Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0

Answer:

Step-by-step explanation:

Because this is a greater than or equal to, we will set up the inequality system to look like this:

[tex]\frac{1}{4}x-2\leq -7[/tex]  OR  [tex]\frac{1}{4}x-2\geq 7[/tex] and solve both inequalities, one at a time.

[tex]\frac{1}{4}x\leq -5[/tex] so

[tex]x\leq -20[/tex]

The other one:

[tex]\frac{1}{4}x\geq 9[/tex] and

[tex]x\geq 36[/tex]

The graph would show all numbers less than or equal to -20 and those grater than or equal to 36. This is a true disjunction, so our answer is viable.

The total amount of money in the savings account after 3 years will be $1,614.00. This is calculated by multiplying $1500 by 1.04 three times, which equals $1,614.00.

1. 1500 x 1.04 = 1560

2. 1560 x 1.04 = 1624.40

3. 1624.40 x 1.04 = 1683.76

4. 1683.76 rounded to two decimal places = $1,614.00

Annie invests $1500 in a savings account that earns 4% simple interest annually. After 3 years, the amount of money in the savings account can be calculated by multiplying the initial investment of $1500 by 1.04 three times. This results in a total of $1,614.00 in the savings account after 3 years, without any additional deposits or withdrawals. This is because 4% simple interest annually means that the interest earned each year is 4% of the initial investment. This is calculated by multiplying the initial investment by 1.04. The 1.04 is the amount of interest earned which is then added to the initial investment. This process is repeated for 3 years, resulting in the total of $1,614.00.

Learn more about amount here

https://brainly.com/question/28970975

#SPJ4

The answer to the question is 17/140 fraction.

A fraction is a numerical expression that represents a part of a whole or a ratio of two numbers. It consists of two parts: a numerator (the number on top) and a denominator (the number on the bottom). For example, 3/4 is a fraction that represents 3 parts out of 4. It can also represent the ratio of 3 to 4.

To move the fraction to each box, you would need to multiply the denominator of the first fraction (10) by the numerator of the second fraction (14). The result is 140. Then, you would add the numerator of the first fraction (3) to the numerator of the second fraction (14), giving you 17. The answer to the question is 17/140.

To know more about fraction click-
https://brainly.com/question/78672
#SPJ1

Answer:

Tonicity is a measure of the concentration of solute particles in a solution compared to another solution. It is used to describe the effects of a solution on a cell.

If a cell is placed in a 15% solute solution and the cell shrinks, it means that the solution is hypertonic to the cell. Hypertonic solutions have a higher concentration of solute particles than the inside of the cell, which causes water to move out of the cell by osmosis. As water leaves the cell, it shrinks.

So, in this case, the tonicity of the 15% solution is hypertonic.

Answer: 0.06

Also could you mark my answer as brainliest? It helps and doesnt hurt

Answer: 0.06

Step-by-step explanation:

The derivative of a logarithmic function is the inverse of the exponential function. That is, if y = logb(x) then the derivative of y is given by dy/dx = 1/xb.

Step 1: Recall that the derivative of a function is defined as the rate of change of the output of the function with respect to the input.

Step 2: Logarithmic functions are inverse of exponential functions, which means that the output of a logarithmic function is the input to an exponential function.

Step 3: Therefore, the derivative of a logarithmic function is the inverse of the derivative of an exponential function.

Step 4: The derivative of an exponential function is given by dy/dx = bx, where b is the base of the exponential function.

Step 5: Therefore, the derivative of a logarithmic function is given by dy/dx = 1/xb, where b is the base of the logarithmic function.

The derivative of a logarithmic function is the inverse of the exponential function. That is, if y = logb(x) then the derivative of y is given by dy/dx = 1/xb.

learn more about logarithm here

https://brainly.com/question/30085872

#SPJ4

Answer:

y=-2/3x-4

Step-by-step explanation:

y=mx+b

-8=-2/3(6)+b

-8=-4+b

-4=b

y=-2/3x-4

If the composite figure consists of of a cube of side length 6cm and a hemisphere of radius 3cm , then the surface area of composite figure is  [tex]236.52 \; cm^{2}[/tex] .

The Composite Figure consists of a Cube and Hemisphere ;

the radius of the hemisphere is given as = 3 cm ;

So, formula for curved surface area of hemisphere is = [tex]2\pi r ^{2}[/tex] ;

= [tex]2\pi 3 ^{2}[/tex] = [tex]56.52cm^{2}[/tex] ;

the side length of the cube is = 6cm ;

only the area of the 5 sides will be calculated because on one side there is a hemisphere ;

Surface Area of Cube = [tex]5a^{2}[/tex]

= [tex]5\times 6^{2}[/tex] ;

= [tex]5 \times 36[/tex] = [tex]180 \; cm^{2}[/tex] .

So , the surface area of the composite figure = Area of hemisphere + area of 5 sides cube ;

Substituting the areas ,

we get ;

= [tex]56.52 + 180[/tex] ;

= [tex]236.52 \; cm^{2}[/tex] .

Therefore, Surface Area of given composite figure is [tex]236.52 \; cm^{2}[/tex] .

The given question is incomplete , the complete question is

Explain how to find the surface area of the composite figure that consists of a cube of side length 6cm and a hemisphere of radius 3cm .

Learn more about Surface Area here

https://brainly.com/question/27525009

#SPJ4

The statement which is true about the two equations include the following: D. The lines are perpendicular.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-5 × 1/5 = -1

-1 = -1 (perpendicular).

In conclusion, the two equations represent perpendicular lines because there slope is an inverse that equals to one (1).

Read more on slope here: brainly.com/question/3493733

#SPJ1

The average speed of the car is 40 km/hr.

It would take a car 3 hours to cover 120 km at a speed of 40 km/h.

The car moves for a time period of 3 hours.

The car has to travel a total distance of 120 km.

As we know the formula of speed is distance/time,

Hence, s = d/t km/hr

Let speed, distance and time be s, d, t respectively.

So by putting the values,

speed s = d/t = 120/3 = 40 km/hr.

Hence it can be said that the car would cover 120 km at the speed of 40 km/hr in 3 hours.

To learn more about speed visit: brainly.com/question/7359669

#SPJ4

Option B is Correct. An specific place in space is called a point. A dot indicates a point.

A point in space is a location. No length, width, or thickness exist in a point. In geometry, a dot stands in for a point. We typically use a (capital) letter to name a point. The simplest basic geometric object is a point. It is named with a capital letter and symbolised by a dot.

A point has no size and solely represents position (that is, zero length, zero width, and zero height). In a line, a line segment has two distinct endpoints. The line segment's length, which is the separation of two fixed points, is constant.

Learn more about Point Visit: brainly.com/question/26865

#SPJ4

Correct Question:

An exact location in space is called a _______

A. Line

B. Point

C. Circle

D. Line segment

The probability of rolling a 5 on at least one of the dice is P(A)=8/9 ways

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

As given in the question if two six-sided dice are rolled, the probability of rolling a 5 on at least one of the dice:

for two six-sided dice total outcomes =36 ways

the probability of rolling a 5 on at least one of the dice is 4 ways.

P(A)=1-4/36

36-4/36

32/36

P(A)=8/9

Therefore, The probability of rolling a 5 on at least one of the dice is P(A)=8/9 ways.

To know more about Probability:

https://brainly.com/question/25839839

#SPJ4

Therefore , the solution of the given problem of fraction comes out to

be  = 43/9.

To represent a whole, any number of equal parts or fractions may be employed. The quantity of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. In mathematics, the exponent to denominator ratio is used to represent numbers. These are all simple fractions of integers.

Here,

Given :

Let's transform the mixed fraction to an improper fraction with an equivalent value.

1 [tex]\frac{4}{9}[/tex] = 3[tex]\frac{1}{3}[/tex]

Consequently, the second fraction is now 13/9 = 10/3.

The LCD is now located. The LCD is nine.

We now set each denominator to LCD, which equals 9. Therefore, we multiply the second fraction's numerator and denominator by 3.

=> 13/9 + 10*3 /3*3

=> 13/9 + 30/9

Given that the denominator is equal, now.

As a result, we may simply add numerators.

=> 43/9

Therefore , the solution of the given problem of fraction comes out to be  

= 43/9.

To know more about fraction visit:

https://brainly.com/question/10354322

#SPJ1

Explanation:

We have

(2x+3)(4x^2-5x+6)

Distribute it

(2x) (4x^2)=8x^3

(2x)(-5x)=-10x^2

(2x)(6)=12x

(3)(4x^2)=12x^2

(3)(-5x)=-15x
(3)(6)=18

Now we add all of them up:

8x^3-10x^2+12x^2+12x-15x+18

Now we simply it:

8x^3+2x^2-3x+18

In the given cube-shaped cake, the value of c + s = 32/5.

In the given figure of the cube-shaped cake, let [RNQ] be the area of the triangle RNQ. The volume of the corresponding piece c = 2[RNQ]. The cake piece has icing on the top and on the vertical side that contains the edge QR. Hence the total area with icing is [RNQ] + 2^2 = [RNQ] + 4. Hence, c+s = 3[RNQ] + 4.

In order to determine [RNQ], introduce a coordinate system. Let Q be the origin. As the length of each edge is 2. Hence,

Q = (0,0)

P = (2, 0)

R = (0, 2)

In the coordinate system, as M is the midpoint of PS, M = (2, 1). The equation of the line QM is:

m = (1- 0)/(2 – 0) = ½

y – 0 = ½(x – 0)

2y – x = 0

As the line RN is orthogonal to QM, it has an equation is y + 2x + q = 0. As the point R lies on the line RN,

2 + 2(0) + q = 0

q = -2

Hence, RN is y + 2x -2 = 0

Substituting x = 2y into the line RN,

y + 2(2y) -2 = 0

5y = 2

y = 2/5

x = 2(2/5) = 4/5

In the triangle RNQ, x is the height from N onto RQ, the area [RNQ] = (x*RQ)/2 = 2x/2 = x = 4/5.

Hence, 3[RNQ] + 4 = 3(4/5) + 4 = 32/5.

Note: The question is incomplete. The complete question probably is: A cubical cake with edge length 2 inches is iced on the sides and the top. It is cut vertically into three pieces as shown in this top view, where M is the midpoint of a top edge. The piece whose top is triangle B contains c cubic inches of cake and s square inches of icing. What is c+s?

Learn more about Area of the triangle:

https://brainly.com/question/17335144

#SPJ4

The functions when evaluated are

Function (1)

Given that

f(n) = -4n³ - 17n² - 10n + 8 at n = -3

This means that

f(-3) = -4(-3)³ - 17(-3)² - 10(-3) + 8

Expand the brackets

f(-3) = 108 -153 + 30 + 8

Evaluate the like terms

f(-3) = -7

Function (2)

Here, we have

f(n) = -6n⁴ + 38n³ - 16n² + 28n - 29 at n = 6

This means that

f(6) = -6(6)⁴ + 38(6)³ - 16(6)² + 28(6) - 29

Expand the brackets

f(6) = -7776 + 8208 - 576 + 168 - 29

Evaluate the like terms

f(6) = -5

Function (3)

Here, we have

f(a) = 3a³ + 6a² - 15a - 19 at a = -3

This means that

f(-3) = 3(-3)³ + 6(-3)² - 15(-3) - 19

Expand the brackets

f(-3) = -81 + 54 + 45 - 19

Evaluate the like terms

f(-3) = -1

Function (4)

Incomplete

Function (5)

Here, we have

f(a) = a⁴ - 6a³ + 2a² + 25a - 9 at a = 4

This means that

f(4) = (4)⁴ - 6(4)³ + 2(4)² + 25(4) - 9

Expand the brackets

f(4) = 256 - 384 + 32 + 100 - 9

Evaluate the like terms

f(4) = -5

Function (6)

Here, we have

f(x) = x⁴ + 3x³ - x² + 13x + 13 at x = -4

This means that

f(-4) = (-4)⁴ + 3(-4)³ - (-4)² + 13(-4) + 13

Expand the brackets

f(-4) = 256 - 192 -16 - 52 + 13

Evaluate the like terms

f(-4) = 9

Read more about functions at

https://brainly.com/question/28277110

#SPJ1

Answer: We can start by using the identity sin^2(A) + cos^2(A) = 1.

We can square the equation 3 sin A + 4 cos A = 5, to get:

9sin^2(A) + 12sin(A)cos(A) + 16cos^2(A) = 25

Substituting the identity sin^2(A) + cos^2(A) = 1, we get:

9sin^2(A) + 12sin(A)cos(A) + 16(1-sin^2(A)) = 25

12sin(A)cos(A) = 6

Now,we can use identity tan(A) = sin(A) / cos(A) and sec(A) = 1 / cos(A)

tan(A) = sin(A) / cos(A) = (2sin(A)cos(A)) / (cos^2(A)) = 2 * (sin(A)cos(A)) / (1-sin^2(A)) = 2 * (6 / 12) = 1

sec(A) = 1 / cos(A) = 1 / sqrt(1 - sin^2(A)) = 1 / sqrt(1 - (3/5)^2) = 1 / sqrt(1 - 9/25) = 5/sqrt(16) = 5/4

Now we can add them:

tan(A) + sec(A) = 1 + 5/4 = (4+5) / 4 = 9/4 = 2.25

Hence proved that tan A + sec A = 2.25

Step-by-step explanation:

Answer:

77.5

Step-by-step explanation:

55 and 100 average provides comprehensive information about what is the average of 55 and 100, and how it is being calculated mathematically. To calculate the average, the given quantities 55 and 100 can be of any physical quantity but both should have been expressed in the same measurement units.

55 and 100 average:

= (55 + 100)/2,

= 155/2,

= 77.5

Depending on how many variables there are in the equations, there are several ways to solve algebraic problems.

There is only one way to solve a one-variable equation, which involves bringing all the terms that include the variable to one side before determining the value of the variable.

There are several ways to solve a problem when there are two variables, starting with the

1.  Elimination technique.

2. The substitution approach.

and several additional techniques

An algebraic equation is a mathematical sentence when two algebraic expressions are related with an equality sign (=).

To know more about algebraic equations on brainly : brainly.com/question/6036877

#SPJ4

The exponential function that grows the least quickly is given as follows:

f(x).

The general format of an exponential function is defined as follows:

y = ab^x.

In which:

To grow the least quickly, we want a function with the lowest rate of change, hence it is function f(x), which has a rate of change of b = 3, while the other functions have a rate of change of 3.5 and of 4.

This means that the correct option is given by the first option.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

Answer:

Step-by-step explanation:

You want to find the values of the variables in various expressions for angles, sides, or diagonals of parallelograms.

A parallelogram is a quadrilateral (4-sided polygon) with opposite sides parallel. The opposite sides are also the same length.

Opposite angles in a parallelogram are congruent (have the same measure), and adjacent angles are supplementary (total 180°).

The diagonals of a parallelogram bisect each other, so the halves of a diagonal are the same length.

These are the relationships you need to know in order to solve these problems.

Opposite sides are the same length.

  XY = WZ

  3a -4 = a +2

  2a = 6 . . . . . . . . . add 4-a to both sides

  a = 3

and ...

  YZ = XW

  2b = b +1

  b = 1 . . . . . . . . . subtract b

Opposite angles are congruent.

  ∠C = ∠A

  2y -40 = y +10

  y = 50 . . . . . . . . . . add 40-y to both sides

Adjacent angles are supplementary

  (y+10) +4x = 180

  50 +10 +4x = 180 . . . use the above value for y

  4x = 120 . . . . . . . . . . subtract 60

  x = 30 . . . . . . . . . . . divide by 4

Diagonals bisect each other. Call the center point X where the diagonals cross.

  HX = PX

  x -3 = 15

  x = 18 . . . . . . . add 3

and ...

  EX = QX

  y +3 = 12

  y = 9 . . . . . . . subtract 3

Same as problem 3.

  NX = LX

  4x = x +6

  3x = 6 . . . . . . . subtract x

  x = 2 . . . . . . . divide by 3

and ...

  MX = OX

  5y -8 = 3y +1

  2y = 9 . . . . . . . . add 8-3y to both sides

  y = 4.5 . . . . . . . divide by 2

__

Additional comment

In general, geometry problems of this sort are solved by making use of the relationships between angles, sides, perimeter, and area of geometric figures. You are expected to remember facts and formulas about these figures that would help you write equations and solve problems like this.

A rhombus is a special parallelogram that has perpendicular diagonals. A rectangle is a special parallelogram that has right-angle corners and congruent diagonals. A square is a special of both of those: a rectangle with perpendicular and congruent diagonals.

Answer:

x = -4

Step-by-step explanation:

4(2-x)=24

8 - 4x = 24

-4x = 16

x = -4

Let's check

4(2 -( -4)) = 24

4 (6) = 24

24 = 24

So, x = -4 is the correct answer!

Answer:

x=4

Step-by-step explanation:

4(2-x)=24

4*2= 8   4*x = 4x

8-4x = 24

24-8 = 16

4x = 16

16/4 = 4

x=4

Answer: b = 2/ 81

Step-by-step explanation: From the question

11 + 2/ 9b = 23

Subtract 11 from both sides

11 - 11 + 2/ 9b = 23 -11

It becomes 2/ 9b = 12 (12 can also be written like this: 12/ 1)

Cross multiply

9b * 12 = 2 * 1

81b = 2

b = 2 / 81

Answer:

b= 54

Explanation:

11 + 2/9b = 23

2/9b = 23 -11

2/9b = 12

2 x 9b/9b = 12 x 9b

2 = 12 x 9b

12 x 9b = 2

108b = 2

b = 2/108

b = 1/54

Name of quantity displayed on axis and units of quantity displayed on axis.

What is axis?

In a graph, chart, or plot, an axis is a reference line that is used to compare or measure values of a variable along a certain axis. The horizontal (x) axis and the vertical (y) axis are typically the two axes of a two-dimensional graph, and each axis is used to depict a separate variable. The origin, which serves as the beginning point for measuring the variables on the graph, is where the two axes connect. The values of the variables being plotted are represented by the positions of the data points along the axes.

The following details ought to be written next to each axis of a graph when labelling it:

Name of the quantity shown on the axis: This label clearly and succinctly identifies the variable being plotted on the axis. For instance, the label for a time plot on the x-axis can be "Time (seconds)" or just "Time".

Quantity units shown on the axis: The scale for the measurements is provided by this information, which also enables appropriate data interpretation.

Learn more about label and axis of graph at https://brainly.com/question/30465181

#SPJ4

Name of quantity displayed on axis and units of quantity displayed on the axis.

An axis is a reference line that is used in a graph, chart, or plot to compare or measure the values of a variable along a particular axis. The two axes of a two-dimensional graph are commonly the horizontal (x) and vertical (y) axes, and each axis is used to represent a different variable. The intersection of the two axes is known as the origin, and it is here that measurements of the variables on the graph are to start. The data points' locations along the axes represent the values of the variables being plotted.

When labeling a graph, the information listed below should be written next to each axis:

The name of the quantity represented on the axis is: The variable being plotted on the axis is identified in this label in a clear and concise manner. For example, "Time (seconds)" or "Time" are both acceptable labels for the x-axis of a time plot.

The axis displays quantity units as follows: This information gives the measurements a scale, which also allows for accurate data interpretation.

Learn more about graph at

brainly.com/question/29129702

#SPJ4

Answer:

8.9

Step-by-step explanation:

There are no letters to define this properly, but the hypotenuse of the triangle with the sides 2 and 4 is = √(2²+4²) = √20 (pythagorean theorem)

Now we can find x, using pythagorean theorem again.

√20²+ x² = 10²

100 - 20 = x²

x = √80 = 4√5 ≈ 8.9

Cheers!

Pablo and Johanna have too many D. variables that they didn't control and not enough replicates.

Variables are generally referred to as such due of their diversity. The term "control variable" refers to a variable that is purposefully kept constant in scientific research (or sometimes simply just a control). Information is stored in variables so it may be accessed and changed.

They also give us a means to give data a name that is descriptive, which helps the reader and us understand our programmes better. Variables can be thought of as storage spaces for data, which is a useful metaphor. A term can either be a variable, a constant with an associated mathematical operation, a product of variables, or a combination of a number and a variable.

To learn more about variable: https://brainly.com/question/28248724

#SPJ4

Yes, f/x )= x² is a one to one function

One-to-one functions are those where each element in the domain has a unique and different element in the range. In other words, a one-to-one function has no repeating elements in its range.

To determine if f(x) = x² is a one-to-one function, we can look at the range of the equation. The range of f(x) = x² is all positive real numbers, and since all elements in the range are unique and different, we can conclude that f(x) = x² is a one-to-one function.

A one to one function is a function in which each element in the range is associated with exactly one element in the domain.

In the case of f/x )= x², each element in the range has exactly one associated element in the domain, which means it is a one to one function.

To learn more about function, click here:

https://brainly.com/question/12431044

#SPJ4

Carlos has 28 pennies, 28 dimes, and 20 quarters.

Value is a concept that is used to describe the worth or importance of something or someone. It is often related to an individual's beliefs and opinions and is used to measure the quality of an item or service. Value is a subjective concept, as what is considered valuable to one person may not be valuable to another. Value can also be measured in terms of money, with items or services valued at a certain price.

The total value of the coins is $6.59. Each penny is worth 1 cent, each dime is worth 10 cents, and each quarter is worth 25 cents. Therefore, 28 pennies plus 280 dimes (28 x 10) plus 500 quarters (20 x 25) equals 858 cents, which is equal to $6.59.

To know more about value click-
https://brainly.com/question/27882730
#SPJ1

The IQR (interquartile range) of the data set expressed by this box plot is 22 units.

Each number of the data set pictured as a box plot is something the numbers have individually. The lowest number there (the first number), 38, is known as the minimum. The highest number there (the last number), 75, is known as the maximum. The second number there, 45, is known as the lower quartile. The third number there, 50, is known as the median or middle quartile. The fourth number, 67, is known as the higher quartile. In order to find the interquartile range, we need to find the difference between the lower quartile and higher quartile, which means subtracting.

67 (highest quartile)- 45 (lower quartile) = 22 (interquartile range)

Therefore, the IQR (interquartile range) of the data set expressed by this box plot is 22 units.

Read more about the interquartile range:

https://brainly.com/question/17083142

#SPJ4

The required symbol of logarithmic function is [tex]\log_{e}x[/tex].

A logarithmic equation is one that uses the logarithm of an expression involving a variable. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 is equal to 103, its logarithm in base 10 is 3, or log10 (1000) = 3. When there is no possibility of mistake or when the base is irrelevant, The logarithm of x to base b is expressed as logb (x), logb x, or even without the specified base, log x, just like in big O notation.

To know more about logarithmic function visit:

brainly.com/question/30284289

#SPJ4