write an inequality for the word phrase below: a number squared is less than 45

The estimate of 179% of 41 by rounding is about 73.19.

To find this estimate, first convert the percentage to a decimal by dividing it by 100: 179/100 = 1.79. Then, multiply this decimal by 41: 1.79 * 41 = 73.39.

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The correct option for the pentagons is:

Option d: The angle measure of the pentagon P'Q'R'S'T' are congruent to the corresponding angle measures of pentagon PQRST.

What is a pentagon?

A geometric figure with five sides and five angles is called a pentagon. A standard pentagon's internal angles add up to 540 degrees. The shape is created when all of a pentagon's sides come together end to end. If a pentagon is regular, all of its sides have the same length, and its five angles are all the same size. An irregular pentagon is one that does not have equal side length and angle measurements.

The complete question is given below.

We will now look into each option.

a) After rotating, the size of the pentagon is the same.

So the area of both pentagons remains the same.

This statement is not true.

b) Congruent figures are identical in terms of both size and shape. Their size and shape are unaltered by reflection, rotation, or translation.

So both the pentagons are congruent.

This statement is not true.

c) The side lengths of the pentagons are not changed. They are just rotated.

So the perimeter of both the pentagons is the same.

This statement is also not true.

d) The corresponding angles of the pentagons are the same and the sizes are the same.

So this is the true statement.

Therefore the correct option for the pentagons is:

Option d: The angle measure of the pentagon P'Q'R'S'T' are congruent to the corresponding angle measures of pentagon PQRST.

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The matrix after the row operation is:

\(\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right]\)

We have,

We use the operation R1 → R1/9.

This will give us,

Row 1 values will change to 9/9, 4/9, -9/9

So,

1, 4/9, -1

Now,

\(\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right]\)

Thus,

The matrix after the row operation is:

\(\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right]\)

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Answer:

17

Step-by-step explanation:

Jason is 15 his sister 4 years younger: 15-4=11+(6years)=17

The total area they need to paint is:

The function that expresses f(x) is f(x) = 1.99x + 3, and its graph is continuous.

A continuous function is one that doesn't have any sudden or unexpected changes in value. It means that if we make small enough changes to its input, the output will also change by a small amount.

We can express the total cost of an order as a function of the number of books sold, x, using the formula:

f(x) = 1.99x + 3

This function takes the number of books sold, multiplies it by the cost per book ($1.99), and adds a fixed fee of $3.

For example, if we sold 3 books, we can use the function to find the total cost:

f(3) = 1.99(3) + 3 = 9.97

This means that selling 3 books would cost $9.97 in total.

The graph of this function is continuous, which means that as we move along the x-axis, the y-values change smoothly and without any sudden jumps.

The term "continuous" refers to a function that can take on any value between two given points and can be broken down into infinitely many fractions and decimals.

In contrast, a discrete function can only take on specific values, usually whole numbers or integers.

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There are 10% of the 60 students which is 6 students who are 18 years old or younger.

To get number of students who are 18 years old or younger, we have to determine percentage of students who fall into this category.

The percentage of students who are 18 years old or younger will be derived by subtracting the sum of the percentages of students who are 19 years old, 30 years old and over 20 years old from 100%.

The percentage of students who are 18 years old or younger is:

= 100% - (20% + 30% + 40%)

= 100% - 90%

= 10%.

Translated question:

A university course has 60 students. If 20% are 19 years old, 30% 30 and 40% over 20 years old, how many students can there be 18 years old or younger?

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By the tangent-secant theorem, the length of the variable 'x' will be 15 units.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The product of the measurements of the secant segment and its exterior component is equal to the square of the dimension of the tangent section if a tangent length and a secant portion cross out of a circle.

By the tangent-secant theorem, the equation is written as,

9 × (9 + x) = 8 × (8 + 19)

Simplify the equation, then we have

9 × (9 + x) = 8 × (8 + 19)

81 + 9x = 64 + 152

9x = 64 + 152 - 81

9x = 135

x = 15

The length of the variable 'x' will be 15 units.

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Answer:

Two Equal Angles = 45°

Third Angle = 90°

Step-by-step explanation:

Given information

Two equal angles of an isosceles triangle are half the third angle

Set variables

Let x be the angle of the equal angles of the isosceles triangle

Let 2x be the angle of the third angle

Set equations

x + x + 2x = 180 (Triangle angle sum theorem)

Combine like terms

2x + 2x = 180

4x = 180

Divide 4 on both sides

4x / 4 = 180 / 4

\(\Large\boxed{x=45^\circ}\)

Substitute the x value into the expression to find the third angle

Third angle = 2x

                   = 2 (45)

                   = \(\Large\boxed{90^\circ}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

y=-1/10x-5

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=-1/10(x-(-10))

y+4=-1/10(x+10)

y=-1/10x-10/10-4

y=-1/10x-1-4

y=-1/10x-5

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

Work Shown:

\(x = 0.\overline{4}\\\\x = 0.4444\ldots\\\\10x = 4.4444\ldots\\\\10x-x = 4.4444\ldots-0.4444\ldots\\\\9x = 4\\\\x = \frac{4}{9}\\\\\frac{4}{9} = 0.\overline{4}= 0.4444\ldots\\\\\)

The idea is that when we subtract 10x and x, the infinite decimal pattern (the 4s that go on forever) will cancel. That leads to 9x = 4 which solves to x = 4/9

Answer:

I need to go and take my shower now.

Answer:

x= -3/2y + 1/2 p

Step-by-step explanation:

p=2x + 3y

2x + 3y =P   subtract 2x from both sides

3y=P -2x      divide both sides by 3 and simplify

y = P/3 - 2x/3

Answer:

Hi,

Step-by-step explanation:

We can't solve that but reduce it to the same denominator.

\(\dfrac{x+5}{x}+\dfrac{x+8}{x-1}\\\\=\dfrac{(x+5)(x-1)+x(x+8)}{x(x-1)}\\\\=\dfrac{x^2+5x-x-5+x^2+8x}{x(x-1)}\\\\=\dfrac{2x^2+12x-5}{x(x-1)}\\\)

We are given a system of equations,

\(\begin{cases}-x+2y=0\\y=-2\\ \end{cases}\)

This will translate into a 2x2 matrix of coefficients (because 2 equations and 2 unknowns),

\(\begin{bmatrix}-1&2\\0&1\\ \end{bmatrix}\)

The matrix will then be applied to the vector (lower dimensions on top),

\(\begin{bmatrix}x\\y\\ \end{bmatrix}\)

And the result vector will be whats on the other side of equals sign,

\(\begin{bmatrix}0\\-2\\ \end{bmatrix}\)

So to put everything together,

\(\begin{bmatrix}-1&2\\0&1\\ \end{bmatrix}\begin{bmatrix}x\\y\\ \end{bmatrix}=\begin{bmatrix}0\\-2\\ \end{bmatrix}\)

Hope this helps :)

Answer:

41 meters

Step-by-step explanation:

\(\frac{31}{64}\) = \(\frac{19.8}{x}\)

31x = (19.8)(64)

31x = 1267.2  Divide both sides by 31 and round

x = 41

Answer:

I'm not so clear with the question but I hope this helps

Based on the definition of  parallelogram, the conclusion about the quadrilateral is that: D. The quadrilateral is a parallelogram, because there are two pairs of equal slopes, and thus two pairs of parallel opposite sides.

If a quadrilateral is a parallelogram, the two pairs of opposite sides will be parallel to each other.

If two sides of a shape have the same slopes, it then means the shape is a parallelogram.

The quadrilateral that is given is said to have the following:

Two equal slopes of 5/4 and 5/4; and 2/5 and 2/5, this means the sides that have the same slope values are opposite to each other.

Since they are opposite to each other and they have the same slope, therefore, the conclusion about the described shape is: D. The quadrilateral is a parallelogram, because there are two pairs of equal slopes, and thus two pairs of parallel opposite sides.

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Answer:

Step-by-step explanation:

B because after having the star and the circle comes the square.

The fraction of the original passengers remaining on the bus is 11/21.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A crowded bus makes several stops along a city street, with no passengers boarding the bus at any stop.

.At the 1st stop 1/3 of the passengers exit.

At the 2nd stop, 3/7 of the remaining passengers exit the bus.

Therefore, The fraction of the original passengers who remain on the bus is,

= [(1 - (1×1/3) - (1)×(1/3)×(3/7)].

= [ 1 - (1/3) - (3/21)].

= [ (2/3) - (3/21)].

= [(14 - 3)/21].

= 11/21.

So, 11/21 remains on the bus.

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Each person buys a number of cakes

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Andy buys x cakes, Betty buys 4 times as many cakes as andy, and colin buys 3 more cakes than andy

So,

Andy has = x Cakes

Betty have = 4x Cakes

Clin has = x +3 Cakes

Since each cake costs 65p and the total cost of the cakes is £52.65

thus,

0.65( x + 4x + x +3) = 52.62

x + 4x + x +3 = 81

6x = 78

x = 13

Therefore,

Andy has = 13 cakes

Betty has = 4x = 4*13 = 52 cakes

Colin has = x + 3 = 16 cakes

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The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.

A stew recipe uses 3 teaspoons of salt for every 4 cups of water.

There is a ratio issue here.

As X is to three, 3 is to 4.

3 : 4 :: X : 3

To eliminate the fractions, multiply each integer in the ratio by 12.

9 : 12 :: 9X : 12

This is a portion of what is

9 / 12 = 9X / 12

to obtain, cross-multiply.

9 / 12 = 3 teaspoons of salt,

Check: 3 cup of flour yields 3 cups, which is a 4x increase.

The amount of salt in 9/12 tablespoons is four times that of 3 tablespoons.

The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.

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The mean for the number of people with the genetic mutation in such groups of 600 is 18.

Given that,

About 3% of the population has a particular genetic mutation.

This means that for any group of people, 3% of the people has a particular genetic mutation.

This is a binomial distribution.

Probability that people having genetic mutation = 3% = 0.03

Random sample size = 600

Mean for a binomial distribution can be calculated as,

Mean = n × p

         = 600 × 0.03

         = 18

Hence the mean number of people having genetic mutation is 18.

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Answer: 22.4402

Step-by-step explanation:

Answer:

84.4% of 23 is 19.412.

Step-by-step explanation:

Let the unknown number be x.

Now, 84.4% of x = 19.412.

∴ (84.4 ÷ 100) × x = 19.412.

By simplifying the equation,

x = (19.412 × 100) ÷ 84.4

x = 1941.2 ÷ 84.4

∴ x = 23

Thus, 84.4% of 23 is 19.412.

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To write the height of Debbie as a fraction of the height of Leo in its simplest form is this: 17/18.

Writing one figure as a fraction of another can be done by representing the figures as numerators and denominators. In this case, what we will have is 85/90. That is the height of Debbie divided by the height of Leo.

To express this fraction in its simplest form will mean dividing the figures until they can no longer be divided. Using 5 as a common factor for dividing, we can conclude that the simplest form of the answer is 17/18.

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Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.

An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.

Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.

Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.

Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.

In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

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Answer:

The answer is below

Step-by-step explanation:

A rectangle is a quadrilateral (four sides) with two pairs of equal opposite and parallel sides. All the four angles in a rectangle are equal to 90° (right angle). The diagonals of a rectangle are equal and bisect each other.

The area of a rectangle = length * breadth

a) Area = length * breadth = 8 cm * 3 cm = 24 cm²

b)  Area = length * breadth = 5.2 cm * 7.7 cm = 40.04 cm²

a)The value of acceleration will be 4.8 m/s²

b)The total distance travelled is 505 m.

a) As all the movement happens along a straight line, we need to define an axis only, which we call x-axis, being the positive direction the one followed by the car.

We can choose to place our origin at the location where the motorcycle was stopped at the side of the road (assuming that it is the same point  for the car when it passes him), so our initial position is 0.

We can also choose our time origin to be the same as the instant that the motorcycle starts from rest, so t₀ = 0.

With these assumptions, and assuming also that the acceleration is constant, we can write two equations, one for the car (at constant speed) and the another one for the motorcycle, as follows:

xc = vx*t

xm= 1/2*a*t²

When the motorcycle passes the car, both distances traveled from the origin will be equal each other, i.e., xc = xm :

⇒ vx*t = 1/2*a*t²

We have as givens vx=35 m/s and t = 14.5 sec when both equations are equal each other.

⇒ 35 m/s* 14.5 s = 1/2*a*(14.5)²(s)²

Solving for a:

a = (2* 35 m/s) / 14.5 s = 4.8 m/s²

b) Replacing the value of a in the equation for xm, we have:

xm = 1/2*4.8 m/s²* (14.5)²s² = 505 m.

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Answer:

65

Step-by-step explanation:

Joshua has 390 photos, you need to divide that number by the each amount of photos in each page to figure out how many pages he needs to paste all them.

So you'd divide it like. 390 / 6


And that gives you 65.

Answer:

65

Step-by-step explanation:

It is 360 divided by 6 and you will get 65 (if you need help with long division contact me)

The constant of variation, k, is defined as the ratio between the two variables' values, multiplied by their respective powers:  \(k = y/x^a \times z/x^b,\) where a and b are the powers of x in the expressions for y and z, respectively. when   \(x = -3\)  and \(y = 4\) , z is equal to -81/16.

In this case, we have x = 8, y = 54, and z = 144, so we need to determine the powers of x in the expressions for y and z:

\(y = 54 = (8^a) \times k = > a = 3\)

\(z = 144 = (8^b) \times k = > b = 2\)

Substituting these values into the formula for k, we get:

\(k = y/x^a \times z/x^b = 54/8^3 \times 144/8^2 = 27/64\)

Therefore, the constant of variation is 27/64.

Using the same formula as above, we can solve for z when x = -3 and y = 4:

\(k = y/x^a \times z/x^b\)

We need to determine the powers of x in the expressions for y and z:

\(y = 4 = (-3)^a * k = > a = -1\)

\(z = ? = (-3)^b * k = >\) we don't know b or z yet

Substituting these values into the formula for k, we get:

\(k = y/x^a * z/x^b = 4/(-3)^(-1) * z/(-3)^b = -12z/(-3)^2\)

Simplifying this expression, we get:

\(k = -12z/9 = -4z/3\)

Now we can solve for z:

\(-4z/3 = 27/64\)

Multiplying both sides by 3/(-4), we get:

\(z = -81/16\)

Therefore, when  \(x = -3\) and   \(y = 4, z\) is equal to   \(-81/16.\)

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