The diagram shows a triangle
What is the value of b

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

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 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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The measures of all unknown angles and side lengths of δpqr of m∠R = 50 degrees, PR ≈ 5.74 cm, after solving the Pythagorean theorem equation, and PQ ≈ 8.53 cm, after solving the Law of Cosines equation.

In order to determine the measures of all unknown angles and side lengths of ΔPQR, we can use the properties of a triangle. In particular, we can use the fact that the sum of the angles in a triangle is 180 degrees and the Pythagorean theorem.

You can use the above information to find the value of PR and PQ using trigonometric functions and/or squares.

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The question is -

Determine the measures of all unknown angles and side lengths of ΔPQR. Round side lengths to the nearest hundredth.

m∠R =

PR ≈

PQ ≈

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. 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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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:

w(n)= -20

Step-by-step explanation:

w(9)=-2(9)-2

= -18-2

=-20

Answer:

w(9) = -20

Step-by-step explanation:

w(n) = −2n – 2

w(9) = −2(9) – 2

w(9) = -18 - 2

w(9) = -20

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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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:  

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.

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:

D

Step-by-step explanation:

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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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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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.

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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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​

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.

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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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?

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

The number of possible outcomes for each case is given as follows:

i) 64 outcomes.

ii) 6 outcomes.

The combination is composed by four digits, and each digit is independent of other digits, meaning that the Fundamental Counting Theorem is used to obtain the possible number of combinations.

The Theorem states that the total number of combinations is given by the multiplication of the number of outcomes for each digit.

For item i, as repetition is allowed, the first digit assumes a value of 1, hence there is only one possible outcome, while each of the remaining three digits can assume three values, hence the number of combinations is given as follows:

N = 4 x 4 x 4 = 4³ = 64 combinations.

When repetition is not allowed, and the number starts with the number one, we have that:

Hence the number of combinations is obtained as follows:

N = 1 x 3 x 2 x 1 = 6 combinations.

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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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The solution is Option B.

The area of the triangle is A = 10 units which is one-half the area of a rectangle of length 4 units and width 5 units

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Let the coordinates of the triangle ABC be

The coordinate of A = A ( 4 , 6 )

The coordinate of B = B ( 6 , 1 )

The coordinate of C = C ( 2 , 1 )

Now , the base of the triangle B = 4 units

The height of the triangle H = 5 units

And , The area of the triangle = ( 1/2 ) x Length x Base

Substituting the values in the equation , we get

The area of the triangle = ( 1/2 ) x 4 x 5

The area of the triangle = 10 units

Now , one-half the area of a rectangle of length 4 units and width 5 units

Substituting the values in the equation , we get

Area of rectangle = ( 1/2 ) Length x Width

Area of rectangle = ( 1/2 ) 4 x 5

Area of rectangle = 10 units

Hence , the area of triangle is 10 units

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Answer:

31,360

Step-by-step explanation:

896 x 35 = 31360

Brenna would take 20 min to cut the same wood into sixths.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let x be the rate at which Brenna cuts the wood in a single piece,
So, She can cut a log into thirds in 10 min.
x = 3/10

x = 0.3 cuts per minute for single wood,

Now,
time took to cut the same wood into 6 pieces
= 6 / x
= 6 / 0.3
= 20 min

Thus, Brenna would take 20 min to cut the same wood into sixths.

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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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