Create a trinomial that can be factored and write it in standard form.
To create a trinomial, use a basic factored form like (x+a)(x+b), and expand this via the distributive property. This yields as an example x²+8x+15, a trinomial in standard form.
Explanation:To create a trinomial that can be factored and to write it in standard form, we need to consider a basic factored form first. Let's use (x+a)(x+b) as our basic factored form. In this form, 'a' and 'b' are the roots of the trinomial.
To create the trinomial, we then expand this expression by using the distributive property: (x+a)(x+b) = x² + bx + ax + ab, which simplifies to x² + (a+b)x + ab. This is now our trinomial in standard form.
Let's take a concrete example. If we let 'a' be 3 and 'b' be 5, our factored form is (x+3)(x+5). Expanding this, we get x² + 5x + 3x + 15, which simplifies to x² + 8x + 15. Thus, x² + 8x + 15 is a trinomial that can be factored and is written in standard form.
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For this figure, find the value of x.
x = _____?
Im not sure if i take 77 + 58 + x=180 or 77+28+x=180 or something else.
5+3i/4-2i written as a complex number?
The expression (5 + 3i)/(4 - 2i) can be simplified as (-7 + 11i)/10, which is a complex number.
How to write 5+3i/4-2i written as a complex numberTo write the expression (5 + 3i)/(4 - 2i) as a complex number, we can multiply the numerator and denominator by the conjugate of the denominator to eliminate the imaginary part in the denominator.
The conjugate of 4 - 2i is 4 + 2i.
Multiplying both the numerator and denominator by the conjugate:
((5 + 3i) * (4 + 2i))/((4 - 2i) * (4 + 2i))
Expanding the numerator and denominator:
(20 + 10i + 12i + 6i^2) / (16 - 8i + 8i - 4i^2)
Simplifying and combining like terms:
(20 + 22i - 6) / (16 + 4)
(-14 + 22i) / 20
Now, we can simplify the expression further by dividing both the numerator and denominator by their greatest common divisor, which is 2:
(-7 + 11i) / 10
Therefore, the expression (5 + 3i)/(4 - 2i) can be simplified as (-7 + 11i)/10, which is a complex number.
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What is the value of the expression when a = 5 and b = 2? a 2b−3
Which CANNOT be used in a proof?
A. Theorems
B.Postulates
C.Properties
D.Undefined Terms
At a pet show, the ratio of dogs to cats is 4:3. if the number of cats is 45, find the number of dogs at the show.answer:
The number of dogs would be 60 when the ratio of dogs to cats is 4:3.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
Given that the ratio of dogs to cats is 4:3. if the number of cats is 45
We have to determine the number of dogs.
Let the number of dogs would be x
As per the given condition, we can write a proportion as
4 dogs : 3 cats = x : 45 cats
⇒ 4 / 3 = x / 45
Apply the cross-multiplication operation,
⇒ 45 × 4 = x × 3
⇒ x = (45 × 4)/3
⇒ x = 15 × 4
⇒ x = 60
Therefore, the number of dogs would be 60.
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At president bush's inauguration in 2005,the newspaper headline stated there were about 400,000 people in attendance of the newspaper rounded to the nearest 10,000 what is the largest number of smaller number of people who could been there
What is the additive inverse of the polynomial 9xy^2 + 6x^2y – 5x^3?
A.9xy2 – 6x2y + 5x3
B. 9xy2 – 6x2y – 5x3
C. 9xy2 + 6x2y + 5x3
D. 9xy2 – 6x2y + 5x3
Answer:
The answer is B.
Step-by-step explanation:
The additive inverse of the given polynomial is:
-9xy^2 - 6x^2y + 5x^3
How to find the additive inverse of a polynomial?The additive inverse of a polynomial would be another polynomial, such that when we add the two, the outcome is zero.
For a given polynomial the additive inverse is given by multiplying the given polynomial by -1.
Here we have:
p(x) = 9xy^2 + 6x^2y – 5x^3
Then the additive inverse is:
q(x) = -p(x) = -9xy^2 - 6x^2y + 5x^3
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Four milliliters of ink A is added to 10 milliliters of ink B, forming a mixture of inks. Ink A contains 10% blue pigment. Ink B contains an unknown percentage of blue pigment. The mixture of the two inks contains 35% blue pigment.
What percentage of blue pigment is in the mixture of the two inks?
45%
49%
60%
75%
Answer:
45%
Step-by-step explanation:
I took the test!
Witch Decimal is equal to six-tenths?
0.6 0.15 0.2 0.3 0.4
The triangle PQR shown on the coordinate grid below is reflected once to map onto triangle P´Q´R´.
If vertex P’ is at (7, -6), what are the coordinates of vertex R’?
A)(5, -3)
B)(3, -5)
C) (3, -2)
D)(5, -2)
The answer is (5,-2)
To find the coordinates of vertex R' in the reflected triangle, we can use the midpoint formula. Using the given point P' at (7, -6) and the original point P at (x, y), the x-coordinate of vertex R' is 5. Similarly, using the given point P' at (7, -6) and the original point R at (x, y), the y-coordinate of vertex R' is -2.
Explanation:To find the coordinates of vertex R', we need to map the reflection of triangle PQR onto triangle P'Q'R'. Since vertex P' is at (7, -6), we can use the midpoint formula to find the coordinates of the reflected point R'.
The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the two endpoints.
Using the given point P' at (7, -6) and the original point P at (x, y), we can write the equation:
(x + 7) / 2 = 7
Solving for x, we get x = 5.
Similarly, using the given point P' at (7, -6) and the original point R at (x, y), we can write the equation:
(y - 6) / 2 = -2
Solving for y, we get y = -2.
Therefore, the coordinates of vertex R' are (5, -2).
A painting crew bought 30 gal of paint for a job. The crew members used 3 gal of paint per hour until they used all the paint.
Which sketch represents this situation?
If the crew members used 3 gal of paint per hour and bought 30 gal of paint for a job, then they will work 30:3=10 hours.
They start at x=0 hours with y=30 gal of paint;They end at x=10 hours with y=0 gal of paint (they worked until they used all the paint).The dependence between x and y is linear.Conclusion: the only possible sketch is A.
Answer: correct choice is A.
Rock music accounted for 30.5% of the total sales of recorded music in 1999 , and 20.4% of the total sales of recorded music in 2009 . Find the average rate of change of the percentage of sales of rock music from 1999 to 2009 .
Round to the nearest hundredth of a percent. Note that the percentage sign is already given in the answer, so you do not need to enter it.
The average rate of change is
Which absolute value function, when graphed, will be narrower than the graph of the parent function, f(x) = |x|? f(x) = |x| – 3 f(x) = |x + 2| f(x) = 0.5|x| f(x) = 4|x|
f(x) = 4|x| is the function narrower than the parent function , Option D is the correct answer.
What is an absolute function ?An Absolute function is a function that returns a positive value at any given point.
It is given that
The parent function is
f(x) = |x|
To find the function which will be narrower , it will be plotted to check
It is the known fact that when a function is multiplied by a number greater than 1 , the resulting function gets narrower , This can be easily identified from the graph.
f(x) = 4|x| is the function narrower than the parent function , Option D is the correct answer.
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Choose the words or phrases that best complete the sentences.
A fifth degree polynomial (could or must) have 5 linear factors. The factors (could, but do not have to be, or must) be distinct.
Answer: A fifth degree polynomial could have 5 linear factors. But the factors do not have to be be distinct.
Step-by-step explanation:
The fundamental theorem of algebra tells that every non-constant single-variable polynomial with complex coefficients has at least one complex root.Corollary to the fundamental theorem tells that every polynomial of m>0 degree has exactly m zeroes.Thus by corollary to fundamental theorem of algebra, a fifth degree polynomial must have 5 zeroes . But A fifth degree polynomial could have 5 linear factors if all zeroes are real numbers.
The factors could be distinct or similar.
Thus , The factors do not have to be distinct .
becky works 16 days each month.how many days will she work in 6 months
Becky will work 96 days in 6 months.
Explanation:To find out the number of days Becky will work in 6 months, we need to multiply the number of days she works each month by the number of months. Given that Becky works 16 days each month, we can calculate the number of days she will work in 6 months as follows:
Number of days Becky works each month = 16Number of months = 6Number of days Becky will work in 6 months = 16 days/month * 6 months = 96 daysLearn more about number of days worked here:
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10. Mr. Falcone's pizza shop offers three sizes of pizza. The small, medium and large pizzas have diameters of 8 inches, 10 inches and 12 inches. Small Medium Large a) What is the circumference of each size of pizza? Small = _________________ Medium = ___________________ b) What is the area of each size of pizza? Small = _________________ Medium = _________________ Large = _______________ Large = _________________ c) Joey is very hungry. He says he wants to eat a 100-square-inch area of pizza. Which size(s) of pizza should he order? Why?
Answer:
Step-by-step explanation:The employees must sell 78 pizzas in order to get the bonus.
The percentage decrease is 0.05%
Step-by-step explanation:
Number of pizzas sold yesterday is 65 pizzas.
The owner offers the employees a bonus if the number of pizzas sold increases by 20%
So 20% of 65 pizzas is, pizzas.
Therefore, the employees must sell 65+13=78 pizzas in order to get the bonus.
But the actual number of pizzas sold today was 60. So the number of pizza sold has decreased. Then the percent decrease is,
Therefore, the percentage decrease
the formula a= d/g gives the average gas milege a of a vehicle that uses g gallsons of gas to travel d miles. use the formula to find how many gallons of gas a vehicle with average gas mileage of 20.2 miles per gallon will use to travel 75 miles. round your answer to the nearest tenth.
Answer: 3.7 gallons
Step-by-step explanation:
Given : The formula [tex]a=\dfrac{d}{g}[/tex] gives the average gas mileage a of a vehicle that uses 'g' gallons of gas to travel 'd' miles.
The average gas mileage : a =20.2 miles per gallon
Distance : d=75 miles.
To find : g
Substitute all the values in the above formula , we get
[tex]20.2=\dfrac{75}{g}\\\\\Rightarrow\ g=\dfrac{75}{20.2}=3.71287128713approx3.7\ \ \ \text{ Rounded o the nearest tenth}[/tex]
Hence, the required amount of gas = 3.7 gallons
The Sky High Ski Club dues are $450 per season. This fee includes transportation to and from the slopes and lift tickets. Skis cost $159.90, boots $78.25, and poles $19. What is the total cost?
Answer:
The total cost is $707.15.
Step-by-step explanation:
The Sky High Club dues are = $450 per person
and the Skis costs = $159.90
Cost for boots = $78.25
Cost of poles = $19.00
To find the total cost we will add all the amounts.
Total cost = 450 + 159.90 + 78.25 + 19.00
= $707.15
The total cost is $707.15.
The diagonals of a rhombus divide it into four triangles of equal area.
True
False
Answer:
True
Step-by-step explanation:
What is the percentage of 13/18?
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What is the equation in point slope form of the line that passes through the point (1, –2) and has a slope of 3?
y−2=3(x+1)
y+2=3(x−1)
y+1=3(x−2)
y−1=3(x+2)
What is 43/50 as a percent?
The altitude dropped to the base of an isosceles triangle is a median, an angle-bisector, and a perpendicular bisector?
True
False ...?
The length of a rectangle is five centimeters more than its width w if the perimeter of the rectangle is 26 centimeters what is the area of the rectangle i'm square centimeters
What is 9 x ( 3 x 5 ) = ( 9 x n ) x 5?
Answer:
n=3
Step-by-step explanation:
1. Which best describes the relationship between the successive terms in the sequence shown?
9, –1, –11, –21, …
a)The common difference is –10.
b)The common difference is 10.
c)The common ratio is –9.
d)The common ratio is 9.
2. A sequence is defined recursively using the formula f(n + 1) = f(n) – 5 . Which sequence could be generated using this formula?
a)1, –5, 25, –125, ...
b)2, 10, 50, 250, ...
c)3, –2, –7, –12, ...
d)4, 9, 14, 19, ...
What is used to repair big, brass instruments
Repairing big, brass instruments requires the use of specialized tool kits made of steel alloys and brass instrument repair kits. These tools are designed to be gentle on the brass surface, ensuring the instrument's quality and longevity.
Explanation:Repairing big, brass instruments, such as trombones and trumpets, often requires the use of certain materials and techniques. Since brass is an alloy of copper and zinc, it is prone to tarnish and damage over time. Hence, it is important to use cleaning and repair tools made of similar or non-abrasive materials to avoid causing further damage to the instrument.
The most common methods of repairing dents and scratches in brass instruments involve specialist tool kits composed of various steel alloys, which are strong and durable, but also gentle on the brass surface. Additionally, using specialized brass instrument repair kits, which include various mutes, cleaning agents, and brushes, can help maintain the instrument's quality and longevity.
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When point E (-9, 3) is rotated 180� about the origin, its coordinate becomes (3, 9).
True
False
...?
what capital letters are reflect symmetry