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3 years ago

5. Which statement is true about the triangles?

Mathematics

2 answers:

Lynna [10]3 years ago

6 0

I think it’s D, none of the triangles are similar. Hope this helps!

Vadim26 [7]3 years ago

5 0

Hey there! I'm happy to help!

It appears that we are trying to figure out which triangles are similar, which means that their side lengths have the same ratio. In ΔABC, we see that two sides have a length of 10 and the shorter has a length of 5. This means that the ratio between the long sides and the short sides must be 2:1 to be similar to this triangle.

Let's look at ΔJKL. Our long side has to be double our short side. If we double 2.5, it will be 5, not six, so JKL is not similar with ABC.

Now, let's look at ΔDEF. We see that it's long sides are double the short sides because 6 is double three. This means that the triangles ABC and DEF are similar.

The answer is A) ΔABC ~ ΔDEF.

I hope that this helps! Have a wonderful day!

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What is the common difference of the following sequence: -6, -2, 2, 6

o-na [289]

Answer:

Step-by-step explanation:

Subtract a number from the number after it.

6 - 2 = 4

8 0

3 years ago

(c) a farm brings 15 tons of watermelon to market. find a 90% confidence interval for the population mean cash value of this cro

Nina [5.8K]

Answer:

First we need to name some of the variables we are given:n = 38 the sample sizex = 6.88 the sample mean = 1.86 the population standard deviationWe need to find a 90% confidence interval for the mean price per 100 lbs of watermelon: = 1-.90 = .10/2 = .05z(/2) = -1.64-z(/2) = 1.64This can give us a probability expression:P(-1.645 < z < 1.645) = .90The margin of error is calculated with the formula: E = z(/2)(/√n)E = 1.645(1.86/√38) = $.4963(300) = $148.89 Then to calculate the upper and lower limit we add and subtract E from x:lower limit = 6.88 - .4963 = $7.38(300) = $2214upper limit = 6.88 + .4963 = $6.38(300) = $1914Note: We multiply the E, upper and lower limits by 300 because 15 tons is 30000lbs and we need the price per 100 lbs, so we divide 30000/100 and get 300.

Step-by-step explanation:

7 0

2 years ago

What is the squared root of 9 times by 1,000,000,001 divided by 4 and subtracted by 8672 then cubed twice

Delicious77 [7]

The answer would be 9.650055637900878
Hope this helped!!

3 0

3 years ago

Prove that C(50,3) + C(50,4) = C(51,4)

valkas [14]

By definition of the binomial coefficient,

$C(n,k) = \dfrac{n!}{k!(n-k)!}$

so we have

$C(50,3) + C(50,4) = \dfrac{50!}{3!47!} + \dfrac{50!}{4!46!} \\\\ = \dfrac{50!}{3!46!} \left(\dfrac1{47} + \dfrac14\right) \\\\ = \dfrac{50!}{3!46!} \times \dfrac{51}{188} \\\\ = \dfrac{51!}{3!46!} \times \dfrac1{4\times47} \\\\ = \dfrac{51!}{4!47!} \\\\ = \dfrac{51!}{4!(51-4)!} = C(51,4)$

as required.

5 0

2 years ago

Find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y, z) = xy2z2 has a maximum value.

irina1246 [14]

Lagrange multipliers:

$L(x,y,z,\lambda)=xy^2z^2+\lambda(x+y+z-5)$

$L_x=y^2z^2+\lambda=0$
$L_y=2xyz^2+\lambda=0$
$L_z=2xy^2z+\lambda=0$
$L_\lambda=x+y+z-5=0$

$\lambda=-y^2z^2=-2xyz^2=-2xy^2z$

$-y^2z^2=-2xyz^2\implies y=2x$ (if $y,z\neq0$ )

$-y^2z^2=-2xy^2z\implies z=2x$ (if $y,z\neq0$ )

$-2xyz^2=-2xy^2z\implies z=y$ (if $x,y,z\neq0$ )

In the first octant, we assume $x,y,z>0$ , so we can ignore the caveats above. Now,

$x+y+z=5\iff x+2x+2x=5x=5\implies x=1\implies y=z=2$

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of $f(1,2,2)=16$ .

We also need to check the boundary of the region, i.e. the intersection of $x+y+z=5$ with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force $f(x,y,z)=0$ , so the point we found is the only extremum.

4 0

3 years ago