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Juli2301 [7.4K]
3 years ago
15

Match each equation to the situation it represents.

Mathematics
1 answer:
Alik [6]3 years ago
6 0

Answer:

See below.

Step-by-step explanation:

******************************************************************************

Kate buys 10 tickets to  a show. She also pays a $5 parking fee. She spent $35 to see the  show.

Each ticket costs x.

10 tickets cost 10x.

Parking is $5.

Total is $35

10x + 5 = 35

******************************************************************************

Ram has 35 gel pens. He gives an equal number of pens to each of his 5 friends and has  10 pens left for himself.

The number of pens he gives each friend is x.

The total number he gives is 5x.

He started with 35 pens ands ended up with 10 pens.

35 - 5x = 10

5x + 10 = 35

******************************************************************************

Yin spends 10 hours on homework this week. She spends 5 hours on science homework  and then answers 35 math problems.

Total time spent on homework is 10 hours.

Science homework is 5 hours.

She spends x time on each of the 35 problems, so the total time spent of the 35 problems is 35x.

35x + 5 = 10

You might be interested in
Which statement describes the inverse of m(x) = x2 – 17x?
stealth61 [152]

Answer:

The correct option is;

The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}

Step-by-step explanation:

The given information is that m(x) = x² - 17·x

The above equation can be written in the form;

y = x² - 17·x

Therefore;

0 = x² - 17·x - y

From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;

x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}

By comparison to the equation,0 = x² - 17·x - y, we have;

a = 1, b = -17, and c = -y

Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;

x = \dfrac{-(-17)\pm \sqrt{(-17)^{2}-4\times (1) \times (-y)}}{2\times (1)} = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}

Which can be simplified as follows;

x =  \dfrac{17\pm \sqrt{289+4\cdot y}}{2}= \dfrac{17}{2} \pm \dfrac{1}{2}  \times \sqrt{289+4\cdot y}} = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +\dfrac{4\cdot y}{4} }}

And further simplified as follows;

x = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +y }} = \dfrac{17}{2} \pm \sqrt{y + \dfrac{289}{4} }}

Interchanging x and y in the function of the inverse, m⁻¹(x), we have;

m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}

We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;

m'(x) = 2·x - 17 = 0

x = 17/2

Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;

m''(x) = 2 > 0, therefore, the point is a minimum point on the graph

Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;

The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }} to increase m⁻¹(x) above the minimum.

8 0
3 years ago
Predict the number of pancakes that would have 48 chocolate chips
Montano1993 [528]
The answer would be 6 number of pancakes. Hope it helps
5 0
3 years ago
A car dealership has various combinations of vehicles in their car lot, all of which have an equally likely change of being sele
Effectus [21]

Answer:

The probability of a car being selected will be given by :the number of car required/ the total number of cars

Step-by-step explanation:

Probability is the likelihood of an event occurring.

This is given by : number of required outcome/number of possible outcome

7 0
3 years ago
Ed wants to borrow $20,000 from a bank to open a small gym. Three banks charge different interest rates. To help decide the best
Delicious77 [7]

Answer:

First bank = $6792

City bank = $6803

Star bank = $6817  

Step-by-step explanation:

The lists of banks and their annual interests rates are attached.

For first bank, since the interest is 7.5%, The total interest = 7.5% of $20000 = 0.075 × $20000 = $1500

For city bank, since the interest is 8.2%, The total interest = 8.2% of $20000 = 0.082 × $20000 = $1640

For Star bank, since the interest is 9%, The total interest = 9% of $20000 = 0.09 × $20000 = $1800  

The loan plus interest for the banks annually are:

First bank = $20000 + $1500 = $21500

City bank = $20000 + $1640 = $21640

Star bank = $20000 + $1900 = $21900

The monthly payments for the banks are:

First bank = $21500 / 12 months = $1792

City bank = $21640 / 12 months = $1803

Star bank = $21800 / 12 months = $1817

Since The cost to run the gym each month is $5,000. Ed's total monthly expenses for each loan option = monthly payments + cost for each month. It is calculated as:

First bank = $5000 + $1792 = $6792

City bank = $5000 + $1803 = $6803

Star bank = $5000 + $1817 = $6817  

3 0
3 years ago
Un jardín rectangular de 50 cm de largo por 34 m de ancho está rodeado por un camino de arena uniforme.Halla la anchura de dicho
Anastasy [175]

Answer:

5.85 m

Step-by-step explanation:

The width of the sand road can be calculated knowing its area and the dimensions of the rectangular garden as follows:

A_{g} = a.b

<u>Where:</u>

Ag: is the area of the rectangular garden

a: is the length of the rectangular garden = 50 cm = 0.5 m

b: is the width of the rectangular garden = 34 m

A_{s} = 540 m^{2}

<u>Where</u>:

As: is the area of the sand road

The relation between the area of the sand road and the area of the rectangular garden is the following:

A_{s} + A_{g} = (a+2x)*(b+2x)

540 m^{2} + 0.5m*34m = ab + 2ax + 2bx + 4x^{2}

557 m^{2} = ab + 2x(a + b) + 4x^{2}

557 m^{2} - 17m^{2} - 2x(34.5 m) - 4x^{2} = 0

540 - 69x - 4x^{2} = 0                              

By solving the above equation for x we have two solutions:

x₁ = -23.10 m

x₂ = 5.85 m

Taking the positive value, we have that the width of the sand road is 5.85 m.

I hope it helps you!

7 0
3 years ago
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