Which polynomial represents the sum below?
(4x²+1)+(4x² + x + 2)
A. 16x²+x+2
B. 8x²+x+2
C. 16x²+x+3
D. 8x²+x+3
Answer: D. 8x² + x + 3
Sum means the answer to an addition problem. To find the sum of polynomials, we will add like terms.
What are like terms?Like terms can be combined using addition or subtraction and have the same variables. Constants are also like terms with each other because they have no variables.
Solve(4x² + 1) + (4x² + x + 2) Starting equation from the question
= 4x² + 1 + 4x² + x + 2 Remove brackets
= 4x² + 4x² + x + 1 + 2 Rearrange to group like terms together
= 8x² + x + 1 + 2 Add like terms with the same 'x²' variables
= 8x² + x + 3 Add like terms that are constants
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The short leg of a 90-45-45 triangle is 3 and the long leg is 7. What is the hypotenuse?
The short leg of a 90-45-45 triangle is 3 and the long leg is 7. The hypotenuse would be [tex]c = \sqrt{58}[/tex].
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
The short leg of a 90-45-45 triangle is 3 and the long leg is 7.
Since this is a right triangle, we can use the Pythagoras theorem
a^2+b^2 = c^2
where a and b are the legs and c is the hypotenuse
[tex]3^2 + 7^2 = c^2\\\\9 + 49 = c^2\\\\58 = c^2\\\\c = \sqrt{58}[/tex]
Hence, The hypotenuse would be [tex]c = \sqrt{58}[/tex].
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(7 x 10 ^5) + (4 x 10 ^2)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(7\times 10^5) + (4 \times 10^2)}\\\mathsf{= 7\times 10^5 + 4 \times 10^2}[/tex]
[tex]\large\textsf{Let's solve for the LEFT SIDE first}[/tex]
[tex]\mathsf{7\times 10^5}\\\\\mathsf{10^5}\\\mathsf{= 10\times10\times10\times10\times10}\\\mathsf{= 100 \times 100\times 10}\\\mathsf{= 10,000 \times 10}\\\mathsf{= 100,000}\\\\\mathsf{7\times100,000}\\\mathsf{= 700,000}[/tex]
[tex]\large\textsf{NEW EQUATION: }\bold{700,000} + {4}\times 10^2[/tex]
[tex]\large\textsf{Now, let's solve for the RIGHT SIDE last}[/tex]
[tex]\mathsf{4\times 10^2}\\\\\mathsf{10^2}\\\mathsf{= 10\times10}\\\mathsf{= 100}\\\\\mathsf{4\times100}\\\mathsf{= 400}[/tex]
[tex]\large\text{NEW EQUATION: 700,000 + \bf 400}[/tex]
[tex]\large\text{700,000 + 400}\\\\\large\text{SIMPLIFY IT!}\\\\\large\text{= 700,400}[/tex]
[tex]\huge\text{Therefore, the answer should be: \boxed{\mathsf{700,400}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Calcular la edades actuales de una madre y sus dos hijos sabiendo que hace 14 años la dad de la madre era 5
veces la suma de las edades de los hijos en aquel momento, que dentro de 10 madre será la suma de las edades
que los hijos tendrán en ese momento y que cuando el hijo mayor tenga la edad actual de la madre, el hijo
menor tendrá 42 años.
The present age of mother and her daughter respectively are; 40 and 10 years respectively.
How to Solve Algebra Word Problems?Let x and y be the present age of mother and her daughter respectively.
Therefore;
x + y = 50
x = 50 − y .....(1)
After 20 years, mother's age will be twice her daughter's age at the time. Thus;
x + 20 = 2(y + 20)
x − 2y = 20 .....(2)
Plugging eq 1 into eq 2 gives us;
50 − y − 2y = 20
3y = 30
y = 10
Thus;
x = 50 − 10
x = 40
Thus, the present age of mother and her daughter is 40 and 10 years respectively.
Translation of the question into English is;
The sum of the present ages of mother and her daughter is 50 years. After 20 years, mother's age will be twice her daughter's age at the time. Find their present ages.
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What is the product of (2x - 1) (x + 4)
Answer: 2[tex]x^{2}[/tex]+7x-4
Step-by-step explanation:
Product implies multiplication so just multiply it out.
(2x-1) (x+4)
2x^2+8x-1x-4 (Combine like terms)
2x^2+7x-4
f(x) = x². What is g(x)?
g(x) is the inverse of f(x)
[tex]f(x) = {x}^{2} [/tex]
[tex]g(x) = \sqrt{x} [/tex]
[tex] \bold{(10x - 6x³ + 8x²) - (5x² + 12x³ - 4)}[/tex]
Answer:
[tex]\boxed{\sf -18x^3+3x^2+10x+4}[/tex]
Explanation:
[tex]\rightarrow \sf (10x - 6x^3 + 8x^2) - (5x^2 + 12x^3 - 4)[/tex]
distribute
[tex]\rightarrow \sf 10x - 6x^3 + 8x^2 - 5x^2 - 12x^3 + 4[/tex]
collect terms
[tex]\rightarrow \sf -6x^3-12x^3+3x^2+10x+4[/tex]
add similar terms
[tex]\rightarrow \sf -18x^3+3x^2+10x+4[/tex]
Answer:
[tex]-18x^3+3x^2+10x+4[/tex]
Step-by-step explanation:
Given:
[tex](10x-6x^3+8x^2)-(5x^2+12x^3-4)[/tex]
Apply the rule (a) = a:
[tex]\implies 10x-6x^3+8x^2-(5x^2+12x^3-4)[/tex]
[tex]\textsf{Use the distributive law} \quad -(a+b)=-a-b:[/tex]
[tex]\implies 10x-6x^3+8x^2-5x^2-12x^3-(-4)[/tex]
Apply the rule -(-a) = a:
[tex]\implies 10x-6x^3+8x^2-5x^2-12x^3+4[/tex]
Collect like terms:
[tex]\implies -6x^3-12x^3+8x^2-5x^2+10x+4[/tex]
Combine like terms:
[tex]\implies -18x^3+3x^2+10x+4[/tex]
What is the area of a circle with 20cm diameter
Answer:
area of the circle
area=7.54
What happened in this situation?
........................................................................................................
(Maya raises her hand)
Ms. Teacher: Yes, Maya?
Maya: Someone passed gas.
(Another student, Nylo, begins silently laughing)
(Another student, Lia, notices Nylo laughing)
Lia: it was Nylo.
(the entire class begins laughing, except for Maya)
...............................................................................................
Why did Lia think it was Nylo and expose them? And why didn't Maya laugh?
Answer:
It's because Maya friend did not pass gas
Use the grouping method to factor this polynomial completely.
4x³ + 8x²+3x+6
O A. (4x2 + 2)(x+3)
OB. (4x2+2)(x+2)
O C. (4x²+3)(x+3)
D. (4x² + 3)(x + 2)
Answer:
D. [tex](4x^2 + 3)(x + 2)[/tex]
Step-by-step explanation:
Hello!
We can group the first two terms and the last two terms and factor each group.
Factor by Grouping[tex]4x^3 + 8x^2 + 3x + 6[/tex][tex](4x^3 + 8x^2) + (3x + 6)[/tex][tex]4x^2(x + 2) + 3(x + 2)[/tex]Now we can combine the like factors:
[tex](4x^2 + 3)(x + 2)[/tex]The answer is Option D.
its about efficiency in systems
.......................
The function f(x)= –StartRoot negative x EndRoot is shown on the graph.
The range of the required function f(x) = -√-x is all real values less than or equal to 0.
The nature of the function is imaginary because of the negative sign present inside the root. Hence the range of the function exists only and only if the function gives real values in each of its outcomes.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.
As per question
f(x) = -√-x
clearly, for each positive real number the function becomes imaginary.
So the domain of the given function lies (-∞, 0).
and for every x in its domain function has its exists in range of all real values less than and equal to zero.
Thus, the range of the function f(x) ≤ 0.
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Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.54 and a standard deviation of 0.42. Using the empirical rule, what percentage of the students have grade point averages that are less than 2.96? Please do not round your answer.
Using the Empirical Rule, it is found that 84% of the students have grade point averages that are less than 2.96.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, 2.96 is one standard deviation above the mean. We have that:
The normal distribution is symmetric.Of the 50% of the measures below the mean, all are below 2.96.Of the 50% of the measures above the mean, 68% are below 2.96.Hence the percentage is given by:
P = 50% + 0.68 x 50% = 50% + 34% = 84%.
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How would you classify the following expression by the number of terms?
42−8+4
Solution
First, consider how many terms are in the expression.
This expression has ______ terms.
Therefore, this expression is called a trinomial.
Classify the expression by the number of terms: 43−8
Solution
First, consider how many terms are in the expression.
This expression has ____ terms.
The answer is a ______. (monomial, binomial, or trinomial)
Classify the expressions by the number of terms.
2+3+9 = (monomial, binomial, polynomial or trinomial)
6= (monomial, binomial, polynomail or trinomial)
Answer:
1. This expression has 3 terms.
2. This expression has 2 terms
3. Solution 43-8=35
3. binomial
2+3+9= trinomial
6=monomial
Step-by-step explanation:
function F(x)=x+1 and g(x)=5x+1 find the f(4)=g(x+1)
The function of f(4) = g(x+1) gives the value of x that is -1/5.
What is the function addition?It is the addition of two functions similar to the addition of any two polynomial functions.
Given;
F(x)=x+1
g(x)=5x+1
We need to find f(4)=g(x+1)
First substitute x = 4 in f(x)
F(x)=x+1
F(4) = 4 + 1
F(4) = 5
Now substitute x = x + 1 in g(x)
g(x)=5x+1
g(x + 1) = 5(x + 1) + 1
g(x + 1) = 5(x + 1) + 1
g(x + 1) = 5x + 5 + 1
g(x + 1) = 5x + 6
Then ,
F(4) = g(x + 1)
5 = 5x + 6
5x = 5 - 6
5x = -1
x = -1/5.
The function of f(4) = g(x+1) gives the value of x that is -1/5.
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The United States Postal Service reports that 90% of first-class mail within the same city is delivered in two days of the time of mailing. Ten letters are randomly sent to different locations. a. What is the probability that all 10 will arrive within two days? b. What is the probability that exactly 8 will arrive within two days? c. What is the probability that 5 or fewer will arrive within two days? d. What is the mean number of letters that will arrive within two days? e. What is the standard deviation of the number of letters that will arrive within two days?
a)The probability that all 10 will arrive within two days is 0.3486.
b) P(x = 8) = 0.1937
c) P(x=5)= 0.0014
d) mean = 9
e) Standard deviation = √0.90 = 0.9486
What is Binomial Probability?The binomial distribution model allows us to compute the probability of observing a specified number of "successes" when the process is repeated a specific number of times and the outcome for a given patient is either a success or a failure.
Given:
p = 90/100 = 0.90
q(probability of success) = 1 - p = 1 - 0.90 = 0.10
n = 10
a)The probability that all 10 will arrive within two days
P(x = 10) = 0.3486
b) P(x = 8) = 0.1937
c) P(x=5)= 0.0014
d) mean = np = 10 × 0.90 = 9
e) Variance = npq = 10 × 0.90 × 0.10 = 0.90
Standard deviation = √0.90 = 0.9486
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A media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 degrees C. The difference from the previous year is less than the margin of error of about 0.13 degrees C, so that difference should be ignored. What is the best counterargument?
The difference is only 0.04, but that is still a significant change.
The margin of error is quite small compared to the change year over year, so it is a significant issue.
The change of 0.09 is not a lot and thus should be ignored.
The margin of error is larger than the increase, so we should consider it an issue of just extra information and thus can be ignored.
The correct option would be The margin of error is quite small compared to the change year over year, so it is a significant issue option third is correct.
What is the margin of error(MOE)?It is defined as an error that provides an estimate of the percentage of errors in real statistical data.
The formula for finding the MOE:
[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]
Where Z is the z-score at the confidence interval
s is the standard deviation
n is the number of samples.
We have:
A media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 degrees C.
As the value of MOE is 0.13 degrees
It is a serious problem because the margin of error is quite narrow in comparison to the shift from year to year.
Thus, the correct option would be The margin of error is quite small compared to the change year over year, so it is a significant issue option third is correct.
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Which of the following is the center and radius of the circle?
x2 + y2 + 4x – 14y + 46 = 0
Center (2, –7); r = 7
Center (–4, 14); r equals square root 46
Center (4, –14); r = 46
Center (–2, 7); r equals square root 7
The centre of the circle is (-2,7) and the radius is √7 , Option D is the right answer.
What is the standard equation of a Circle ?The standard equation of a Circle is
(x-h)² +(y-k)² = r²
where h and k is the centre of the circle , r is the radius
The given equation is
x² + y² + 4x – 14y + 46 = 0
x² +4x +4 -4 +y² -2.7y + 49-49+46 = 0
(x + 2)² + (y-7)² -4-49+46 = 0
(x + 2)² + (y-7)²= 7
Therefore the centre of the circle is (-2,7) and the radius is √7 ,
Therefore Option D is the right answer.
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I need it now!!! pls
Answer:
To answer 5)
First we know that...
[tex]\frac{235}{360}[/tex] of the circle = 94 people
To find total people=
[tex]\frac{235}{360}[/tex]×x=94
x=144 people
To find the number of hokey players: 360-(235+90) =35
so, [tex]\frac{35}{360}[/tex]×144=14
So, 14 people are chose hockey
Alana, Brianna and Carla divided $171 between them in the ratio 4 colon 7 colon 8. How much did Brianna receive?
Answer:
$63
Step-by-step explanation:
Alana has 4 units of the $171.
Brianna has 7 units of the $171.
Carla has 8 units of the $171.
Total units = 4 + 7 + 8 = 19
19 units = $171
1 unit [tex]\frac{171}{19} \\= $9[/tex]
Brianna has 7 units, so she receives 7 x $9 = $63.
Which of the following describes the behavior of the graph shown over the interval (-2,2)?
Hello!
We are trying to describe the behavior of the graph given in the question.
To help us understand how to solve this question, we would need to understand concavity.
There are two types of concavity:
Concave upConcave downWhen a graph is concave up, the slope of the line would look like a "U".
When a graph is concave down, the slope of the line would look like a "U" that is flipped upside down.
In this case, we can see that the graph is concave down.
We can tell that the slope is negative due to the fact that the slope is going down, which results in the graph having a negative slope.
We can also tell that the graph is decreasing due to the fact that the line is doing downward.
Answer:
C). negative and decreasing
Which of the following is a sum of cubes?
Answer:
x^3 + 8y^6
Step-by-step explanation:
Answer:
the answer is B !!!
Step-by-step explanation:
thank me later lol
What are the possible values of xin 8x² + 4x=-1?
Answer:
hey
Step-by-step explanation:
4
Answer:
(-½,0)
Step-by-step explanation:
please mark me brainliest
4
Which are correct representations of the inequality 6x ≥ 3 + 4(2x - 1)? Select three options.
01 ≥ 2x
O
O
6x ≥ 3 + 8x - 4
-1.5
-1.5
0- -1.5
-1
-1
-1
-0.5
-0.5
-0.5
0
0
0
0.5
0.5
0.5
1
1
1.5
1.5
1.5
Answer:
6x > 3+4(2x -1)
6x > 3+ 8x - 4
6x > (-1) + 8x
6x - 6x > (-1) + 8x - 6x
subtracting 6x from both sides
0 > 2x - 1
adding +1 on both sides
1 > 2x
1/2 > x
x < 1/2
The correct representations of the inequality 6x ≥ 3 + 4(2x - 1) is,
⇒ x ≤ 1/2
What is mean by Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequality is,
⇒ 6x ≥ 3 + 4(2x - 1)
Now, We can simplify as;
⇒ 6x ≥ 3 + 4(2x - 1)
⇒ 6x ≥ 3 + 8x - 4
⇒ 6x ≥ 8x - 1
⇒ 1 ≥ 8x - 6x
⇒ 1 ≥ 2x
⇒ x ≤ 1/2
Thus, The correct representations of the inequality 6x ≥ 3 + 4(2x - 1) is,
⇒ x ≤ 1/2
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The reciprocal of 15 is
1.
Answer:
1/15 is the answers for the question
Step-by-step explanation:
please mark me as brainlest
Which of these is the algebraic expression for the verbal expression "twelve times the difference of a number and four?"
12 ⋅ x − 4
x − 4 ⋅ 12
4(x − 12)
12(x − 4)
Answer:
[tex]12(x - 4)[/tex]
Step-by-step explanation:
The question says, "twelve times the difference of a number and four"
Let's start with the first number, which is twelve = 12. Moving on, we have times = ×, then the difference which is minus(-). A number is unknown, any aphabet can be used to represent the number, so, we represent with 'x', and then four = 4.
Arranging them, we have:
[tex]12 \times x - 4[/tex]
in algebraic equations, times is always represented by bracket. Therefore, our final answer is:
[tex]12(x - 4)[/tex]
I hope this helps.
There are 60 minutes in an hour. The total number of minutes is a function of the number of hours, as shown in the table. Does this situation represent a linear or non-linear function, and why?
Answer:
linear; the rate of change is constant
Which expression is equivalent to √48x5, if x> 0?
A. 12x³√3x
B. 4x³√3
C. 4x²√3x
D. 12x²√
Answer:
C. 4x²√(3x)
Step-by-step explanation:
if x > 0
[tex]\sqrt{48x^{5}} =\sqrt{48} \times \sqrt{x^{5}}[/tex]
[tex]=\sqrt{16\times 3} \times \sqrt{x^{4}\times x}[/tex]
[tex]=\sqrt{16} \times \sqrt{3} \times \sqrt{x^{4}} \times \sqrt{x}[/tex]
[tex]=4\times \sqrt{3} \times \sqrt{\left( x^{2}\right)^{2} } \times \sqrt{x}[/tex]
[tex]=4\times \sqrt{3} \times x^{2}\times \sqrt{x}[/tex]
[tex]=4\times x^{2} \times \sqrt{3} \times \sqrt{x}[/tex]
[tex]=4\times x^{2}\times \sqrt{3x}[/tex]
Answer please! I need this!
Step-by-step explanation:
The top has been multiplied by 5 so multiply the bottom by 5, 2 x 5 = 10. also why is there a pig lol
What is the equation of the line passing through the point (2,-4)
Answer:
y = m(x - 2) - 4
Step-by-step explanation:
Equation of a straight line is given by;
y = mx + c
Take a point on the line (x, y) and the given point (2, -4)
gradient = change x/ change in y
gardient(m) = y +4/ x - 2
m(x-2) = y + 4
y = m(x - 2) - 4
