Find the midpoint between two points on a number line if one of the points is at -7, and the other point is at 12.
A. 9.5
B. 5
C. -2
D. 2.5​

Answer:

a. The required proof is obtained from triangles OAB and ABC formed by joining AB and that we have;

A[tex]\hat O[/tex]B + 2∠C = 180°, 2·A[tex]\hat P[/tex]B + 2∠C = 180°

∴ A[tex]\hat O[/tex]B = 2·A[tex]\hat P[/tex]B

b. i) P[tex]\hat S[/tex]S = P[tex]\hat R[/tex]Q, given that angles subtended by the same arc or chord are equal, therefore, in ΔPQS, we have;

[tex]\left | PS \right |[/tex] = [tex]\left |PQ \right |[/tex]

ii) S[tex]\hat Q[/tex]P = 45°, [tex]S\hat R Z[/tex] =90°

Step-by-step explanation:

a. The given parameters are;

The center of the circle is point O

Points on the circumference of the circle = A, B, and P

Required to be proved, A[tex]\hat O[/tex]B = 2·A[tex]\hat P[/tex]B

Let ∠O represent A[tex]\hat O[/tex]B and let ∠P' represent A[tex]\hat P[/tex]B

We draw a line from the center O to the point P, and a line joining points A and B on the circumference of the circle

In ΔOAB, we have;

∠O + 2∠C = 180° (The sum of the interior angles of a triangle)

In ΔAPB, we have;

∠P' + ∠(C - a) + ∠(P' + C + a) = 180°

∴ 2·∠P' + 2·∠C = 180°

Therefore, by addition property of equality, we get;

∠O = 2·∠P'

Therefore;

A[tex]\hat O[/tex]B = 2·A[tex]\hat P[/tex]B

b. i) The given parameters are;

Points on the circle = P, Q, R, and S

P[tex]\hat Q[/tex]S = P[tex]\hat R[/tex]Q

According to circle theory, the angles which an arc or chord subtends in a given segment are equal, therefore;

P[tex]\hat S[/tex]S = P[tex]\hat R[/tex]Q

Therefore, P[tex]\hat S[/tex]S = P[tex]\hat Q[/tex]S by transitive property of equality

P[tex]\hat S[/tex]S and P[tex]\hat Q[/tex]S are base angles of ΔPQS, given that P[tex]\hat S[/tex]S = P[tex]\hat Q[/tex]S, we have;

ΔPQS is an isosceles triangle with base QS and therefore, the sides PS and PQ are the equal sides

Therefore, we have;

[tex]\left | PS \right |[/tex] = [tex]\left |PQ \right |[/tex]

ii) Given that SQ is the diameter of the circle, we have by circle theorem, the angle subtended on the circumference by the diameter = 90°

∴ [tex]S\hat PQ[/tex] = 90°

From (i), we have that P[tex]\hat S[/tex]S = P[tex]\hat Q[/tex]S, therefore, in triangle ΔPQS, we have;

[tex]S\hat PQ[/tex] + P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 180°

Therefore;

90° + P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 180°

P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 180° - 90° = 90°

P[tex]\hat S[/tex]S = P[tex]\hat Q[/tex]S, therefore, P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 2·S[tex]\hat Q[/tex]P

P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 2·S[tex]\hat Q[/tex]P = 90°

S[tex]\hat Q[/tex]P = 90°/2 = 45°

S[tex]\hat Q[/tex]P = 45°

Similarly, given that SQ is the diameter, of the circle the angle [tex]S\hat R Q[/tex] formed by jointing S to Q is 90°

[tex]S\hat R Q[/tex] = 90°

[tex]S\hat R Q \ and \ S\hat R Z[/tex] are angles on a straight line and are therefore, supplementary, therefore;

[tex]S\hat R Z[/tex] = 180° - [tex]S\hat R Q[/tex]

[tex]S\hat R Z[/tex] = 180° - 90° = 90°

[tex]S\hat R Z[/tex] =90°.

Answer:

Another example of a number who's square root is greater than the number is  [tex]\sqrt{0.49}[/tex] which is 0.7

Step-by-step explanation:

This square root is larger than the number because it is a decimal. When you multiply a decimal by a decimal, the decimal point becomes greater. For example: 0.7 multiplied by 0.7 equals 0.49 which has 2 decimal places, while 0.7 only has one.

Answer:

The slope is -3/4 and a point on the line is (-5,4)

Step-by-step explanation:

This equation is in point slope form

y -y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

Y-4=-3/4(x+5)

Y-4=-3/4(x -  -5)

The slope is -3/4 and a point on the line is (-5,4)

Answer:

There is a slight problem with this question

Do numbers starting with "0" count as a digit position

I would say no, thus the answer is 4...

if you are allowed to use 0 then the answer is 8

in other words if the question was using only 4's and 1's then the answer would be 8  

Step-by-step explanation:

000

004

040

044

400

404

440

444

Answer:

desmos .com

Step-by-step explanation:

Answer: See the graph below

Step-by-step explanation:

Concept:

Formula for circle: (x - k )² + (y - h)² = r²

Center = (k, h)

Radius = r

**Disclaimer** variables used can be different

------------------------------------------------------------------------

Solve:

Given: (x - 2)² + (y + 3)² = 16

Center = (2, -3)

Radius = √16 = 4

Hope this helps!! :)

Please let me know if you have any questions

Answer:

1

Step-by-step explanation:

9514 1404 393

Answer:

  B.  3x² +2 = 0

Step-by-step explanation:

The equation of A has a couple of real roots. We're pretty sure there are complex numbers that will satisfy this equation, but we don't know how to find them. (We suspect a typo, and that the equation is supposed to be 2x² +1 = 7x, which has only real roots.)

__

The equation of B can be rewritten as ...

  x² = -2/3

This will have complex roots.

__

The discriminants of both equations C and D are positive, so those have only real roots.

  2x² -5x -1   ⇒   d = (-5)² -4(2)(-1) = 33

  3x² -6x -1   ⇒   d = (-6)² -4(3)(-1) = 48

Answer: 16:81

Step-by-step explanation:

Answer:

V = 24.28 in ^3

Step-by-step explanation:

The area of the base is

A =5/2 × s × a  where s is the side length and a is the apothem

A = 5/2 ( 2.13) * .87

A = 4.63275

The volume is

V = Bh  where B is the area of the base and h is the height

V = 4.63275 ( 5.24)

V =24.27561 in^3

Rounding to the  hundredth

V = 24.28 in ^3

Answer:

f (x) = x3 – 3x2 – 5x + 15

Step-by-step explanation:

i just took the test

The required polynomial is [tex]\bold{f(x)=x^{3}-3x^{2}-5x+15}[/tex]

The correct answer is an option (C)

"It is an algebraic expression that consist of variables and coefficients."

For given question,

The polynomial function has the zeros 3, radical 5, and negative radical 5.

The polynomial function has zeros 3, √5, -√5

This means the factors of the polynomial function are (x - 3), (x - √5) and (x - (-√5)) = (x + √5).

Using the Factor theorem the polynomial function would be,

[tex]\Rightarrow f(x)=0\\\\\Rightarrow (x - 3)\times (x - \sqrt{5} )\times (x + \sqrt{5} ) = 0\\\\\Rightarrow (x-3)\times (x^{2} - (\sqrt{5} )^{2} )=0\\\\\Rightarrow (x-3)\times (x^{2} - 5)=0\\\\\Rightarrow x \times (x^{2} - 5) - 3\times (x^{2} - 5) =0\\\\\Rightarrow x^{3}-5x-(3x^{2}-15)=0\\\\\Rightarrow x^{3}-3x^{2}-5x+15=0[/tex]

Therefore, the required polynomial is [tex]\bold{f(x)=x^{3}-3x^{2}-5x+15}[/tex]

The correct answer is an option (C)

Learn more about the factors of the polynomial here:

https://brainly.com/question/26354419

#SPJ2

Answer:

the first one...

the cost of renting the ally for 14 hours

Step-by-step explanation:

Answer:

the first one

the number of dollars it costs to rent the bowling lane for14 hours

Answer:

see explanation

Step-by-step explanation:

Under a clockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ) , then

(3, 3 ) → (- 3, 3 )

(3, 4 ) → (- 4, 3 )

(5, 3 ) → (- 3, 5 )

Answer:

4x -12

Step-by-step explanation:

8 - 4(-x + 5)

Distribute

8 -4(-x) -4(5)

8 +4x -20

4x -12

answer 4( - 3 + x)

answer

[tex]4( - 3 + x)[/tex]

[tex]8 - 4( - x + 5)[/tex]

answer

[tex] - 12 + 4x[/tex]

Answer:

y = -4.9/5.4x - 1.17

Step-by-step explanation:

First let's convert the equation to standard form of y = mx + b.

4.9x + 5.4y = 3

Subtract 4.9x from both sides.

5.4y = -4.9x + 3

Divide each term by 5.4.

y = -4.9/5.4x + 0.56

If two lines are parallel to each other, they have the same slope slopes.

The first line is y = -4.9/5.4x + 0.56. Its slope is -4.9/5.4. A line parallel/perpendicular to this one will also have a slope of -4.9/5.4.

Plug this value (-4.9/5.4) into your standard point-slope equation of y = mx + b.

y = -4.9/5.4x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (-3.6, 2.1). Plug in the x and y values into the x and y of the standard equation.

2.1 = -4.9/5.4(-3.6) + b

To find b, multiply the slope and the input of x (-3.6)

2.1 = 3.27 + b

Now, subtract 3.27 from both sides to isolate b.

-1.17 = b

Plug this into your standard equation.

y = -4.9/5.4x - 1.17

This equation is parallel/perpendicular to your given equation (y = -4.9/5.4x + 0.56) and contains point (-3.6, 2.1)

Hope this helps!

Answer:

v =  14 km/h

Step-by-step explanation:

d = 0.0067[tex]v^{2}[/tex] + 0.15v

differentiate the function with respect to v to have;

d = 0.0134v - 0.15

given that the distance without skidding = 37 m (0.037 km) , then;

0.037 = 0.0134v - 0.15

0.0134v = 0.037 + 0.15

             = 0.187

v = [tex]\frac{0.187}{0.0134}[/tex]

  = 13.9552

v =  14 km/h

The speed of the car travelling would be 14 km/h to be able to stop within 37m.

1. a= 19

2.2 ( second option)

3.C

4D

Answer:

[tex]\begin{array}{ccccccc}&Natural&Whole &Integer&Rational&Irrational&Real\\-3\dfrac{3}{9}&&&& \checkmark&&\checkmark\\\sqrt{11} &&&&&\checkmark &\checkmark\\125&\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\4\cdot \sqrt[3]{125} &\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\7.\overline {17} &&&& \checkmark&&\checkmark\end{array}[/tex]

Step-by-step explanation:

The given numbers and their categories are;

1) [tex]-3\dfrac{3}{9}[/tex]  is not a natural number, because, natural numbers are whole number positive integers. It is not an integer, because it is a fraction.

It is a real number, because it has no imaginary part and it is a rational number because it can be expressed as a fraction

2) √11 is not a rational number, because it cannot be expressed as a fraction, and it is real number because it has no imaginary parts.

Therefore, is an irrational and real number

3) 125; The options selected are correct

4) 4·∛125 = 4 × 5 = 20; The options selected are correct

5) 7.[tex]\overline {17}[/tex] = 710/99; Therefore, 7.[tex]\overline {17}[/tex] is a rational number and it is also a real number as all natural, whole, integers, rational, and irrational numbers are real numbers

We get;

[tex]\begin{array}{ccccccc}&Natural&Whole &Integer&Rational&Irrational&Real\\-3\dfrac{3}{9}&&&& \checkmark&&\checkmark\\\sqrt{11} &&&&&\checkmark &\checkmark\\125&\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\4\cdot \sqrt[3]{125} &\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\7.\overline {17} &&&& \checkmark&&\checkmark\end{array}[/tex]

Answer:

25 girls and 50 boys

Step-by-step explanation:

let x be the number of boys

let x/2 be the number of girls

x + x/2 = 75

3x/2 = 75

3x = 150

x = 50

there are 50 boys and 50/2 = 25 girls.

check:

50 + 25 = 75

Answer:

0 because there is no image....

t=2w-1

OPTION A is the correct answer...

Answer:

B) 9

Step-by-step explanation:

Because there's a square between the 2 angles, that means these angles are complementary (angles that add up to 90°). So:

5x - 9 + 6x = 90

11x - 9 = 90

11x = 90 + 9

11x = 99

x = 9

Answer:

B.9

Step-by-step explanation:

The way to solve this is by noticing that these angles are complementary(they add up to 90 degrees). So you add the equations together and equal them to 90. 5x-9+6x=90.Then you solve to find that x=9.

Answer:

i am not sure about this answer but i got r^2+10r+25

Answer:

A

Step-by-step explanation:

Got it right!! <3

Pls mark brainliest ^^

Answer:

1/8

Step-by-step explanation:

9/16 * 4/18

Rewriting

9/18 * 4/16

9/18 = 1/2   and 4/16 = 1/4

1/2 * 1/4

1/8

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

[tex]\frac{9}{16}[/tex] x [tex]\frac{4}{18}[/tex] = [tex]\frac{(9)(4)}{(16)(18)}[/tex]

[tex]\frac{(9)}{(18)}[/tex] = [tex]\frac{1}{2}[/tex]

[tex]\frac{4}{16}[/tex] = [tex]\frac{1}{4}[/tex]

[tex]\frac{(1)(1)}{(2)(4)}[/tex] = [tex]\frac{1}{8}[/tex]

Answer:

O-2(x+5)=2x-10

Explanation

O-2(x+5)=2x-10

SOLUTION

-2x(x)= -2x

-2x+5 = -10

Answer:

G = 78°

H = 98°

Step-by-step explanation:

Opposite angles in a cylic quadrilateral are supplementary. Therefore:

G + E = 180°

Substitute

8x + 1 + 11x + 8 = 180°

Add like terms

19x + 9 = 180°

19x + 9 - 9 = 180° - 9

19x = 171

19x/19 = 171/19

x = 9

G = 8x + 1

Plug in the value

G = 8(9) + 1 = 73°

H + F = 180° (opposite angles of a cyclic quadrilateral is equal?

Plug in the values

6y - 4 + 5y - 3 = 180°

Add like terms

11y - 7 = 180

11y = 180 + 7

11y = 187

y = 187/11

y = 17

H = 6y - 4

Plug in the value of y

H = 6(17) - 4

H = 98°

Answer:

sink at 1.28 g/cm^3

v = 4/3 [tex]\pi r^{3}[/tex]

v = 4/3 [tex]\pi 1.4^{3}[/tex]

v =11.49 /9 =1.28

Step-by-step explanation:

Answer:

B. [tex]T(x) = 2.9\cdot (1.05)^{4\cdot x + 5}[/tex]

Step-by-step explanation:

The approximate population in the region is the product of the number of cities in a region and the approximate number of people per city, that is:

[tex]T(x) = C(x)\cdot P(x)[/tex] (1)

If we know that [tex]C(x) = 2.9\cdot (1.05)^{x}[/tex] and [tex]P(x) = (1.05)^{3\cdot x + 5}[/tex], then the formula for the approximate population in the region is:

[tex]T(x) = [2.9\cdot (1.05)^{x}]\cdot [(1.05)^{3\cdot x + 5}][/tex]

[tex]T(x) = 2.9\cdot (1.05)^{4\cdot x + 5}[/tex]

Hence, correct answer is B.

Hello!

32 students (girls+boys)

20 (girls)

32-20 = 12 (boys)

The ratio of girls to the boys

= 20:12

= 5:3

D is the answer.

Good studies!

Answer:

280

Step-by-step explanation:

Use the formula: (a((r^n)-1))/(r-1)

= (7((3^4)-1))/(3-1)

The sum of the given geometric series is 280.

We have given that,

a1=7, n=4 and r=3

We have to determine the sum of a geometric series

[tex]S_n=(a((r^n)-1))/(r-1)[/tex]

[tex]= (7((3^4)-1))/(3-1)[/tex]

[tex]=280[/tex]

Therefore the sum of the given geometric series is 280.

To learn more about the geometric series visit:

https://brainly.com/question/25630111

#SPJ2