For the given equation the value of x is, x = 12.
What is solving an equation?
Finding an equation's solutions, which are values (numbers, functions, sets, etc.) that satisfy the equation's condition and often consist of two expressions connected by an equals sign, is known as solving an equation in mathematics. One or more variables are identified as unknowns when looking for a solution.
Consider, the given equation[tex]\frac{2}{3}x - 1=9-\frac{1}{6}x[/tex]
Add 1 on both sides,
[tex]\frac{2}{3}x -1+1 = 9-\frac{1}{6}x+1\\ \frac{2}{3}x=10-\frac{1}{6}x[/tex]
Add 1/6(x) to both sides,
[tex]\frac{2}{3}x + \frac{1}{6}x = 10 - \frac{1}{6}x+\frac{1}{6}x\\ \frac{5}{6}x = 10[/tex]
Multiply both sides by 6/5
[tex]\frac{5}{6}x (\frac{6}{5}) = 10(\frac{6}{5}) \\ x = 12[/tex]
Hence, the value of x is, x = 12.
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A motorboat takes 5 hours to travel 200 miles going upstream. The return trip takes 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? Rate of the boat still in water=Rate of the current=
Given,
Time taken by motorboat to going 200 miles upstream is 5 hours.
Time taken by motorboat to going 200 miles downstream is 4 hours.
At upstream,
The speed of boat is offosed by the speed of current.
At downstream,
The speed of boat is incraesed by the speed of current.
Consider,
The speed of boat is b.
The speed of current is c.
The speed is calculated as,
[tex]\begin{gathered} \text{Speed=}\frac{dis\tan ce}{time} \\ b-c=\frac{200}{5} \\ b-c=40 \\ b=c+40\ldots\text{.}\mathrm{}(1) \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} \text{Speed=}\frac{dis\tan ce}{time} \\ b+c=\frac{200}{4} \\ b+c=50 \\ b=50-c\ldots\text{.}(2) \end{gathered}[/tex]Substituting the value of b from equation (2) then,
[tex]\begin{gathered} c+40=50-c \\ 2c=10 \\ c=5\text{ mile per hour} \end{gathered}[/tex]Substituting the value of c in equation (1) then,
[tex]\begin{gathered} b=5+40 \\ b=45\text{ mile per hour} \end{gathered}[/tex]Hence, the speed of boat is 45 mile per hour and speed of current is 5 mile per hour.
what is another way to write the following expression?(8x+24)+(9y+81)A) 8(x+3)+9(y+9)B) 17(x+3)+(y+9)C) 8(x+16)+9(y+72)D) 17xy+105
The given expression is
[tex](8x+24)+(9y+81)[/tex]The greatest common factor of the first expression is 8, and the greatest common factor is 9. Let's factor out it
[tex]8(x+3)+9(y+9)[/tex]Hence, the answer is A.(-2, 8) (r, 4) when m=-1/2
Please help! I need explanation on why the answer is what it is.
The y-intercept of the given equation is (B) -2.
What is the y-intercept?When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0. A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.So, the y-intercept will be:
Equation: 3x + 4y = -8Plot the equation on the graph as follows:
We can clearly see that the line intersecting on the y-axis is (0, -2).So, the y-intercept will be -2.Therefore, the y-intercept of the given equation is (B) -2.
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Can someone please help me out with this
The value of UR = 13 mm
Given:
HGJI ≅ RSTU
proportional sides:
HG = JI
GJ = ST
JI = TU
IH = UR
From the figure:
IH = 13 mm
so IH = UR = 13
UR = 13 mm.
Therefore the value of UR = 13 mm.
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Which sequence is generated by the rule 3n - 1, where n represents the position of a term in the sequence? Select one: 1) 3, 6, 9, 12, 15... 2) 4,7, 10, 13, 16 ... 3) 4,5,6,7,8,9... 4) 2,5, 8, 11, 14 ..
The answer is 4 .
HELPPP!!!!!! MEEEEEEE!!!!!!!!! There are 2 parts to this! TY
Module 01: Project Option 1
Instructions
Scientific notation is a tool that is used frequently in science, including astronomy, chemistry, biology, and more. In this activity, imagine that you are a student intern at NASA and are researching information about travel within our solar system. You will complete a series of tasks using what you know about scientific notation and what you discover about our solar system to calculate distances that astronauts may use for their next trip to space.
Part 1
Using technology or other resources, research the average distance that each planet is from the Sun (in kilometers). Once you have found the distance, create a chart showing each planet's distance from the Sun. The Sun itself will not receive a label since it is your starting point. For example, Mercury is located an average of 57,909,000 km from the Sun, so on the chart, Mercury would be labeled with a distance of 57,909,000. Use the example of the chart below to help you get started:
Planet
Distance from Sun (in Km)
Distance in scientific notation
Mercury
57,909,000
5.7909 x10^7
venus
108,200,000
earth
149,600,000
mars
227,900,000
jupiter
778,300,000
saturn
1,427,000,000
uranus
2,871,000,000
neptune
4,497,100,000
Part 2
Answer the following questions using the data you have found. Show your work on all questions as indicated.
A. If a spacecraft was parked on Venus and needed to make a flight to Jupiter, how far would it need to travel? Show your work and provide your answer in scientific notation.
B. Mercury, Venus, and Earth are the three planets closest to the Sun. Would their combined distance from the Sun be greater or less than the distance from the sun to Neptune? Show your work and justify your answer.
C. If Earth was 10 times farther away from the Sun than it is now, which planet would it be closest to? Compare Earth's new distance to that planet. How far apart would they be in standard notation? How far apart in scientific notation? Show your work.
D. The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. Show your work. Convert your answer into scientific notation if necessary
Distance divided by speed equals time. Distance is calculated by subtracting the planets' distances.
What is meant by distance?The length of the line connecting two points is the distance between them. If the two points are on the same horizontal or vertical line, the distance can be calculated by subtracting the non-identical coordinates.
Distance = speed × time is the formula.
Therefore,
1. Assume that the sun and both planets are in line and that they are on the same side of the sun.
from the sun: Jupiter is 778,300,000
from the sun, Venus is 108,200,000
778,300,000 - 108,200,000 = 670,100,000
It would have to travel 670,100,000/6.701*10 with 8 square kilometers.
2. The three planets that are nearest to the sun are Mercury, Venus, and Earth.
Mercury's distance from the sun is 57,909,000 km.
Venus's distance from the sun is 108,200,000 km.
Earth's distance from the sun is 149,600,000 km.
combined distance between Mercury, Venus, and Earth
57,909,000+108,200,000+149,600,000 = 315,709,000
Because 315,709,000 km is less than 4,503,443,661 km, the distance from the sun to Neptune is less than the sum of the distances from the sun.
3. Assume that every planet is on the same side of the sun and is in alignment with it.
Earth is equal to Earth at ten solar distances is 149,600,000 km *10.
New distance to Earth = 1,496,000,000km
Earth would be closest to Saturn at its distance from the sun is
1,496,000,000 - 1,296,000,000 =67,000,000
and the two would be 67,000,000 km apart.
4. Notation used in science: with a 7 square kilometer. The space shuttle moves at around 28,000 km/h.
To locate Time
Time = Distance /speed
1,200,000,000 -28,000 =40,000 hrs.
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The Metzgers want to seed theirbackyard. The seed they selectcovers 375 m² per box. Howmany boxes of seed will theyneed to buy? Use the yarddiagram. Round any portionof a box to the next box?
In order to find how many boxed they need, first they need to know the area they will have to cover:
In order to find it, we have find the total area of the rectangle and take off the area of the House and the area of the shed:
We know that all those areas are rectangles, their area are found multiplying their sides lenght:
House area = 5m x 16m = 80m²
Shed area = 3m x 3m = 9m²
Since the lateral side of the total area is
5m + 16m + 5m = 26m, then
Total area = 26m x 50m = 1300m²
Then, the area they need to cover is
total area - house area - shed area = 1300m² - 9m² - 80m²
= 1211m²
Since the seed they select covers 375 m² per box, in order to find how many boxes they need, we just need to divide the area they are going to cover with this number:
1211m² ÷ 375 m² = 3.229
We round it to 4 boxes as indicated.
Answer: they need to buy 4 boxes of seeds
What is the behavior of the graph y=-³-52-3x+9 at each of its zeros?
Answer:
A.
Explanation:
Using a graphing tool, we the that the graph of y = -x³ - 5x² - 3x + 9 is
Then, the zeros are the points where the graph crosses the x-axis. Therefore, we can say that one of the zeros resembles a linear function and one resembles a quadratic function because the graph looks like a line at (1, 0) and it looks like a parabola at (-3, 0).
So, the answer is
A.
Find a monthly payment on a 48 month new car loan for $15,000 with a credit score of 700Find a monthly payment on a 48 month new car loan for $15,000 with a credit score of 600
We know that with a 700 credit score we pay $23 per $1000 financed, then the monthly payment will be:
[tex]\frac{15000+48\cdot15\cdot23}{48}=657.50[/tex]Therefore for a 700 credit score tour monthly payment is $657.50
Answer : $28.00
Step-by-step explanation: because it says on the chart the 590-619 it would be $28.00.
Reduce the rational expression to lowest terms.cd — c+d —1/ cd +c+d+1=
we have the expression
[tex]\frac{cd-c+d-1}{cd+c+d+1}[/tex]Group terms
[tex]\frac{(cd+d)+(-c-1)}{(cd+d)+(c+1)}[/tex][tex]\frac{d(c+1)-(c+1)}{d(c+1)+(c+1)}[/tex]factor (c+1)
[tex]\frac{(c+1)(d-1)}{(c+1)(d+1)}[/tex]Simplify
[tex]\frac{(d-1)}{(d+1)}[/tex]Let g(y)= - y2 +9y + 10. Find g(-2).
To find g(-2)
We will have to replace y in the function with -2
[tex]g(-2)=-(-2)^2\text{ + 9(-2) + 10}[/tex]g(-2) = - 1x 4 + 9 x -2 + 10
g(-2) = -4 -18 + 10
g(-2) = -22 + 10
g(-2) = -12
Answer:
Step-by-step explanation:
g(y) = -y^2 + 9y +10
g(-2) = (-2)^2 + 9(-2) +10
g(-2) = 4 - 18 + 10
g(-2) = -4
write the number in scientific notation0.000471
Given the number :
[tex]0.000471[/tex]The scientific notation is a method to the write the numbers as two parts
The first part is the number as between 1 and 9
the second part as 10 to powers
so,
[tex]0.000471=\frac{471}{100000}=\frac{471}{10}\cdot\frac{1}{10000}=4.71\cdot10^{-4}[/tex]
A teacher gives 5 points for correctly completing an "easy" homework question and 10 points for correctly completing a "challenge" question. To get an A on a homework assignment, a student must get at least 100 points. Using x to represent the number of easy questions and y the number of challenge questions, what inequality models the number of questions a student needs to complete correctly in order to earn an A on an assignment?
The inequality models the number of questions a student needs to complete correctly in order to earn an A on an assignment is x + y > 100
A teacher gives 5 points for correctly completing an "easy" homework question and 10 points for correctly completing a "challenge" question.
To get an A on a homework assignment, a student must get at least 100 points.
Let x to represent the number of easy questions and y the number of challenge questions,
x + y > 100
Therefore, the inequality models the number of questions a student needs to complete correctly in order to earn an A on an assignment is x + y > 100
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Solve the system of equations.
2x - 4y -z = 10
4x - 8y - 2z = 16
3x + y + z = 12
Answer:
no solution
Step-by-step explanation:
Divide both sides of the second equation by 2.
2x - 4y - z = 8
The first equation is
2x - 4y - z = 10
Subtract the simplified second equation from the first equation.
2x - 4y - z = 10
- 2x - 4y - z = 8
---------------------------
0 = 2
Since 0 = 2 is false, there is no solution.
Answer:no solution
Step-by-step explanation:
Which describes the Coriolis effect?(1 point)
Responses
the circulation pattern of air near the equator
the circulation pattern of air near the equator
the density of hot and cold air
the density of hot and cold air
the uneven heating patterns between the equator and the poles
the uneven heating patterns between the equator and the poles
the direction of air currents in the Northern and Southern Hemispheres
the direction of air currents in the Northern and Southern Hemispheres
The option that describes the Coriolis effect is D. the direction of air currents in the Northern and Southern Hemispheres.
What is the Coriolis effect?The effect of the Earth's rotation on weather patterns and ocean currents is known as the Coriolis effect. Storms swirl clockwise in the Southern Hemisphere and counterclockwise in the Northern Hemisphere due to the Coriolis effect. Circulating air is deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere as the Earth rotates on its axis. The Coriolis effect refers to this deflection.
The rotation of the Earth causes the Coriolis effect. Moving objects in the Northern Hemisphere tend to curve to the right of their intended paths; moving objects in the Southern Hemisphere tend to curve to the left of their intended paths. The Coriolis effect causes moving objects to accelerate or decelerate.
Therefore, based on the information given, it should be noted that the correct option is D.
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i need to answer this question then find the matching graph
we have
[tex]\begin{gathered} 5a-2\ge8 \\ \text{solve for a} \\ 5a\ge8+2 \\ 5a\ge10 \\ a\ge2 \end{gathered}[/tex]the solution is the interval {2, infinite)
In a number line the solution is the shaded area at right of a=2 (close circle)
therefore
the answer is
First option
The population of white-tailed deer is growing rapidly in the United States. In 1905 the population was approximately 5×105 and in 2000 the population was approximately 2×107.
How many times larger was the population of white-tailed deer in 2000 than it was in 1905?
40 times larger was the population of white-tailed deer in 2000 than it was in 1905 and it solved by using exponent formula.
What is the exponent?
The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 2³) means 2 x 2 x 2 = 8. 2³ and 2 x 3 = 6 are not equivalent.
Given that the population of white-tailed deer in 1905 was 5 × 10^5. The population of of white-tailed deer in 2000 was 2 × 10^7.
To find how many times larger was the population of white-tailed deer in 2000 than it was in 1905, divide 2 × 10^7 by 5 × 10^5
The value of the expression (2 × 10^7)/(5 × 10^5)
Applying the power rule a^m/a^n = a^(m-n)
=(2 × 10^(7-5))/5
=(2 × 100)/5
= 40
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27. A pyramid has a volume of 20 cubic inches and the
area of the base is 15 square inches. What is the
height of the pyramid?
what is 2+2?
I just cant figure it out.
Answer:4
Step-by-step explanation
If you have 2 fishes in an aquarium and add 2 more fishes to the aquarium you have 4 fishes! :D
Answer:
4
Step-by-step explanation:
Select all the relations that represent a function.A. (1,3), (2,5), (2,7) (4,9)B. (1,3), (2,5), (3, 7) (4,9)C. (1, 3), (1,5), (1, 7) (4,9)D. (1,3), (2, 3), (3, 3) (4, 3)E. (1, 2), (2,5), (2, 1) (4,5)
Explanation:
A relation is a function if and only if for each value of x there's only one value of y. In other words, if we find one value of x more than once, the relation is not a function.
Relation A is not a function because x = 2 shows up twice: (2, 5) and (2, 7)
Relation C is not a function because x = 1 shows up three times: (1, 3), (1, 5) and (1, 7)
Relation E is not a function because x = 2 shows up twice: (2, 5) and (2, 1)
Relations B and D have only one time each value of x
Answers:
how do i find the distance between -6 and 3 in a number line
Find the absolute value in the difference of the coordinates.
evaluate each inverse trig expression below. include a diagram of a unit circle justifying your solution.
The given expression :
Find the slope intercept of the line that passes through 0,-5 and has a slip of -1/2
The slope intercept of line with point (0,-5) and slope=-1/2 will be x+2y=-10 as the definition of slope intercept form is "The meaning of SLOPE-INTERCEPT FORM is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept."
What is slope intercept form of line?Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are immediately visible. This form is frequently known as the y = mx + b form. Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.
Here,
Slope intercept form of line,
y=mx+ b
(x, y)=(0,-5)
m=-1/2
-5=-1/2*0+b
b=-5
y=mx+b
y=-1/2x+5
2y+x=-10
Since the definition of slope intercept form is "The meaning of SLOPE-INTERCEPT FORM is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept," the slope intercept of a line with point (0,-5) and slope=-1/2 will be x+2y=-10.
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Below are the data collected from two random samples of 500 American adults on the number of hours they spend doing leisure and sports activities per day (rounded to the nearest hour):Number of hours spent doing leisure and sports activities per day 1 2 3 4 5Sample A: Number of adults 70 90 135 140 65Sample B: Number of adults 80 80 130 135 75Dan concludes that adults spend a mean of 3 hours each day doing leisure and sports activities. Bret thinks the mean is 4 hours. Who is correct—Dan or Bret? Explain your answer in two or three sentences.
Dan is correct, because if you spend a mean of 3 hours each day doing leisure and sports activities, you have to add people that spend 4 and 5 Hours and verify that addition will be more than 51% of 500 people (250) and it its the case, adding 340 for both samples.
A line passes through point A(2,5) and B(-8,-4). Find the slope of the line.
We are going to use the formula for the slope of the line with points A(2,5) and B(-8,-4). x1= 2, x2=-8, y1=5 and y2=-4
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-4-5}{-8-2}=\frac{-9}{-10}=\frac{9}{10}[/tex]The slope of the line is 9/10
According to the statements provided, name the lines that are parallel to each other. If there is notenough information to conclude parallel, write "not enough info" and explain why.
For the given figure:
According to the statements provided, we will name the lines that are parallel to each other:
1) ∠1 ≅ ∠3; The parallel lines are (c, d)
2) ∠6 ≅ ∠9; the parallel lines are (a, b)
3) ∠6 is supplementary to ∠10; the parallel lines are (a, b)
4) ∠1 ≅ ∠11: Not enough info
5) ∠5 is supplementary to ∠8; the parallel lines are (c, d)
6) ∠3 ≅ ∠11; The parallel lines are (a, b)
7) ∠1 ≅ ∠6; Not enough info
8) ∠1 ≅ ∠14: the parallel lines are (a, b)
9) ∠15 is supplementary to ∠16; Not enough info
10) ∠13 ≅ ∠15; the parallel lines are (c, d)
what is 4.4.4 as an exponent
Answer:
4*4*4=4^3
Step-by-step explanation:
4 is multiplied by itself 3 times so it's to the third power which equals [tex]4^{3}[/tex]
Ms.Chen announced the grade distribution for this week's book reports. Of the 20 students in the class, 7 received A's for their book reports, 8 received B's and 5 received C's. One of the students in the class will be chosen at random to read his or her book report to the class. What is the probability that the student that will be chosen had received an A for the book report?
Answer:
7/20
Step-by-step explanation:
7 students received an A out of the total 20.
Please help! I need explanation on why the answer is what it is.
I can’t understand slope and graphs :(
The slope (m) that passes through the given points (4, 3) and (6, 7) is (B) 2.
What is the slope?The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on a straight line, a slope can be determined using a variety of approaches. A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).So, the slope will be:
Points are: (4, 3) and (6, 7)Slope formula: m = y2 - y1/x2 - x1Now, calculate as follows:
m = y2 - y1/x2 - x1m = 7 - 3/6 - 4m = 4/2m = 2Therefore, the slope (m) that passes through the given points (4, 3) and (6, 7) is (B) 2.
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