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muminat
2 months ago
15

Find the x is qs bisects pqr and pqr=82

Mathematics
3 answers:
Svet_ta [12.7K]2 months ago
5 0

Given ∠PQR = 82°, and ray QS bisects it, the ray divides the angle into two equal parts: ∠PQS and ∠RQS, each measuring 82/2 = 41°.


\bf \stackrel{\measuredangle PQS}{10x+1}=41\implies 10x=40\implies x=\cfrac{40}{10}\implies x=4

tester [12.3K]2 months ago
3 0

Answer:

x=4

Detailed Solution:

We know that ray QS bisects angle PQR, with ∠PQR measuring 82°. The task is to find the value of x.

Since QS divides ∠PQR equally, both angles created by QS are half of 82°.

m\angle PQS=\frac{m\angle PQR}{2}

10x+1=\frac{82}{2}

10x+1=41

10x+1-1=41-1

10x=40

\frac{10x}{10}=\frac{40}{10}

x=4

Hence, the value of x is 4.

Inessa [12.5K]2 months ago
0 0

lnbbgdjdidi

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Mr. Barth is creating an arrow across the school parking lot. The area covered by the arrow is calculated to be 70 square units. Step-by-step explanation: I've marked the points on a coordinate grid and connected them with a rough red line, which is shown in the attached image. The arrow's shape consists of a triangle and a rectangle. Therefore, the total area of the arrow equals the triangle's area plus the rectangle's area. The triangle's area is determined using the formula 0.5 * base * height, where the base measures 12 units while the height is 7 units, giving an area of 42. The rectangle's area is calculated as length * height, where length equals 7 and height equals 4, resulting in an area of 28. Hence, the total area of the arrow equals 42 + 28 = 70 square units.
4 0
27 days ago
In general, the probability that it rains on Saturday is 25%. If it rains on Saturday, the probability that it rains on Sunday i
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Answer:

40%

Step-by-step explanation:

According to the provided information:

The likelihood of rain on Saturday stands at 25%.

P(Sunday)=25%=0.25

If it rains on Saturday, the probability of rain on Sunday rises to 50%.

P(Sunday|Saturday)=50%=0.5

If it does not rain on Saturday, the chance of Sunday rain is 25%.

P(Sunday|No Rain on Saturday)=25%=0.25

We aim to find the probability of rain on Saturday given that it rained on Sunday, P(Saturday|Sunday).

P(No rain on Saturday)=1-P(Saturday)=1-0.25=0.75

Using Bayes' theorem for conditional probabilities:

P(Saturday|Sunday)=\frac{P(Sunday|Saturday)P(Saturday)}{P(Sunday|Saturday)P(Saturday)+P(Sunday|No Rain on Saturday)P(No Rain on Saturday)}

=\frac{0.5*0.25}{0.5*0.25+0.25*0.75}

=0.4

Thus, there is a 40% likelihood that it rained on Saturday given the conditions on Sunday.

5 0
1 month ago
A train travels train travels 288 kilometre at a uniform speed. If the speed had been 4 kilometre per hour more it would have ta
PIT_PIT [12445]

Answer:

Let the train's speed be denoted as x km/h.

Scenario 1:

Distance = 288 km

Speed = x km/h

Time = Distance divided by Speed

= 288/x hours

Scenario 2:

Distance = 288 km

Speed = (x + 4) km/h

Time = 288/(x + 4) hours

As 288/x is greater than 288/(x + 4)

288/x - 288/(x + 4) = 1

288[1/x - 1/(x + 4)] = 1

[x + 4 - x] / [x(x + 4)] = 1/288

[4 / (x^2 + 4x)] = 1/288

x² + 4x = 1152

x² + 4x - 1152 = 0

x² + 36x - 32x - 1152 = 0

x(x + 36) - 32(x + 36) = 0

(x + 36)(x - 32) = 0

x + 36 = 0, x - 32 = 0

x = -36, x = 32

x = -36 is not valid as speed cannot be negative.

Conclusively, the train's speed = 32 km/h

4 0
1 month ago
CALC 1: Spud's mom is going to make him a round birthday cake, and has asked for your help. Spud is a bit weird, and has already
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Answer:

15.7 inches

Step-by-step breakdown:

A slice of a round pie is a sector of a circle.

The perimeter of a slice equals the arc length s plus two times the radius r. P = s + 2r

s = rθ = r(16/360) = r/22.5. Therefore,

16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5

16 × 22.5 = 46r

360 = 46r

r = 7.826

D = 2r = 2 × 7.826 = 15.7 inches

Thus, the diameter of the cake should be 15.7 inches.

Verification:

\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}

It is accurate.

 

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Answer:

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Detailed explanation:

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Denote the profit function as P(x).

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Hence, selling 240 phones yields a profit of $16,850

5 0
2 months ago
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