Answer:
Part a) [tex]x^{2}+4x+4[/tex]
Part b) [tex]x^{2}-10x+25[/tex]
Step-by-step explanation:
we know that
A perfect square trinomial is equal to
[tex](x+a)^{2} =x^{2}+2ax+a^{2}[/tex]
Part a) we have
[tex]x^{2}+4x[/tex]
Compare with the formula of a perfect square trinomial
[tex]x^{2}+4x=x^{2}+2ax+a^{2}[/tex]
so
[tex]4x=2ax[/tex]
[tex]4=2a[/tex]
[tex]a=2[/tex]
therefore
[tex](x+a)^{2} =(x+2)^{2}=x^{2}+4x+4[/tex]
Part b) we have
[tex]x^{2}-10x[/tex]
Compare with the formula of a perfect square trinomial
[tex]x^{2}-10x=x^{2}+2ax+a^{2}[/tex]
so
[tex]-10x=2ax[/tex]
[tex]-10=2a[/tex]
[tex]a=-5[/tex]
therefore
[tex](x+a)^{2} =(x-5)^{2}=x^{2}-10x+25[/tex]
The values are needed to make each expression a perfect square trinomial x^2 + 4x + 4 and x^2 – 10x + 25.
What is a perfect square?A perfect square is a number system that can be expressed as the
square of a given number from the same system.
A. [tex]x^{2} +4x+4[/tex]
A perfect square trinomial is
[tex](x+a)^2 = x^2 + 2ax + a^2[/tex]
Compare with the formula of a perfect square trinomial
4x = 2ax
4 = 2a
a = 2
Therefore, [tex](x+a)^2 = (x+2)^2 = x^{2} +4x+4[/tex]
B. [tex]x^{2} -10x + 25[/tex]
A perfect square trinomial is
[tex](x+a)^2 = x^2 + 2ax + a^2[/tex]
Compare with the formula of a perfect square trinomial
-10x = 2ax
-10 = 2a
a = -5
Therefore, [tex](x+a)^2 = (x-5)^2 = x^{2} -10x+25[/tex].
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Convert 12 over 5 to a decimal using long division.
solve for y, then find the value of y when given x = -2. 6x = 7 - 4y
To solve for y in the equation 6x = 7 - 4y, isolate the y-term by subtracting 7 and dividing by -4. When x = -2, y = 15/4.
Explanation:To solve for y in the equation 6x = 7 - 4y, we can start by isolating the y-term. First, subtract 7 from both sides of the equation to get 6x - 7 = -4y. Then, divide both sides by -4 to isolate y and change the sign, giving us y = -6x/4 + 7/4. To find the value of y when x = -2, we substitute -2 into the equation:
y = -6(-2)/4 + 7/4 = 3 + 7/4 = 3 3/4 = 15/4
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what is the scientific notation of 97,700,000,000,000,000,000
The preventative maintenance plan for your automobile is $896. If you were required to replace your water pump and starter for $316 and $443, respectively, how much did the repairs cost you?
A. $896 (Would the maintenance plan cover it so it would just be 896?)
B. $316
C. $661
D. $1,655
Answer:
Option A is correct because the maintenance plan covers the cost of repair.
Step-by-step explanation:
We are supposed to replace water pump and starter for $316 and $443, respectively.
So, total cost = [tex]316+443[/tex]
= $759
Since we are given that the preventative maintenance plan for your automobile is $896.
The total cost of repair is under the maintenance plan .
So, the answer is $896.
Option A is correct because the maintenance plan covers the cost of repair.
the coffee pub has cans of coffee that weight 3 1/4 pounds each. the pub has 8 1/2 cans of coffee left. What is the total weight of 8 1/2
To find the total weight of 8 1/2 cans of coffee, multiply the weight of each can by the number of cans. The total weight is 27 1/2 pounds.
The total weight of 8 1/2 cans of coffee can be found by multiplying the weight of each can (3 1/4 pounds) by the number of cans left (8 1/2).
3 1/4 pounds x 8 1/2 = 27 1/2 pounds
Therefore, the total weight of 8 1/2 cans of coffee is 27 1/2 pounds.
224 7/10 in decimal form
The fraction 2247/10 can be expressed in decimal form as 224.7.
To express the fraction 2247/10 in decimal form, we perform long division to divide the numerator by the denominator.
Dividing 2247 by 10, we obtain a quotient of 224 with a remainder of 7, The quotient represents the whole number part of the decimal, while the remainder becomes the decimal part.
Adding the decimal point, we can write the result as 224.7. So, 2247/10 as a decimal is 224.7,
This means that if we divide 2247 into 10 equal parts, each part represents 224.7 units,
Therefore, the decimal representation of 2247/10 is 224.7.
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The given question is incomplete, the complete question is
Express the fraction 2247/10 in decimal form.
In a recent 10 year period, the change in the number of visitors to U. S. National Park was about -11,150,000.
Answer:
1115000
Step-by-step explanation:
the midpoint of AB has coordinates (4, -9). Endpoint A has coordinates (-3,-5). what are the coordinates of B
The co-ordinates of B are (11,-23)
what is the Cartesian coordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,
Given here: The midpoint of the line AB is (4,-9) and A (-3,5)
let the co-ordinates for B be (x,y) Thus using the formula for midpoint we get
4=x-3 /2
x-3=8
x=11
-9= 5+y /2
y=-23
Hence, The co-ordinates of B are (11,-23)
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Pls help. First answer marked as brainliest
There are 13 dancers in the front row.7dancers are in the back row. How many fewer dancers are in the back row than are in the front row?
Answer this question please. (It shows the question in the picture)
A). B). C) D)
Which unit rate is the lowest price per ounce? Choice A: 25 ounces of potato chips for $3.49. Choice B: 45 ounces of potato chips for $4.79
Choice A
Choice B
Both are equal
Not determined
which is bigger 3/8 or 0.38
0.38 is bigger than 3/8.
Explanation:To compare 3/8 and 0.38, we need to convert them to the same form. Since 0.38 is already in decimal form, we need to convert 3/8 to decimal form as well. Dividing 3 by 8 gives us 0.375.
Comparing 0.375 and 0.38, we can see that 0.38 is bigger than 0.375. So, 0.38 is bigger than 3/8.
HELP ME PLEASE!!!!!!
Write the following equation in slope intercept form. y – 3 = -2 (x -5)
Find (3 × 10^4) + (7 × 10^2).
A) 3.07 × 10^2
B) 3.07 × 10^4
C) 3.70 × 10^2
D) 3.70 × 10^4
I need a correct answer please
the forth term of an arithmetic seaquence is 19 and the fifth term is 13 . what is the third term
Find the solution to the system of equations: x + 3y = 7 and 2x + 4y = 8 1. Isolate x in the first equation: 2. Substitute the value for x into the second equation: 3. Solve for y: 4. Substitute y into either original equation: 5. Write the solution as an ordered pair: x = 7 – 3y 2(7 – 3y) + 4y = 8 14 – 6y + 4y = 8 14 – 2y = 8 –2y = –6 y = 3 x + 3(3) = 7 (, )
Answer:
Thx. (-2, 3) is correct
Step-by-step explanation:
a geologist noticed that land along a fault line moved 24.8 cm over 175 yrs on average how much did the land move each year
4x − 3/3=7
Solve for x.
To solve the equation 4x - 3/3 = 7 for x, follow the steps below: add 3/3 to both sides to eliminate the fraction, simplify the right side, and divide both sides by 4 to isolate x. The solution is x = 2.
Explanation:To solve the equation 4x - 3/3 = 7 for x, we will follow the steps below:
Add 3/3 to both sides of the equation to eliminate the fraction. This gives us 4x = 7 + 3/3.Next, simplify the right side of the equation. 7 + 3/3 is equal to 7 + 1, which is 8.Now, divide both sides of the equation by 4 to isolate the variable x. This gives us x = 8/4, which simplifies to x = 2.So, the solution to the equation 4x - 3/3 = 7 is x = 2.
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There are 318 fiction books in the class library.the number of nonfiction books is 47 less than the number of fiction books about how many nonfiction books are there in the class library?explain
Answer:
271 books
Step-by-step explanation:
Given: There are 318 fiction books in the class library.the number of nonfiction books is 47 less than the number of fiction books.
To find: About how many nonfiction books are there in the class library
Solution: It is given that 318 fiction books in the class library.
Also it is given that the number of nonfiction books is 47 less than the number of fiction books.
Let us assume that there are x nonfiction books,
So, we have
[tex]x=318-47[/tex]
[tex]x=271[/tex]
Hence, the number of nonfiction books is 271.
Anthony is making a collage for his art class by picking shapes randomly. He has five squares, two triangles, two ovals, and four circles. Find P(a square is not chosen first).
PLEASE HELP!
15 POINTS
Answer:
C) P = [tex]\frac{8}{13}[/tex]
Step-by-step explanation:
Square: 5
Triangle: 2
Ovals: 2
Circles: 4
Using formula of probability:
Probability = [tex]\frac{Favourable Outcomes}{Total Outcomes}[/tex] ----- 1
Total Outcomes: 5 + 2 + 2 + 4 = 13
Favourable Outcomes: 2 + 2 + 4 = 8 (Excluding 5 squares)
A sqaure is not chosen first, which means that any shape of the rest of 8 shapes can be chosen
so eq 1 becomes
P = [tex]\frac{8}{13}[/tex]
Sophia has read 75 pages in a 250-page book. What percent of the book has Sophia read?
what do you notice about the slopes of opposite sides
Find the LCM of 63 and 84.
given the inequality 3(x - 4)>bx, for what value of "b" are there no solutions?
what is the greatest common factor of 24 and 36
The greatest common factor of 24 and 36 is 12
What is Greatest Common Factor?
The Greatest Common Divisor is the highest number that divides exactly into two or more numbers. It is also expressed as GCF
Given data ,
The two numbers are 24 and 36
Now , we need to find the factors of both numbers to determine the greatest common factor of the two numbers
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36
From the two set of factors , we can see that 12 is the greatest common factor of both 24 and 36
Hence , the Greatest Common Factor of 24 and 36 is 12
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35 multiplied by the quantity r less than 45
In the inequality 3x + 14 ≤ 44, x represents the cost of CDs Tim bought. Which phrase most accurately describes the cost of CDs?
the correct answer is A.
an angle measures 16 degrees less than three times its supplement find the measure of the angle