[tex]f( - 4) = - 122[/tex]
And
[tex]g(5) = - 21[/tex]
Step-by-step explanation:
Greetings !
For the first expression
[tex]f(x) = 2x {}^{3} + 6[/tex]
plug in -4 at the variable x and solve the expression.
[tex]f( - 4) = 2( - 4) {}^{3} + 6[/tex]
Follow the PEMDAS order of operations
calculate the exponents
[tex]( - 4) {}^{3} = - 64[/tex]
Apply exponent rule
[tex]( - a) {}^{n} = - a {}^{n} . \: if \: n \: is \: odd[/tex]
Thus,
[tex]( - 4) {}^{3} = - 4 {}^{3} = - 64[/tex]
Multiply and divide (left to right )
[tex]2( - 64) = - 128[/tex]
[tex] = - 128 + 6 \\ = - 122[/tex]
Fairly follow the same. process for the second function
Hope it helps !!
I need step by step solution of this question.i will give brainliest to who gives step by step answer.
Answer:
(- 1, - 2/3, 1/2)
======================
Factorize as below and find roots:
6x³ + 7x² - x - 2 = 06x³ + 6x² + x² - x - 2 = 06x²(x + 1) + x² + x - 2x - 2 = 06x²(x + 1) + x(x + 1) - 2(x + 1) = 0(x + 1)(6x² + x - 2) = 0(x + 1)(6x² + 4x - 3x - 2) = 0(x + 1)(2x(3x + 2) - (3x + 2)) = 0(x + 1)(3x + 2)(2x - 1) = 0x + 1 = 0 or 3x + 2 = 0 or 2x - 1 = 0x = - 1 or x = - 2/3 or x = 1/2Answer:
[tex]x=-1, \quad x=\dfrac{1}{2}, \quad x=-\dfrac{2}{3}[/tex]
Step-by-step explanation:
Given polynomial:
[tex]f(x)=6x^2+7x^2-x-2[/tex]
[tex]\boxed{\begin{minipage}{6 cm}\underline{Factor Theorem}\\\\If $f(x)$ is a polynomial, and $f(a) = 0$,\\ then $(x-a)$ is a factor of $f(x)$.\\\end{minipage}}[/tex]
Since the constant of the given polynomial is -2, the possible factors are ±1 and ±2.
Apply the Factor Theorem to check the possible values:
[tex]f(1)=6(1)^3+7(1)^2-(1)-2=10 \neq 0[/tex]
[tex]f(-1)=6(-1)^3+7(-1)^2-(-1)-2=0[/tex]
[tex]f(2)=6(2)^3+7(2)^2-(2)-2=72 \neq 0[/tex]
[tex]f(-2)=6(-2)^3+7(-2)^2-(-2)-2=-20 \neq 0[/tex]
Therefore, (x + 1) is a factor of the polynomial:
[tex]f(x)=(x+1)(ax^2+bx+c)[/tex]
Compare with the original function to find the coefficients of the quadratic:
[tex]6x^3=ax^3 \implies a=6[/tex]
[tex]7x^2=(b+a)x^2 \implies b=1[/tex]
[tex]-2=c \implies c=-2[/tex]
Therefore:
[tex]f(x)=(x+1)(6x^2+x-2)[/tex]
Factor the quadratic:
[tex]f(x)=(x+1)(6x^2+4x-3x-2)[/tex]
[tex]f(x)=(x+1)[2x(3x+2)-1(3x+2)][/tex]
[tex]f(x)=(x+1)(2x-1)(3x+2)[/tex]
Set the polynomial function to zero:
[tex](x+1)(2x-1)(3x+2)=0[/tex]
Apply the zero product property:
[tex](x+1)=0 \implies x=-1[/tex]
[tex](2x-1)=0 \implies x=\dfrac{1}{2}[/tex]
[tex](3x+2)=0 \implies x=-\dfrac{2}{3}[/tex]
Therefore, the solutions are:
[tex]x=-1, \quad x=\dfrac{1}{2}, \quad x=-\dfrac{2}{3}[/tex]
When you look at a pencil in water, it looks bent. This illusion is due to refraction, or the bending of light when it moves from one substance to the next.
a. What is m∠1 ? Classify this angle as acute, right, or obtuse.
The measure of angle 1 from the given figure is an obtuse angle.
Given that, when you look at a pencil in water, it looks bent. This illusion is due to refraction, or the bending of light when it moves from one substance to the next.
What is refraction?Refraction is the "bending" of light (or any electromagnetic wave) when entering a different medium.
In the given figure, the three angles, are angle 1, angle 2 and angle 3.
Angle 1 and 2 are formed with the surface of the water. Angle 1 in the medium air and angle 2 is in the medium water.
From the figure, given below we can see that angle 1 is greater than 90° and less than 180°.
Therefore, the measure of angle 1 from the given figure is an obtuse angle.
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hlp!!!
The sum of two numbers is 27. The larger number is 6 more
than twice the smaller number. Which system of equations
can be used to find the two numbers?
Answer:
[tex]x+y=27[/tex]
[tex]y=2x+6[/tex]
Step-by-step explanation:
Letting [tex]x[/tex] and [tex]y[/tex] represent the smaller and larger number, respectively we create these equations.
Complete each statement based on the property being used.
Transitive Property of Equality:
Ifm/MLI=mZYGF and mZYGF = 201°, then:
m/MLI=
and m/CJW = 181°, then
Substitution Property of Equality: If mZCJW+m/HAV = 287°
0
+m/HAV=
Based on the transitive property of equality, m<MLI = 201°
181° + m<HAV = 287°, based on the substitution property of equality.
What is the Transitive Property of Equality?The transitive property of equality states that, if d = e and e = f, then d = f.
What is the Substitution Property of Equality?Given that a = 3, if a + 5 = 8, then, based on the substitution property of equality, we would replace a with 3 into the equation as shown below:
3 + 5 = 8.
Based on the transitive property of equality, we are given that:
m<MLI = m<YGF
m<YGF = 201°
Then, we would have:
m<MLI = 201°
Also, we are given that:
m<CJW + m<HAV = 287°; and m<CJW = 181°.
Then, 181° + m<HAV = 287°, based on the substitution property of equality.
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assignment dueee helppp 40 points
Answer:
1) 38
2) 18
Step-by-step explanation:
1) 4m - 2t
m = 10
t = 2
(4 * 10) - (2 * 2)
40 - 4 = 36
Answer : 36
2) t + 2m - 4
m = 10
t = 2
2 + (2 * 10) - 4
22 - 4 = 18
Answer : 18
3) m/2t
m = 10
t = 2
10/(2*2) = 2.5
Answer : 2.5
-4x + 15 + -49
please show work
Answer:
12
Step-by-step explanation:
that is my answer and I don't need your
How long would Joey need to invest his $300 at 4% annual interest if he wants to end up with $400? Assume simple interest, I = PRT and round to the nearest tenth of a year
The time it would take Joey is 3 years
How to determine the valueGiven that the formula for simple interest is;
I = PRT
Where;
I is the simple interest = $400R is the rate = 4%T is the time in years P is the principal amount = $300Substitute into the formula
400 = 300 × 4 × t/ 100
cross multiply
4000 = 1200 t
Make 't' the subject
t = 4000/ 1200
t = 3. 3
t = 3 years in the nearest tenth
Thus, the time it would take Joey is 3 years
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Ann is 4 years older than julie. 4 years ago ann was twice as old as julie find their present ages
The present ages of Ann and Julie are 12 years and 8 years, respectively.
What are the current ages of Ann and Julie?Let x, y are the current ages of Ann and Julie, whose features are synthetized in the following linear equations:
Ann is 4 years older than Julie;
x = y + 4
x - y = 4 (1)
4 years ago, Ann was twice as old as Julie;
x - 4 = 2 · (y - 4)
x - 4 = 2 · y - 8
x - 2 · y = - 4 (2)
Now we proceed to determine the ages of Ann and Julie by solving the system of linear equations;
(x, y) = (12, 8)
Hence, The present ages of Ann and Julie are 12 years and 8 years.
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Answer:12
Step-by-step explanation:
given the function h(x)=x^2-9x+18, determine the average rate of change of the function over the interval 4<_ x <_ 11
To calculate average rate of change of a function f(x) over an interval between 2 points (a. f(a)) and (b, f(b)) is given by
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
The given function is [tex]h(x)= x^{2} -9x+18[/tex]
and the given interval is [tex]4\leq x\leq 11[/tex]
Now, h(b) = h(11) = [tex](11)^{2} -9(11)+18[/tex]
= [tex]121-99+18[/tex]
= [tex]40[/tex]
h(a) = h(4) = [tex](4)^{2} -9(4)+18[/tex]
= [tex]16 -36+18[/tex]
= [tex]-2[/tex]
The average rate of change between (4, -2) and (11, 40) is
= [tex]\frac{40-(-2)}{11-4}[/tex]
= [tex]\frac{40+2}{11-4}[/tex]
= [tex]\frac{42}{7}[/tex]
= [tex]42[/tex]
∴ The average rate of change between (4, -2) and (11, 40) is 42
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Suppose that today the exchange rate between the u.s. dollar and the chinese yuan is $1 =.12 yuan. if next week the exchange rate is $1 = .20 yuan, it is clear that:____.
Suppose that today the exchange rate between the u.s. dollar and the chinese yuan is $1 =.12 yuan. if next week the exchange rate is $1 = .20 yuan, it is clear that yuan has depreciated relative to dollar.
What is meant by the exchange rate?
The price of one currency relative to another is known as the exchange rate. When nations employ gold or another accepted standard, and each currency is worth a particular amount of the metal or other standard, the exchange rate is "fixed."Last week: $1 = 0.12 yuan
Therefore, for exchange of $1, 0.12 yuan will be given
Today: $1 = 0.2
Therefore, for exchange of $1, 0.2 yuan will be given.
So, yuan will be given for same amount of $. Thus yuan has depreciated.
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please just answer I want an even 2,000 point's
but here's the question
Whats the best animal?
(Hint say Platypus)
Answer:
perry da platypus
Step-by-step explanation:
Australia's short beaked platypus
Step-by-step explanation:
sorry if am wrong
16+16 divided by 4^2
HELP ASAP I'M TIMED!!!! Which expression is equivalent to (x y) z?
O (x + y) + z
O 2 z (x y)
O x (y z)
O x (y + z)
Answer:
I believe its O x(yz)
Step-by-step explanation:
Help quickly please I need to answer this quickly
Help with problems 8 10 and 11
8) The equation of the line in slope-intercept form is y = 5 · x - 8. (Correct choice: A)
10) The slope of the line is equal to 0. (Correct choice: A)
11) The equation for a graph that is a vertical line is 3 · x - 2 = 0. (Correct choice: C)
How to analyze and interpret linear equations and their features
Herein we must analyze and understand linear equations and their features. 8) The first exercise consists in looking for a linear equation in slope-intercept form with a slope of 5 and y-intercept of - 8, linear equations in slope-intercept form are defined by the following expression:
y = m · x + b
Where:
m - Slopeb - y-Interceptx - Independent variabley - Dependent variableIf we know that m = 5 and b = - 8, then the equation of the line in slope-intercept form is y = 5 · x - 8. (Correct choice: A)
10) The slope can be determined by the secant line formula:
m = (3 - 3) / [5 - (-4)]
m = 0
The slope of the line is equal to 0. (Correct choice: A)
11) Vertical lines on a Cartesian plane are of the form x = a or x - a = 0. Then, the equation for a graph that is a vertical line is 3 · x - 2 = 0. (Correct choice: C)
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19
Type A batteries and type B batteries were tested.
The cumulative frequency diagram shows information about the battery life of type A.
19 (a)
80
70
60
50
Cumulative
frequency 40
30
20
10
of
0
Type A
800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800
Battery life (hours)
Estimate the interquartile range for type A.
Answer
hours
[2 marks]
300 Hours will be the Interquartile range for the batteries of type A
In the given data there is a total number of 11 terms for Hours. We have to calculate the median value of Hours by using the formula :
=> Median = [tex]\frac{n+1}{2}[/tex], and we know that Q2 = Median so Q2 can be calculated by Q2 = [tex]\frac{n+1}{2}[/tex] => Q2 = 6 => 6th term Will be the Median.
Median = Q2 = 1300 Hours.
Now we have to Calculate Lower Quartile Q1 & Upper Quartile Q3. Since We have our Median 1300 Hours. So, the lower quartile will be :
Q1 = 1100 Hours
and, the Upper Quartile will be Q3 = 1400 Hours.
We have our Upper and Lower Quartiles. We can Calculate Interquartile Range be using the formula Q3 - Q1
=> IQR = Q3 - Q1
Putting values of Q3 and Q1, We get :
=> IQR = 1400 - 1100 => IQR = 300 Hours
Hence, the Interquartile Range IQR is 300 Hours.
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eugfweuifwefuwefuwed
Answer:
1/8 = 0.12500
Step-by-step explanation:
23 divided by 26 = 2(3 - 6) = 2(-3) = 1/23
since a likert scale is an example of an ordinal level of measurement, explain why the mean should not be used to measure central tendency of the likert scale data values? provide an example in real life where you may have encountered the use of the mean to measure central tendency of ordinal data.
The mean, which is a measure of central tendency for quantitative data should not be used for likert scale data values, which are ordinal (qualitative) data.
The use of the mean as a measure of central tendency for ordinal data may be encountered, in the customer satisfaction data analysis systems used in some banks
What is ordinal data?Ordinal data are a data form that specified categories that are scaled or have a set order.
However, ordinal scales are not standard, such that they cannot be manipulated quantitatively.
The mean specifies the average value, which the sum of the quantitative measurements, divided by the number of measurements
Therefore;
The mean should not be used as a measure of central tendency of the likert scale, which is based on ordinal data.An example in real life where the mean could be used as a measure of central tendency of ordinal data is in customer satisfaction survey at the bank, where customers have five levels to select how happy they are with the bank services.
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Express 48 as a product of prime factors.
Give your answer in index form.
Emily buys 14 balloons. 3 are red, 4 are white, and the rest are blue. what is the ratio of blue balloons to the total number of balloons a. 1/2 b. 2 to 1 c. 11:14
The ratio of blue balloons to the total number of balloons a. 1/2.
To find the ratio of blue balloons to the total number of balloons, firstly we need to find the number of blue balloons. Performing addition and subtraction for the same as follows -
Total number of balloons = Number of blue balloons + number of red balloons + number of white balloons
Number of blue balloons = 14 - (3 + 4)
Number of blue balloons = 14 - 7
Number of blue balloons = 7
Ratio = Number of blue balloons to the total number of balloons
Ratio = 7:14
Performing division of both digits by 7
Ratio = 1:2
Hence the ratio of blue balloons to the total number of balloons a. 1/2.
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An inlet pipe on a swimming can be used to fill the pool in 10 hours. the drain pipe can be used to empty the pool in 30 hours. if the pool is 1/5 filled and then the inlet pipe and drain pipe are open, how long from that time will it take to fill a pool?
12 hours will it take to fill the given pool .
we can solve this problem using unitary method ,
10 hours is required to fill the full pool
1 hour is required to fill 1/10th of the pool
30 hours is required to empty the pool
1 hour is required to empty 1/30th of the pool
If two pipes are open then in 1 hour ( 1/10 - 1/30 = 2/30 = 1/15 ) pool will be filled .
The pool is 1/5th filled already as it is mentioned .
So , remaining is ( 1 - 1/5 = 4/5 )
If 1/15th is filled in 1 hour , then 4/5th will be filled in ( 15 × 4/5 ) hours = 12 hours
So, it will take 12 hors to fill the pool .
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Ebony earned scores of 71 , 70, 87, 97 , and 82 on five math tests. Determine her
score on the sixth test if her average for the six tests was 83? Enter your answer as a
whole number
The answer is 91
Step-by-step explanation:
Average Marks = (Total Marks) ÷ Total Tests
83 = (71 + 70 + 87 + 97 + 82 + x) ÷ 6
83 × 6 = 407 + x
498 = 407 + x
x = 498 - 407
x = 91
What are the terms of the expression -9h + 5y - 6h?
Please answer
The terms of the expression are: -15h and 5y.
How to Find the Terms of an Expression?A term of an expression can be a constant, a variable multiplied by a constant, or a variable standing alone.
Given the expression, -9h + 5y - 6h, simplify the expression in order to determine the terms of the expression:
-9h + 5y - 6h
Combine like terms
-9h - 6h + 5y
-15h + 5y
Therefore, the terms of the expression are: -15h and 5y.
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6х-10 = -8 + 3x
What's the answer I can't figure it out
Answer:
So,x=2/3
Step-by-step explanation:
6x-10=-8+3x
6x-3x=-8+10
3x=2
x=2/3
Hope its helpful for you
Answer:
[tex]6x - 10 = - 8 + 3x \\ 6x - 3x = - 8 + 10 \\ 3x = 2 \\ \boxed{x = \frac{2}{3}}[/tex]
What is the value of x if 3x+2=8?
F. -2
G. 0
H. 2
J. 6
What is the ratio of triangles to stars?
CHALLENGE! Can you simplify the ratio above? Why or why not?
3:5
Answer:
3 : 5 also = 0.6
Step-by-step explanation:
Yes, you are able to simplify the ratio into a decimal.
Which statement about the points (5, 7) and (10, 12) is true? CLEAR CHECK There is not enough information to determine if the points show direct variation. They show direct variation because y = x + 2 and 10 – 5 = 12 – 7. The line they are on does not show direct variation. They show direct variation because the line they are on has a positive slope.
Step-by-step explanation:
direct variation means that
y = kx
that means it is a line with y-intercept = 0.
in other words, when x = 0, then y = 0 too.
for 2 given points the first part is automatically true. 2 points always define a line.
so, what we need to find out is, if (0, 0) is also on the line.
if not, it is not a direct variation.
the 2 points imply the equation
y = x + 2
as the y value is always larger than the x value by 2.
this has a y-intercept larger than 0 (2).
and so, (0, 0) is NOT on the line, and it is NOT a direct variation.
so, the 3rd answer option is correct.
Math Sets. Answer 1-9 Below.
Answer:
1. { 1 , 3, 4, 6, 7, 0, 5, 2 }
2. { 6 ,7 ,0 }
3. { 9 ,2 ,4 ,3 ,0 ,7 ,6 }
4. { 1 ,8 ,5 ,9 ,11 }
5. { 1 ,8 ,6 ,7 ,3 ,4 ,11 }
6.
7 . { 0 }
8. { 0 }
9. { 6 ,7 ,0 ,2 }
Step-by-step explanation:
for the 6th one I'm not sure about that , that's why i didn't write the answer for it
please make my answer as brainelist
The temperature in Juno, Alaska was 5 degrees at 7am. The temperature dropped 15 degrees every hour for 3 hours. What was the temperature at 10am?
Work Shown:
7 AM, temp = 5
8 AM, temp = -10
9 AM, temp = -25
10 AM, temp = -40
Shortcut: 5 - 3*15 = 5 - 45 = -40
I recommend drawing a vertical number line to see what's going on.
Side note: -40 degrees Celsius = -40 degrees Fahrenheit
Categorical data? must be numeric. cannot be numeric. may be either numeric or nonnumeric. must be nonnumeric.
Categorical data can be either numeric or nonnumeric.
What are Categorical Data?Categorical data can be described as a type of data that can be divided into group and given labels or numerical value for the sake of identification.
Some examples of numerical data are age group, race, sex, educational level, among others.
For example, we can give numerical values like 1 for male, and 2 for female when categorizing people based on sex.
Therefore, categorical data can be either numeric or nonnumeric.
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