Here is a linear equation: y = 1/4x +5/4
Are (1, 1.5) and (12, 4) solutions to the equation?
Yes or No?
PLEASE NEED HELP

The Special Product Formula for the "square of a sum" is [tex](A+B)^{2}[/tex]= [tex]A^{2}[/tex] + 2AB + [tex]B^{2}[/tex] .

So

[tex](2x + 3)^{2}[/tex]  = [tex](2x)^{2}[/tex]   +2⋅(2x)⋅3+[tex]3^{2}[/tex]  =4[tex]x^{2}[/tex]  +12x+9.

​

The well-known for squaring the difference between two numbers or

[tex](a+b)^{2}[/tex]=[tex]a^{2}[/tex]+2ab+[tex]b^{2}[/tex]  (1)

It can be calculated by multiplying the binomial a + b by one.

The square can also be obtained for a total of three sums:

[tex](a+b+c)^{2}[/tex]=[tex]a^{2}[/tex] + [tex]b^{2}[/tex] + [tex]c^{2}[/tex] + 2bc+ 2ca+ 2ab (2)

The contents of it might be described as the

Rule : The square of a sum is equal to the product of all the double products of the summands in twos plus the sum of all the squares of all the summands:        

(∑i ai)2=∑i [tex]a^{2}[/tex]i+2∑i<j [tex]a_{i}[/tex][tex]a_{j}[/tex]

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Option C. p= 1/6; a= 8 values for p and a will cause the function [tex]f(x) = Pa^x[/tex]  to be exponential growth.

An exponential growth function is a function in which the variable x is the exponent of the base. In the function, [tex]f(x) = Pa^x,[/tex] the variable x is the exponent and the constant a is the base. For the function to be an exponential growth function, the base must be greater than 1.

In option A, P=6 and a=1/8. The base is less than 1 (1/8 < 1) so this function is not an exponential growth function.

In option B, P=6 and a=1. The base is equal to 1, which is not greater than 1, so this function is not an exponential growth function.

In option C, P=1/6 and a=8. The base is greater than 1 (8 > 1) so this function is an exponential growth function.

In option D, P=1/6 and a=1/8. The base is less than 1 (1/8 < 1) so this function is not an exponential growth function.

Therefore, the only option that causes the function [tex]f(x) = Pa^x,[/tex] to be an exponential growth function is option C. P=1/6; a=8.

Complete Question:

Which of these values for P and a will cause the function  [tex]f(x) = Pa^x[/tex]  to be an exponential growth function?

A. P=6; a = 1/8

B. P = 6; a = 1

C. P= 1/6; a=8

D. p= 1/6; a= 1/8​

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P= 1/6; a=8

Is a exponential growth function, because a > 1 and P is not zero

Now, According to the question:

We know that

The equation of a exponential growth function is given by:

[tex]f(x)=pa^x[/tex]

where

P is the initial value or y-intercept (this vale cannot be equal to zero)

a is the base of the exponential function ( in a exponential growth function the value of a is greater than 1)

Verify each case

case A) P=6; a = 1/8

Is not a exponential growth function, because a < 1 (is a decay exponential function)

case B) P=6; a = 1

Is not a exponential function

case C) P= 1/6; a=8

Is a exponential growth function, because a > 1 and P is not zero

case D) P=1/6; a = 1/8

Is not a exponential growth function, because a < 1 (is a decay exponential function)

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The complete question is this:

Which of these values for P and a will cause the function f(x) = Pa^x to be an exponential growth function?

A. P=6; a = 1/8

B. P = 6; a = 1

C . P= 1/6; a=8

D. p= 1/6; a= 1/8​

The expression are given as;

x + y : positive.

y - x : negative.

x - y : positive.

y + (-x) :negative.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.

We are given that the x and y are two numbers on the number line

y = negative number.

x = positive number

Therefore, the expression are;

x + y

The expression is positive.

y - x

The expression is negative.

x - y

The expression is positive.

y + (-x)

The expression is negative.

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Answer:

Total Surface Area

= 24 in^2

Step-by-step explanation:

A cube has 6 sides (faces). Each side is a square. The square face (all of them) is a 2 by 2 square. The area of each square face is 2 × 2 = 4 square inches. There 6 faces that are 4 square inches each. The total surface area is all of the 6 sides added together.

TSA = 4+4+4+4+4+4

TSA = 24 square inches

The total surface area is 24 in^2.

The common ratio of 2 , 3 , 9/2 is 3/2

Solution:

Given, series of elementes are 2, 3, 9/2

We have to find the common ratio of the above given series .

We know that , common ratio of an G.P is division of any number in that series with the previous number of the series.

let, those numbers be a1 , a2 and a3

So now,

a1 = 2

a2 = 3

a3 = 9/2

Now,

[tex]\frac{a2}{a1}[/tex] =  [tex]\frac{3}{2}[/tex]

[tex]\frac{a3}{a2}[/tex] = [tex]\frac{9/2}{2}[/tex]

          = [tex]\frac{9}{2}[/tex] x [tex]\frac{3}{1}[/tex]

          = ([tex]\frac{27}{2}[/tex]) Which is the multiple of 3

Hence ,the common ratio of 2 , 3 , 9/2 is 3/2

A local area network (LAN) connects two or more devices in a limited geographical area.

A local area network (LAN) is a type of network that links computers and other devices within a certain geographic region, such as a house, a school computer lab, an office building, or a cluster of nearby structures.

The nodes, or individual computers or devices that make up a network, frequently share resources like printers, big hard drives, and software. Cables are frequently used to connect the nodes. A LAN without physical wires is known as a wireless LAN (WLAN). A cable LAN and a WLAN frequently communicate in order for a WLAN to access its resources.

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13+h is the expression which indicates the total hours of volunteer done by Veronica.

An expression is combination of variables, numbers and operators.

Given that Each week, Veronica volunteers 13 hours at the animal shelter.

If she volunteers for h hours, then we need to find the total number of hours she volunteered.

13+h because 13 hours Veronica volunteers at the animal shelter and total she volunteered h hours.

Hence, 13+h is the expression which indicates the total hours of volunteer done by Veronica.

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Answer:

31,360

Step-by-step explanation:

896 x 35 = 31360

A lifeline in a sequence diagram is a line that is used to represent an active object, such as a class, interface, or object, and is typically identified by a solid line.

A lifeline in a sequence diagram is a graphical element used to depict the active objects in an interaction or sequence diagram. The lifeline is typically represented as a solid line running from the top of the diagram to the bottom, which represents the object's lifetime. The lifeline is used to show the messages that are sent and received between objects, as well as the sequence in which they occur. Additionally, the lifeline is often used to represent any changes of state in the objects, such as method calls, data values, and more. By depicting the lifelines of the active objects in a sequence diagram, it is possible to gain a better understanding of the interactions between the objects, and how they are related.

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Answer:

First, distribute the 3 on the left side of the equation: 3 * 9 + 3 * 4a - 19 = 32

Next, combine like terms on the left side of the equation: 27 + 12a - 19 = 32

Add 19 to both sides of the equation to isolate the variable term: 27 + 12a = 51

Subtract 27 from both sides of the equation to isolate the variable term: 12a = 24

Divide both sides of the equation by 12 to solve for the value of "a": a = 2

So the solution to the equation is "a = 2".

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The system of inequalities representing the graph is option A.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

There are two lines drawn on the graph.

Dashed line passes through (0, 3) and (1, 1).

Slope = change in y coordinates / change in x coordinates

          = (1 - 3) / 1 - 0 = -2

Intercept along the y axis is 3.

Equation in slope intercept form is y = -2x + 3.

Solution region of the line does not pass through origin.

At origin 0 = 0 + 3, 0 < 3 is true, but since the solution region of the line does not pass through origin, we take the inequality results as 0 > 3.

So the inequality is y > -2x + 3.

Solid line passes through (0, -1) and (1, 1).

Slope = (1 - -1) / (1 - 0) = 2

Intercept along y axis is -1.

Equation in slope intercept form is y = 2x - 1.

Solution region of the line does not pass through origin.

At (0, 0), 0 = 0 - 1, 0 < -1 is the result of inequality.

Since it is a solid line, inequality will be ≤.

So inequality is y ≤ 2x - 1.

Hence the correct option is A.

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Calamitous Clod creates a geometric sequence with common ratio 2 by adding 2 to the second term and 11 to the third term. The first term is 7.

Let the numbers are: a₁, a₂, a₃.

These three numbers form an arithmetic sequence, which means the differences between 2 consecutive terms are the same.

Hence,

a₃ - a₂ = a₂ - a₁

a₃ = 2a₂ - a₁   ..... (equation 1)

Calamitous Clod creates a geometric sequence with common ratio 2 by adding 2 to the second term and 11 to the third term.

Hence, the geometric sequence is:

a₁, a₂ + 2, a₃ + 11.

with common ratio =  2

common ration = (a₃ + 11) / (a₂ + 2) = 2

a₃ + 11 = 2a₂ + 4

a₃ = 2a₂ - 7  ..... (equation 2)

Substitute equation 2 into equation 1

2a₂ - 7  = 2a₂ - a₁

a₁ = 7

Hence,

The first term =  a₁ = 7

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The cost of a slice of pizza is $2.5.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Let x be the price of 1 slice of pizza and y be the price of a drink.

Cost of a bag of chips = 50 cents = $0.5

A family buys 3 slices of pizza, 2 drinks, and one bag of chips for $10.

Another family bought 2 slices of pizza, 4 drinks, and a bag of chips for $9.50.

We have two linear equations,

3x + 2y + 0.5 = 10 or 3x + 2y = 9.5

2x + 4y + 0.5 = 9.5 or 2x + 4y = 9

So we have

3x + 2y = 9.5

2x + 4y = 9

Multiplying throughout the first equation with 2 and subtracting the second equation from the resultant equation, we get

[2(3x + 2y) - (2x + 4y) = (2 × 9.5) - 9

6x - 2x = 10

4x = 10

x = 2.5

Hence $2.5 is the cost of a slice of pizza.

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The ratio to represent the relationship between hallies donation of jeans and Mattie’s donations of jeans is C 1:2.

The ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this situation, Hallie donated 3 pairs of blue jeans. Mattie donated 6 pairs of blue jeans.

The ratio to represent the relationship between hallies donation of jeans and Mattie’s donations of jeans will be:

= 3/6

= 1/2

= 1:2

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Answer:

c

Step-by-step explanation:

I got right on the quiz

Angle a is 18 degrees.

The Mesure of ∠b ⇒∠B=180∘−120∘=60∘

Answer:

A = 72

B = 108

Step-by-step explanation:

5y - 3 = 3y + 27

5y - 3y = 27 + 3

2y = 30

y = 30/2 = 15

A = 5y - 3 = 5(15) - 3 = 72

B = 180 - 72 = 108

To draw a line perpendicular to AB through A and B, respectively, use the following steps of construction.

(i) Draw a line segment AB = 4cm.

(ii) Take A as the centre and radius more than [tex]\frac{1}{2}[/tex]AB(i.e., 2cm) and draw an arc which intersects AB at E.

(iii) Take E as the centre and with the same radius as above draw an arc which intersects the previous arc at F.

(iv) Again, taking F as the centre and with the same radius as above draw an arc which intersects the previous arc( obtained in step (ii)) at G.

v) Taking G and F are centres, draw arcs which intersect each other at H.

(vi) Join AH, thus AX is perpendicular to AB at A. similarly, draw BY perpendicular to AB at B.

Now, we know that if two lines are parallel, then the angle between them will be 0° or 180°.

∠XAB = 90°

And

∠YBA =90°

∠XAB + ∠YBA  = 90° + 90°

                         = 180°

So, lines XA and YB are parallel.

[ since, if the sum of interior angles on the same side of transversal is

180°, then the two lines are parallel.]

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The correct question is:

Draw a line segment AB of 4cm in length. Draw a line perpendicular to AB through A and B, respectively. Are these lines parallel?

Answer:

Parallel lines and their transversal all have equal slopes.

Step-by-step explanation:

I say this is wrong because the slope of parallel lines is equal but the transversal has a different slope.

One real-world application for adding and subtracting polynomials is in the field of electrical engineering, specifically in circuit analysis.

Problem: Design an electrical circuit that combines two input signals and produces an output signal that is the sum of the two input signals.

Solution: The input signals can be represented by two polynomials, say A(x) and B(x), where x represents time. To find the output signal, we need to add the two input polynomials, resulting in a new polynomial C(x) = A(x) + B(x). This polynomial C(x) represents the output signal of the circuit.

To solve the problem, the circuit designer would need to identify the specific forms of the input signals, A(x) and B(x), and then use polynomial addition to find the output signal C(x). Depending on the complexity of the input signals, this could be done by hand or with the help of a computer program.

Once the output signal C(x) has been found, the circuit designer can use this information to select the appropriate components and design the circuit layout to produce the desired output.

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Answer:  

18x=.75*24

18x=18

x=1 cup is needed for 2 doz. cookies.

Step-by-step explanation:

Therefore, the amount of sugar needed to make two dozen cookies is 1 cup. Explore all similar answers.

Answer:

ok

Step-by-step explanation:

The number of terms in the given expression "7x² +5x -5" is three terms .

An Algebraic Expression is defined as the expression that contains combination of constants and variables joined by mathematical operators .

For Example ; 2x + 3y .

The given Algebraic Expression is 7x² +5x -5 ;

we can see that the terms joined by the mathematical operators + and - ;

the given expression cannot be simplified further ,

So ,the first term is 7x² ;

the second term is 5x and the third term is 5 .

Therefore , the expression 7x² +5x -5 has three terms .

The given question is incomplete , the complete question is

How many terms are there in the expression 7x²+5x -5 ?

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There are three terms in the expression 7x² 5x 5.

The expression 7x² 5x 5 contains three terms. The first term is 7x² which is the product of 7 and x². The second term is 5x which is the product of 5 and x. The third term is 5 which is a constant term. All together, these three terms make up the expression 7x² 5x 5. The 7x² term is a quadratic term, since it contains a squared variable, while the 5x and 5 terms are linear terms, since they only contain a single variable. When these three terms are combined, the expression 7x² 5x 5 is formed.

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Answer:

2x + 1 = 79 (being alternate angel )

2x = 79-1

2x = 78

x = 78/2

x = 39

Answer:

5.86 lbs

Step-by-step explanation:

6.93 - 1.07 = 5.86

You subtract the weight of the basket from the weight of the basket full of apples to get the weight of just the apples

The option (A) (7,-7), (-7,-5), (-7,-3), (-7,-1) ordered pair is y a function of x.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

In a mathematical relation, for a given value of x, there can only be one unique value of y.

It is a requirement that a function must follow.

In option A, the x values are all different, so y is a function of x

In option B, there are two (0,0) and (0,9) which means for x=0 there are two possible values of y, thus y is not a function of x.

In option C, there is a repetition of the x-value, 15, so y is not a function of x

In option D, there is a repetition of the x-value, 13, so y is not a function of x.

So, the correct option is A (7,-7), (-7,-5), (-7,-3), (-7,-1)

Hence, the option (A) (7,-7), (-7,-5), (-7,-3), (-7,-1) ordered pair is y a function of x.

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a. If A says "The two of us are both knights" and B says "A is a knave," then we know that one of them must be lying, and thus that one of them is a knave. However, we cannot determine from this information alone which of them is the knave and which is the knight.

b. If A says "At least one of us is a knave" and B says nothing, then we know that one of them is a knave, but we cannot determine from this information alone which of them is the knave and which is the knight.

In the first scenario, person A claims that both he and person B are knights, which is a true statement if A is a knight. However, person B says that A is a knave, which means that A is a liar. These statements contradict each other, so we know that one of them is not telling the truth and is therefore a knave. But we cannot determine which one of them is the knave, because we don't have enough information.

In the second scenario, person A says that at least one of them is a knave, and person B remains silent. This means that A could be telling the truth, or could be lying. If A is a knight, then he is telling the truth and at least one of them, B, is a knave. But if A is a knave, then he could be lying and both of them could be knights. So we don't have enough information to know who is a knave and who is a knight.

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The correct answer is the Intermediate value theorem (Option B).

The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b], then for any value y between the minimum and maximum values of the function on that interval, there exists at least one x-value in the interval such that f(x) = y. In other words, if f(x) is a continuous function on a closed interval, then for any value y between the minimum and maximum values of the function on that interval, there exists at least one x-value in the interval such that f(x) = y, or in other words if a function is continuous in an interval [a,b], any zero of the function must be in that interval.

Therefore, The correct answer is the Intermediate value theorem (Option B)

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