Question 1 (Multiple Choice Worth 1 points)
(03.01 MC)
Simplify √5 (8+3√6).
8√5 +3√30
O 5√10
130
O√40+15√6

For y = 10x the constsnt of proportionality is 10

We know that the quantity m is proportional to quantity n if there is a constant p such that m = pn

Here, p is called as the constsnt of proportionality.

This means, the constsnt of proportionality is nothing but the ratio between two proportional quantities.

Two variables are proportonal to each others means, when the variable increase the other one would also increase at some rate and that rate is the constant of proportionality.

We have been given an equation y = 10x.

Comparing given equation y = 10x with y = kx (here k is the constsnt of proportionality)

we have k = 10

This means, the constsnt of proportionality is k = 10

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The Wien Apetrol UC 20142000 was a unique and innovative venture that aimed to provide clean energy solutions to the people of Austria.

x = -7

ma = 54

m23 = 54

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Answer: P

Step-by-step explanation:

The piecewise-defined function for M(x), the cost for x megabytes of data used in a month [tex]$m(x)=\left\{\begin{array}{c}10, i f x \leq 2 \\ 0.1 x+9.8, i f x > 2\end{array}\right.$[/tex].

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Data exceeding 2 MB is charged at a rate of $0.10 per MB; one-time fee is $10;

The cost per month for x MB of data is:

Up to 2 Mb of data utilized; $10

Data use of over 2 MB

One off charge = $ 10

Charge for data over 2 Mb is $ 0.10 per MB

The monthly charge for x MB data is:

Data ta used up to 2 Mb

$ 10

Data used more than 2 Mb

m(x) = 10 + 0.1(x-2)

m(x) = 10 + 0.1 x-0.2

m(x) = 0.1 x + 9.8

So the function is:

[tex]$m(x)=\left\{\begin{array}{c}10, i f x \leq 2 \\ 0.1 x+9.8, i f x > 2\end{array}\right.$[/tex]

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Answer:

Step-by-step explanation:

15 tiles

An expression to represent the perimeter of the rectangle with  10/(x² + 11x +24) and (x+1)/(x+3) would be (x+12)(x+6)//(x+8)/(x+3).

What is the perimeter?

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.

Here, we have

Given: Sides = 10/(x² + 11x +24) and (x+1)/(x+3)

The perimeter is when you add all the sides of a shape.

In a rectangle, two sides are the same, and so are the other two. therefore, if the two sides are 10/(x² + 11x +24) and (x+1)/(x+3) the expression will be:

= 2(10/(x² + 11x +24)) + 2(x+1)/(x+3)

= 20/(x² + 11x +24) + 2(x+1)/(x+3)

= 20/(x+8)/(x+3) + 2(x+1)/(x+3)

= {20 + 2(x+1)(x+8)}/(x+8)/(x+3)

= {20 + 2(x² + 9x + 8)}/(x+8)/(x+3)

= { 20 + 2x² + 18x + 16}/(x+8)/(x+3)

= {2x² + 18x + 36}/(x+8)/(x+3)

= (x+12)(x+6)//(x+8)/(x+3)

Hence, an expression to represent the perimeter of the rectangle with  10/(x² + 11x +24) and (x+1)/(x+3) would be (x+12)(x+6)//(x+8)/(x+3).

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3×3×3×3×3 in exponential form is 3⁵.

When we represent a number in the exponential form then we can say that its power has been raised by an exponent. The exponential form is an easier way of representing repeated multiplication involving base and exponents.

For example, If we have to write the exponential form of a×a×a×a×a, we can write it as a base and the number of a's as the power that is

a×a×a×a×a = a⁵

Where

a is the base

5 is the power of a

We can simply write 3×3×3×3×3 in exponential form by raising the power to the base 3,

3×3×3×3×3 = 3⁵

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The equation for the line is y = 3/5x + 5.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

y = mx + b

8 = 3/5(5) + b

8 = 15/5 + b

b = 5

∴ equation is y = 3/5x + 5

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The angle also should be known to prove congruency.

It states that two triangles are said to be congruent if they are exact copies of one another and completely cover one another when superposed. In other words, two triangles are congruent if their corresponding sides and angles are equal to those of the first triangle.

It is ineffective to only know angle-angle-angle (AAA), as this can result in triangles that are similar but not congruent. There are four short cuts that can be used to check whether two triangles are congruent.

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1. |5+m|<13 is an "or" compound inequality. 2. 4|y + 6| ≥ 3 is neither compound inequality. 3. null set.

1. The inequality is given in the question, is as follows:

|5+m| < 13

The absolute value of the expression "5+m" is less than 13.

To solve the inequality, we need to split the inequality in two separate inequalities: 5+m < 13 and -5-m < 13.

Thus, |5+m|<13 is an "or" compound inequality.

2. 4|y + 6| ≥ 3 is neither compound inequality because we have just one inequality.

3. The absolute value of a number is always positive, so it is impossible for |g - 3| = -2. So the answer is c. null set.

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The expected value of Isabel's game is given as follows:

E(X) = 0.

The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.

The game is composed by choosing eight balls, which are equally as likely to be chosen.

Then the probability distribution of earnings is given as follows:

Hence the expected value of the price is given as follows:

E(X) = 1/8 x (1 + 2 + 5 + 6 + 8 + 10) - 16 x 2/8.

E(X) = 0.

The problem asks for the expected earnings.

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The height of a triangle if its base is 24 cm and its area is 216 cm² is 18 cm.

The area of triangle is calculated using the below mentioned formula -

Area = 1/2 × base × height. We will use the formula of area of triangle to calculate the height of triangle.

Keep the values in formula -

216 × 2 = 24 × height

Firstly multiplying the values given on Left Hand Side of the equation

height × 24 = 432

Shifting 24 to Right Hand Side of the equation

Height = 432/24

Now dividing the values

Height = 18 cm

Thus, the height of the triangle is 18 cm.

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Integers are a type of real number that just includes positive and negative whole numbers and natural numbers. Real numbers can include fractions due to rational and irrational numbers, but integers cannot include fractions.

$75.50 and 18 cents - $35.50 and 8 cents = $40.00 and 10 cents per mile. For x miles, we multiply $40.00 and 10 cents by x miles.

Also, we could convert dollars to cents by multiply it by 100 Since $1 =100 cents.

7568 - 3558 cents = 4010 cents. For x miles, 4010X cents.

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You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values.

The table depicts a proportionate relationship if all of those ratios are the same.

If all of the ratios of the variables are equal, then there is a proportional link between the two variables.

In proportional relationships, one variable is, in other words, always a constant value multiplied by the other variable. The proportionality constant is the name given to the constant value. A mathematical equation of the form y=kx, where k is the proportionality constant, can be used to model any proportional relationships. The unit rate is another name for the proportionality constant.

Dustin, for instance, spends $8 each month for a music streaming service. The total cost of the service, c, and the number of months Dustin pays for the streaming service, m, are proportionate. 

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The vertex of the parabola is at (0, 0), the focus of parabola is at (2, 0) and axis of symmetry of parabola is x-axis.

A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

One definition of a parabola includes a line and a point (the focus) (the directrix). The directrix is not the main focus. The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

Given a horizontal parabola centered on the origin opens to the left,

the equation for a horizontal parabola,

(y − b)² = 4p(x − a), p≠0

a and b are the vertex of parabola,

since the parabola is centered on the origin, a and  b are (0, 0)

vertex of parabola is at (0, 0),

and for horizontal parabola axis of symmetry is the x-axis.

focus of parabola is at (a + p, b)

given p = 2

focus of parabola is at (0 + 2, 0) = (2, 0)

Hence vertex at (0, 0), focus at (2, 0), and symmetry with the x-axis.

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The statement that must be true since the average rate of change T(d) for the interval d = 4 and d = 10 is 0 is this:

C: The same number of tickets was sold on the fourth day and tenth day.

The average rate of change is a measurement that shows how much the function of a unit changes over a given interval. In the above question, we can see that the average rate of change given the two intervals is zero and this means that there was no change among the variables.

Thus, we can conclude that the number of tickets that were sold on day 4 was also the number of tickets sold on day 10.

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Answer:

Step-by-step explanation:

V=(1/3)hπr^2

<=> 4487 = 1/3x21πxr^2

<=> r^2 = 641/π

<=> r = squrt( 641/π)

The value of k are the graphs (equations) equal is k = -3/2

Equations are mathematical expressions that show the relationship between two variables.

Since we have the two equations  12y = -3x + 8 and 6y = kx -5, re-writing them, we have

12y = -3x + 8

3x + 12y - 8 = 0  (1)

Also, 6y = kx - 5

-kx + 6y + 5 = 0  (2)

For a pair of equations ax + bx + c = 0 (3) and a'x + b'x + c' = 0 (4) to be equal (or consistent), then

a/a' = b/b' = c/c'

Comparing with (1) and (2), with (3) and (4) above, we have that

So, using a/a' = b/b', we find k.

So, substituting the values of the variables into the equation, we have that

a/a' = b/b'

⇒ 3/-k = 12/6

Cross-multiplying, we have that

3 × 6 = -k × 12

k = -3 × 6/12

k = -3/2

So, the value of k = -3/2

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(x - 4) is a factor of the expression 5x³ − 7x² − ax − 28, when a = 28

Here we are given the expression 5x³ − 7x² − ax − 28

now we need to find a value of a for which (x - 4) is a factor of

5x³ − 7x² − ax − 28

This implies that 5x³ − 7x² − ax − 28.must be divisible by (x - 4)

On dividing 5x³ − 7x² − ax − 28. by x - 4 will give us

[tex]x-4) \overline{5x^{3}-7x^{2}-ax-28.}(5x^{2}+14x+(56-a)\\{\hspace{1cm} 5x^{3}-20x^{2}\\\\\hspace{2cm}\overline{14x^{2}-ax}\\{\hspace{2cm}14x^{2}-56x\\\\{\hspace{3cm} \overline{(56 - a)x - 28}\\{\hspace{3cm} (56-a)x-(56-a)\\{\hspace{5cm} \overline{28-a}[/tex]

Since (x - 4) is a factor of 5x³ − 7x² − ax − 28, there should not be any remainder left

Hence, 28 - a = 0

or, a = 28

Hence (x - 4) is a factor of 5x³ − 7x² − ax − 28, when a = 28

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Correct Question

Find the value of a such that (x−4) is a factor of 5x³ − 7x² − ax − 28.

The table shows the temperature of a substance at the start of a science experiment which - 16.8°C and we were told that it changed by 3/4 of the value which therefore means that the final temperature at 2:35pm is - 29.4°C.

This is referred to as the degree of hotness or coldness of a substance and it is measured in Celsius, kelvin etc.

In this scenario we were told that the temperature - 16.8°C changed by 3/4 of the value which means that:

3/4 × - 16.8°C = - 12.6°C

The temperature at 2:35pm will therefore be  - 16.8°C - 12.6°C = - 29.4°C.

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Given that the one side of a right-angled triangle is 12 and its angle is 19, the value of c is 36.85.

Trigonometry, a branch of mathematics, studies how triangle side lengths and angles relate to one another. Around the third century BC, the use of geometry in astronomical study led to the first appearance of the area. The study of specific trigonometric functions and how they could be applied to calculations is a topic covered in the branch of mathematics known as precise techniques. Trigonometry includes six well-known trigonometric operations. The names and acronyms for each are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle properties, specifically of right triangle properties. But geometry is the study of geometric figures and their features.

given

a/sinA = c / sinB

12 / sin19 = c / sin90

36.85 = c /1

c = 36.85

Given that the one side of a right-angled triangle is 12 and its angle is 19, the value of c is 36.85.

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Answer:

4 loaves of bread

Step-by-step explanation:

Cost of 1 loaf of bread = $3

Cost of 1 roll = $1

The baker needs to sell both items and it should be worth $24.

To find the linear equation,

Suppose, the baker sells

x

loaves of bread and

y

rolls.

Then the total cost of the sales has to be $24.

So, the linear equation will be:

3

x

+

1

y

=

24

.......................(A)

Now, it is given that the baker sold 12 rolls and we need to know how many loaves he has to sell.

For that, replace the

y

in equation (A) with 12 as

y

represents number of rolls sold.

Then the new equation becomes:

3

x

+

1

×

12

=

24

0r

3

x

=

24

−

12

or

3

x

=

12

Solving for

x

,

x

=

12

3

=

4

loaves

We will convert between volume units by multiplication or division process depending on the standard metric units.

What is unit conversion?

Unit conversion is done either by multiplication or division process between numerical values. There are some standard metric units. By following the standard, we can convert one unit to another. As example we have a box that is 2 square feet area, now we want to know the area in inches. So, we will multiply it by 144 to convert in square inches.

How do we convert between volume units?

We convert between volume units either by multiplication or division process depending on the standard unit. If we find a volume in liter and we can convert it in cubic meter by multiplying the number by 0.001. Assume, we measured a volume in cubic feet, but someone want to know this volume in cubic meter that time we divide this value by 35.32 to convert in required unit.

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If Elena earn y = 8.40x dollars where x represent how many hours she work and Jada earn $7 per hour, it would take Elena approximately 17.86 hours and Jada approximately 21.43 hours to earn $150

To find out how many hours it would take for Elena to earn $150, we need to solve the equation:

y = 8.4x

150 = 8.4x

x = 150/8.4

x ≈ 17.86 hours

So it would take Elena approximately 17.86 hours to earn $150.

To find out how many hours it would take for Jada to earn $150, we divide 150 by her hourly rate:

= $150 /( $7/ hour)

≈ 21.43

So it would take Jada approximately 21.43 hours to earn $150.

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Answer: x = 2, 1

Step-by-step explanation:2x^2 - 6x + 4 = 0

Firstly, simplify. Divide by 2 to get

2(x^2-3x+2) = 0

Move the constant to the other side.

2(x^2-3x) = -2

Divide the x term by 2 and square it

-3/2^2 = 9/4

Add this result to both sides.

2(x^2-3x+9/4) = 1/4.
Put the perfect sq on both sides
2(x-3/2)^2=1/4
Then solve the equation:

take the sqrt of both sides and isolate x for each solution

x-3/2= +/-1/2
x = 3/2 + 1/2
x= 3/2-1/2
x= 2, 1

Scale Factor. To create a scaled copy, we multiply all the lengths in the original figure by the same number.

A 1.5 GPA, or Grade Point Average, is comparable to a D+ letter grade on a scale of 4.0 GPA. This corresponds to a grade of around 69%. The Scale Factor. To make a scaled replica, multiply all of the original figure’s lengths by the same number. This figure is known as the scaling factor. The scale factor in this case is 1.5 since 4(1.5)=6, 5(1.5)=7.5, and 6(1.5)=9.

An Over 1.5 Goals bet is simply a betting on there being two or more goals scored in a given game. The scoreboard is irrelevant; as long as the two sides collaborated for at least two goals, your bet will win.

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Angle 5 is congruent to angle 8 by (vertically opposite angle )

Angle 5 is also Congruent to Angle 4 (alternate Angles)

Angle 5 is also Congruent to Angle 1 ( corresponding Angles )

When two figures or things are similar in size and shape, or when one is the mirror image of the other, they are said to be congruent.

It states that two triangles are considered to be congruent if they are identical duplicates of one another and completely cover one another when superposed. In other words, two triangles are congruent if their corresponding sides and angles are equivalent to those of the first triangle.

Two line segments are said to be congruent if their lengths are identical. In addition, two congruent line segments have the same length. Two angles are congruent if they have the same measure.

Angle 5 is congruent to angle 8 by (vertically opposite angle )

Angle 5 is also Congruent to Angle 4 (alternate Angles)

Angle 5 is also Congruent to Angle 1 ( corresponding Angles )

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Angle 5 is congruent to angle 8 by (vertically opposite angle )

Angle 5 is also Congruent to Angle 4 (alternate Angles)

Angle 5 is also Congruent to Angle 1 ( corresponding Angles )

When two figures or things are similar in size and shape, or when one is the mirror image of the other, they are said to be congruent.

It states that two triangles are considered to be congruent if they are identical duplicates of one another and completely cover one another when superposed. In other words, two triangles are congruent if their corresponding sides and angles are equivalent to those of the first triangle.

Two line segments are said to be congruent if their lengths are identical. In addition, two congruent line segments have the same length. Two angles are congruent if they have the same measure.

Angle 5 is congruent to angle 8 by (vertically opposite angle )

Angle 5 is also Congruent to Angle 4 (alternate Angles)

Angle 5 is also Congruent to Angle 1 ( corresponding Angles )

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Angular speed of the fan in radians per minute is 421 (crad /min) , The linear speed of the tip of a blade in inches per minute is

Suppose the dan turns at a rate of 69 revolutions per minute.

Angular speed of the fan in radians per minute is

According to the problem

w = 2zn

(a)  w = 2z * 67  

= 134z

≈ 421 crad /min)

Angular speed of the fan in radians per minute is 421 (crad /min)

The linear speed of the tip of a blade in inches per minute is

(b) v = 2z * 19 * 67

{ v = 2zrn}

=2546z

7988(cin / m * in)

The linear speed of the tip of a blade in inches per minute is 7988(cin / m * in)

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The result after multiplication = 6/X, 1, 1/ 7

When one is divided by a number or value it is called the reciprocal of that number or value. It is also said the inverse form of the value or number. As example, reciprocal of 12 is written as 1/12.

What is the result?

There are four values 6, X, 6 and 42.

multiply the first number by the reciprocal of others.

reciprocal of X = 1/X

reciprocal of 6 = 1/6

reciprocal of 42 = 1/42

now we multiply, 6×1/X = 6/X

6×1/ 6 = 1

6×1/ 42 = 1 /7

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