The number he should add on both sides of the equation to complete the square is 36.
What number should be added to both sides to complete the square ?The given equation is [tex]x^{2} - 12x = 16[/tex]
Thus, to make it a complete square, both sides of the equation must be a perfect square.
If we add number 36 on both sides of the equation, then the resulting equation is a perfect square.
⇒ [tex]x^{2} - 12x + 36= 16 + 36[/tex]
⇒ [tex](x-6)^{2} = 52[/tex]
∴ [tex](x-6)^{2} = (2\sqrt{13} )^{2}[/tex]
Thus, the given equation is a complete square from both sides.
Therefore, the number he should add on both sides of the equation to complete the square is 36.
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Final answer:
Add 36 to both sides of the equation x²- 12x = 16 to complete the square, transforming it into a perfect square trinomial.
Explanation:
To complete the square for the equation x² - 12x = 16, you need to take half of the coefficient of x, which is -12, and square it. This process transforms the left-hand side into a perfect square trinomial. Therefore, you calculate (12/2)² which equals 36. This is the value that needs to be added to both sides to complete the square. The equation then becomes x² - 12x + 36 = 16 + 36, which simplifies to (x - 6)²= 52
Nicole opens a savings account with an initial deposit of $5,000. since then, she has never made any other deposits or withdrawals. her savings account earns 4℅ intrest compounded monthly. which equation gives the approximate amount, A(x), she has in her savings account as a function of x, the number of years since her initial deposit?
1. A(x)= 5,000^(0.96x)
2. A(x)= 5,000(0.959)^x
3. A(x)= 5,000 + 0.04x
4. A(x)= 5,000^(1.04x)
5. A(x)= 5,000(1.041)^x
Answer:
Option 5. [tex]A(x)=\$5,000(1.041)^{x}[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=x\ years\\ P=\$5,000\\ r=0.04\\n=12[/tex]
substitute in the formula above
[tex]A=\$5,000(1+\frac{0.04}{12})^{12x}[/tex]
[tex]A=\$5,000(1.041)^{x}[/tex]
What is the exact area of a circle having radius 7 in.?
the school put up a new fence the East and West sides were each 12 meters long the North and South sides where each 10 m long how many meters of fencing did they use
Answer:
12+12 for east and west equals 24
10+10 for north and south equals 20
24+20 equals 44
In the end they used 44 meters of fence
Step-by-step explanation:
Answer:
44Step-by-step explanation:
How do you solve 16 = 17 - t
So I looked it up on another math helper app called ( Socratic )and this is what popped up on my screen Simplifying
16 = 17 + -1t
Solving
16 = 17 + -1t
Solving for variable 't'.
Move all terms containing t to the left, all other terms to the right.
Add 't' to each side of the equation.
16 + t = 17 + -1t + t
Combine like terms: -1t + t = 0
16 + t = 17 + 0
16 + t = 17
Add '-16' to each side of the equation.
16 + -16 + t = 17 + -16
Combine like terms: 16 + -16 = 0
0 + t = 17 + -16
t = 17 + -16
Combine like terms: 17 + -16 = 1
t = 1
Simplifying
t = 1
So I’m pretty sure that’s the answer:) if not I’m truly sorry.
Answer:
what u do on one side u gotta do to the other
Step-by-step explanation:
Michael is organizing 5,272 blocks into bins at the toy store. He needs to put the same number of blocks in each bin without any leftover blocks. How many bins could Michael use for the blocks? A) 3. B) 4. C) 5. D) 9.
B. plz mark brainly
Answer: B) 4 bins
Step-by-step explanation:
The criteria of divisibility are rules that serve to know if a number is divisible by another without having to perform the division.
Divisibility by 3 (or 9)A number is divisible by 3 (or 9) if and only if the sum of its digits is divisible by 3 (or 9).
5,272
5 + 2 + 7 + 2 = 16
1 + 6 = 7 →This number isn't divisible by 3, therefore 5,272 isn't divisible by 3
Divisibility by 5Divisibility by 5 is easily determined by checking the last digit in the number , and seeing if it is either 0 or 5. If the last number is either 0 or 5, the entire number is divisible by 5.
5,272 → the last digit is 2; isn't 0 or 5, therefore 5,272 isn't divisible by 5.
Divisibility by 4The basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4
5,272
the last two digits are 72, and 72/4 = 18
72 is divisible by 4, therefore 5,272 is divisible by 4
Since 5,272 is divisible by 4, Michael can use 4 bins to organize the blocks, and he needs to put 5,272/4 = 1,318 blocks in each bin.
Answer: B) 4 bins
[tex]\textit{\textbf{Spymore}}[/tex]
32 lb 12 oz = ____ lb
Answer:
32.75
Step-by-step explanation:
12 oz = 0.75 lbs
0.75 lbs + 32 lbs = 32.75 lbs
Which situation describes INDEPENDENT events?
Answer:
In B, One card is chosen from a standard deck, it is set aside, then a second card is drawn. That "set aside" is where we have a problem. We began with 52 cards, but now have 51. This fact WILL change the probability or probabilities. Chances of obtaining a red heart from the full 52-card deck are 4/52; whereas chances of obtaining a red heart from the remaining 51 cards (assuming that you got a red heart earlier and set it aside) is 3/51.
Which statements about the graph of the function y=(1/3)^x are true?
The function is increasing.
The function is decreasing.
The x-intercept is (1, 0).
The y-intercept is (0, 1).
The range of the function is all real numbers.
Answer: B and D
Step-by-step explanation: Just answered on edg.
About the graph of the function option (B) the function is decreasing and option (D) the y-intercept is (0, 1) is the correct answer.
What is graph of a function?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).
For the given situation,
The function is y=(1/3)^x.
Plot this function in the graph as shown below.
From the graph, the y-intercept is (0,1) and the function is decreasing function.
Hence we can conclude that about the graph of the function option (B) the function is decreasing and option (D) the y-intercept is (0, 1) is the correct answer.
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Jorge has $138.22 in his savings account. He deposits $10.75 every week and withdraws $31.68 every four weeks. What will his balance be in 8 weeks?
Answer:
Pretty sure the answer is $160.86
Step-by-step explanation:
you start off by multiplying 10.75 x 8 because that's how much he'll deposit at the end of an 8 week spand.
adding 86+138.22= 224.22
then you subtract 31.68 two times from that as he withdraws 2 times in the 8 weeks, giving you the answer of 160.86.
hope this helps xx have a good day :)
I’m guessing the end total would be $299.08. Somewhere around that number.
What’s This Answer I Need Help I’m struggling with man
Area: 3915
L X W
Perimeter: 264
Add all sides
I don't know what it means by type, sorry
area: 3915 mm
perimeter: 264
type: rectangle
Step-by-step explanation:
to find the area multipluy 87 and 45
to fin perimeter add 87 and 45. then multipluy by 2
a-b+c=3
a+b+c=7
Find a+c using substitution.
a+c=5. Please look at the attached image to see what I did
At lunch, 6 friends share 4 pizzas equally. What fraction of a pizza does each friend get? May 5th, 2019. (8:34pm.)
Answer:
each friend would get about 2/3 of a pizza
Step-by-step explanation:
you would take the total amount of pizza (4) and divide it by the friends (6) which would look like this: 4 / 6 = 0.6666 (repeating) which is equal to 2/3
i hope this helps :)
what is the best desert in a math teachers cafe law of sines riddle
is a good desert. people love cake
Final answer:
The question regarding the "best desert in a math teacher's cafe" related to the Law of Sines is likely a pun involving math terms, with "pi" being the intended humorous answer due to its dual significance as a mathematical constant and a type of dessert.
Explanation:
The "best desert in a math teacher's cafe" when mentioned alongside the Law of Sines is likely a playful riddle rather than a straightforward question. The Law of Sines is a mathematical formula used in trigonometry to find missing angles or sides of a triangle, given enough information. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides and angles in the triangle. Therefore, this riddle might be a pun or a play on words related to mathematics or trigonometry terms rather than an actual desert item.
In essence, to solve such riddles, one needs to think creatively, connecting the concept of desert with mathematical terms or principles. A common pun could be "pi," as it sounds like "pie," a type of dessert, and is also an essential constant in mathematics used to calculate the circumference and area of a circle. In the context of a math-themed cafe, "pi" could very well be considered the "best dessert," cleverly linking the world of mathematics with culinary delights in a humorous way.
An office manager reported that he spent $350 on gifts for employees. He said that $240 was spent on clothing with each man receiving a $20 T-shirt and each woman receiving a $40 sweatshirt. He said that $110 was spent on desk accessories with each man receiving a $5 calendar and each woman receiving a $15 stapler. If m equals the number of men and wequals the number of women, the system of equations that represents the expenses is as follows:
m+2w=12
m+3w=22
Answer:
So I assume we are figuring out the number of men and women here, so:
m + 2w = 12
m = 12 - 2w
12 - 2w + 3w = 22
w = 10
m + 2w = 12
m + 2(10) = 12
m + 20 = 12
m = -8
complementary or supplement and also solve for X.
Answer:
see explanation
Step-by-step explanation:
The 2 indicated angles form a straight angle and are supplementary.
4x + 5 + 41 = 180
4x + 46 = 180 ( subtract 46 from both sides )
4x = 134 ( divide both sides by 4 )
x = 33.5
Use the grouping method to factor the polynormial below completely. 10x^3 - 35x^2 + 6x - 21
The polynomial 10x^3 - 35x^2 + 6x - 21 is factored using the grouping method to obtain (2x - 7)(5x^2 + 3).
To factor the polynomial 10x^3 - 35x^2 + 6x - 21 using the grouping method, we first look for a common factor in each group separately and then factor out the common binomial factor.
Split the polynomial into two groups: (10x^3 - 35x^2) and (6x - 21).
Factor out the greatest common factor from each group: 5x^2(2x - 7) and 3(2x - 7).
Now we have 5x^2(2x - 7) + 3(2x - 7). Since both terms have a common binomial factor of (2x - 7), we can factor this out: (2x - 7)(5x^2 + 3).
So, the factored form of the polynomial 10x^3 - 35x^2 + 6x - 21 using the grouping method is (2x - 7)(5x^2 + 3).
a rectangular solid has sides of 7 cm, 9 cm and 11 cm. what is the surface area?
Answer:
7multiply by 9=63
7by11=77
9by11=99
Answer=63+77+99=239
Step-by-step explanation:
Solve system of equation.
2x+y=10
-2x+2y=5
Answer:
(2.5,5)
Step-by-step explanation:
thats the answer
Answer:
The solution point is (2.5, 5)
Step-by-step explanation:
This is one of the very first steps you need to take in order to solve 2 equations with 2 unknowns. This does not require that you make any adjustments.
2x + y = 10
-2x +2y = 5 Just add. The xs cancel.
3y = 15 Divide by 3
3y/3 = 15/3
y = 5
=========
Now use one of the equations (the top one is easier) to solve for x
2x + y = 10 Substitute y = 5
2x + 5 = 10 Subtract 5
2x +5-5 = 10-5
2x = 5 Divide by 2
x = 2.5
The solution point is (2.5 , 5)
Write the equation that is the translation of y=|x| right 7 units and down 9 units.
Answer:
[tex]y=|x-7|-9[/tex].
Step-by-step explanation:
The given function is [tex]y=|x|[/tex].
When this function is translated to the right 7 units and down 9 units, then the equation becomes
[tex]y=|x-7|-9[/tex].
Always remember that; [tex]y=|x-c|-k[/tex] is a transformation that translates the graph of [tex]y=|x|[/tex] c units to the right and k units down.
The correct choice is the first option.
Four-fifths of a number is -24. What is the number ?
-20 is the anwser
4*(-24)/5 =-20
Answer: -30
(4/5)x=-24
x=(-24)(5/4)=-6*5=-30
Point P (-1, 2) is the center of a circle. The radius of the circle is 3 units. Which point lies on the circle? PLEASE HELP!
Answer:
(2,2), (-1,5), (-3,2), (-1,-1)
Step-by-step explanation:
The radius is the distance from the center of the circle to the outside. So, adding or subtracting 3 from the x-value of the center point will give you a point that lies on the circle. Doing the same to a y-value will as well. However, never add or subtract from both.
I need to know what the answers is
Answer:
The most reasonable answer would be 7.
Step-by-step explanation:
ED is shorter than both EC and CD, and the root of 220 is 11 point something, so it would hae to be 7.
The answer would be 7.
Solve the system of equations below by graphing both equations with a pencil and paper. What is the solution? y=-x-1 y=x+3
Answer:
C. (-2, 1)
Step-by-step explanation:
See the attached graph.
The slope of the first line is -1, and its y-intercept is -1.
The slope of the second line is +1 and its y-intercept is +3.
The solution is the point that is common to both lines, (-2, 1).
Answer:
C. (-2, 1)
Step-by-step explanation:
APEX
The dimensions of a box are x, 2x, and 3x. Each dimension is decreased by 2. Calculate the volume of the box.
A) 3x^3-12-8
B)-1x^6
C)6x^3-22^2+24x-8
D)40x^3
Answer:
Correct choice is C) [tex]6x^3-22x^2+24x-8[/tex].
Step-by-step explanation:
Given that the dimensions of a box are x, 2x, and 3x.
Now each dimension is decreased by 2.
Then new dimensions of a box are (x-2), (2x-2), and (3x-2).
Now let's calculate the volume of the box which is given by
Volume = (Length) x (Width) x (Height)
[tex]=(x-2)(2x-2)(3x-2)[/tex]
[tex]=(2x^2-6x+4)(3x-2)[/tex]
[tex]=(2x^2-6x+4)(3x-2)[/tex]
[tex]=6x^3-22x^2+24x-8[/tex]
Hence correct choice is C) [tex]6x^3-22x^2+24x-8[/tex].
The white shape can be transformed into the blue one using
A) a dilation, then a rotation.
B) a rotation, then a reflection.
C) a translation, then a dilation.
D) a reflection, then a translation.
Answer:
B) a rotation, then a reflection
Step-by-step explanation:
you will make a rotatio of 90° about clockwise and reflection about Y- axix
Answer:
B) a rotation, then a reflection.
Step-by-step explanation:
From the given graph, the white shape transformed into blue shape.
If you look at the white shape and the blue shape.
The white shape rotated 45° counter clock wise and reflected over the origin x = y to get the blue figure.
For example, let's take a vertex (2, -1) in the white figure. The corresponding in the blue shape is (-2, 1) which is reflection about the origin.
Therefore the answer is B) a rotation, then a reflection.
K= 2/3 is a solution to the inequality 18k + 4 >18 true or false
Answer:
The answer will be: false.
18k = 12
12 + 4 = 16
16 > 18
So the equation is false.
Hope this helps! :D
Step-by-step explanation:
Please help !
The point slope form of the equation of the line that passes through -5 -1 and 10 -7 is y+7=-2/5(x-10). What is the standard form of the equation for this line?
A - 2x-5y=-15
B - 2x-5y=-17
C - 2x+5y=-15
D - 2x+5=-17
Answer:
C. 2x +5y = -15
Step-by-step explanation:
You want the form ax +by = c. To get that form, you need to put the x-term on the left (making sure its sign is positive) and the constant on the right.
Multiply by 5:
5y +35 = -2(x -10)
Eliminate parentheses:
5y +35 = -2x +20
Add 2x-35
2x + 5y = -15 . . . . . . corresponds to selection C
_____
Be careful of dashes when writing answers. They can be confused with minus signs.
Circular flower bed is 17 m in diameter and has a circular 2 around it is that to meters wide find the area of the sidewalk in square meters use 3.14 for pi
The area of the sidewalk surrounding a circular flower bed with a diameter of 17 meters and a 2-meter wide sidewalk is 119.32 square meters.
The question involves finding the area of a sidewalk that surrounds a circular flower bed. The flower bed has a diameter of 17 meters, and the sidewalk is 2 meters wide. This is a geometry problem that requires us to calculate the area of two circles and then find the difference between them.
Calculate the radius of the inner circle (flower bed): radius = diameter / 2 = 17 m / 2 = 8.5 m.
Calculate the area of the inner circle using the formula A = 3.14 * 8.5 m * 8.5 m = 226.865 m
Calculate the radius of the outer circle (flower bed + sidewalk): radius_outer = radius_inner + width of the sidewalk = 8.5 m + 2 m = 10.5 m.
Calculate the area of the outer circle: A_outer = 3.14 * 10.5 m * 10.5 m = 346.185 m.
Calculate the area of the sidewalk by subtracting the area of the inner circle from the area of the outer circle: Area_sidewalk = A_outer - A_inner
= 346.185 m - 226.865 m
= 119.32 m.
The area of the sidewalk is 119.32 square meters.
Can someone pls tell me the answer to this . I’ll give you the brainly
Answer:
(10^7)y
Step-by-step explanation:
raise 10 to the 7th power
10 ^7
Multiply this and y
10^7 * y
(10^7)y
Which fraction is equivalent to 0.75?
Answer:75/100
or 3/4
Step-by-step explanation:
Answer:
3/4ths
Step-by-step explanation:
100 divided by 4 is 25. 25 times 3 is 75.