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3 years ago

What is the measure of angle RPS?

Mathematics

2 answers:

liq [111]3 years ago

8 0

Answer:

Step-by-step explanation: the type of angle it is

Anastasy [175]3 years ago

7 0

Answer:

∠RPS = 70°

Step-by-step explanation:

∠RPT is a right angle and

∠RPS + ∠SPT = ∠RPT ← substitute values

∠RPS + 20° = 90° ( subtract 20° from both sides )

∠RPS = 70°

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3 years ago

Help asap do all these show work posting more after this one

ivanzaharov [21]

Answer:

1) (2,10) is solution of y=4x+2

2) (7,5) is not solution of 2x+y=5

3) (-3,3) is not solution of y=6-x

4) (10,-1) is solution of x+8y=2

5) (2,21) is not solution of y=6x+7

6) (6,-8) is solution of 3x-y=26

Step-by-step explanation:

1) y=4x+2 (2,10)

Put x=2 and y=10 and check if both sides are equal or not

10=4(2)+2

10=8+2

10=10

So, (2,10) is solution of y=4x+2

2) 2x+y=5 (7,5)

Put x=7 and y=5 and check if both sides are equal or not

2x+y=5

2(7)+5=5

14+5=5

19≠5

So, (7,5) is not solution of 2x+y=5

3) y=6-x (-3,3)

Put x=-3 and y=3 and check if both sides are equal or not

y=6-x

3=6-(-3)

3=6+3

3≠9

So, (-3,3) is not solution of y=6-x

4) x+8y=2 (10,-1)

Put x=10 and y=-1 and check if both sides are equal or not

x+8y=2

10+8(-1)=2

10-8=2

2=2

So, (10,-1) is solution of x+8y=2

5) y=6x+7 (2,21)

Put x=2 and y=21 and check if both sides are equal or not

y=6x+7

21=6(2)+7

21=12+7

21≠19

So, (2,21) is not solution of y=6x+7

6) 3x-y=26 (6,-8)

Put x=6 and y=-8 and check if both sides are equal or not

3x-y=26

3(6)-(-8)=26

18+8=26

26=26

(6,-8) is solution of 3x-y=26

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3 years ago

find the area of the isocele triangle formed by the points of intersection of parabolas y=-x^2+9 and y=2x^2-3 and the origin

leonid [27]

Answer:

$10\ \text{sq. units}$

Step-by-step explanation:

The parabola's are

$y=-x^2+9$

$y=2x^2-3$

$-x^2+9=2x^2-3\\\Rightarrow 12=3x^2\\\Rightarrow \\\Rightarrow x=\sqrt{\dfrac{12}{3}}\\\Rightarrow x=\pm 2$

$y=-x^2+9=-(2)^2+9\\\Rightarrow y=5$

$y=-(-2)^2+9=5$

So, the points at which the parabola's intersect each other is $(2,5)$ and $(-2,5)$

The three points of the triangle are $(2,5)$ , $(-2,5)$ and $(0,0)$

Area of a triangle is given by

$A=\dfrac{1}{2}[x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)]\\\Rightarrow A=\dfrac{1}{2}[2(5-0)+(-2)(0-5)+0(5-5)]\\\Rightarrow A=10\ \text{sq. units}$

Area of the triangle formed is $10\ \text{sq. units}$ .

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3 years ago

Tom went with his dad to a shooting range. His dad bought him 10 bullets. For every time he got bullseye, the father gave his so

marusya05 [52]

Answer: Tom hit the bullseye 23 times .

Step-by-step explanation:

Let the number of times Tom hit the bullseye be 'x'

Since we have given that

Total number of times Tom shot = 55

Number of times he missed the shot be '55-x'

Number of bullets he already have = 10

According to question, For every time, he got bullseye, the father gave him an extra bullet and after every miss he took one away.

At last he ran out of bullets.

So, it becomes,

$10+1\times x-1(55-x)=0\\\\10+x-55+x=0\\\\2x-45=0\\\\2x=45\\\\x=\frac{45}{2}=22.5\\\\\text{ But number of times can't be in decimal }\\\\So,\ x=23$

Hence, Tom hit the bullseye 23 times .

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3 years ago