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3 years ago

Point O is the center of the circle. What is the value of x?

Mathematics

2 answers:

Bad White [126]3 years ago

8 0

OQ = 8 + 9 = 17
x^2 = 17^2 - 8^2
x^2 = 289 - 64
x^2 = 225
x = 15

Aleonysh [2.5K]3 years ago

7 0

Answer:

x = 15 cm.

Step-by-step explanation:

Given :Point O is the center of the circle.

To find : What is the value of x?

Solution : We have given that a circle of radius 8 cm .

The tangent to a circle is perpendicular to the radius at the point of tangency.

By applying the Pythagorean theorem

OQ² = OP² + PQ²

Plugging the values OQ = 9 +8 , OP = 8 , PQ = x

(17)² = (8)² + (x)².

289 = 64 + (x)².

On subtracting 64 from both sides

289 -64 = (x)²

225 = (x)²

On taking square root both side

x = 15

Therefore, x = 15 cm.

You might be interested in

Solve for x -2^2(-5x+10)=100

masha68 [24]

Answer:

$x=7$

Step-by-step explanation:

Hi there!

$-2^2(-5x+10)=100$

Solve -2^2:

$-4(-5x+10)=100$

Divide both sides by -4:

$\displaystyle \frac{ -4(-5x+10)}{-4}=\frac{100}{-4} \\\\-5x+10=-25$

Subtract 10 from both sides:

$-5x+10-10=-25-10\\-5x=-35$

Divide both sides by -5:

$\displaystyle \frac{-5x}{-5} = \frac{-35}{-5} \\\\x=7$

Therefore, x = 7.

I hope this helps!

3 0

3 years ago

What are the coordinates of P' if P (-5,-4) undergoes a dilation, centered at the origin, with a scale factor of K=2?

Margaret [11]

Answer:

$P' = (-10,-8)$

Step-by-step explanation:

Given

$P = (-5,-4)$

$k =2$

Required

Determine the image P'

P' is calculated by multiplying P and k.

i.e.

$P' = P * k$

This gives:

$P' = (-5,-4) * 2$

$P' = (-5* 2,-4* 2)$

$P' = (-10,-8)$

Hence, the image P' after dilating P is (-10,-8)

7 0

3 years ago

PLS Help me Error Analysis

Maksim231197 [3]

we have

Pieces of mail delivered in December by the US postal service

$7.14*10^{10}$

Pieces of mail delivered in January by the US postal service

$3.21*10^{10}$

To find the total mail delivered for these two months, sum the two quantities

$7.14*10^{10}+3.21*10^{10}=(7.14+3.21)*10^{10}\\=10.35*10^{10} \\=(1.035*10)*10^{10} \\=1.035*(10* 10^{10})\\=1.035*10^{(10+1)} \\= 1.035*10^{11}$

therefore

the correct solution is $1.035*10^{11}$

the error is in this part

$10.35*10^{10}$

To move decimal over one place 10 to the power of 10 should be 10 to the power of 11

$1.035*10^{10}$

3 0

3 years ago

The length and width of a rectangle are measured as 55 cm and 49 cm, respectively, with an error in measurement of at most 0.1 c

valentina_108 [34]

Answer:

The maximum error in the calculated area of the rectangle is $10.4 \:cm^2$

Step-by-step explanation:

The area of a rectangle with length $L$ and width $W$ is $A= L\cdot W$ so the differential of A is

$dA=\frac{\partial A}{\partial L} \Delta L+\frac{\partial A}{\partial W} \Delta W$

$\frac{\partial A}{\partial L} = W\\\frac{\partial A}{\partial W}=L$ so

$dA=W\Delta L+L \Delta W$

We know that each error is at most 0.1 cm, we have $|\Delta L|\leq 0.1$ , $|\Delta W|\leq 0.1$ . To find the maximum error in the calculated area of the rectangle we take $\Delta L = 0.1$ , $\Delta W = 0.1$ and $L=55$ , $W=49$ . This gives

$dA=49\cdot 0.1+55 \cdot 0.1$

$dA=10.4$

Thus the maximum error in the calculated area of the rectangle is $10.4 \:cm^2$

4 0

3 years ago

Two sides of a triangle are as follows: 2 centimeters and 5 centimeters. Describe the possible lengths of the third side

Elden [556K]

Answer:

3cm < Third side < 7cm

Thus third side can take any value between 3cm and 7 cm

(note: excluding 3 cm and 7 cm)

If the value are integral then possible values of third side are

4cm, 5cm,6cm

Step-by-step explanation:

This question can be solved using given by Triangle Inequality Theorem Given below.

Sum of two sides is always greater than value of third side
Difference of two sides is always less than value of third side

Given two sides are 2cm, 5cm

Sum of two sides = (2+5)cm = 7 cm

Difference of two sides = (5-2) = 3 cm

Let the third side be X

thus according to Triangle Inequality Theorem

X < Sum of two sides of given triangle

X < 7cm -----1

X > Difference of two sides

X > 3cm ----1

combining expression 1 and 2 we have

3cm < X < 7cm

Thus third side can take any value between 3cm and 7 cm

(note: excluding 3 cm and 7 cm)

If the value are integral then possible values are

4c, 5cm,6c

7 0

2 years ago