Assuming no denominator equals zero which expression is equivalent to the given expression

we know that the endpoints of AB are

and the distance formula is given by

By substituying these points, we have that

which is equal to

then

On the other hand, if

similarly to the previous case, the distance between the endpoint for A'B' is

which is equal to

Now, by comparing equation A and equation B, we can see that, the scale factor is 1/3.

Then, the answer is B.

Answer:

b)

Step-by-step explanation:

this is so becuz a fair die contains or has six parts meaning if its rolled once there are 6 probabilities so if its rolled twice the probabilities increase the chances are (1,1),(1,2),(1,3)... to (1,6) there is only one probability that its(3,3) so giving u 1/12 which when divided hives u b)

Given:

CK = 3x + 23

KT = 5x + 7

If K is the midpoint of CT, then CK = KT. Then,

Finding x:

Subtracting 3x from both sides:

Subtracting 7 from both sides:

And dividing both sides by 2:

x = 8.

Finding CT:

K is the midpoint of CT, then CT = CK + KT

CT = 94.

Answer:

x = 8

CT = 94

Through the given statement measurements we find that the height of the tree is = 33 m.

The right-angled triangle's relationship between its sides is explained by the Pythagorean Theorem, often known as Pythagoras Theorem, a key concept in mathematics.

The Pythagorean triple describes the sides of the right triangle. For the most part, the Pythagorean theorem is employed to determine a triangle's angle and the length of an ambiguous side.

The base, perpendicular, and hypotenuse formulas are derived by means of this theorem. The perpendicular, base, and hypotenuse of this triangle are its three named sides.

As it is on the other side of the angle of 90 degrees, the hypotenuse in this case is the longest side.

An equation, commonly known as a Pythagorean triple, is created by squared values for the sides of a right triangle that have positive integer values.

Let the Height of the Christmas tree be 'h' meters.

Length of the wire = (h + 9) meters

Distance from the base = (h - 23) meters

This scenario forms a right-angled triangle, with height = h m, base = (h-23) m and hypotenuse = (h+9) m

Now, as this is a right-angled triangle,

h^2 + (h-23) ^2 = (h+9) ^2           (Pythagoras theorem)

⇒ h^2 + h^2 - 46h + 529 = h^2 + 18h + 81

⇒ 2h^2 - h^2 - 46h - 18h = 81 - 529

⇒h^2 - 64h = -448

⇒ h^2 - 64h + 448 = 0

⇒ h^2 - (56 + 8) h + (56 x 8) = 0

⇒ (h - 56) x (h - 8) = 0

⇒ h = 56 or h = 8

Since the distance from the base = (h - 23) m cannot be a negative value,

therefore, h = 56 m

Therefore,

The height of the tree = 56 m,

The length of the wire = h + 9 = 56 + 9 = 65 m

The distance from the base of the tree to the wire = h -23

= 56 - 23 = 33 m

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The measure of the unknown central angle is 84°.

We are given that Titus drew a circle with the compass. The circle has five central angles, which measure 55°, 37°, 96°, 88°, and one of the angles is unknown.

A circle is a shape formed by all points in a plane that are at a particular distance from the centre. It is the curve sketched out by a point moving in a plane so that its distance from a particular point remains constant.

We know that the measure of the complete angle is 360°. Thus, the sum of all the central angles must be equal to 360°. Let the measure of the unknown angle be "x". The equation is given below :

55° + 37° + 96° + 88° + x = 360°

276° + x = 360°

x = 84°

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Answer: $17, 535

Evaluate the value of expression.

Answer is - 2.

Answer: х=-8  gooood luck

Step-by-step explanation:

This is a linear function whose graph cuts the origin.

Therefore, any increase in the x axis will lead to a corresponding increase in the y axis by the same factor.

Thus, C is the answer

Answer:

166.07

Step-by-step explanation:

Given:

Points: (3, -9) and (6, -2) on a coordinate plane

To find:

The distance between the two points

To determine the distance between the points, we will apply the formula:

function y = 3.75 + 2.5(x - 3)

dy/dx = 0 + 2.5 - 0

dy/dx = 2.5

The rate of change of the cost in dollars = 2.5

Given the number 133, we list the first prime numbers and then look for a possible factor of 133:

Prime_list = {2, 3, 5, 7, 11, ...}

133 is not an even number, so we discard 2. 133 does not end with 0 or 5, so 5 can not be a factor. We evaluate 3, 7, and 11:

The only division with no rest is 133/7 = 19, and we know that 7 and 19 are prime numbers. We conclude that 133 is composite and can be represented as a product of 7 and 19:

Given

defect rate = 3%

Number of items chosen at random = 6

Find

probability that at least one will have a defect

Explanation

Probability of defective items = 3% = 0.03

Probability of non defective items = 1 - 0.03 = 0.97

so ,

probability that at least one will have a defect = 1 - Probability of 0 defects

Final Answer

Hence , the probability that at least one will have a defect is 0.167(approx)

The discriminant and the point of tangency are used to find the values of the variables as follows;

7. The line y = m·x is tangent to the curve x² + 2·x·y + 2·x = 1 when m = 1

8. The line y = 2·x - k is tangent to the curve x² + y² = 5, when k = ±5

Exercise 11.

1. The discriminant of the equation x² - 6·x + y² - 2·y + 2 = 0 is zero when y = x - 6, therefore the line x - y = 6 is tangent to the curve x² - 6·x + y² - 2·y + 2

2. The exact values of k for which the line 2·x + 3·y = k is tangent to the curve C = 4·x² + 9·y² = 36 is k = ±6·√2

The discriminant is the values which are within the radical sign of the quadratic formula.

7. At the point of tangency, the discriminant is 0

The equation is; x² + 2·x·y + 2·x = 1

The equation of the line is; y = m·x

Rewriting the equation of the curve, we get;

x² + 2·x·y + 2·x = 1

2·x·y = 1 - x² - 2·x

[tex]y = \dfrac{1 - x^2 - 2 \cdot x}{2\cdot x}[/tex]

At the point of tangency, we have;

[tex]y = \dfrac{1 - x^2 - 2 \cdot x}{2\cdot x} = m\cdot x[/tex]

1 - x² - 2·x - 2·m·x² = 0

1 - x² - 2·m·x² - 2·x  = 0

1 - x²·(1 - 2·m) - 2·x  = 0

The discriminant is zero at the point of tangency, which gives;

((-2²) - 4× (-(1 - 2·m)) × 1) = 0

8 - 8·m = 0

8 = 8·m

m = 8 ÷ 8 = 1

8. The line y = 2·x - k is tangent to the curve, x² + y² = 5 where we have;

y² = 5 - x²

y² = (2·x - k)²

5 - x² = (2·x - k)²

Which gives;

k² - 4·k·x + 5·x² - 5

5·x² - 4·k·x + k² - 5

At a tangent point the discriminant is therefore;

(-4·k)² - 4 × 5 × (k² - 5) = 100 - 4·k² = 0

100 - 4·k² = 0

4·k² = 100

k² = 100 ÷ 4 = 25

k = √(25) = ±5

Exercise 11

1. The equation of the line is; x - y = 6

The equation of the curve is; x² - 6·x + y² - 2·y + 2 = 0

From the equation, x - y = 6, we get; y = x - 6

Which gives; x² - 6·x + (x - 6)² - 2·(x - 6) + 2 = 0

x² - 6·x + (x - 6)² - 2·(x - 6) + 2 = 2·x² - 20·x + 50 = 0

2·x² - 20·x + 50 = 0

x² - 10·x + 25 = 0

The discriminant is; (-10)² - 4 × 1 × 25 = 0

Therefore;

3. The curve 4·x² + 9·y² = 36 has the tangent line 2·x + 3·y = k, when we have;

4·x² + 9·y² = 36

9·y² = 36 - 4·x²

y² = (36 - 4·x²)/9 = 4 - (4/9)·x²

y² = 4 - (4/9)·x²

2·x + 3·y = k

3·y = k - 2·x

y = (k - 2·x)/3

y² = ((k - 2·x)/3)²

4 - (4/9)·x² = ((k - 2·x)/3)²

4 - (4/9)·x² - ((k - 2·x)/3)² = 0

8·x² - 4·k·x + k² - 36 = 0

(-4·k)² - 4 × 8 × (k² - 36) = 0

1152 - 16·k² = 0

16·k² = 1152

k² = 1152 ÷ 16 = 72

k = √(72) = ±6·√2

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The ratio of height of the building to the number of floors is 119/7 and the unit ratio is 17 which means that the height of each floor is 17 ft.

In the given question,

The height of a building is proportional to the number of floors.

In the building have 7 floors.

That means, n = 7

the height of building H = 119 ft.

Since the height of a building is proportional to the number of floors.

So [tex]\frac{H}{n}=k[/tex] where k = constant.

Firstly we have to find the ratio of height of the building to the number of floors.

As we know, H = 119 ft, n = 7

So the ratio,

[tex]\frac{H}{n}=\frac{119}{7}[/tex]

The ratio of height of the building to the number of floors is 119/7.

Now we have to find the unit rate.

To find the unit rate we have to divide the height of building to the number of floors.

As we know,

[tex]\frac{H}{n}=\frac{119}{7}[/tex]

now simplifying the ratio by dividing the both number by 7

Unit ratio [tex]=\frac{H}{n}[/tex]

Unit ratio [tex]=\frac{119/7}{7/7}[/tex]

Unit ratio [tex]=\frac{17}{1}[/tex]

Unit ratio = 17

Hence, the unit ratio is 17 ft which means that the height of each floor is 17 ft.

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We have different steps for bisecting a line segment using a reflective device, and these steps are as follows:

And we have to select three of them to complete the process.

To determine the steps, we need to remember that the reflective device permits us to see through it, and also see reflections on it. Then the steps for bisecting a line segment AB are:

1. Place the reflective device anywhere on the segment - It does not matter the position at which we need to put the reflective device.

2. Move the reflective device around on the paper until the reflection of point A coincides with point B.

3. Draw the line of the reflection using the edge of the reflective device as a guide.

Therefore, in summary, the three steps are:

• Place the reflective device anywhere on the segment (,first box,).

• Move the reflective device around on the paper until the reflection of point A coincides with point B (,third box,).

• Draw the line of the reflection using the edge of the reflective device as a guide (sixth box),.

Answer:

3x=14

Explanation:

Given the two equations:

Adding the two equations gives:

The values of the numbers will be:

1. 162

2. 162

3. 1 99/100.

4. 11.4

5. 72

1. 6³ - 8² + 300 ÷ ( 5 + 5)²

It should be noted that this will follow the rules or PEDMAS. This implies that the parentheses will be solved first and that subtraction comes last.

6³ - 8² + 300 ÷ ( 5 + 5²)

= 216 - 64 + 300 ÷ 30

= 216 - 64 + 10

= 216 - 54

= 162

2. 6³ - 8² + 300 ÷ ( 5 + 5²)

= 216 - 64 + 300 ÷ 30

= 216 - 64 + 10

= 216 - 54

= 162

3. (1/5 + 1/2)² + 3/10 × 5

= (7/10)² + 3/10 × 5

= 49/100 + 1 1/2

= 1 99/100

4. 8.1 ÷ 0.9 + 0.4³ ÷ 0.8 × 30

= 9 + 0.064 ÷ 0.8 × 30

= 9 + 0.08 × 30

= 9 + 2.4

= 11.4

5. (18 - 4² + 2)² / (1 ÷ 4 1/2)

= 4² / 2/9

= 16 × 9/2

= 72

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Answer:  she will need about 2 gallons of juice

Step-by-step explanation:

The circumferance of a circle with radius of 6cm is 37.68cm

To find:

Circumferance of a circle

Given:

Radius of circle is 6cm

Solution:

Circumference is similar to perimeter as it is the total length required to draw a circle.

Let c be the perimeter.

c = 2πr

or

c = πd

This depends on knowing the radius (r) or diameter (d).

For example, let's calculate it manually.

If r = 6 cm, the circumference in π is c = 2π(6) = 12π cm.

When expressed numerically, it is 37.7 cm after the decimal point is rounded off.

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Value of m for which the graph of y = 3x² + 7x + m have two

x- intercepts is equal to m < 49 /12.

As given in the question,

Given graph equation:

y = 3x² + 7x + m

Graph y = 3x² + 7x + m has two x-intercepts if and only if

3x² + 7x + m<0 __(1)

Formula used to calculate x value is x = -b/2a

Compare with the standard form:

a= 3

b=7

c=m

x= -7/ 2(3)

  = -7/6

Substitute x=-7/6 in (1)

3(-7/6)² + 7(-7/6) +m<0

⇒49/12 -49/6 +m <0

⇒-49/12 +m<0

⇒m< 49/12

Therefore, Value of m for which the graph of y = 3x² + 7x + m have two

x- intercepts is equal to m < 49 /12.

The complete question is:

For what values of m does the graph of y = 3x²+ 7x + m have two x-intercepts?

a. m > 25/3

b. m < 25/ 3

c. m < 49 /12

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Using the law of indices

This can further be simplify into;

Answer

Explanation

Given the figure, we can deduce the following information:

a and b cut by transversal lines

To determine the value of x, we redraw the figure as shown below:

Since a and b are parallel lines, y must be equal to 36°. We also note that the angles on a straight add up to 180°. So,

Therefore, the equation that can be used to solve for x is:

Now, we get the value of x:

Therefore, the value of x is 79°.

The expression representing the time Philip spent in the challenge is 30x+750.

If an expression was created utilizing integer variables, constants, and algebraic operations, it is said to be algebraic (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

Transcendental numbers, like such and e, are not algebraic, though, as they are not produced by the application of algebraic operations and numerical constants.

While it is common to produce with Euclidean expressions, the definition of e requires an unlimited number of algebraic operations.

An expression is considered to be rational if it can be completely reduced to a reasonable fraction using the principles of arithmetic operations ( associative properties and commutative properties of multiplication and addition, distributive property and rules for the operations on the fractions).

For the first 10 days:

read =10 x wrote 15 × 10 = 150

For the last 20 days

read =20 x

wrote = 30×20 = 600

Hence the total expression is 30x+750.

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To obtain x, we can sum the angles < AQB and < BQC

=> 5X + 8X - 24

=> 13X -24

we are also told that that the sum of their angles is 80

13X - 24 = 80

13 X = 24 + 80

13X = 104

Divide both sides by 13

x = 104/13

x = 8

Let x be the profit of a bracelet and y the profit of a necklace.

Yesterday she sold: 9 bracelets and 3 necklaces, for a profit of $144:

Today, she made a profit of $279 by selling 10 bracelets and 9 necklaces:

System of equations:

To solve by elimination:

1. Multiply the first equation by -3:

2. Add equation you get in step 1 and the second equation in the system:

3. Use the equation you get in step 2 to solve x:

4. Use the value of x to solve y:

Then, the solution for the system is :

Kaylee earns a profit of $9 from every bracelet and $21 from every necklace

The probability that she does not choose a Stephen king novel is 12/17.

What is probability?

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

Given,

1) total books no shelf = 17

Novel of Stephen king = 5

The probability of stephen king = 5/17

The probability of not choosing Stephen novel = 1-5/17

= (17-5)/17

=12/17

2) total number of executives = 11

Number of men = 5

Number of women = 6

probability of a man = 5/11

Probability of a woman = 6/11

Given, one woman and 3 men are selected

therefore, using combination.

Total combinations = n! / (r! x (n - r)!)

n = 4

r = 3

Therefore, probability = n! / (r! x (n - r)!)[tex](5/11)^{1} (6/11)^{3}[/tex]

=4!/3!(1!)(5/11)^{1} (6/11)^{3}

=4(5/11)(216/1331)

=4320/14641

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Given:

P(A) = 0.31

P(B) = 0.5

P(A or B) = 0.585

To find:

P(A and B)

To determine P(A and B), we will apply the formula:

Answer:

Explanation;

The set will be a right angled triangle as shown;