2. Complete the table below by stating the number of solutions and explaining orsolving to show your reasoning.a) x2 - 25 = 0b) (x - 2)2 = 0c) (x - 3) ? = 81Number of solutions: Number of solutions: Number of solutions:0101201N2Type Here:Type Here:Type Here:Explain or show yourreasoning on how yousolved the aboveproblem.Explain or show yourreasoning on how yousolved the aboveproblem.Explain or show yourreasoning on how yousolved the aboveproblem.Type Here:Type Here:Type Here:I

Answer:

The counter example is:

Explanation:

We want to show that the statement "The sum of any two different odd numbers is divisible by 4" is false.

We need to use the smallest positive numbers. T

We will use the relation [tex]\frac{QS}{SR}=\frac{PO}{OR}[/tex]

The correct option is option C)

What is similarity in triangle?

We say two triangles are similar if all the corresponding angles of the two triangle are equal and all the corresponding sides are in equal proportions.

We are given the diagram

We first prove that Δ[tex]POR[/tex]≅Δ[tex]QSR[/tex]

∠[tex]PRO[/tex]≡∠[tex]QRS[/tex]                   (Same angle)

∠[tex]RPO[/tex]≡∠[tex]RQS[/tex]                   (Corresponding angle)

Hence by AA test of similarity the two triangles are similar

And therefore the corresponding sides of two triangles are in same ratio

Therefore we have,

[tex]\frac{PO}{QS}} =\frac{OR}{SR} =\frac{PR}{QR}[/tex]

[tex]\frac{PO}{QS}} =\frac{OR}{SR}[/tex]

And hence, [tex]\frac{QS}{PO}} =\frac{SR}{OR}[/tex]

[tex]\frac{QS}{SR}} =\frac{PO}{OR}[/tex]

Hence we will select option C)

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Given:

n = 700

p = 0.09

q = 1 - p = 0.91

The formula for standard deviation is:

hence:

ANSWER

σ ≈ 7.57

Since we're working on a circumference, the sum of all the angles must be 360°

This way,

Solving for x :

Given the expression:

ANSWER

x = -2, y = 7, z = 2

EXPLANATION

We are given a system of three equations:

2x + 3y - 4z = 9 ________(1)

4y - 6z = 16 ___________(2)

z = 2 ________________(3)

Since we have been given the value of z, from (3) we have that (2) becomes:

4y - 6(2) = 16

4y - 12 = 16

4y = 12 + 16 = 28

y = 28 / 4

y = 7

Put the values of y and z in (1):

=> 2x + 3(7) - 4(2) = 9

2x + 21 - 8 = 9

2x + 13 = 9

Collect like terms:

2x = 9 - 13 = -4

x = -4 / 2

x = -2

So, x = -2 and y = 7 and z = 2

Given:

Vic bought a new plasma TV for ​$2400.

He made a down payment of ​$100 and then financed the balance through the store.​

The interest per month is 4% on the balance.

To find:

Vic's monthly interest​ payment.

Explanation:

The cost of a plasma Tv is $2400.

The down payment made is $100.

Balance amount for financing is $2400 - $100 = $2,300.

Since the interest rate is 4% per month

So, the monthly interest payments will be,

The monthly interest payments will be $92.

Final answer:

The monthly interest payments will be $92.

The measure of angle x in each of the triangles is:

1) 20°

2) - 49°

3) 8°

4) 33.33°

5) 10°

6) 3°

7) 1°

8) 2°

9) 6°

1) The measure of the inner angles in the triangle are 100°, 40°, and 2x°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

100° + 40° + 2x = 180°

140° + 2x = 180°

2x = 40°

x = 20°

2) The measure of the inner angles in the triangle are 99°, 37°, and (- x - 5)°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

99° + 37° + ( - x - 5 )° = 180°

136° + (- x - 5)° = 180°

( - x - 5 )° = 44°

x = - 49°

3) The measure of the inner angles in the triangle are 60°, 60°, and ( - 12 + 9x)°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

60° + 60° - 12 + 9x = 180°

120° - 12° + 9x = 180°

108° + 9x = 180°

9x = 72°

x = 8°

4) The measure of the inner angles in the triangle are 36°, 46°, and ( 2 - 3x)°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

36° + 46° - 2° + 3x° = 180°

82° - 2° + 3x° = 180°

80° + 3x° = 180°

3x = 100°

x = 33.33°

5) The measure of the inner angles in the triangle are 71°, 50°, and ( 6x - 1 )°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

71° + 50° - 1° + 6x° = 180°

121° - 1° + 6x° = 180°

120° + 6x° = 180°

6x = 60°

x = 10°

6) The measure of the inner angles in the triangle are 45°, 90°, and ( 8x + 21 )°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

45° + 90° + 21° + 8x° = 180°

156° + 8x° = 180°

8x = 24°

x = 3°

7) The measure of the inner angles in the triangle are 85°, 64°, and ( 4x + 27 )°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

85° + 64° + 27° + 4x° = 180°

176° + 4x° = 180°

4x = 4°

x = 1°

8) The measure of the inner angles in the triangle are 44°, 104°, and ( 7x + 18 )°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

44° + 104° + 18° + 7x° = 180°

166° + 7x° = 180°

7x = 14°

x = 2°

9) The measure of the inner angles in the triangle are 125°, 25°, and ( - 5x )°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

125° + 25° - 5x° = 180°

150° + 5x° = 180°

5x = 30°

x = 6°

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Jenny's deck is a square deck and has a side length equal to that of the back of Jenny's house. The area of a square of length L is;

Thus, we have;

Therefore, the length of the back of Jenny's house is 18 feet.

We need to solve the following inequality:

To do that we have to isolate the variable on the left side. The first step is to add "4" on both sides.

The value of x must be greater than -4 for this inequality bo be valid.

To graph this result we need to draw a line at the point that x = -4, then we collor the side that is greater than that.

A better drawing can be seen below:

To graph it at the line we need to go to the point that solves the equation, in this case is -4 and if the signal is ">" we collor the right part of the line.

Solution:

Given that Maria has 5 7/8 yards of fabrics, and she makes a jacket with 3 3/4 yards, this implies that the amount of fabric left after making her own jacket is evaluated as

Since she is to make the same jacket for her friend, she requires another

But the amount of fabric left after Maria has made her own jacket is

Hence, Maria does not have enough fabric left for her friend.

The given expression is,

As the area is equal to 45 and equating the areas.

(taking positive values)

The answer is 7

The graph is based on amplitude.

Given the function:

f(t) = 5sin3t

To draw the graph of above function.

The function g(t) = sin t is a periodic function with amplitude [tex]a_{0}[/tex] = 1 and period [tex]t_{0}[/tex] = 2[tex]\pi[/tex]

For our case, the 5 that multiplies g (t) increases the amplitude so that,

a = 5 x 1 = 5 and the 3 that multiplies the variable increases the period being t = 2[tex]\pi[/tex] x 1/3 = 2[tex]\pi[/tex]/3

What is Graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.

See the graph in the bottom of explanation.

Hence, The graph is based on amplitude.

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From the arc-angle relationship

By comparing both pictures, we have that

now, we must isolate MJH, hence we have

and we must move 76 to the right hand side as -76, this gives

Finally, mJH is 34.

The question has already provided a formula to determine the width (W). The question also provides the thickness as well as the number of times (n) the paper would be folded. Hence, we have;

The notebook paper would have to be 0.45216 inches wide

The formula has also been provided that would help in calculating the length of a long rectangular piece of paper. We've been given the thickness of the paper and the number of times it (n) it would be folded. Therefore, we now have;

The point (11 , 37 ) does not lies in the given  function f(x) = 4x - 3. Since the values x , y does not satisfy the condition .

How to check whether the points satisfy the equation :

Given function, f(x) = 4x - 3

also given a point (11 , 37)

to check whether the given point satisfies the given function,

(x , y) = (11,37)

substitute values of x and y in the given function,

y = 4x - 3

37 = 4 x (11) - 3

37 = 44 -3

37 ≠ 41

∴ the given points (11,37 ) does not satisfy the given function

f(x) = 4x-3.

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Given that:

Rate at which the hits occur between 7 PM and 10 PM = 1.4 per minute

Then:

Number of hits between 9:30 AM and 9:35 AM

The probability distribution function of Poisson distribution is

(a) P(x=4)

(b) P(x < 4) = P(x=0)+P(x=1)+P(x=2)+P(x=3)

(c) To find

Since the border has a width of 2cm, the length of the printed material and its border

is 2 + 6 + 2 = 10cm

and it's width iis

2 + 8 + 2 = 12cm

Hence the area is 10 x 12

Therefore,

the area of the border = 10x12 - 6x8 = 120 - 48 =72 square centimeters

Answer:

8.74$

Step-by-step explanation:

so first what you want to do is that you want to add $7 with 4.25 dollars plus 1.99 dollars the next thing you want to do is take 85% of this number you will get 0.85 times that sum

that sum is 13.24. now because she is getting 15% off of her purchase that means you want to take 85% of that 13.24 number . so you will get 1 1.254 you will need to round this because it is in dollars . so you will get 11.25 as her purchase price . now because she gave a $20 bill you need to subtract that number from 20 and you will get 8.746 which is rounded to 8.74 because it is in dollars that is the answer that is her change

============================================================

Explanation:

Let y be the angle just to the left of angle x. Angle x and angle y are adjacent.

Since line a is parallel to line b, this means y = 120 because the 120 degree angle and angle y are alternate interior angles.

Then we can say:

x+y = 180

x+120 = 180

x = 180-120

x = 60

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

An alternative method:

Let w be the angle just above angle x

The angle marked "120 degrees" and angle w are corresponding angles. They are congruent if and only if line a is parallel to line b.

This makes w = 120

Solving w+x = 180 leads to x = 60 similar to the previous set of steps.

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

Side note:

The 115 degree angle is never used. It was probably put in there as a distraction.

Simplify the equation.

Thus to complete the square 9 is added to both side of the equation.

Answer: 9

The value of x for the given algebraic expression  is 36.

A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=9x+1.

The question gives the linear expression in text format. Therefore, you should convert the text in algebraic expression. See some tips:

Converting the text into algebraic expression, you have:

[tex]\frac{-7}{6}[/tex] * x - 6 = -48

-7x -6*6=  -48*6 ( Multiply both sides by 6)

-7x -36 = -288

-7x = -288 +36

-7x = -252

x= -252 / -7

x=36

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Answer:

647 ft

Explanation:

Given the below figure;

To determine the value c, we have to take the sine of angle 18 degrees as seen below;

Let's cross multiply;

Let's divide both sides by sin 18;

So the distance the plane has flown is 647 ft

The number of students which are either in algebra or physics are 23 which is the second option.

Given that:-

Total number of students = 30

Number of students both in physics and algebra = 4

Total number of students in Physics = 12

Total number of students in Algebra = 19

We have to find the number of students which are either in algebra or physics.

Number of students in physics but not in algebra = 12 - 4 = 8

Number of students in algebra but not in physics =  19 - 4 = 15

We know that:-

Number of students which are either in algebra or physics = Number of students in physics but not in algebra + Number of students in algebra but not in physics

Hence, we can write,

Number of students which are either in algebra or physics = 8 +15 = 23.

We can also do this question using Venn diagram.

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The quadratic equation is factorizable if the result of the discriminant gives a perfect square. This is a kind of a perfect square test

We know that a quadratic equation is factorizable by the use of the discriminant. The discriminant is something that could tell us about the character of the quadratic equation.

We know that the discriminant is the square root of b^2 - 4ac. If the result of this operation is a perfect square, then we can know that the equation as we have it in any particular situation is factorizable.

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Given:

The radius of a can is (3x^2-10). The height of the can is 2x.

To find:

The surface area of a label that would be glued around the can.

Solution:

It is known that the curved surface area of the cylinder is given by:

So, the curved surface area of the given cylinder is:

Thus, the answer is given above.

Giveb data:

The given expression is (-8/5)x-6=-54.

The given expression can be written as,,

Thus, the value of x is 30.

ANSWER and EXPLANATION

We want to identify the first term of the algebraic expression given:

The first term of the expression is:

The variable in the expression is the algebraic term. The algebraic term is:

Therefore, the coefficient of the first term is:

Answer:

5x + 3 = 0

OR

35*35 /35 -35

hope this helps