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3 years ago

PLEASE ANSWER FAST WILL GIVE BRANLIEST DONT RESPOND WITH LINKS

Mathematics

1 answer:

Virty [35]3 years ago

7 0

Answer:

<6, <5, <7 all equal 48 degrees.

<1, <2, <3, <4 all equal 132 degrees.

Step-by-step explanation:

Straight angles (like <5 & <2) are supplementary, so they equal 180 when added together

Vertical angles (like <2 & <1) have the same measurments

Corresponding angles (like <8 & <6) have the same measurements

Alternate interior angles (like <8 & <5) have the same measurments

Alternate exterior angles (like <6 & <7) have the same measurements

Same-side interior angles (like <8 & <2) are supplementary, so they add to 180.

There's more, and there's other ways to do this, this is just an example. Good luck! <3

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The figures below show a pattern.

yarga [219]

Answer:

The number of blocks in the nth figure will be (3n + 1).

Step-by-step explanation:

See the attached figure where few arrangements are there.

The number of blocks in the first arrangement is (3 + 1)

Now, the number of blocks in the second arrangement is (3 × 2 + 1)

Again, the number of blocks in the third arrangement is (3 × 3 + 1)

So, the pattern says that the number of blocks in the nth arrangement will be (3 × n + 1) = (3n + 1) (Answer)

7 0

4 years ago

Find the average of e^-x over [0,3]

yaroslaw [1]

The average value of a continuous function f(x) over an interval [a, b] is given by the integral,

$\displaystyle \frac1{b-a}\int_a^b f(x)\,\mathrm dx$

Compute the integral for f(x) = e ⁻ˣ over [0, 3] :

$\displaystyle \frac1{3-0}\int_0^3e^{-x}\,\mathrm dx=\frac13(-e^{-x})\bigg|_0^3=\frac13(-e^{-3}-(-e^{-0})) = \frac13 \left(1-\frac1{e^3}\right) = \boxed{\frac{e^3-1}{3e^3}}$

8 0

3 years ago

Look at the following expression.

FinnZ [79.3K]

C is not equivalent to all the expressions

3 0

3 years ago

Find the coordinates of the centroid of the triangle formed by the x-axis, the y-axis, and the line 12x + 9y = 36, show work ple

emmainna [20.7K]

Given the line 12x + 9y = 36

the line intersects the x-axis when y = 0,

i.e. 12x = 36 ⇒ x = 3

Thus the x-intecept is (3, 0)

the line intersects the y-axis when x = 0,

i.e. 9y = 36 ⇒ y = 4

Thus, the y-intercept is (0, 4)

Thus, the coordinates of the vertices of the triangle are (0, 0), (0, 4) and (3, 0)

The midpoint of the side of the rectangle joining points (0, 0) and (0, 4) is (0, 2) and the equation of the median joining points (0, 2) and (3, 0) is given by

$\frac{y-2}{x} = \frac{-2}{3} \\ \\ \Rightarrow3(y-2)=-2x \\ \\ \Rightarrow y=- \frac{2}{3} x+2$

The midpoint of the side of the rectangle joining points (0, 0) and (3, 0) is (1.5, 0) and the equation of the median joining points (1.5, 0) and (0, 4) is given by

$\frac{y}{x-1.5} = \frac{4}{-1.5} \\ \\ \Rightarrow1.5y=-4(x-1.5)=-4x+6 \\ \\ \Rightarrow y=- \frac{8}{3} x+4$

The point of intersetion of the two medians is given by

$- \frac{2}{3} x+2=- \frac{8}{3} x+4 \\ \\ \Rightarrow2x=2 \\ \\ \Rightarrow x=1 \\ \\ \Rightarrow y=-\frac{2}{3}+2=\frac{4}{3}$

Therefore, the centroid of the given triangle is located at point $\left(1, \frac{4}{3} \right)$

4 0

3 years ago

A company receives a 10%, 120-day note for $1,500. The total interest due on the maturity date is

DochEvi [55]

Assuming a simple interest model for this information, the interest due at maturity will be:
I=(PRT)/100
where:
P=principle
R=rate
T=time
thus
I=1500×120/364×10/100
I=$49.45
Answer: $49.45

3 0

3 years ago