Answer:
[tex]x+3[/tex] if [tex]x>2[/tex]
Step-by-step explanation:
Recall some following basic ideas about absolute value:
[tex]|0|=0[/tex] or I guess [tex]-(0)=0[/tex]
[tex]|3|=3[/tex]
[tex]|-3|=-(-3)[/tex] or just [tex]3[/tex] but there is a reason why I wrote it the way I did.
You see that the absolute value returned the same value if the value was positive.
You see that the absolute value returned the opposite value if the value was negative.
You can include 0 in either.
Let's look at [tex]|x+3|[/tex] alone for a second.
*[tex]|x+3|=x+3[/tex] if [tex]x+3[/tex] is positive or zero.
When is [tex]x+3[/tex] positive or zero? [greater than or equal to 0]
[tex]x+3\ge 0[/tex]
Subtract 3 on both sides
[tex]x\ge -3[/tex]
*[tex]|x+3|=-(x+3)[/tex] if [tex]x+3[/tex] is negative or zero.
When is [tex]x+3[/tex] negative or zero? [less or equal to 0]
[tex]x+3\le 0[/tex]
Subtract 3 on both sides
[tex]x\le -3[/tex]
So looking at the bullet points (the *), [tex]x>2[/tex] fits into the first inequality.
Therefore, [tex]|x+3|=x+3[/tex].
Nick is practicing kicking field goals. His first kick is modeled by the parabola that passes through (0,0), (1,6.86), and (2,3) where x is the number of seconds that the ball is in the air, and y is the height of the ball in yards.
Answer:
6.3 yards high
Step-by-step explanation:
The three given points are (0,0), (1,6.86), and (2,3). Use these values in f(x) = ax2 + bx + c.
For (0,0), 0 = 0 + 0 + c.
So, c = 0.
For (1,6.86), 6.86 = a + b + c. Since c = 0:
a + b = 6.86(equation 1)
For (2,3), 3 = 4a + 2b + c. Since c = 0:
4a + 2b = 3(equation 2)
Multiply equation 1 by 2, and subtract the result from equation 2:
2a + 2b = 13.72
4a + 2b - (2a + 2b) = 3 - 13.72
2a = -10.72
a = - 5.36
Plug this value into equation 1:
-5.36 + b = 6.86
b = 12.22
So the function is f(x) = -5.36x2 + 12.22x.
When the ball hits the ground, the height is 0, or f(x) = 0:
Use the function to determine the height of the ball, f(x), after x = 1.5 seconds.
f(x) = -5.36x2 + 12.22x
= -5.36(1.5)2 + 12.22(1.5)
= 6.27
0 = -5.36x2 + 12.22x
0 ≈ x − 2.27(Divide both sides by -5.36x.)
x ≈ 2.27 ≈ 2.3
So, the ball will be about 6.3 yards high after 1.5 seconds.
The range of a projectile that is launched with an initial velocity v at an angle of with the horizontal is given by R-
where g is the acceleration due to gravity or 9.8 meters per second squared. If a projectile is launched with an initial velocity of 15
meters per second, what angle is required to achieve a range of 20 meters? Round answers to the nearest whole number.
Answer: theta ≈ 30°
Step-by-step explanation:
It said on the "show me" box at the bottom of the screen :)
The required angle of the projectile motion having range 20 m and initial velocity 15 m is 30.29°
Range of the projectile motion:
The formula for finding projectile motion is given by
Range R = [tex]\frac{v^2sin2\theta}{g}[/tex]
where v is the initial velocity and g is acceleration and [tex]\theta[/tex] is the projectile angle of the object
How to calculate angle ?If we have given range and initial velocity with acceleration then by substituting above range formula we can find angle of the projectile
Here we have given that
R = 20 m
v = 15 m/s
g = 9.8 m/s^2
Therefore
[tex]20=\frac{15^2sin2\theta}{9.8}[/tex]
[tex]sin2\theta=\frac{20(9.8)}{225}[/tex]
[tex]\theta[/tex] = 30.29
This is the required angle of the projectile
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-18x-17=-53
( Complete the steps:)
1. Write the original equation
2. Apply the Addition Property of Equality.
solve step by step
-18x-17=-53 /add 17 to both sides
-18x-17+17=-53+17
-18x=-36
x=(-36)/(-18)
x=2
Mrs. Anderson surveyed her class and asked each student, "How many hours do you spend
playing sports per week?" The results are below.
0,0,0,0.2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,8,12
Part A: Construct a dot plot of the data and choose the best graph from the choices below.
Part B: What observations can you make about the shape of the distribution?
Part C: Are there any values that don't seem to fit? Justify your answer.
Answer: Part A is the graph with 4 dots for 0, 2 dots for 2, 10 dots for 4, 9 dots for 6, 2 for 7(in between 6 and 8) 1 dot for 8, and 1 dot for 12.
Part B: Answer: Most are clumped together and smaller than 8, with one data point far away from the others.
Part C: Answer; 12 hours seems to much higher than the other data values.
Step-by-step explanation: Hope that helped:) I just did it and checked and it’s correct. Have a good day!
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
x+5 x+4
The area of a rectangle is represented by the multiplication of its length and width. For a rectangle with dimensions 'x + 5' and 'x + 4', the area is given by the standard form polynomial ' [tex]x^2 + 9x + 20[/tex]'.
Explanation:The area of a rectangle is calculated by multiplying the length by the width of the rectangle. Here, the length and width of the rectangle are given by the expressions 'x + 5' and 'x + 4'. Therefore, to find the area, you multiply those two expressions together:
(x + 5) * (x + 4)
When you multiply these two expressions, you get:
[tex]x\times x + 4\times x + 5\times x + 5\times 4 = x^2 + 9x + 20[/tex]
This is the polynomial in standard form that represents the area of the rectangle,
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PLEASE help me it is about rate tables.
Answer:
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
you take 18-12 wich gives you 6, then you do 18+6 wich equals 24. hope this helps. good luck in the future :)
What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 5:8? Round to the nearest tenth, if necessary.
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1
(–2.2, –6.3)
(–2.4, –6.4)
(2.7, –0.7)
(1.2, –4.7)
Answer: D) (1.2,-4.7)
Step-by-step explanation:
plug in the end corrdinates like it says in the equation that the problem gives you.
The x and y-coordinates of the point C will be equal to (1.2, -4.7).
What is a coordinate system?Using one or even more integers, or coordinates, a coordinate system in geometry establishes a unique way to locate points or other geometrical objects on a manifold, such as Euclidean space.
The order of the values is important, and they can sometimes be distinguished by their place in an arranged tuple or by a letter, such as "the x-coordinate."
As per the given information in the question,
Coordinates are the location of a point in an (x,y) plot.
The given coordinates are:
A = (7,-2)
B = (-8,-9)
m:n = 5:8
Use the formula given below,
(x, y) = 1/(m + n)(nx₁ + mx₂, ny₁ + ny₂)
(x, y) = 1/(5 + 8)[5(-8) + 8(7), 5(-9) + 8(-2)]
(x, y) = (1.2, -4.7)
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Boxes A and B contain some counters.is
8y + 1
counters
6y + 9
counters
Box A
Box B
The number of counters in each box is the same.
Work out the value of y
Answer: y=4
Step-by-step explanation:
8y+1=6y+9 -Because y is equal the equations are as well.
2y+1=9- Take 6y to the other side by -6y
2y=8-Take one over by -1
y=4-Divide 8 by 2 to get y=4
Answer:
The value of y is 4
Step-by-step explanation:
If the some of the counters in each box are the same, then A = B
If A is 8y + 1 and B is 6y + 9
Since A = B, we can say
8y + 1 = 6y + 9
Collecting like terms, we will have
8y - 6y = 9 - 1
2y = 8
Dividing both sides by 2, we will have
y = 8/2
y = 4
The distance between home and school is 4.5 miles. On a map it shows the distance to be 9 cm. What is the scale?
The scale factor for the measurements on the map would be 11 x 10 ⁻⁵.
What is scale factor?Scale factor is used to compare the size of two objects. Mathematically, we can write -
{K} = S{O1}/S{O2}
Given is that the distance between home and school is 4.5 miles. On a map it shows the distance to be 9 cm.
The distance between home and school : 4.5 miles.
On the map the distance between home and school is 9 cm.
We can write the scale factor as -
{K} = (9 x 5.5 x 10 ⁻⁵)/4.5
{K} = 11 x 10 ⁻⁵
Therefore, the scale factor for the measurements on the map would be 11 x 10 ⁻⁵.
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When a movie is released to theaters, production companies monitor revenues from individual cities for that movie on its release date. Below is a scatter plot that shows 10 different movie revenues from opening night in both Tallahassee and Gainesville. Revenue is reported in millions of dollars.
Part B: According to the model found in Part A, if a movie brought in $32.2 million in total revenue in Tallahassee, what would the expected revenue be for Gainesville? (Round your answer to the nearest thousandths *three decimal places*)
Answer:
$13.299 million
Step-by-step explanation:
We need the model from Part A to answer Part B to three decimal places,
The point marked by the blue arrow is clearly an outlier. I ignored it in "eyeballing" the best-fit line.
My line has four points above and five points below the line,
You probably had to use a statistical calculator to get the equation for the line of best fit.
Assume it was
y = 38.9016 - 0.7951x
You would use that equation to predict y when x = 32.2.
y = 38.9016 - 0.7951 × 32.2 = 39.1588 - 25.6022 = 13.299
If a movie brought in $32.2 million on opening night in Tallahassee, it should bring in $13.299 million in Gainesville.
The expected revenue be for Gainesville is $13.299 million.
Calculation of the expected value:here we assume that
y = 38.9016 - 0.7951x
Here that equation to predict y
when x = 32.2.
So,
y = 38.9016 - 0.7951 × 32.2
= 39.1588 - 25.6022
= 13.299
hence, The expected revenue be for Gainesville is $13.299 million.
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Last month, took Lucas 32 minutes to run 3 miles. This month is took him 28 minutes. Find the percent of change.
Answer:12.5%
Step-by-step explanation:
Percentage=(32-28)/32 x 100
Percentage=4/32 x 100
Percentage=(4x100)/32
Percentage=400/32
Percentage=12.5%
4x + 3y = 6
-4x + 2y = 14
Solve the system of equations.
Answer:
Systems of equations equals (-1.5, 4)
Step-by-step explanation:
1. isolate the y in both equations
2. a. 4x+3y=6
3y=-4x+6
y=-4/3x+2
b.
2y=4x+14
y=2x+7
3. Solve the system of equations
-4/3x+2=2x+7
2=3 1/3x+7
-5=3 1/3x
-1.5=x
4. Solve for y by plugging x into one equation
y=2x+7
y=2(-1.5) + 7
y= -3+7
y=4
5. Systems of equations equals (-1.5, 4)
6. If this was helpful for you, it would mean a lot if you could click the braniest button on my answer so I could move up in the ranks. Good luck!
Answer:
your answer would be x= -3/2
help!! study island
Answer:
The answer is b
Step-by-step explanation:
If a bill cost $125. And they leave a $21.25 for a tip what percentage did they tip
Answer:
17%
Step-by-step explanation:
Divide $21.25 by $125
Find the sum of 10x^2-10x-6 and x+6.
Answer:
10x²−9x
Step-by-step explanation:
10x²−10x−6+x+6
=10x²−10x−6+x+6
Combine Like Terms:
=10x²−10x−6+x+6
=(10x²)+(−10x+x)+(−6+6)
=10x²−9x
Hope this helps!
The sum of the equations 10x^2 - 10x - 6 and x + 6 is achieved by combining like terms, which results in 10x^2 - 9x.
Explanation:To find the sum of 10x^2-10x-6 and x+6, you combine the like terms from each equations. You do this by adding the coefficients of like terms, which are terms with the same variable. In this case, the variable x is the like term. Let's do it step by step:
First, identify the like terms. In the expression 10x^2 - 10x - 6, 10x^2 is a term, -10x is a term, and -6 is a term. In the expression x + 6, x is a term and 6 is a term.Combine the terms that have similar variables. The coefficients of 10x^2 and x are 10 and 1 respectively. Since there's no like term for 10x^2, carry it as it is. The coefficients for -10x and x are -10 and 1. When you add these together, you get -9x (-10 + 1 = -9).Combine the constant terms -6 and 6. When you add these, you get 0 (-6 + 6 = 0).The sum of the two expressions 10x^2 - 10x - 6 and x + 6 therefore is 10x^2 - 9x.
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What is 5 log 3 + log 4 written as a single logarithm?
Is this a piecewise graph function? Check using vertical line test.
HELP!
HURRY!!!!!!!!!
Given P(5,10,8) and Q(7,11,10), find the midpoint of the segment PQ.
Answer:
[tex]P_{m}=(6,10.5,9)[/tex]
Step-by-step explanation:
The mid point can be found with the formula
[tex]P_{m}=(\frac{x_{1}+x_{2} }{2},\frac{y_{1} +y_{2} }{2} ,\frac{z_{1}+z_{2} }{2} )[/tex]
The given coordinates are [tex]P(5,10,8)[/tex] and [tex]Q(7,11,10)[/tex].
Replacing coordinates in the formula, we have
[tex]P_{m}=(\frac{5+7}{2},\frac{10+11 }{2} ,\frac{8+10}{2} )=(\frac{12}{2},\frac{21 }{2} ,\frac{18}{2} )\\P_{m}=(6,10.5,9)[/tex]
Therefore, the mid point of the segment PQ is [tex]P_{m}=(6,10.5,9)[/tex]
Answer:
^its C if ur too lazy to read the equation like me
Step-by-step explanation:
What is 1 3/4 divided by 1/3 equal
A bag contains white marbles and red marbles, 90 in total. The number of white marbles is 6 less than 5 times the number of red marbles. How many white marbles are there?
Answer:
W = 72
Step by step explanation:
White = W
Red = R
W + R = 90
Write an equation
W = 5R - 6
Substitute
5R - 6 = 90
Add 6 to both sides of the equation
5R = 90
Simplify
90 ÷ 5 = 18
R = 18
90 - 18 = W
W = 72
Hope this was useful to you!
Final answer:
By setting up an algebraic equation, we determine that there are 74 white marbles in the bag when the total number of marbles is 90 and the white marbles count is 5 times the number of red marbles minus 6.
Explanation:
Calculating the Number of Marbles
To figure out how many white marbles are in the bag, we can set up a simple algebraic equation. Let's define the number of red marbles as x. According to the problem, the number of white marbles is 5 times the number of red marbles minus 6. We can represent this as 5x - 6. Since we know the total number of marbles is 90, we can write the equation as:
x + (5x - 6) = 90.
Combining like terms results in:
6x - 6 = 90.
Adding 6 to both sides gives us:
6x = 96.
Dividing both sides by 6, we get:
x = 16.
So, there are 16 red marbles. Now, to find the number of white marbles, we plug this back into the equation for white marbles:
5(16) - 6 = 80 - 6 = 74.
There are thus 74 white marbles in the bag.
This Question: 1 pt
Find the equation of the line that has the given properties.
Contains (-4,-2); parallel to the line y = – 5x + 3
The equation of the parallel line is .
(Type your answer in slope-intercept form.)
Answer: y = -5x - 22
Step-by-step explanation:
Use the Point-Slope formula: y - y₁ = m(x - x₁)
m = -5 (parallel means it has the same slope)(x₁, y₁) = (-4, -2)y - (-2) = -5(x - (-4))
y + 2 = -5(x + 4)
y + 2 = -5x - 20
y = -5x - 22
Water flows at a constant rate out of a faucet. Suppose the volume of water that comes out in three minutes is 10.5 gallons. How many gallons of water come out of the faucet in any number of minutes?
Answer:
3.5 Gallons Per Minute or 3.5m
Step-by-step explanation:
Since there is 10.5 Gallons in 3 minutes, do
10.5/3 = 3.5
(please mark brainliest if this helps!)
Final answer:
The flow rate from the faucet is 3.5 gallons per minute. To determine the amount of water that comes out in any number of minutes, we multiply the flow rate by the number of minutes desired.
Explanation:
Given that 10.5 gallons of water are dispensed in three minutes, we can calculate the rate of flow, which will allow us to determine how many gallons of water would come out of the faucet in any other number of minutes.
We start by finding the flow rate per minute by simply dividing the volume of water dispensed by the number of minutes it took. So, the flow rate is 10.5 gallons / 3 minutes = 3.5 gallons per minute. Now, to find out how many gallons flow in any number of minutes, we multiply the flow rate (3.5 gallons per minute) by the number of minutes.
For example, if we want to know how much water comes out in 5 minutes, we calculate it as follows: Flow rate x Time = 3.5 gallons/minute x 5 minutes = 17.5 gallons. Therefore, 17.5 gallons of water would come out of the faucet in 5 minutes.
Find the slope of the line on the graph below:
Slope = [ ]
Answer:
slope =0
Step-by-step explanation:
its on the point (4,0) its not moving up and down therefor there's no slope
Answer:
0
Step-by-step explanation:
Hello!
Slope can be calculated using the formula [tex]\frac{Rise}{Run}[/tex]
Rise is the change in y between two pointsRun is the change in x between two pointsThe two points I'll pick are (0,4) and (1,4).
The change in y (4 and 4) is 0.
The change in x (0 and 1) is 1.
Put it into the slope format and you get a slope of [tex]\frac01[/tex] or [tex]0[/tex].
Kerry bought a conical tent to put on the back porch. The tent instructions reveal the height at the tallest point to be
4.5 feet and the space inside to be 10.5 cubic feet. About how many square feet of the back porch will be covered by
the tent?
Which measure of the cone needs to be calculated to answer the problem?
A. diameter
B. Radius
C. Base area
D. Volume
Which equation represents the scenario?
A. V= (1/3)(10.5)(4.5)
B. 4.5 = (1/3)(10.5)(h)
C. 10.5 = (1/3)(4.5)(h)
D. 10.5= (1/3)B (4.5)
How many square feet of the back porch will the tent cover?
A. 2.33 square feet
B. 6 square feet
C. 7 square feet
D. 15.75 square feet
1) The measure needed is the C. Base area, 2) the scenario represents the equation D. 10.5= (1/3)B (4.5)
and 3) the tent will cover C. 7 square feet of the back porch.
Use the appropriate formulas to solve it step-by-step.
We know the height (h) of the conical tent is 4.5 feet.The volume (V) of the tent is given as 10.5 cubic feet.The formula for the volume of a cone is:
[tex]V = \frac{1}{3} \pi r^2 h[/tex]
We need to find the base area of the cone (which is a circle) to determine the area covered by the tent on the back porch. The base area (A) of the cone is:
[tex]A = \pi r^2[/tex]
To calculate this, we must first determine the radius (r) of the cone. Let's rearrange the volume formula to solve for the radius (r):
[tex]10.5 = \frac{1}{3} \pi r^2 4.5[/tex]
Simplifying this equation, we get:
[tex]10.5 = \frac{1}{3} \pi r^2 4.5[/tex]
Multiply both sides by 3 to get rid of the fraction:
[tex]31.5 = \pi r^2 4.5[/tex]
Divide both sides by 4.5:
[tex]\frac{31.5}{4.5} = \pi r^2[/tex]
[tex]7 = \pi r^2[/tex]
Divide both sides by π:
[tex]r^2 = \frac{7}{\pi}[/tex]
Taking the square root of both sides, we find the radius (r):
[tex]r = \sqrt{\frac{7}{\pi}}[/tex]
Now we can calculate the base area (A) of the cone:
[tex]A = \pi r^2[/tex]
Substitute r^2 back into the equation:
[tex]A = \pi \left( \frac{7}{\pi} \right) = 7 \text{ square feet}[/tex]
Please answer this quickkkkkkk
Answer:
A = 12 units^2
Step-by-step explanation:
The area of a trapezoid is
A = 1/2 (b1+b2)* h where b1 and b2 are the bases (which are parallel)
b1 = AT = 4 units
b2 = SR = 2 units
The heights is along the x axis which is 4 units
A = 1/2 ( 2+4) *4
A = 1/2 (6)*4
A = 12 units^2
Use the data in the table to complete the sentence.
The function has an average rate of change of....
The Average of rate is -1.
Step-by-step explanation:
Everytime it goes up by one the y goes down by 1 so it would be -1.
The function has an average rate of change of -1. It is denoted by R.
What is the average rate?The single rate applies to property in several locations and is a weighted average of the separate rates that apply to each place.
The function has an average rate of change of -1.
[tex]\rm R = \frac{4-5}{1-0} \\\\ R=-1[/tex]
Hence, the function has an average rate of change of -1.
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At a sale, a table is being sold for 27% of the regular price. The sale price is $156.60.
What is the regular price?
Answer:
$580
Step-by-step explanation:
Original price = $156.60 / 0.27
Original price = $580
Use the multiplier method to increase £258 by 43%
You must show your working.
Answer:£368.94
Step-by-step explanation:
258*1.43= 368.94
What is the point-slope form of a line that has a slope of 3 and passes through point (1, 4)? y minus 4 = 3 (x minus 1) 1 minus y = 3 (x minus 4) y 1 minus 4 = 3 (1 minus x 1) 1 minus y 1 = 3 (4 minus x 1) I NEED IT NOW PLEASEEEE!!!!
Answer:
y - 4 = 3(x - 1)
Step-by-step explanation:
It looks like you have slope 3 and a point (1, 4)
so it should be y - 4 = 3(x - 1)
which is your first choice: y minus 4 = 3 (x minus 1)
The point-slope form of a line is y - 4 = 3(x-1) which is correct option(A).
What is linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
GIven equation,
Slope of line (m) = 3
Slope form of a line is y-y₁ = m(x-x₁)
Line passes through point (1, 4)
⇒ y - 4 = 3(x-1)
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Tacy deposited $6900 into a savings account that earns 3.1% simple interest
each year, calculated annually. What will be the value of Tacy's account after
9 years?
O A. $1925.10
O B. $8825.10
Oc. $71,113.90
OD. $19,251.00
SUBMIT
Answer:
$8825.10
Step-by-step explanation:
Interest total= P x r x t
P = principal amount, or $6900
r= interest rate, or 0.031
t = time, or 9 years
6900 x 0.031 x 9 = 1925.10
You now add this to the original amount
6900 + 1925.10 = $8825.10