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CaHeK987 [17]
3 years ago
8

The difference of two integers is thirty. the larger integer is two more than five times the smaller integer. Find the integers

Mathematics
1 answer:
Mnenie [13.5K]3 years ago
5 0
X=2+5y
x-y=30

basically, all you're doing here is solving a system of equations. use the second equation to find out what x or y means. i'm going to solve it for x.

this is the new equation : x=30+y

now i plug this equation into the first one.

30+y=2+5y

30=2+5y-y
30=2+4y
28=4y
y=7

now that you know what y is, take that second equation we did in the beginning and plug in y.

x-7=30

solve for x

x=37



the two integers are 37 and 7.
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Put the following equation in standard form and determine the quadratic, linear, and constant coefficients. -3x2 - 8 = 5x - 7
marusya05 [52]

Answer:

  • -3x² -5x -1 = 0
  • -3 (quadratic)
  • -5 (linear)
  • -1 (constant)

Step-by-step explanation:

The equation will be in standard form when terms are listed in order of decreasing degree, and the right side of the equation is 0.

<h3>Standard form</h3>

We can subtract the right-side expression from both sides to get standard form.

  -3x² -8 -(5x -7) = 5x -7 -(5x -7)

  -3x² -8 -5x +7 = 0 . . . . . . . simplify a bit

  -3x² -5x -1 = 0 . . . . . . . . . collect terms

The standard form equation can be written ...

  -3x² -5x -1 = 0

<h3>Coefficients</h3>

The quadratic coefficient is the coefficient of the term with degree 2. The quadratic coefficient is -3.

The linear coefficient is the coefficient of the term with degree 1. The linear coefficient is -5.

The constant coefficient is the coefficient of the term with no variables. The constant is -1.

__

<em>Additional comment</em>

We can make the leading coefficient positive by multiplying the equation by -1. This gives ...

  3x² +5x +1 = 0

with quadratic, linear, and constant coefficients 3, 5, 1.

This is a legitimate answer to this question. In the case of linear equations, the "standard form" has the constant on the right side of the equal sign, and the leading coefficient is required to be positive. A negative leading coefficient can sometimes lead to errors (when the sign is overlooked), so having a positive leading coefficient is often preferred.

8 0
2 years ago
What are the roots of the equation? x^2−x−42=0 Enter your answers in the boxes. x = and x =
Natasha_Volkova [10]
Your roots are x=7 and x=-6
8 0
3 years ago
Read 2 more answers
AnimeBrainly PleaseHelp!
jekas [21]

1.

Platinum Gym charges a one-time registration fee of $60, and membership is $20 a month.

Super Fit charges a one-time registration fee of $150, and membership is $10 a month.

(a) Write a expression to represent the membership cost of Platinum Gym for x months.

Let x = months

20x + 60 is your expression

(b) Write an expression to represent the membership cost of Super Fit for x months

Let x = months

10x + 150 is your expression

(c) You are solving for both one month and twelve months of membership.

<u>One month:</u> Plug in 1 for x.

20(1) + 60 = 20 + 60 = 80

10(1) + 150 = 10 + 150 = 160

Platinum Gym is cheaper overall for one month by $80

<u>One year:</u> There are twelve months in a year. Plug in 12 for x.

20(12) + 60 = 240 + 60 = 300

10(12) + 150 = 120 + 150 = 270

Super Fit is cheaper than Platinum Gym overall for one year by $30

(d) Set the two expression equal to each other.

20x + 60 = 10x + 150

Isolate the x. Subtract 10x and 60 from both sides

20x (-10x) + 60 (-60) = 10x (-10x) + 150 (-60)

20x - 10x = 150 - 60

Simplify

20x - 10x = 150 - 60

10x = 90

Isolate the x. Divide 10 from both sides

10x/10 = 90/10

x = 9

It takes 9 months for the cost to be the same.

(e) It really depends on how long you want to work out at a gym. If you are working out for less than a year, than Platinum Gym is the better choice. If more than a year, then Super Fit is the better choice.

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

hope this helps

5 0
3 years ago
Read 2 more answers
Dr. Silas studies a culture of bacteria under a microscope. The function b(t)=50(1.4)^t represents the number of bacteria t hour
saul85 [17]
a) Remember that the y-intercept of a exponential function f(x)=a^{x} is f(0), so the only thing to do to find the y-intercept in our functions is evaluate it at t=0:
b(t)=50(1.4) ^{t}
b(0)=50(1.4)^{0}
b(0)=50(1)
b(0)=50
We can conclude that the y-intercept of our function is (0,50), and it represents the initial bacteria population in the sample.

b) To find if the function is growing or decaying, we are going to convert its decimal part to a fraction. Then, we will compare the numerator and the denominator of the fraction. If the numerator is grater than the denominator, the function is growing; if the opposite is true, the function is decaying.
Remember that to convert a decimal into a fraction we are going to add the denominator 1 to our decimal and then we'll multiply both of them by a power of ten for each number after the decimal point:
\frac{1.4}{1} . \frac{10}{10} = \frac{14}{10} = \frac{7}{5}
Now we can rewrite our exponential function:
b(t)=50( \frac{7}{5})^{t}
Since the numerator is grater than the denominator, it is growing faster than the denominator; therefore the function is growing.

c) The only thing we need to do here is evaluate the function at t=5:
b(t)=50(1.4)^{t}
b(5)=50(1.4)^{5}
b(5)=50(5.37824)
b(5)=268.912

We can conclude that after 5 hours <span>Dr. Silas began her study will be 268.9 bacteria in the sample.</span>
4 0
3 years ago
Cameron went to McEats and bought items costing $1.49, 93¢, $1.29, and 79¢. How much total did he spend, including sales tax at
n200080 [17]
The total would come out to $4.86
4 0
3 years ago
Read 2 more answers
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