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3 years ago

In circle S, angle QTR is an inscribed angle. What is the measure of angle QRS?

Mathematics

1 answer:

docker41 [41]3 years ago

7 0

<h2>Answer:</h2>

angle QRS = 51°

<h2>Step-by-step explanation:</h2>

The diagram for the question has been attached to this response.

From the diagram, some circle theorems can be applied.

<em><u>Circle theorem:</u></em>

The angle subtended by an arc of a circle at the centre is twice the angle subtended by it at any other point on the remaining part of the circle.

From the diagram, QR is the arc and therefore:

∠QSR = 2 x ∠ QTR

<em>Since ∠QTR = 39°</em>

=> ∠QSR = 2 x 39°

=> ∠QSR = 78°

<u><em>Other theorem:</em></u>

(i)The base angles of an isosceles triangle are equal.

Triangle QSR is an isosceles triangle, therefore, angles SQR and QRS are equal. i.e

∠SQR = ∠QRS

(ii) The sum of angles of a triangle is 180°. i.e

∠SQR + ∠QRS + ∠QSR = 180°

<em>Since ∠SQR = ∠QRS and ∠QSR = 78°</em>

=> ∠QRS + ∠QRS + 78° = 180°

=> 2(∠QRS) = 180° - 78°

=> 2(∠QRS) = 102°

<em>Divide both sides by 2</em>

=> ∠QRS = 51°

Therefore, angle QRS = 51°

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Which system of equations below has infinitely many solutions? y = –3x 4 and y = –3x – 4 y = –3x 4 and 3y = –9x 12 y = –3x 4 and

Flura [38]

the equations y = –3x + 4 and 3y = –9x + 12 have infinitely many solutions. option B is correct.

<h3>What is the linear system?</h3>

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.

Condition for the parallel lines.

L1, ax + bx + c = 0

L2, dx + ey + f = 0

If $\rm \dfrac{a}{d} = \dfrac{b}{e} = \dfrac{c}{f}$ then lines have infinitely many solutions.

<h3>Which system of equations below has infinitely many solutions?</h3>

y = –3x + 4 and 3y = –9x + 12

On comparing we have

a = -3 , b = 1, and c = 4

d = -9 , e = 3, and f = 12

Then their ratio will be

$\rm \dfrac{1}{3} = \dfrac{-3}{-9} = \dfrac{4}{12}\\\\\rm \dfrac{1}{3} = \dfrac{1}{3} = \dfrac{1}{3}$

Hence y = –3x + 4 and 3y = –9x + 12 have infinitely many solutions.

Thus the option B is correct.

More about the linear system link is given below.

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3 years ago

Please help someone

Romashka-Z-Leto [24]

Answer:

(-2, ∞)

Step-by-step explanation:

A function is "increasing" when its graph goes up to the right, the slope is positive. At a turning point (maximum or minimum), the function is neither increasing nor decreasing.

<h3>Increasing interval</h3>

The graph has a minimum at x = -2. To the left of that point, the graph goes up to the left, which is the same as down to the right (decreasing).

To the right of x = -2, the graph goes up to the right (increasing). It continues to increase for all values of x > 2. The interval where the function is increasing is said to be ...

-2 < x < ∞

The lack of "or equal to" tells you the interval is "open" and is delimited by parentheses in interval notation:

increasing; (-2, ∞)

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2 years ago

Which of the following is a sine of a in the right triangle below

seraphim [82]

Answer:

$\frac{5}{13}$

Step-by-step explanation:

sine of A = $\frac{opposite}{hypotenuse}$

opposite = 5

adjacent = 12

hypotenuse = 13

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3 years ago

Mrs. Smith is shopping for a toy chest to go in her kids' playroom. She looks at the options shown.

AfilCa [17]

The volume of a cuboid toy chest is equal to their product of the length,

width, and height.

The correct option for the toy chest she should purchase is; <u>Only toy chest A will provide the necessary storage space</u>.

Reasons:

The dimensions of the toy chest are;

Toy chest A;

Length = 5 feet

Width = 4 feet

Height = 2 feet

Toy chest B;

Length = 4 feet

Width = 2 feet

Height = 4 feet

Volume of Toy chest A = 5 ft. × 4 ft. × 2 ft. = 40 ft.³

Volume of Toy chest B = 4 ft. × 2 ft. × 4 ft. = 32 ft.³

The volume of the toy chest Mrs. Smith needs = 35 ft.³

The toy chest Mrs. Smith should purchase is Toy chest A, that has a volume of 40 ft.³, which can store items that with a volume of 35 ft.³

The correct option is; <u>Only toy chest A will provide the necessary storage space</u>

<em>Possible question options obtained from a similar question found online are;</em>

<em>Either toy chest have the storage space needed</em>

<em>Neither has the storage space needed</em>

<em>Only toy chest A</em>

<em>Only toy chest B</em>

<em />

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3 years ago

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kolbaska11 [484]

Answer:

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Step-by-step explanation:

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