12. Which is the simplified expression of -8(2m + 9k-13)?
-16m+9k-13
A.-16m +9k - 13
B. -16m - 72k + 104
C. -16m-72k - 104
D. 16m - 72k - 104

The domain of the function:{x|x<-1 and x>1} or (-∞,-1] ∪[1,∞) and the range of the function {y|y∈R} or (-∞,∞) .

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation.

In the given graph we can see that the values of x are all real values greater than 1 and all real values less than 1

Therefore the domain of the function is set-builder notation is given by:

{x|x<-1 and x>1}

The domain of the function in interval notation is given by:

(-∞,-1] ∪[1,∞)

Therefore the range of the function is set-builder notation is given by:

{y|y∈R}

The range of the function in interval notation is given by:

(-∞,∞)

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The integer solutions of each of the system of inequalities are 0, 1, 2, 3, .....65, 66, 67, 68. There are total 69 integer values that y can take.

In the question, we are given the inequalities:-

y ≥ 0 and 72 - y  ≥ 4

We have to find the integer solutions of each of the system of inequalities.

From 72 - y  ≥ 4, we can write,

72-4 ≥ y

68 ≥ y

Hence, from 68 ≥ y and y ≥ 0, we can write,

68 ≥ y ≥ 0

Hence, y can take 69 integer values from 0 to 68, both included.

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Answer:

Answer: 11x10^4 is greater. Step-by-step explanation: 23x10^3 = 23x10x10x10 = 23000. 11x10^4 = 11x10x10x10x10 = 110000. 110000 is greater than 23000.

Step-by-step explanation:

cos

The formula for the general term and of the sequence is ±8.

To find the formula for the given sequence:

Therefore, the formula for the general term and of the sequence is ±8.

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Answer:

(i)  2² · 3 · 7

(ii)  3024

(iii) k = 16

(iv) 12 cm

Step-by-step explanation:

The first few prime numbers are:  2, 3, 5, 7, 11, 13, 17, ...

To find which prime numbers multiply together to make 84, start by dividing 84 by the first prime number, 2:

⇒ 84 ÷ 2 = 42

As 42 is not a prime number, we need to divide again:

⇒ 42 ÷ 2 = 21

As 21 is not a prime number, we need to divide again.  

21 is not divisible by 2, so let's try dividing by the next prime number, 3:

⇒ 21 ÷ 3 = 7

As 7 is a prime number, we can stop.

Therefore, 84 is the product of:

⇒ 84 = 2 · 2 · 3 · 7

As 2 appears two times, we can write this using exponents:

⇒ 84 = 2² · 3 · 7

Lowest Common Multiple (LCM):  The lowest multiple shared by two or more numbers.

Prime Factors Method of finding LCM

Step 1

Find the prime factorization of each number.

From part (i):            84 = 2² · 3 · 7

Given in part (ii):    432 = 2⁴ · 3³

Step 2

Write each number as a product of primes, matching primes vertically where possible:

[tex]\begin{array}{ r c c c c c c c ccccccccc}84&=& 2 & \cdot & 2 & \cdot & & & & & 3& \cdot & & & && 7\\\\432 &=& 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3\\\\\cline{1-17} \\\sf LCM & = & 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3 &\cdot & 7\end{array}[/tex]

Step 3

Bring down the primes in each column then multiply the factors to get the LCM:

⇒ LCM = 2 · 2 · 2 · 2 · 3 · 3 · 3 · 7

⇒ LCM = 2⁴ · 3³ · 7

⇒ LCM = 3024

From part (ii) we know that the prime factorization of 432 is:

432 = 2⁴ · 3³

A perfect cube is a number multiplied by itself three times.

One of the factors of 432 is a perfect cube → 3³.

Therefore,

[tex]\begin{aligned}432 & = 2^4 \cdot 3^3\\\\\implies \dfrac{432}{2^4} & = 3^3\\\\\dfrac{432}{16} & = 3^3\end{aligned}[/tex]

So we need to divide 432 by 2⁴ to get the perfect cube 3³.

Therefore,

⇒ k = 2⁴

⇒ k = 2 · 2 · 2 · 2

⇒ k = 16

To find the largest possible length of the side of the square, we need to find the greatest common factor of 432 and 84.

Prime Factors Method of finding GCF

Step 1

Find the prime factorization of each number.

From part (i):            84 = 2² · 3 · 7

Given in part (ii):    432 = 2⁴ · 3³

Step 2

Write each number as a product of primes, matching primes vertically where possible:

[tex]\begin{array}{ r c c c c c c c ccccccccc}84&=& 2 & \cdot & 2 & \cdot & & & & & 3& \cdot & & & && 7\\\\432 &=& 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3\\\\\cline{1-17} \\\sf GCF & = & 2 & \cdot & 2 & \cdot & & & & & 3& & & & && \end{array}[/tex]

Step 3

Bring down the primes in the columns where both numbers have the factor, then multiply the factors to get the GCF:

⇒ GCF = 2 · 2 · 3

⇒ GCF = 12

Therefore, the largest possible length of the side of the square is 12 cm.

The value of the functions are:

a. g(-4) + f(-2) = 24

b..  f(1) - g(0) = 1

A function can be defined as an expression showing the relationship between two variables.

Given the functions;

g(-4); substitute the value of x as - 4 in g(x)

g(-4) = (-4)² + 1

g(-4) = 16 + 1

g(-4)  = 17

f(-2); substitute the value of x as - 2 in f(x)

f(-2) = 3(-2) - 1

f(-2 = -7

a.  g(-4) + f(-2) = 17 -(-7)

g(-4) + f(-2) = = 24

f(1) = 3(1) - 1

f(1)  = 2

g(0) = (0)² + 1

g(0) = 1

b. f(1) - g(0) = 2 - 1

f(1) - g(0) = 1

Thus, the value of g(-4) + f(-2) and f(1) - g(0)  are 24 and 1 respectively.

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Answer:

24:40

Step-by-step explanation:

3:5

This means there are 8 divisions altogether - 8 parts to be split (3+5=8)

64 / 8 = 8

8x3 = 24

8x5 = 40

£24:£40

Hope this makes sense!

Answer:

x = - 4 , x = 0

Step-by-step explanation:

7x³ + 28x² = 0 ← factor out 7x² from each term on the left side

7x²(x + 4) = 0

equate each factor to zero and solve for x

7x² = 0 ⇒ x² = 0 ⇒ x = 0

x + 4 = 0 ⇒ x = - 4

Answer:

Step-by-step explanation:

the answer is 30

Answer:

Option 3

Step-by-step explanation:

First tke lcm i.e. 6 then multiply the dinominator to make six.

Multiply tje above no. With the same digit the sub. The numerators

Answer:

c) 7/6

Step-by-step explanation:

The difference will be,

→ (5/3) - (1/2)

→ (10/6) - (3/6)

→ (10 - 3)/6

→ 7/6

So, the answer is 7/6.

Answer:

8.97 x [tex]10^{6}[/tex]

Step-by-step explanation:

To add in scientific notation, the exponents need to be the same for the bases of 10.  You can either make them both to the exponent of 6 or 5.  It does not matter.  I made them both to the power of 5

(8.6 x [tex]10^{6}[/tex]) + (3.7 x [tex]10^{5}[/tex])

(86 x [tex]10^{5}[/tex]) + (3.7x[tex]10^{5}[/tex])  

(86 x 3.7) x [tex]10^{5}[/tex]

89.7 x[tex]10^{5}[/tex]  Rewrite in scientific notation

8.97 x [tex]10^{6}[/tex]

Based on the context, the range of this function is given by: C. [−7, 7]

A range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values, which are shown on the y-axis of a graph.

The vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of function f(x) shown, we can infer and logically deduce the following:

Range = [−7, 7]

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Answer:

is that the equation ? is that all they gave you

im going to answer but do you mean

(x +2y+3)

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

[tex]3 \times 4\\= 12\\= 12 + 52\\= 64[/tex]

Answer:

64

Step-by-step explanation:

first 3 x 4 = 12

12+52=64

Answer:

Angle 1: 141 degrees

Angle 2: 39 degrees

Angle 3: 141 degrees

Step-by-step explanation:

Angle 2 and Angle 4 are equal since they are vertical angles. This means that Angle 2 is equal to 39 degrees.

Angle 1 and Angle 4 add up to 180 degrees. We call these supplementary angles. This means that Angle 1 is equal to 180-39=141 degrees.

Angle 1 and Angle 3 are vertical angles, so Angle 3 is also equal to 141 degrees.

Answer:

Find the rate of change for each set of ordered pairs. What is

the average rate of change of all three sets?

(1, 15), (2, 12)

(-1,14), (3, 10)

(3,11), (5, 15)

Write your answer to the average rate of change as a fraction,

a/b.

Step-by-step explanation:

Answer:

If real GDP in a particular year is $80 billion and nominal GDP is $240 billion, the GDP price index for that year is: 300.

Step-by-step explanation:

Step-by-step explanation:

photo please ......................

Answer:

Step-by-step explanation:

need to see the graph

Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior: FALSE

As in the description, it is given that a sophomore in high school is equivalent to a tenth-grade or Class-10 student.

So, the above-given statement becomes false as it says that every student is a sophomore but the class has juniors and seniors.

Therefore, the statement "suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior" is FALSE.

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The complete question is given below:

Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior. Is the following statement true or false:

"The course must have at least five sophomores, or at least 20 juniors, or at least 10 seniors."

Answer:

17 because you have to sutract them

Step-by-step explanation:

The weights that are significantly low z₁ = 5.361308 grams and significantly high z₂ = 5.48057 grams  

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

z -score = (z₁ - μ₀) / σ

where μ₀  is the mean and σ the standard deviation.

Consider a value to be significantly low if its z score is less than or equal to -2 or consider a value to be significantly high if its z score is greater than or equal to 2.

Here μ₀ = 5,37215 and σ = 0.05421

Substitute z -score = -2

⇒ -2  = (z₁ - 5,37215)/0.05421

⇒ (-2)(0.05421) = z₁ - 5.37215

⇒ -0.10842 = z₁ - 5.37215

⇒ z₁ = 5.37215 - 0.010842

⇒ z₁ = 5.361308

And if z = 2

Here μ₀ = 5,37215 and σ = 0.05421

Substitute z -score = 2

⇒ 2(0.05421) = z₂ -  5.37215

⇒ 0.10842 = z₂ - 5.37215

⇒z₂ = 5.37215 + 0.10842

⇒ z₂ = 5.48057  

Therefore, the weights that are significantly low z₁ = 5.361308 grams and significantly high z₂ = 5.48057 grams

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Your question is incomplete, probably the complete question is:

A data set lists the weights​ (grams) of a type of coin. Those weights have a mean of 5.37215 g and a standard deviation of .05421 g. Identify the weights that are significantly low or significantly high.

Consider a value to be significantly low if its z score is less than or equal to -2 or consider a value to be significantly high if its z score is greater than or equal to 2.

Answer:

3 3/5

Step-by-step explanation: