Drag and drop the correct answer choice to each answer blank.

Answer:

[tex]x=2+2\sqrt{ 26}[/tex]

[tex]x=2-2\sqrt{ 26}[/tex]

Step-by-step explanation:

Given logarithmic equation:

[tex]\log_{10}(x^{2}-4x)=2[/tex]

[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies 10^2=x^2-4x[/tex]

[tex]\implies 100=x^2-4x[/tex]

[tex]\implies x^2-4x=100[/tex]

Add the square of half the coefficient of the term in x to both sides of the equation:

[tex]\implies x^2-4x+\left(\dfrac{-4}{2}\right)^2=100+\left(\dfrac{-4}{2}\right)^2[/tex]

[tex]\implies x^2-4x+\left(-2\right)^2=100+\left(-2}\right)^2[/tex]

[tex]\implies x^2-4x+4=100+4[/tex]

[tex]\implies x^2-4x+4=104[/tex]

Factor the perfect square trinomial on the left side of the equation:

[tex]\implies (x-2)^2=104[/tex]

Square root both sides:

[tex]\implies x-2=\pm \sqrt{104}[/tex]

[tex]\implies x-2=\pm \sqrt{4 \cdot 26}[/tex]

[tex]\implies x-2=\pm \sqrt{4} \sqrt{ 26}[/tex]

[tex]\implies x-2=\pm 2\sqrt{ 26}[/tex]

Add 2 to both sides:

[tex]\implies x=2\pm 2\sqrt{ 26}[/tex]

Therefore, the solutions are:

The answer choice which represents a combination of ticket and snacks Edward may purchase is; 7 tickets and 8 snacks.

The given word problem can be expressed as a system of equations as follows;

Let x = number of tickets and

Let y = number of snacks;

Therefore; the system of equations is;

x + y = 15.............(I)

7.50x + 3.75y = 85

The second equation can be expressed as follows;

2x + y = 68 / 3.........(II)

Therefore, by subtracting equation 1 from we have that;

x = 68/3 - 15

x = 7.667 tickets.

And y = 15 - 7.667

y = 7.333 snacks.

On this note, the best combination of tickets and snacks he can get is; 7 tickets and 8 snacks.

By checking; 7 tickets cost; $52.5 and 8 snacks cost; $30. Total = $52.5 + $30 = $82.5.

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Answer:

The answer for the problem on the left is 70

The answer to the problem on the right is 120

Step-by-step explanation:

Left Problem:

The sum of the interior angles is 360

(n -2)180 is one formula to find the sum of the interior angles of a polygon.  n stands for the number of sides

(4-2)180

2(180

360

We know three of the angles we subtract them from 360 to find the missing angle

360-60-110-120 = 70

Right Problem:

We can find the bottom left and the bottom right angles by subtracting the exterior angle from 180.  A straight line has an angle measurement of 180.

180-60 = 120

180 - 50 = 130

Now we just need to find x.  

The sum of the interior angles is

(n-2) 180

(5-2)180

3(180) = 540    Subtract what we know

540 -50 - 130 - 120 = 240

The x's have the same value so 2402 is 120 .

Each x is 120

The answer to the problem on the left is 70 and the answer to the problem on the right is 120.

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, angles and relative position.

Left Problem:

The sum of the interior angles is 360.

(n -2)180 is one formula to find the sum of the interior angles of a polygon.  n stands for the number of sides

(4-2)180

2(180

360

We know three of the angles we subtract them from 360 to find the missing angle

360-60-110-120 = 70

Right Problem:

We can find the bottom left and the bottom right angles by subtracting the exterior angle from 180.  A straight line has an angle measurement of 180.

180-60 = 120

180 - 50 = 130

The sum of the interior angles is

(n-2) 180

(5-2)180

3(180) = 540    Subtract what we know

2x =  540 -50 - 130 - 120 = 240

x = 240 / 2 = 120

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The factors are (x + 1)(x + 2)(x + 10)

The process of breaking down an entity—for instance, a number, a matrix, or a polynomial—into a product of another entity—or factors—that, when multiplied together, yield the original number, matrix, or other entity is referred to as factorization or factoring.

Given Equation x³ + 13x² + 32x + 20

so The value of x³ + 13x² + 32x + 20 is

x³ + x² + 12x² + 12x + 20x + 20

=x² (x+1) + 12x (x+1) + 20(x+1)

=(x + 1)(x² + 12x + 20)

=(x + 1)(x² + 10x + 2x + 20)

=(x + 1)[x(x + 10) + 2(x + 10)]

=(x + 1)(x + 2)(x + 10)

Hence the factors are (x + 1)(x + 2)(x + 10).

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The correct question is

Factorize x³ + 13x² + 32x + 20

The graph of a two-variable inequality is the set of points that describe all solutions to the inequality.

The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the symbol for inequality with that for equality.

Step 3: In the xy plane, graph the boundary line from step 2. You are creating the boundary line that would divide or cut the xy-plane into two sections in this stage.

Step 4: Shading one side or area of the boundary line is the final step.

Step 5: Use this optional step to check or confirm that you have shaded the boundary line's side appropriately.

Here show an example for better understanding:

Let us take a equation, 4x + 8y ≤ -24

Now, solve the above equation in the form of slope-intercept.

4x + 8y ≤ -24

or, 8y ≤ - 4x - 24

or, y ≤ -(1/2)x - 3

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Answer:

145

Step-by-step explanation:

y = 5(25) + 20

y = 125 + 20

y = 145

y = -(5/3)x + 4 is slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept

rewrite the equation of the given line in to slope-intercept form by solving for y

 3y + 5x = 6    

    3y = -5x + 6               (subtract 5x from both sides)

       y = -(5/3)x + 2           (divide both sides by 3)

Our line is parallel to this line, so it has the same slope, and a

y-intercept of 4, so we have...

 y = -(5/3)x + 4  

the equation ofa line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = 1 and c = 3, hence

y = x + 3 ← is the equation of the line  

*slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept

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One had all three,  had exactly two and 21 had life skill book according to given situation.

A mathematical problem is one that can be represented, examined, and potentially resolved using mathematical techniques.

Jack has two dogs and eight cats. Jill owns 4 dogs and 7 cats. In total, how many dogs are there? How many more cats does Jane have than I do if she has 23 and I have 2, and then Jane gives me 5 cats?

Let X people have all three books then

three books=X

Math and Eng=7-X

Math and Life= 6-X

Eng and Life= 9-X

Then:

X+(7-X)+(6-X)+(9-X)+[22-(7-X)-(6-X)]+[21-(7-X)-(9-X)]+[25-(16-X)-(9-X)]=50

After simplification

X=1

(i). One had all three books

(ii) 6 had two

(iii). 21 had life skill book.

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The distance between the points (3 ,7) and (15 ,16) on a coordinate plane is 15 units.

In coordinate geometry, every point is denoted by definite coordinates since every point is situated at a fixed distance from the origin point (0,0). Any two points on a coordinate space are situated at a constant distance since their coordinates are fixed with respect to the origin. A line segment has two endpoints, and the coordinates of the endpoints help to determine the length of the line segment. Let us suppose (x1,y1) and (x2,y2) are the two points on a coordinate space then the distance between these two points is given by the distance formula as per the below:

            [tex]d = \sqrt{(x1 - x2)^2 + (y1 -y2)^2}[/tex]

given points are (3 ,7) and (15 ,16).

(x1,y1) = (3,7) and (x2,y2) = (15,16)

We know that two points on a plane have a constant distance in between them, and the distance formula gives the distance between these two points.

                  d =[tex]\sqrt{(x1 - x2)^2 + (y1 - y2)^2}[/tex]

              ∴  d = √(3 - 15)^2 + (7 - 16)^2

              ∴  d = 15 unit.

The distance between the points (3 ,7) and (15 ,16) on a coordinate plane is 15 units.

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-6.48 > -6.5

5.983 < 5.99

3.09 > 3.01

Hope it helps

By using multiplication and subtraction, it can be calculated that-

Austin has to pay $9 for 3 pounds of chicken

Austin has to pay $(10.50 [tex]\times[/tex] p- 1.50)  for p pounds of chicken

What is subtraction and multiplication?
To find how big or small one number is from the other, then the operation used is called subtraction of numbers

Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers

Here, subtraction and multiplication is used

Cost of one pound of chicken = $3.50

Cost of three pounds of chicken = $3.50 [tex]\times[/tex] 3 = $10.50

He has a coupon for $1.50 off the final amount.

Amount of money Austin has to pay for 3 pounds of chicken =

$(10.50 - 1.50) = $9

Amount of money Austin has to pay for p pounds of chicken =

$(10.50 [tex]\times[/tex] p- 1.50)

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Copying of line segment involves 6 steps.

Steps to copy line segment are:

1) Draw a point that will serve as the new line segment's endpoint.

2) Open the compass width from the original line segment's beginning with the compass pin in that position.

3)Place the compass pin at the new line segment's plotted point using the above-mentioned step's adjusted compass width, and then draw an arc in the area where the new line segment is to be situated.

4) Decide where the other end of the new line will be on the arc.

5) Draw a line from the location chosen in the previous step to the point designated as the start of the new line segment.

6) The original line segment's length and the length of the line depicted above are equal.

Copying of line segment involves 6 steps.

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Q Which of the following is the first step when copying a line segment to construct a new line segment?

a. draw a line segment

b. use a straight edge to connect the point not on the line segment to a point in the arc

c. plot a point not on the original line segment

d. draw an arc​

The domain of a function as described by the question, can be found by solving a given function for x such that the values of  x satisfy the equation. And the vertical asymptotes  can be found by solving for x values which make the equation go towards positive or negative infinity.

A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. To put it another way, an asymptote is a line that a curve travels towards as it approaches infinity.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f(x) make up this set x.

As asked by the question, the domain of a function can be found by solving the equation f(x) = y for values of x such that the values of x give out a single value y. Similarly, the vertical asymptotes can be found from a rational function [tex]\frac{p(x)}{q(x)}[/tex] by equating the denominator q(x) to 0 and solving for x.  i.e q(x) = 0.

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Answer:

6. X, Y and Z are different numbers. X is a factor of Y. Z is a multiple of Y. Which of the following is DEFINITELY true?

7. The following graph shows Vinit's journey as he cycled from his home to a park, 4 kilometers away in 800 seconds. Which of these can be said based on this graph?

8. How many TENS must be added to 7 000 to make it 70 000.

Step-by-step explanation:

Yes, △ ABC appears to be the same size and shape as △ XYZ by SAS similarity, and △ ABC can be mapped by translation and rotation, so option A is correct

What is triangle?

Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.

Right triangles ABC and XYZ. ABC has a shorter leg equal to 5 and a hypotenuse equal to 13,

The triangles ABC and XYZ are similar by SAS similarity, as,

AC = XZ = 5,

AB = YZ = 13

∠ ACB = ∠ XZY

When you translate and then rotate triangle ABC, you will get triangle XYZ.

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The value of g(2) = -1/4 and the value of g(-2) = π/2 - 3/2

The graph of function g is having a point of inflection at x=-2 and  x=0 and x = 1 because g''(x) = f'(x) changes at each of these values.

A function is basically a relation between two sets having a domain , range and a co-domain.

We can represent functions graphically by plotting their equations and putting the value of co- ordinates.

A graph consists of four quadrants two positive and two negative. It helps to visualize data in a clear manner and helps to present data more efficiently.

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The ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent.

To use a congruence criterion in the given situation, you will need to determine which criterion is most appropriate based on the information provided. There are several congruence criteria that can be used to determine whether two triangles are congruent, including the Side-Side-Side (SSS) criterion, the Side-Angle-Side (SAS) criterion, the Angle-Side-Angle (ASA) criterion, and the Angle-Angle-Side (AAS) criterion.

In this case, the ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent. Given that ∠A=∠C=90∘ and AE=CB, you can use the ASA criterion to conclude that triangles AEB and CED are congruent.

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The question is -

Which congruence criterion do you use in the following? Given: EB = BD, AE = CB, ∠ A = ∠ C = 90°.

Having seven sides, a heptagon is a polygon.It is also occasionally referred to as a septagon.

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In the triangle LMN, the angle opposite side LM is indicated by the supplied figure as being ∠N.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint.

The Latin word "angulus," which means "corner," is the source of the English term "angle."

The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.

So, according to the given figure, the angle opposite to side LM in triangle LMN is ∠n.

Therefore, in the triangle LMN, the angle opposite side LM is indicated by the supplied figure as being ∠N.

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It was 5:50 p.m. when Camilla and Megan left the mall.

Add 1 hour and 25 minutes to 12:55 p.m. to determine the time when Camilla and Megan finished shopping for clothes:

12:55 p.m. + 1 hour and 25 minutes = 2:20 p.m.

Add 55 minutes to 2:20 p.m. to determine the time when Camilla and Megan finished eating at the food court:

2:20 p.m. + 55 minutes = 3:15 p.m.

Add 2 hours and 35 minutes to 3:15 p.m. to determine the time when Camilla and Megan left the mall:

3:15 p.m. + 2 hours and 35 minutes = 5:50 p.m.

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Types of expressions in math:

The types of expressions in math listed above are all valid and commonly used expressions in mathematics. Algebraic expressions are used to represent equations, while trigonometric, logarithmic, exponential, factorial, polynomial and rational expressions are used to represent different types of functions.

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333 integers,  there are 333 integers between 1 and 1,000 which are divisible by 3.

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

here

add all the numbers,

1 + 2+ 3 + 4+ 5 = 15

and 15/3 = 5

so it is divisible by 3

not by 9

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Answer:

k = -0.25

Step-by-step explanation:

If z varies jointly, that means z = k * x * y

putting in the numbers it gives us,

6 = k * (3) * (-8)

6 = k * (-24)

k = -(1/4) = -0.25

Discontinuity function is an explanation of development that emphasizes sudden changes or shifts, rather than gradual progressions, in development. Examples include Piaget’s stages of cognitive development and Erikson’s psychosocial stages.

Discontinuity function is an explanation of development that emphasizes sudden changes or shifts, rather than gradual progressions, in development. This theory suggests that development does not occur in an orderly, linear fashion, but instead involves abrupt changes in which an individual moves from one distinct stage to the next. Examples of discontinuity theory include Piaget’s stages of cognitive development and Erikson’s psychosocial stages, which are made up of distinct stages of development that an individual must progress through before reaching the next stage. According to discontinuity theory, development is not a gradual, continuous process, but rather is made up of distinct stages with abrupt changes in between. This theory has been useful in helping to explain the development of various aspects of an individual, such as cognitive, social, and emotional development.

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Answer: 8.9 units

Step-by-step explanation:

We can use the distance formula for a 2d plane:

distance = √[tex](x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]

Plugging in our values for x1, y1, x2, and y2:

x1 = -7

y1 = 0

x2 = -3

y2 = 8

√[tex](-3 - -7)^2 + (8 - 0)^2[/tex]

= √[tex](4)^2 + (8)^2[/tex]

= √[tex]16 + 64[/tex]

= √[tex]80[/tex]

= [tex]8.944271921[/tex]

= 8.9 rounded to the 10th

The required value of the C in the algebraic measure of the angles is 61.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

here,
The property of the triangle states that the sum of the remote interior angles is equal to the exterior angle,
So, adding c - 18 and c -15 will be equal to c +28
c - 18 + c - 15 = c + 28
c = 28 + 33
c = 61

Thus, the required value of the C in the algebraic measure of the angles is 61.

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In geometry, there are several ways to prove that two triangles are congruent, which means that they have the same size and shape. Here are three common methods for proving triangle congruence SSS congruence, ASA congruence, and SAS congruence.

Side-Side-Side Congruence: If all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent. This can be written as:

If AB = DE, AC = DF, and BC = EF, then ∆ABC ≅ ∆DEF

Angle-Side-Angle (ASA) Congruence: If two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the triangles are congruent. This can be written as:

If ∠A = ∠E, ∠B = ∠F, and AC = EF, then ∆ABC ≅ ∆DEF

Side-Angle-Side (SAS) Congruence: If two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent. This can be written as:

If AB = DE, ∠A = ∠E, and BC = EF, then ∆ABC ≅ ∆DEF

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Answer:

55percent

Step-by-step explanation:

[tex]\frac{44}{80} =0.55\\0.55x100\\55[/tex]

Among the given equation, AX - BY = K is the example of a literal equation.

What is literal equation?

A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas. Every variable in the equation "literally" represents a crucial aspect of the overall relationship that the equation expresses. The letter "L" stands for the rectangle's one side's length.

Given equations are:

A. AX - BY = K: is a literal equation as per definition.

B. 5X + 9Y: is not an equation.

C. 4 + 12= 4^2: it is not an equation.

D.8 - 2x = 14: it is not an equation. It is a linear equation with variable 'x'.

Hence, among the given equation, AX - BY = K is the example of a literal equation.

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