Given:
[tex]\begin{gathered} u(x)=-2x^2+3 \\ v(x)=\frac{1}{x} \end{gathered}[/tex]Required:
To find the range of the function (uv)(x).
Explanation:
We know that
[tex]\begin{gathered} (uv)(x)=u(v(x)) \\ \\ =u(\frac{1}{x}) \\ \\ =-2(\frac{1}{x^2})+3 \\ \\ =-\frac{2}{x^2}+3 \end{gathered}[/tex]The horizontal asymptote of this function is at y=3.
So, the range of this function is from
[tex](-\infty,3)[/tex]Final Answer:
The range of (uv)(x) is
[tex](-\infty,3)[/tex]Tabitha has 6 music files, each with 9 songs in it. She is dividing the songs into 7 groups. If each of group will have the same number of songs, how many songs will be left over?
A.
0
B.
3
C.
5
D.
1
Answer:
5
Step-by-step explanation:
6*9= 54
54/7 = 7 with remain 5
8x - 7=7x - 2What is the answer?
The given equation is
[tex]8x-7=7x-2[/tex]First, we subtract 7x on each side.
[tex]\begin{gathered} 8x-7x-7=7x-7x-2 \\ x-7=-2 \end{gathered}[/tex]help meeeeeeee pleaseee
thank you
The Domain of the relation is: -∞ < x < ∞
The Range of the relation is: -∞ < y ≤ -3
What are Domain and Range?
The Domain of the function is the set of x-values for which the function is defined, whereas the Range of the function is the set of y-values for which it is defined.
Let us first determine the Domain.
On the x-axis, the curve starts from x = -∞, and ends at x = ∞
So, the domain of the relation is: -∞ < x < ∞
Next, let us now determine the Range.
On the y-axis, the curve starts from y = -∞, and it ends at y = -3
The Range of the relation is: -∞ < y ≤ -3
Hence the domain and the Range of the graph are: -∞ < x < ∞ and -∞ < y ≤ -3
Know more about Domain and Range: - https://brainly.com/question/28229059
#SPJ9
Here is a scatter plot: weight (pounds) 25 15 age (weeks) Select all the following that describe the association in the scatter plot. Linear association Non-linear association Positive association Negative association No association
A linear association is a straight-line relationship between two variables
positive association when above-averagevalues of one tend to accompany above-average values of the
other, and when below-average values also tend to occur together
Hence Linear association and positive association describe the scatter plot in the diagram
The first and the third option is correct
Label the coefficient constant exponent and verbal 5X^2-7
The labels of the expression given as 5x² - 7 are
Coefficient = 5Constant = 7Exponent = 2Variable = xHow to label the expression?The expression is given as
5x² - 7
As a general rule:
Expressions are represented using variables, terms, factors, coefficients, operators, constant, etc.
Each of these make up an expression
Take for instance, the following expression
axⁿ + b
The features are
Coefficient = aConstant = bExponent = nVariable = xUsing the above as a guide, the labels of 5x² - 7 are:
Coefficient (5), Constant (7), Exponent (2) and Variable (x)
Read more about expressions at
https://brainly.com/question/723406
#SPJ1
Proportions relay puzzle
Can you please show work for 11,12,13,14,15,16
What is cross multiplication?
To discover the unknown values in a mathematical equation, we cross multiply the numbers in the equation. The method of cross multiplication is frequently employed to identify the missing variable in an equation. We multiply both the numerator and denominator of the provided expression or fractions.
If w/e = r/t is the given expression, then the formula for cross multiplication can be given as: w*t = r*e
For 11, comparing numerators by multiplying the 'x' on right with 2.5 we get, x - y = 2.5x ⇒ 1.5x + y = 0, only possible if y = -1.5x
Therefore, the blank in 11 should be filled using (-1.5x).
For 12, comparing numerators by multiplying LHS with 6 and RHS with 4, we get, 6(h + y) = 4(h - 12) ⇒ 6h + 6y = 4h - 12 ⇒ 6y = -2h -12
⇒ y = (-1/3)h -2
Therefore, the blank in 12 should be filled using (-1/3)h -2.
Similarly, using cross multiplication and equating denominators for the next four, the blank spaces can be constructively filled.
To learn more about this, tap on the link below:
https://brainly.com/question/973146
#SPJ9
solve the system by substitution.-3x—6y=45 -5y=x
The second equation already has the value of x isolated, so in order to solve the system by substitution, we can apply this value of x from the second equation in the first one:
[tex]\begin{gathered} x=-5y \\ \\ -3x-6y=45 \\ -3\cdot(-5y)-6y=45 \\ 15y-6y=45 \\ 9y=45 \\ y=\frac{45}{9}=5 \end{gathered}[/tex]Now that we have the value of y, we can find the value of x:
[tex]x=-5y=-5(5)=-25[/tex]So we have that x = -25 and y = 5.
A bag contains 7 red, 4 blue, and 6 yellow marbles. If 3 marbles are selected in succession, what is the probability of selecting blue, then yellow, then blue, if no replacement occurs each time?
The probability of selecting blue, yellow and blue marble without replacement is 3/170
Number of red marbles = 7
Number of blue marbles = 4
Number of yellow marbles = 6
Total number of marbles = 17
Probability of selecting a red marble = 7/17
Probability of selecting a blue marble = 4/17
Probability of selecting a yellow marble = 6/17
Now the probability of selecting the first blue marble = Number of blue marbles/Total number of marbles. = 4/17
Probability of selecting the yellow marbles = Number of yellow marbles/Number of marbles left after the first draw = 6/16
Probability of selecting the third blue marble = Number of blue marbles/Total number of marbles left after the second draw = 3/15
So the probability of blue, yellow and blue marble is:
4/17*6/16*3/15 = 3/170
Learn more about probability:
https://brainly.com/question/11234923
#SPJ1
PLEASE I NEED THIS REALLY REALLY BAD
The quadratic function that includes the given points is given by y = 3/5x² + 6/5x + 6.
what is a quadratic function?When a polynomial function has one or more variables and the highest exponent of any one of the variables is two, the function is said to be quadratic. A "polynomial function of degree 2," then, is a quadratic function.
The definition of a quadratic function:A quadratic function is one that has the formula f(x) = ax2 + bx + c, where a, b, and c are all integers with a not equal to zero. A parabola is the shape that makes up the graph of a quadratic function. The basic "U" shape of a parabola is the same whether it opens upward or downward, or with a different "width" or "steepness."
According to the given data:If we put the values of points in the above equation, then we get.
Putting point (0,6) we get
6 = 0 + 0 + c
=> c = 6
Putting point (2,8) we get
8 = 4a + 2b + 6
=> 2 = 4a + 2b
=> = 2a + b ......(1)
Putting point (3,-3) we get
-3 = 9a + 3b + 6
=> -9 = 9a + 3b
=> -3 = 3a + b ......(2)
From equation (1) b = 2a. Substitute the value of b in equation (2) we get
3 = 3a + 2a
=> a = 3/5
Now, b = 6/5
The quadratic function that includes the given points is given by y = 3/5x² + 6/5x + 6.
To know more about quadratic function visit:
https://brainly.com/question/28805314
#SPJ13
1. WHAT IS THE STANDARD DEVIATION FOR THE FOLLOWING DATA. ROUND YOUR ANSWER TO TWO DECIMAL PLACES 6 8 5 11 4 22.WHAT IS THE STANDARD DEVIATION FOR THE FOLLOWING DATA.90 90 90 90 90 90?3.) IF THE STANDARD DEVIATION IS 9, WHAT IS THE VARIANCE?
Solution:3.16
Analysis: In the first step, we need to find the mean of values we have in the exercise:
[tex]Mean=(6+8+5+11+4+2)/6=36/6=6[/tex]Now, let's find the standard deviation:
Subtract the mean from each of the data values and list the differences.
6-6=0
8-6=2
5-6=-1
11-6=5
4-6=-2
2-6=-4
Now, let's square each of the differences from the previous step and make a list of the squares.
[tex]\begin{gathered} 0^2=0 \\ 2^2=4 \\ (-1)^2=1 \\ 5^2=25 \\ (-2)^2=4 \\ (-4)^2=16 \\ \end{gathered}[/tex]Now, let's add the squares from the previous step:
0+4+1+25+4+16=50.
Let's use the formula
[tex]S=\sqrt{\frac{\sum_{i=1}^n(x_i-\bar{x})^2}{n-1}}=\sqrt{\frac{50^{}}{6-1}}=\sqrt{10}=3.16[/tex]help meeeeeeeeeeeeeeeeeeeeeee
thank you
The amount of coffee that was imported in 2007 is 2.0606 million pounds.
What is a function?It should be noted that a function simply s used to illustrate the relationship between the variables given.
From the information, the function is illustrated as:
= 0.7166x² + 6.267x + 1.344
x represents 1997 which was given as 0.
Therefore, the amount in 1997 will be:
= 0.7166x² + 6.267x + 1.344
= 0.7166(0)² + 6.267(0) + 1.344
= 0.7166 + 1.344
= 2.0606 million pounds.
Learn more about functions on:
brainly.com/question/25638609
SPJ1
What’s the correct answer answer asap for brainlist i really need help
Answer:
C, a transcript of information from DNA
Step-by-step explanation:
mRNA is option C.) “a transcript of information from DNA.”
The role of messenger RNA is to transfer information across the cell. This process has to work this way because DNA cannot leave the nucleus, while RNA can. mRNA uses ribose to provide instructions to ribosomes on how the cell makes proteins.
if 275 suals equals 800 cuals and 26 duals equals 10 cuals, how many duals equal 2250 suals?
Answer:
D=17018.18
Step-by-step explanation:
275S=800C
26D=10C
- - -
275S=800C, so 1S=2.9090C
26D=10C, so 1C=2.6D
2250S=6545.4545C
6545.4545C=17018.18D
D=17018.18
hope this helps :) i would much appreciate brainliest
what 10/4 in a fraction
adam owns a restaurant. a new dish is being added to the restaurant's menu. the cost of making the dish is $6.75, and he wants to make a 33% profit on each dish he sells.
what is adam's selling price?
question 1 options: 10.08 5.22 11.33 26.05
If the cost of making the dish is $6.75, and he wants to make a 33% profit on each dish he sells. adam's selling price is: $8.98.
How to determine the selling price?Using this formula to find the selling price
Selling price = Cost price + (Cost price × Profit percentage)
Let plug in the formula
Selling price = $6.75 + ($6.75 × 33%)
Selling price = $6.75 + $2.2275
Selling price = $8.977
Selling price = $8.98 (Approximately)
Therefore the selling price is the amount of $8.98
Learn more about selling price here: https://brainly.com/question/1153322
#SPJ1
I NEED HELP ASAP PLEASE!
The output value of the function is 8 when the input value is -2
What is input and output value ?
A relation's input value is its first value, and its output value is its second. A particular kind of relation called a function is one in which every input value has only one and only one output value.
The value of an input is the independent value, but the value of an output is dependent on the value of the input.
Only data flows, mining flows, and sub processes can use input variables. The variable value that was modified inside a sub process is output using output variables.
To learn more about input and output value refer to :
https://brainly.com/question/25983065
#SPJ13
Consider the functions f(x) = (x - 5)^2 + 2 and g(x) = (x + 6)^2 - 4. Which of the following statements is true?
To solve the question, we can plot the two functions on the same graph as shown below
The blue graph is that for the function g(x)
While that of the red graph is that of the function f(x)
We can observe that the graph of g(x) is
[tex]\begin{gathered} 2-(-4)=6 \\ 6\text{units below f(x)} \end{gathered}[/tex]Also,
[tex]g(x)\text{ is 11 units to left of f(x)}[/tex]Thus, we can see that
The graph of g(x) is shifted 6 units below and 11 units to the left of the graph f(x)
Thus, option C is correct
A math student has a plan to solve the following system by the elimination method. To eliminate the x-terms, he wants to multiply the top equation by 7 . What should he multiply the second equation by so that when he adds the equations, the x-terms are eliminated?
Answer
To eliminate x, we will multiply the second equatio by -3.
x = 7
y = 5
Explanation
To solve this, we first write the two equations
-3x - 7y = -56
-7x + 10y = 1
So, to solve this, we need to make sure the factors of x are the same numbers and of opposite signs
So, if we multiply the first equation by 7, we will need to multiply the second equation by -3 to obtain 21x and -21x for the two of them.
(-3x - 7y = -56) × 7
(-7x + 10y = 1) × -3
-21x - 49y = -392
21x - 30y = -3
We will then add the two equations and then the solution for the equation is obtained by solving for y first.
-21x + 21x - 49y - 30y = -392 - 3
0 - 79y = -395
-79y = -395
Divide both sides by -79
(-79y/-79) = (-395/-79)
y = 5
We can then solve for x using any of the two equations
-7x + 10y = 1
-7x + 10(5) = 1
-7x + 50 = 1
-7x = 1 - 50
-7x = -49
Divide both sides by -7
(-7x/-7) = (-49/-7)
x = 7
Hope this Helps!!!
prove that the medians to the legs of an isosceles triangle are congruent
I need the step by step proof on this
The median of the legs of a triangle joins the vertex to the midpoint of the opposite side of the triangle. Hence, they are congruent. The correct postulate is (D) SAS See proof below.
What exactly are Congruent Triangles?Congruent triangles are those with the same size and form. This signifies that the respective sides are equal, as are the corresponding angles.
The median of a triangle's legs connects the vertex to the midway of the opposing side of the triangle. An isosceles triangle has two sides and angles that are congruent.
This suggests that postulates AAA and SSS are ruled out.
This is because both postulates entail that the triangles' sides and angles are congruent.
Sides AB and AC are congruent (S)
Sides CD and BD are also congruent (S)
Angles at D on both triangles are congruent (A)
These mean that:
The triangles are congruent by the SAS postulate. Thus, the correct postulate is (d) SAS
Learn more about similar triangles:
https://brainly.com/question/14285697
#SPJ1
Full Question:
Prove that the medians to the legs of an isosceles triangle are congruent. What rule did you use to prove triangles congruent:
1. AAA
2. ASA
3. Cannot be determined
4. SAS
5. SSS
The length of the longer leg of a right triangle is three less than twice the length of the shorter leg, and the length of the hypotenuse is five more than twice the length of the shorter leg. If the length of the shorter leg is k, write an equation to find the value of k
length of the shorter leg = k
length of the longer leg = 2k - 3
length of the hypothenus = 5 + 2k
to solve this problem, we have to use pythagorean theorem
pythagorean theorem states that
[tex]\text{hyp}^2=\text{adj}^2+\text{opp}^2[/tex]hyp = hypothenus
adj = adjacent
opp = opposite
now let's plug in our variables into the equation
[tex](5k+2)^2=(2k-3)^2+k^2[/tex]this is an equation to find the value of k
we can further simplify this to get a quadratic equation
[tex]\begin{gathered} (5k+2)^2=(2k-3)^2+k^2_{} \\ 10k^2+20k+4=(4k^2-12k+9)+k^2 \\ 10k^2+20k+4=4k^2-12k+9+k^2 \\ \text{collect like terms} \\ 10k^2+20k+4-4k^2+12k-9-k^2 \\ (10-4-1)k^2+(20+12)k-9+4_{} \\ 5k^2+32k-5=0 \end{gathered}[/tex]the above written equation can be used to solve for k
note: in opening the bracket
[tex]\begin{gathered} (5k+2)^2=a^2+2ab+b^2 \\ \text{that is the how the bracket opens} \\ a=5 \\ b=2 \end{gathered}[/tex]If T is the midpoint of SU, find TU.
S 9x
T 5x+28 U
The length of each segment ST = 63, TU = 63, SU = 126
What is a midpoint theorem?The midpoint theorem states that “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”
From the given figure
ST = 9x
TU = 5x+28
According to midpoint theorem,
ST = TU
9x = 5x+28
9x-5x = 28
4x = 28
x = 7
It means,
ST = 9×7 = 63
TU = 5×7+28 = 35+28 = 63
SU = ST+TU
= 63+63
ST = 126
Hence, The length of each segment ST = 63, TU = 63, SU = 126
To learn more about midpoint theorem from the given link:
https://brainly.com/question/11015073
#SPJ9
Jamila has a weather station in her backyard. She uses a rain gauge to track the total rainfallduring two storms3) next Jamilia a graph the function describing thursdays rainfall is this graph liner or non-liner? how do you know?4) what does the Y intercept of the graph on Mondays storm mean? does the Y intercept of the graph of Thursday storm have the same meaning?
a) It's a linear function because if time increases, precipitation increases. I'll graph it. On the graph we observe that the points form a line.
b) Both intercepts have the same meaning.
It means the amount of water (rain) at time = 0, when it still does not started to rain.
2) Explain the steps on how you would write x + 2y < 8 in slope intercept form.
ANSWER
[tex]y\leqslant-\frac{1}{2}x+4[/tex]EXPLANATION
The slope-intercept form of a line is,
[tex]y=mx+b[/tex]In this case, we have an inequality but the steps to rewrite it in the slope-intercept form are similar to the ones we would use if we had an equality.
Step 1: subtract x from both sides of the inequality,
[tex]\begin{gathered} x-x+2y\le8-x \\ \\ 2y\le-x+8 \end{gathered}[/tex]Step 2: divide both sides by 2,
[tex]\begin{gathered} \frac{2y}{2}\le\frac{-x+8}{2} \\ \\ y\le\frac{-x+8}{2} \end{gathered}[/tex]Step 3: distribute the denominator and simplify the fractions if possible,
[tex]\begin{gathered} y\le\frac{-x}{2}+\frac{8}{2} \\ \\ y\le-\frac{1}{2}x+4 \end{gathered}[/tex]Hence, the inequality in slope-intercept form is,
[tex]y\leqslant-\frac{1}{2}x+4[/tex]WILL GIVE BRAINLIEST
Question 4(Multiple Choice Worth 2 points)
(01.03 LC)
Simplify 4x√3x-x√√3x-2x√√3x.
Ox√3x
x√9x
2x√6x
2x√6x³
Answer:
[tex]x\sqrt{3x}[/tex]
Step-by-step explanation:
Given expression to simplify:
[tex]4x\sqrt{3x}-x\sqrt{3x}-2x\sqrt{3x}[/tex]
Factor out the common term [tex]\sqrt{3x}[/tex] :
[tex]\implies \sqrt{3x}(4x-x-2x)[/tex]
Carry out the operations inside the parentheses:
[tex]\implies \sqrt{3x}(3x-2x)[/tex]
[tex]\implies \sqrt{3x}(x)[/tex]
Therefore the simplified expression is:
[tex]\boxed{x\sqrt{3x}}[/tex]
Answer:
a) x√(3x)
Step-by-step explanation:
We have to simplify,
→ 4x√(3x) - x√(3x) - 2x√(3x)
Then the simplest form is,
→ 4x√(3x) - x√(3x) - 2x√(3x)
→ 4x√(3x) - 3x√(3x)
→ x√(3x)
Hence, option (a) is correct.
What is equivalent to 7-5x=10-(6x+7)
In order to find the equivalent of the expression we will need to simplify it, this is done by combining terms with the same variable.
[tex]\begin{gathered} 7\text{ - 5x = 10 -6x + 7} \\ 7\text{ - 5x = 17 - 6x} \end{gathered}[/tex]The correct answer would be the fourth option.
how to solve 2-(×+4)=10
Given 2-(×+4)=10, to find x, our 1st step will be to open the bracket;
[tex]\begin{gathered} 2-(x+4)=10 \\ 2-x-4=10 \\ -2-x=10 \end{gathered}[/tex]The 2nd step is to add 2 to both sides of the equation, this will give us the below;
[tex]-x=12[/tex]The final thing to do is to multiply both sides of the equation with -1;
[tex]x=-12[/tex]Therefore. x
Assume that when adults with smartphones are randomly selected 42% use them in meetings or classes. If 30 adult smartphones users are randomly selected find the probability that exactly 18 of them use their smartphones in meetings or classes
0.0095 is the probability that exactly 18 of them use their smartphones in meetings or classes.
How does probability explain work?
In a random experiment, probability is the indicator of how likely an occurrence is to take place. A number between 0 and 1 is used to quantify probability, with 1 roughly corresponding to certainty and 0 roughly indicating impossibility. The likelihood that an event will occur increases with its probability.Given that ,
p = 0.42
1 - p = 1 - 0.42 = 0.58
n = 30
Using binomial probability formula ,
P(X = x) = (n C x) * px * (1 - p)n - x
P(X = 19 ) = (30 C 19) * (0.42)19 * (0.58)11
= 0.009481
Probability = 0.0095
Learn more about probability
brainly.com/question/11234923
#SPJ13
2(a + b) + 4m(a + b)
Answer:
(a+b) 2+4m
Step-by-step explanation:
(a+b) 2+4m
take (a+b) out
Answer: 4am+4bm+2a+2b
Step-by-step explanation:
Distribute: 2(a+b)+4m(a+b)
2a+2b+4m(a+b)
Distribute: 2a+2b+4m(a+b)
2a+2b+4am+4bm
Rearrange terms: 2a+2b+4am+4bm
4am+4bm+2a+2b
Solution: 4am+4bm+2a+2b
write an equation for each translation of y=|x|a) 3 units upb) left to units
In a translation, the general translation of y=f(x) is that y=f(x+a) if f(x) is translated by a units towards left direction or downward and y = f(x) = f(x-a) is f(x) is translated by "a" units towards right direction or upward
Hence:
Translation of y =|x|
a) 3 units up
y = | x - 3|
b) left 2 units
y = | x+2|
Find the length of side x
[tex]\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ x = \sqrt{18^2+15^2~-~2(18)(15)\cos(105^o)} \implies x = \sqrt{ 549 - 540 \cos(105^o) } \\\\\\ x\approx\sqrt{549-(-139.76)}\implies x\approx\sqrt{688.76}\implies {\Large \begin{array}{llll} x\approx 26.2 \end{array}}[/tex]
Make sure your calculator is in Degree mode.
