In grade 7, one common method to solve absolute value equations is by isolating the absolute value on one side of the equation and then solving for the two possible solutions.
Here is a step-by-step process to solve an absolute value equation:
Isolate the absolute value on one side of the equation by adding or subtracting the same value to both sides of the equation.
For example, |x| = 3 can be rewritten as x = 3 or x = -3
Split the equation into two separate cases, one for when the value inside the absolute value sign is positive, and one for when it is negative.
Solve each case separately.
Check your solutions by plugging them back into the original equation and making sure they are valid solutions.
Write your answer in interval notation if the solutions are continuous or list them as individual values if they are not.
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Another soccer team had tryouts for the fall season. This team had 60 players show up for the tryouts and had 9 players return for a second evaluation. What percent of the players at the tryout were asked back for a second evaluation? part = whole = percent= Substitute and solve:
Find the area of the circle with circumference πd cm
Answer:3.41
Step-by-step explanation:it is pie
how many ways are there for $8$ people to sit around a circular table if none of alice, bob, and eve (three of the $8$ people) want to sit next to each other? two seatings are considered the same if one is a rotation of the other.
There are 7!/3! ways for 8 people to sit around a circular table if Alice, Bob, and Eve do not want to sit next to each other.
What is rotation?Rotation is the process of rotating an object in two or three dimensions around an axis. This axis can be a point in space, a line, or a plane. Rotation can also refer to a continuous change of direction, such as the rotation of the Earth around its axis. Rotation can be described using terms such as clockwise, counterclockwise, and angular velocity. Rotation can also be described using mathematical equations, such as Euler's rotation theorem. Rotation can be used to create symmetry in design, or to create motion in an animation.
This is because we can pick any of the 7 people to be seated first, then any of the 6 people to be seated second, then any of the 5 people to be seated third, and so on. However, since Alice, Bob, and Eve do not want to sit next to each other, we must divide the 7! by 3! to account for the fact that the order in which Alice, Bob, and Eve are seated does not matter. The 3! accounts for the fact that we could arrange the three of them in 3! = 6 different orders. Therefore, the total number of ways for 8 people to sit around a circular table if Alice, Bob, and Eve do not want to sit next to each other is 7!/(3!) = 840 ways.
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bc pills are about 99% effective in perfect use, about how effective are they in typical use (because people may forget to take them at the same time every day and other reasons due to human error)?
The tablet is 99% effective if used correctly.
However, since individuals make mistakes and it's easy to forget or overlook pills, the actual effectiveness of the pill is only about 93%. Accordingly, 7 out of every 100 women who take pills annually become pregnant.
Depending on the type of pills you're utilizing and when you start taking them. The birth control pill can be started on any day of the month. However, for up to 7 days, you might need to use a backup birth control method, such as condoms, depending on when you start and the type of pill you're taking.
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You need to get to the mall to buy some new shoes, but you're not sure how to get there. Your city is a nxm rectangular grid of blocks, where you home is located at the coordinates (x1, y1) and the mall's location is (x2, y2).
To get to the mall, you'll need to find the shortest path from your home to the mall.
The Manhattan Distance formula is an efficient way to calculate the shortest path between two points on a rectangular grid. The formula is as follows:
MD = |x1-x2| + |y1-y2|
Where MD is the Manhattan Distance, x1 and y1 are the coordinates of your home, and x2 and y2 are the coordinates of the mall.
To find the shortest path, simply plug in the coordinates for your home and the mall into the formula and calculate the Manhattan Distance. The result is the shortest number of blocks you need to travel to get to the mall.
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Which best describes how the government tried to prevent the New York Times from publishing articles on the Vietnam War? kaitlannalniii avatar
kaitlannalniii
07/19/2016
Mathematics
High School
answered • expert verified
Which best describes why the government tried to prevent the new york times from publishing articles on the vietnam war?
On solving the provided question, we can say that The pieces were dangerous to interests in national security
what is interest ?Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily.
The pieces were dangerous to interests in national security . A general who opposed the US involvement in Vietnam sent the Times a number of documents from 1971 that have come to be known as the "Pentagon Papers." On the basis of security concerns, the US attempted to prevent them further dissemination but failed.
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pedro bought 4 pounds of chopped meat for a barbecue party. he plans to make 1/5 pound burgers for his guests. how many guests can he feed?
Answer:
20
Step-by-step explanation:
4 ÷ 1/5 Multiply by the reciprocal (turn the fraction upside down)
4 x 5 = 20
A graphical plot with sales on the Y axis and time on the X axis is a
a. Scatter diagram.
b. Trend projection.
c. Radar chart.
d. Line graph.
e. Bar chart.
A graphical plot with sales on the Y axis and time on the X axis is a:
a. Scatter diagram.
What is Scatter diagram?Using a single variable on each axis, the scatter diagram plots pairings of numerical data in an effort to identify any relationships between them. A line or curve will be formed by the points if the variables are correlated. The points will hug the line closer the more highly correlated the data is. You may also visualise the strength of any relationship. If the researcher believes there may be a correlation, a line of greatest fit can also be drawn on the graph.
Data points are shown on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another.
Thus, correct option: a
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What are acute triangles called?
Answer: acute-angled triangles.
Step-by-step explanation:
Equilateral Acute Triangle. An equilateral acute triangle is that type of acute triangle that has all its interior angles measuring 60°.
Isosceles Acute Triangle.
Scalene Acute Triangle
pls help
If the eggs in a basket are removed six at a time, five eggs will remain. If the eggs are removed five at a time, only four will remain. If the eggs are removed four, three, or two at a time, then three, two, and one egg will remain, respectively. But if the eggs are taken out seven at a time, no eggs will be left over. What is the least number of eggs that could be in the basket?
Answer:
119 eggs
Step-by-step explanation:
To start off, we know that this number has to be of some multiple of 7. Because if the eggs are taken out 7 at a time, and no eggs are left over, then the total number of eggs can be divisible by 7. Because there is however a multiple if you take out the eggs 2-6 times, there are eggs left over. The smallest multiple of 7 we can test is simply 7. To check, we can start with dividing 7 by 6 and getting a remainder of 1 instead of 5. So we know that 7x1 doesn't work.
The next smallest multiple of 7 that isn't multiplied from 2-6 is 7x7 to get 49. from here we can check that 49/6 = 8 r1 (r meaning remainder). So we know that 7x7 can't work. From here, the next smallest number would be 7x11.
7x11 = 77. 77/6 is 12 r5. This so far looks good. Now we can try 5. 77/5 = 15 r2. This doesn't work, so we try the next largest number which is 7x13 which is 91.
91/6 = 15 r1 which doesn't work. Next we try 7x17 which is 119. 119/6 is 19 r5 (looks good), 119/5 = 23 r4 (looks good), 119/4 is 29 r3, 119/3 is 39 r2, and 119/2 is 59 r1! Which means our answer is that the least number of eggs in the basket is 119.
The hypothesis becomes the basis of
what?
A. as atistical analysis
B. the data to interpret
C. alw
4
D. the experiment
Answer:
D. the experiment
Step-by-step explanation:
The hypothesis becomes the basis of the experiment.
Determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.
–x+y= –5
3x+5y=15
Answer:
(5, 0)
Step-by-step explanation:
The slope of the first line is -(-1 / 1) = 1.
The slope of the second line is -(3 / 5) = -3/5.
Since the lines have different slopes, they intersect at a single point. Therefore, there is only one solution. To find it, solve the system of equations.
Using elimination, multiply the first equation by 3 and add it to the second.
-3x + 3y = -15
3x + 5y = 15
-------------------
8y = 0
y = 0
Using substitution, find x:
-x + 0 = -5
x = 5
The solution is (5, 0).
Your team scores 10 points in the first game, 3 points in the second game, 2 points in the third game, 5 points in the fourth game, and 0 points in the fifth game. What was the mean number of points your team scored for all 5 games?
The mean number of points for all 5 games is 4 points.
What is arithmetic mean?The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.
The formula for the mean of a given set of data is as follows:
Mean = Sum of Observations/Total number of observations
As per the question,
Here, n = 5
⇒ ∑x = Sum of Observations
⇒ ∑x = 10 + 3 + 2 + 5 + 0 = 20
Mean = ∑x/n
Mean = 20/5
Mean = 4
Hence, the mean of the given data is 4.
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a cell phone plan has a basic charge of $45 a month. the plan includes 500 free minutes and charges 10 cents for each additional minute of usage. write the monthly cost c (in dollars) as a function of the number x of minutes used.
The cost function is [tex]C(x)=[/tex] [tex]\left \{ {{35} \atop {(0.1t-5)}} \right.[/tex] .
The application of the idea of kinds of functions is the foundation of this issue. We will create and classify the sort of function we have using the provided information.
According to the given information, the cell phone plan has a basic charge of $45 a month. The plan includes 500 free minutes and charges 10 cents for each additional minute of usage.
Let t be the number of minutes the cell phone is used.
So, for 0≤t≤500 it will cost only the basic charge of $45.00
For an additional minute of usage, it costs 10 cents or $0.1 in addition to the basic charge. So, our function looks like:
f(x)=45+0.1(t-500)=45+0.1t-50 = (0.1t-5), for 500 ≤ t ≤ 700.
Thus, the cost function looks like:
C(x) = [tex]\left \{ {{35} \atop {(0.1t-5)}} \right.[/tex]
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what is the answer for the probability question?
Answer:
0.15
Step-by-step explanation:
Factors of 12 are 1, 2, 3, 4, and 6.
Only 5 is not a factor of 12.
The probability of rolling a 5 is 15 / 100, or 0.15, or 15%.
The difference of twice a number and 9 is at least -25.
Answer:
x≥-8
Step-by-step explanation:
Because we don't know the first number mentioned, we can name it as x
Since the problem starts off with "twice a number" so we mark it as 2x and then it states to take the difference of that number and 9. So the new problem we have is 2x-9=?. Now, the answer that we have is at least -25, so the answer is no longer an equal sign, but a greater-than or equal-to sign. Making our new equation 2x-9≥-25. Now we can act as if its a normal equation, adding 9 to both sides making it 2x≥-16, divide both sides by 2 to get x≥-8.
An extra step to ensure our answer is more than or equal to -8 is by plugging in -8 AND another number that is more than -8. 2(-8)-9=? which we would find that ? is -25. A number that is greater than -8 could be -1, which we would test by doing 2(-1)-9=?. ? would be equal to -11 so we know that our final answer of x≥-8 is correct.
You saved 17 dimes and your brother saved 8 dimes. How many more dimes did you save? Your answer is (?).
Answer:
p
Step-by-step explanation:
no of dimes you have =17
no of dimes your brother have=8
now
no of dimes more you have save =17-8
=9
hence you have saved 9 more dimes
Triangle ABC is transformed to triangle A′ B′ C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0. A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0. Which equation shows the correct relationship between the measures of the angles of the two triangles? (1 point) The measure of angle CAB = The measure of angle C prime B prime A prime The measure of angle BCA = The measure of angle A prime B prime C The measure of angle CAB = The measure of angle C prime A prime B prime The measure of angle BCA = The measure of angle C prime A prime B prime
The correct option when Triangle ABC is transformed to triangle A′ B′ C is A.The measure of angle BCA = The measure of angle C prime A prime B prime.
How to illustrate the triangle?Triangle ABC is changed into triangle A′B′C′ and on the x- and y-axes, a coordinate grid ranging from -4 to -4 to 4 is displayed. A is at ordered pair negative 1, 3, B is at ordered pair 0, 1, and C is at ordered pair negative 3, 0 in the triangle ABC.
A triangle Primes A, B, and C have A prime is at ordered pair minus 1, minus 3, B prime is at ordered pair minus 0, and C prime is at ordered pair minus 3, 0.
A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.
Therefore,
<BAC = <B'A'C'
<ABC = <A'B'C'
<ACB = <A'C'B'
In this case, the correct option is A.
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four marbles are chosen from the jar with replacement. what is the probability that they are all white?
The probability that four marbles are chosen from the jar with the replacement and that they are all white is p^4 (p raised to the fourth power).
If four marbles are chosen from a jar with replacement, the probability that they are all white is (probability of drawing a white marble)^4.
If the marbles are chosen with replacement, the probability of choosing a white marble on any one draw is the same as the proportion of white marbles in the jar. Let's call this probability p. The probability that all four marbles chosen are white is p^4 (p raised to the fourth power).
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what is the area of a regular octagon inscribed in a circle of radius 4 meters? 5.657 square meters 6.807 square meters 45.255 square meters 54.458 square meters
The area of a regular octagon inscribed in a circle of radius 4 meters is 45.255 square meters. So, option C is correct
An octagon is a polygon with 8 sides, and a regular octagon has all sides of equal length. To find the area of a regular octagon inscribed in a circle of radius 4 meters, we can use the formula:
Area = (2 * (4^2) * (1 + sqrt(2))) / (4 * tan(pi/8))
Plugging in the values we get:
Area = (2 * (4*cos(pi/8))^2 * (1 + sqrt(2))) / (tan(pi/8)) = 16 * (1 + sqrt(2)) * (sqrt(2) / sqrt(2+ sqrt(2)))
= 8 * 1/2 * 4 * 4 * sin45°
= 32√2
= 45.255 square meters.
Therefore, the area of a regular octagon inscribed in a circle with a radius of 4 meters is 45.255 square meters.
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Solve the system of equations using substitution.
=================================================
Work Shown:
Plug the first equation into the second equation.
2x - y = 5
2x - (3x-1) = 5
2x - 3x+1 = 5
-x+1 = 5
-x = 5-1
-x = 4
x = -4
Use this to find the value of y.
y = 3x-1
y = 3*(-4)-1
y = -12-1
y = -13
The solution is (x,y) = (-4,-13)
This points to choice A as the final answer.
You can use graphing software like Desmos or GeoGebra to confirm that the two lines intersect at (-4,-13).
How many and what type of solutions does 4x² 12x 9 0 have?
The equation [tex]4x^2+12x+9=0[/tex] has only one solution, and the type of solution is rational.
Finding the value of the given equation's unknown variables is a step in the equation-solving process. The value of the variable satisfies the requirement that the two expressions are equal. When a linear equation has one variable, there is only one solution; when there are two variables, there are two solutions. A quadratic equation's solution yields two roots. To solve an equation, a variety of techniques and steps are used. Let's go over each method for solving an equation in detail one by one.
Here steps for solving an equation are given below.
[tex]4x^2+12x+9=0\\4x^2+6x+6x+9=0\\2x(2x+3)+3(2x+3)=0\\(2x+3)(2x+3)=0\\2x=-3\\x=\frac{-3}{2}[/tex]
Here both solutions are same so the equation [tex]4x^2+12x+9=0[/tex] has only one solution and the type of solution is a rational solution.
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Kent multiplies both sides of the equation below by an expression. Then he moves all the terms to one side of the equal sign in the resulting equation. Which equation must he solve now
The equation must satisfies the Kent calculation is k² - 8k + 12 = 0
The term equation in math is called as a mathematical expression that contains an equals symbol.
Here we have given that Kent multiplies both sides of the equation below by an expression.
And then he moves all the terms to one side of the equal sign in the resulting equation.
Here we have the given equation is
=> k+12/k= 8
When we multiply both sides by k.
=> k² + 12 = 8k
Now we have to subtract 8k from both sides to move all the terms to one side of the equal sign then we get
=> k² + 12 - 8k = 0
Hence the required equation is k2 - 8k + 12 = 0.
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urgent help needed w this pls
Answer:
Based on the given information, we know the following:
Solid A is formed by joining one hemisphere to the frustum of a cone.
Solid B is formed by joining the other hemisphere to the small cone that was removed from the large cone.
The volume of solid A is 6 times the volume of solid B.
We can use the formulas for the volume of a hemisphere and a frustum of a cone to represent the volumes of solids A and B.
The volume of a hemisphere is (2/3)πr^3, where r is the radius of the hemisphere.
The volume of a frustum of a cone is (1/3)πh(R^2+r^2+Rr), where h is the height of the frustum, R is the radius of the larger base and r is the radius of the smaller base.
The volume of a cone is (1/3)πr^2h
Let's call the height of the frustum h, the radius of the large base R and the radius of the small base r
We can set up the equation: (2/3)πr^3 = 6((1/3)πr^2h + (1/3)πR^2h + (1/3)πRrh)
After simplifying, we get:
2h = 12r + 12Rh + 6Rr
We know k = (R/r)^(1/3)>(7)^1/3, we can substitute it into the equation:
2h = 12r + 12rk + 6rk^2
Solving for h, we get:
h = 6rk + 6rk^2
So h is expressed in terms of k and r.
The table shows the distance why in meters that a person runs an ex seconds graph the line that passes through the points in a table then write an equation that represents the line (1,4.5),(2,9),(3,13.5).
How to find the answer
s= 7; 6s²
Answer:
294
Step-by-step explanation:
We will take our equation, and substitute in 7 for s, wherever we see it, so we have:
[tex]6 * 7^{2}[/tex]
Simplifying, we have:
[tex]6 * 49[/tex]
Which finally we multiply to:
6 * 49 = 294
So, your answer is 294.
Hope this helped!
If you dissolved 50g of sugar in 30g of water, what would the sugar concentration be
Make y the subject of the formula.- A=r(y + 2 ) / 5
[tex] \frac{5a}{r} \: - 2 = y[/tex]
Step-by-step explanation:
A = r(y +2) /5
A×5 = r(y+2)
(5A)/r = y+2
(5A)/r - 2 = y
•: y = (5A)/r - 2
(only applicable when
[tex]a = \frac{ry + 2r}{5} [/tex]
expand)
Graph the system of equations 8x+8y=64 2x-2y=-4
To graph a system of equations, you can first solve each equation for y, and then plot the solutions on the same coordinate plane.
For the first equation, 8x + 8y = 64, we can solve for y by subtracting 8x from both sides, which gives us 8y = 64 - 8x. Then we divide both sides by 8 to get y = (64 - 8x)/8.
For the second equation, 2x - 2y = -4, we can solve for y by adding 2x to both sides, which gives us 2y = 2x - 4.
So the solutions for y in the first equation are:
y = (64 - 8x)/8
and in the second equation are:
y = 2x - 4
We can now plot these two lines on the same coordinate plane. The point of intersection of these two lines will be the solution of the system of equations
Answer is attached in the graph.
Step by step
The easiest way to solve these is to graph on an internet or app graphing calculator.
To graph by hand you need to simplify them and arrange in slope intercept form y=mx + b
(#1)
8x + 8y = 64 all are divisible by 8
8/8x + 8/8y = 64/8
Simplify
x + y = 8
Arrange in slope intercept form
subtract x from both sides to isolate y
x - x + y = -x + 8
y = -x + 8
We plot the first point of y intercept of 8 (0,8) and plot the 2nd point by slope of -1/1 or
( 1, -1). Draw your line
(#2)
2x - 2y = -4 are all divisible by 2
2/2x - 2/2y = -4/2
Simplify
x - y = -2
Arrange in slope intercept form
subtract x from both sides to isolate y
x - x - y = -x -2
Simplify
-y = -x -2
Change the signs by multiplying all by -1
y= x +2
We plot the first point of y intercept
of 2 (0, 2) and plot the 2nd point by slope of 1/1 or ( 1, 1). Draw your line
Now you can find the solution is where the lines intersect. At (3, 5)
See my attached graph for your two line equations below
y = x + 2
y = -x + 8
If x = 11 , evaluate the following expression: x + 4
Answer:
Substitute x = 11 to x + 4, you get,
11 + 4 = 15
Thanks
[tex]x+4[/tex] when x is equal to 11
Evaluate:
[tex](11)+4[/tex]
[tex]=15[/tex]
