Independent Practice For each pair of expressions below, without substituting in specific values, determine which of the expressions in the given pairs is larger. Explain your reasoning in a sentence or two.​

Answer: -8/21

Step-by-step explanation:

-5/7= -15/21

1/3=7/21

-15/21+7/21= -15+7=18

(15-7=8)

-8/21

Simplified Solution:

[tex]-\frac{8}{21}[/tex]

Hope this helps!

Answer:

1) 38

2) 18

Step-by-step explanation:

1) 4m - 2t

m = 10

t = 2

(4 * 10) - (2 * 2)

40 - 4 = 36

Answer : 36

2) t + 2m - 4

m = 10

t = 2

2 + (2 * 10) - 4

22 - 4 = 18

Answer : 18

3) m/2t

m = 10

t = 2

10/(2*2) = 2.5

Answer : 2.5

The difference between the surface areas is 198 square inches

The side lengths are given as:

L = 7 inches

l = 4 inches

The difference between the surface areas is calculated as:

Difference = 6(L^2 - l^2)

Substitute the known values in the above equation

Difference = 6(7^2 - 4^2)

Evaluate

Difference = 198

Hence, the difference between the surface areas is 198 square inches

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Answer:

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

Factorize as below and find roots:

Answer:

[tex]x=-1, \quad x=\dfrac{1}{2}, \quad x=-\dfrac{2}{3}[/tex]

Step-by-step explanation:

Given polynomial:

[tex]f(x)=6x^2+7x^2-x-2[/tex]

[tex]\boxed{\begin{minipage}{6 cm}\underline{Factor Theorem}\\\\If $f(x)$ is a polynomial, and $f(a) = 0$,\\ then $(x-a)$ is a factor of $f(x)$.\\\end{minipage}}[/tex]

Since the constant of the given polynomial is -2, the possible factors are ±1 and ±2.

Apply the Factor Theorem to check the possible values:

[tex]f(1)=6(1)^3+7(1)^2-(1)-2=10 \neq 0[/tex]

[tex]f(-1)=6(-1)^3+7(-1)^2-(-1)-2=0[/tex]

[tex]f(2)=6(2)^3+7(2)^2-(2)-2=72 \neq 0[/tex]

[tex]f(-2)=6(-2)^3+7(-2)^2-(-2)-2=-20 \neq 0[/tex]

Therefore, (x + 1) is a factor of the polynomial:

[tex]f(x)=(x+1)(ax^2+bx+c)[/tex]

Compare with the original function to find the coefficients of the quadratic:

[tex]6x^3=ax^3 \implies a=6[/tex]

[tex]7x^2=(b+a)x^2 \implies b=1[/tex]

[tex]-2=c \implies c=-2[/tex]

Therefore:

[tex]f(x)=(x+1)(6x^2+x-2)[/tex]

Factor the quadratic:

[tex]f(x)=(x+1)(6x^2+4x-3x-2)[/tex]

[tex]f(x)=(x+1)[2x(3x+2)-1(3x+2)][/tex]

[tex]f(x)=(x+1)(2x-1)(3x+2)[/tex]

Set the polynomial function to zero:

[tex](x+1)(2x-1)(3x+2)=0[/tex]

Apply the zero product property:

[tex](x+1)=0 \implies x=-1[/tex]

[tex](2x-1)=0 \implies x=\dfrac{1}{2}[/tex]

[tex](3x+2)=0 \implies x=-\dfrac{2}{3}[/tex]

Therefore, the solutions are:

[tex]x=-1, \quad x=\dfrac{1}{2}, \quad x=-\dfrac{2}{3}[/tex]

Answer:

120 pounds

Step-by-step explanation:

26+0.25p=c

c=56

26+0.25p=56

Subtract 26 from both sides.

0.25p=30

Divide 0.25 from both sides.

p=120

It costs $56 for 120 pounds.

Hope this helps!

Please mark as brainliest if correct!

From the given situation, we have that:

A. The table is completed as follows:

B. The unit rate is of 20 pounds of ray per horse.

C. There is a proportional relationship between the pounds of hay eaten daily and the number of horses, because the division of the output(pounds of hay) by the input(number of horses) always results in a constant.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

Each horse at a ranch eats 20 pounds of hay each day, hence the proportional relationship that models the total amounts of hay consumed by x horses is given by:

y = 20x.

The table is completed as follows, with the bolded numbers being the empty positions in the table.

Considering the relationship y = 20x, we have that:

B. The unit rate is of 20 pounds of ray per horse.

C. There is a proportional relationship between the pounds of hay eaten daily and the number of horses, because the division of the output(pounds of hay) by the input(number of horses) always results in a constant.

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a)

Soln,

Given,

Radius(r) = 8cm

Length/height(h) = 50cm

Then,

Volume of given prism = πr^2h

= 22/7×(8cm)^2×50cm

= 10057.14286cm^3

Therefore,The volume of the given prism is 10057.14286cm^3

b)

Soln,

Given,

Radius(r) = 8cm

Length/height(h) = 50cm

Then,

C.S.A. of the given prism = 2πrh

=2×22/7×8cm×50cm

=2514.285714cm^2

Therefore,C.S.A. of the given prism is 2514.285714cm^2

Step-by-step explanation:

direct variation means that

y = kx

that means it is a line with y-intercept = 0.

in other words, when x = 0, then y = 0 too.

for 2 given points the first part is automatically true. 2 points always define a line.

so, what we need to find out is, if (0, 0) is also on the line.

if not, it is not a direct variation.

the 2 points imply the equation

y = x + 2

as the y value is always larger than the x value by 2.

this has a y-intercept larger than 0 (2).

and so, (0, 0) is NOT on the line, and it is NOT a direct variation.

so, the 3rd answer option is correct.

The distance of 7 units from 1 on a number line give the number 8 and -6.

The chosen number on number line is 1.

When moving 7 units from 1 on the right hand side;

Add 7 units to 1 gives 8.

thus, moving 7 units to the right of number line gives 8.

For, moving 7 units to the left of number line;

subtract 7 units from 1.

1 - 7 = -6

Thus, moving 7 units to the left of number line gives -6.

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3/25  is the possibility that the range on her card might be a a couple of of two or 5.

what does a possibility mean?

The possibility serves as a gauge for the way probably an occasion is to occur. It gauges how probably an occasion is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the method for possibility.

Total range of playing cards = 25 (Given)

Total viable range of playing cards which can be top range = 8

[ They are 2, 3, 5, 7, 11, 13, 17, 23 ]

P(top range) = 8/25

Total viable range of playing cards which can be even = 12

[They are 2, 4, 6, 8, 10, 12, 14, 16, 18. 20, 22, 24]

P(even range) = 12/25

Total viable range of playing cards which can be multiples of 5 = 5

[They are 5, 10, 15, 20 ,25]

P(multiples of 5) = 5/25

P(multiples of 5) = 1/5

Total viable range of playing cards which can be divisible through 6 = 4

[They are 6, 12, 18, 24]

P(Divisible through 6) = 4/25

Total viable range of playing cards that with the range 4 = 3

[They are 4, 14, 24]

P(with the range 4) = 3/25

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The mean, which is a measure of central tendency for quantitative data should not be used for likert scale data values, which are ordinal (qualitative) data.

The use of the mean as a measure of central tendency for ordinal data may be encountered, in the customer satisfaction data analysis systems used in some banks

Ordinal data are a data form that specified categories that are scaled or have a set order.

However, ordinal scales are not standard, such that they cannot be manipulated quantitatively.

The mean specifies the average value, which the sum of the quantitative measurements, divided by the number of measurements

Therefore;

An example in real life where the mean could be used as a measure of central tendency of ordinal data is in customer satisfaction survey at the bank, where customers have five levels to select how happy they are with the bank services.

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To calculate average rate of change of a function f(x) over an interval between 2 points (a. f(a)) and (b, f(b)) is given by

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

The given function is [tex]h(x)= x^{2} -9x+18[/tex]

and the given interval is [tex]4\leq x\leq 11[/tex]

Now, h(b) = h(11) = [tex](11)^{2} -9(11)+18[/tex]

= [tex]121-99+18[/tex]

= [tex]40[/tex]

h(a) = h(4) = [tex](4)^{2} -9(4)+18[/tex]

= [tex]16 -36+18[/tex]

= [tex]-2[/tex]

The average rate of change between (4, -2) and (11, 40) is

= [tex]\frac{40-(-2)}{11-4}[/tex]

= [tex]\frac{40+2}{11-4}[/tex]

= [tex]\frac{42}{7}[/tex]

= [tex]42[/tex]

∴ The average rate of change between (4, -2) and (11, 40) is 42

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Answer:

first answer is 5535 second answer is 11934 third answer is 4140 fourth answer is 10373 the fifth answer is 17408 sixth answer is 3240 seventh answer is 12773 eighth answer is 4928 ninth answer is 13325

Step-by-step explanation:

this took to long

Answer:

[tex]x+y=27[/tex]

[tex]y=2x+6[/tex]

Step-by-step explanation:

Letting [tex]x[/tex] and [tex]y[/tex] represent the smaller and larger number, respectively we create these equations.

Suppose that today the exchange rate between the u.s. dollar and the chinese yuan is $1 =.12 yuan. if next week the exchange rate is $1 = .20 yuan, it is clear that yuan has depreciated relative to dollar.

What is meant by the exchange rate?

Last week: $1 = 0.12 yuan

Therefore, for exchange of $1, 0.12 yuan will be given

Today: $1 = 0.2

Therefore, for exchange of $1, 0.2 yuan will be given.

So, yuan will be given for same amount of $. Thus yuan has depreciated.

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The time it would take Joey is 3 years

Given that the formula for simple interest is;

I = PRT

Where;

Substitute into the formula

400 = 300 × 4 × t/ 100

cross multiply

4000 = 1200 t

Make 't' the subject

t = 4000/ 1200

t = 3. 3

t = 3 years in the nearest tenth

Thus, the time it would take Joey is 3 years

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The answer is 91

Step-by-step explanation:

Average Marks = (Total Marks) ÷ Total Tests

83 = (71 + 70 + 87 + 97 + 82 + x) ÷ 6

83 × 6 = 407 + x

498 = 407 + x

x = 498 - 407

x = 91

Answer:

c) Both values are 5

Step-by-step explanation:

Value of x when it is 5,

→ |5| = 5

Value of x when it is -5,

→ |-5| = 5

Hence, both values are 5.

According to the given statement,

the perimeter is 10.99 units.

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. The measurement of the fence needed to completely enclose a yard or garden is called the perimeter. How far a wheel or circle will roll in one revolution is determined by its circumference, or perimeter. Similar to this, the circumference of a spool is related to the length of string looped around it; if the string's length were correct, it would match the circumference.

According to the given value ,

We have a triangle with points in:

  X    //   Y

N    2    //   0

P    -1    //  -2

M    4    //   0

We can solve for the side of the triangle by subtracting the points to calculate the distance between them, AKA the side of the triangle.

M - N = NM = 4 - 2 = 2 units of X

M - N = NM = 0 - 0 = 0 units of Y

This has a length of 2 units of X and 0 units of Y thus, we already have a line of size 2.

Next side:

N - P = 2 -(-1) = 3 units of x

N - P = 0 - (-2) = 2 units of Y

We have a length of 3 units of X and 2 of Y we use Pythagoras to get the length of NP:

Now, we do the same with MP:

M - P = 4 - (-1) = 5 units of X

M - P = 0 - (-2) = 2 units of Y

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According to the given statement the mean would decrease.

All of the data values fall within the range [-2.3,8 .9]              

Methods for calculating the forces between objects are studied in statics. Body motion and shape changes are caused by forces, which are also responsible for keeping bodies in equilibrium.

A dataset's mean is calculated by dividing the sum of all values even by total number of values. The geometric mean is not the same as this one; it is called the arithmetic mean. The term "average" is frequently used to describe it because it is the most widely used central tendency metric.

We have, the given data set

2.4, 2.7, 1.6 , 1.3 , 6.2, 1.3, 5.6, 1.1, 2.2, 1.9, 2.1, 4.4, 4.7, 3.0, 1.9, 2.5, 7.5, 5.0

Arrange the data in ascending order.

1.1, 1.3, 1.3, 1.6, 1.9, 1.9, 2.1, 2.2, 2.4, 2.5, 2.7, 3.0, 4.4, 4.7, 5.0, 5.6, 6.2, 7.5,

Divide the data in 4 equal parts.

(1.1, 1.3, 1.3, 1.6), 1.9, (1.9, 2.1, 2.2, 2.4),( 2.5, 2.7, 3.0, 4.4), 4.7, (5.0,5.6, 6.2, 7.5)

Q1  = 1.9

Q3 = 4.7

IQR = Q3 - Q1

      = 4.7 - 1.9

      = 2.8

SO,

The interval [Q1 - 1.5IQR ,Q3 +  1.5IQR]

The interval [Q1 - 1.5(2.8) ,Q3 +  1.5(2.8)]  

The interval [-2.3 , 8.9]

All of the data values fall within the range [-2.3,8 .9]            

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I understand that the question you are looking for is:

How much storage space does your music use? Here is a dot plot of the file sizes (to the nearest tenth of a megabyte) for 18 randomly selected files on Nathaniel's mp3 player: The distribution of file size has a mean of

2.4 2.7 1.6

13

6.2

1.3

5.6

1.1 2.2

1.9

2.1

4.7

3.0

1.9

2.5

7.5

500

Based on the transitive property of equality, m<MLI = 201°

181° + m<HAV = 287°, based on the substitution property of equality.

The transitive property of equality states that,  if d = e and e = f, then d = f.

Given that a = 3, if a + 5 = 8, then, based on the substitution property of equality, we would replace a with 3 into the equation as shown below:

3 + 5 = 8.

Based on the transitive property of equality, we are given that:

m<MLI = m<YGF

m<YGF = 201°

Then, we would have:

m<MLI = 201°

Also, we are given that:

m<CJW + m<HAV = 287°; and m<CJW = 181°.

Then, 181° + m<HAV = 287°, based on the substitution property of equality.

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a) Reflection points Q'R'S'T' are as follows:

Q' ( -2, -1 )

R' ( -7, 1 )

F' ( -6, -2 )

G' ( -1, -4 )

b) Translation points Q''R''S''T'' as follows

Q'' ( -1, -8 )

R'' ( 4, -6 )

F'' ( 3, -9 )

G'' ( -2, -11 )

Given data

Q(2, -1),

R(7, 1),

S(6, -2),

T(1, -4).

The reflection in y axis is gotten by changing the signs of the x instance:

Reflecting across y axis is done for example A ( x, y ) to AA

AA will be ( -x, y ).

a) Using this procedure we get reflection points Q'R'S'T' as follows

Q ( 2, -1 ) ⇒ Q' ( -2, -1 )

R ( 7, 1 ) ⇒ R' ( -7, 1 )

S ( 6, -2 )  ⇒ F'' ( -6, -2 )

T ( 1, -4 ) ⇒ G'' ( -1, -4 )

Translation about a given value is done as follows say point B ( 5, 10 ) and the translation of ( x - 2, y - 3 ) the new points will be

BB ( 5 - 2, 10 - 3 ) = BB ( 3, 7)

b) Using this procedure we get  translation points Q''R''S''T'' as follows

Q ( 2, -1 ) ⇒ Q'' ( -1, -8 )

R ( 7, 1 ) ⇒ R'' ( 4, -6 )

S ( 6, -2 )  ⇒ F' ( 3, -9 )

T ( 1, -4 ) ⇒ G' ( -2, -11 )

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The present ages of Ann and Julie are 12 years and 8 years, respectively.

Let x, y are the current ages of Ann and Julie, whose features are synthetized in the following linear equations:

Ann is 4 years older than Julie;

x = y + 4

x - y = 4                                (1)

4 years ago, Ann was twice as old as Julie;

x - 4 = 2 · (y - 4)

x - 4 = 2 · y - 8

x - 2 · y = - 4                         (2)

Now we proceed to determine the ages of Ann and Julie by solving the system of linear equations;

(x, y) = (12, 8)

Hence, The present ages of Ann and Julie are 12 years and 8 years.

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Answer:12

Step-by-step explanation:

A ratio indicates how many times one number contains another.

2/3 is the ratio of sports games to video games.

A ratio indicates how many times one number contains another.

A video game store has 60 games to choose from, including 40 sports games. We need to find the  ratio of sports games to video games.

To find the  ratio of sports games to video games. We need to divide Number of sports games by number of video games.

Ratio=Number of sports games/number of video games.

=40/60

Divide numerator and denominator by 20.

=2/3

Therefore the required ratio is 2/3 for sports games to video games.

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The statement "An increase in sales represents a positive integer" is; True

Positive integers are actually part of a larger group of numbers called integers. Integers are all the whole numbers, both positive and negative

Now, when there is an increase in sales, we can term this as a positive sign. However, it should be noted that increase in sales cannot be fraction or decimal and as such must be a whole number. Thus, an increase in sales is termed as a Positive Integer.

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The measure of angle 1 from the given figure is an obtuse angle.

Given that, when you look at a pencil in water, it looks bent. This illusion is due to refraction, or the bending of light when it moves from one substance to the next.

Refraction is the "bending" of light (or any electromagnetic wave) when entering a different medium.

In the given figure, the three angles, are angle 1, angle 2 and angle 3.

Angle 1 and 2 are formed with the surface of the water. Angle 1 in the medium air and angle 2 is in the medium water.

From the figure, given below we can see that angle 1 is greater than 90° and less than 180°.

Therefore, the measure of angle 1 from the given figure is an obtuse angle.

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