The vertex form of the provided equation y = (x 3)2 (x 4)2 is expressed as (x+3.5)²+0.5.
What is the vertex form of parabola?Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.
The standard equation of the vertex form of parabola is given as,
y=a(x-h)^2+k
Here, (h, k) is the vertex point.
The given equation is
[tex]y = (x +3)^2 +(x+ 4)^2\\y=x^2+9+6x+x^2+16+8x\\y=2x^2+14x+25[/tex]
To convert this equation, into the vertex form, follow the following steps,
[tex]y=2(x^2+7x+12.5)\\y=2((x+3.5)^2-12.25+12.5)\\y=(x+3.5)^2+0.5[/tex]
Thus, the vertex form of the provided equation y = (x 3)2 (x 4)2 is expressed as (x+3.5)²+0.5.
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Find the SURFACE AREA of the shape below.
Answer:
292 CM
Step-by-step explanation:
8x7 = 56 (2 such sides)
6x8 = 48 (2 such sides)
7x6 = 42 (2 such sides)
56(2) + 48(2) + 42(2)=
292
How do I do number 9?
Answer:
b
Step-by-step explanation:
There are 8 possibilities
2 up and 4 up are the up and even moves ===> 2 out of 8
2/8 = 1/4
Can anyone help me out??
madi sells 23oz cans of jelly beans for 63 cents and 15oz cans for 45 cents. assume that the price varies linearly with the number of ounces.
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
B
Step-by-step explanation:
subtract 4 from 9 to get 5 and then since both fractions have 12 on bottom, you can subtract 3 form 7 to get 4
since 4*3 is 12, you can factor 12 to become 3 and 4 becomes 1
LES
Algebra 1 -Mock EOC
COUNT
3. Melissa and John get a combined monthly allowance of $300. Melissa's monthly allowance is
$20 more than half of John's monthly allowance. If x represents John's allowance, in dollars, which
equation is true?
A. x- (0.5x+20) = 300
B. x + (20+0.5x) = 300
C. x + 300=0.5x + 20
D. x + (0.5x20) = 300
Answer:
B. x-(0.5x+20)=300
Step-by-step explanation:
Because you add 20 to half of John's monthly allowance, and 0.5x is saying John's allowance divided by 2. Then you have Melissa's allowance, which then you add to John's allowance to get the total of $300 combined.
The equation that describes the situation would be; A. x-(0.5x+20)=300
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We are given that Melissa and John get a combined monthly allowance of $300. Melissa's monthly allowance is $20 more than half of John's monthly allowance.
When x represents John's allowance, in dollars
Since we add 20 to half of John's monthly allowance, 0.5x is saying John's allowance is divided by 2.
Now we have Melissa's allowance, which then adds to John's allowance to get a total of $300 combined.
The equation becomes as;
x-(0.5x+20)=300
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A square is a polygon, so all polygon are squares true or false
Answer:
false
Step-by-step explanation:
polygons have more then 3 sides and are enclosed figures such as a pentagon may be classified as a polygon.
determine whether each of the following sequences are arithmetic, geometric or neither. If arithmetic, state the common difference. If geometric, state the common ratio. -29, -34, -39, -44, -49, ...
Is this: common difference =5?
arithmetic?
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
[tex] \textbf{Let's see if the sequence is Arithmetic :} [/tex]
[tex] \textsf{If the difference between successive terms is } [/tex] [tex] \textsf{equal then, the terms are in AP} [/tex]
[tex] \textsf{-34 - (-29) = -5 } [/tex][tex] \textsf{-39 - (-34) = -5 } [/tex][tex] \textsf{Since the common difference is same, } [/tex] [tex] \textsf{we can infer that it's an Arithmetic progression} [/tex] [tex] \textsf{with common difference of -5} [/tex]
Sequence: -29, -34, -39, -44, -49, ...
First we need to identify the terms:
1st term = -292nd term = -343rd term = -394th term = -445th term = -49If the sequence is arithmetic, [tex]\boxed{\sf \bold{second \ term = \dfrac{first \ term+third \ term}{2} }}[/tex]
If the sequence is geometric, [tex]\boxed{\sf \bold{second \ term = \sqrt{first \ term \ x \ third \ term} }}[/tex]
=======================================
Check for arithmetic
[tex]\rightarrow \sf -34 = \sf \dfrac{-29 +(-39)}{2}[/tex]
[tex]\rightarrow \sf -34 = \sf \dfrac{-68}{2}[/tex]
[tex]\rightarrow \sf -34 = -34[/tex] [Hence it's arithmetic series]
To find common difference. we have to think of how to go to next term.
first term: -29
to go the second term, subtract by -5
-29 -5 = -34, second term
-34 - 5 = -39, third term
Hence, common difference: -5
Solutions:
Arithmetic Sequence
Common Difference: -5
place a check mark in the box next to each set of lengths that could be the sides of a triangle. Select all that apply
Answer:
This question has no content for me to answer, Iwant the points so I will be taking them anyway Thankyou. Also may I please have brainliest on the only 2 questions you asked.
Step-by-step explanation:
the answer is C. triangle
Answer:
in future please attach photo of question aswell :]
Step-by-step explanation:
unfortunately you haven't provided the neccasary context to answer. with no idea what the boxes might be or what the triangles look like i cannot give an educated response.
The volume of a hemisphere that has a radius of 8centimeter to the nearest tenth.
[tex]\textit{volume of a hemisphere}\\\\ V=\cfrac{1}{2}\cdot \cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=8 \end{cases}\implies \begin{array}{llll} V-\cfrac{1}{2}\cdot \cfrac{4\pi (8)^3}{3}\implies V=\cfrac{1024\pi }{3} \\\\\\ V\approx 1072.3 \end{array}[/tex]
Need help with system of equation 3 variable.
Answer:
Here is an example of a systems equation with 3 variables:
x+y+z=2
6x-4y+5z=31
5x+2y+2z=13
Step-by-step explanation:
Using elimination:
x+y+z=2
5x+2y+2x=13
5x+2y+2x=13
- 2x-2y-2z-4
____________
3x=9
x=9
Using substitution:
9+y+z=2
y=z-7
9+z-7+z=2
2+2z=2
z=0
Using substituion again:
9+y=2
y=-7
8 + 40 + 200 + ... + 15625000
Sum of a finite geometric series:
Sn=a1-a1r / 1-r
Answer:
19,531,248
Step-by-step explanation:
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where [tex]a[/tex] is the first term and [tex]r[/tex] is the common difference)
Given geometric series: 8 + 40 + 200 + ... + 15625000
[tex]\implies a_1=8[/tex]
[tex]\implies a_2=40[/tex]
[tex]\implies a_3=200[/tex]
To find the common ratio [tex]r[/tex], divide consecutive terms:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{40}{8}=5[/tex]
Therefore:
[tex]\implies a_n=8(5)^{n-1}[/tex]
To find n when [tex]a_n=15625000[/tex] :
[tex]\implies 8(5)^{n-1}=15625000[/tex]
[tex]\implies (5)^{n-1}=1953125[/tex]
[tex]\implies \ln (5)^{n-1}=\ln1953125[/tex]
[tex]\implies (n-1)\ln 5=\ln1953125[/tex]
[tex]\implies n=\dfrac{\ln1953125}{\ln5}+1[/tex]
[tex]\implies n=10[/tex]
Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Therefore, sum of the first 10 terms:
[tex]\implies S_{10}=\dfrac{8(1-5^{10})}{1-5}[/tex]
[tex]\implies S_{10}=19,531,248[/tex]
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
Lamar is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $35 for the meal, plus $4 per kilogram for the lobster he picks. At the second restaurant, Lamar would pay $3 per kilogram for the lobster, in addition to $44 for the meal. Lamar realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Lamar pay for his dinner? What is the weight?
Dinner would cost $__ at either restaurant if Lamar's lobster weighed __ kilograms.
Answer:
The weight : 9 pound
Lamar would pay for his dinner : $71
Step-by-step explanation:
Let x represent the weight of the lobster
the cost of the dinner at restaurant 1 is 4x + 35
the cost of the dinner at restaurant 2 is 3x + 44
Now ,we have to solve the equation :
4x + 35 = 3x + 44
-3x - 35 -3x - 35 -> trying to get all x terms on one side. other just #
4x - 3x = 44 - 35
⇔ 1x = 9
⇔ x = 9
In this case Lamar would pay the same amount for his dinner at any restaurant:
the price = 4×(9)+35 = 71
= 3×(9)+44 = 71.
Hope this helps, Let me know if you have any question/concerns !
Have a nice rest of your day :)
What is the sine ratio b2
keeping in mind that a rhombus is also a parallelogram, namely a quadrilateral with parallel opposite sides, however, a rhombus sides are all the same length, and its diagonals meet at right-angles, Check the picture below.
The ratio of the required trigonometric function sin b₂° as per the given measurement of the quadrilateral is equal to 39/ 50.
Let us consider quadrilateral ABCD be rhombus.
Using the properties of the rhombus,
All the sides are congruent to each other.
Here, AB = 5 cm
This implies,
AB = BC = CD = AD = 5 cm
And Intersection of the diagonal is point 'O'.
In rhombus diagonals bisects each other at 90 degrees.
Measure of angle BOC = 90 degrees.
Triangle BOC is right angled triangle.
OC = 3.9 cm
sin b₂° = opposite side / hypotenuse
= OC / BC
= 3.9 / 5
= 0.78
= 78 / 100
= 39 / 50
Therefore, the ratio of the function sin b₂° is equal to 39 / 50.
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Direction:find the volume of each solid figure below.
Step-by-step explanation:
9) volum = width× lenght × height
= 2×3×7 = 42 m³
10) = 7³ = 343 cm³
Answer:
Question 9: Volume = 42m
Question 10: Volume = 343cm
Step-by-step explanation:
Volume for a rectangular prism: V = length x height x width
Question 9:
Length = 7m
Width = 2m
Height = 3m
V = (7m) x (2m) x (3m)
V = 14m x 3m
Volume for a cube: V = a^3 → this is the formula since all sides are the same length
Question 10:
Length = 7cm
Width = 7cm
Height = 7cm
V = (7cm) x (7cm) x (7cm)
V = 49cm x 7cm
V = 343
OR
V = a^3 → (7)^3
For all x, (2x + 1)^2= ?
Answer:not sure but it’s either a b c d e maybe don’t hold me to that
Step-by-step explanation:♀️♂️♀️♂️♀️♂️♂️♀️♀️
Answer: hii :)
E. 4x2+4x+1
Step-by-step explanation:
Expand the expression.
Hopefully this helps you!
- Matthew
Find the surface area of a box that is 14 inches deep, and 7 inches tall and 7 inches wide
Answer:
The answer is 686 inches
Step-by-step explanation:
Answer:
The surface area of a box is 686 inches
Step-by-step explanation:
You can do it by muliplying;
[tex]14*7*7=686[/tex]
Give the guy about brainliest!
I already have too many TvT
Hope this helped! :^)
✉️Message me if you have any more questions!✉️
- ✨7272033Alt✨
Submitted on 4/14/2022 at 6:37 PM
(To avoid plagarism, by users whom decide to copy.)
Which net represents this solid figure?
Please help, so that I'll get a 100%
please help me with this graphing worksheet
Answer:
240
Step-by-step explanation:
Explain what the acronym PEMDAS means and how you use it when evaluating expressions.
If the solution to a linear system of equations is x=6 and y= 2 and you graphed the two equations, where would the two lines intersect? How do you know?
This is simply because the x coordinate is 6 and the y coordinate is 2.
The line x = 6 is a vertical line in which all points on it have an x coordinate of 6. It goes through 6 on the x axis.
The line y = 2 is horizontal where all points on it have a y coordinate of 2.
The vertical and horizontal lines intersect at (6,2)
Suppose that the heights of 4-year old boys are normally distributed with a mean of 103cm and a standard deviation of 4. 5. Half of all 4-year olds are shorter than:
Answer:
103 cm
Step-by-step explanation:
Half are above and half are below the mean
pls help!!!!!!!
20-27
Answer:
The probabilities would be 4/11 and 7/11 respectively.
Step-by-step explanation:
1) Total length of the given word i.e. Mathematics = 11
2) Number of vowels in the given word = 4 i.e. a,e,a,i
3) Number of consonants in the given word = 7 i.e. m,t,h,m,t,c,s
4) The probability of choosing a vowel would be 4/11 = 0.3636..
5) The probability of choosing a consonant would be 7/11 = 0.6363...
Step-by-step explanation:
What is the sum of the complex numbers 2 + 4i,and 3 − 7i, where i=-1
Answer:
5 - 3i.
Step-by-step explanation:
2 + 4i + 3 - 7i Bring like terms together:
= 2 + 3 + 4i - 71
= 5 - 3i.
Answer:
5 - 3i
Step-by-step explanation:
Real numbers are a subset of the complex numbers. Therefore it would only make sense that the complex numbers follow the same rule of additivity and multiplication as real numbers do:
[tex](2+4i)+(3-7i)=2+3+4i-7i=5-3i[/tex]
What is the length of the missing leg? If necessary, round to the nearest tenth
1. Let f =( (1,2) ,(2,3) ,(2,3), (5,6), (7,8) )
a.find domain and range of f
b.evaluate f (2) and f (5)
Step-by-step explanation:
Domain=1,2,5,7
Range=2,3,6,8
f(2)=3
f(5)=6
The dot plot shows the mass, in grams, of several substances in an experiment.
How many substances has their mass recorded during the experiment?
Enter the answer in the box.
substances
A number line ranging from 60 to 68 with four dots over 64, one dot over 65, two dots over 66, two dots over 67, and four dots over 68.
Answer:
The answer is 13. Just count the dots.
Step-by-step explanation:
Answer:13
Step-by-step explanation:
bc i said so
Jose wants to walk to the store from his house but he is not sure how far away it is. Find the distance between his house (-8, -9) and the store (-4,-10). Each unit is equal to one
mile.
Answer:
You need to go 8 squares to the left and then go 9 square down. (-8, -9)
for the second one you need to go 4 squares to the left and 10 squares down. (-4, -10)
The distance between the coordinates of house and store is D = 17 miles, or about 4.12 miles
What is the distance of a line between 2 points?The distance of a line between 2 points is always positive and given by the formula
Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )
The distance between A and B is D , and the distance D is
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Given data ,
Let the first point be P = P ( -8 , -9 )
Let the second point be Q = Q ( -4 , -10 )
Now , Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
D = √ ( -8 + 4 )² + ( -9 + 10 )²
On simplifying , we get
D = √ ( 4 )² + ( 1 )²
D = √17 units
And , 1 unit = 1 mile
So , √17 units = 4.12 miles
Hence , the distance between Jose's house and the store is √17 miles, or about 4.12 miles
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write in arithmetic series in summation notation
6+12+18+24+30
The dance committee hired DJ Emanuel for the fall
dance. DJ Emanuel charges $I25 per hour plus $55 for
an assistant. The committee wants to keep the total
cost under $600. What is the maximum number of
hours that DJ Emanuel can play at the dance?
I need the inequality, inequality answer, final answer
Answer:
Inequality: 125x + 55 < 600
Solution of inequality: x < 4.36
Final answer: 4 hours
Step-by-step explanation:
Let the number of hours be x.
1 hour costs $125.
2 hours cost $125 × 2
3 hours cost $125 × 3
x hours cost $125 × x or simple 125x.
The assistant costs $55.
The total cost is 125x + 55.
The cost must be under $600, so
125x + 55 < 600
Subtract 55 from both sides.
125x < 545
Divide both sides by 125.
x < 4.36
In theory he can be hired for any amount of hours under 4.36 hours, but he probably works only full hours, so you need to round down to 4 hours.
4 hours