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‘question’ 1 options: yes / no

‘question’ 2 options:

p= 5,184a
or
a = 5,184p
or
p= 0.0001929a

The restriction on the variable x for the expression 5x+15/10x-10÷x²+6 x+9/3x²-3 is  x ≠ -3 .

Restriction in algebraic expression is defined as the value that makes the denominator as 0  or the whole expression as not defined.

For Example: 1/(x+2)   , here the restriction is x ≠ -2 as -2 will make the denominator 0.

In the given question

[tex]=\frac{5x+15}{10x-10} \div\frac{x^{2} +6x+9}{3x^{2} -3}[/tex]

rewriting the expression

[tex]=\frac{5x+15}{10x-10} \times\frac{3x^{2} -3}{x^{2} +6x+9}[/tex]

Simplifying the numerator and denominator we get

=5(x+3)/10(x-1) x 3(x² -1)/(x²+3x+3x+9)  ...( by splitting the middle term )  

=5(x+3)/10(x-1) x 3(x-1)(x+1)/(x+3)(x+3)  ...( using identity a²-b²=(a+b)(a-b)   )

On further simplifying we get ,

=5*3*(x+1)/10(x+3)

=3(x+1)/2(x+3)

For finding restriction;

denominator, 2(x+3)≠0

means (x+3)≠0 ⇒ x ≠ -3.

Therefore , the restriction on the variable x is x ≠ -3 as -3 will make the expression not defined, and the value after division is 3(x+1)/2(x+3).

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f (4) = 61

g (4) = 2

Step-by-step explanation:

f(4) = 2(4)² - 3

f(4) = 8² - 3

f(4) = 64 - 3

f(4) = 61

g (4) = -4 + 6

g (x) = 2

Volume of baseball is 1.24 times greater than volume of tennis ball.

We are given the diameter of baseball and tennis ball. So, firstly we will calculate the volume of tennis ball and baseball.

Volume of ball = 4/3πr³, where r stands for radius of ball.

Taking value of π as 3.14.

Volume of tennis ball = 4/3×π×2.7³

Volume of tennis ball = 82.4 m³

Volume of baseball = 4/3×π×2.9³

Volume of baseball = 102.1 m³

Now, finding the number of times volume of baseball is greater than volume of tennis ball.

Comparison -  volume of baseball ÷ volume of tennis ball

Comparison - 102.1 ÷ 82.4

Comparison - 1.24

Hence, volume of baseball is 1.24 times of volume of tennis ball.

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Interior angles in triangles are all equal to 180 degrees. A triangle's angles are equal to the sum of the angles at each of its three vertices. The sides of the triangle are 35cm, 21cm, and 42cm.

Due to the fact that one outside angle of a triangle is equal to the sum of its other two angles, all of its angles add up to 180 degrees. In other words, the third angle must be added to the other two angles in the triangle (the ones that add up to generate the outer angle) to form a 180-degree angle.

The perimeter of the triangle = 98cm

The ratio of the 3 sides is 5: 3: 6

Take it as 5x, 3x, 6x

where, x is the scaling factor

5x + 3x + 6x = 98

simplifying the above variables, we get

14x = 98

x = 7

The sides of the triangle are

5x = 5 × 7 = 35 cm

3x = 3 × 7 = 21 cm

6x = 6 × 7 = 42 cm

Therefore, the sides of the triangle exists 35 cm, 21 cm and 42 cm.

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A scatter plot is a series of points plotted on horizontal and vertical axes. If there is no correlation between variables, the points appear randomly scattered on the coordinate plane. If the correlation is high, the points will be clustered around a straight line. A scatter chart is a data visualization tool that helps show trends.

The scatter plot shows not only the correlation's magnitude but also the correlation's direction.

As the vertical (or Y-axis) variable increases, the correlation is positive as the horizontal (or X-axis) variable increases.

The correlation is negative if the y-axis variable decreases and the x-axis variable increases, or vice versa.

The correlation is zero if none of the above criteria can be established.

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The slope of the line containing (-3,3) and (4,3) is Zero (0).

The slope of a straight line can be written as follows,

m =  [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex]                 equation1

The line is containing the points (-3,3) and (4,3). So, we can write

[tex]y_{2}[/tex] = 3 , [tex]y_{1}[/tex] = 3 , [tex]x_{2}[/tex] = 4 , and [tex]x_{1}[/tex] = -3 .

On substituting the values of variables in equation1, we will get

m = ( 3-3 ) / ( 4-(-3) ) = (0/7) = 0.

As the slope of a line is Zero (0), so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing  (-3,3) and (4,3) is Zero (0).

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The range of the graph is 0 <= y <= 12

The graph represents the given parameter

On the graph, we have the following observations

Minimum y value = 0

Maximum y value = 12

The range of the graph is represented as

Minimum y value <= y <= Maximum y value

So, we have

0 <= y <= 12

Hence, the range of the graph is 0 <= y <= 12

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R (-90°) = (x, y) — > (y, -x)  is the x - and y -coordinates change.

How is a point rotated with respect to the origin?

As it turns out, however, I don’t need to look at options. I can tell you that a clockwise rotation of 90° of a point about the origin is actually considered a rotation of -90°.

(For positive rotations are counterclockwise, while negative rotations are clockwise.) The rule for the type of rotation you speak of is

R (-90°) = (x, y) — > (y, -x)

One more point, if I may. It appears that you copied this problem verbatim right out of a textbook.

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The distance from B to E is 4/3 when wall AB covered in a mirror.

The virtual image created by reflection in a plane mirror is the mirror image of an object or two-dimensional figure; it is the same size as the original but different, unless the object or figure has reflection symmetry.

Angle ∠1 = Angle ∠2

So Triangle ADC = Triangle EBD

A line of reflection is required to accomplish a geometry reflection; the two figures' consequent orientations are opposing. Comparable distances separate the corresponding regions of the figures from the line of reflection. Ordered pair rules appear on the x-axis as (x, -y), the y-axis as (-x, y), and the line y=x as follows (y, x).

tan ADC = AC / AD

= 2/3

tan EBD = BE/BD

= x/2

if Triangle ADC = Triangle EBD

than AC / AD = BE / BD

2/3 = x/2

x = 4/3

Thus , when wall AB is covered in mirrors, the distance from B to E is 4/3.For point E see the attachment below -

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The length of the hypotenuse c is 6

The given parameters are

Legs = a and b

Hypotenuse = c

a = 2√3

c = 2b

Make b the subject in c = 2b

b = 1/2c

By Pythagoras theorem, we have:

c^2 = a^2 + b^2

This gives

c^2 = (2√3)^2 + (1/2c)^2

Evaluate the exponents

c^2 = 12 + 1/4c^2

Evaluate the like terms

1/3c^2 = 12

This gives

c^2 = 36

Take the square roots

c = 6

Hence, the length of the hypotenuse c is 6

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Answer:

The answer and explanations are in the pictures.

Step-by-step explanation:

To calculate the fixed point for the given function that is f(x)= x^5

The value of ‘x’ can take from one to infinity that means the range is (1,infinity)

Therefore,

The function can be represented as: [tex]f(x)= x^5[/tex]

The interval of the variable 'x' is: [tex]0 < x <[/tex]∝ (infinity)

And finally the range of the variable 'x' as: (1, 32,......,infinity)

What is the fixed point?

Fixed points are those points which do not change when they are mapped with different functions. It is also called as invariant points. The fixed point method is used for the calculation of those function which are in the form of constant.

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The slope of the line through each pair of points. (-5,-7) and (0,10) is 17 / 5

A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two locations, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

The given points are (-5,-7) and (0,10)

Formula to calculate slope is - y2 - y2 / x2 - x1

= 10 + 7 / 0 + 5

= 17 / 5

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No, the regular polygon pentagon will not tessellate in the plane.

A tessellation or tiling is the seamless application of one or more geometric shapes, known as tiles, to a surface, frequently a plane. Tessellation in mathematics can be expanded to include other geometries and higher dimensions.

A tiling constructed of materials like cemented ceramic hexagons or squares is referred to as a real-world tessellation. Such tilings may be ornamental designs or serve practical purposes such providing long-lasting and water-resistant pavement, floor, or wall coverings.

Tessellations were historically employed in Islamic art, such as the Moroccan architecture and the ornamental geometric tiling of the Alhambra palace. They were also used in Ancient Rome.

Regular polygons tessellate if their interior angles divide by 360° evenly or if the total of their interior angles is a factor of 360°. A tessellation is a pattern made of identical forms that fit together seamlessly.

So lets find out how pentagon won't tessellate.

First we find the measure of the interior angles of pentagon,

[tex]\frac{540\°}{5} = 108\°[/tex]

Now divide the interior angle by 360°

[tex]\frac{360\°}{108\°}[/tex] = 3.333

Hence, the measure of the interior angle does not divide by 360°.

Therefore, we conclude that the regular polygon pentagon will not tessellate in the plane.

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When an angle exists encircled by a circle, its measure exists equivalent to the intercepted arc's measure divided by two. The measure of m DH is 162.

The arc that is inside the inscribed angle and whose endpoints are on the angle is known as the intercepted arc. Anywhere on the circle that the sides of an inscribed angle intersect to produce an intercepted arc can serve as the angle's vertex.

Angles with vertices on a circle and that cross an arc on the circle are said to be inscribed angles. Half of the intercepted arc's length and half of the central angle's length intersecting that same arc make up the measure of an inscribed angle. Congruent inscribed angles are those that intersect the same arc.

According to the Inscribed Angle Theorem, an inscribed angle's measure is equal to half of its intercepted arc's measure. Congruent inscribed angles are those that intersect the same arc.

An angle's measure is equal to the intercepted arc's measure divided by two when it is surrounded by a circle.

m DH = 2(m ∠F) = 162

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The slope of the line  through each pair of points (0,0) and (2,6) is 3.

The increase divided by the run, or the ratio of the rise to the run, is how a line's slope is calculated. It gives information about the line's slope in the coordinate plane. Finding the slope between two locations and calculating the slope of a line are related tasks.

The following formula is used to determine slope:

The slope of the line between two points is given by y2 - y1 / x2 - x1.

Given the points are -

(0,0) and (2,6)

The slope of the line passing through the points is -

= 6 - 0 / 2 - 0

= 6/2

= 3

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The simple interest earned on the principal of $550 is $12.1.

The formula for simple interest is;

SI = PRT/100

where,

P is principal amount = $550

R is rate of interest = 4.4%

T is the total time in year; 6 months = 0.5 years.

Put the values in formula;

SI = 550×4.4×0.5 / 100

On simplification;

SI = 12.1

Thus, the simple interest incurred on the deposited principal is $12.1.

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Δp≥5.2755∗10−25ms−1

According to the Heisenberg uncertainty principle, we have

δx∗δp≥ℏ2

Since Δx=1angstrom=10−10m,

Δp≥6.626∗10−344∗3.14∗10−10

Δp≥5.2755∗10−25ms−1

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Answer: A. -2.2 B. -2.7

Step-by-step explanation: To find the rate of change is y2-y1/x2-x1.

For A y2=184.3, y1=140.3 x2=0 and x1=20. 184.3-140.3 will give you 44. 0-20 is -20. So 44 divided by -20 is -2.7.

For B its the same thing: y2=109.3, y1=28.3, x2=30, and x1=60. 109.3-28.3 is 81 and 30-60 is -30. 81 divided by -30 is -2.7.

Using basic mathematical operations such as addition and subtraction, they purchase 2054 more books for Oak Hill than Elm Street and Woodland combined.

Elm Street = 4,432 books

Oak Hill = 12,398 books

Woodland = 5,912 books

Using addition, we can determine how many books are purchased for Elm Street and Woodland combined by adding their values.

Elm Street + Woodland

4,432 + 5,912 = 10,344

Using subtraction, determine how many more books did they purchase for Oak Hill than Elm Street and Woodland combined.

Oak Hill - (Elm Street + Woodland)

12,398 - 10,344 = 2054 books

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Answer:$19,829.10

Step-by-step explanation:

Compounded quarterly so use [tex]A = P(1+\frac{r}{n})^{nt}[/tex]

-Quarterly means 4 times a year

Initial Amount (P) = $4700
Rate = 5.8%

Time = 25 years

Plug everything into equation

[tex]A = 4700(1+\frac{0.058}{4})^{4*25}[/tex]

Insert into calculator and get:

$19,829.0996305 which is approximately $19,829.10

Round to the nearest hundredth because when dealing with money there are only two decimal places.

Answer:

$19,829.10

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=4700\left(1+\dfrac{0.058}{4}\right)^{4 \times 25}[/tex]

[tex]\implies \sf A=4700\left(1+0.0145\right)^{100}[/tex]

[tex]\implies \sf A=4700\left(1.0145\right)^{100}[/tex]

[tex]\implies \sf A=4700(4.2189573...)[/tex]

[tex]\implies \sf A=19829.0996...[/tex]

Therefore, the account balance after 25 years will be $19,829.10 (nearest cent).

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Exact Form:

23

266

Decimal Form:

0.08646616...

Answer: 70º

Step-by-step explanation: isosceles triangle (2 equal sides) means 2 equal angles

Answer:

Hi,
Answer 111

Step-by-step explanation:

This shape (a kite) has an axis of horizontal symmetry

For given situation the events are dependent.

In this question,

Alita's basketball team is in the final four.

we have been given two events.

event A: Alita's basketball team win.

event B: Alita's basketball team play in the championship game.

From given condition, If they win, they will play in the championship game.

We can clearly observe that the occurrence of event B is dependent on the other event A.

If event A occurs only then event B would be true.

Therefore, for given situation the events are dependent.

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Answer:

11/61

Step-by-step explanation:

Cos is equal to Adjacent over hypotenuse

For angle B, the adjacent side is side BC which is 11 units long

the hypotenuse is 61

11/61

Answer:

The answers are 45f - 42 and -42+45f

Step-by-step explanation:

-5(-9f + 7) - 7

45f (-35 -7)

45f -42

also

-42 + 45f

The required value of y is 21.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of y

let k be a constant of proportion

When a quantity varies directly with others, then we have a relation, y = kx,      —-- 1

Now, find k for given x = 3 and y = 7, we need to put these values in equation 1, i.e.

7 = k(3)

k = 7/3

k = 7/3

Further calculate y for given x = 6 and constant of proportion = 7/3 i.e.

y = (9)(7/3)

y = 21

Hence, the required value of y is 21.

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Answer:

5 days

Step-by-step explanation:

Answer:

All of theses are correct.

4.5

4 1/2

9/2

About 5.