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3 years ago

Simplify quantity x squared plus 3 x plus 2 end quantity over quantity x plus 1

Mathematics

1 answer:

Alenkasestr [34]3 years ago

6 0

Answer:

<u>After factorizing the equation on the numerator, we simplify and the answer is: x + 2</u>

Step-by-step explanation:

1. Let's simplify the following expression:

x squared plus 3 x plus 2 over x plus 1

(x ² + 3x + 2) / (x + 1)

Now, we are going to factorize the numerator, this way:

(x + 2) (x + 1) / ( (x + 1)

x * x = x ²; 2x + x = 3x ; 2 * 1 = 2 ⇒ x² + 3x + 2

We simplify (x + 1) both in the numerator and in the denominator and we have:

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7. (07.05 LC) What is the value of x in the equation −x = 4 − 3x + 6? (5 points) 5 10 −5 −10

Lelechka [254]

Answer:

Step-by-step explanation:

-x = 4 - 3x + 6

3x-x = 4 + 6

2x = 10

x = 5

5 0

3 years ago

Read 2 more answers

Ten college students were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 a

solong [7]

Answer:

The 95% confidence interval for the true slope is (0.03985, 0.14206).

Step-by-step explanation:

For the regression equation:

$\hat y=\alpha +\hat \beta x$

The (1 - <em>α</em>)% confidence interval for the regression coefficient or slope $(\hat \beta )$ is:

$Ci=\hat \beta \pm t_{\alpha/2, (n-2)}\times SE(\hat \beta )$

The regression equation for current GPA (Y) of students based on their GPA's when entering the program (X) is:

$\hat Y=3.584756+0.090953 X$

The summary of the regression analysis is:

Predictor Coefficient SE t-stat p-value

Constant 3.584756 0.078183 45.85075 5.66 x 10⁻¹¹

Entering GPA 0.090953 0.022162 4.103932 0.003419

The regression coefficient and standard error are:

$\hat \beta = 0.090953\\SE (\hat \beta)=0.022162$

The critical value of <em>t</em> for 95% confidence level and 8 degrees of freedom is:

$t_{\alpha/2, n-2}=t_{0.05/2, 10-2}=t_{0.025, 8}=2.306$

Compute the 95% confidence interval for $(\hat \beta )$ as follows:

$CI=\hat \beta \pm t_{\alpha/2, (n-2)}\times SE(\hat \beta )\\=0.090953\pm 2.306\times 0.022162\\=0.090953\pm 0.051105572\\=(0.039847428, 0.142058572)\\\approx (0.03985, 0.14206)$

Thus, the 95% confidence interval for the true slope is (0.03985, 0.14206).

6 0

3 years ago

Helppppp nowwwww please

andrew11 [14]

P = d - 5.50
The cost of buying materials will be subtracted from what he earns. Therefore, what’s left over is the profit

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4 years ago

Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D

Ivahew [28]

Check the picture below.

$\bf \textit{Law of Cosines}\\ \quad \\
c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies 
c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}
\\\\\\
\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}=cos(C)\implies cos^{-1}\left(\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}\right)=\measuredangle C\\\\
-------------------------------\\\\
\begin{cases}
d=10\\
e=18\\
f=22
\end{cases}\implies cos^{-1}\left(\cfrac{{{ 18}}^2+{{ 22}}^2-10^2}{2(18)(22)}\right)=\measuredangle D$

$\bf \implies cos^{-1}\left(0.893\overline{93}\right)=\measuredangle D\implies 26.63^o\approx \measuredangle D$

7 0

3 years ago

The functions f(x) and g(x) are described using the following equation and table: f(x) = −6(1.05)x x g(x) −4 −9 −2 −6 0 −3 2 2 W

kiruha [24]

Based on our examination of the y-intercepts, we can deduce that the y-intercept of function f(x) is equivalent to two times the y-intercept of function g. (x)

<h3>What is the examination of the y-intercept?</h3>

The value of the function at the point where the value of x is equal to zero is known as the y-intercept.

f(x)=-6(1.05)^x

Considering x

x=0

f(0)=-6(1.05)^0

f(0)=-6(1)

f(0)=-6

Therefore, the y-intercept is point (0,-6)

Generally, the equation for the function of the y-intercept of g(x) is mathematically given as

From table

at x=0

The y-intercept is the point (0,-3)

Based on our examination of the y-intercepts, we can deduce that the ty-intercept of function f(x) is equivalent to two times the y-intercept of function g. (x)