Given the function and the graph below, which of the following best describes the continuity, interval of increase and interval of decrease?
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Given the function:
[tex]f(x)=(-x-1)^2+3[/tex]As we can see, there is no restriction for x, it can be any real value. Additionally, looking at the graph, we do not see any discontinuity ("jumps" or "holes"). We conclude that the function is always continuous.
The vertex of the parabola is at (-1, 3), so x = 1 separates the intervals of increase and decrease. Going from -∞ to -1, we see a decrease in the y-values. Similarly, from -1 to +∞, we see an increment. Then:
Interval of increase: -1 < x < +∞
Interval of decrease: -∞ < x < -1
Related Questions
Please help me!! This is really hard for me and I need a tutor to explain it to me
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SOLUTION
We want to find the solution of the equation
[tex]x^2=64[/tex]This becomes
[tex]\begin{gathered} x^2=64 \\ we\text{ move the square to the other side it becomes square root, we have} \\ x=\sqrt{64}\text{ the square root sign attracts }\pm,\text{ so we have } \\ x=\pm\sqrt{64} \\ x=\pm8 \end{gathered}[/tex]Hence the answer is
[tex]\pm8[/tex]Note that square root of 64 is 8
QUESTION 16Find anequation of the circle that satisfies the given conditions.Radius 6 and center (3.-5)
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A circle can be represented by the following equation:
[tex]\mleft(x-h\mright)^2+(y-k)^2=r^2[/tex]Where the radius is r and the center is (h, k).
Using the radius 6 and the center (3, -5), we have that:
[tex]\begin{gathered} (x-3)^2+(y-(-5))^2=6^2 \\ (x-3)^2+(y+5)^2=36 \end{gathered}[/tex]So the equation of the circle that satisfies radius = 6 and center = (3, -5) is:
(x-3)^2 + (y+5)^2 = 36
I will share a photo of the question it is to complicated to right
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Answer : 6
We are given the above fraction to be
[tex]\frac{3}{4}\text{ divided by }\frac{1}{8}[/tex][tex]\begin{gathered} To\text{ proc}eed\text{ with this expression, we n}eed\text{ to find the reciprocal of }\frac{1}{8} \\ \text{Hence, the reciprocal of }\frac{1}{8}\text{ is 8} \\ \frac{3}{4}\text{ x }\frac{8}{1} \\ =\text{ }\frac{3\text{ x 8}}{4} \\ =\text{ }\frac{24}{4} \\ =\text{ 6} \end{gathered}[/tex]The answer is 6
Before you can change a division operator to a multiplication operator, we need to find the reciprocal of the left hand side fraction
The fraction at the left hand side is 1/8
The reciprocal of 1/8 is 8
The graph shows the equation x=y^2 use the slider for a to move the vertical line on the graph. According to the vertical line test, is this equation a function why or why not?
Answers
Explanation
We are given the equation:
[tex]x=y^2[/tex]We are to use the vertical line test to determine if the equation is a function or not
The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.
The typical example below helps give a better explanation
So for the function
[tex]x=y^2[/tex]We can observe that the equation is not a function because the vertical line cuts the graph in more than one point
This is shown below for values of x = and x =8
which expression means the same as an increase of 20%
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ANSWER:
[tex]x+0.2x[/tex]STEP-BY-STEP EXPLANATION:
We have that an increase in 20% is the original value added to 20% of that original value, just like this:
[tex]x+\frac{20}{100}x=x+0.2x[/tex]Estimate the mean of the data given in the following grouped frequency table.Value IntervalFrequency0−3124−7208−118Select the correct answer below:4.577.857.663.535.10
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The mean (or average) of observations is the sum of the values of all the observations divided by the total number of observations.
The mean for grouped data is given by:
[tex]Mean=∑(f_i.x_i)/∑f_i[/tex]• So; first we calculate each class mark xi, as:
(0 + 3)/2 = 1.5
(4 + 7)/2 = 5.5
(8 + 11)/2 = 9.5
• Now; we calculate fixi, as:
1.5 x 12 = 18
5.5 x 20 = 110
9.5 x 8 = 76
• Hence, the mean is given by:
[tex]Mean=\frac{18+110+76}{12+20+8}=5.10[/tex]ANSWER
5.10
If the distance from South Bend to Grand Rapids has been rounded to the nearestten and is listed as 120 miles, the actual distance is between what two mile numbers?
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We need to have two numbers between 116 and 124. If we have these two numbers and average them, we can have:
[tex]\frac{116+124}{2}=120[/tex]If we rounded 116 to the nearest ten, it will be 120.
If we rounded 124 to the nearest ten, it will be also 120.
Then if we have these two numbers and average them, we finally have 120 miles.
The actual distance must be between 116 and 124.
Students were asked to prove the identity (cot x)(cos x) = csc x − sin x. Two students' work is given.Part A: Did either student verify the identity properly? Explain why or why not.Part B: Name two identities that were used in Student A's verification and the steps they appear in.
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Part A
Looking at the work done by each student, both students verified the identity properly because the trigonometric identities were properly applied where necessary, the steps were clear, mathematical operations were applied correctly and at the end, both sides of the equation were the same.
Part B
Looking at student's A verification,
In step 3, the pythagorean identity was used
In step 5, the reciprocal identity was used
How many tablespoons of blue paint should Elena mix with 6 cups of white paint and blue paint? How many batches would this make?
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According to the given graph, 2 cups of white paint are in the same ratio as 6 tablespoons of blue paint.
So, if she has 6 cups of white paint, we just have to multiply the number of tablespoons by 3.
[tex]6\times3=18[/tex]So, Elena needs 18 tablespoons of blue paint.Additionally, this would make three batches because the given ratio is being multiplied by 3.Cole's Ice Cream Shop sold 16 sundaes with nuts and 30 sundaes without nuts. What is the
ratio of the number of sundaes with nuts to the total number of sundaes?
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Answer:
16:46
Step-by-step explanation:
Rita is applying for a job as an engineer. Her starting salary at Company A will be $80,000 with an $800 yearly raise. Her starting salary at company B will be $65,000 with a 5% increase each year. If Rita is working at a company for 5 years. Which company should she pick?
Answers
Given:
In company A, starting salary is $80,000.
The yearly increment is $800.
So,
80,000+800=80,800
80,800+800=81,600
81,600+800=82,400
82,400+800=83,200
83,200+800=84,000
So, at the 5 year, she will get $84,000
In company B,
The initial salary is $65000 with a 5% increase each year.
So,
[tex]\begin{gathered} 65000\times\frac{105}{100}=68250 \\ 68250\times\frac{105}{100}=71662.5 \\ 71662.5\times\frac{105}{100}=75245.625 \\ 75245.625\times\frac{105}{100}=79007.906 \\ 79007.906\times\times\frac{105}{100}=82958.30 \end{gathered}[/tex]In the 5th year, she will get $82,958.30.
If Rita is working at a company only for 5 years, then she would choose company A. Because she will get salary in company A more than company B.
But, if she works for more than 5 years, she will get a salary in company B more than company A.
how do i find the type of relationship of a table? whether it is linear or quadradic and how do i find the formula for either relationship?
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By finding the differences between dependent values, you can determine the degree of the model for data given as ordered pairs. If the first difference is the same value, the model will be linear. If the second difference is the same value, the model will be quadratic.
Also you can solve it by plotting the dots. If the graph seems a straight line it is linear and quadratic if it is a parabola.
For the data set given it is a linear relation
Line of best fit: y=3.18x+54.92
For x=7;
y=3.18*7+54.92
y=77.18
Drag each figure to show if it is similar to the figure shown or why it is not similar.
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It is found that all the figures in the options except the fourth figure are similar to the given figure.
What are geometric shapes called?Geometric forms are figures in mathematics that depict the shape of items we observe in our daily lives. Shapes are the forms of things in geometry that have boundary lines, angles, and surfaces. There are several sorts of 2d and 3d shapes.
The given figure is a rectangle with dimensions 4 feet and 8 feet for length and breadth respectively.
We need to determine similar figure from the given options.
The first figure has a rectangle shape with different dimensions which is similar to given figure.
The second figure is also similar to given figure as it is also a rectangle with different dimensions.
By looking at the third figure, we can see that it has same rectangle shape and dimensions as the given figure which is 4 feet and 8 feet for length and breadth respectively.
The fourth figure is not a rectangle so it is not similar to the given figure.
Also, the last figure is a rectangle with different dimensions so it is similar to given figure.
Thus, we conclude that all the figures in the options except the fourth figure are similar to the given figure.
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-20 increased by 4
translating words to algebraic expressions
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The algebraic expression is -20 +4.
What is algebraic expression?
An algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3x2 − 2xy + c is an algebraic expression.
Given, situation -20 increased by 4.
Translate the phrase -20 increased by 4 into an algebraic expression.
You probably already know that more than is associated with addition so the sign is not going to change. But what about the order of the terms?
Think about it this way: we have a number (some unknown value) and this phrase represents -20 increased by whatever that value is. So, in this case, you will start with the number -20 and add 4.
we get -20+4.
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Which is more 1163 millimeters or 1meters?
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Given : 1163 millimeter and 1 meters
We need to compare between them
First make both numbers at the same units :
1163 millimeter
1 meters = 1000 millimeters
So, 1163 millimeters > 1000 millimeters
So, 1163 millimeters is more than 1 meters
Find the area of this irregular shape.
[Round off to the nearest whole number.]
sq. units
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Answer:
Step-by-step explanation:
number of complete squares=14
number of half or more than half squares=4
whole squares=4/2=2
area≈14+2=16 sq. units
The graph of f(x) = 4+ is shown below in blue. This graph in red is a transformation of f(x). Write a function thatdescribes the
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Solution
Step 1:
Write the parent function
[tex]f(x)\text{ = 4}^x[/tex]Step 2:
Transformation of f(x) to g(x)
First, f(x) was reflected across the x-axis
[tex]f(x)\text{ }\rightarrow\text{ -4}^x\text{ }\rightarrow\text{ g\lparen x\rparen}[/tex]Step 3:
Then the function is later shifted 3 units vertically down.
[tex]g(x)\text{ = -4}^x\text{ - 3}[/tex]Final answer
[tex]g(x)\text{ = -4}^x\text{ - 3}[/tex]If point B, shown on the coordinate plane below, is reflected over the y-axis to create B’, what will be the coordinates of B’?(-5, 2)(5, 2)(-5, -2)(5, -2)
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Solution
- The transformation for reflection over the y-axis is given below:
[tex](x,y)\to(-x,y)[/tex]- We have been given the coordinate of B to be (-5, -2) as shown below:
- Thus, applying the transformation formula given above, we have:
[tex]\begin{gathered} (x,y)\to(-x,y) \\ (-5,-2)\to(-(-5),-2)=(5,-2) \end{gathered}[/tex]- Thus, the reflected point B' is
[tex](5,-2)[/tex]- This is shown below:
Graph the line 3x - 5y = 18
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Given:
3x - 5y = 18
To graph this line, rewrite the equation in slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
Subtract 3x from both sides:
3x - 3x - 5y = -3x + 18
-5y = -3x + 18
Divide all terms by -5:
[tex]\begin{gathered} \frac{-5y}{-5}=\frac{-3x}{-5}+\frac{18}{-5} \\ \\ y=\frac{3}{5}x-\frac{18}{5} \end{gathered}[/tex]Thus, the slope intercept form of the equation is:
[tex]y=\frac{3}{5}x-\frac{18}{5}[/tex]Any line can be graphed using two or more points.
Let's determine two points on the line.
Input 6 for x and solve for y:
[tex]\begin{gathered} y=\frac{3}{5}\ast6-\frac{18}{5} \\ \\ y=\frac{18}{5}-\frac{18}{5} \\ \\ y=0 \end{gathered}[/tex]Also, the y-intercept is:
[tex](0,-\frac{18}{5})[/tex]convert the fraction to decimal:
[tex]-\frac{18}{5}=-3.6[/tex]Thus, we have the points:
[tex]\begin{gathered} (0,-3.6) \\ (6,\text{ 0)} \end{gathered}[/tex]x y
0 -3.6
6 0
Mark the points on a graph and make a straight line that passes through the points.
The graph is attached below:
In the X Y -plane, a line crosses the Y - axis at the point (0,3) and passes through the point ( 4,5). Which of the following is an equation of the line?A. y = x + 3 2B. y = 2x + 31 C. y = x – 4 2D. y = 2x – 4
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Given two points of a line (x1, y1) and (x2, y2), the equation of the line is:
[tex]\begin{equation*} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \end{equation*}[/tex]We are given the points (0, 3) and (4, 5). Plugging in these values:
[tex]y-3=\frac{5-3}{4-0}(x-0)[/tex]Operating and simplifying:
[tex]\begin{gathered} y-3=\frac{2}{4}x \\ \\ y=\frac{1}{2}x+3 \end{gathered}[/tex]Thomas runs 34 of a mileevery day for 5 days. Howfar has he run total?
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Guven:
Miles per day = 34 miles
Number of days = 5 days
To find the total distance(miles), we have:
Total distance = distance covered per day x Number per days
= 34 x 5 = 170 miles
Therefore, the total distance he has covered is 170 miles
ANSWER:
170 miles
I need help to find the indicated operation:g(n)= 2n-2h(n)= n^2+3nFind (g×h)(n)
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Composition of functions:
You combine two functions bycomposition by using one of the functions to substitute the independient variable in the other one.
To find (g o h)(n) you substitute the n in the function g(n) for the function h(n):
[tex](g\circ h)(n)=2(n^2+3n)-2[/tex]Simplify:
[tex](g\circ h)(n)=2n^2+6n-2[/tex](-5,-11) and (17,-22)
Find the slope
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Answer:
-1/2
Step-by-step explanation:
if p || , m<7 = 131°, and m<16 = 88°, find the measure of the missing angle m<13 = ?
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Answer:
[tex]m\angle13=92^o[/tex]Explanation:
First, we match the angles
9 = 11
10 = 12
16 = 14
15 = 13
Therefore, if we find angle 15, we find an angle 13.
Angle 15 is supplementary to angle 16; therefore,
[tex]\angle16+\angle15=180^o[/tex]Since
[tex]\angle16=88^o[/tex]Therefore,
[tex]88^o+\angle15=180^o[/tex]subtracting 88 from both sides
[tex]\angle15=180^o-88^o[/tex][tex]\angle15=92^o[/tex]which is our answer!
Determine whether the function Y = 7- (3)represents exponential growth orexponential decay.a) exponential decayb) exponential growth
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Given any exponential function in the form
[tex]y=ar^x[/tex]• If ,r >1, ,the function represents ,growth
,• If ,1 > r > 0,, the function represents ,decay
Notice that for
[tex]y=7\cdot(\frac{2}{3})^x[/tex]The exponential factor (2/3) is between 0 and 1 (0.66)
Therefore, the function represents decay.
Answer: Option A
What are the solutions to the equation x- 8x = 10?1) 4 102) 4-263) 41104) 4+ 26
Answers
First, let's equal the expression to zero:
[tex]\begin{gathered} x^2-8x=10 \\ \rightarrow x^2-8x-10=0 \end{gathered}[/tex]Now, let's use the general formula for quadratic equations:
[tex]\begin{gathered} \text{For} \\ ax^2+bx+c=0 \\ \\ \rightarrow x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]This way,
[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(-10)}}{2(1)} \\ \\ \rightarrow x=\frac{8\pm\sqrt[]{64+40}}{2} \\ \\ \rightarrow x=\frac{8\pm\sqrt[]{104}}{2} \\ \\ \rightarrow x=\frac{8\pm2\text{ }\sqrt[]{26}}{2} \\ \\ \Rightarrow x=4\pm\sqrt[]{26} \end{gathered}[/tex]Answer: Option 2
(4t^2-5u)^2What does this simplify to?What is the degree of the simplified answer?
Answers
Answer:
simplified expression = 16t⁴ - 40t²u + 25u²
degree = 4
Explanation:
The initial expression is:
[tex](4t^2-5u)^2[/tex]To simplify, we can solve the expression as:
[tex](4t^2-5u)(4t^2-5u)[/tex]Applying the distributive property, we get:
[tex]\begin{gathered} 4t^2(4t^2)+4t^2(-5u)-5u(4t^2)-5u(-5u) \\ 16t^4-20t^2u-20t^2u+25u^2 \end{gathered}[/tex]Adding the like terms, we get that the simplified expression is
[tex]16t^4-40t^2u+25u^2[/tex]Then, the degree of the simplified expression is 4 because it is the maximum exponent.
So, the answers are:
16t⁴ - 40t²u + 25u²
degree = 4
pls help me here pls I need answers ty
Answers
2)
Answer: 87 liters
Explanation:
1 m^23 = 0.001 L
87000 cm^3 = 87000 * 0.001
= 87 liters
Each month Mark‘s phone company charges a flat fee of $12 plus $0.05 per minute his bill for last month was $18 how many minutes did Marty talk on the phone last Month
Answers
Given:
Flat fee = $12
Per minute charge = $0.05
Total bill for last month = $18
To find the number of minutes, we have the equation:
18 = 12 + 0.05M
Where M represents number of minutes
Let's solve for M:
Subtract 12 from both sides:
18 - 12 = 12 - 12 + 0.05M
6 = 0.05M
Divide both sides by 0.05:
[tex]\begin{gathered} \frac{6}{0.05}=\frac{0.05M}{0.05} \\ \\ 120\text{ = M} \end{gathered}[/tex]Therefore, Marty spent 120 minutes talking on the phone last month.
ANSWER:
120 minutes
Find remaining zereos of f
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the function is:
degree: 4
and we know that some zeros are:
[tex]x=7i,3,-3[/tex]because the function is degree 4 we know that it should have 4 zeros. we also know that the function is symetric because of the real solutions, so the las solution will be the negative of the imaginari root so the remaining zeros are:
[tex]x=-7i[/tex]