5x−2+x=9+3x+10 what is x?

Answer:

  x = 1, x = 5

Step-by-step explanation:

You want the solutions to the absolute value equation ...

  |x -7| = |2x -8|

Each of the absolute value functions is equivalent to a piecewise-defined function. The boundary for the pieces is the turning point of the absolute value function, where its argument is zero.

The turning points are ...

  x -7 = 0   ⇒   x = 7

  2x -8 = 0   ⇒   x = 8/2 = 4

This means the equivalent piecewise equation will have 3 pieces. We know the absolute value function is defined as ...

  [tex]|x|=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x\ge0\end{cases}[/tex]

If we write the equation in the form |x -7| - |2x -8| = 0, we have ...

  [tex]0=\begin{cases}-(x-7)-(-(2x-8))&\text{for }x < 4\\-(x-7)-(2x-8)&\text{for }4\le x < 7\\(x-7)-(2x-8)&\text{for }7\le x\end{cases}[/tex]

The equation simplifies to ...

  -x +7 +2x -8 = 0

  x -1 = 0 . . . . collect terms

  x = 1 . . . . . . a value in the domain. This is one solution.

The equation simplifies to ...

  -x +7 -2x +8 = 0

  15 = 3x . . . . . . . . . . add 3x

  5 = x . . . . . . . . a value in the domain. This is another solution

The equation simplifies to

  x -7 -2x +8 = 0

  -x +1 = 0

  x = 1 . . . . . . . . . not in the domain 7 ≤ x, so not a solution

The solutions are x = 1 and x = 5.

__

Check

  |1 -7| = |2·1 -8|   ⇒   |-6| = |-6| . . . . true

  |5 -7| = |2·5 -8|   ⇒   |-2| = |2| . . . . true

Both solutions check in the original equation.

Worker B appears to be more consistent in performance, while Worker B is more efficient from an overall point of view.

To determine who appears to be more consistent in performance, we need to compare the standard deviations of A and B. Both A and B have a standard deviation of 1.5 hours, which means that they have the same level of consistency in their performance.

To determine who is more efficient from an overall point of view, we need to compare the mean times of A and B. Worker B has a mean time of 4 hours, which is less than the mean time of Worker A (5 hours). This means that Worker B is more efficient than Worker A in completing the job from an overall point of view.

To know more about standard deviations:

https://brainly.com/question/23907081

#SPJ4

Answer:

$105.00

Step-by-step explanation:

To find the total cost of the mirror, we need to first calculate its area. The area of the mirror can be found by multiplying its length by its width.

So, the area of the mirror would be:

Area = Length x Width

Area = 7 feet x 5 feet

Area = 35 square feet

Now that we know the area of the mirror, we can calculate the total cost by multiplying the area by the price per square foot:

Total Cost = Area x Price per square foot

Total Cost = 35 square feet x $3.00 per square foot

Total Cost = $105.00

Therefore, the total cost of the mirror would be $105.00.

Answer:105$

Step-by-step explanation: all you need to do is 5x7=35

35 is the amount of square feet the square has. Then you do 35 x 3.00=

105$

Answer:

Hopes this helps

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be the angle Y has a value of roughly 76.4 degrees.

What precisely is a triangle?

Because a triangle has four or more extra parts, it is a polygon. Its form is a straightforward rectangle. A triangle is a rectangle with the edges A, B, and C. A singular plane but instead cube are produced by Euclidean geometry when the sides aren't truly collinear. A triangular is a shape if it has three sides and three angles. Angles are the points where a quadrilateral three sides meet. A triangle's sides add up to 180 degrees.

Here,

We can determine the images of locations A, B, and C using the following method:

=> A': (-yA, xA)

=> B': (-yB, xB)

=> C": (-yC', xC')

where C' is the rotated version of location C.

We can determine the side lengths of triangular ABC using the Law of Cosines:

Assume that

=>  a = BC = 2R sin(A/2) = 2R sin(45/2) 1.441R,

=> b = AC = 2R sin(B/2) = 2R sin(55/2) 1.663R, and

=> c = AB = 2R sin(C/2) = 2R sin(80/2) 2.219R.

where R represents the triangular ABC's circumradius.

Now, by turning point C 90 degrees anticlockwise with respect to the origin, we can determine the coordinates of point C':

xC' = -yC

yC' = xC

Then, to obtain the picture of point C, we can reflect point C' across the line y = x:

xC"=yC' and yC"=xC'

Again employing the Law of Cosines, we can determine the triangular XYZ's side lengths:

=> x = YZ = 2R sin(A'/2) = 2R sin(35) ≈ 1.189R

=> y = XZ = 2R sin(B'/2) = 2R sin(45) ≈ 1.414R

=> z = XY = 2R sin(C'/2) = 2R sin(55) ≈ 1.630R

where the picture angles of angles A, B, and C are A', B', and C', respectively.

Last but not least, we can apply the Law of Cosines once more to determine the size of angle Y:

cos(Y) i= t (x2 + z2 - y2)/ (2xz)

cos(Y) = 0.224 Y = 76.4 °

As a result, the angle Y has a value of roughly 76.4 degree

According to the solving volume of the cylinder where the Brianna has collected approximately 99.1 grams of trace element (rounded to one decimal place).

The cylinder has a circular base and is a three-dimensional shape. A group of circular discs placed on top of one another might be thought of as a cylinder. Consider a situation where we need to figure out how much sugar can fit inside a cylindrical box.

In other words, we want to figure out the volume or capacity of this box. A cylindrical box's capacity is essentially equal to the volume of the cylinder inside. As a result, the volume of a three-dimensional shape is determined by how much space it takes up.

The volume of the cylinder is given by the formula V = πr²h

where r is the radius and h is the height.

Substituting the given values,

we get V = π(9.6 cm)²(11.6 cm) = 3,301.57 cm³ (rounded to two decimal places).

Since the sample contains 0.03 grams of trace element for every cubic centimeter of water,

Brianna has collected approximately 0.03 × 3,301.57 = 99.05 grams of trace element (rounded to two decimal places).

To know more about volume of cylinder visit:

brainly.com/question/16134180

#SPJ1

Step-by-step explanation:

4.25 inches  *   16 miles / 1 inch  = 68 miles

Answer:

v = 10

Step-by-step explanation:

[tex] \dashrightarrow \: { \sf{ {v}^{2} - {u}^{2} = 2as}} \: \: \: \\ \\ \dashrightarrow \: { \sf{ {v}^{2} = {u}^{2} + 2as }} \: \: \: \\ \\ \dashrightarrow \: { \sf{v = \sqrt{ {u}^{2} + 2as} }} \\ \\ \: \: \: \: \: \: \: { \colorbox{lightblue}{substitute \: variables}} \\ \\ \dashrightarrow \: { \sf{v = \sqrt{ {4}^{2} + 2(2 \times 21) } }} \\ \\ \dashrightarrow \: { \sf{v = \sqrt{16 + 84} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\\dashrightarrow \: { \sf{v = \sqrt{100} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \dashrightarrow \: { \sf{v = 10}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer:

incomplete question, could u provide the whole question please?

The probability that a student chosen at random will play the bass is 12/43.

What is probability?

Probability is a branch of mathematics that deals with the study of random events or experiments. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1. An event with a probability of 0 means it is impossible, while an event with a probability of 1 means it is certain to occur. Probabilities between 0 and 1 indicate the degree of uncertainty of the event occurring.

To find the probability that a student chosen at random will play the bass, we need to find the total number of students who play the bass and divide it by the total number of students in the middle school School of Rock.

The total number of students who play the bass is the sum of the number of seventh-grade students who play bass and the number of eighth-grade students who play bass:

Total number of bass players = 14 + 10 = 24

The total number of students in the middle school School of Rock is the sum of the number of seventh-grade students and the number of eighth-grade students:

Total number of students = 12 + 14 + 9 + 5 + 10 + 36 = 86

Therefore, the probability that a student chosen at random will play the bass is:

P(bass) = Total number of bass players / Total number of students = 24/86

To simplify this fraction, we can divide both the numerator and denominator by 2:

P(bass) = (24/2) / (86/2) = 12/43

Therefore, the probability that a student chosen at random will play the bass is 12/43.

To know more about Probability visit :-

https://brainly.com/question/13604758

#SPJ1

Answer:198.447

Step-by-step explanation:

just search 7 ounces to grams

describe four right that individuals in relationships have when they stay together

Answer:

The Place Value of '4' will be 400 if we keep it in the Hundreds place
The Face Value of '4' will remain the same

Answer:

1.31313123x10^{46}

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Isosceles triangle has two congruent angles.

∠ + ∠ + 130 = 180

2∠ = 50

∠ = 25

Answer:

25°

Step-by-step explanation:

In an isosceles triangle, 2 angles are equal.

The sum total of all angles in a triangle = 180

Assume unknown angle as x.

As 1 angle is already given, the equation is

130 + x + x = 180

130 + 2x = 180

2x = 50

x = 25°

Answer:

around 82.45 cubic cm

Step-by-step explanation:

The formula for the volume of a sphere is (4/3) * pi * r^3.

Since the radius is 2.7, we can plug this into the formula to get (4/3) * pi * 19.683.

This simplifies to 26.244pi, which is around 82.45 cubic cm.

A telephone call center uses two customer service representatives (csrs) during the 8:30 a.m. to 9:00 a.m. time period. the standard service rate is 2.0 minutes per telephone call per csr. assuming a target labor utilization rate of 70 percent, Therefore, these two CSRs can handle approximately 3 calls during this half-hour period.

Given a telephone call center uses two customer service representatives (CSRs)

during the 8:30 a.m. to 9:00 a.m. time period, and the standard service rate is 2.0 minutes per telephone call per CSR. Assuming a target labor utilization rate of 70%,

we have to determine the number of calls these two CSRs can handle during this half-hour period.

The formula to calculate the number of calls that can be handled during this half-hour period is:

Number of calls = (number of servers x utilization rate x service time) / arrival rate

                          = (2 x 0.70 x 2) / 1

                          = 2.8 calls (rounded to the nearest whole number)

Therefore, these two CSRs can handle approximately 3 calls during this half-hour period.

for such more question on calls

https://brainly.com/question/29497021

#SPJ11

The probability of spinning purple on the spinner is 1/4 or 25%.

Calculating the variety of ways to select or arrange a collection of items is a key component of the probability theory concepts of permutation and combination. The key distinction between combination and permutation is whether or not order matters. Contrarily, combination refers to the variety of ways to choose a smaller subset of items from a larger collection, where the order of the items is irrelevant. For instance, there are three potential two-letter combinations if you have the letters A, B, and C: AB, AC, and BC.

Given there are 4 stations, thus he spinner is equally likely to land on any of the four colors.

The probability of spinning purple is 1/4 or 25%.

Hence, the probability of spinning purple on the spinner is 1/4 or 25%.

Learn more about probability here:

https://brainly.com/question/13604758

#SPJ1

Answer:0.08

Step-by-step explanation:If you divide the (1/3)/4 that will get you 0.08

Answer:

Step-by-step explanation:

Domain: D=R-{2}

Asymptote vertical: x=2

Asymptote horizontal: y=1

Hey, I tried to graph this function, I hope you understand something here...

The Volume of the pyramid.

Volume = 288.67 m³

As the volume of the pyramid is the amount of space enclosed inside the pyramid, the formula to find the volume of a square pyramid is given as;

Volume = (1/3) × base area × height.

Where: Base area (B) = s²

Where; s = length of the square pyramid side

And, Height (h) = perpendicular height to the base.

Substituting the given values in the formula we get;

Volume = (1/3) × s² × h

Given, s = 8.5m and h = 12m

Therefore, Volume = (1/3) × 8.5² × 12

= (1/3) × 72.25 × 12

= 288.67 m³

Thus, the volume of the given square pyramid is 288.67 m³, to the nearest hundredth of a cubic meter.

The volume of any pyramid is a measure of the total amount of space enclosed within the pyramid. If you have a pyramid of a specific shape and size, you can calculate its volume by using an appropriate formula. In this case, we have been given the length of the square pyramid side (s) and the perpendicular height (h) of the pyramid to the base. We can use the formula to calculate the volume of the pyramid.

The formula is Volume = (1/3) × base area × height.

For a square pyramid, the base area is the area of the square that forms the base. Since all four sides of the square are of equal length, the area is given as the square of the length of one of the sides. Thus, Base area (B) = s².

Know more about Volume of the pyramid here:

https://brainly.com/question/218706

#SPJ11

Answer:

Step-by-step explanation: frost add the vertical and horizontal axis to find your nearest angle

Answer:450,000

Step-by-step explanation:It becomes 450,000 thousand because anything under 5 in the ten thousands place becomes a zero and anything in front of it which is the 4 will stay the same.

According to the solution we have come to find that, Write the two equations in the form y = mx + b, where m is the slope and b is the y-intercept.

In mathematics, a graph is a collection of vertices or nodes and edges, where each edge connects a pair of nodes.

To solve a system of equations by graphing, follow these steps:

Write the two equations in the form y = mx + b, where m is the slope and b is the y-intercept.

Plot the y-intercept of each equation on the y-axis.

Use the slope of each equation to find one or two more points on the line, and plot these points.

Draw a line through the plotted points for each equation.

Look for the point where the two lines intersect. This point represents the solution to the system of equations.

Check the solution by plugging in the coordinates of the intersection point into both equations. If the coordinates satisfy both equations, then the point is the correct solution.

To learn more about graph visit:

https://brainly.com/question/19040584

#SPJ9

It is likely that Batter A, who swings the bat from a resting position on his shoulder, will hit the ball a greater distance than Batter B, who hits the ball with the bat directly behind it. This is because Batter A is able to generate more power and momentum with his swing, whereas Batter B's swing may be more limited in its range of motion and force.

The amount of grams per serving that are not carbohydrates or protein in the new cereal is 24.05 grams.

In the preceding question, we were told that the amount of carbohydrates in both Cornbits and Tasty Oats is 700% of the amount of protein. The amount of protein is 12 grams. So, we can conclude that the amount of carbohydrates is 700% 0f 12 grams which equal 84 grams. Also, we know that there are 5 grams of protein in 45 grams of Cornbits cereal.

Now 20% less grams of carbohydrates gives us 0.8 × 84 = 67.2

while 75% more grams of protein per serving than Cornbits gives us 175% × 5 = 8.75

The number of grams per serving that are not carbohydrates or protein in the new cereal will be:

100 - 67.2 - 8.75 = 24.05.

Learn more about percentage increase and decrease here:

https://brainly.com/question/11360390

#SPJ1

There are 16 ways to choose a chairman, vice chairman, and secretary under these conditions

Since, the chairman must be a Democrat and the vice chairman must be a Republican, we have one choice for the chairman (out of the 10 Democrats) and one choice for the vice chairman (out of the 7 Republicans).

For the secretary, we have 16 people left to choose from (since we have already chosen the chairman and vice chairman), and it can be either a Democrat or a Republican.

Therefore, the number of ways to choose a chairman, vice chairman, and secretary is:

¹⁶C₁ = 16

So, there are 16 ways to choose a chairman, vice chairman, and secretary under these conditions

Learn more about the combination visit:

brainly.com/question/28065038

#SPJ12

Answer:

Step-by-step explanation:

To graph the average and standard deviation of a given list of values, you should use a bar graph or a histogram.

1. Calculate the average (mean) of the given list of values.
2. Calculate the standard deviation of the given list of values.
3. Create a bar graph or histogram with two bars.
4. Label the first bar as "Average" and set its height to the calculated average value.
5. Label the second bar as "Standard Deviation" and set its height to the calculated standard deviation value.

This graph will visually represent the average and standard deviation of the given list of values.

Learn more about Standard deviation at:
https://brainly.com/question/24298037

#SPJ11

The odds of spinning a 3 on any given turn is 1 out of 7 or 14%. This can be expressed as a decimal by dividing 14 by 100, which yields  probability of 0.14.

To calculate this, we divide the number of favorable outcomes (1) by the total number of possible outcomes (7). This is the same as the probability of spinning a 3 on a given turn, which can be expressed as a decimal, fraction, or percentage.The odds of spinning a 3 on any given turn is 1 out of 7 or 14%. This can be expressed as a decimal by dividing 14 by 100, which yields 0.14. To calculate this, we divide the number of favorable outcomes (1) by the total number of possible outcomes (7). This is the same as the probability of spinning a 3 on a given turn, which can be expressed as a decimal, fraction, or percentage.

P(Spin a 3) = favorable outcomes/ total outcomes

= 1/7

= 0.14

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

AAS

Step-by-step explanation:

They share the same side, and the 2 angles are the same as well and match