what is the vertex form of the equation y equals 3x squared + 6x - 4
Answer:
y = 3(x + 1)² - 7
Step-by-step explanation:
y = 3x² + 6x - 4
First, factor out the coefficient of the quadratic eq'n:
y = 3(x² + 2x - ⁴/₃)
Use the "complete the square" rule;
The "x² + 2x" should be rewritten as "(x + 1)² - 1", i.e. place into squared brackets x (without the power 2) and add half the coefficient of the x-term, you then need to subtract the square of the constant term in the squared brackets and then simplify:
y = 3((x + 1)² - 1 - ⁴/₃)
y = 3((x + 1)² - ⁷/₃)
Finally, multiply the 2 terms you end up with by the 3, factored out initially:
y = 3(x + 1)² - 7
If 2^x = 5, what is 2^3x - 4?
Answer:
the value of x is 2^9/4 then 2^3x-4=2^11/4
HELP ME RN PLEASEEEE
[WILL GIVE BRAINLY TO CORRECT AND BEST EXPLAINED ANSWER]
Answer:
[tex]\boxed {\boxed {\sf d= \sqrt{34}}}[/tex]
Step-by-step explanation:
We want to find the distance between two points, so the following formula is used.
[tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Where (x₁, y₁) and (x₂, y₂) are the points we are finding the distance between.
We are given the points (-2, -1) and (3,2). If we match the corresponding value and variable we see that:
x₁= -2 y₁= -1x₂= 3 y₂= 2Substitute the values into the formula.
[tex]d= \sqrt {(-2-3)^2+(2--1)^2[/tex]
Solve the parentheses.
-2 -3 = -5 2--1 = 2+ 1 = 3[tex]d= \sqrt{(-5)^2+(3)^2[/tex]
Solve the exponents.
(-5)²= -5*-5= 25 (3)²= 3*3=9[tex]d= \sqrt{25+9}[/tex]
Add.
[tex]d= \sqrt{34}[/tex]
This radical cannot be simplified, so the distance between the two points is √34 and choice 3 is correct.
Solve for x. Write your answer as “x=__”
Don’t put the 8 into equation
Answer: x=45
Step-by-step explanation:
2x+6=96
2x=90
x=45
A community group sells 2,000 tickets for its raffle. The grand prize is a car. Neil and 9 of his friends buy 10 tickets each. When the winning ticket number is announced, it is found to belong to Neil's group. Given this information, what is the probability that the ticket belongs to Neil?
Answer:
1/10 if its is in the group
Step-by-step explanation:
but if its as the whole thing it would be 1/200 because he has 10 and 10 of 2000 is 1/200
The probability that the winning ticket belongs to Neil is 5%.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
There are a total of 2,000 tickets, and Neil and his 9 friends bought 10 tickets each, so they bought a total of 100 tickets (10 tickets/person x 10 people = 100 tickets).
The probability of Neil's group winning the car is equal to the number of tickets they bought divided by the total number of tickets sold:
Probability = Number of tickets bought by Neil's group / Total number of tickets sold
Probability = 100 / 2000
Probability = 0.05 or 5%
Therefore, the probability that the winning ticket belongs to Neil is 5%.
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Solve for x. Round to the nearest tenth, if necessary.
Answer:
Step-by-step explanation:
take 60 degree as reference angle
using cos rule
cos 60=adjacent/hypotenuse
1/2=80/x
x=80*2
x=160
_________________ polygons have congruent angles and proportional side lengths.
answers are:
Regular
Similar
Congruent
Parallel
Step-by-step explanation:
I think its similar
Identify the vertex
Answer:
The vertex is (-2,10)
Step-by-step explanation:
The vertex is the maximum point on a downward facing parabola
The maximum is (-2,10)
The vertex is (-2,10)
What is the value of X in simplest radical form?
Answer:
Step-by-step explanation:
pythagoras theorem
a^2+b^2=c^2
24^2+10^2=x^2
576+100=x^2
676=x^2
[tex]\sqrt{676[/tex]=x
26=x
Matt is saving to buy a new motorcycle. If he deposits $70 at the end of each month in an account that pays an annual interest rate of 3.5%, how much will he have in
60 months? Assume that the compounding is being done monthly
Answer:
bro I don't know. I just need the points so I can keep getting answers. good luck tho I guess.
At what point do these lines intersect? A
-24x - 4y =-164
y=41 - 6x
Answer:
Infinite points
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
FunctionsTerms/CoefficientsSolving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
-24x - 4y = -164
y = 41 - 6x
Step 2: Solve for x
Substitute in y [1st Equation]: -24x - 4(41 - 6x) = -164[Distributive Property] Distribute -4: -24x - 164 + 24x = -164[Addition] Combine like terms: -164 = -164Here we see that -164 does indeed equal -164.
∴ We have an infinite amount of solutions.
219.44 in word form
Answer:
two hundred nineteen and 44
OR
two hundred nineteen point 44
Step-by-step explanation:
do not say AND before nineteen. saying AND represents a decimal point. Both can be used (point or and)
Which equation represents a linear function?
please help, thank you
Answer:
B
Step-by-step explanation:
He asked me to make sure I had enough 20 words. But this question is really simple, Just move c to the right. And then change the symbol.
Find the value of X a,57
b,3
C,81
D,27
Answer:
D. 27
Step-by-step explanation:
sum of exterior angles = 360
2x + 56 + 57 + 85 + 4x = 360
6x + 198 = 360
6× = 360 - 198
6× = 162
× = 27
Help
Will
Give
Brainlist
Answers
:)))))) and
Answer:
26%
Step-by-step explanation:
complete the solution find the value of y when x equals 1 9x+7y=-12
please help stuck on probelem
=========================================================
Explanation:
Draw a horizontal line to cut the figure into a rectangle on top and a triangle down below.
The rectangle has length and width of 6 and 4 (horizontal and vertical components respectively). The area of this rectangle is 6*4 = 24 square units.
The triangle has a base of 6 and a height of 4. The base and height of any triangle are always perpendicular.
The area of the triangle is base*height/2 = 6*4/2 = 24/2 = 12 square units. If you were to cut out half of the triangle and rearrange things, you'll find that a rectangle can be formed. This rectangle is half in area that of the first rectangle we found. This is why we divide by 2 when finding the area of the triangle.
Once you know the two sub-areas, we add them up to get the overall area: 24+12 = 36 square units.
Directions: Type your answer in the box. Do not use spaces.
If triangles EFG and GHE are congruent, what is the measure of angle FEG?
F
G
110°
+
360
(x + 24)
E
H
ub
degrees
10
Answer:
36 cuz they are congruent
Step-by-step explanation:
In a Gallup Poll in 2003, 590 of 1,116 randomly selected adults aged 18 and older said they had too little time for relaxing or doing nothing. Identify the upper level of a 95% confidence interval of the true proportion of adults who say they have too little time for relaxing.
Answer:
hope this helps
Step-by-step explanation:
what do you have to do
A card is drawn from a standard deck. Find the probability of drawing a heart or a 7.
=======================================================
Explanation:
There are A = 13 hearts and B = 4 copies of "7"
The count A+B = 13+4 = 17 may seem like it's the count of hearts or "7" cards, but we're double counting the 7 of hearts. So the true count is actually 17-1 = 16
There are 16 cards we want (either a heart or a "7") out of 52 total. Therefore, the probability is 16/52 = (4*4)/(4*13) = 4/13
If f(x) = −4x 2 + 15, then f(−3)
Answer:
-21
Step-by-step explanation:
f(-3) = -4(-3)² + 15 = -4(9) + 15 = -36 + 15 = -21
Answer:
f(-3) = -21
Step-by-step explanation:
f(x) = −4x²+ 15
f(-3) = -4(-3)² + 15
f(-3) = -4(9) + 15
f(-3) = -36 + 15
f(-3) = -21
Help me solve this question for geometry !
Answer:
X²–49
Step-by-step explanation:
(x+7)(x-7)
x²+7x-7x-49
x²-49
Find x and y
(y+23)
(2x-17)
Answer:-2
Step-by-step explanation:
A parabola and its focus are shown on the graph. The vertex of the parabola is at (0,0).
On a coordinate plane, a parabola opens to the right. It has a vertex at (0, 0) and a focus (3, 0).
What is the equation of the directrix of the parabola?
y = 3
y = –3
x = 3
x = –3
Answer:
y = -3
Step-by-step explanation:
the length from directrix to vertex is equal to the length from focus to the vertex.
Answer: y=-3
Step-by-step explanation: y = -3 Step-by-step explanation: the length to vertex is equal
9 x 10^2 is _ times as much as 3 x 10^2
Answer:
3
Step-by-step explanation:
3 × 3 × 10²
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 10 feet and a height of 8 feet. Container B has a diameter of 12 feet and a height of 7 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is full after the pumping is complete?
Answer:
79.4%
Step-by-step explanation:
the volume of a cylinder is as for any other regular 3D object
base area × height
the base area is for a cylinder a circle.
so, it is
pi×r² × height
the radius (r) is always half of the diameter.
so, volume of cylinder A is
Va = pi×(10/2)² × 8 = pi×25 × 8 = 200pi ft³
the volume of cylinder B is
Vb = pi×(12/2)² × 7 = pi×36 × 7 = 252pi ft³
therefore, in a volume of 252pi ft³ we have 200pi ft³ filled with water.
252pi = 100% filling
1% = 100%/100 = 252pi/100 = 2.52pi
how many % are 200pi ?
as many as times 1% fit into 200pi :
200pi/2.52pi = 200/2.52 = 79.36507937... ≈ 79.4%
What is the value of X in the figure show
Answer:
x=11
Step-by-step explanation:
The equation for the problem is 4x-2=42. The angle (4x-2) is equal to 42 degrees because it is vertical to the angle with 42 degrees. If angles are vertical, they are equal to each other.
Add 2 to both sides of the equation.
4x+2=4x 42+2=44
Simplify.
4x=44
Divide 4 by both sides.
4x/4=x 44/4=11
Simplify to get the final answer.
x=11
help please will be marked as brainliest if correct and first person to respond
Answer: Unlock code = 76
==========================================================
Explanation:
Use a factor tree to find the prime factorization of each value
22 = 2*11
30 = 2*3*5
Both values have '2' in common and this is the largest such value. Therefore, the GCF of 22 and 30 is 2.
So E = 2
----------------------------
Since 3 and 8 have no factors in common (other than 1), this means the LCM is 3*8 = 24
We can say that F = 24.
If the numbers had some larger number in common, then we'd have to do a bit more work to find the LCM.
----------------------------
As the hint suggests, we'll use the distributive property to show that
3*(7+10) = G + 30
3*7 + 3*10 = G + 30
21 + 30 = G + 30
21 = G .... subtract 30 from both sides; they cancel and go away
G = 21
----------------------------
Use the same idea for the other equation as well
5*(3 + H) = 15 + 45
5*3 + 5*H = 15 + 45
15 + 5H = 45
5H = 45 ............ subtract 15 from both sides; they go away
H = 45/5 ......... divide both sides by 5
H = 9
------------------------------
The unlock code is
E+F+G+H = 2+24+21+29 = 76
The middle school is 2.72 kilometers from Marsha's house and 1.54 kilometers from Ryan's house. How much farther does Marsha live from the middle school than Ryan? Group of answer choices
Answer:
1.18 kilometers
Step-by-step explanation:
The middle school is 2.72 kilometers from Marshal house
The school is also 1.54 kilometers away from Ryan house
Therefore the distance of Marshal house from the school can be calculated as follows
= 2.72-1.54
= 1.18 kilometers