Complete each statement in the steps to solve x2 – 6x – 7 = 0 using the process of completing the square.
Answers
Answer:
x = -1, 7
Step-by-step explanation:
Given question is incomplete; find the complete question in the attachment.
x² - 6x - 7 = 0
Step 1,
Isolate the constant by ADDING 7 both the sides of the equation.
x² - 6x - 7 + 7 = 0 + 7
x² - 6x = 7
Step 2
Add 9 to both sides of x² - 6x = 7 to form a perfect square trinomial while keeping the equation balanced.
x² - 6x + 9 = 7 + 9
Step 3
Write the trinomial x² - 6x + 9 as (x - 3) squared.
x² - 2(3)x + 9 = 16
(x - 3)² = 4²
Step 4
Use the square root property of the equality to get x - 3 = ± 4
(x - 3)² = 4²
[tex]\sqrt{(x-3)^2}=\sqrt{4^2}[/tex]
(x - 3) = ±4
Step 5
Isolate the variable to get solution of -1 and 7
x - 3 = ± 4
x = -3 ± 4
x = -1, 7
Answer:
1. Isolate the constant by adding 7 to both sides of the equation.
2. Add 9 to both sides of x2 – 6x = 7 to form a perfect square trinomial while keeping the equation balanced.
3. Write the trinomial x2 – 6x + 9 as x – 3 squared.
4. Use the square root property of equality to get x – 3 = ± 4.
5. Isolate the variable to get solutions of –1 and 7.
Step-by-step explanation:
just completed this on edge
Related Questions
The large stones of Stonehenge are arranged in a circle about 30 meters in diameter. What
is the radius?
Answers
Answer:
The radius is just the diameter split in half, so r = 15 meters.
Explanation:
D = 30
30/2 = 15
r = 15
D=30/2 =15=r
Order the numbers from least to greatest.
LEAST
1
8
= 0.13
= 0.12222...
12.7%
Answers
Can someone help me please
Answers
Answer:
The answer is D
Step-by-step explanation:
1/8 is the equivalent to 0.12
square root of 0.02 is 0.14
18% is equal to 0.18
Answer:
d. [tex]\sqrt{0.02}[/tex]
Step-by-step explanation:
1/8 = 0.125
18% = 0.18
1/5 = 0.2
1.6
0.09
[tex]\sqrt{0.02}[/tex] = 1.141
How much commission would a salesperson ear for selling a car that costs $29,389? He receives 16% commission on each sale.
Answers
Answer:
Commission on car = $4,702.24
Step-by-step explanation:
Given:
Sales price of car = $29,389
Commission on sale of car = 16% = 0.16
Find:
Commission on car
Computation:
Commission on car = Sales price of car x Commission on sale of car
Commission on car = 29,389 x 16%
Commission on car = 29,389 X 0.16
Commission on car = $4,702.24
What is the solution to the equation?
√2x+10−6=2
*Picture of the Problem Below*
Answers
Answer:
x = 27
Step-by-step explanation:
Given
[tex]\sqrt{2x+10}[/tex] - 6 = 2 ( add 6 to both sides )
[tex]\sqrt{2x+10}[/tex] = 8 ( square both sides )
2x + 10 = 8² = 64 ( subtract 10 from both sides )
2x = 54 ( divide both sides by 2 )
x = 27
2
Which of the following is equivalent to the expression
: 4?
5
Answers
Have a great day
Ancient slingshots were made form straps of leather that cradled a rock until it was released. One would spin the slingshot
in a circle, and the initial path of the released rock would be a straight line tangent to the circle at the point of release.
The rock will travel the greatest distance if it is release when the angle between the normal to the path and the horizontal
is -450. The center of the circular path is the origin and the radius of the circle measure 1.25 feet.
Write and equation of the initial path of the rock in standard form.
Answers
Answer:
Step-by-step explanation:∠ MON= -45°→→ angle lies in fourth quadrant.
Where, MN represents the path of rock, which is a straight line.
Taking the Horizontal and vertical component of OM,to get the coordinate of point M
The coordinate of point M will be [1.25 cos (-45°), 1.25 sin(-45°)]=
Taking O as center and Coordinates of O as (0,0) and Coordinates of M as () we get the equation of line OM as
y= tan (315°)× x
As general form of equation of line passing through the origin will be,
y= m x, where m is angle made by line with positive direction of x axis.
m= (360-45)°= 315°
→→y=-x
→→ y + x=0
equation of line perpendicular to OM will be
→→ x - y + k=0
Since it passes through .
→→
So, equation of initial path of stone will be:
What is the positive square root of 16?
Answers
Answer:
4
Step-by-step explanation:
because The square root of 16 is 4, which is a rational number.
Answer:
4
Step-by-step explanation:
Can someone plz help me with this Math problem and plz explain how you got your answers
Answers
PLEASE HELP ASAPPP!!!
Answers
Step-by-step explanation:
hope it helps you......
A triangles angles add up to 180 degrees.
52+78=130
180-130=50
Angle m = 50 degrees
What expression is equivalent to (5x6)x(3x2)
Answers
(5x6)x(3x2) = (30x6)= 180
WILL MARK BRAINLIEST IF GOTTEN RIGHT
Answers
Solution: 20 ft
Answer:
20 ft.
Step-by-step explanation:
Diameter is length across the circle/ across the middle
GO GO GO
<3
Find the interquartile range (IQR) of the data in the dot plot below
Answers
Answer:
2 cm
Step-by-step explanation:
As we know, the iqr is found by subtracting Q3-Q1. So that means we need to find them first. Finding the median will help us accomplish this task. So when writing out the numbers to solve it 81,82,83,83,84,84,84,85 because the amount of data points are an even number, we will have two data points which will help us solve our median which in this case is where the 83 and 84 meet. Our median is thus 83+84/2 which is 83.5. Now look on both sides of the two numbers which make up our median. On either side of the 2 data points needed for the median, the is another 3 data points. To find your q1 and q3, you need to find the median of these numbers. For Q1 look for the median between the numbers 81,82,83 and for Q3, look for the median in the numbers 84,84,85. So, knowing this information, our Q1 value is 82 and our Q3 value is 84. So..... input these into the equation we have up top which is Q3-Q1=IQR so...... 84-82=IQR, thus, our IQR is 2.
Anyone know the answer? Correct gets Brainliest!
Answers
Answer:
Try posting another question with an image of the problem attached
Step-by-step explanation:
Answer:
What's the question
Step-by-step explanation:
A nickel has a mass of 5 grams. What is the mass of the nickel in milligrams?
Answers
Answer:
5,000 milligrams
Step-by-step explanation:
Know That One 1 gram equals = 1,000 milligrams
Hope this Helps!
What is the difference between a trapezoid and a rhombus?
A) A trapezoid is a parallelogram and a rhombus is not.
B) A rhombus always has 4 equal sides and a trapezoid does not.
C) A rhombus always has 4 right angles and a trapezoid does not have to.
Eliminate
D) A rhombus never has 2 sets of parallel sides and a trapezoid always does.
Answers
PLEASE HELP I WILL GIVE BRAINIEST. What is the range?
Answers
Answer:
range= 8
Step-by-step explanation:
to find range> subtract highest number to the lowest
so 10- 2= 8
A principal wanted to survey students who took a standardized college entry exam about how prepared they felt for
the exam. The principal put together a bag of marbles. There was 1 marble for each student, and 20 of the marbles
were red. Each student chose a marble, and those who chose the red marbles took the survey. Which sampling
method was used?
O cluster sampling
simple random sampling
O stratified random sampling
O systematic random sampling
Answers
Answer:
B. Simple Random Sampling
Step-by-step explanation:
Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population. Each member of the population has an equal chance of being selected
Five years ago today, Artie was four times as old as his sister Carrie. In five years time, Artie will be twice as old as Carrie. Find their current ages using a system of linear equations.
Answers
Answer: 25 , 10 years
Step-by-step explanation:
Suppose the present age of Artie and Carrie is x and y
According to the question, 5 years ago
[tex]\Rightarrow x-5=4(y-5)\\\Rightarrow x-4y=-15\quad \ldots(i)\\[/tex]
In five year time
[tex]\Rightarrow x+5=2(y+5)\\\Rightarrow x-2y=5\quad \ldots(ii)[/tex]
Solving (i) and (ii) we get
[tex]x=25,y=10[/tex]
The current age of Artie and Carrie is 25 and 10 years
6TH GRADE MATH!
Which of these expressions are equivalent to p over 3?
Select each correct answer.
A. 3 divided by p
B. 1/3p +1/3p +1/3p
C. p-2/3p
D. 1/3p
E. p-3
F. 3p over 9
Please hurry, i only have 20 minutes left :(
Answers
Answer:
D. 1/3p and F. 3p over 9
Step-by-step explanation:
1/3p and 3p over 9
One equation in a system of equations is y=2x+4. Which of the following would be the second equation so that the system has (1,6) as its only solution
1. y=-2(x+2)
2. y=2x+8
3. y=5x+1
4. y=4x-7
Answers
Answer:
1. y = 2(x + 2)
Step-by-step explanation:
if we substitute the values,
we get 6 = 2*1 + 4
6 = 6
therefore, it is correct.
The system of equations has no solution. hence option d is correct.
What is Equation?Equation is described as the state of being equal, and it is commonly represented as a math expression with equal values on both sides, or it refers to a problem involving numerous variables.
here, we have,
to find solution to the system:
The given equation is
y=2x+8 ..(1)
3(-2x + y) = 12 ...(2)
Substitute the y value in equation 2 from equation (1)
3(-2x + 2x+8) = 12
3(8)=12
24≠12
Hence the system of equations has no solution.
Learn more about equation here:
brainly.com/question/1884491
#SPJ3
complete question:
What is the solution to the system of equations
below?
y=2x+8
3(-2x + y) = 12
1) no solution
2) infinite solutions
3) (-1,6)
4) (1/2,9)
find the value of two numbers if their sum is 12 and difference is 8
Answers
HELPP ME PLEASE ILL GIVE BRAINLIST :)
Answers
Answer:
C 7ft/yr
Step-by-step explanation:
1
Factorise 2x2 + 11x + 12. You can use the grid to help.
2x
3x
8x
1
12
2x2 + 11x + 12 =
Answers
Answer:
(2x+3)(x+4)
Step-by-step explanation:
hope the picture helps.
Can someone please help
1 answer choices are
A 122.2
B 68.115
2nd drop down menu answer choices are
A dollars
B square feet
C dollars per square foot
D square feet per dollar
3rd answer choices are
A increase
B decrease
4 are
A 122.20
B 68.115
Answers
Answer:
A 122.2B square feet A increaseB 68.115Water is filling a cylindrical water tank. As it is filled the radius of the tank expands at 0.2cm/s and the height decreases at the rate of 0.5cm/s. Find the rate at which the volume of the tank is changing at the instant the radius equals 1.8cm and height equals 65 cm. What is the volume of water at this point? Show all working. Volume, V, of the cylinder is given by V = ϖr2h.
Recall that V is a function of both r (radius of the cylinder) and h (the height of the cylinder). This is a partial differentiation problem. The volume is also changing with time.
Answers
Answer:
141.94 cm³/s
Step-by-step explanation:
Since the volume of the tank V = πr²h, and both the height and radius of the tank change with time, we find the rate of change of the volume with time, dV/dt from
dV/dt = dV//dr × dr/dt + dV/dh × dh/dt
where dV/dr = 2πrh, dr/dt = + 0.2 cm/s (since the radius of the tank expands), dV/dh = πr² and dh/dt = -0.5 cm/s (since the height of the tank decreases)
So,
dV/dt = dV/dr × dr/dt + dV/dh × dh/dt
dV/dt = 2πrh × + 0.2 cm/s + πr² × -0.5 cm/s
dV/dt = 0.4πrh cm/s - 0.5πr² cm/s
dV/dt = πr(0.4h - 0.5r) cm/s
We now find the rate at which the volume is changing when r = 1.8 cm and h = 65 cm.
So,
dV/dt = π(1.8 cm)(0.4 × 65 cm - 0.5 × 1.8 cm) cm/s
dV/dt = π(1.8 cm)(26 cm - 0.9 cm) cm/s
dV/dt = π(1.8 cm)(25.1 cm) cm/s
dV/dt = π(45.18 cm²) cm/s
dV/dt = 141.94 cm³/s
6. MGSE7.RP.2: The points on the coordinate grid represent the costs for the different numbers
of peaches.
Cost of Peaches
(8,6)
Cost (dollars)
Woo
(4.3)
(1.0.75)
0 1 2 3 4 5 6 7 8 9 10
Number of Peaches
Select THREE statements that are true about the graph.
A. There is a proportional relationship between the number of peaches and the cost because a
line can be drawn passing through the origin and connecting all the points shown.
B. There is a proportional relationship between the number of peaches and the cost because the
X-value is always greater than the y-value.
C. The point (1, 0.75) can be used to represent the unit rate of 0.75 dollars per peach.
D. The point (1, 0.75) can be used to determine the total cost by subtracting 0.25 from the
number of peaches.
E. The point (4, 3) represents 4 peaches at a cost of $3.
Answers
Answer:
C i think if wrong im so sorry
Step-by-step explanation:
Free to whoever gets it
Answers
LolAnswer:
Step-by-step explanation:
Wanna be in a hangouts gc?
one package of strawberries costs $4.50 how many will 3 packages cost?
if you can please show your work:)
Answers
I think you have to multiply them to get the answer $13.5
what is the inequality for more than 100,000
Answers
Answer:
>100,000
Step-by-step explanation: