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
1. Provide an example of a variable term.
2. Provide an example of a constant term.
3. When looking at an expression and/or equation, how can we tell that we need to distribute?
4. When solving an equation, if you get the solution, x=0, how many solutions to the equation are there?
(One solution, no solution, or infinite solutions)
5. When solving an equation, if you get 5 = 11, what does this mean? (One solution, no solution, or infinite
solutions)
6. When solving an equation, if you get 5 = 5, what does this mean? (One solution, no solution, or infinite
solutions)
Answer:
Step-by-step explanation:
1) a variable term contains a variable. If x is a variable
5x is an example of a variable therm
2) a constant therm is not a variable
3 is an example
3) for example when a number multiply a sum or a difference between a constant and a variable
Example:
2(x-3) = 5(x+4)
4) one solution: only if x is equal to 0 the equation is true
5) no solution: the equation can’t be true for ever value of the variable
6) infinite solutions: the equation is ever true for every value of the variable
use graph to answer question
Given:
A figure of a right angle triangle.
To find:
The length of BC.
Solution:
In a right angle triangle,
[tex]\tan \theta =\dfrac{Perpendicular}{Base}[/tex]
In the given triangle,
[tex]\tan A =\dfrac{BC}{AC}[/tex]
[tex]\tan 23^\circ =\dfrac{BC}{6}[/tex]
[tex]0.42447\times 6 =BC[/tex]
[tex]2.54682 =BC[/tex]
Approximate the value to the nearest hundredth.
[tex]BC\approx 2.55[/tex]
Therefore, the measure of side BC is 2.55 units.
Suzanne has one 10p coin one 50p coin and some 20p coins altogether she has £1.40 how many 20p coins does she have
Answer:
She has FOUR 20p coins altogether.
Step-by-step explanation:
1.40-0.10-0.50=0.8
0.8/0.2=4
Class A has 27 pupils and class B has 11 pupils.
Both classes sit the same maths test.
The mean score for class A is 26.
The mean score for both classes is 36.
What is the mean score (rounded to 2 DP) in the maths test for class B?
Answer:
10
Step-by-step explanation:
If there is 26 is in class a and altogether you get 36 you must take 26 from 36
Which value of x is in the domain of f(t) = squared x - 7
O A. x= 8
O B. x = 0
C. x= -3
O D. x = 6
SUBMIT
Given:
The given function is:
[tex]f(x)=\sqrt{x-7}[/tex]
To find:
The value of x that is in the domain.
Solution:
Domain is the set of input values.
We have,
[tex]f(x)=\sqrt{x-7}[/tex]
We know that the square root is defined for non negative values. So,
[tex]x-7\geq 0[/tex]
[tex]x\geq 0+7[/tex]
[tex]x\geq 7[/tex]
Thus, the domain of the given function is all real number that are greater than or equal to 7.
In the given options 0, -3, 6 are less than 7 but 8 in option A is the only value that is greater than 7. So, [tex]x=8[/tex] is in the domain of the given function.
Therefore, the correct option is A.
I made a mistake while solving the inequality below. What mistake did I make? Explain what I should’ve done instead.
Answer:
Mistakes:
Used addition
Didn't flip inequality form
Corrections:
Divide each term
Instead of a positive value it should be negative
flip the direction of the inequality form
Step-by-step explanation:
[tex] - 9x \div - 9 \leqslant 90 \div – 9 [/tex]
cancel the common factor
[tex] \times \leqslant 90 \div - 9[/tex]
Divide 90 by – 9
Answer is:
[tex] \times \leqslant - 10[/tex]
Hope this helps!
What’s the length of EF?
Answer:
Step-by-step explanation:
If the whole length of DEF is given as 7, and segment DE is 2, then segment EF is 7 - 2 = 5
Triangle A has sides 7, 12, and 18. Triangle B has sides 5, 9, and 5. Triangle C has sides 8, 8, and 8. What kind is each triangle? *
1. A: Scalene, B: Equilateral, C: Isosceles
2. A: Scalene, B: Isosceles, C: Equilateral
3. A: Isosceles, B: Scalene, C: Equilateral
4. A: Isosceles, B: Equilateral, C: Scalene
Find the average rate of change of a function that contains the points (-2,3) and (2,5)
Answer: [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Rate of change are typically found using [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1} }[/tex].
[tex](x_{1}, y_{1}) = (-2, 3)\\(x_{2}, y_{2}) = (2, 5)\\\\\frac{5-3}{2-(-2)} =\frac{2}{2+2} =\frac{2}{4} =\frac{1}{2}[/tex]
Therefore, the rate of change(aka slope) is [tex]\frac{1}{2}[/tex].
why can’t these lines be marked parallel ?
Answer:
there not the same and eqjral
Step-by-step explanation:
When solving the equation 6x - 8 = 12, the first step is to move the
constant, 8, to the right side by adding 8 to both sides. What is the
equation after step one?*
6x - 8 = 12 + 8
14x - 8 = 20
6x = 12 + 8
6x = 20
Answer:
6x= 12+8
Step-by-step explanation:
Can someone please help me out ~ASAP~? In the triangle below, what is the length of the side opposite the 60 degree angle?
Answer:
3√3
Step-by-step explanation:
no time to explain
A movie theater can hold 125 people. It is 2/5 of the way full
. How
many more people can the theater still hold?
Answer:
People: 75 hope this helps ;)
Step-by-step explanation:
So, we first see that there is a movie theatre that can hold 125 people and it is 2/5 full, so we would do 2/5 x 125 = 50 then we would do 125 - 50 = 75
The resulting row 1 entries are:
7.12
7.10
7,9
Answer:
OPTION C is the correct answer
7,9
Answer:
option 3 is correct
Step-by-step explanation:
hope it helped
have a good day!
Express in simplest radical form. 48
Answer: 4[tex]\sqrt{3\\}[/tex]
Step-by-step explanation:
It is because to get rid of radical of 48, because you factor 48 and it comes out to be 12 and 4, factor of 4 is 2 x 2. Factor of 12 is 6 x 2. Simplify the 6 to
3 x 2. You find the pair and the ones that have a pare become one and go outside of the radical sign on the left. 2 has 2 pairs so it is only 2 x 2 = 4. So 4 goes outside of the radical sign. Then the number that is alone with no pair is 3 so you put the number 3 inside the radical sign.
4[tex]\sqrt{3}[/tex] is your answer.
Hope this helps, sorry if not...
pls help me solve any of these pls show how you got the answer to the question you chose
First round 7.35 to the nearest one.
7.35 rounds to?
The cost to play the game is $2. The winner gets $6 for making green. Suppose 36 people play the game. How much money will the school take in from this game before giving out prize money? *
Answer:
$72
Step-by-step explanation:
I did 36 x 2. I did not subtract the -6 for the prize money because it says not to.
Answer:
$72
Step-by-step explanation:
You are trying to determine how much money the school will take in before giving out prize money. Knowing this, you can actually ignore the $6 that the winner will get because you are not worried about giving out the prize money yet. You are only worried about how much you will make before the prize money.
So, you can do simple multiplication to find the answer:
price per game * amount of people playing game = money made from games
$2 * 36 = x
$72 = x
Please help me I need to answer this before tomorrow!
Answer:
Quadrant IV or D
Step-by-step explanation:
It is Quadrant IV or D, since it is a positive x (meaning it must be 1 or 4) and it has a negative y (so 3 or 4). You then find the common answer which is 4 or IV.
The cost of having a window fixed is $100 plus $20 per hour of labor. Using h for the number of hours of labor, write an expression that represents the total cost.
Answer: 100+20h=x
Step-by-step explanation:
100 for the cost of the window Plus $20 times amount of hours the person does i equal the total amount you want to get which is x
Answer:
100 + (20 x H)
Step-by-step explanation:
100 dollars plus the amount paid for each hour of labor, so it would be 20 x H. Altogether it should be 100 + (20 x H).
Hope I helped!
Which triangle doesn’t belong?
Answer:
C because it is not a right angle unlike the others
Step-by-step explanation:
Solve for w:
w +6 > -18
Ow<-16
Ow>-16
Ow<-36
W > -36
Answer:
w> -24
Step-by-step explanation:
w +6 > -18
Subtract 6
w+6-6 > -18-6
w> -24
Triangle XYZ is pictured below.
Select the ratio that represents sin(x)
A) 21/29
B) 29/21
C) 20/29
D) 20/21
E) 29/20
F) 21/20
Answer:
C
Step-by-step explanation:
sine uses opposite over hypotenuse
the opposite of x is 20 and the hypotenuse is 29
so the answer is 20/29
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
Each fraction of the shape is 1/3 the whole shape. So the answer is B.
Answer:
I think C
Step-by-step explanation:
Evaluate the expression when m=7 and n=5.
8n+m
what is the answer?
Answer:
47
Step-by-step explanation:
8n + m =
8(5) + m =
40 + 7 = 47
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
47
Step-by-step explanation:
8n + m
n = 5
m = 7
Plug each variable's value into the equation.
8(5) + (7)
Multiply.
40 + (7)
Add.
47
Hope this helps!
Vijay started out with 1 fourth gallons of paint He used 3/8 gallon of paint on his boat how much paint is left?
Answer:
1/8
Step-by-step explanation:
1/4 -> 2/8
3/8 - 2/8 = 1/8
Answer:
he has -1/8 left
Step-by-step explanation:
he used more paint then he had if thats possible
the diameter of a circle is 4 inches. What is the area ? Give the exact answer in the simplest form.
Answer:
50.27
Step-by-step explanation:
the formula the find the are of a cricle is A = pie r^2
pi · 4^2
Answer:
4π
Step-by-step explanation:
A(Circle) = πr²
r = d/2 = 4/2 = 2
A(Circle) = π(2)² = 4π
An item is regularly priced at $85. It is on sale for 40% off the regular price. How much in dollars) is discounted from the regular price?
Answer:
34 dollars were discounted
Step-by-step explanation
40 percent of 85 is 34
write down a pair of integers whose sum is 0
Answer:
this might help
Step-by-step explanation:
2-2=0
integers
what is the median of 4, 4, 7, 13, 12, 9
Answer:
8.11
Step-by-step explanation:
4+4+7+13+12+9 = 49
divide that by 6
========================================================
Explanation:
Sort the data set to go from {4,4,7,13,12,9} to {4,4,7,9,12,13}
Next, cross off the first and last items to get this smaller set: {4,7,9,12}
Repeat the last step to get this even smaller set: {7,9}
We can see that 7 & 9 are tied for the middle most positions. Add them up and divide by 2 to find the midpoint
(7+9)/2 = 16/2 = 8
The median is 8