Answer:
Step-by-step explanation:
Hello, please consider the following.
The "vertex form" is as below.
[tex]y=a(x-h)^2+k\\\\\text{Where (h, k) is the vertex of the parabola.}\\[/tex]
Let's do it!
[tex]f(x)=\dfrac{1}{2}x^2+3x-2\\\\f(x)=\dfrac{1}{2}\left(x^2+3*2*x\right) -2\\\\f(x)=\dfrac{1}{2}\left( (x+3)^2-3^2\right)-2\\\\f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{9}{2}-\dfrac{4}{2}\\\\f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{9+4}{2}\\\\\large \boxed{\sf \bf \ \ f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{13}{2} \ \ }[/tex]
Thank you.
What are the solutions to the quadratic equation below?
4X2 +28x + 49 = 5
The linear scale factor of two shapes is 3:4. If the area of the smallest shape is 72^2 what is the area of the big shape?
Answer:
[tex]\boxed{6912 units^2}[/tex]
Step-by-step explanation:
Hey there!
Well using the given ratio,
3:4
And the area of the small shape we need to do,
72*72 = 5184
Now we can make the following fractions,
[tex]\frac{3}{4}[/tex] = [tex]\frac{5184}{x}[/tex]
Now we can solve,
3*x = 3x
4 * 5184 = 20736
3x = 20736
20736 / 3
x = 6912
So the area of the bigger shape is 6912 units^2
Hope this helps :)
Recall the difference between an equation and an inequality. Then, identify whether these mathematical statements represent an equation or an inequality.
Answer:
If it were an equation, it would be in the form ax+by+c=0, however if it were an inequality, instead of the equal sign it would be an inequality sign like greater than or less than.
Step-by-step explanation:
What is the other endpoint of a segment with a midpoint of M(6, 1) and an endpoint S(5,-3)?
ANSWERS ASAP!!!!
Answer:
(7, 5)
Step-by-step explanation:
(x+5)/2, ( y-3)/2)=(6,1)
(x+5)/2=6, x= 7
( y-3)/2=1, y=5
PLEASE HELP I NEED HELP ;(
Answer: second choice
Explanation:
all the answers are prime factorized, meaning that everything under the sign should multiply up to 180. the second answer, 2*2*3*3*5=180 works
find the third term of the geometric sequence when a1 = 1/4 and r=-2
Answer:
1
Step-by-step explanation:
(-2)(1/4)=-1/2
(-2)(-1/2)
=1
the third term of the geometric sequence with first term = 1/4 and common ratio r = -2 is 1
We have a geometric sequence in which the first term is [tex]\frac{1}{4}[/tex] and the common ratio is -2.
We have to find the third term of this geometric sequence.
What is the formula to find the [tex]n^{th}[/tex] term of a geometric sequence?The formula to find the [tex]n^{th}[/tex] term of a geometric sequence with first term [tex]a_{1}[/tex] and common ratio r is -
[tex]a_{n} =a_{1} r^{n-1}[/tex]
In our question, [tex]a_{1}[/tex] = [tex]\frac{1}{4}[/tex] and r = -2 and n =3.
Substituting the values, we get -
[tex]a_{3} =\frac{1}{4}(-2)^{3-1} = \frac{1}{4} (-2)^{2} =\frac{1}{4}\times4=1[/tex]
Hence, the third term of the geometric sequence with first term = 1/4 and common ratio r = -2 is 1.
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what is the best approximation of the projection of (2,6) onto (5,-1)
Answer:
0.15(5,-1)
Step-by-step explanation:
[tex]\frac{v_{1} * v_{2} }{|v_{2}|^{2} }*v_{2}[/tex] ⇒ [tex]\frac{(2)(5)+(6)(-1)}{\sqrt{5^2+(-1)^2} }(5,-1)[/tex] ⇒ [tex]\frac{4}{26} (5,-1)[/tex] ⇒ [tex]0.15(5,-1)[/tex]
The best approximation of the projection IS ( 5,-1).
What is the projection of a vector?The sometimes-indicated vector projection of a vector an onto (or onto) a nonzero vector b The orthogonal projection of an onto a line parallel to b is referred to as (also known as the vector component or vector resolution of an in the direction of b).Although the word "projection" has several different connotations, they all refer to sending something out or forward. A projection is something that sticks out from a wall; it can be a movie; it can be an actress who speaks into a big auditorium without seeming shouty; or it can be something that is projected onto a screen.Vector A ,
(2,6) in terms of vectors is represented by = 2 i +6 j
Vector B,
(5,-1) in terms of vectors is represented by =5 i - 1 j
Projection of Vector A on Vector B
[tex]\frac{(A . B)(B)}{IBI^{2} } \\[/tex] = [tex]\frac{[(2i + 6j).(5i - j)]( 5i - j)}{\sqrt{5^{2} }+ (-1)^{2} }[/tex]
[tex]= \frac{(2)(5) +(6)(-1)}{\sqrt{5^{2} }+(-1)^{2} }[/tex]
= ( 5 ,-1 ) ⇒ 0.15 (5,-1)
Therefore, The best approximation of the projection IS ( 5,-1) .
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How do -11.5 and -9.5 compare? Choose the correct symbol.
-11.5 _ -9.5
A.<
B.=
C.>
Answer:
A. <
Step-by-step explanation:
-9.5 is greater than -11.5
Answer:
A) <
less than
Step-by-step explanation:
-11.5 < -9.5
Someone pls help . Will be marking someone brainliest !
Answer:
27.89 hours.
Step-by-step explanation:
I hope this helps! If you would like an explanation, let me know!
Answer:
First question, 28 hours
Second question, 20 minutes
Step-by-step explanation:
$9.50 for each hour + $75 for showing up on time
Let's say the employee showed up on time
(340 - 75) ÷ 9.5 = 28 hours approximately
120 ÷ 6 = 20 minutes
Find the difference between8/15 and −2/3. Show all calculations in your final answer.
Answer:
6/5
Step-by-step explanation:
8/15 - (-2/3)
8/15 + 2/3
24 + 30/45
54/45 = 6/5
Thus, the difference between 8/15 and -2/3 is 6/5
Start by changing the minus a negative to plus a positive.
So we have 8/15 + 2/3.
To add these two fractions together, we need a common denominator.
The common denominator is simply the
least common multiple for the two denominators.
You should find that the least common multiple is 15.
Since 8/15 already has 15 as its denominator, leave it.
To get a denominator of 15 in 2/3, we multiply top
and bottom of 2/3 by 5 to get 10/15.
So we have 8/15 + 10/5.
This simplifies to 18/15.
Now reduce to get 6/5.
PLEASE ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!!!The technology stock has risen to $9.80 today. Yesterday's price was $9.67. Find the percentage increase
Answer:
1.34%
Step-by-step explanation:
First of all subtract the 2 values
9.84−9.71=0.13
use this value and find the percentage from the original price which was 9.71
0.13
------- ⋅100
9.71
percentage increase is
1.34%
Find the formula for the 4th of the following A.P.S a)3,7,11........ b)12,7,2.......
Answer:
A = 15
B = -3
Step-by-step explanation:
3 ,7,11..... You add 4 each time so 11+4 is 15
12,7,2.... You take 5 each time so 2-5 is -3
Resolve 36x2 – 81y2 into factors
Answer:
(6x + 9y)(6x - 9y)
Step-by-step explanation:
We can use the difference of squares which states that a² - b² = (a + b)(a - b), in this case, a = 6x and b = 9y so the answer is (6x + 9y)(6x - 9y).
225 tickets were sold for a Schools Winter Play. The tickets for the adults cost $8.00 and for the children $4.50. The total receipts for the performance were $1275.00 How many of each type of ticket were sold?
Answer:
75 of the adult ones and 150 of the children ones.
A vehicle has a will 15 inches in diameter. If the vehicle travels 2 miles, how many revolutions does the wheel make? This is Applications of unit conversions
Find the circumference of the wheel:
Circumference = PI x Diameter = 3.14 x 15 = 47.1 inches.
Every revolution the tire travels 47.1 inches.
1 mile = 5,280 feet, so 2 miles = 5280 x 2 = 10,560 feet.
1 foot = 12 inches.
2 miles = 10,560 feet x 12 = 126,720 inches.
Revolutions = total distance / distance per revolution:
Revolutions = 126,720 / 47.1 = 2,690.45 revolutions ( round answer as needed.)
A quadratic polynomial whose zeroes are 5 and -3 is
Answer:
Well, we can write a really simple quadratic polynomial as:
P(x) = a*(x - c1)*(x - c2)
Where a is a constat, and c1 and c2 are the roots, here we have:
c1 = 5 and c2 = -3
P(x) = a*(x -5)(x + 3) = a*x^2 + a*x*3 - a*5*x - a*15
then the quadratic polynomial can be:
P(x) = a*x^2 + a*(3 - 5)*x - a*15
P(x) = a*x^2 - 2*a*x - a*15
Where a can be any real number.
Simplify the following rational expression and state for what values they are undefined.
Answer:
d-2 and d cannot = 8
Step-by-step explanation:
d^2 -10d+16
-----------------------
d-8
Factor the numerator
( d-8)(d-2)
-------------------
d-8
The undefined values occur when the denominator is equal to zero
d-8 = 0
d= 8
This means d cannot equal 8
Now cancel like terms in the equation ( d-8)
This yields d-2
Answer: d - 2 and d cannot equal 8
Step-by-step explanation: To simplify this rational expression, start by factoring both the numerator and the denominator.
So factoring the numerator in this problem, we have a
trinomial that factors as the product of two binomials.
So we are looking for factors of +16 that add to -10 which are -8 and -2.
So we have (d - 8)(d - 2) in the numerator.
The denominator doesn't factor however.
So we have [tex]\frac{(d - 8)(d - 2)}{(d - 8)}[/tex] and the d - 8's cancel leaving us with d - 2.
The values d cannot be happen when the denominator is set equal to 0.
So we have d - 8 = 0 which means d = 8.
This means d = 8 wouldn't work!
Which transformation can be used to map one triangle onto the other select two options
Answer:
Reflection only and rotation then translation.
Step-by-step explanation:
im not sure
Answer:
look at the picture below
Step-by-step explanation:
52 divided by 5424
198 div by 8549 but need to see how to get the correct answer . Don’t want to use a calculator
Answer:
52 / 5424 = 0.00958..
198 / 8549 = 0.0231 ..
Step-by-step explanation:
52 / 5424
First of all, you need to add 0 plus a coma → 0.
52 becomes 520, but this value is smaller than 5424, so we need to add another 0
5200 → another 0 → 52000
So now, we have 52000 / 5424.
We start, 5424 . 10 = 54240, we are higher than 52000, so let's try 9
5424 . 9 = 48816, great!
52000 - 48816 = 3184
This is smaller than 5424, so we need a zero, again. But we do not add 0 to the result, because we are in the decimal side
31840 → 31840 / 5424. We would try 6,
5424 . 6 = 32544. It's bigger!, We use 5
5424 . 5 = 27120!
31840 - 27120 = 4720. We get another 0
47200, and we try 8.
5424 . 8 = 43392
47200 - 43392 = 3808.
So we are going to add 0, until we have four digits that can be divided by 5424 and decimals are infinte.
52 / 5424 = 0.00958..
198 / 8549 → Need to add, the first 0 to convert 198 to 1980
1980 = 0. → Another zero
19800 = 0.0 → 19800 / 8549
We try 2 → 8549 . 2 = 17098
19800 - 17098 = 2702 → we add 0
27020 / 8549 → We try 3
8549 . 3 = 25647 → 27020 - 25647 = 1373 → we add 0
13730 / 8549 → We use 1 → 13730 - 8549 = 5181
As decimal are infinite, we can express the result as:
198 / 8549 = 0.0231 ..
which of the following is true regarding number sets? a. all integers are whole numbers b. all irrational numbers are real numbers c. all real numbers are integers d. all rational numbers are natural numbers
Answer:the answer is A
Step-by-step explanation:
The step is
Real number - rational(irrational)_ - integer - whole - then natural
The true statement regarding number sets are b. all irrational numbers are real numbers.
What are irrational numbers ?Irrational numbers are those numbers which have a non-repeating, non-terminating pattern after decimal place.
According to the given statements we have to determine which is true.
a. all integers are not whole numbers as 0 contains in the set of whole numbers but not in the set of integers.
b. all irrational numbers are real numbers this is a true statement because all the real numbers consist of rational and irrational numbers.
We don't need to check other options because we have been asked which of the following is true not which of the following is/are true.
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please i need help lol The amount of clay students used for their last art project is weighed. The line plot displays the amounts of clay. How much more clay did the students who used of a pound use than the students who used of a pound?
Answer:
2 1/4
Step-by-step explanation:
We need to see how much clay they used if each person in that group used 3/4 clay. There are 4 people in the group.
=> 3/4 x 4 = 12/4 = 3
Now, we need to see how much clay they used if each person in that group used 1/4 clay. There are 3 people in the group
=> 1/4 x 3 = 3/4
Now, we need to see how much more clay was used.
=>3 - 3/4
=> 3/1 - 3/4
=> Take the LCM of the denominators and make the denominators equal.
=> 12/4 - 3/4
=> 9/4
They used 9/4 more clay.
Since there are no options with 9/4, we need to make this improper fraction into a proper fraction.
=> 9/4 = 2 1/4
They used 2 1/4 more clay.
1. At the end of one school day a teacher had 17 crayons left. The teacher remembered
giving out 14 crayons in the morning, getting 12 crayons back at recess, and giving out
11 crayons after lunch. How many crayons did the teacher have at the start of the
day?
Answer:
30 crayons
Step-by-step explanation:
Let x be the number of crayons he started with
gave out 14 crayons
x-14
Got 12 back
x-14+12
Gave out 11 after lunch
x-14+12 -11
This equals 17
x-14+12 -11 =17
Combine like terms
x-13 = 17
Add 13 to each side
x -13+13 =17+13
x = 30
Answer: 30
Step-by-step explanation:
For this problem work backwards. Start from 17 and add 14. You should get 31. Then subtract 12, which equals 19. Finally add 11 to 19, which equals 30. Basically you are doing the inverse operation to get your answer. Hope this helps!
I need the answers for Q10 part b and Q11 ASAP!!!
Answer:
Q10ii: x axis horizontal, y axis vertical, a straight line through the origin and point (5,20)
Q11i: z = 8y
Q11ii: y axis horizontal, z axis vertical, a straight line through the origin and (6,48)
Step-by-step explanation:
Linear proportions will always produce straight lines when graphed. Also, they will have to go through the origin when there is not some kind of offset.
P(x)=3x2-x-4
Then alpha + bita by alpha*bita =
Answer:
[tex] = ( \frac{ - b}{a} )( \frac{c}{a} )[/tex]
[tex] = ( \frac{ 1}{3} )( \frac{ - 5}{3} )[/tex]
[tex] = \frac{ - 5}{9} [/tex]
Answer:
- [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Given
P(x) = 3x² - x - 4
with a = 3, b = - 1 and c = - 4
If α and β are the roots of the quadratic then
α + β = - [tex]\frac{b}{a}[/tex] and αβ = [tex]\frac{c}{a}[/tex] , thus
α + β = - [tex]\frac{-1}{3}[/tex] = [tex]\frac{1}{3}[/tex] and αβ = - [tex]\frac{4}{3}[/tex]
Thus
α + β by αβ
= [tex]\frac{\frac{1}{3} }{-\frac{4}{3} }[/tex] = [tex]\frac{1}{3}[/tex] × - [tex]\frac{3}{4}[/tex] = - [tex]\frac{1}{4}[/tex]
Given that the quadrilateral is a parallelogram, m∠S = + 19 and m ∠T = 8x - 4, what is m∠Q?
Answer:
32
Step-by-step explanation:
Brainlist plz
Answer:
[tex]\Large \boxed{161\°}[/tex]
Step-by-step explanation:
Adjacent angles in a parallelogram add up to 180 degrees.
m∠Q and m∠S add up to 180 degrees.
m∠Q + m∠S = 180
m∠Q + 19 = 180
Subtract 19 from both sides.
m∠Q + 19 - 19 = 180 - 19
m∠Q = 161
A triangular tent has a perimeter of 29 meters. Side a is 3 meters shorter than twice side b and side c is 4 meters longer than side b, Find the length of side b.
A) 11 meters
B) 14 meters
C) 9 meters
D) 7 meters
Answer:
D) 7 meters
Step-by-step explanation:
So I would start this off by plugging in the variables into side B. So if we were to plug 7 into B there would be 22 meters left of the perimeter. Therefore meaning 22 between A and C. Now A is 3 meters shorter than TWICE of B. So 7 times 2 is 14 and 14 minus 3 is 11. now we have 11 and 7 which equals 18. 29 minus 18 giving us 11 left. 11 is C. Now it says c is 4 meters longer than B so it 7 plus 4 is 11. And everything adds up. HOPE THIS HELPS.
Answer:
Side b=7 meters
Step-by-step explanation:
Given:
Perimeter of triangle=29m
Side a=2b-3
Side b=b
Side c=4+b
To find:
Side b
Solution:
P of triangle=a+b+c
29=2b-3+b+4+b
29=2b+b+b+4-3
29=4b+1
29-1=4b
b=28/4
b=7m
I hope my answer is right.
dan had 2 1/2 cookies and ate 1/2 of a cookie. Of the original number of cookies, the fractional part that he ate was
help brainlist will mark brainlist
Answer:
1/2 is the fractional part of cookie which was eaten by Dan.
Step-by-step explanation:
Dan has 2 1/2 cookies and ate 1/2, so we can just subtract the 2 1/2-1/2
which cancels out the 1/2, which is the fractional part.
He has 2 cookies left.
The fractional part that he ate will be 5/4.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.
Dan had 2 1/2 cookies and ate 1/2 of a cookie.
Of the original number of cookies.
Then the mixed fraction is converted into fraction.
2 1/2 = 5/2
The fractional part that he ate will be
⇒ (5/2) / 2
⇒ (5/2) x (1/2)
⇒ 5/4
The fractional part that he ate will be 5/4.
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Please help me in finding the answer. Find x. (Congruent triangles)
Answer:
6.71cm
Step-by-step explanation:
a²+b²=c²
6²+3²=x²
sqrt(6²+3²)=6.71
Answer:
[tex]\Large \boxed{\sf 6.71 \ cm}[/tex]
Step-by-step explanation:
The triangle is a right triangle. We can use Pythagorean theorem to solve for the hypotenuse.
a² + b² = c²
a and b are the lengths of the legs. c is the length of the hypotenuse.
6² + 3² = x²
Evaluate.
36 + 9 = x²
45 = x²
Take the square root of both sides.
√(45) = √(x²)
6.7082039325... = x
What is the solution of −83 = b4? A. b = –332 B. b = –87 C. b = –79 D. b = –20.75
Answer:
D; b = -20.75
Step-by-step explanation:
Here in this question, we want to find solution to the given linear equation.
The linear equation is;
-83 = b4
Now, to find the value of b, we will need to divide both sides by its coefficient.
Looking at the question, the coefficient of b is 4
Mathematically, that would be :
-83/4 = b4/4
b = -83/4
b = -20.75
Answer:
b = -20.75
Step-by-step explanation:
Given:
-83 = b4
It can also be written as
-83 = 4b
divide both sides by the coefficient of b which is 4
-83 / 4 = 4b / 4
-20.75 = b
Therefore,
b = -20.75
Check:
-83 = b4
-83 = -20.75(4)
-83 = -83
-5+6
What’s the answer
-5+6=1 because if it's not a normal equation it has a negative
Answer:
1
Step-by-step explanation:
When adding a negative and a positive number, subtract the biggest number from the smallest (ignore the signs), so :
[tex]6-5=1[/tex]
After you have your answer, keep the symbol of the bigger number (pay attention to the signs now). Since positive 6 is greater than negative 5, keep the positive. Add this symbol to the answer, making the answer positive.
[tex]-5+6=1[/tex]
