Sketch the graph of each function. Then State the domain, range and increasing, decreasing intervals. Part 1
Answers
Problem 15
Answers:
Graph: Shown belowDomain: [3, infinity) Range: [2, infinity)Increasing interval: [2, infinity)Decreasing interval: NoneEach interval is interval notation.
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Explanation:
To get the graph, you can plug in various x values to find their paired y values, then draw a curve through those points. You can only plug in x values that are 3 or larger, as I'll mention later in the next paragraph. A quicker way to get the graph is to use technology. I used GeoGebra to generate the graphs below.
To get the domain, we need to ensure that the stuff under the square root is never negative. So we need to make the x-3 to be 0 or larger. Solving \(x-3 \ge 0\) leads to \(x \ge 3\) showing that 3 is the smallest value we can plug in. The domain is the interval from 3 to positive infinity. We can write that as \(3 \le x < \infty\) which condenses to the interval notation [3, infinity). Note how the square bracket is used to include the endpoint.
The range can be determined from the graph. The lowest point is when y = 2, so the range consists of y outputs that are 2 or larger. We write the interval notation [2, infinity) to mean \(2 \le y < \infty\)
The graph also helps us see where the curve is increasing or decreasing. In this case, the curve goes uphill as we move from left to right. Therefore, the graph is increasing over its entire domain. We write the domain as the answer here. Because the function increases over the entire domain, there's no room for the function to decrease.
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Problem 16
Answers:
Graph: Shown belowDomain: [-1, infinity) Range: [-3, infinity)Increasing interval: [-1, infinity)Decreasing interval: None----------------------------------
Explanation:
We follow the same idea as the previous problem.
This time we want the x+1 under the square root to be 0 or larger, so \(x+1 \ge 0\) solves to \(x \ge -1\) telling us the smallest input allowed. The value of x can be this or larger.
Since this is an increasing function throughout the domain (similar to the previous problem), this means that the smallest domain value corresponds exactly to the smallest range value. Plugging in x = -1 leads to y = -3 which is the smallest possible output. As x gets bigger, so does y. The graph shows that the lowest point occurs when y = -3 to visually confirm this.
The increasing interval is over the entire domain, so we just write the domain again for the increasing interval. This means we write "none" for the decreasing interval.
Side note: The graphs are shown together on the same xy coordinate axis, but for your hw problem, you'll have the graphs on their own separate grid.
Related Questions
Which of the following statements are true and which are false? Give reasons for your answers.(i) Only one line can pass through a single point.(ii) There are an infinite number of lines which pass through two distinct points.(iii) A line can be produced indefinitely on both sides.(iv) If two circles are equal, then their radii are equal.(v) if AB=PQ and PQ=XY, then AB=XY.
Answers
Complete Question
Which of the following statements are true and which are false? Give reasons for your answers.
(i) Only one line can pass through a single point.
(ii) There are an infinite number of lines which pass through two distinct points.
(iii) A line can be produced indefinitely on both sides.
(iv) If two circles are equal, then their radii are equal.
(v) if AB=PQ and PQ=XY, then AB=XY.
A (i),(ii) - True
(iii),(iv),(v)-False
B(i),(ii),(iii) -True
(iv),(v)-False
C (i),(ii) -False
(iii),(iv),(v)-True
D (i),(ii),(iii) -False
(iv),(v)-True
Answer:
The correct option is C
Step-by-step explanation:
i is false because several lines can pass through a single point
ii is false because only one line can pass through two distinct points
iii is true because you can extend a line from both points (start and end points )
iv is true because when two equal circle are placed together and radius is trace we will discover that they are equal
v is true because from Euclid's First Axiom , if a= c and c = d the a = d
Write down the coordinates of point B?
Answers
Answer:
The answer is 4,5.
Step-by-step explanation:
Go over 4 times and go up 5, and there is your answer.
Simplify the product using the distributive property
(3h - 5)(5h + 4)
Answers
Step-by-step explanation:
(3h - 5)(5h + 4) = 3h * 5h + 3h * 4 - 5*5h - 5 *4
= 15h^2 - 13h -20
\((3h-5)(5h+4)\)
\(=(3h+-5)(5h+4)\)
\(=(3h)(5h)+(3h)(4)+(-5)(5h)+(-5)(4)\)
\(=15h^2+12h-25h-20\)
Answer:
\(\bold{=15h^2-13h-20}\)Please help and show how you found the answer step by step.
Answers
According to the information, the perimeter of the triangle is ≈ 31.18
How to calculate the perimeter of the triangle?To find the distance between two points, we can use the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's label the coordinates as follows:
Point 1: (-2, 3)
Point 2: (3, -2)
Now we can substitute these values into the distance formula:
distance = sqrt((3 - (-2))^2 + (-2 - 3)^2)
distance = sqrt((5)^2 + (-5)^2)
distance = sqrt(25 + 25)
distance = sqrt(50)
distance ≈ 7.07
Therefore, the distance from (-2, 3) to (3, -2) is approximately 7.07 units.
To find the perimeter of the triangle, we need to find the length of all three sides of the triangle and then add them up.
Using the distance formula, we can find the length of the sides:
Side 1: (-2,3) to (3,-2)
d = √[(3 - (-2))^2 + (-2 - 3)^2]
= √[5^2 + (-5)^2]
= √50
= 5√2
Side 2: (3,-2) to (-7,-2)
d = √[(-7 - 3)^2 + (-2 - (-2))^2]
= √[(-10)^2 + 0^2]
= 10
Side 3: (-7,-2) to (-2,3)
d = √[(-2 - (-7))^2 + (3 - (-2))^2]
= √[5^2 + 5^2]
= 5√2
Therefore, the perimeter of the triangle is:
5√2 + 10 + 5√2 = 15√2 + 10 ≈ 31.18 (rounded to two decimal places)
An two of the three sides are equal, so it is an isosceles triangle.
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Find the value ofx, y, and z in the parallelogram below.
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Answer:
Step-by-step explanation:
Is 2/10 greater than or lesser than 3/5?
Answers
Answer:
2/10 is lesser than 3/5Step-by-step explanation:
Is 2/10 greater than or lesser than 3/5?
fraction = division
2/10 = 0.2
3/5 = 0.6
2/10 is lesser than 3/5
what is this please help
Answers
Answer:
Absolute value means how far are you from zero on the number line.
absolute value of | -18| for example is 18
this means that you are at -18 on the number line that is 18 points away from zero.
and absolute value of |18 | is 18
this means that you are at point 18 on the positive direction on the number line. That is 18 points away from zero.
Step-by-step explanation:
Find how much money needs to be deposited now into an account to obtain $1,200 (Future Value) in 15 years if the interest rate is 7% per year compounded monthly (12 times per year).
Answers
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1200\\ P=\textit{original amount deposited}\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}\)
\(1200 = P\left(1+\frac{0.07}{12}\right)^{12\cdot 15} \implies 1200=P\left( \frac{1207}{1200} \right)^{180} \\\\\\ \cfrac{1200}{ ~~ \left( \frac{1207}{1200} \right)^{180} ~~ }=P\implies 421.21\approx P\)
Find the greatest common factor of 14 and 16
Answers
Answer:
the answer is 2
Step-by-step explanation:
Answer:
Step-by-step explanation:
It is 2, because it is the only factor that can go with both of the numbers.
Consider the following system of two linear equations:
4y + 3x = 0
4y - x = 16
What is the point of intersection?
Answers
Answer: The two lines intersect at (-4,3)
Step-by-step explanation:
So our first step would be to turn both of these into standard slope-intercept form.
1.)
4y + 3x = 0
4y = -3x
y = -3/4x
2.)
4y - x = 16
4y = x + 16
y = 1/4x + 4
Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)
A, b birer sayı olmak üzere a. b =12 ise a+b nin en büyük ve en küçük değerini bulunuz?
Answers
Answer:
en büyük 13 en küçük 7 dir
find the measure of angle A
Answers
Answer:
30
Step-by-step explanation:
Right angle = 90 degrees
180-90 = 90, hence the right side of the equation.
x+37+x+67 = 90
2x + 104 = 90
2x = -14
x = -7
Plug in x.
-7+37 = 30 (angle a)
Angle a = 30
Answer:
angle A = 30 degrees
Step-by-step explanation:
*All triangles have an interior angle that adds up to 180 degrees
The triangle is the picture is a right triangle so one of the angles is 90 degrees.
First, we must figure out what "x" is:
⇒ 180 = 90 + x + 37 + x + 67
Combine like terms:
⇒ 180 = 2x + 194
Subtract 231 from both sides:
⇒ 180 - 194 = 2x + 149- 194
⇒ -14 = 2x
The divide both sides by 2:
⇒ \(\frac{-14}{2} + \frac{2x}{2}\)
⇒ -7 = x
Now, we can figure out what angle A is by taking the equation "x + 37" and subtituting x by -7:
⇒ x + 37
⇒ -7 + 37
⇒ 30
To check out answers, take all of the eqautions in the picture and subtitute x by -7, (remember that it must add up to 180):
⇒ 90 + x + 37 + x + 67 = 180
⇒ 90 + (-7) + 37 + (-7) + 67 = 180
⇒ 180 = 180
WILL MARK YOU AS BRAINLIEST IF ANSWER IS CORRECT 25 PT
if AC = 20, AE = 4y, and EC = 4, what is the value of y?
Answers
Answer:
y = 4
Step-by-step explanation:
Point E is on segment AC such that AC=20, AE=4y, and EC=4. You want the value of y.
SetupThe whole is the sum of the parts of a line segment.
AC = AE +EC
20 = 4y +4 . . . . . substitute given values
SolutionDivide by 4
5 = y +1
4 = y . . . . . . . . subtract 1
The value of y is 4.
Please help!
Explain how changes in the dimensions of a cube dimensions affect the volume of a cube. Be specific, explaining how much the volume will change with each increase of 1 unit on the side lengths.
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Answer:
Difference = 3x² + 3x + 1
See Explanation
Step-by-step explanation:
Required: How changes in sides of a cube affects its volume.
Take for instance the side of the cube is x.
The initial volume would be:
Volume = x * x * x
Volume = x³
When then dimension is increased by 1 unit, the new volume would be
Volume = (x + 1) * (x + 1) * (x + 1)
Expand the brackets
New Volume = (x² + 2x + 1)(x + 1)
New Volume = x³ + 3x² + 3x + 1
[Calculate the difference between both volumes]
Difference = New Volume - Initial Volume
Difference = x³ + 3x² + 3x + 1 - x³
[Collect like terms]
Difference = x³ - x³ + 3x² + 3x + 1
Difference = 3x² + 3x + 1
So, there will be a difference of 3x² + 3x + 1 when the dimension is increased from x to x + 1
Take for instance: a dimension of 2 units is increased to 3 units
Initial Volume = 2³ = 8
New Volume = 3³ = 27
Difference = 27 - 8
Difference = 19
Using the derived formula (x = 2)
Difference = 3x² + 3x + 1
Substitute 2 for x
Difference = 3 * 2² + 3 * 2 + 1
Difference = 3 * 4 + 6 + 1
Difference = 12 + 6 + 1
Difference = 19
Please Solve, Thank you!
Answers
Answer:
1711
Step-by-step explanation:
\(4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711\)
Make sure to follow order of operations!
given the qintic equation below, solve it to find the values of x. 2x^5_6x^3_4x^2_2x+4 =0
Answers
9514 1404 393
Answer:
x = {-0.5-√1.25, -0.5+√1.25, 2, -0.5+i√0.75, -0.5-i√0.75}
Step-by-step explanation:
I like to use a graphing calculator to find clues as to the roots of higher-degree polynomials. Here, we see that x=2 is the only real rational root. Dividing that out by synthetic division, we see the remaining quartic factor is ...
2x^5 -6x^3 -4x^2 -2x +4 = 0
2(x -2)(x^4 +2x^3 +x^2 -1) = 0
We can recognize that the quartic factor is actually the difference of two squares:
x^4 +2x^3 +x^2 -1 = (x^2 +x)^2 -1 = 0
So it resolves to two quadratic factors.
(x^2 +x +1)(x^2 +x -1) = 0
One will have real roots, as shown by the graph. The other will have complex roots.
x^2 +x + 1/4 = 1 +1/4 . . . . complete the square for the factor with real roots
(x +1/2)^2 = 5/4
x = -1/2 ± √(5/4) . . . . . . irrational real roots
__
x^2 +x = -1 . . . . . . . . . . the quadratic factor with complex roots
(x +1/2)^2 = -1 +1/4 . . . complete the square
x = -1/2 ± i√(3/4) . . . . irrational complex roots
__
In summary, the values of x that satisfy the equation are ...
x = 2
x = -1/2 ± √(5/4)
x = -1/2 ± i√(3/4)
The average person burns approximately 221 calories per half-hour while bicycling. If a person
does 2 hours of bicycling per day then how many calories will they burn in a week if they work
out 5 days a week?
Answers
I need help with this urgently
Leo has purchased a fee-for-service health insurance plan from Leroux Health Insurance. Plan A includes a $225.00 monthly premium and an annual deductible of $5,500.00 (not including co-pays). Except for chronic back pain, Leo is a fairly healthy man. He visits his primary care physician four times a year on scheduled visits. He sees a chiropractic specialist every two weeks to help with his lower back pain. He has no current prescriptions that need refilling regularly. Assuming Leo maintains his regular visits with his primary care physician and his chiropractor, and avoids any trips to the emergency room or urgent care, how much will Leo pay in health care related fees this year, including his premium payments? See the table below: *
$8300.00
$1960.00
$4660.00
$6216.00
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20,000 ten thousands equals how many hundred thousands
Answers
20,000 ten thousand equals 2000 Hundred thousand.
As per the question statement, we are provided with a value: "20,000 ten thousand".
We are required to calculate how many hundred thousand are equal to 20,000 ten thousand.
To solve this question, let us first write down 20,000 ten thousand into the numerical format, i.e, \((20000*10,000)=200000000\).
As we know, a hundred thousand when written down in the numerical format becomes 100,000, let us assume that 20,000 ten thousand equals to "x" number of Hundred thousand.
Therefore, we can form a linear equation in one variable "x" based on the condition, in the above-mentioned statement, which goes as \((100,000*x)=200000000\)
\(or, (100,000x)=200000000\\or,x=\frac{200000000}{100,000}\\or,x=\frac{2*10^{8} }{10^5\\}or,x=(2*10^3)\\or,x=2000\)
Hence, 20,000 ten thousands equals 2000 Hundred thousands.
Linear Equation: linear equations: In Mathematics, a linear equation is an algebraic equation which when graphed, always results in a straight Line and hence comes the name "Linear". Here, each term has an exponent of 1 and is often denoted as (y = mx + c) where, 'm' is the slope and 'b' is the y-intercept. Occasionally, it is also called as a "linear equation of two variables," where y and x are the variables.Variable: n Mathematics, a variable is a symbol or a representative of a value, which is unknown.To learn more about Linear Equations, click on the link below.brainly.com/question/27664510
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Help me plzz ehehsbbdd
Answers
Answer:
90
Step-by-step explanation:
as the hours of training increase by 10 the monthly salary increases by 150
Answer:
19.6 hours
Step-by-step explanation:
you 1st do 1250/10=125
125x19 = 2375
then take a decimal
125x19.6=2450 :) enjoy!
I WILL GIVE 20 POINTS PLUS IM GIVING BRAINLIEST!!!!!!!
Answers
Answer:
I'm thinking B
Step-by-step explanation:
but I'm not 100
What is the equation for the translation of x2 + y² = 64 three units to the left and two units down
(x - 3)² + (y-2)² = 64
(x+3)2 + (y + 2)2 = 64
(x-3)² + (y + 2)² = 64
(x+3)² + (y-2)² = 64
Answers
The equation for the translation of \(x^{2} +y^{2}=64\), three units to the left and two units down is option (b) \((x+3)^2+(y+2)^2=25\)
The equation is \(x^{2} +y^{2}=64\)
The standard form of the circle
\((x-h)^2+(y-k)^2=r^{2}\)
Where r is the radius of the circle
(h,k) are the coordinates of the center of the circle.
The equation is \(x^{2} +y^{2}=64\)
The center is (0,0)
Here the circle translated three units to the left
Therefore h = -3
The circle is translated two units down
k = -2
Substitute the values in the standard form of the circle
\((x--3)^{2}+(y--2)^{2}=25\)
\((x+3)^2+(y+2)^2=25\)
Hence, the equation for the translation of \(x^{2} +y^{2}=64\), three units to the left and two units down is option (b) \((x+3)^2+(y+2)^2=25\)
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4. What is the acceleration of the car in each section?
b
с
d
a
Answers
The acceleration for each section is shown below.
We know the formula
Acceleration = change in haste/ time taken
1. For a
= (12-0)/4
= 12/4
= 3
For b:
= (12-12)/ 5
=0
For c:
= (6-12)/ (2)
= -3
For d:
= (10-6) / 4
= 4/4
= 1
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SOLVE FOR U
7 = –3(u − 9) + 1
Answers
Answer:
u = 7
Step-by-step explanation:
What is the reason why bubbling occurs when vinegar is mixed with baking soda? A. a precipitate forms thus producing gas
B. a color change occurs thus creating a gas
C. a chemical change occured and a gas is released
*it’s not A .
Answers
Answer:
c
Step-by-step explanation:
Answer: A sign a chemical reaction has occurred is the formation of gas, which can be seen in the form of bubbles. Once the vinegar is added to the baking soda, carbon dioxide is released as a product. The bubbling is the release of CO2.
I am NOT exactly sure about the answer but with my explination and reasearch I THINK the answer is C
Hope this helps
At Glenn Middle school, 535 students chose football as their favorite sport to watch. That is 58 less than the number of students who chose basketball. Write and solve and equation to find b.
Please help, we just need to know how to set it up. Thank you!
Answers
Answer:
\(b= 535 +58\)
Step-by-step explanation:
It is the oppisite so its jsut b( for basketball) then 535 PLUS becase the question says "58 people LESS"
Original price: $22 Discount percent: 25%
Answers
Answer: 16.5
Step-by-step explanation:
Original price is 22 remove 25% by multiplying 22 by 0.75
If trying to find the original price when the discount is 25% and the discounted price is 22 take 22 and divide it by 3 and then multiply it by 4
Given f(x) = 1/2 (3 - x) ^ 2, what is the value of f(15)?
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If Given f(x) = 1/2 (3 - x) ^ 2 , the value of f(15) is 72.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.
The given function is:
f(x) = 1/2 (3 - x)²
To find the value of f(15), we need to substitute 15 for x in the function:
f(15) = 1/2 (3 - 15)²
Here, we subtract 15 from 3 to get -12 in the parentheses, and then we square it to get 144. We can simplify the expression further by multiplying 144 by 1/2, which gives us 72:
f(15) = 1/2 (144)
f(15) = 72
Therefore, the value of f(15) is 72.
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A rectangular field is 0.4 m longer than it is wide. If its length is 6m find its Perimeter.. When the breadth of the rectangle is reduced by 0.5m. the length is increased such that the perimeter is increased by 1/4 of its Original What is the Change in the length of the rectangle ?
Answers
The original perimeter of the rectangle would be:
P = 2 (x) + 2 (x + 0.4) = 4x + 0.8
We know that the perimeter increased by 1/4 of its original value, so:
P' = P + P/4 = 4x + 0.8 + (4x + 0.8)/4 = 4x + 0.8 + x + 0.2 = 5x + 1
So, the new perimeter is 5x + 1 m.
We also know that the width of the rectangle was reduced by 0.5 m, so the new width is x - 0.5 m. And the new length was increased, but we don't know by how much, so let's call that increase ΔL.
The new perimeter would be:
P' = 2 (x - 0.5) + 2 (x + ΔL + 0.4) = 4x + 2ΔL - 1
So, equating the two expressions for P' that we derived above:
5x + 1 = 4x + 2ΔL - 1
Solving for ΔL, we get:
ΔL = (5x + 2 - 4x)/2 = (x + 2)/2 = (6 + 2)/2 = 4 m
So, the change in the length of the rectangle is 4 m.
Use distributive property to rewrite each algebraic expression: 15(2+r)
Answers
Answer:
15 x 2 + 15 x r
Step-by-step explanation:
I hope this helps and hope u have an Amazing day!!