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zmey [24]
2 years ago
9

The sum of two consecutive integers is -95. Find the integers. State the unknov-

Mathematics
1 answer:
kvasek [131]2 years ago
8 0

Let the unknown consecutive integers be x, x+1

x+x+1=-95

2x+1=-95

2x=-95-1

2x=-96

x=-96/2

x=-48

x=-48

x=-48x+1=-48+1=-47

-48 and -47 are the two consecutive integers

Please mark as Brainliest

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blsea [12.9K]
1) Distribute 8(2x-14) + 13 = 4x - 27 then simplify like terms to get: 16x - 99 = 4x - 27.
2) Subtract 4x on both sides and at the same time add 99 to both sides to get: 12x=72.
3) Divide both sides by 12 to get x=6.
PART B: 6 makes the equation true because you just solved for it.
8 0
3 years ago
Mrs. Robinson, an insurance agent, earns a salary of $4,800 per year plus a 3% commission on her sales. The average price of a p
nekit [7.7K]

Answer:

Required inequality is 4800+183x>8000.

Step-by-step explanation:

Given that Mrs. Robinson, an insurance agent, earns a salary of $4,800 per year plus a 3% commission on her sales. The average price of a policy she sells is $6,100. Write an inequality to find how many policies Mrs. Robinson must sell to make an annual income of at least $8,000.

Calculation is given by:

Salary per year = $4,800

Average price of a policy = $6,100.

commission on her sales = 3%

Then commission on $6,100 = 3% of $6,100 = 0.03 ($6,100) = $183

Let number of policies Mrs. Robinson must sell to make an annual income of at least $8,000 = x

then total commission on x policies = 183x

Total income using x policies = 4800+183x

Since she wants to make an annual income of at least $8,000. so we can write inequality as:

4800+183x>8000

Hence required inequality is 4800+183x>8000.

5 0
3 years ago
The sum of three consecutive terms in an arithmetic sequence is 27, and their product is 585. find the three terms.
sammy [17]
\text{the three consecutive terms in an arithmetic sequence}\\a;\ a+d;\ a+2d\\\\\text{system of equals}\\\\ \left\{\begin{array}{ccc}a+a+d+a+2d=27\\a(a+d)(a+2d)=585\end{array}\right\\ \left\{\begin{array}{ccc}3a+3d=27&|:3\\a(a+d)(a+2d)=585\end{array}\right\\ \left\{\begin{array}{ccc}a+d=9&\to d=9-a\\a(a+d)(a+2d)=585\end{array}\right\\
\text{substitute to the second equation}\\\\a(a+9-a)(a+2(9-a))=585\\\\a(9)(a+18-2a)=585\\9a(18-a)=585\ \ \ |:9\\a(18-a)=65\\18a-a^2=65\ \ \ |\text{change the signs}\\a^2-18a=-65\\a^2-2a\cdot9=-65\ \ \ |+9^2\\\underbrace{a^2-2a\cdot9+9^2}_{(a-b)^2=a^2-2ab+b^2}=-65+9^2\\(a-9)^2=16\to a-9\pm\sqrt{16}\\a-9=-4\ \vee\ a-9=4\ \ \ |+9\\a=5\ \vee\ a=13\\\\d=9-5=4\ \vee\ d=9-13=-4
Answer:\ a=5;\ a+d=9; a+2d=13\ vee\ a=13;\ a+d=9;\ a+2d=5

5 0
3 years ago
Write the total money amount.then write the amount as a fraction or mixed number and as a decimal in terms of dollars
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6 0
3 years ago
Draw an angle in standard position whose terminal side contains the point
kvasek [131]

Answer:

The distance of the point from the origin = 9.29 units.

Step-by-step explanation:

Given point:

(7,-6)

The angle lies such that the terminal side of the angle contains the given point.

To draw the angle and find the distance from the origin to the given point.

Solution:

The terminal side of the angle is where the angle ends with the initial side being the positive side of the x-axis.

So, we can plot the point (7,-6) by moving 7 units on the x-axis horizontally and -6 units on the y-axis vertically.

We can find the distance of the point from the origin by find the hypotenuse of the triangle formed.

Applying Pythagorean theorem.

Hypotenuse^2=Shorter\ Leg^2+Shortest\ Leg^2

Hypotenuse^2 = (7)^2+(-6)^2

Hypotenuse^2=49+36\\Hypotenuse^2=85

Taking square root both sides :

\sqrt{Hypotenuse^2}=\sqrt{85}

Hypotenuse = 9.29\ units

Thus, the distance of the point from the origin = 9.29 units.

The figure is shown below.

5 0
3 years ago
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