The given function is f(x) = x^2 - 3x + 10
this means that the expression is a function of x
f(6) means replace x with 6
f(6) = (6)^2 - 3(6) + 10
f(6) = 36 - 18 + 10
f(6) = 18 + 10
f(6) = 28
The answer is 28
help meeeeeeeeee pleaseee !!!!!
The values of the functions are determined as:
a. (f + g)(x) = 3x² + 2x
b. (f - g)(x) = -3x² + 2x
c. (f * g)(x) = 6x³
d. (f/g)(x) = 2/3x
How to Determine the Value of a Given Function?To evaluate a given function, substitute the equation for each of the functions given in the expression that needs to be evaluated.
Thus, we are given the following functions as shown above:
f(x) = 2x
g(x) = 3x²
a. To find the value of the function (f + g)(x), add the equations for the functions f(x) and g(x) together:
(f + g)(x) = 2x + 3x²
(f + g)(x) = 3x² + 2x
b. To find the value of the function (f - g)(x), find the difference of the equations of the functions f(x) and g(x):
(f - g)(x) = 2x - 3x²
(f - g)(x) = -3x² + 2x
c. To find the value of the function (f * g)(x), multiply the equations of the functions f(x) and g(x) together:
(f * g)(x) = 2x * 3x²
(f * g)(x) = 6x³
d. To find the value of the function (f/g)(x), find the quotient of the equations of the functions f(x) and g(x):
(f/g)(x) = 2x/3x²
(f/g)(x) = 2/3x.
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How many 7 digit phone numbers can be created if the first digit cannot be a zero, and the lastnumber must be an odd number?
Given:
Number of digits = 7
The first digit cannot be zero
Last number = odd number
The possible numbers between other than zero is 9
and there are 5 odd numbers.
Hence, the number of possible combinations is:
[tex]\begin{gathered} =\text{ 9 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 5} \\ =\text{ 4500000} \end{gathered}[/tex]Answer: Option A
Sally wishes to purchase an IPhone 12. the price of the item is $849. the amount of money she save's per month is $70. The amount of money Sally already have's is $17. , , , : write your function and define your variables. your function should be in a slope-intercept form. what is ()input = number of months. and ()output = amount of money you need :: complete your input/output tabel. select 6 values for your input (). They can be consistent (, , , , , , ) Whatever the case, it should match your function. Substitute those values into your function to solve for your output () : create your graph. Clearly label your - and - axis and use an appropriation scale. Use the ordered pair from your input/output table to place on the graph. Connect your points with a straight line. : 1. how long will it take you to reach your goal and purchase your item? 2. looking at your data (table and graph) what is one observation you can make? 3. if you double your savings each month, how does this affect the time it takes to reach your goal amount? 4. how do you know your equation is a function?
when doing right triangle trigonometry how do you determine which sine you use like sin, cos etc?
Let's draw a right triangle to guide us:
Every right triangle will have one hypotenuse side and two leg sides. The hypotenuse is always the bigger one and it is always opposite to the right angle, so in this triangle the hypotenuse is a (the letter can change from exercise to exercise, but it is always the opposite to the rignt angle).
The legs can be classified as adjancent or opposite legs, but this is with respect to the angle we are using.
So, if we are using angle C, the opposite leg is the leg that is opposite to angle C, that is, c.
Thus, the adjancent leg is the leg that is touching the angle C, that is, b.
So, with respect to angle C, we have:
Hypotenuse - a
Opposite leg - c
Adjacent leg - b
The sine is the ratio between the opposite leg and the hypotenuse, always.
The cosine is the ratio between the adjacent leg and the hypotenuse, always.
The tangent is the ratio between the opposite leg and the adjacent leg, always.
For, for angle C, we have:
[tex]\begin{gathered} \sin C=\frac{c}{a} \\ \cos C=\frac{b}{a} \\ \tan C=\frac{c}{b} \end{gathered}[/tex]For angle B, we do the same, however now, the legs are switched, because the leg that is opposite to angle B is b and the leg that is adjance to angle B is c, so, for angle B:
Hypotenuse - a
Opposite leg - b
Adjacent leg - c
And we follow the same for sine, cosine and tangent but now for angle B and with the legs switched:
[tex]\begin{gathered} \sin B=\frac{b}{a} \\ \cos B=\frac{c}{a} \\ \tan B=\frac{b}{c} \end{gathered}[/tex]Questions regaring these ratios normally will present 2 values and ask for a third value. One of the values will be an angle, the other will be side (usually). So, we need to identify which angle are we working with and which sides are the hypotenuse, the opposite leg and adjancent leg with respect to the angle we will work with. Then we identify which of the side we will use and pick the ratio thet relates the sides we will use.
List all real values of x such that f(x) = 0, if there are no such real x, type DNE in the answer blank. If there is more than one real x, give a comma separated list (i.e: 1, 2) X =
Given the function defined as:
[tex]\begin{gathered} f(x)=-7+\frac{-8}{x-6} \\ \end{gathered}[/tex]The function can further be expressed as:
[tex]f(x)=-7-\frac{8}{x-6}[/tex]Find the LCM of the function;
[tex]\begin{gathered} f(x)=\frac{-7(x-6)-8}{x-6} \\ f(x)=\frac{-7x+42-8}{x-6} \\ f(x)=\frac{-7x+34}{x-6} \\ \end{gathered}[/tex]If f(x) = 0, then the value of x is calculated as:
[tex]\begin{gathered} \frac{-7x+34}{x-6}=0 \\ -7x+34=0 \\ -7x=0-34 \\ -7x=-34 \end{gathered}[/tex]Divide both sides of the equation by -7:
[tex]\begin{gathered} \frac{\cancel{-7}x}{\cancel{-7}}=\frac{\cancel{-}34}{\cancel{\square}7} \\ x=\frac{34}{7} \end{gathered}[/tex]Therefore the value of x if f(x) = 0 is 34/7
Simplify the expression.
the expression negative one seventh j plus two fifths minus the expression three halves j plus seven fifteenths
negative 19 over 14 times j plus 13 over 15
negative 19 over 14 times j minus 13 over 15
negative 23 over 14 times j plus negative 1 over 15
23 over 14 times j plus 1 over 15
The correct option is negative 23 over 14 times j plus negative 1 over 15
Given,
The expression negative one seventh j plus two fifths minus the expression three halves j plus seven fifteenths
The expression; -1/7j + 2/5 - 3/2j + 7/15
negative one seventh j = - 1/7j
two fifths = 2/5
three halves j = 3/2 j
seven fifteenths = 7/15
Now,
Substitute the values;
- 1/7j + 2/5 - 3/2j - 7/15
- 1/7j - 3/2j + 2/5 - 7/15
-2j - 21j /14 + 6 7 /15
-23j/14 + -1/15
Therefore,
The correct option is negative 23 over 14 times j plus negative 1 over 15
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match the function rule with the graph of the function (number 24)
It is given that the function is:
[tex]y=\frac{3}{4}\times4^x[/tex]Therefore y=0 then the value of x will be:
[tex]\begin{gathered} 0=4^x \\ x=-\infty \end{gathered}[/tex]Now at x=0, y will be:
[tex]y=\frac{3}{4}[/tex]at x=1, y will be:
[tex]y=\frac{3}{4}\times4=3[/tex]These 3 points that is (-inf,0),(0,3/4),(1,3) are on graph D.
Hence option D is coreect.
how do you find the x intercept for -(x-3)^2+12
This is the equation for the line.
Here the given equation is,
[tex]-(x-3)^2+12[/tex]We can calculate x intercept by substituting 0 for y, as there is no value of y,
the x intercept is none here. The graph is as follows,
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representations of the inequality -3(2x-5)<5(2-x) are -6x + 15 < 10 - 5x and "an open circle is at 5 and a bold line that starts at 5 and is pointing to the right" , the correct option is (c) and (d) .
In the question ;
it is given that
the inequality -3(2x-5)<5(2-x)
on solving this inequality further , we get
-3(2x-5)<5(2-x)
-6x+15<10-5x
which is option (c) .
Further solving
Subtracting 15 from both the sides of the inequality , we get
-6x + 15 -15 < 10 -5x -15
-6x < -5 -5x
-6x +5x < -5
-x < -5
multiplying both sides by (-1) ,
we get
x > 5 .
x> 5 on number line means an open circle is at 5 and a bold line starts at 5 and is pointing to the right .
Therefore , the correct representations of the inequality -3(2x-5)<5(2-x) are -6x + 15 < 10 - 5x and "an open circle is at 5 and a bold line that starts at 5 and is pointing to the right" , the correct option is (c) and (d) .
The given question is incomplete , the complete question is
Which are correct representations of the inequality -3(2x - 5) < 5(2 - x)? Select two options.
(a) x < 5
(b) –6x – 5 < 10 – x
(c) –6x + 15 < 10 – 5x
(d) A number line from negative 3 to 7 in increments of 1 , An open circle is at 5 and a bold line that starts at 5 and is pointing to the right.
(e) A number line from negative 7 to 3 in increments of 1, An open circle is at negative 5 and a bold line that starts at negative 5 and is pointing to the left.
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Select all rational numbers
help ASAP please
15 points
The resulting rational number is √100
Rational numbers:
A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0.
Given,
Here we have the following list of numbers
√75, -√25, 2√7, √100, √0.36, √0.0144, √3/7 , -√36/49
Now, we need to identify whether these are the rational numbers or not.
AS per the definition of rational number,
When we take the root for the value √75, we get 8.660 that is a non-whole square root, 8.660 is not a rational number.
The value -√25 takes the negative value so it is not a rational number.
The number 2√7, this one also produce on-whole square root, so this one is not a rational number.
The value of √100 is 10, and it is a rational number.
The value of √0.36 is 0.6 which is less than 0, so it is not a rational number.
The value of √0.0144 is 0.012 which is less than 0, so it is not a rational number.
The value of √3/7 this one also produce on-whole square root, so this one is not a rational number.
The value -√36/49 takes the negative value so it is not a rational number.
Therefore, the rational number is √100.
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Rewrite 20 - 4x³ using a common factor.
O 4x(5-x²)
O4(5 - 4x³)
02x(10-2x²)
02(10-2x³)
Answer:
[tex]20 - 4 {x}^{3} = 4(5 - {x}^{3} )[/tex]
Rewrite 4x + 16 using a common factor.
Answer 4(x + 4)
Which of the following is equal to the rational expression below when x+112x² – 121x +11A. +11B.X+ 11c. -11XD. X-11
SOLUTION
From the question we have
[tex]\frac{x^2-121}{x+11}[/tex]from difference of two squares, we have
[tex]\begin{gathered} \frac{(x-11)(x+11)}{x+11} \\ x+11\text{ above cancels the one below, we have } \\ x-11 \end{gathered}[/tex]Hence the answer is option D
In boot camp, a cadet must use a rope swing to cross an obstacle withoutfalling into the water hazard below. Unfortunately, they miss the platform onthe other side and swing back to where they started. If it takes the cadet 3.5seconds to swing from one side of the obstacle to the other and back, howlong is the rope swing? Use the formula:
Answer:
Choice C: 3.0 m
Explanation:
We are basically asked to solve for L using
Suppose the coordinate of p=2 and PQ=8. Whare are the possible midpoints for PQ?
The midpoint for segment PQ can be calculated as:
[tex]\frac{P+Q}{2}[/tex]Then, the midpoint of PQ is:
[tex]\frac{2\text{ + Q}}{2}=1+0.5Q[/tex]Additionally, PQ can be calculated as:
[tex]PQ=\left|Q-P\right|[/tex]So:
[tex]\begin{gathered} \left|Q-P\right|=8 \\ \left|Q-2\right|=8 \end{gathered}[/tex]It means that:
[tex]\begin{gathered} Q-2=8\text{ or } \\ 2\text{ - Q = 8} \end{gathered}[/tex]Solving for Q, we get:
Q = 8 + 2 = 10 or Q = 2 - 8 = -6
Finally, replacing these values on the initial equation for the midpoint, we get:
If Q = 10, then:
midpoint = 1 + 0.5(10) = 1 + 5 = 6
If Q = -6, then:
midpoint = 1 + 0.5(-6) = 1 - 3 = -2
The possible midpoints for PQ are 6 and -2
Ronda ate 2/5 of the pie. Connor ate .375 of the pie. How much did they eatcombined? (Express your answer either as a fraction or decimal)
To convert 2/5 to a decimal;
[tex]undefined[/tex]PLS HELP!!! Ill give 20 points!!!
Answer:
Step-by-step explanation:
22.57 cm inches are the net weight of the slope
Solve the equation by working backward through the number trick.
x = 3
Explanations:The given equation is:
[tex]\frac{4(x+3)-6}{2}=\text{ 9}[/tex]Step 1: Cross multiply
4 ( x + 3) - 6 = 9(2)
Step 2: Remove the brackets by expanding the equation
4x + 12 - 6 = 18
4x + 6 = 18
Step 3: Collect like terms
4x = 18 - 6
4x = 12
Step 4: Divide both sides by 4
4x / 4 = 12 / 4
x = 3
Help please not sure if I am right or wrong thank you
Given:
[tex]-1+\sqrt[]{-4}[/tex]To find the simplified complex number
[tex]\begin{gathered} -1+\sqrt[]{-4}=-1\pm2i \\ -1+\sqrt[]{-4}=-1+2i,-1-2i \end{gathered}[/tex]points E,D and H are the midpoints of the sides of TUV, UV=100,TV=126,and HD=100, find HE.
Since the triangles are similar there exists correspondance in the angles, so in order to solve this you just have to clear the function:
[tex]\begin{gathered} \frac{VD}{VU}=\frac{HD}{TU} \\ \end{gathered}[/tex]Since D is the midpoint of VU, VD=50
[tex]\begin{gathered} \frac{50}{100}=\frac{100}{TU} \\ 50\times TU=100\times100 \\ TU=200 \end{gathered}[/tex]then
[tex]\begin{gathered} \frac{HE}{UV}=\frac{HD}{TU} \\ \frac{HE}{100}=\frac{100}{200} \\ HE=\frac{100}{200}\times100 \\ HE=50 \end{gathered}[/tex]A business could not collect $5,000 that it was owed. The total owed to the business was $100,000. What fraction of the total was not collected? (Express As Fraction)
Total owed to the business = $100,000
amount that could not be collected = $5000
Fraction of total not collected
[tex]\text{fraction not collected=}\frac{5000}{100000}=\frac{5}{100}=\frac{1}{20}[/tex]The table shows the numbers of ships that visited a port in the past 5 years. Identify a polynomial function for thenumber of ships in thousands that visited the port in a given year.
The function is f(x) = 1.3x^2 + 0.1X
A dilation with a scale factor of 4 is applied to the 3 line segment show on the resulting image are P'Q', A'B', And M'N'. Drag and drop the measures to correctly match the lengths of The images
Given:
Scale factor = 4 (Dilation)
PQ = 2 cm
AB = 1.5 cm
MN = 3 cm
Find-:
[tex]P^{\prime}Q^{\prime},A^{\prime}B^{\prime}\text{ and }M^{\prime}N^{\prime}[/tex]Explanation-:
Scale factor = 4
So,
[tex]\begin{gathered} P^{\prime}Q^{\prime}=4PQ \\ \\ A^{\prime}B^{\prime}=4AB \\ \\ M^{\prime}N^{\prime}=4MN \end{gathered}[/tex]So the value is:
[tex]\begin{gathered} P^{\prime}Q^{\prime}=4PQ \\ \\ P^{\prime}Q^{\prime}=4\times2 \\ \\ P^{\prime}Q^{\prime}=8\text{ cm} \end{gathered}[/tex][tex]\begin{gathered} A^{\prime}B^{\prime}=4AB \\ \\ A^{\prime}B^{\prime}=4\times1.5 \\ \\ A^{\prime}B^{\prime}=6\text{ cm} \end{gathered}[/tex][tex]\begin{gathered} M^{\prime}N^{\prime}=4MN \\ \\ M^{\prime}N^{\prime}=4\times3 \\ \\ M^{\prime}N^{\prime}=12\text{ cm} \end{gathered}[/tex]Make a tree diagram, Please complete number 18.Please be quick, I am in a hurry.
Explanation:
The question wants us to list out all the possible outcomes in question 18
From the question
We have a spinner that has 5 possible outcomes
[tex]\mleft\lbrace\text{Red, Orange, Green, Purple, Yellow}\mright\rbrace[/tex]The outcomes of flipping a coin are
[tex]\begin{gathered} \mleft\lbrace\text{Head, Tail}\mright\rbrace\text{ } \\ \text{which can be written as} \\ \mleft\lbrace H,T\mright\rbrace \end{gathered}[/tex]Thus, to get the possible outcomes, we will have
How much should be invested now at an interest rate of 7% per year, compounded continuously, to have 2000 dollars in three years? Do not round intermediate computations, and round your answer to the nearest cent
Answer:
The amount that should be invested is $1621.16
Explanation:
The formula for continuous compound interest is:
[tex]A=Pe^{rt}[/tex]Where:
A is the amount of money after t years
P is the invested amount (what we want to find, in this case)
r is the rate of compounding in decimal
t i the amount of time compounding, in years
Then, in this case:
A = $2000
r = 0.07 (to convert percentage to decimal, we divide by 100: 7% / 100 = 0.07)
t = 3 years
Then:
[tex]2000=Pe^{0.07\cdot3}[/tex][tex]2000=Pe^{0.21}[/tex][tex]P=\frac{2000}{e^{0.21}}\approx1621.16849[/tex]To the nearest cent, P = $1621.16
4(3c+3)-3c+1=3(3c+5)-2
The given equation is,
[tex]4(3c+3)-3c+1=3(3c+5)-2[/tex]The above equation can be simplified as follow,
[tex]undefined[/tex]Which relation is a function? choose all the correct answers.[1] (1, 0), (3, 0), (1, 1), (3, 1) (1, 3) [2] (1, 1), (2, 2), (3, 3), (4, 4), (5, 8)[3] (2, 7), (6, 5), (4, 4), (3, 3), (2, 1)[4] (9, −3), (9, 3), (4, −2), (4, 2), (0, 0)
A relation is a function if an input value has only one output value. This means that a value of x must have only one value of y. Looking at the options,
1) for x = 1, there are different values of y. They include y = 0, 1, 3
for x = 3, y = 0, 1
This means that it is not a function
2) No value of x has more than one value of y. Thus, no input has more than one output. This means that it is a function
3) for x = 2, there are different values of y. They include y = 7, 1
This means that it is not a function
4) for x = 9, there are different values of y. They include y = - 3, 3
for x = 2, there are different values of y. They include y = - 2, 2
This means that it is not a function
Thus, the correct option is
[2] (1, 1), (2, 2), (3, 3), (4, 4), (5, 8)
if the population of a city is 158,000 and isdecreasing by 8% every year, what will thepopulation be in 5 years?
Solution:
From the question, we use the population decay formula expressed as
[tex]\begin{gathered} P(t)=P(1-r)^t \\ where \\ P\Rightarrow initial\text{ population} \\ r\Rightarrow decay\text{ rate} \\ t\Rightarrow time \\ P(t)\Rightarrow population\text{ at time t} \end{gathered}[/tex]Given that:
[tex]\begin{gathered} P=158000 \\ r=8\%=\frac{8}{100}=0.08 \\ t=5 \end{gathered}[/tex]By substituting these values into the population decay formula, we have
[tex]\begin{gathered} P(t)=158000(1-0.08)^5 \\ =104134.88066 \end{gathered}[/tex]Hence, the population in 5 years will be
[tex]104134.88066[/tex]a local business Club has 11 exclusive board members and 22 General members how many committees of 7 members can be chosen so that only General members are excluded
we have:
general members are excluded then
[tex]11C7=330[/tex]answer: 330
what is the value of the q that makes the equation true? 3(q+4)-10q=2q+3
If the revenue function for a certain item is R(x)=20x−0.25x2, what is the marginal revenue for the 8th item? Do not include the dollar sign in your answer.
The marginal revenue of the 8th item from the revenue function is 16
How to determine the marginal revenue?From the question, the revenue function is given as
R(x) = 20x - 0.25x^2
To calculate the marginal revenue, we start by differentiating the revenue function
This is calculated as follows
R(x) = 20x - 0.25x^2
Differentiate the function
R'(x) = 20 - 0.5x
The above represents the marginal revenue function
So, we have
M(x) = 20 - 0.5x
For the 8th item, we have
M(8) = 20 - 0.5 x 8
Evaluate
M(8) = 20 - 4
Evaluate
M(8) = 16
Hence, the marginal revenue is 16
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