Help, I need answer ASAP

Mathematics

1 answer:

Kryger [21]2 years ago

3 0

Step-by-step explanation:

HL states that a hypotenuse and leg of a right triangle must be congruent, so you would need to know the hypotenuses are congruent and a leg is congruent. For 6, You're only given 2 sides instead of 3, and since this is a Side-Side-Side Postulate, you must have the third sides be congruent. For 7, Angle-Side-Angle requires to known congruent angles and a side <em>in between </em>them, so you would need to know that angle I is congruent to angle L. Lastly, Side-Angle-Side needs two sides and an angle between them, so you would need to know that side JI is congruent to HD. HI is already congruent to itself by the Reflexive Property, so you only need to know JI ≅ HD.

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Estimate the integral ∫6,0 x^2dx by the midpoint estimate, n = 6

Anettt [7]

Splitting up the interval [0, 6] into 6 subintervals means we have

$[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]$

and the respective midpoints are $\dfrac12,\dfrac32,\dfrac52,\ldots,\dfrac{11}2$ . We can write these sequentially as ${x_i}^*=\dfrac{2i+1}2$ where $0\le i\le5$ .

So the integral is approximately

$\displaystyle\int_0^6x^2\,\mathrm dx\approx\sum_{i=0}^5({x_i}^*)^2\Delta x_i=\frac{6-0}6\sum_{i=0}^5({x_i}^*)^2=\sum_{i=0}^5\left(\frac{2i+1}2\right)^2$

Recall that

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$
$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$
$\displaystyle\sum_{i=1}^n1=n$

so our sum becomes

$\displaystyle\sum_{i=0}^5\left(\frac{2i+1}2\right)^2=\sum_{i=0}^5\left(i^2+i+\frac14\right)$
$=\displaystyle\frac{5(6)(11)}6+\frac{5(6)}2+\frac54=\frac{143}2$

8 0

2 years ago

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ddd [48]

Answer:

$\frac{x - 10}{8}$

Step-by-step explanation:

$\frac{3x}{8} - \frac{x + 5}{4}$

The common denominator of both fractions is 8. Therefore,, divide the denominator of each fraction, then multiply what you get by the numerator of each fraction.

Thus:

$\frac{1(3x) - 2(x + 5)}{8}$

$\frac{3x - 2x - 10}{8}$

$\frac{x - 10}{8}$

5 0

2 years ago

The graph of g(x) is a transformation of the graph of f(x)=2x. Enter the equation for g(x) in the box. g(x) =

Lunna [17]

<h3>Answer: $g(x) = 2^x - 3$ </h3>

The -3 is not in the exponent

Explanation:

The parent function is $f(x) = 2^x$ . Plugging in x = 0 leads to y = 1. So the point (0,1) is on the f(x) curve. Going from (0,1) to (0,-2) is a vertical shift of 3 units downward. To represent this shift, we tack on a "-3" at the end of the f(x) function.