Complete the square:
2x² + 9x - 18
2(x² + 9/2 x) - 18
2(x² + 9/2 x + 81/16 - 81/16) - 18
2(x² + 2 (9/4) x + (9/4)²) - 81/8 - 18
2(x + 9/4)² - 225/8
If you're not familiar with the method, the idea is to get a quadratic from the standard form
ax² + bx + c
into its vertex form
a (x - h)² + k
where (h, k) is the vertex of the parabola associated with the quadratic.
Expand the vertex form to get
a (x² - 2xh + h²) + k
ax² - 2ahx + ah² + k
For the two forms to be equivalent, we must have
-2ah = b
ah² + k = c
which means
h = -b/(2a)
k = c - ah² = c - b²/(4a)
In this case, a = 2, b = 9, and c = -18, so
h = -9/(2 • 2) = -9/4
k = 18 - 9²/(4 • 2) = -225/8
Please help me with math!!!
Answer:
x= 4
y= 116
Step-by-step explanation:
Are the ratios 3:6 and 1:9 equivalent?
Answer:
no they are not equivalent
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
The ratio would have to be 1:2 or 6:12 or with other factors of the two numbers but the numbers have to be multiplied or divided by the same number to get to those factors in order for them to remain equivalent.
For example: If you were to multiply the 3 by 2 but the 6 by three you'd get 6:18 which simplified is 3:9 not 3:6 but if you multiply both the 3 and the 6 by 3 you'd get 9:18 with can by simplified to 3:6
Earl runs 70 meters in 20 seconds. How many meters does Earl run per second
Answer:
3.5 meters
Step-by-step explanation:
70/2=3.5 meters
Answer:
3.5
Step-by-step explanation:
70/20= 3.5
Hope this helps! :)
Someone please help me answer this
Answer
Sorry about that comment
Step-by-step explanation:
My brother was being annoying and messed with my computer
I'm new here
Which point is on the line described by the equation below?
4x−3y=−4
Answer:
[tex]D)\ -1,0[/tex]
Step-by-step explanation:
Given
[tex]4x - 3y= -4[/tex]
Required
Determine which of the options is on the line
The question requires options.
However, I'll answer using the following:
[tex]A) -3, 4[/tex]
[tex]B) -4,3[/tex]
[tex]C)\ 3, 4[/tex]
[tex]D)\ -1,0[/tex]
A point is always of the form (x,y).
So, we have to substitute values for x and y in the given equation
Considering option A:
[tex](x,y)= (-3,4)[/tex]
Substitute [tex]-3\ for\ x\ and\ 4\ for\ y[/tex] in [tex]4x - 3y= -4[/tex]
[tex]4(-3) -3(4) = -4[/tex]
[tex]-12 -12 = -4[/tex]
[tex]-24 \neq -4[/tex]
The above represents an inequality.
Hence, -3,4 does not lie on the equation
Considering option B:
[tex](x,y) = (-4,3)[/tex]
Substitute [tex]-4\ for\ x\ and\ 3\ for\ y[/tex] in [tex]4x - 3y= -4[/tex]
[tex]4(-4) - 3(3) = -4[/tex]
[tex]-16 - 9 = -4[/tex]
[tex]-25 \neq -4[/tex]
The above represents an inequality.
Hence, -4,3 does not lie on the equation
Considering option C:
[tex](x,y) = (3,4)[/tex]
Substitute [tex]3\ for\ x\ and\ 4\ for[/tex] y in [tex]4x - 3y= -4[/tex]
[tex]4(3) - 3(4) = 4[/tex]
[tex]12 - 12 = 4[/tex]
[tex]0 \neq 4[/tex]
The above represents an inequality.
Hence, 3,4 does not lie on the equation
Considering Option D:
[tex](x,y) = (-1,0)[/tex]
Substitute [tex]-1\ for\ x\ and\ 0\ for[/tex] y in [tex]4x - 3y= -4[/tex]
[tex]4(-1) - 3(0) = -4[/tex]
[tex]-4 - 0 = -4[/tex]
[tex]-4 = -4[/tex]
The above represents an equality.
So, -1,0 lies on the equation
b) The points (5, -3) and (-3, -7)
Step-by-step explanation:
what are you doing with the points then I can help you
What is the value of x in the equation
1 x – 8 = 4x + 12?
Answer:
The value of x is -20/3.
Step-by-step explanation:
Answer:
x = - [tex]\frac{20}{3}[/tex]
Step-by-step explanation:
Given
x - 8 = 4x + 12 ( subtract 4x from both sides )
- 3x - 8 = 12 ( add 8 to both sides )
- 3x = 20 ( divide both sides by - 3 )
x = - [tex]\frac{20}{3}[/tex]
Consider the triangles shown. Triangles V U T, U T S, and T S R are connected. Sides V T, U T, T S, and T R are congruent. If mAngleUTV mAngleUTS > mAngleSTR by the converse of the hinge theorem.
Answer:
A :)
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Sarah's new puppy weighed 5 2/7 pounds. After a month it had gained 5 7/10 pounds.
What is the weight of the puppy after a month? Answer as a mixed number.
Answer:
769/70
Step-by-step explanation:
5 2/7 = 37/7
5 7/10 = 57/10
The lowest common multiple is 70
37*10/(7 * 10) = 370/70
57/10 = 57*7/(7*10) = 399/70
Now add
370/70 + 399/70
769/70
Is 769 prime? I think it might be.
Yes it is.
What is the area of AA'B'C'?
Consider a triangle with two sides that
measure 6 cm and 10 cm forming an angle
that measures 80°.
Find the length of the third side of the triangle to the nearest tenth centimeter
A) 10.1 cm
B) 10.7 cm
C) 11.1 cm
D) 11.4 cm
Answer:
c
Step-by-step explanation:
c
Identify the equation of the circle J with center K(-7,3) and radius 6.
Answer:
equation of the circle J with center K(-7,3) and radius 6 is=
x^2+y^2+14x-6y+22=0
Step by step explanation:
Equation of circle with given centre (h,k) and radius r is
(x-h)^2+(y-k)^2=r^2
Given centre are K(-7,3) and radius 6.
So equation of Circle=
(x- -7)^2+(y-3)^2=6^2
x^2+14x+49+y^2-6y+9=36
x^2+y^2+14x-6y+22=0 answer
Answer:
(x + 7)² + ( y − 3)² = 36
Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is (x − h)² + (y − k)² = r².
Define h, k and r using the given values. So, h= −7, k = 3, and r = 6.
Substitute the values into the equation of a circle.
(x − (−7))² + (y −3)²= 62
Simplify.
(x + 7)² + (y − 3)²= 36
Therefore, the equation of the circle J with center K (−7, 3) and radius 6 is (x + 7)² + (y − 3)²= 36.
Can someone please help me???
Answer:
313
Step-by-step explanation:
133+133+47=313
C would be 47 cuz 180-133=47
Marco volunteered to help with a home remodeling project at his grandparents' house, but he also needs to study to maintain good grades. He decided he can spend no more than 36 hours on painting walls and framing windows. He needs 2
hours to paint a wall and 3 hours to frame a large window. Write an inequality to represent the constraints.
Answer:
2w + 3x ≤ 36
Step-by-step explanation:
Given that :
Hours needed to paint wall = 2 hours
Hours required to frame window = 3 hours
Total hours to spend ≤ 36
Let :
Number of walls to paint = w
Number of windows to frame = x
Hence,
Hours required to paint a wall * number of waas to paint) + (hours required to frame a window * Number of windows to frame.)
(2*w) + (3*x) ≤ 36
2w + 3x ≤ 36
What is the area of the regular trapezoid below?
A trapezoid has a base of 10 centimeters, height of 8 centimeters, and top side length of 6 centimeters.
64 Centimeters squared
80 Centimeters squared
240 Centimeters squared
480 Centimeters squared
Answer:
its D
Step-by-step explanation:
The weights of three kittens at one week old were 4.1 ounces, 3.5 ounces, and 3.4 ounces. If each kitten gained 2.5 ounces, how much would each of the kittens weigh? A 11 ounces B 6.6 ounces, 6 ounces, and 5.9 ounces C 1.6 ounces, 1 ounce, 0.9 ounces
Answer:
B 6.6 ounces, 6 ounces, and 5.9 ounces
Step-by-step explanation:
First Kitten
Weighed: 4.1 ounces
Current weight => 4.1 ounces + 2.5 ounces
=>6.6 ounces
Second Kitten
Weighed: 3.5 ounces
Current weight => 3.5 ounces + 2.5 ounces
=>6 ounces
Third Kitten
Weighed: 3.4 ounces
Current weight => 3.4 ounces + 2.5 ounces
=> 5.9 ounces
Each of the kittens would weigh :
6.6 ounces, 6 ounces, and 5.9 ounces
How many solutions does the following equation have?
7x−(x−4)=6x−7
A.There is no way to determine the answer to this equation.
B. An infinite number of solutions will solve this equation.
C.There is only one real solution for the equation.
D.There is no real solution for this equation.
Answer:
12x-11
Step-by-step explanation:
There is no known solution, but this can be simplified. Add up all of the coefficients(# connected by the variable). Since after 7x is a - , the x following has to be negative. After adding the coefficients, you should have below, 12x. Then, you add up all of your constants.(# w/ no variable). Adding negative and positive, you should get below, -11. Finally, you should of simplified your equation to 12x-11.
Equation:
7x- (x-4)= 6x -7
7x- (x-4)= 6x -7
12x
7x- (x-4)= 6x -7
-11
12x-11
Solve the inequality W > Y Plus H all divided by P for H
Answer:
W - Y > H
Or
H < W - Y
Step-by-step explanation:
From the word problem/ information given from the problem, we can formulate a full inequality:
[tex]\frac{W > Y+H}{P}[/tex]
And we are trying to solve for H:
What we must do is solve by following the process of PEMDAS
P - () (Parenthesis)
E - [tex]x^{2}[/tex] (Exponents)
M - x (Multiply)
D - [tex]\frac{x}{y}[/tex] (Division)
A - + (Addition)
S - [-] (Subtraction)
1) Look through PEMDAS until you notice one:
We find that there is Division!
In order to get one step closer to finding H, we must do the opposite of dividing which is multiplying:
P([tex]\frac{W > Y+H}{P}[/tex])
This will cancel out P, leaving you with:
[tex]{W > Y+H}[/tex]
2) Now we must get H alone by subtracting Y on both sides:
[tex]{W > Y+H}\\[/tex]
-Y - Y
---------------
W - Y > H
Your final answer is W - Y > H
This scatter plot shows the number of books read and the
number of days passed.
Based on the information in the scatter plot, what is the best prediction for the number of books read in 9 days?
o 5 books
o 9 books
0 12 books
o 15 books
Answer:
the answer would be 15 books
Step-by-step explanation:
.
sharons magazine subscriptions costs $25 per month. What is the change in the amount of money in her account after 2/3 of a year
Answer:
200 for 2/3 of a year
Step-by-step explanation:
8 × 25 = 200
slope for (2,-5) (1,5)
Answer:
Slope (m) = 0
Step-by-step explanation:
13w + 9 = 178
What’s the first step in solving this equation
Step-by-step explanation:
I don't know if you do this the same way I did, but..
The first step is to subtract 9 on both sides, like this.
13w + 9 = 178
-9 -9
You'll end up with:
13w = 169
I don't know if you need the answer or not but I'll help you out.
For the second step, divide both sides by 13w.
13w = 169
/13w /13w
w = 13
Hope this helped!
Answer:
The first step is that you have to subtract 9 from both sides and you are left with 13w=169 now divide both sides by 13 and you get 13 as your answer.
Step-by-step explanation:
Which function can best be used to find the cost of renting the concert hall for h hours ?
Helpp Please..........
Answer:
50
Step-by-step explanation:
Mark as brainliest
Heeeeeeeeeeeelp !!!!!!!!!!!!
Answer:
Step-by-step explanation:
6x2 + 5x - 4
6x2 + 8x - 3x - 4
2x(3x + 4) - 1(3x + 4)
(2x - 1) (3x + 4)
These are the factors
How many solutions does this equation have? x = x + 9
Answer: infinte
Step-by-step explanation:
Answer:
unlimited because x can be any number
Step-by-step explanation:
branliest?
Please Help me solve for x
3x-m=10
Answer:
x=(10+m)/3
Step-by-step explanation:
3x-m=10
3x=10+m
x=(10+m)/3
Answer:
You can't solve for this since there are two variables. We can only solve this when we either know the value of one variable or we have another equation with these two variables.
Which type of line is necessary at the ends of arrowheads on a dimension line?
A.
break line
B.
cutting-plane line
C.
extension line
D.
section line
Answer: c. extension line
Step-by-step explanation:
In a game, a student loses 5 points, loses 3 points, gains 16 points. What is the students score?
Answer:
8
Step-by-step explanation:
NEED HELP ASAP, WILL GIVE BRAINLIEST
What is the sum of all of the coefficients of the binomial expansion (6x-y)^4
Answer:
srry do t know
Step-by-step explanation:
