Write the equation the line through the point b) (1,3) with slope = -4

Answer:

The answer for the first question is 24 medium pizzas, because:

5 times 15 = 75

291 - 75 = 216

216/9 = 24

The answer to the second question is 364.

39 + 52 = 91

91 times 4 = 364

Step-by-step explanation:

Hope it helps!

All the possible values of each expression is given as an inequality as;

3 < y - x < 6

We are given the inequalities of the domain and range as;

6 < x < 7

10 < y < 12

Thus, we can say that the maximum value of y-x will be the difference between the maximum value of y and the minimum value of x to give;

(y - x)max = 12 - 6

(y - x)max = 6

Similarly, minimum value of y - x will be the difference between the maximum value of x and the minimum value of y to give;

(y - x)min = 10 - 7

(y - x)min = 3

Thus, all possible values would be expressed as;

3 < y - x < 6

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A recursive algorithm to find a^2n, where a is a real number and n is a positive integer, is as follows:

This algorithm uses the property of exponentiation that a^(2n) = (a^n)^2, and divides the problem of finding a^2n into a smaller subproblem of finding a^n. It takes advantage of the recursive nature of the problem by calling the same algorithm with a smaller value of n.

The time complexity of this algorithm is O(log n) as it divides the problem into half at each recursive step.

It should be noticed that this algorithm assumes that the input value of n is positive, otherwise it would be necessary to add a check for a negative value or zero.

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The number of miles each car travels in 1 hour is 16 1/4 miles

From the question, we have the following parameters that can be used in our computation:

Given rate. 97 1/2 miles in 3/2 hours

The number of miles each car travels in 1 hour can be calculated as

Number of miles = 97 1/2 miles/3/2 hours * 1 hour

This gives

Number of miles = 97 1/2 miles/3/2

Evaluate the quotient

So, we have the following representation

Number of miles = 16 1/4 miles

Hence, the number of miles is 16 1/4 miles

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Answer: True

Step-by-step explanation:

Answer: £18704.32.

Step-by-step explanation:

To increase a value by a certain percentage, you can use the formula:

New value = Original value + (Original value x (Percentage increase/100))

In this case, to increase £16470.45 by 13.5%:

New value = 16470.45 + (16470.45 x (13.5/100))

New value = 16470.45 + 2233.8675

New value = 18704.3175

Rounded to 2 decimal places, the new value would be £18704.32.

Answer:

18704.32

Step-by-step explanation:

The given lines are intersecting but not perpendicular.

What is intersecting lines?

In Euclidean geometry, the empty set, a point, or another line can intersect another line. For instance, computer graphics, motion planning, and collision detection can all benefit from differentiating these cases and locating the intersection.

Given:

          y = 6x - 2

2x - 12y = 24

⇒  6x - y = 2         ..(1)

2x - 12y = 24       ..(2)

Multiply second equation by 3,

6x - 36y = 72           ..(3)

Subtract equation (1) from equation (3).

     6x - 12y = 24

-    6x -    y  = 2

_______________

          -11y = 22

    y = -2

Plug y = -2 in equation (1)

6x - (-2) = 2

 6x + 2 = 2

       6x = 2 - 2

       6x = 0

         x = 0

The solution of the given system is (0, -2).

Hence, the given lines are intersecting but not perpendicular.

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The volume of image of triangular pyramid A which is triangular pyramid B would be = 28km³

A triangular pyramid is the type of pyramid that is made up of edges which are triangular in shape.

The image of the triangular pyramid A = Triangular pyramid B.

The volume of triangular pyramid A = 56 km³

The dilation factor = 1/2

The volume of the image of triangular pyramid A which is triangular pyramid B;

= volume of triangular pyramid A × scale factor

= 56 × 1/2

= 28km³

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Answer: hi :)

Step-by-step explanation: <3

The formula for for Rn is given as Rn = Σ 18/n (1 - 12i/n + 36i²/n²).

We are given the function f(x) = 3x² on the interval [-1, 5] . This gives

Δx =6/n and xi= -1 + 6i/n.

Therefore,

Rn =  Σ f(xi) Δx

     = Σ 3 (-1 + 6i/n)² 6/n

     = Σ 18/n (1 - 12i/n + 36i²/n²)

The limit of a function in mathematics is a key idea in calculus and analysis regarding the behavior of that function close to a specific input.

Informally, a function f gives each input x an output f(x). If f(x) approaches L as x approaches input p, we say that the function has a limit L at that location. More specifically, any input that is sufficiently close to p when f is applied forces the output value arbitrarily close to L.

The concept of limit is specifically used in the various definitions of continuity. Roughly speaking, a function is continuous if all of its limits agree with the values of the function. The term "limit" is also used in the definition of the mathematical term "derivative," which in one-variable calculus refers to the maximum value of the slope of secant lines on a function's graph.

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[tex]\underset{same~base \qquad }{e^{4x}=e^{x^2+3}}\implies 4x=x^2+3\implies 0=x^2-4x+3 \\\\\\ 0=(x -3)(x - 1)\implies x= \begin{cases} 3\\ 1 \end{cases}[/tex]

The measure of the smallest angle in the diagram is given as follows:

29º.

The angle addition postulate states that if two angles share a common vertex and a common angle, forming a combination, the larger angle will be given by the sum of the smaller angles.

From the diagram presented at the end of the answer, we have that angle FLI is formed by a combination of angles FLG, GLH and HLI.

Then the value of x can be obtained as follows:

m < FLI = m < FLG + m < GLH + m < HLI

2x - 1 + x + 17 + 4x - 15 = 106

7x + 1 = 106

7x = 105

x = 105/7

x = 15.

Then the angle measures are given as follows:

Meaning that the measure of the smallest angle is of 29º.

The diagram is presented at the end of the answer.

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The polynomial function:

f(x) = x³ - 125

Can be factorized into

f(x) = (x - 5)*(x² + 1*x + 5)

We want to factorize the polynomial expression:

f(x) = x³ - 125

And we want to factorize this in the following way:

f(x) = (x + a)*(x² + bx + c)

Trivially, 5 is a root of the function:

f(5) = 5³ - 125 = 0

Then we can write the function as:

f(x) = (x - 5)*(x² + bx + c)

And that must be equal to the original function:

(x - 5)*(x² + bx + c) = x³ - 125

Expanding the left side we will get:

x³ - 5x² + bx² + cx - 5bx - 5c = x³ - 125

x³ + (b - 5)x² + (c - 5b)x - 5c = x³ - 125

Then we can write the equations:

b - 5 = 0

c - 5b = 0

-c*5 = 125

Then we have:

c = 5

And with this equation:

c - 5b = 0

5 - 5b = 0

5 = 5b

5/5 = b

1  = b

Then the function can be written as:

f(x) = (x - 5)*(x² + 1*x + 5)

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Answer:

2

2Step-by-step explanation:

2

Answer:

y = 7x

Step-by-step explanation:

I answered a similar question posted by you. The logic is the same so you should be able to figure it out

To graph y = 7x, use a graphing calculator.

If you wish to plot manually, take 2 values of x, find the y value using the equation and draw a straight line through those points

Point 1: When x = 0, y = 7 · 0 = 0. So (0,0) is one point

Point 2: When x = 1, y = 7; y = 7 · 1 = 7 So (7, 1) is the second point.

Draw a straight line through these points and you get your graph

The graph will be as shown.

The rate of change of the given function is -1/2.

       [tex]$r(a) = {\frac {f(x+h)-f(x)}{h}}\\\\[/tex]

       [tex]$r(i) =\lim _{h\to 0}{\frac {f(x+h)-f(x)}{h}}\end{aligned}}}[/tex]

Given is the function as follows -

y = - 12 - (1/2)x

We have the function f(x) as -

y = - 12 - (1/2)x

dy/dx = d/dx(12 - x/2)

dy/dx = 0 - 1/2

dy/dx = -1/2

Therefore, the rate of change of the given function is -1/2.

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Step-by-step explanation:

Hello!

Point-slope form is this: y - y_{1} = m(x - x_{1})y−y

1

=m(x−x

1

) . In this form, m is the slope, x_{1}x

1

and y_{1}y

1

is an ordered pair, or point.

To find the slope, we need to use the slope formula. The slope formula is: \frac{y_{2}-y_{1} }{x_{2}-x_{1} }

x

2

−x

1

y

2

−y

1

. We can assign the point (-9, 6) to x_{1}x

1

and y_{1}y

1

and (-7, -8) to x_{2}x

2

and y_{2}y

2

.

Now, we can substitute the ordered pairs into the formula and solve.

m = \frac{-8 - 6}{-7 - (-9)} = \frac{-14}{2} = -7m=

−7−(−9)

−8−6

=

2

−14

=−7

Since the slope is equal to -7, we can substitute the slope and a point into the point-slope form.

Therefore, your point-slope formula is y - 6 + -7(x + 9) or y + 8 = -7(x + 7).

Answer:

B

Step-by-step explanation:

The probability that the sum is a multiple of three is 0.2778

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event will definitely occur.

If a pair of six-sided dice is rolled, and the sum is recorded, then the possible sum is the numbers from (1 + 1) = 2 to (6 + 6) = 12.

From 1 to 12, the multiples of 3 are 3, 6, 9, and 12. These can be resulted from having the following dice rolled.

3 : 1 & 2, 2 & 1

6 : 1 & 5, 2 & 4, 3 & 3, 4 & 2, 5 & 1

9 : 3 & 6, 6 & 3

12 : 6 & 6

Since there are 10 possible outcomes wherein the sum is a multiple of 3, and there are (6 x 6) total outcomes, then the probability is

p = 10 / 36 = 0.2778

Hence, the probability that this sum is a multiple of three is 0.2778.

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Answer:

Step-by-step explanation:

1 times 28

2 times 14

4 times 7

7 times 4

14 times 2

28 times 1

The amount of spacing needed to allow for expansion is 0.09 m

Length is the distance between two point.

To calculate the amount of spacing needed to allow for expansion, we use the formula below.

Formula:

Where:

From the question,

Substitute these values into equation 1

Hence, the amount of spacing is 0.09 m.

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Answer:

Step-by-step explanation:

The wrong with following piece of mRNA, TACCAGGATCACTTTGCCA is that it contains T and not U. So, option(D) is right choice here.

Messenger RNA (mRNA) is present in DNA. DNA uses four bases in its code, adenine (A), guanine (G), cytosine (C) and thymine (T). RNA also uses four bases. However, instead of using "T" as DNA, it uses uracil (U). So, if your DNA sequence is 3' T C G T T C A G T 5', the mRNA sequence would be 5' A G C A A G U C A 3'. A strand of DNA is a template strand that has a nucleotide sequence on it that is read by RNA polymerases. Rna polymerase reads the template strand and encodes the m-RNA using the base-pairing rule. According to the rule, adenine pairs with thymine and guanosine with cytosine. So if the template DNA reads TAC GTT ACG, RNA polymerase will read it as AUG CAA UGC. Since no thymine is present in RNA, it will code for U instead of T.

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On solving the provided question we can say that 1/4 means , 1 divides 4, so it its a division not expression.

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

here,

darius says that 1/4 is a division expression

Badru says that 1/4 is a division

1/4 means , 1 divides 4, so it its a division not expression

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A scatter plot is a data visualization technique in data analysis that uses a graph to show the relationship between two variables. It is used to display the relationship between two variables in a two-dimensional graph, with one variable on the x-axis and the other variable on the y-axis.

Scatter plots are used to explore the relationship between two variables, identify any patterns, and detect outliers. Scatter plots can also be used to compare the trends between groups of data, such as the relationship between different age groups and salary, or the relationship between different countries and GDP.

Scatter plots can provide insights into which variables are most important when predicting a response variable. Scatter plots are a powerful tool for understanding relationships between variables and can be used in a wide variety of data analysis tasks.

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Answer: 5,850

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf Mean = \$ \ 5850}[/tex]

Step-by-step explanation:

[tex]\displaystyle Mean = \frac{Sum \ of \ data}{No. \ of \ data}[/tex]

Here,

Data: $7500, $6500, $5750, $4900, $6250, $4200

So,

[tex]\displaystyle Mean =\frac{Sum \ of \ all \ prices }{No. \ of \ prices} \\\\Mean =\frac{7500+6500+5750+4900+6250+4200}{6} \\\\Mean = \frac{35100}{6} \\\\Mean = \$ \ 5850\\\\\rule[225]{225}{2}[/tex]

Based on the use of substitution, The answer will be: (x, y) = (1, -2)

3x - 4y = 11

y + 3x = 1

Step 1: Solve one of the equations for one of the variables.

Let's solve the second equation for y:

y = -3x + 1

Step 2: Substitute this expression for y into the first equation:

3x - 4(-3x + 1) = 11

3x - (-12x + 4) = 11

3x + 12x = 15

15x = 15

x = 1

Step 3: Substitute this value of x back into one of the original equations to find the value of y:

y = -3(1) + 1 = -2

The solution is (x, y) = (1, -2)

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See transcribed text below

Solve the system using substitution.

3x-4y = 11 y + 3x = 1

([?], [_])

Enter

Answer:quantitative

Step-by-step explanation:

To find the domain of a function f, you need to identify the set of all possible input values for which the function produces a meaningful output. To find the range of a function f, you need to identify the set of all possible output values that the function produces when given a valid input.

The domain of a function f is the set of all possible input values for which the function produces a meaningful output, while the range is the set of all possible output values that the function produces when given a valid input.

To find the domain of a function f, you need to identify the set of all possible input values for which the function produces a meaningful output. To find the range of a function f, you need to identify the set of all possible output values that the function produces when given a valid input.

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Answer:

Step-by-step explanation:

the 3rd option is the correct answer.