A tangent PQ at a point P of a circle of radius. 5cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :

A)12 cm

B) 13 cm

C) 8.5 cm

D) √119 cm​

[tex]~~~~~~6=2x^2 -11x\\\\\implies 2x^2 -11x -6 = 0\\\\\implies 2x^2 -12x +x-6=0\\\\\implies 2x(x-6) +(x-6) = 0\\\\\implies (2x+1)(x-6) = 0\\\\\implies x = -\dfrac 12,~~ x= 6\\\\\text{Since }~p > q,}~~ p =6~ \text{and}~ q = -\dfrac 12\\ \\\text{So,}~ p-q = 6 -\left(- \dfrac 12 \right)\\\\~~~~~~~~~~~~~=6+\dfrac 12 \\\\~~~~~~~~~~~~~=\dfrac{13}2\\\\~~~~~~~~~~~~~=6.5[/tex]

The value of p -q is 6.5.

Suppose that the given quadratic equation is

ax^2 + bx + c = 0

Then its roots are given as:

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

The equation 6 = 2x^2 - 11x has two solutions, p and q, with p being greater than q.

[tex]6 = 2x^2 - 11x \\\\ 2x^2 - 11x - 6 = 0\\\\ 2x^2 - 12x + x- 6 = 0\\[/tex]

(2x + 1) (x-6) = 0

Thus, x = -1/2 , 6

Since p>q

p = 6 , q = -1/2

So, p -q = 6 - (-1/2)

= 6 + 1/2

= 13/2

= 6.5

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Answer & step-by-step explanation:

to arrive at the similarity, the transformation must be as follow:

the small circle will be dilated for a specific scale factor,

the radius of X circle is R= 6, and the radius of the small circle is r = 2

besides, two circles are similar if and only if R = r, (their radius ar equal)

therefore  r = 2*k = 6, and from where k = 6 / 2 = 3 units

the answer is

Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.

Answer:

Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.

Step-by-step explanation:

To prove circles are similar:

Translate the circles so that they share a common center point. (The circles are now concentric as they have the same center).

Dilate the smaller circle to increase its size to coincide with the larger circle.  The amount that the circle needs to be dilated by is the scale factor.

As the radius of circle Y is 2 and the radius of circle X is 6, determine the scale factor by dividing the larger radius by the smaller radius:

scale factor = 6 ÷ 2 = 3

Solution:

Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.

By the way, you forgot to give us the image:

Answer:

Circle

Step-by-step explanation:

The THREE statements that would produce the truth value F when p is true and q is false are (a) p → q (b) ¬ p ∧ ¬ q (d) q ∨ ¬ p

To do this, we simply analyze each option

The given parameters are:

p = true

q = false

(a) p → q

This means that:

If p then q

So, we have:

If true then false

The above statement would return false.

(b) ¬ p ∧ ¬ q

This means that:

If not p and not q

So, we have:

If not true and not false

i.e.

If false and true

The above statement would return false.

(c) p → ¬ q

This means that:

If p then not q

So, we have:

If true then not false

i.e.

If true then true

The above statement would return true.

(d) q ∨ ¬ p

This means that:

If q and not p

So, we have:

If false and not true

i.e.

If false and false

The above statement would return false.

Hence, the THREE statements that would produce the truth value F when p is true and q is false are (a) p → q (b) ¬ p ∧ ¬ q (d) q ∨ ¬ p

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Answer: HCF=130

Step-by-step explanation:

According to Heron's formula, the area of a triangle whose vertices are R(x, y) = (3, 4), S(x, y) = (6, 2) and T(x, y) = (7, 10) has a value of approximately 14.525 units.

In this question we must determine the lengths of the three sides of the triangle by Pythagorean theorem and then the area is determined by Heron's formula.

First, we determine the length of each side:

[tex]RS = \sqrt{(6-3)^{2}+(2-4)^{2}}[/tex]

[tex]RS = \sqrt{3^{2}+(-2)^{2}}[/tex]

[tex]RS = \sqrt{13}[/tex]

[tex]ST = \sqrt{(7-6)^{2}+(10-2)^{2}}[/tex]

[tex]ST = \sqrt{1^{2}+8^{2}}[/tex]

[tex]ST = \sqrt{65}[/tex]

[tex]RT = \sqrt{(7-3)^{2}+(10-4)^{2}}[/tex]

[tex]RT = \sqrt{4^{2}+6^{2}}[/tex]

[tex]RT = \sqrt{80}[/tex]

Now we calculate the area of the triangle by Heron's formula:

[tex]s = \frac{\sqrt{13}+\sqrt{65}+ \sqrt{80}}{2}[/tex]

s ≈ 10.306

[tex]A = \sqrt{10.306 \cdot (10.306 - \sqrt{13})\cdot (10.306 - \sqrt{65})\cdot (10.306 - \sqrt{80})}[/tex]

A ≈ 14.525

According to Heron's formula, the area of a triangle whose vertices are R(x, y) = (3, 4), S(x, y) = (6, 2) and T(x, y) = (7, 10) has a value of approximately 14.525 units.

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Answer:

F

Step-by-step explanation:

Evaluating the expression :

4 is clearly a rational number.

Hence, the right option is F.

Answer: Second statement is false

Step-by-step explanation: You cannot subtract 89 from 500 and get 500. You get 411.

The above is not a function because -2 is mapped to two elements 2 and -4.

A function relates an input to an output. The three main parts of a function are the inputs, outputs and the relationship.

The formal definition of a function is that it relates each element of a set with exactly one element of another set (possibly the same set).

In other words, one element must be mapped to another element.

Each element cannot be mapped to two elements.

Therefore, the above is not a function.

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A square simply means a shape that has four equal sides and four equal angles.

Your information is incomplete. Therefore, an overview of a square will be given.

A square is a quadrilateral. It's also a rectangle that has two equal length adjacent sides. The four angles are equal to 90° each and are congruent to each other.

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Answer:

[tex]x-8y=-24[/tex]

Step-by-step explanation:

Standard form of a linear equation:  [tex]Ax+By=C[/tex]

(where A, B and C are integers, and A shouldn't be negative)

Given equation:

[tex]y=\dfrac{1}{8}x+3[/tex]

Multiply both sides by 8:

[tex]\implies 8 \cdot y=8 \cdot \dfrac{1}{8}x+8 \cdot 3[/tex]

[tex]\implies 8y=x+24[/tex]

Subtract 8y from both sides:

[tex]\implies 8y-8y=x+24-8y[/tex]

[tex]\implies 0=x+24-8y[/tex]

Subtract 24 from both sides:

[tex]\implies 0-24=x+24-8y-24[/tex]

[tex]\implies -24=x-8y[/tex]

In standard form:

[tex]\implies x-8y=-24[/tex]

The means of simplifiying is by factoring. The simplified form of the expression is 2x² + 3x - 5

The means of simplifiying is by factoring

Given the expression

(2x - 9) (x+ 6)

Expand

(2x - 9) (x+ 6)

2x² +12x -9x - 54
2x² + 3x - 54

Hence the simplified form of the expression is 2x² + 3x - 54

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Answer: It's

c

Step-by-step explanation:

The probabilities are: 20/52, 31/52, 651/2704, 14/31

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in to predict how likely events are to happen.

given: Event A is “game played when warmed up” and Event B is “more shots made than missed.”

Now, P(A)= 20/52

P(B)= 31/52

P(A and B)= P(A)*P(B)

                 = 20/52*31/52

                  = 651/2704

P(A|B)= 14/52÷31/52

        =14/31

Hence, the probability is: 20/52,31/52,651/2704 and 14/13

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Answer:

Volume = 144

V = length(9) × width(6) × height(8) ÷ 3 = 144

Answer:

The solution set is {-6, -2}.

Step-by-step explanation:

x^2 + 8x + 15 = 3

x^2 + 8x = -12

Completing the square:

(x + 4)^2 - 16 = -12

(x + 4)^2 = 4

Taking square roots of both sides:

x + 4 =  +/- 2

x = 2 - 4 = -2  or x = -2-4 = -6.

Answer:

1

Step-by-step explanation:

x = +2 you add 2 every time

y = +2 you add 2 every time

2/2 = 1

Answer:

x=38 degrees

Step-by-step explanation:

Vertical angles are congruent. In the image, angle x is vertical to the angle that is given. Therefore, x=38 degrees

Answer:

With the assumption being made that the 401-k deductions are pre-tax deductions your calculation is as follows:78,300 - 6,500 = 71,800 (this is your new taxable value)71,800 * 0.27 = 19,386 (This is the amount that will be withheld in income taxes per year.Your answer is A.

Answer:

Step-by-step explanation:

With the assumption being made that the 401-k deductions are pre-tax deductions your calculation is as follows:

78,300 - 6,500 = 71,800 (this is your new taxable value)

71,800 * 0.27 = 19,386 (This is the amount that will be withheld in income taxes per year.

Length × Width = Area

Answer:

The length x the widith. If there's more then 4 sides I think you just multiply them all together

Step-by-step explanation:

As it's already graphed their inetresection point is solution for both functions

The solution is (1,5)

Answer:

(1, 5)

Step-by-step explanation:

The solution to the system of equations would be where the lines of the two intersect. The point of intersection (based on the graph) is :

Answer

8.08

Use the distance formula:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

where (x1, y1), (x2, y1) are points

[tex]\rightarrow \sf d =\sqrt{(7-(-8))^2 + (4-(-2))^2}[/tex]

[tex]\rightarrow \sf d =\sqrt{(15)^2 + (6)^2}[/tex]

[tex]\rightarrow \sf d =3\sqrt{29}[/tex]

This is the length of diameter.

Then radius:

· diameter/2

[tex]\sf \cdot \dfrac{3\sqrt{29} }{2}[/tex]

[tex]\sf \cdot 8.0777[/tex]

[tex]\sf \cdot 8.08 \ \ (rounded \ to \ nearest \ hundreth)[/tex]

Hello!

First we should figure out what 7 x 800 is.

7x800 is 5,600.

Next, start step 1.

7 x 8 is already 56, so you would multiply 1 in the box

(7x8x1)

Second, step 2.

56 x 100 is 5,600, so you would put 100 in the box.

(56x100)

Finally, step 3.

Put your total in the box

(TOTAL: 5,600)

Hope this helps!

Answer:

= -6

Step-by-step explanation:

-12/2

= -6

The maximum percentage of individuals who own a bike is 21.5%.

Margin of error is the percentage points a researcher's value would differ from the real population's value. The maximum percentage is the sum of the margin of error and the true value.

The maximum percentage = margin of error + true value

(1/5) x 100 + 1.5% = 21.5%

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Answer:

See image

Step-by-step explanation:

Plato

The number of stray cats in the town in t=0 years will be 243.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

The given function is:-

[tex]f(t) = 243(\dfrac{1}{3})^t[/tex]

f(t) is representing the number of the stray cats in t years so in t=0 years the number of the cats will be:-

[tex]f(t) = 243(\dfrac{1}{3})^0= 243[/tex]

f(t) = 243 cats

It states that initially at t=0 years there were 243 cats in the town.

Therefore the number of stray cats in the town in t=0 years will be 243.

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Answer:

[tex]a = \frac{7b}{5} -11[/tex]

Answer

Hope it helps