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2 years ago

Which descriptions from the list below accurately describe the relationship between QRS and TUV

Mathematics

2 answers:

Nata [24]2 years ago

8 0

Answer is A. similar

hope it helps

Vera_Pavlovna [14]2 years ago

3 0

Answer:

A. Similar

Step-by-step explanation:

We are given the measurements of ΔQRS and ΔTUV as,

QR = RS = 4, QS = 2 with ∠Q = ∠S = 76°, ∠R = 28°

TU = UV = 12, TV = 6 with ∠T = ∠V = 76°, ∠U = 28°

Now, we see that,

These triangles have different side lengths. So, option C i.e. same sides is not correct.

Also, they are different in size. So, option D i.e. same size is not correct.

Since, they do not have same size, they cannot overlap each other. Thus, are not congruent. So, option B is also not correct.

Thus, we see that from SAS Similarity and the measurements,

QR = RS = 4 and ∠R = 28°

TU = UV = 12 and ∠U = 28°

<em>Both the triangles are similar to each other.</em>

Hence, option A is correct.

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Wanahton purified a portion of water with 900 grams of contaminants. Each hour, a third of the contaminants was filtered out.

Ray Of Light [21]

Answer:

B. Geometric sequence.

$g(n)=900\cdot (\frac{2}{3})^{n-1}$

Step-by-step explanation:

We have been given that Wanahton purified a portion of water with 900 grams of contaminants. Each hour, a third of the contaminants was filtered out.

The amount of contaminants remaining after each hour would be 2/3 of the previous hour amount as 1/3 of contaminants was filtered.

Since amount is not constant, therefore, the sequence would be geometric.

We know that explicit formula for geometric sequence is in form $a(n)=a\cdot r^{n-1}$ , where,

a = First term,

r = Common ratio.

For our given scenario $a=900$ and $r=\frac{2}{3}$ , so our required formula would be:

$g(n)=900\cdot (\frac{2}{3})^{n-1}$

Therefore, an explicit formula for the given geometric sequence would be $g(n)=900\cdot (\frac{2}{3})^{n-1}$ .

8 0

2 years ago

Circle O has a center at (-2, -2) and a diameter of 10 units. What point lies on circle O?

Sophie [7]

The point r(-6,-5) lies on the circle.

Explanation

Given that the center of the circle=(-2,-2)

diameter=10 units

we have to determine which point among the given points lies on the circle.

radius=diameter/2=10/2=5 units

let (x,y) be a point on the circle

The distance between the center and (x,y) is equal to the radius of the circle

The distance between them= $\sqrt{(x-(-2))^2+y-(-2))^2}=5\\\\ \sqrt{(x+2)^2+(y+2)^2} =5\\\\$

squaring both sides $(x+2)^2+(y+2)^2=25\\$

The option (-6,-5) satisfies the equation

therefore the point that lies on the circle is (-6,-5)

8 0

2 years ago

a crane cable can support a maximum load of 15,000 kg. if a bucket has a mass of 2,000 kg and gravel has a mass of 1,500 kg for

Brut [27]

2000 + 1500g ≤ 15000
1500g ≤ 15000 - 2000
1500g ≤ 13000
g ≤ 13000/1500
g ≤ 8 2/3

Therefore, the crane can safely lift a maximum of 8 2/3 cubic meters of gravel.

7 0

2 years ago

Read 2 more answers

Which graph represents y=3 sqrt x+2

ziro4ka [17]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$y=3\sqrt{x+2}$

Remember that the radicand must be greater than or equal to zero

$x+2\geq 0$

solve for x

subtract 2 both sides

$x\geq -2$

The domain is the interval [-2,∞)

All real number greater than or equal to -2

For x=-2

$y=3\sqrt{-2+2}=0$

The range is the interval [0,∞)

All real number greater than or equal to 0

Find the y-intercept

Remember that the y-intercept is the value of y when the value of x is equal to zero

For x=0

$y=3\sqrt{0+2}$

$y=3\sqrt{2}$

$y=4.243$

The y-intercept is the point (0,4.243)

therefore

The graph in the attached figure

7 0

2 years ago

A survey found that 89% of a random sample of 1024 American adults approved of cloning endangered animals. Find the margin of er

Kobotan [32]

Answer:

The margin of error for the survey is 0.016

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 1024

Sample proportion:

$\hat{p} = 89\% = 0.89$

We have to find the margin of error associated with a 90% Confidence interval.

Formula for margin of error:

$z_{stat}\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.10} = 1.64$

Putting the values, we get:

$M.E = 1.64\times (\sqrt{\dfrac{0.89(1-0.89)}{1024}})\\\\M.E=0.016$

Thus, the margin of error for the survey is 0.016

3 0

2 years ago