3 − 1 = 5 + 10 = −5 1/2 Check whether the given value of is a solution to the equation. Justify your answer.

Answers

Answer 1

Answer:

[tex]x = -5\frac{1}{2}[/tex] is the solution

Step-by-step explanation:

Given

[tex]3x - 1 = 5x + 10[/tex] --- Correct expression

[tex]x = -5\frac{1}{2}[/tex]

Required

Determine if the given solution is correct

To do this, we simply solve for x in the given equation.

So, we have:

[tex]3x - 1 = 5x + 10[/tex]

Collect like terms

[tex]3x - 5x = 1 + 10[/tex]

[tex]-2x = 11[/tex]

Divide both sides by -2

[tex]\frac{-2x}{-2} = \frac{11}{-2}[/tex]

[tex]x = -\frac{11}{2}[/tex]

[tex]x = -5\frac{1}{2}[/tex]


Related Questions

suppose the length of time (in minutes) going through customs at u.s. airports with global entry (goes) is normally distributed with a population mean of 40 minutes and a population standard deviation of 12 minutes. what is the approximate wait time for the fastest 4% of passengers?

Answers

The approximate wait time for the fastest 4% of passengers is approximately 29.29 minutes.

What is Standard Deviation?

It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

To find the approximate wait time for the fastest 4% of passengers, we need to use the normal distribution and the inverse normal distribution function.

The normal distribution is a continuous probability distribution that is symmetrical around the mean, and is defined by the mean and standard deviation. In this case, the mean wait time for passengers with global entry is 40 minutes and the standard deviation is 12 minutes.

The inverse normal distribution function is a mathematical function that takes a probability as input and returns the corresponding value from the normal distribution. In other words, it allows us to find the value that corresponds to a given percentile of the normal distribution.

To find the wait time for the fastest 4% of passengers, we need to find the value that corresponds to the 4th percentile of the normal distribution. To do this, we can use an inverse normal distribution calculator or a normal distribution table.

Plugging in the mean and standard deviation of the wait time and the percentile of 4, we get a value of approximately 29.29 minutes. This is the wait time for the fastest 4% of passengers.

So, The approximate wait time for the fastest 4% of passengers is approximately 29.29 minutes.

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select the statement regarding the correlation coefficient (r) that is true. a.) a correlation coefficient of 1 implies a weak correlation between two variables. b.) the correlation coefficient describes the direction of the association between two variables. c.) the sign of the correlation coefficient might change when we combine two subgroups of data. d.) correlation coefficient cannot be calculated for all scatterplots.

Answers

The statement regarding the correlation coefficient (r) that is true is b) "the correlation coefficient describes the direction of the association between two variables."

The correlation coefficient is a measure of the strength and direction of the relationship between two variables. A correlation coefficient of 1 implies a strong positive correlation between the variables, meaning that as one variable increases, the other variable also tends to increase.

A correlation coefficient of -1 implies a strong negative correlation between the variables, meaning that as one variable increases, the other variable tends to decrease. A correlation coefficient of 0 implies no correlation between the variables. The sign of the correlation coefficient (positive or negative) indicates the direction of the association between the variables, while the magnitude of the coefficient (closer to 1 or -1) indicates the strength of the association.

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What are the roots of the quadratic equation 4x 2 − 7x 2 0?

Answers

The roots of the quadratic equation 4x2 − 7x + 0 are -7/4 and 0.

What is quadrtic ic equation?

A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. Quadratic equations are used to solve problems involving areas, lengths, and other geometric figures, as well as to find unknown values. Such equations are often used in calculus and physics.
To find the roots, you can use the quadratic formula, which is x = -b ± √b2 - 4ac/2a. In this case, a = 4, b = -7, and c = 0, so the roots are -7/4 and 0.
Another way to find the roots is to use the factoring method. To factor 4x2 − 7x + 0, you can factor out 4x and then group the terms to get 4x(x − 7) + 0. Then you can set each factor equal to zero to get x = 0 and x = 7. Therefore, the roots of the equation 4x2 − 7x + 0 are -7/4 and 0.
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What is the difference between transform and reform?

Answers

Students are pushed by reform mathematics curricula to make sense of novel mathematical concepts through investigations and projects, frequently in practical settings.

What is a transform in math?

A point, line, or geometric object can be changed in four different ways that are all collectively referred to as transformations. The pre-image is the shape of the object as it was originally, and the transformed shape of the object is termed the image.

Students are pushed by reform mathematics curricula to make sense of novel mathematical concepts through investigations and projects, frequently in practical settings. Writing and speaking clearly, cooperating in groups, and drawing connections between ideas and representations are all stressed in reform textbooks.

Translation, rotation, reflection, and expansion are the four different types of transformation. Each change must be carried out, and you must be able to tell which transformations have been carried out.

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Bisecting Bakery sells cylindrical round cakes. The most popular cake at the bakery is the red velvet cake. It has a radius of 15 centimeters and a height of 12 centimeters.

If everything but the circular bottom of the cake was iced, how many square centimeters of icing is needed for one cake? Use 3.14 for π and round to the nearest square centimeter.

Answers

The Answer Is 1,837 cm

Which congruence theorem can be used to prove WXS = YZS?

O SSS
O ASA
O SAS
OHL

Answers

Congruence theorem can be used to prove WXS = YZS is  ASA.

What is Congruence theorem ?

If two triangles are identical in size and shape, they are said to be congruent. Corresponding sides (sides in the same location) and corresponding angles (angles in the same position) are congruent when triangles are congruent (equal).

Point S makes the two connected angles the same. They both have right angles.

And one side of each is congruent.

This means you know 2 angles are the same and one side is the same.

You would use ASA (Angle, Side, Angle).

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What are three ways you can determine if two triangles are similar explain one of the methods in detail?

Answers

You may use three triangle-specific theorems to quickly distinguish similar triangles.

There are three theorems that may be used to determine whether two triangles are similar: Angle - Angle (AA), Side - Angle - Side (SAS), and Side - Side - Side (SSS).

SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle.

That is what the SAS regulation says. The triangles are congruent if the two sides and included angle of one triangle are the same as the two sides and included angle of another triangle. Any angle that is created by two specified sides is an included angle.

According to the AA postulate of Euclidean geometry, two triangles are similar if their two corresponding angles are congruent. The fact that the sum of a triangle's internal angles is always equal to 180° leads to the AA postulate.

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IQ scores are collected from a sample of 36 students
at a large university. The scores are summarized in
the histogram below.


Which of the following statements is true of the mean
and median?

O The mean is equal to the median IQ.

O The mean is less than the median IQ

O The mean is greater than the median IQ.

O It cannot be determined because we cannot tell the
exact values of the IQ scores in the sample.

Answers

Answer: The mean is less than the median IQ

Step-by-step explanation:

When a distribution is skewed left (there is an obvious tail going in the left direction, which is true in this case), then the mean is drawn down because it is not resistant to any outliers, or unusual data points.

The median, however, is resistant to outliers and will not move as much.

Therefore, the mean will be less than the median.

Final answer:

The relationship between the mean and median of a data set is determined by whether the data is symmetrically distributed, positively skewed, or negatively skewed. However, without a visual representation or specific values, we cannot definitively compare the mean and median of the IQ scores.

Explanation:

In order to determine the relationship between the mean and the median of a data set, we need to know the nature of its distribution. If the data is symmetrically distributed, the mean and the median will be equal. If the data is positively skewed (has a long right tail), the mean will be larger than the median. If the data is negatively skewed (has a long left tail), the mean will be less than the median.

However, in the absence of the actual histogram in your question, the correct answer would be 'It cannot be determined because we cannot tell the exact values of the IQ scores in the sample.' This is because without a visual representation or specific values, we cannot determine the distribution's skewness, and by extension, cannot compare the mean and median.

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pls help due asap!!!!!!!!!!!!!!!!

Answers

3 because you go up three and over one between two points on the line, and then 3 times 10 to the power of 8 (exponent of 8)

Multiple choice math. Please make sure you are correct. What symmetry does the graph show?

Answers

Answer:

D. Line symmetry

Step-by-step explanation:

I am pretty sure it is Line symmetry because it has a line pass through the vertex and divides the graph into two equal halves. If I am wrong, I am sorry!

What is the slope to a line perpendicular to 3x y 1?

Answers

The slope to a line perpendicular to y = 3x + 1 is -1/3.

Define slope.

The ratio of how much y grows as x grows by a certain amount is called the slope of a line. A line's slope, or the amount by which y rises as x rises, indicates how steep a line is. Nowhere on the line has a different slope; it is constant. We frequently seek to quantify the steepness in mathematics. The difference between slope A and slopes B and C is obvious. While slope A is just four units high, they both stand at seven. It would therefore seem that steepness and height are related.

Given

Equation

y = 3x + 1

Using slope intercept from,

y = mx + b

m = slope

m = 3

Slope which is perpendicular

= -1/m

= -1/3

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Select TWO expressions equal to the area of this figure in square centimeters

Answers

The two expressions equal to the area of the figure are (6×10) + (6×6) + (6×10) square centimeters and (6×4) + (18×6) + (6×4) square centimeters. Select these options

How to determine two expressions equal to the area of the figure in square centimeters?

Consider the images I attached:

First image:

The area of the figure = area of rectangle A + area of rectangle B + area of rectangle C

The area of the figure = (6×10) + (6×6) + (6×10)

Second image:

The area of the figure = area of rectangle D + area of rectangle E + area of rectangle F

The area of the figure = (6×4) + (18×6) + (6×4)

Thus, (6×10) + (6×6) + (6×10) square centimeters and (6×4) + (18×6) + (6×4) square centimeters are the two expressions equal to the area of this figure

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The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots. How many two-point and three-point shots did the Cruisers score?

Answers

The number of two-points and three points shot The Cruisers scored are 24 and 19 points respectively.

How to find the number of two and three points made?

The Cruisers scored a total of 105 points in a basketball game. They also had a total of 43 baskets, of which some were two-point shots and some of were three-point shots.

Therefore, the number of two-points and three-points the cruiser scored is as follows:

x = number of two-points

y = number of three-points

So;

x + y = 43 -------1

Also;

2x + 3y = 105 -----2

Multiplying equation(1) by 2

2x + 2y = 86

2x + 3y = 105

Subtract equation(i) from equation(ii)

y = 19

To find x:

x = 43 - 19

x = 24

Therefore,

number of two-points = 24

number of three-points = 19

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How do you solve an inequality and graph it on a number line?

Answers

Solving and graphing of inequality can be done by following rules of simplification and graphing accordingly.

What is number line?

The horizontal straight lines in mathematics known as number lines are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. The endpoints of this line go on forever. Integers are arranged on a number line in the image above.

How do you solve the number line?

On the number line, find the first number. To add, take as many steps to the right as the second number. Move as far to the right as the second number in order to subtract. The solution is the number you finally select.

When resolving an inequality, you can do one of the following: • Add the same amount to each side; • Subtract the same amount from each side; • Multiply or divide each side by the same positive amount. You must flip the inequality sign if you multiply or divide each side by a negative number.

To represent an inequality on a number line, such as x>3, first draw a circle around the number (e.g., 3). Fill in the circle if the sign also says equal to (). Leave the circle blank if the sign doesn't include equal to (> or <).

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What is the value of x 12 15 20 or 24?

Answers

The value of x is 20 units.

The correct answer is 20 units .

According to the triangle,

ST = 9, TQ = 16 and RQ = x

From similar triangles,

Δ SRQ ⩭ Δ STR ------(1)

{∵ RT 丄 Hypotenuse SQ}

Δ SRQ ⩭ Δ RTQ ------(2)

{∵ Δ SRQ, Δ STR and Δ RTQ are similar triangles}

⇒ SR/ST = SQ/SR = RQ/TR

⇒ SR/9 = 25/SR = x/TR

⇒ SR2 = 25 × 9

⇒ SR = 5 × 3 = 15

[tex]SR^2[/tex] + [tex]RQ^2[/tex] = [tex]SQ^2[/tex]

[tex]RQ^2 = SQ^2 - SR^2[/tex]

[tex]RQ^2 = 25^2 - 15^2[/tex]

RQ = x = √(625 - 225) = √400

x = 20 units.

Hence, The value of x is 20 units.

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The complete question is this:

What is the value of x?

12 units, 15 units, 20 units, 24 units

0.25 of what number
is 40?

Answers

Answer: 10

Step-by-step explanation:

Because 0.25 or 25%

We take 40 times 0.25 =  10

How do you write more than a number?

Answers

“5 more than a number” written as an algebraic expression is “x+5”.

In a formula or equation involving mathematical operations, the representation of numbers by alphabet is referred to as algebra. Similar to how a statement explains the link between certain words, algebraic equations describe the connection between unknown variables. 

We are given a mathematical statement and have to convert it into an algebraic expression using the information above.

Let there be a number “x”.

A number 5 more than this number is obtained after adding 5 to the given number.

So a number 5 more than x is equal to x+5.

Hence “5 more than a number” written as an algebraic expression is “x+5”.

Complete question: How do you write 5 more than a number?

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Which equation is the inverse of 2 x 2 )= 8 7 y?

Answers

[tex]y=2[/tex] ± [tex]\sqrt{28+4x}[/tex] is the equation that equals 2(x - 2)2 = 8(7 + y).

Addition and subtraction, multiplication, and division are examples of inverse operations, which are pairs of mathematical operations where one operation reverses the effects of the other. In most cases, a number's inverse refers to its reciprocal, or x - 1 = 1 / x. When a number is combined with its reciprocal, or inverse, the result is 1, or 1.

Considering the equation:

[tex]2(x-2)^2=8(7+y)[/tex]

Change the x and y variables.

[tex]2(y-2)^2=8(7+x)[/tex]

In terms of x, solve for y.

We have two sides, therefore divide them by two.

[tex](y-2)^2=4(7+x)[/tex]

Using the distribution property, [tex]a.(b+c)=a.b+a.c[/tex]

[tex](y-2)^2=28+4x[/tex]

Square-rooting both sides yields:

[tex]y-2=[/tex]±[tex]\sqrt{28+4x}[/tex]

our two sides plus two;

[tex]y=2[/tex]±[tex]\sqrt{28+4x}[/tex]

As a result, equation [tex]y=2[/tex]±[tex]\sqrt{28+4x}[/tex] is the opposite of [tex]2(x-2)^2=8(7+y)[/tex]

The complete question is:-

Which equation is the inverse of 2(x – 2)2 = 8(7 + y)?

Options:

–2(x – 2)^2 = –8(7 + y)

y= 1/4 x^2 -x -6

y= -2 +/- sqrt of 28+4x

y= 2 +/- sqrt of 28+4x

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solve this equation using zero product property and show the work

(x-5)(x+7)=0

Answers

According to question,

Given data,

We know that;

Zero product property,

ab =0

either a or b or both must be zero.

(x-5) (x+7) = 0

Where a=(x-5)

b= (x+7)

then,

x-5=0(both side equation adding +5)

 +5=+5

So,

x = 5

therefore,

x+7=0(both side equation substrate -7)

 -7=-7

So,

x=7

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what’s the equation when the points are (3,-6) and (5,-5)

Answers

Answer:0.5x - y -7.5 = 0

Step-by-step explanation:

What is the result when -7/8 is multiplied by -3.5

Answers

Answer: 49/ 16

Step-by-step explanation:

-3.5 or -35/ 10 = - 7/2

-7/8 times -7/2 = 49/ 16

Negative time negative will be positive!

Willka can cover 13. 5\,\text{m}^213. 5m 2 13, point, 5, start text, m, end text, squared with 3\,\text{l}3l3, start text, l, end text of paint. Complete the table using equivalent ratios.

Answers

Completing the table using equivalent ratios Willka can cover 4.5 m² of the area with 1 - liter paint.

Given :

What are equivalent ratios?

Equivalent ratios are the ratios that express same relation or numbers that are equivalent.

so area covered for 1 paint

13.5 / 3 = 4.5

4.5 for 1 paint

for 10 paint :

Area covered = 4.5 * 10

= 45

Table :

Area covered  ( m^2 )        paint ( L )

13.5                                      3

4.5                                        1

45                                         10

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How do you tell if a slope intercept form is parallel or perpendicular?

Answers

Lines that have the same slope are said to be parallel, and if the slope of one line is equal to the negative reciprocal of the slope of the other, the two lines are said to be perpendicular; otherwise, they are merely intersecting lines.

A line's slope is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively. and

m = Δy/Δx = dy/dx = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

A line's slope often indicates the steepness and direction of the line.

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Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively. and

m = Δy/Δx = dy/dx = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

Given an angle t that corresponds to the point (- 3 squared/2, 1/2) on the unit circle show
below, find cos(t) and sin(t).

Answers

Answer:

Step-by-step explanation:

Your question asks what is  -[tex]3^{2}[/tex] / 2    but,  since it's on the Unit circle, I know you meant   - [tex]\sqrt{3}[/tex] /2    Also, it's one of those known angles on the unit circle.

note that the angles can all be put in the form of  [tex]\sqrt{x}[/tex] / 2 , where x = 0,1,2,3,4 ,  for the five special points on the unit circle.  

as the attached pic shows,   Cos(t) for the given point would be 180-150°= 30 and sin(t) would be 90 - 30 = 60 °

it's not easy to understand how I got those angles,  just ask if you don't get it.  :)

If a polygon has four right angles, then it is either a square or a rectangle. Which is a counterexample for the conditional?.

Answers

If the polygon has four right angles , then it is a square when all four sides are equal and a rectangle when the opposite sides are equal .

The Polygon is defined as closed object that is made of line segments rather than curves on a 2 - D plane .

A square is defined as a polygon in which all the angles are right angles and pair of opposite sides are equal .

A rectangle is defined as polygon that have all the angles as right angles and all four sides are equal .

From above definitions , we can say that ,

A polygon that has four right angles , is a square when all four sides are equal and it is a rectangle when pair of opposite sides are equal .

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Calculate the approximate degree measure of the angle, given the following expression: tan(y°) = 4.12 Round your answer to the nearest tenth.​

Answers

Answer:

y ≈ 76.4°

Step-by-step explanation:

To solve for the angle a trigonometric function is being used on, we have to use the inverse of the trigonometric function.

Inverse of tan(y°) = 4.12:

[tex]tan^-1(4.12) = y[/tex]

Next, I used a scientific calculator to find the angle measure of y.

[tex]76.4 = y[/tex]

What is the relationship between base height and area?

Answers

Area in term of height- This method works well with right-angled triangles or in situations where the base as well as height are known:

Area = 1/2 x base x  height

Describe the relationship between base height and area?

TRIANGLE REGION: Triangles' areas can be determined in three simple ways. Each method works best with a specific kind of triangle.

These techniques:

A triangle's area in terms of its base and heightHeron-populated areaEquilateral triangle's surface areaArea calculated by trigonometry.

Lets assume a triangle.

The base of this triangle is assumed to be c.The height that corresponds to the base is perpendicular to the base and touches the triangle's apex. We have a straightforward formula to calculate the triangle's area:

Area is equal to half of a base times a height.

Area = 1/2 x base x  height.

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Graphing root functions
Really need help with the 4 questions

Answers

What is the end of behavior

How do you find the horizontal and vertical?

Answers

To find horizontal line,its equation is y=b where b is constant.Horizontal line is parallel to x-axis of the coordinate plane.To find vertical ,its equation is x=b where b is constant.Vertical line is parallel to y-axis.

How do we find horizontal line?

A horizontal line is a line extending from left to right and right to left.The slope of horizontal line is always zero.Horizontal lines are always parallel to x-axis.The y-intercepts of a horizontal line y=b is the point (0,b).

How do we find vertical lines?

A vertical line is a line extending from up to down and downward to upward.Its never moves left to right.Vertical lines are always parallel to y-axis.The equation of a vertical line is x=a and x=-a where x is the x-coordinate of ant point on the line and a is the point where he line crosses the x-intercepts.

Hence we can find horizontal and vertical lines on the graph or paper easily.

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If the interior angle of triangle are 3x,4x,and5x find the ize of angle of the traingle. Alo fing the difference between larget and malleat angle

Answers

Answer:

45, 60, 75

Difference between the largest and smallest angles

75 - 40 = 35

Step-by-step explanation:

First solve for x.  The sum of the interior angles of a triangle is 180

3x + 4x + 5x =180  Combine like terms

12x + 180  Divide both sides by 12

[tex]\frac{12x}{12}[/tex] = [tex]\frac{180}{12}[/tex]

x = 15

3x = 3(15) = 45

4x = 4(14) = 60

5x  = 5(15) = 75

Step-by-step explanation:

please, burn this into your brain for life :

the sum of all angles in a triangle is always (yes, no exceptions) 180°.

so,

3x + 4x + 5x = 180

12x = 180

x = 180/12 = 15

3x = 3×15 = 45°

4x = 4×15 = 60°

5x = 5×15 = 75°

the difference between largest and smallest angle is therefore

75 - 45 = 30°

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