Talia took the bus from her home to the bank and then walked back to her home along the same route. The bus traveled at an average speed of 40 km/h and she walked at an average speed of 5 km/h. To determine the time, x, that it took Talia to walk home, she used the equation 40(0.9 – x) = 5x.

Becky will work 96 days in 6 months.

To find out the number of days Becky will work in 6 months, we need to multiply the number of days she works each month by the number of months. Given that Becky works 16 days each month, we can calculate the number of days she will work in 6 months as follows:

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Answer:

The total cost is $707.15.

Step-by-step explanation:

The Sky High Club dues are = $450 per person

and the Skis costs = $159.90

Cost for boots = $78.25

Cost of poles = $19.00

To find the total cost we will add all the amounts.

Total cost = 450 + 159.90 + 78.25 + 19.00

                = $707.15

The total cost is $707.15.

The expression (5 + 3i)/(4 - 2i) can be simplified as (-7 + 11i)/10, which is a complex number.

To write the expression (5 + 3i)/(4 - 2i) as a complex number, we can multiply the numerator and denominator by the conjugate of the denominator to eliminate the imaginary part in the denominator.

The conjugate of 4 - 2i is 4 + 2i.

Multiplying both the numerator and denominator by the conjugate:

((5 + 3i) * (4 + 2i))/((4 - 2i) * (4 + 2i))

Expanding the numerator and denominator:

(20 + 10i + 12i + 6i^2) / (16 - 8i + 8i - 4i^2)

Simplifying and combining like terms:

(20 + 22i - 6) / (16 + 4)

(-14 + 22i) / 20

Now, we can simplify the expression further by dividing both the numerator and denominator by their greatest common divisor, which is 2:

(-7 + 11i) / 10

Therefore, the expression (5 + 3i)/(4 - 2i) can be simplified as (-7 + 11i)/10, which is a complex number.

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Answer:

n=3

Step-by-step explanation:

Answer:

The answer is

y = 6

Repairing big, brass instruments requires the use of specialized tool kits made of steel alloys and brass instrument repair kits. These tools are designed to be gentle on the brass surface, ensuring the instrument's quality and longevity.

Repairing big, brass instruments, such as trombones and trumpets, often requires the use of certain materials and techniques. Since brass is an alloy of copper and zinc, it is prone to tarnish and damage over time. Hence, it is important to use cleaning and repair tools made of similar or non-abrasive materials to avoid causing further damage to the instrument.

The most common methods of repairing dents and scratches in brass instruments involve specialist tool kits composed of various steel alloys, which are strong and durable, but also gentle on the brass surface. Additionally, using specialized brass instrument repair kits, which include various mutes, cleaning agents, and brushes, can help maintain the instrument's quality and longevity.

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f(x) = 4|x| is the function narrower than the parent function , Option D is the correct answer.

An Absolute function is a function that returns a positive value at any given point.

It is given that

The parent function is

f(x) = |x|

To find the function which will be narrower , it will be plotted to check

It is the known fact that when a function is multiplied by a number greater than 1 , the resulting function gets narrower , This can be easily identified from the graph.

f(x) = 4|x| is the function narrower than the parent function , Option D is the correct answer.

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Answer:

The correct answer is A. $388

Step-by-step explanation:

The 28/36 Rule states that : A household should spend a maximum of 28% of its gross monthly income on total housing expenses and not more than 36% on total debt service.

Maximum expense on housing expense = 28% of 4850

                                                                    = $1358

Maximum expense on total debt service = 36% of 4850

                                                                    = $1746

Therefore, the maximum allowable recurring debt with a monthly income of $4,850 = 1746 - 1358 = $388

Hence, The option A is correct.

Answer:

a

Step-by-step explanation:

got it right on edge

The number of dogs would be 60 when the ratio of dogs to cats is 4:3.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

Given that the ratio of dogs to cats is 4:3. if the number of cats is 45

We have to determine the number of dogs.

Let the number of dogs would be x

As per the given condition, we can write a proportion as

4 dogs : 3 cats = x : 45 cats

⇒ 4 / 3 = x / 45

Apply the cross-multiplication operation,

⇒ 45 × 4 = x × 3

⇒ x = (45 × 4)/3

⇒ x = 15 × 4

⇒ x = 60

Therefore, the number of dogs would be 60.

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Answer: 3.7 gallons

Step-by-step explanation:

Given : The formula [tex]a=\dfrac{d}{g}[/tex] gives the average gas mileage a of a vehicle that uses 'g' gallons of gas to travel 'd' miles.

The average gas mileage : a =20.2 miles per gallon

Distance : d=75 miles.

To find : g

Substitute all the values in the above formula , we get

[tex]20.2=\dfrac{75}{g}\\\\\Rightarrow\ g=\dfrac{75}{20.2}=3.71287128713approx3.7\ \ \ \text{ Rounded o the nearest tenth}[/tex]

Hence, the required amount of gas = 3.7 gallons

To create a trinomial, use a basic factored form like (x+a)(x+b), and expand this via the distributive property. This yields as an example x²+8x+15, a trinomial in standard form.

To create a trinomial that can be factored and to write it in standard form, we need to consider a basic factored form first. Let's use (x+a)(x+b) as our basic factored form. In this form, 'a' and 'b' are the roots of the trinomial.

To create the trinomial, we then expand this expression by using the distributive property: (x+a)(x+b) = x² + bx + ax + ab, which simplifies to x² + (a+b)x + ab. This is now our trinomial in standard form.

Let's take a concrete example. If we let 'a' be 3 and 'b' be 5, our factored form is (x+3)(x+5). Expanding this, we get x² + 5x + 3x + 15, which simplifies to x² + 8x + 15. Thus, x² + 8x + 15 is a trinomial that can be factored and is written in standard form.

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Answer:

Area is 45000 square feet.

Step-by-step explanation:

Let x be the length of fenced side parallel to the river side.

Let y be the length of other two sides.

Then,

[tex]x+ 2y 600[/tex]

So, we get [tex]x=600-2y[/tex]

Area of this rectangle = xy

= [tex]y(600-2y)[/tex]

[tex]x=-2y^{2}+600y[/tex]

Now attached is the graph of the area function, which is a parabola opening downward.

We can see ta the maximum area occurs when y=[tex]-600/[2(-2)][/tex] = 150

And [tex]x = 600-2(150)[/tex]

x =[tex]600-300=300[/tex]

Therefore, to maximize the area, the side parallel to the river is to be 300 feet long, and the other two fenced sides should be 150 feet long.

The area is = [tex]300\times150= 45000[/tex] square feet.