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3 years ago

What is the quotient? x+5√3x^2+4x+5

Mathematics

1 answer:

lana [24]3 years ago

7 0

Answer:

the quotient is 3x-9 with a reminder of 50

Step-by-step explanation:

Start the division by looking into the leading terms of both polynomials (3x^2 in the dividend, and x in the divisor):

What algebraic expression would you need to multiply x by in order to get 3x^2?. The answer is: "3x". This would be the first term of your quotient polynomial.

You continue now with the normal division as shown in the attached image.

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Consider the system of equations.

nalin [4]

We know that
The subtraction property of equality tells us that if we subtract from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same

that means

if a=b and c=d
a-c=b-d

then
−8x+4y=0----------> equation 1
a=(-8x+4y) b=0

−8x+7y=6----------> equation 2
c=(-8x+7y) d=6

therefore

(-8x+4y)-(-8x+7y)=0-6
-8x+4y+8x-7y=-6
-3y=-6

the answer is the option
Subtraction Property of Equality

4 0

3 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Consider this s

Brut [27]

Answer:

The solution of this system of equation is ( 3, - 8)

Step-by-step explanation:

1. Let's solve the system of equations:

First equation:

x + 2y = - 13

x = - 13 - 2y

Second equation:

12x + 5y = -4

12 * (- 13 - 2y) + 5y = - 4 (Replacing x with - 13 - 2y)

-156 -24y + 5y = - 4

-24y + 5y = - 4 + 156 (Like terms)

-19y = 152

y = - 152/19

y = -8 (Dividing by 19)

Solving x

x + 2y = -13

x + 2 (- 8 ) = - 13

x - 16 = - 13

x = - 13 + 16

x = 3

2. Proving that x = 3 and y = - 8 are correct:

12x + 5y = -4

12 * 3 + 5 * -8 = -4

36 - 40 = - 4

- 4 = - 4

We proved that x = 3 and y = - 8 are correct

8 0

3 years ago

Pls help ! given: DR tangent to circle O. if m RDC= 150, then m DAC. a. 75 b. 150 c. 300

Sergeu [11.5K]

Check the picture below.

3 0

3 years ago

A person on tour has dollar 360 for his daily expenses. If he extends his tour for 4 days, he has to cut down his daily expenses

mash [69]

Answer:

The original duration of the tour = 20 days

Step-by-step explanation:

Solution:

Total expenses for the tour = $360

Let the original tour duration be for $x$ days.

So, for $x$ days the total expense = $360

Thus the daily expense in dollars can be given by = $\frac{360}{x}$

Tour extension and effect on daily expenses.

The tour is extended by 4 days.

Tour duration now = $(x+4)$ days

On extension, his daily expense is cut by $3

New daily expense in dollars = $(\frac{360}{x}-3)$

Total expense in dollars can now be given as: $(x+4)(\frac{360}{x}-3)$

Simplifying by using distribution (FOIL).

$(x.\frac{360}{x})+(x(-3)+(4.\frac{360}{x})+(4(-3))$

$360-3x+\frac{1440}{x}-12$

$348-3x+\frac{1440}{x}$

We know total expense remains the same which is = $360.

So, we have the equation as:

$348-3x+\frac{1440}{x}=360$

Multiplying each term with $x$ to remove fractions.

$348x-3x^2+1440=360x$

Subtracting $348x$ both sides

$348x-348x-3x^2+1440=360x-348x$

$-3x^2+1440=12x$

Dividing each term with -3.

$\frac{-3x^2}{-3}+\frac{1440}{-3}=\frac{12x}{-3}$

$x^2-480=-4x$

Adding $4x$ both sides.

$x^2+4x-480=-4x+4x$

$x^2+4x-480=0$

Solving using quadratic formula.

For a quadratic equation: $ax^2+bx+c=0$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Plugging in values from the equation we got.

$x=\frac{-4\pm\sqrt{(4)^2-4(1)(-480)}}{2(1)}$

$x=\frac{-4\pm\sqrt{16+1920}}{2}$

$x=\frac{-4\pm\sqrt{1936}}{2}$

$x=\frac{-4\pm44}{2}$

So, we have

$x=\frac{-4+44}{2}$ and $x=\frac{-4-44}{2}$

$x=\frac{40}{2}$ and $x=\frac{-48}{2}$

∴ $x=20$ and $x=-24$

Since number of days cannot be negative, so we take $x=20$ as the solution for the equation.

Thus, the original duration of the tour = 20 days

6 0

2 years ago

What is the probability that the web site has between 3 million and 4 million visitors in a single day? If needed, round your an

faust18 [17]

Answer:

0.2196

Step-by-step explanation:

Given that

Mean = 4.56 million visitors per day

Standard deviation = 820,000 visitors per day

According to the given situation the calculation of probability is shown below:-

Here we will find the value of P (3 ≤ X ≤ 4)

$P 93\leq X\leq 4)=P(X\leq 4) - P(X\leq 3)$

$\\=P(\frac{X-\mu}{\sigma}\leq \frac{4-4.56}{0.82})-P(\frac{X-\mu}{\sigma}\leq \frac{3-4.56}{0.82})$

$\\=P(Z\leq -0.683)-P(Z\leq -1.9024$

= 0.2483 - 0.0287

= 0.2196

Therefore the probability that the web site has between 3 million and 4 million visitors in a single day is 0.2196

4 0

3 years ago