Answers
Answer:
Option B
Domain: all real numbers
Range [tex]f(x) \le -8[/tex]
Step-by-step explanation:
Given function is:
[tex]f\left(x\right)=-\dfrac{5}{6}\:\left(x\:+\:2\right)^2\:-\:8[/tex]
The domain is the set of all x values that result in a real and defined value for f(x).
The function has no undefined points and x is free to range from -∞ to +∞
So the domain is -∞ < x <∞ which is
All real numbers
The range is the set of all possible values for f(x) given a specific domain. In order to determine the range without too much hard work, let's first examine the function f(x)
The above function is the equation for a parabola.
Some things to note about a parabola equation:
The vertex form equation of a parabola is:[tex]f(x) = a(x - h)^2 + k[/tex]
where the vertex is the point (h, k). So the x-value of the vertex = h and corresponding y-value is A vertex is the maximum or minimum point in the parabola If the coefficient a > 0 then the parabola opens upward and the vertex i(h, k) s a minimumIf the coefficient, a < 0 the parabola opens downward and the vertex (h, k) is a maximum
Let us compare the general vertex form equation of the parabola with the specific f(x) equation given
General Equation: [tex]a (x - h)^2 + k[/tex]
This example: [tex]-\dfrac{5}{6}\:\left(x\:+\:2\right)^2\:-\:8[/tex]
Comparing the similarity between the two equations we easily see that
[tex]\boxed{a = -\dfrac{5}{6}}[/tex]
This means the parabola opens downward and (h, k) represents a max point in the parabola
[tex]x - h = x + 2\\\\-h = 2\\\\h = -2\\[/tex]
[tex]k = -8[/tex]
So the vertex is at (-2, -8)
Since -8 is the maximum value for f(x), and the parabola extends to infinity on both sides, the range is :
[tex]\boxed{f(x) \le -8}[/tex]
The attached graph may help you understand better
Related Questions
the length of a rectangular platform i 2 feet longer than three time it width. The area of the platform i 56 quare feet. Write a polynomial that repreent the area of the platform
Answers
This polynomial represents the area of the platform.A = w(w + 2)^2. the area of the rectangular platform is 56 square feet and the length of the platform is 2 feet longer than 3 times its width
A = w(w + 2)^2
A = Area of the platform
w = width of the platform
Since the area of the rectangular platform is 56 square feet and the length of the platform is 2 feet longer than 3 times its width, we can represent this statement mathematically as:
A = w(w + 2)^2
This polynomial represents the area of the platform.
A = w(w + 2)^2
A = w^2 + 2w^2
A = 3w^2
A = 56
3w^2 = 56
w^2 = 56/3
w = √56/3
A = w(w + 2)^2, area of the rectangular platform is 56 square feet and the length of the platform is 2 feet longer than 3 times its width.
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If you can't see it zoom in
Answers
The SAS congruency is applied here.
Hence,
[tex] \frac{TR}{JK} = \frac{RS}{JL} = \frac{TS}{KL} \\ \frac{24}{x} = \frac{12}{6} = \frac{y}{15} \\ \frac{24}{x} = 2 \\ x = 48 = JK[/tex]
[tex] \frac{y}{15} = 2 \\ y = 30[/tex]
Perimeter =
[tex]6 + 30 + 48 \\ 36 + 48 \\ = 84[/tex]
I do not understand please 5(x-3)-x=
Answers
Answer:4x-15
Step-by-step explanation:
Answer:
4x-15 <---
Step-by-step explanation)
1) Distribute the X to both the x and the -3
2) You'll end up with, 5x-15-x=...
3) And, now look at the like terms. The like terms in this case are 5x and the -x.
4) 5x-x =4x
5) And, now put them together, and you'll get 4x-15!
HOPE IT HELPS! <3
Write an equation in point slope form for the line that passes through (-4, 3) and whose slope is 3.
Answers
An equation in point slope form for the line that passes through (-4, 3) and whose slope is 3 is equal to y - 3 = 3(x + 4).
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represents the data points.m represents the slope.Next, we would determine the linear equation representing the line which passes through the points (-4, 3) and has a slope of 3 by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 3 = 3(x - (-4))
y - 3 = 3(x + 4)
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Solve and reduce to lowest terms: 5 x 2/7
Answers
The multiplication of the numbers given to the reduced form is 10/7.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
The given expression is 5 × 2/7
One of the number is a whole number and the other is a fraction.
We can write 5 as 5/1 in terms of fraction and then multiply the numerators and the denominator.
(5/1) × (2/7) = (5×2) / (1 × 7) = 10/7, which is in the lowest form.
Hence the solution of the multiplication is 10/7.
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4. Describe the graph of the line x = 12.
O vertical line
Oline with slope of 12
crosses the y-axis
O horizontal line
Answers
Answer:
The graph of the line x = 12 is a vertical line.
A vertical line is a line with a constant x-value, in this case x = 12, so all the points on the line will have an x-coordinate of 12, regardless of their y-coordinate. All the point on the line will have the same x-coordinate and it will be parallel to the y-axis.
It does not have a slope, does not cross the y-axis, it is not horizontal.
the length of a rectangular field is twice its breadth. Meghna jogged around it 5 times and covered a distance of 3 km. what is the length of the field?
Answers
The length of the rectangular field is 200 meters.
Given, we have length of the field equal to twice its breadth. Let the breadth of the field be "b". Therefore, length will be "2 x b". Now, Meghna jogged around the field 5 times which means she covered the perimeter of the field 5 times. We know that the perimeter of a rectangular field is [tex]2(l+b)[/tex] where l is the length of the rectangle and b is the breadth.
After jogging around the field 5 times, she covered a distance of 3 km. Converting kilo meters into meters: 3km ⇒ 3 x 1000 = 3000 meters. Now, We can equate the perimeter of the rectangle with the given information like this :
⇒[tex]2(l+b) * 5 = 3000m[/tex]
We already know that length = 2b, therefore putting in the equation gives us :
⇒ 2(2b+b) x 5 = 3000m
⇒2(3b) x 5 = 3000m
⇒10(3b) = 3000m
⇒30b = 3000m
Dividing both sides of the equation with 30,
⇒b = 100 m
Since, length = 2b, Therefore Length ⇒ 2 x 100m = 200m
∴ The length of the field is 200m
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Identify the dependent and independent variables for each relation
The faster you drive your car, the longer it will take to come to a complete stop
The Spanish classes are having a fiesta lunch. Each student that attends is to bring a Spanish side dish or dessert. The more students that attend, the more food there will be
Answers
Answer: The dependent variable is the time it takes to come to a complete stop. The independent variable is the speed at which you drive your car.
The dependent variable is the amount of food there will be. The independent variable is the number of students who attend the fiesta lunch.
Step-by-step explanation:
What is the probability that Andre, Olivia, and Zach all win gift cards that are at least $25?
Answers
The probability that Andre, Olivia, and Zach all win gift cards that are at least $25 is 0.
Since the value of the gift cards is determined by chance, it is impossible to calculate the probability of this exact outcome. Instead, we can calculate the probability of any one person winning a gift card that is at least $25, which is 0.5.
The probability of them all winning would be the product of the individual probabilities, which is 0.5 x 0.5 x 0.5 = 0.125. However, since this is impossible, the probability of this exact outcome is 0.
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1
2. Jim is 8 years old, and his Uncle Bill is 5 times older
2
than he his. What is his Uncl Bill's age?
Answers
Answer:
Uncle Bill is 40 years old.
Step-by-step explanation:
Jim is 8 years old, and Uncle Bill is 5 TIMES older, meaning he is 5x8. Which would be 40 years old.
Which pair of ratios does not form a true proportion? A)6:16 and 21:56 B) 2 to 10 and 15 to 75 C) 9/11 = 27/15 D) y=5x
Answers
The ratios 6:16 and 21:56, 9/11 = 27/15, and y=5x do not form a true proportion. Hence, options A, C, and, D are the correct options.
A true proportion is when both the ratios presented are equal. This can be verified by putting them in their respective fractional form. For example, let's take the ratios in the second option -
= 2/10 and 15/75
Here, we can see that 2*5 = 10 and 15*5 = 75
Hence these can be written as
= 2/2*5 and 15/15*5
Hence, these fractions are the same and as a result, the ratios form a true proportion.
As for the other ratios in question -
A) 6/16 is not equal to 21/56
C) 9/11 is not equal to 27/15
D) y= 5x are not proper ratios and are not equal
Thus, options A, C, and, D are the correct options.
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over the past few decades, public health officials in massachusetts have been examining young-teen smoking. the long-run average smoking prevalence in the state has been 26%. officials have been hopeful that their ad campaigns on billboards and tvs have been effective at lowering smoking rates for this age group. researchers surveyed a group of 273 randomly selected teens living in massachusetts (between 12 and 15 years old). sixty-three said they smoked. is there good evidence that smoking rates for young teens have decreased?
Answers
There is good evidence that smoking rates for young teens in Massachusetts have decreased.
To answer this question, we need to calculate the proportion of teens in the sample who said they smoked (63/273). This gives us a sample proportion of 0.23, which is lower than the long-run average smoking prevalence in the state (26%). This suggests that there is good evidence that smoking rates for young teens have decreased.
We can also calculate a confidence interval to further assess the evidence. A 95% confidence interval for the true proportion of teens in Massachusetts who smoke would be (0.17, 0.29). This confidence interval does not contain the long-run average smoking prevalence of 26%, which suggests that there is a statistically significant decrease in smoking rates for young teens in Massachusetts.
Overall, there is good evidence that smoking rates for young teens in Massachusetts have decreased.
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A family has two cars. During one particular week, the first car consumed 35 gallons of gas and the second consumed 20 gallons of gas. The two cars drove a
combined total of 1575 miles, and the sum of their fuel efficiencies was 60 miles per gallon. What were the fuel efficiencies of each of the cars that week?
Note that the ALEKS graphing calculator can be used to make.computations easier.
First car: miles per gallon
Second car: miles per gallon
Answers
Solving a system of equations we will see that the efficiency of the first car is 25 miles per gallon, and the one of the second car is 35 miles per gallon.
How to find the fuel efficiencies?Let's define the variables:
x = fuel efficiency of the first car.
y = fuel efficiency of the second car.
We know that the sum is equal to 60 miles per galon, thus:
x + y = 60
We also know that the he first car consumed 35 gallons of gas and the second consumed 20 gallons of gas. The two cars drove a combined total of 1575 miles, this can be written as:
35x + 20y = 1575
Then we have a system of equations:
x + y = 60
35x + 20y = 1575
We can isolate x on the first equation to get:
x = 60 - y
And substitute that in the other equation:
35*(60 - y) + 20y = 1575
2100 - 15y = 1575
2100 - 1575 = 15y
525/15 = y
35 = y
And x = 60 - y = 60 - 35 = 25
These are the efficiencies.
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inequality notation of 3 − 5x > −2
Answers
Answer:x<1
Step-by-step explanation:
move constant -5x>-2-3
Add alike numbers (-2 and -3)
-5x>-5
Divide both sides by -5
Then flip the inequality sign
x<1
Answer:
Step-by-step explanation:
Add 3 to the -2
-5x > 1
Divide by -5 the sign switches because of the negative
x < - 1/5 or X < -0.2
order reads: klotrix 0.35 meq/lb po dissolved in 6 oz of orange juice at 8 am; available: klotrix 8 meq/ml. how many ml of klotrix will you add to the orange juice for a 20.5 kg patient? round your answer to the nearest tenth.
Answers
We will add 2 ml of klotrix to the orange juice for a 20.5kg patient.
We know that , 1 kg=2.20462 pounds
Therefore, 20.5kg=20.5x2.20462 pounds= 45.195 pounds or 45.195 lb
Additionally we have, 1 lb = 0.35 mEq
Therefore, 45.195 lb= 0.35 mEq × 45.195 = 15.818 mEq.
Also, 8mEq=1 mL
By using unitary method,
1 mEq=1/8 mL
Converting 15.818 mEq to mL, we get
15.818mEq = 15.818 ÷ 8 = 1.9 mL
Thus, 15.818mEq = 1.9 mL
Rounding off the answer we get,
The amount of klotrix required to add to the orange juice for a 20.5 kg patient is 2mL
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will give brainliest
Answers
When the line of slope of 3 passes through two points, the value of y is -8.
What is slope?The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope is a numerical value that describes the steepness of a line and is typically calculated by dividing the vertical distance by the horizontal distance (rise over run) between two points.
Here,
m=3
m=(y2-y1)/(x2-x1)
3=(y+5)/(-3+(2))
-3=y+5
y=-8
The value of y is -8 when the line of slope of 3 is passing through 2 points as given.
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describes the route of a limousine in a city from its starting position. Describe the route in words. Assume that the positive y-axis points north.
Answers
The description of the route of the limousine is
First, the limousine drives 18 blocks right and 8 blocks down and then it drives 17 blocks left and 2 blocks up
How to describe the route of the limousine in words?From the question, we have the following parameters that can be used in our computation:
T<18, -8> o T<-17, 2>
The above parameters represent the transformation and the positions of the limousine
T<18, -8> represents a movement 18 units right and 8 units downT<-17, 2> represents a movement 17 units left and 2 units upThe above statement represents the direction in words
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1. Jackie gets paid $45 for 2 hours of work. How many
nickels per minute does she get paid? (PLEASE PUT IN ASPECT RATIO FORM)
Answers
Answer:15 nickels per minute (I believe)
Step-by-step explanation:
First, we want to know how much she got paid in total dollar amount, we'll break it up into nickels later. We know Jackie was paid $45 per hour, but we want to figure out how much per minute she makes. There are 60 minutes in an hour, so divide 45 by 60 ( 45/60 in a calculator).
The answer for 45/60 would then be 0.75. This means Jackie gets paid 75 cents a minute. Since a nickel is worth 5 cents, we just need to divide 75 by 5. Then, we get 15.
Now we know Jackie gets paid 15 nickels per minute. I assume this would be put in aspect ratio form by saying "Jackie gets paid 15 nickels per every one minute of work." but that may depend on how your teacher wants you to word your answer. I hope this helps :)
equation=
ordered pair=(3,-4)
Slope(m)=
y-intercept=2
Answers
The equation of the line, given the ordered pair and the y - intercept, is y = -2 x + 2
The slope ( m ) is - 2
How to find the equation ?The equation for a linear model takes the form :
y = mx + b
m = slope
b = y - intercept
As we have the ordered pair, and the y - intercept, we can find the slope:
y = mx + b
- 4 = 3 x slope + 2
3 x slope = - 4 - 2
Slope = - 6 / 3
Slope = - 2
The equation is therefore:
y = -2 x + 2
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Which expression is equivalent to 1/4(3x+4y) + 3(1/4x+ 2/3y)
Answers
The expression is equivalent is 6x/4 + 24y/12
What are algebraic expressions?
Algebraic expressions are described as expressions composed of variables, terms, factors, constants, and coefficients.
These expressions also consisting of mathematical operations, such as;
AdditionParenthesesDivisionSubtractionMultiplicationFloor division, etcGiven the expression;
1/4(3x+4y) + 3(1/4x+ 2/3y)
expand the bracket
3x/4 + 4y/4 + 3/4x + 3/3y
collect like terms
3x/4 + 3/4x + 4y/4 + 3/3y
add like terms
3x + 3x/4 + 12y + 12y /12
add the numerators
6x/4 + 24y/12
Hence, the expression is 6x/4 + 24y/12
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To the nearest hundredth, find the value of x.
Answers
Answer:
Step-by-step explanation:
Two bags each contain five letter tiles. The sample space is shown below. Jennifer selects one tile from each bag without looking. What is the probability that Jennifer selects two vowels
Answers
The probability that Jennifer selects two vowels is 24%.
How to calculate the probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to predict with absolute certainty. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
Here, the probability that Jennifer selects two vowels is:
= 3/5 × 2/5.
= 6 / 25
= 24%.
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Frannie put 1/5 of her music collection on an MP3 player. While on vacation she listened to 1/6 of the music on the player. How much of Frannie’s music collection did she listen to while on vacation? Choose the correct values to describe how to solve the problem.
Draw a rectangular array with 5 rows and A) 5 B) 6 C) 9 rows.
Shade A) 4 B) 1 C) 3 rows gray.
Shade A) 2 B) 1 C) 4 columns black.
Please help me with this I will mark brainliest!!!
Answers
Frannie listened to 1/30 of her music collection while on vacation.
We have been given that Frannie put 1/5 of her music collection on an mp3 player. while on vacation, she listened to 1/6 of the music on the player.
To find the amount of music collection listened to by Frannie, while on vacation, we need to find 1/5 of 1/6.
The amount of music collection listened to by Frannie on the vacation: =1/5*1/6
=1/30
Therefore, Frannie listened to 1/30 of her music collection while on vacation.
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Explain in words how the method for solving equations with fractional or decimal
coefficients and constants compare with the method for solving
Answers
The approach used to solve equations with integer coefficients & constants can also be used to solve equations with fractional / decimal coefficients and constants.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It is a relationship between two or more variables, such as x + y = z. Equations are used to solve a wide variety of problems in mathematics, physics, chemistry, engineering and other scientific fields.
The main difference is that when solving equations with fractional or decimal coefficients and constants. For example, if you have an equation with a decimal coefficient, divide both sides by the coefficient to make the coefficient 1 before you can use the same steps to solve the equation.
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Xander's hedgehog weighs 0.62 pound.
Express his hedgehog's weight in grams.
Round your answer to the nearest gram.
Answers
so 0.62 lb x 453.59237= 281.2272694 g
rounded would be 281.2
The speed of light is 3 x 10 8squared m/s. if its frequency is 4.11 x 10 4squared Hz, what is its wavelengeth
Answers
Taking into account the definition of wavelength, frecuency and propagation speed, the wavelength of a wave with a frequency of 4.11×10⁴ Hz is 7299.27 m.
WavelengthWavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).
FrequencyFrequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).
Propagation speedThe propagation speed is the magnitude that measures the speed at which the wave disturbance propagates along its displacement.
The propagation speed relate the wavelength (λ) and the frequency (f) using the following equation:
v = f×λ
Wavelengeth in this caseIn this case, you know:
v= 3×10⁸ m/s
f= 4.11×10⁴ Hz
λ= ?
Replacing:
3×10⁸ m/s= 4.11×10⁴ Hz× λ
Solving:
λ= 3×10⁸ m/s ÷ 4.11×10⁴ Hz
λ=7299.27 m
In summary, the wavelength of the wave is 7299.27 m.
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Whitch equation represents a cricle with the center t(5,-1) and q radius of 16 units
Answers
(x - h)^2 + (y - k)^2 = r^2 is the equation for a circle with center (h, k) and radius (r).
What exactly is a math equation?
A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra. Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal."
So, an equation that represents a circle with center (5, -1) and radius of 16 units is:
(x - 5)^2 + (y + 1)^2 = 16^2
or
(x - 5)^2 + (y + 1)^2 = 256
The graph of this equation will be a circle centered at the point (5,-1) with a radius of 16 units.
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what is the relationship between the singular values of a and the eigen- values of aat ? what about at a?
Answers
The eigenvectors of AAH are called the left-singular vectors of A and the eigenvectors of AHA are the right-singular vectors of A . They are called this way because of their use in singular value decomposition. Say A=UΣVH , then the columns of U are the left-singular vectors and the columns of V are right-singular vectors.
We know that the non-zero eigenvalues of AAH and AHA are the same, they are the squares of the singular values of A . A singular of value of A is a value σ such that Av=σu AHu=σv where u is a left-singular vector and vs a right-singular vector. This can be taken as the definition of singular value, left-singular vector (which is an eigenvector of AAH) and right-singular vector (which is an eigenvector of AHA).the left-singular and right-singular vector pair works with AAH and AHA
AAHu=σAv=σ2u
AHAv=σAHu=σ2v
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Q: What is the relationship between the eigenvectors of AAT and ATA?
Evaluate the expression.
(13×6)×5
=
Answers
3 pens cost £2.25
5 folders cost £5.80
Chris wants to buy 30 pens and 30 folders
he only has £60
does he have enough to buy 30 pens and 30 folders? yes or no
Answers
Yes, Chris has enough money to buy 30 folders and 30 pens.
How to know if he has enough to buy the pens and folders?The cost of the stationaries Chris bought are as follows:
3 pens cost £2.255 folders cost £5.80Chris wants to buy 30 pens and 30 folders and he has only £60.
Let's check If he has has enough money to buy the products.
Therefore,
3 pens cost £2.25
1 pen = ?
cost of 1 pen = 2.25 / 3 = 0.75 dollars
5 folders cost £5.80
1 folder = ?
cost of 1 folder = 5.80 / 5 = 1.16 dollars
Hence,
30(0.75) + 30(1.16) = 22.5 + 34.8 = 57.3 dollars
Therefore, he has enough money to buy 30 folders and 30 pens
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