Laura just became a personal trainer and is finalizing her pricing plans. One plan is to charge
$55 for the initial consultation and then $41 per session. Another plan is to charge $50 for the
consultation and $46 per session. Laura realizes that the two plans have the same cost for a
certain number of sessions. How many sessions is that? What is that cost?

Answers

Answer 1

Using algebraic equations:

the number of sessions that will give same cost for both plans is: 1

the cost is: $96

Translate the situation into algebraic equations.

Let y = Total cost x = number of sessions

Equation for total cost of the first plan:

y = 41x + 55

Equation for the total cost of the second plan:

y = 46x + 50

To find the number of sessions that would yield same cost for both plans, make both equations equal to each other and solve for x.

41x + 55 = 46x + 50

Combine like terms together

41x - 46x = - 55 + 50

-5x = -5

x = 1

For a session, both plans will yield the same cost.

The cost 1 session will yield for both:

41x + 55 = 46x + 50

Plug in the value of x

41(1) + 55 = 46(1) + 50

96 = 96

Therefore, using algebraic equations:

the number of sessions that will give same cost for both plans is: 1

the cost is: $96

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Related Questions

Which of the following is a perfect square a) 1057 b) 625 c) 928 d) 64000

Answers

Answer:

625

Step-by-step explanation:

625 is the (perfect) square of 25.  The other three numbers are not perfect squares.

b... 625

...............................

A zookeeper is monitoring the population of gazelles. The herd needs to have exactly three times more males than females to thrive. The zoo only has room for a maximum of 12 female gazelles. Let x represent the number of female gazelles and y represent the number of male gazelles. Write the constraints that represent the possible number of male and female gazelles that can live in a thriving population at the zoo. X > 0 and y > 0 0 < x ≤ 12 and 0 < y ≤ 36 0 < x ≤ 12 and y > 36 x > 0 and y < 23.

Answers

Option C is correct.

Given to us:

female gazelles[tex](x)[/tex] can be maximum of 12 only. therefore,

Condition 1 is  [tex]12\geq x>0[/tex].

while,

male gazelles[tex](y)[/tex] should be exactly 3 times more than females to thrive. therefore,

Condition 2 is [tex]36\geq y>0[/tex].

There is only one option among all the options available which is satisfying both the conditions. therefore, option C is the correct option.

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Answer:

c is the answer

Step-by-step explanation:

it took the test and got it correct

Which of the x-values are solutions to the following inequality?
X < 365

Answers

a and b because both values are less than 365

Can someone pls help me

Answers

Answer:

6π Km

Step-by-step explanation:

The arc length is calculated as

arc = circumference of circle × fraction of circle

    = 2πr × [tex]\frac{120}{360}[/tex]

   = 2π × 9 × [tex]\frac{1}{3}[/tex]

   = 18π × [tex]\frac{1}{3}[/tex]

  = 6π Km ← exact value


pls help. will give brainliest :)

Answers

Answer:

its option B

Step-by-step explanation:

Answer:

the answer is d

Step-by-step explanation:

pls answer quickly

This Histogram shows the heights in inches of members of a middle school volleyball team. How many members are between 50 and 70 inches tall?

A. 12
B. 10
C. 6
D. 4​

Answers

Answer:

I need the photo

Step-by-step explanation:

I need the photo

Write and solve an equation for the following:

Answers

Answer:

x = 12

Step-by-step explanation:

The measures of ∠XYW and ∠WYZ would equal m∠XYZ.

[tex]3x + 2 + 72 = 110\\\rule{150}{0.5}\\3x + 74 = 110\\\\3x + 74 - 74 = 110 - 74\\\\3x = 36\\\\\boxed{x = 12}[/tex]

Hope this helps.

Definition of Variable and Constant with examples!
Spam free answers required!​

Answers

Answer:

[tex]\large\boxed{\boxed{\boxed{\mathfrak{variable}}}}[/tex]

Variable is a symbol that represents a quantity in a mathematical expression, as used in many sciences. Variable (research), a logical set of attributes. Variable star, a type of astronomical star.

[tex]\large\boxed{\boxed{\boxed{\mathfrak{constant}}}}[/tex]

A constant, sometimes also called a "mathematical constant," is any well-defined real number which is significantly interesting in some way. A function, equation, etc., is said to "be constant" (or be a constant function) if it always assumes the same value independent of how its parameters are varied.

Write the equation of the line in slope-intercept form that passes through (-3, -5) and (0, 4).

Answers

Answer:

y = 3x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, - 5 ) and (x₂, y₂ ) = (0, 4 )

m = [tex]\frac{4-(-5)}{0-(-3)}[/tex] = [tex]\frac{4+5}{0+3}[/tex] = [tex]\frac{9}{3}[/tex] = 3

The line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = 3x + 4 ← equation of line

A quadrilateral regular pyramid, the area of any of its lateral faces equal the area of its base, if the side
length of the base of the pyramid is = 6 cm, then the volume of the pyramid =..........cm3
a) 36
b) 673
c) 36/15
d) 216V15

Answers

Answer:

  c)  36√15 cm³

Step-by-step explanation:

We can compute the volume of the pyramid if we know the area of its base, and its height.

__

A regular quadrilateral is a square. If one side of the square is 6 cm, its area will be ...

  A = s² = (6 cm)² = 36 cm² . . . . area of the pyramid base

__

Each triangular face will have a slant height that makes its area the same as that of the base.

  A = 1/2bh

  36 cm² = (1/2)(6 cm)h

  (36 cm²)/(3 cm) = h = 12 cm  . . . . .  divide by the coefficient of h

The slant height of a face is the hypotenuse of a right triangle whose short leg is half the side length, and whose long leg is the height of the pyramid. If that height is represented by h, the Pythagorean theorem tells us ...

  (6 cm/2)² +h² = (12 cm)²

  h² = (144 -9) cm²

  h = 3√15 cm . . . . . height of the pyramid

__

The volume of the pyramid is given by ...

  V = 1/3Bh . . . . . . base area B, height h

Using the values we found above, we compute the volume to be ...

  V = (1/3)(36 cm²)(3√15 cm) = 36√15 cm³

The distance between two points, a and b, on a number line is expressed as
|a – b|, where a and b are rational numbers. Think about locating a point halfway between a and b on a number line. How can you find the coordinate for such a point? Develop a formula in terms of a and b that you can use to find the coordinate. Your formula must work for positive and negative values of a and b. Does absolute value play a role in your formula? Why or why not? Under what circumstances might your formula be used in the real world? Explain.

Discuss how you can find the coordinate of a point located other fractional distances from a to b (or from b to a). For example, locate a point three-fourths of the distance from a to b. What kind of calculation is involved?

Answers

The distance between points (a) and (b) is the number of units between the points.

Formula for halfway two

Assume the lesser point is point (a)

To locate the halfway between points (a) and (b)

Calculate the absolute difference between points (a) and (b) i.e. |a - b|Divide the difference into halvesAdd the value of one half to point (a).

The above steps is represented as:

[tex]P = a + \frac{|a - b|}{2}[/tex]

Using the above formula, the halfway point between 5 and 11 would be 8

The formula can be used to calculate the distance between negative points, and absolute values are used to determine the number of units between the points

Real world circumstance

The formula can be used to calculate the halfway distance between two points on a track

Fractional distance

To determine the fractional distance, we simply replace the 1/2 in the original formula with the appropriate fraction.

Take for instance, three-fourths from (a) to (b) would be:

[tex]P = a + \frac{3|a - b|}{4}[/tex]

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Solve the following system: y = x 3 3x y = 19 (7, 4) (â’4, 7) (4, 7) (4, â’7).

Answers

The correct option is C. (4,7).

Given equations,

[tex]y=x+3....(1)\\3x+y=19....(2)[/tex]

We have to solve the equations.

From equation 1 put the value of y in equation 2 we get,

[tex]3x+x+3=19\\4x=16\\x=4\\[/tex]

Now putting the value of x in equation 1 we get,

[tex]y=4+3\\y=7[/tex]

Hence the required solution of the above equations is (4,7).

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help me plz i need help

Answers

Answer:

y-2.0

x-2.3

Step-by-step explanation:

hope it help

Answer:

x- intercept = - 1, y- intercept = - 1

Step-by-step explanation:

The x- intercept is the point on the x- axis where the line crosses

x- intercept = - 1

The y- intercept is the point on the y- axis where the line crosses

y- intercept = - 1

Jim’s backyard is rectangular with dimensions of 80 feet by 120 feet. He is planning to designate part of the yard to plant a vegetable garden. The garden will be a similar rectangle, using a scale factor of 3/4. How much fencing will he need if he wants to enclose the garden on all four sides?

How many feet does he need?

Answers

Solution: 5,400 feet^2
Step by step solution:
3/4=0.75
(80*0.75)(120*0.75)
(60)(90)
5400
5,400 feet^2
Hope that helps :)

13x+y=1
2x+6y=6
HELP PLZ

Answers

Answer:

(0,1)

Step-by-step explanation:

solve the first equation for y. y=1-13x

plug this into the other equation and solve for x.

2x+6(1-13x)=6

2x+6-78x=6

-76x+6=6

subtract 6 from both sides

-76x=0

x=0

plug this into the other original equation.

13(0)+y=1

y=1

(0,1)

100 POINTS PLEASE HELP ME I BEG 100 POINTS

Answers

Answer:

see explanation

Step-by-step explanation:

(1)

Since FE = FG the triangle is isosceles with ∠ E = ∠ G, then

∠ E = [tex]\frac{180-106}{2}[/tex] = [tex]\frac{74}{2}[/tex] = 37°

(2)

Since all 3 sides are congruent then triangle is equilateral with the 3 angles being congruent, 60° each , then

12y = 60 ( divide both sides by 12 )

y = 5

(3)

The 3 angles are congruent then triangle is equilateral with the 3 sides being congruent, then

KL = JL , that is

4t - 8 = 2t + 1 ( subtract 2t from both sides )

2t - 8 = 1 ( add 8 to both sides )

2t = 9 ( divide both sides by 2 )

t = 4.5

(4)

Given ∠ B = ∠ C then triangle is isosceles with 2 legs being congruent , that is

AB = AC

4x + 1 = 9 ( subtract 1 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2

Then

perimeter = AB + BC + AC = 4x + 1 + 2x + 3 + 9

                                            = 6x + 13

                                            = 6(2) + 13

                                            = 12 + 13

                                            = 25

Answer:

full

Step-by-step explanation:

screen

£42 is shared equally between 3 friends.
How much does each friend get?

Answers

Given that £ 42 is distributed among 3 friends.

So, each will get

[tex] = 42 \div 3 \\ = £14[/tex]

Omar drew a line that was 12 centimeters long. Which line is 5 centimeters shorter

Answers

Answer:

12 - 5 is 7 so the line would be 7 centimeters

Step-by-step explanation:

Answer:

the answer is 7

Step-by-step explanation:

12-5=7

A shopkeeper bought 2 mobile set for 5000 each . If he sold a mobile with 20% profit and 20% loss . How much percent profit or loss did he have?​

Answers

Answer: NO GAIN for the shopkeeper

Step-by-step explanation:

20/100 *5000=1000


Marcus is it mixing blue and yellow paint in the ratio of 2 to 3 to make green paint. He wants to make 45 L of green paint. Him being to make a table to help him think about the problem but is unsure of what to do next. Marks find Amandas also mixing paint she wants to make purple paint by mixing 2 cups of blue with a4 cups are red paint. Amanda makes her pain in his left with 48 cups of purple paint how many more cups of purple paint did she use than blue paint? If Amanda has 15 cups of blue paint how many cups repair does she need? Amanda wants her purple paint mixture from part bead to be a little lighter so she mixes in two more cups of white paint what is the ratio of blue paint to repaint the white paint that she used?

Answers

This question is based on the concept of ratio. Therefore, he needs to have 18 liters of blue paint and  27 liters of yellow paint to make 45 liters of green paint.

Given:

Mark was mixing blue and yellow paint ratio of 2:3.

He wants to make 45 liters of green paint.

According to the question,

Blue : Yellow =  Green

2 : 3 : 2+3 (Given)

2 : 3 : 5

Therefore, he wants to make 45 liters of green paint.

So, 5 parts = 45 liters

Now, calculating for each part.

We get,

Each part = 45÷ 5 = 9 liters

Now for 2 parts = 9 x 2 = 18 liters

And, for 3 parts = 9 x 3 = 27 liters

Therefore, he needs to have 18 liters of blue paint and  27 liters of yellow paint to make 45 liters of green paint.

which is a line of symmetry

Answers

Answer:

is there a pic?

Step-by-step explanation:

we are able to see


Each batch of 24 cookies needs 2.25 cups of flour. If Stacy and her mom bake 3.5 batches, how much flour is
needed?
Show work !

Answers

Answer:

7 7/8 cups of flour

Step-by-step explanation:

2.25 times 3.5 equals 7.875

Jae bought 85 tickets to spend on games and rides at an amusement park. Games cost 3 tickets each, and rides cost 8 tickets each. Jae has already used 39 of the tickets. If he uses all of his remaining tickets for rides, how many more times can Jae go on rides?

Answers

Answer:

15

Step-by-step explanation:

Jae can go 15 more times on the rides.

Answer:

Jae can ride 5.75 or 5 more times

Step-by-step explanation:

Total of tickets, Jae buys 85

Jae uses (-) 39 tickets

85 - 39 = 46 remaining tickets

Rides: 8 tickets each

46/8 = 5.75

I hope this helps.

Find the circumference of a circle with a radius of 2.4 m

Answers

Answer:

15.07964

..................

not sure how many decimals you want lol, but here ya go:

15.07964474

for future reference you can plug radius (r) into

c = 2pi x r

to get the circumference :)

What is the equation of the line that passes through the point (16,-7) and has a slope of m=-3/4 written in point-slope form?​

Answers

Answer:

y+7=-3/4(x-16)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-7)=-3/4(x-16)

y+7=-3/4(x-16)

Please mark me as Brainliest if you're satisfied with the answer.

Help me with answer plzzzzz

Answers

Answer:

a

Step-by-step explanation:

Fill in the blank for this graph.

Answers

Answer:

2.22

Step-by-step explanation:

Please help! I forgot how to do it

Answers

3*2 probably I’m sorry if it’s wrong

There are 100 students in the sixth grade. The ratio of boys to girls is 2:3. How many more girls than boys are in the sixth grade?​

Answers

Answer: I Think you will make 100 time 2 divide 3

Step-by-step explanation:

i'm not sure, have a nice day

How long is a bus journey that starts at 8.55 a.m. and ends at 9.17 a.m.?

Please can you put the answer in minutes?

Answers

Answer:

5+17=22 minute

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Write the chemical formulas and names for the following ionic compounds. Cobalt (III) and bromine What is a compound sentence for the word sojourn? Maplewood Furniture Store is having a sale on dining room furniture. When a customer purchases a set of dining chairs, a one-time discount of $55 is applied to the total. During the sale, Rhianna buys a set of 6 chairs that match the table she inherited from her grandmother. Rhianna pays $455 in all. Which equation can you use to find the regular cost, c, of each chair? ( ANSWERS 6c - 55 = 455, 55(c - 6) = 455, 55c - 6 = 455, 6(c - 55) = 455,) What is the regular cost of the chair what happened at the battles of fort ticonderoga and bunker hill Hello hello helppppppppppppp help PLEASEMatch the following: This shape is broken up into rectangles. What is the area of theentire shape? Not every earthquake has a(n) ______, but every earthquake has _____that occur in _____ the mainshock.1. Aftershock Foreshock 9. Anna has 102 quarters. Jazmin has102 dimes. Who has more money, Annaor Jazmin? How much more? Explainyour reasoning. The work of writing a budget is done in Congress, but the president can formulate abudget proposal and HELP ME PLEASEEEEEEE I WILL GIVE POINTS AND BRAINLIEST 5x10^6 is how many times greater than 5x10^4 Chlorine has 7 valence electrons. Describe the type of bond that sodium would havewith chlorine. Write the chemical formula of the compound these two elements would form together. (i figured it out nvm) in the odorant cells of mammals, specific odorants are detected by binding to ________. Francis owns a cake shop. She is currently preparing cupcakes (x) and cookies (y) for two birthdayparties. The first birthday party ordered 20 cupcakes and 40 cookies and their total cost was $61. The second birthday party ordered 30 cupcakes and 30 cookies. Their total cost was $64.50. Write the first five terms of the geometric sequence whose first terns 6, and whose common ratio is 3. The table below shows the proportional relationship between the weight of cereal, in ounces, and the number of packs of cereal:Number of Packsof Cereal Number of Ouncesof Cereal2 343 514 68What is the constant of proportionality? 9 17 34 36 How can a speaker use statistics as supporting material in a presentation? Today, volcanism extends from Haleakala on Maui, through the Big Island, to an _________ volcano called Loihi. Evaluate the expression 5xy+ -2xy+y^2 when x=4 and y=-5