)^2}{24} =1[/tex]

By comparison, we have;

(h, k) = (3, -4)

a = √(24) = 2√6

b = √(12) = 2√3

The length of the major axis is 2a

The length of the minor axis is 2b

The length of the major axis will be;

2a = 2 × 2√6 = 4√6

The length of the minor axis will be;

2b = 2 × 2√3 = 4√3

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Step-by-step explanation:

6×(4 + x) = 7

24 + 6x = 7

6x = -17

x = -17/6 = -2.833333333... = -2 5/6

Answer:

A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line.

Answer:

See below

Step-by-step explanation:

Rotate rectangle A 90 ° clockwise with the center being the lower right hand corner.  Then translate down and right until rectangle A in over rectangle B

The value of interior angle x for the given pentagon if found as 88 degrees.

For the given question;

The exterior angles of the pentagon are given in figure.

Find all the interior angles for given angles using linear pair as all are straight lines.

The sum of all the interior angle of pentagon is 540.

Thus,

118 + 147 + 66 + 121 + x = 540

x = 540 - 452

x = 88

Thus, the value of interior angle x for the given pentagon if found as 88 degrees.

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Answer:

Step-by-step explanation:

V = 4/3.pi.r^3

36 = 4/3 pi r^3

8.6 = r^3

r = 2 in

---------------------

Area of sphere :

A = 4.pi.r^2

A = 4 . Pi . 2^2

A = 16 Pi

A = 50.26 in

From the given figure

The 2 triangles have one equal angle of measure 88

The side of length 3 and the side of length 1 have a ratio 3: 1

The side of length 6 and the side of length 2 have a ratio 6: 2, when we divide both terms of the ratio by 1, it becomes 3: 1

That means we have one equal angle and two proportional sides

Since the angle is between the proportional sides, then

The 2 triangles are similar by the SAS postulate

Answer B