Answer: [tex]x^4+4x^3+6x^2+7x+2[/tex]
Step-by-step explanation:
To solve the exercise you must apply the following proccedure:
- Apply the distributive property.
- Keep on mind that when you multiply two powers with equal base, you must add the exponents.
- Add like terms.
Therefore, you obtain the following product:
[tex]=x^{(2+2)}+x^{(2+1)}+2x^2+3x^{(1+2)}+3x^{(1+1)}}+6x+x^{2}+x+2\\=x^4+x^3+2x^2+3x^3+3x^2+6x+x^2+x+2\\=x^4+4x^3+6x^2+7x+2[/tex]
The answer is: [tex]x^{4}+4x^{3}+6x^{2}+7x+2[/tex]
Why?To find the product of the given expression, we need to apply the distributive property and then, group each like term.
The distributive property states that:
(a+b+c)(d+e+f)=a*d+a*e+a*f+b*d+b*e+b*f+c*d+c*e+c*f
Then, we have to group each like term. Like terms are the terms that have the same variable and exponent , for example:
[tex]x+x+x^{2}=2x+x^{2}[/tex]
For this case, the variable "x" has two Like terms, since both have the same exponent (1), then, we add each other in order to group term.
Also, we must remember the following power property:
Product of powers property,
[tex]a^{n}*a^{m}=a^{n+m}[/tex]
So, solving the product we have:
[tex](x^{2}+3x+1)(x^{2}+x+2)=x^{2}*x^{2}+x*x^{2}+2x^{2}+3x*x^{2}+3x*x+6x+x^{2}+x+2\\(x^{2}+3x+1)(x^{2}+x+2)=x^{2+2}+x^{1+2}+2x^{2}+3x^{2+1}+3x^{1+1}+6x+x^{2}+x+2\\(x^{2}+3x+1)(x^{2}+x+2)=x^{4}+4x^{3}+6x^{2}+7x+2[/tex]
Have a nice day!
a line passes through the point (9,-3) and has a slope of negative 2 over 3. write an equation in slope intercept form for this line
Answer:
y= -2/3x-3, (Word Form: Y equals negative 2 over 3x minus 3.)
Step-by-step explanation:
The formula for slope-intercept form is y=mx+b. m=Slope. b=y-intercept. Therefore the equation would be y= -2/3x-3
Answer:
[tex]y=-\frac{2x}{3}+3[/tex]
Step-by-step explanation:
Hello
I think I can help you with this
if you a have the slope and a point of the line , it is possible to find the equation using:
[tex]y-y_{1}=m(x-x_{1} )[/tex]
where, m is the slope, (x1,y1) are the coordinates of the known point
Step 1
Let
[tex]P1(9,-3)\\slope=-\frac{2}{3}[/tex]
replacing
[tex]y-(-3)=-\frac{2}{3}(x-9 )\\y+3=-\frac{2x}{3}+\frac{18}{3}\\isolating\ y \\y=-\frac{2x}{3}+6-3\\y=-\frac{2x}{3}+3\\[/tex]
Have a good day.
Cups are being manufactured for a set. The diameter of the mouth of the cup must be 5in ± 8%. A sample of cups have the diameters shown in the table. Which cup is not within the specified tolerance?
To identify the cup that is not within the specified tolerance, calculate the upper and lower limits of the tolerance and compare them to the actual diameter of each cup in the sample. The fourth cup with a diameter of 5.5in is not within the specified tolerance.
Explanation:In this question, we are given the tolerance for the diameter of the cup's mouth, which is 5in ± 8%. We have a sample of cups with their diameters listed in a table. To identify the cup that is not within the specified tolerance, we need to calculate the upper and lower limits of the tolerance and compare them to the actual diameter of each cup in the sample.
To calculate the upper limit, we add 8% of 5in to the nominal value of 5in. This gives us 5in + 0.08 * 5in = 5in + 0.4in = 5.4in. To calculate the lower limit, we subtract 8% of 5in from the nominal value of 5in. This gives us 5in - 0.08 * 5in = 5in - 0.4in = 4.6in. Now, we compare the actual diameters of the cups in the sample to these upper and lower limits to determine which cup is not within the specified tolerance.
Looking at the table of cup diameters, we can see that the fourth cup has a diameter of 5.5in, which is greater than the upper limit of 5.4in. Therefore, the fourth cup is not within the specified tolerance.
A baseball team bought 8 boxes of baseballs. If the team spent a total of 1,696,what was the cost of 1 baseballs
Answer:
1 box = 212
1 ball = 16
Which system of equation cannot be directly solved by applying the elimination method?
I think the answer is C
The elimination method may not be applied directly to solve systems involving nonlinear, transcendental, or linearly dependent equations, demanding more complex techniques for solutions.
A system of equations cannot be directly solved by applying the elimination method if the system involves equations that are not linear or if the equations are dependent in such a way that one cannot eliminate variables easily.
For instance, in the case of two simultaneous transcendental equations, it may be impossible to solve the system through algebraic means using elimination.
In such scenarios, iterative methods like an extension of the Newton-Raphson technique might be necessary. Moreover, dealing with systems of differential equations also requires different approaches, such as the use of matrices or integrating factors when the equations are linearly dependent.
which of the following are leisure activities
Leisure activities can be categorized as either active or passive and include a variety of pursuits from bowling, hunting, and team sports to reading, computer games, and television viewing. Technological advancements have led to an increase in sedentary leisure activities such as web surfing.
Explanation:Leisure activities encompass a range of pursuits that individuals engage in during their free time for enjoyment, relaxation, and entertainment.
In contemporary society, leisure activities have evolved to include both active and passive forms.
Examples of active leisure activities that were popular in the past include sports such as bowling, hunting, fishing, boating, and golf, as well as attendance at team sports like baseball, basketball, and football.
These activities usually involve physical exertion and outdoor participation.
On the other hand, sedentary or passive leisure activities have grown in prevalence with advancements in technology, including computer games, web surfing, and television viewing.
Furthermore, cultural activities such as reading books and magazines, enjoying music, dancing, and art have remained significant leisure pursuits.
Examples of recreational goods and services include televisions, cable television, pets and pet products, sports equipment, and admissions to events or locations relating to these activities.
Which odd number comes right after 14?
the odd number after 14 is 15
Answer:
The odd number after 14 is 16
PLEZ NEED HELP ASAP 24.455−18.246
Answer:
The answer is 6.209
You could put it into a calculator and get 6.209 but what's the fun in that
I'll attach how to subtract manually
What is the center of the circle? Please show steps!
Answer:
A. (0, 4)Step-by-step explanation:
The equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the equation:
[tex]x^2+(y-4)^2=25\\\\(x-0)^2+(y-4)^2=5^2[/tex]
h = 0, k = 4, r = 5
How to solve
100x0.25
Answer:
25
Step-by-step explanation:
To solve 100 x 0.25, multiply 100 by 0.25 directly, which is the same as dividing 100 by 4. The solution is simply 25.
To solve the problem of 100 x 0.25, you can think of it as finding a quarter of 100. Since 0.25 is the decimal equivalent of 1/4, when you multiply 100 by 0.25, you are essentially dividing 100 by 4. The steps to solve this are simple:
Write the multiplication: 100 x 0.25.
Perform the multiplication: 100 x 0.25 = 25.
No proportions or conversions are necessary for this calculation; it is a straightforward multiplication problem. The answer to 100 x 0.25 is 25.
The probable question may be:
How to solve 100x0.25?
How to transform this to vertex form 2x^2-18x+8
Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
• The coefficient of the x² term must be 1
y = 2(x² - 9x) + 8
• add/subtract (half the coefficient of the x- term)² to x² - 9x
y = 2(x² + 2 (- [tex]\frac{9}{2}[/tex]) x + (- [tex]\frac{9}{2}[/tex])² - (- [tex]\frac{9}{2}[/tex])²) + 8
y = 2(x - [tex]\frac{9}{2}[/tex])² - 2([tex]\frac{81}{4}[/tex] + 8
= 2(x - [tex]\frac{9}{2}[/tex])² - [tex]\frac{65}{2}[/tex] ← in vertex form
The soccer coach claimed that on average only 80% of the team come to practice each day if the team has 20 members how many team members should come to practice to uphold the coach’s claim
Answer:
16 team members.
Step-by-step explanation:
To find 80% of 20, multiply 20 by 0.8.
20 × 0.8 = 16.
Cindy recycles 54 pounds of paper. She recycles 9 times as many pounds of paper Monica recycles. How can I solve the equation to find the number of pounds of paper Monica recycled?
Answer: 54 times 9 =486 pounds Monica recycled
Step-by-step explanation:
Answer:
Let x be the number of pounds of paper Monica recycled.
Since, it is given that, Cindy recycles 9 times as many pounds of paper Monica recycles.
Thus, the number of pounds of paper Cindy recycled = 9x,
According to the question,
9x = 54
Which is required the equation to find the number of pounds of paper Monica recycled.
Now, divide both sides of the above equation by 9,
We will get,
x = 6
Therefore, Monica recycled 6 pounds of paper.
A house has increased in value by 29% since it was purchased. If the current value is $516,000, what was the value when it was purchased?
X=value of the house before increase
(100%+29%)X=516,000
(129%)X=516,000
1.29x=516,000 | divided by 1.29 both sides
X=400,000$ was the value when it was purchased
Answer:
The value of house $ 400,000
Step-by-step explanation:
Let x be the price of house when it was purchased,
∵ 29% of x = [tex]\frac{29x}{100}[/tex] = 0.29x
According to the question,
x + 29% of x = 516000
x + 0.29x = 516000
1.29x = 516000
[tex]\implies x=\frac{516000}{1.29}=400000[/tex]
Hence, the value of the house is $ 400,000 when it was purchased.
Jack wants to simplify the expression below.
(6.7x -3) - (3.4x - 1) + (2x - 2)
Answer the following questions.
1) How can Jack regroup the expression by Commutative Property?
2) After regrouping in step 1, how can Jack further simplify the expression by
Distributive Property?
3) What is Jack's final simplified expression?
Answer:
5.3x - 4 .
Step-by-step explanation:
(6.7x -3) - (3.4x - 1) + (2x - 2)
1. using the commutative property:
= 6.7x - 3 + 2x - 2 - (3.4x - 1) (we can remove the parentheses around the first 2 groups because they are added).
2. Using the distributive property on the last group:
= 6.7x - 3 + 2x - 2 - 3.4x + 1 (distributing the negative over the parentheses).
3. Now adding like terms we get:
5.3x - 4 (answer).
Help!!! Plzzzz! Thx btw! (If u helped me)
Answer:
-4×5+3=,lost 20 pounds and gained 3 pounds
Step-by-step explanation:
the product of two even consecutive numbers, the smaller of which is equal to 2n.
the second even number is 2n + 2
2n (2n+2)
4n^2 + 4n
[tex]4 {n}^{2} + 4n[/tex]
perform the multiplication
(a–5)^2(5+a)^2
[tex]\bf \textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (a-5)^2(5+a)^2\implies (a-5)^2(a+5)^2\implies [(a-5)(a+5)]^2\implies \stackrel{\stackrel{\textit{difference}}{\textit{of squares}}}{[a^2-5^2]^2} \\[2em] [a^2-25]^2\implies (a^2-25)(a^2-25)\implies \stackrel{\mathbb{F~O~I~L}}{a^4-50a^2+25^2}\implies a^4-50a^2+625[/tex]
3x^2+7x+2 how to factor
[tex]3 {x}^{2} + 7x + 2 \\ = 3 {x}^{2} + 6x + x + 2 \\ = 3x(x + 2) + 1(x + 2) \\ = (3x + 1)(x + 2)[/tex]
Work is attached in the image provided.
For your second pair of binomials, (3x + 1)(x + 2), the product of the outer terms is 6x and the product of the inner terms is 1x and 6x + 1x = 7x which is the middle term in you're original trinomial.
So the second pair of binomials represents your answer.
Which fraction converts to a terminating decimal number
Answer:
C.
Step-by-step explanation:
divide the numerator (top number) by the denominator (bottom number) 3/8= 0.375
Answer:
c
Step-by-step explanation:
Need to show a 5 step problem on how to get the answer. Using x and y
Answer: $5.64
Step-by-step explanation:
Let x represent 1 box of batteries
Let y represent 1 case of batteries
Given: 14x = 3y
Given: 158 = 14x + 3y
Use substitution: 158 = 14x + 14x
Simplify: 158 = 28x
Divide by 28: 5.64 = x
Given the sequence 2, 10, 50, 250,......where x = 0, 1, 2, 3,....., what is the first term?
A: 2
B: 10
C: 50
D: 250
The answer to this question is A
a is the best option
If it takes 4 workers ,4 hours to dig 4 wholes, how long would it take 2 workers to dig 6 holes?
Answer:
2 workers will take 12 hours to dig six holes
Two workers take 12 hours to dig 6 holes.
What is unitary method?The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.
Let t be the time taken by the two workers to dig a six hole.
According to the given question.
4 workers take 4 hours to dig 4 holes.
So, the number of hours taken by the one workers to dig a one hole is given by
Number of hour taken by a single worker to dig 1 hole = [tex]\frac{4 \times 4}{4}[/tex] = 4hours
Therefore,
The time taken by 2 workers to dig 6 holes is given by
[tex]\frac{4\times 4}{4} = \frac{2\times t }{6} \\\implies 4 \times 6 = 2\times t\\\implies 24= 2\times t\\\implies t = \frac{24}{2} \\\implies t = 12 hours[/tex]
Hence, two workers take 12 hours to dig 6 holes.
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The National Research Council recommends keeping 3:1 cooper to zinc ration in a horse’s diet.if the horse is getting 420mg of zinc per day , how many milligrams of copper does the council recommend the horse to have?
Answer:
1,260 mg of copper.
Step-by-step explanation:
This is because in a 3 to 1 ratio, the first number has to be 3 times the second number which is just multiplied by one. since zinc is the second number, it stays the same but the copper as to be 3 times the amount of zinc so 420 mg times 3 which equals 1,260.
Answer:140
Step-by-step explanation:
FGH IS A RIGHT TRIANGLE ? True or false
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷The answer is True.
You can eyeball the triangle or also get a protractor and also see that this is a right triangle. Remember, right triangles have a right angle.
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
DOGE
Answer:
ΔFGH is right triangle
Step-by-step explanation:
Given a triangle with dimensions 10, 7, [tex]\sqrt{51}[/tex]
we have to find FGH is right triangle or not.
[tex]Hypotenuse=10 units[/tex]
[tex]Base=7 units[/tex]
[tex]Height=\sqrt{51}[/tex]
If ΔFGH is right triangle, then by Pythagoras theorem
[tex](Hypotenuse)^2=(base)^2+(height)^2\text{ must be satisfied}[/tex]
[tex]FG^2=GH^2+FH^2[/tex]
[tex]10^2=(\sqrt{51})^2+7^2[/tex]
[tex]100=51+49[/tex]
[tex]100=100[/tex]
which is true
Hence, ΔFGH is right triangle
The answer is True
Help me anyone please
X< or equal to 8 because x is less than 8 or equal to 8 and x is any number that could be 8 or any number that is less.
Solve the system algebraically. Check your work. 5x + 2y = 10 3x + 2y = 6 ANSWER: {( a0)}
I need a 100% right answer
14 pts.
Answer:
[tex]x=2[/tex], [tex]y=0[/tex], or as an ordered pair [tex](x,y)=(2,0)[/tex].
Step-by-step explanation:
We have the system of equations
[tex]5x + 2y = 10[/tex] equation (1)
[tex]3x + 2y = 6[/tex] equation (2)
Since both equations have the term [tex]2y[/tex], we are using the elimination method:
Step 1. Multiply equation (2) by -1 and add the result equation to equation (1):
[tex]\left \{ {{-1(3x + 2y = 6)} \atop +{5x + 2y = 10}} \right.[/tex]
[tex]\left \{ {{-3x -2y = -6)} \atop +{5x + 2y = 10}} \right.[/tex]
Now we can get rid of [tex]-2y[/tex]
[tex]2x=4[/tex]
[tex]x=\frac{4}{2}[/tex]
[tex]x=2[/tex]
Step 2. Replace the value [tex]x=2[/tex] in equation (1) to find the value of [tex]y[/tex]:
[tex]5x + 2y = 10[/tex]
[tex]5(2) + 2y = 10[/tex]
[tex]10 + 2y = 10[/tex]
[tex]2y = 0[/tex]
[tex]y = 0[/tex]
We can conclude that the solution of the system of equations is [tex]x=2[/tex], [tex]y=0[/tex], or as an ordered pair [tex](x,y)=(2,0)[/tex].
how to write 26591 in expanded form
The expanded form is 26,000 + 500 + 90 + 1
Step-by-step explanation:Expanded form of any digit is to divide that number into its units, tens, hundreds, thousands and so on.
Since we are given with 26591
So
The expanded form will be
26,000 + 500 + 90 + 1
What is the area of sector BEC when CE = 9 yd?
A circle is a curve sketched out by a point moving in a plane. The area of sector BEC when CE = 9 yd is 84.823 yds².
How to find the area of a sector of a circle?The sector of a circle is like a slice of a circular pizza. Its two straight edge's having an angle, and the edge's length(the radius of the circle) are two needed factors for finding the area of that sector.
Since the whole circle with radius 'r' units have 360 degrees angle on the centre of the circle, and its area is
πr² unit², thus, as the angle lessens, this area gets lessened.
360 degree => πr² unit²
[tex]\rm area\ 1 degree = \pi r^2 \: \rm unit^2/360 area\\\\x\ degree = \dfrac{x \times \pi r^2}{360} \: \rm unit^2 area[/tex]
Thus, the area of a sector with edge length 'r' units and interior angle 'x' degrees is given as:
[tex]A = \dfrac{x \times \pi r^2}{360} \: \rm unit^2 area[/tex]Given the length of the radius of the circle, CE is 9 yds. Also, the measure of the ∠BEC at the centre of the circle is 120°. Therefore, the area of sector BEC can be written as,
Area BEC = π × r² × (θ/360°)
= π × 9² × (120° / 360°)
= 84.823 yds²
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The student council at woodland middle school is planning a field trip. They polled randomly selected teachers and students and asked what they want to eat for lunch. The result are shown in the table below. Which of the following statements is true?
19 percent of the people polled who preferred burgers were teachers.
Answer:
Option A is correct.
Step-by-step explanation:
According to results shown, we can say that option A is true.
In the burger column in above segment, we see that total number of students are 17 and total teachers are 4. Making it a total of 21.
So, [tex]\frac{4}{21}*100=19.04[/tex] ≈ 19% are teachers.
So, 19% of the polled people who preferred burgers were teachers.
Option B cannot be true as all the teachers were polled. Out of all 19% preferred burgers.
Option C is also not true because 19% was not from all the population. It was only from the teachers.
So, only option A is correct.
Meryl needs to cut down 10.5 trees for every 5 cabins she builds. how many trees will she need to cut down if she builds 7 cabins?
Answer:
14.7 trees
Step-by-step explanation:
First you need to find how many trees she cuts down to build one cabin. So you divide:
10.5/5=2.1
She cuts down 2.1 trees to make one cabin.
Next you multiply:
2.1*7=14.7