From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm find the radius of the circle.​

The analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.

It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.

As we have given about the Euclidean and analytical geometry.

Without using any numerical measurements, we have investigated the connections between points, lines, and planes in Euclidean geometry.

In analytical geometry, we've looked at how the locations of points in a Cartesian coordinate system related to algebra and geometry.

The analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.

If the Euclidean geometry can be more advantageous in particular circumstances

Example: If using terrain or building chart),

Thus, the analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.

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Answer:15

Step-by-step explanation:

Answer:

I dont know what the answer is

Step-by-step explanation:

y=x/14?

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

Let A represent the number of students reading Accountancy, S represent the number of students reading Sociology, and F represent the number of students reading French.

Let X be the number of students reading all three.

From the information given:

A ∩ S = 19

A + S - 27 = 120 - 53 + 19 = 86 (number of students reading Accountancy or Sociology but not French)

S - A - X = 27

S + F - X = 53

F - X = 19

A - X = 86 - 19 = 67

Total = A + S + F - (A ∩ S) - (A ∩ F) - (S ∩ F) + X = 120

Solving, we get X = 6, A = 73, S = 52, F = 25.

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

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Answer:

Option C: 6(7 * 7)

Step-by-step explanation:

There are six faces of the cube. Since each face is 7 by 7 units, there are 6(7 *7) units total.

Answer:

9 units

Step-by-step explanation:

First of all, let us understand the meaning of dilation.

Dilation means to change the size of any image or line or a figure.

Dilation can be used to enlarge (dilation by a factor greater than 1) the original figure.

OR

Dilation can be used to make the image smaller (dilation by a factor lesser than 1) the original figure.

Here, we are given that an image with 4 points ABCD is dilated by a scale factor of \(\frac{1}{3}\).

Its sides will be AB, BC, CD and DA.

Perimeter is equal to the sum of all the sides of a closed figure.

So, perimeter of ABCD = AB + BC + CD + DA = 27 units ...... (1)

Now, it is dilated by a scale factor of \(\frac{1}{3}\).

So, all the sides will become smaller i.e.

A'B' = \(\frac{1}{3}\) AB

B'C' = \(\frac{1}{3}\) BC

C'D' = \(\frac{1}{3}\) CD

D'A' = \(\frac{1}{3}\) DA

Perimeter of A'B'C'D' = A'B' + B'C' + C'D' + D'A' = \(\frac{1}{3}\)AB + \(\frac{1}{3}\)BC + \(\frac{1}{3}\)CD + \(\frac{1}{3}\)DA

\(\frac{1}{3}\) (AB + BC + CD + DA ) = \(\frac{1}{3} \times 27\)(By equation (1))

Perimeter of A'B'C'D' = 9 units

Answer:

62.1371192237

Step-by-step explanation:

Just remeber that one kilometer per hour is equal to 0.62 mph and that one mile per hour is equal to 1.60934 kilometers per hour.

The speed limit of a car on the highway is 62.1 miles/hour.

Given that;

While on a road trip to Canada, you rent a car and discover that the speed limit on the highway is 100km/hr.

We have to find the equivalent speed in miles/hour.

What is relation between miles and hour?

Relation between miles and hour is;

1 kilometer = 0.621 miles.

The speed limit of the car on the highway = 100 km/h

Since, 1 kilometer = 0.621 miles.

Hence,

100 kilometer/hour = 100 x 0.621 miles/hour

                             = 62.1 miles/ hour

So, The speed limit of a car on the highway is 62.1 miles/hour.

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The vertex is a point , V(h,k) on the parabola. It's either at the base or the top of the parabola, depending upon wether it opens upward or downward.

From the graph, we can see that the coordinates of the vertex are:

V(-2,8)

Answer:

1 solution

Step-by-step explanation:

-5 - 11r = 6 ( -2r - 3 )

Distribute:

-5 - 11r = -12r - 18

Add 18 to both sides:

13 - 11r = -12r

Add -11r to both sides:

13 = -r

Divide each side by -1:

-13 = r

1 is your answer

Hope this helps!

Answer:

\(\frac{8}{15}\) of a mile

Step-by-step explanation:

To find a segment of a fraction, you must first find the LCM of each value's denominator:

LCM - Lowest Common Multiple

The lowest common multiple is the number that shows up first in each number's multiple set.

Example: LCM of 4 and 6

Multiples of 4: 4, 8, 12, 16, 20

Multiples of 6: 6, 12, 18, 24, 30

Because 12 is the first number to show up in each multiple set, 12 is the LCM.

So, to be able to solve this problem easy, do the same with 5 and 3:

5, 10, 15, 20, 25

3, 6, 9, 12, 15

Since 15 is the first number in both sets, 15 is the LCM.

The next step is to multiply \(\frac{4}{5}\) by \(\frac{x}{x}\), x being the value that can be multiplied with the denominator to equal 15:

\(\frac{4}{5}\) × \(\frac{3}{3}\) = \(\frac{12}{15}\)

To find how much \(\frac{2}{3}\) of \(\frac{12}{15}\) is, multiply the fractions together:

\(\frac{12}{15}\) × \(\frac{2}{3}\) = \(\frac{24}{45}\)          

Simplify the fraction by dividing the numerator and denominator by 3.

\(\frac{24}{45}\) ÷ \(\frac{3}{3}\) = \(\frac{8}{15}\)

Because the fraction can't be simplified any further, Aimee has walked a total of \(\frac{8}{15}\) of a mile.

Answer:

c

4-7 is four less than 7.

Answer:

C. 7-4

Step-by-step explanation:

You would subtract 4 from 7 and that will give you 7-4.

Hopes this helped :))

Mathematics provides a framework for developing critical thinking, problem-solving, and analytical skills that are valuable in many aspects of life.

What is mathematics?

Mathematics is a fundamental discipline that plays a crucial role in our daily lives and in shaping our understanding of the world.

Mathematics is a field of study that deals with the properties and relationships of numbers, quantities, shapes, and patterns. It involves using logical reasoning, abstraction, and symbolic manipulation to understand and solve problems related to these concepts.

Mathematics is important for many reasons. First and foremost, it is a fundamental tool for understanding and describing the world around us. It plays a crucial role in science, technology, engineering, economics, finance, and many other fields by providing tools for modeling and analyzing complex phenomena.

Mathematics is also essential for making accurate predictions and decisions based on data and evidence, as well as for designing and optimizing systems and processes.

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Answer:

the answer is c because decreased by means the symbol minus so y decreased by 24 will be y-24

Given:

Dimensions of lot is (7+x) and (7-x).

Dimension of house is (3+x) and (3-x)

Taylor is thinking about extending the house by adding 3 feet to the length and width.

So, the dimension of house becomes (6+x) feet and (6-x) feet.

Now, the area of the yard is,

Answer: area for the yard left is 13 square feet.

Answer:

slope = 3/2

Step-by-step explanation:

3x-2y=6

Get this equation in the form y = mx+b where m is the slope and b is the y intercept

Subtract 3x from each side

3x-3x-2y=-3x+6

-2y = -3x+6

Divide each side by -2

-2y/-2 = -3x/-2 +6/-2

y = 3/2x -3

The slope is 3/2 and the y intercept is -3

Answer:

3/2

Step-by-step explanation:

I got this answer by putting it in the form y=mx+b

Step 1: Subtract 3x from each side

-2y = -3x+6

Step 2: Divide each side by -2

y = 3/2x -3

The slope is 3/2 and the y intercept is -3 because m is the slope and b is the y-intercept.

Answer:

$165.38

Step-by-step explanation:

In the question, we are asked to work with percentages. We know that the person had bought three items of a total of 250 dollars (38 + 189 + 23). We are told that the items have a 30% discount, another 10% discount on that and a 5% tax increase on all of that.

First, let's work with the 30% discount. The official way of working out the problem you would use the unitary method. The unitary method is when we divide the total cost by 100. So 250/100, is 2.5. We multiply this by the remaining percent (100%- 30%=70%) so 2.5*70 is 175.

Then, we work with ten percent. The only difference is that instead of using the original price with are using the 30% discounted price. If we use the unitary method again we find that 175/100 is 1.75 and that multiplied by 90 (because we are only subtracting the 10% not 30%) is 157.50.

Finally, we do the same for the 5% percent only difference being we add it to 157.50. 157.50/100 is 1.575 and multiplied by 105 (because we are adding 5% onto 100% so it becomes 105%).

The final answer is 165.375 and when rounded to the nearest cent it becomes $165.38.

y= 150x+50

y= total cost

x= number of hours

150 = cost per hour

50 = fixed cost

Since the equation is in slope-intercept form:

y=mx+b

Where:

m= slope

b= y- intercept (50)

the y-intercept represents the fixed cost of the visit.

Congruency is said to be defined on two triangles when they have exact same length of sides and equal angles between them. The shape and size are supposed to be the same even after rotation or flipping of triangles for them to remain congruent.

There are 4 criteria to test the congruency of the triangle and they are as follows:

In this set of triangles, (ABC, def) AB=DE, AC=DF, and ∠ABC= ∠DEF i.e., two sides and one angle are equal but it is not congruent because according to SAS criteria, the angle should be between AB and AC (or DE and DF)

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We are given:

Probability of passing = p

Probability of Failing = 6p²

__________________________________________________________

Finding the value of 'p':

We know that the sum of the probabilities of an event occurring and not occurring is 1

So, Probability of passing + Probability of Failing = 1

p + 6p² = 1

6p² + p - 1 = 0

We can see that we now have a quadratic equation

Splitting the middle term:

6p² + 3p - 2p - 1 = 0

3p(2p + 1) - (2p + 1) = 0

(3p - 1)(2p + 1) = 0                      [factoring out 2p + 1]

Now, we can either divide both sides by (3p-1) or by (2p + 1) and both the cases will give us different answers.

Dividing both sides by (3p - 1):

2p + 1 = 0/(3p-1)

2p + 1 = 0

p = -1/2

Dividing both sides by (2p+1):

(3p - 1) = 0 / (2p + 1)

3p - 1 = 0

p = 1/3

Now, we have 2 values of p: -1/2 and 1/3

Using the value: -1/2 will mean that the probabilities are negative

but we know that probabilities cannot be negative.

So, -1/2 is not a valid value for p

Therefore, the value of p is 1/3

Answer:

A) Yes...ABC and GFC are similar using AA.

Step-by-step explanation:

The expression for h(x) is,

⇒  h (x) = √(x - 2) + 4

Now, Given that;

Initially the graph f (x) is shifted horizontally to the right.

When the graph shifts to right the function then becomes

f (x) → f (x-b)

Where b is the units by which it is shifted towards right .

So, in the figure we can see that it is shifted 2 units to the right .

So, f(x) → f(x-2)

Since f(x) is,

⇒ f (x) = √x

So, f (x-2) = √x - 2

Now, the new obtained graph is again shifted vertically upward

When the graphs shifts upward;

⇒ f(x) → f(x) + b

where b is the units by which it is shifted upward

So, our obtained f(x-2) when shifted upward by 4 units so using the above given transformation of upward shift

i.e. f(x) → f(x) + b

So, Our new graph h(x) = f(x-2) + 4

⇒  h (x) = √(x - 2) + 4

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The motion of the skier from point A to point B, then to point C, and then point D, indicates that the distances and displacement traveled are;

a) The distance from A to C is 280 meters

b) The distance from point A to point D is 360 meters

c) The displacement of the skier from point B to point C is 120 meters.

Displacement is the change in the position or location of the object.

The possible diagram of the skier in the question can be presented as follows;

A \({}\)                            C                                                   D                          B

t = 0 min      \({}\)         t = 2 min                                       t = 3 min            \({}\)t = 1 min

ʂ         \({}\)                     ʂ                                                     ʂ                           ʂ

-|-------|------|------|------|-----|------|-----|------|------|-------|-------|--------|-------|-------|-----

0           \({}\)   20           40         60          80            100    120    140           160

The above diagram indicates that we get;

a) The distance from point A (t = 0 min) to point C(t = 2 min) is can be found as follows;

The skier moves from point A to point B then from point B to point C, therefore,

The distance from point A to point B = 160 m - 0 m = 160 m

The distance from point B to point C = 160 m - 40 m = 120 m

The distance from point A to point C is therefore;

b) The distance from point A to point D = The distance from point A to point C + The distance from point C to point D as follows;

AD = AC + CD

CD = 120 m - 40 m = 80 m

Therefore;

AD = 280 m + 80 m = 360 m

c) The displacement of the skier from point B (t = 1 min) to C (t = 2 min) can be found as follows;

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......,,........,.....-.......

The median would best describe the centre of the distribution for a highly skewed right histogram of US household income.  The correct option is A.

The median is the value that separates the distribution into two equal parts and is less influenced by extreme values than the mean.

Since a highly skewed right distribution has a long tail on the right side, the mean is likely to be pulled towards that tail, making it an unreliable measure of the centre.

The mode, or most frequently occurring value, may not be useful for describing the centre of a skewed distribution. The variance is a measure of the spread or dispersion of the data, not its centre.

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In statistics, the risk of making an error is referred to as a significance level. A significance level represents the probability of making a Type I error, which occurs when a null hypothesis is rejected even though it is true.

The most common significance level used in statistical analyses is 0.05 or 5%. This means that there is a 5% chance of rejecting a true null hypothesis.

In general, the choice of significance level depends on the specific application and context of the statistical analysis.

The 5% significance level is commonly used in scientific research, particularly in the fields of medicine and psychology.

The choice of this level is based on a balance between the risk of making a Type I error and the risk of making a Type II error, which occurs when a null hypothesis is not rejected even though it is false.

A Type II error is often more serious than a Type I error since it may lead to incorrect conclusions about the relationship between variables or the effectiveness of a treatment or intervention.

A 5% significance level provides a reasonable balance between these two types of errors. However, in some situations, a higher or lower significance level may be more appropriate.

For example, in a clinical trial where the consequences of a Type II error are severe, a lower significance level may be used to reduce the risk of this type of error.

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(A) Triangle ABC, and triangle QPR are similar based on side-side-side (SSS) similarity.

(B) Triangle ABC and triangle DEF are similar based on side-side-side (SSS) similarity.

(C) ) Triangle STU and triangle JPM are similar based on side-angle-side (SAS) similarity.

(D) ) Triangle SMK and triangle QTR are similar based on angle-angle (AA) similarity.

Similar triangles have the same corresponding angle measures and proportional side lengths.

The triangle similarity criteria are:

(A) Triangle ABC, and triangle QPR are similar based on side-side-side similarity.

12/8 = 9/6

1.5 = 1.5

(B) Triangle ABC and triangle DEF are similar base on side-side-side similarity as shown in the side lengths.

(C) ) Triangle STU and triangle JPM are similar base on side-angle-side similarity.

14/10 = 21/15

1.4 =

(D) ) Triangle SMK and triangle QTR are similar base on angle-angle similarity.

SMK = 90⁰, 60⁰, 30⁰

QTR =  90⁰, 30⁰, 60⁰

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Dy/dx = (dy/dt)/(dx/dt) denotes the slope of the tangent line of a parametric curve whose parametric equations are x = /(t) and y = g(t). Wherever dy/dt is zero and dx/dt is zero, a parametric curve has a horizontal tangent.

The x and y coordinates are defined as functions of t when parametric form is used to represent angles: Plot the entire circle by using the equations x = r cos t and y = r sin t. Polar equations are the name given to these parametric equations.

The given x=1+12+ dx=dt 0+12(1) =12

Parametric y Curve is as follows: ts-t dy 5t-1 dt z = ts+t dz dt 5t +1 (dz, dy, dz) = (12, 5t-1, St+1) dt 7 dt dt x = 13 =) When, 1+12 t = 13 12

(x(t), y(t), and z(t)) = (13,0,2) + + (12, 4, 6) x(t), y(t), and 2(t)) = (13+12t, ut, 2+ 6+) x(t) = 13+12t, y(t) = ut, 2(t).

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Full Question = Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

x = 1 + 12 t , y = t5 − t, z = t5 + t; (13, 0, 2)

x(t), y(t), z(t) =

Length = 13 units

width = 2 units

The formula for calculating the area of a rectangle is given as:

where:

l is the length of the rectangle

w is the width of the rectangle

If the width of a rectangle is 11 units less than the length, then;

Substitute the expression for the width and the area into the formula for calculating the area.

Factorize the resulting quadratic expression

Find the length

Recall that A = lw, hence;

Hence the dimensions of the rectangle is 13 units by 2 units