Answer:
x = ±4
Step-by-step explanation:
4x^2 = 64
Divide each by 4
4x^2 /4= 64/4
x^2 = 16
Take the square root of each side
sqrt(x^2) = ±sqrt(16)
x = ±4
Answer:
[tex]\boxed{\boxed{x=\pm 4}}[/tex]
Step-by-step explanation:
[tex]4x^2 = 64[/tex]
Divide both sides by 4.
[tex](4x^2)/4 = 64/4[/tex]
Simplify.
[tex]x^2 =16[/tex]
Take the square root on both sides.
[tex]\sqrt{x^2 } =\pm \sqrt{16}[/tex]
Simplify.
[tex]x=\pm 4[/tex]
Need help please! Oh and the options are
A. 2/3
B. 1/5
C. 4/15
D. 2/7
Answer:
C. 4/15There are 15 spaces in total with 4 shaded columnsStep-by-step explanation:
Answer:
Hey there!
The answer would be C. 4/15.
4/5(1/3)=4/15
Let me know if this helps :)
6 to the third power divided by 4+2 x 9(32x8-17x4)
Answer:
3438.
Step-by-step explanation:
6³ ÷ 4 + 2 × 9 (32 × 8 - 17 × 4)
= 6³ ÷ 4 + 2 × 9 (256 - 68)
= 6³ ÷ 4 + 2 × 9 × 188
= 216 ÷ 4 + 2 × 9 × 188
= 54 + 2 × 9 × 188
= 54 + 3384
= 3438
3438 is the answer.
Which equation can be used to solve for x in the following diagram?
PLS ANSWER I NEED HELP BRAINLIST AND A THANK YOU WILL BE REWARDED
Answer:
D. 4x+5x=180
Step-by-step explanation:
Answer:
D. 4x + 5x = 180
Step-by-step explanation:
The two angles form a straight line and a straight line equals 180°. So, the sum of the two angles has to equal 180°.
4x + 5x = 180
9x = 180
x = 20°
Hope that helps.
A farm has a square fenced-in area with side length x where the farm gives children pony rides. Adjacent to one entire side of the square area, there is a roped-off rectangular area where the children line up. This rectangle is 4 yards wide and x yards long.
1.The total area of the square and rectangular areas together is 2,700 square yards. Write an equation that represents this situation.
2. Use your equation from part a to find the dimensions of the roped-off rectangular area.
please help so i can pass my class!!
Answer:
1) x²+4x=2700
2) 50x50
Step-by-step explanation:
Pony area = x²
line-up area=4x
x²+4x=2700
x²+4x-2700=0
(x-50)(x+54)
So x= 50 or -54. Since it can’t be a negative number, it must be 50.
CHECK:
Square = 50x50 = 2500
Line up area = 50x4 = 200
2500+200=2700 YES
Find the term of each sequence.
32, 80, 200, ...5th term
Answer:
t5 = 1250
Step-by-step explanation:
Each term is derived by multiplying the previous term by 2.5
t2 = t1 * 2.5
t2 = 32 * 2.5
t2 = 80
===========
tn = a*b^(n - 1)
t3 = 32*2.5^2
t3 = 200
That's just to test the formula. It does work.
===============
t5 = 32*2.5^(5 -1)
t5 = 32*2.5^4
t5 = 1250
The generic version was basedOn the brand name and was 2/3 the size of the brand name. If the generic television set is 12 inches by 24 inches what are the dimensions of the brand name television
Answer:
18 inches by 36 inches.
Step-by-step explanation:
Since we have given that
The generic version was basedOn the brand name and was 2/3
And given Dimensions of generic version is given by 12inches ×24inches
If we use the first dimensions of 12inches we have
12=2/3 × brand
12×3/2 = brand
=18inches= brand
we use the first dimensions of 24 inches we have
24=2/3 × brand
24×3/2 = brand
=36 inches= brand
brand= 36 inches
Therefore,the dimensions of brand name will be 18 inches by 36 inches.
Harmony earns a \$42{,}000$42,000dollar sign, 42, comma, 000 salary in the first year of her career. Each year, she gets a 4\%4%4, percent raise.
Which expression gives the total amount Harmony has earned in her first nnn years of her career?
Answer:
FV(n)=42,000(1.04)^n
Step-by-step explanation:
FV=PV(1+r/n)^nt
Where
FV=future value
PV=present value
r=interest rate
n=number of periods
t=time (years)
PV=42,000
r=4%=0.04
n=1
t=n
FV(n)=p(1+r/n)^nt
=42,000(1+0.04/1)^1*n
=420000(1+0.04)^n
=42,000(1.04)^n
FV(n)=42,000(1.04)^n
Answer:
42000(1-1.04^n/-0,04)
Step-by-step explanation:
The equation of C is (x - 2)^2 + (y - 1)^2 = 25. Of the points P(0,5), Q(2,2) R(5,-2), and S(6,6), which point is located outside the circle?
Answer:
( 6,6) is outside
Step-by-step explanation:
(x - 2)^2 + (y - 1)^2 = 25
This is of the form
(x - h)^2 + (y - k)^2 = r^2
where ( h,k) is the center and r is the radius
(x - 2)^2 + (y - 1)^2 = 5^2
The center is at ( 2,1) and the radius is 5
P(0,5), Q(2,2) R(5,-2), and S(6,6)
Adding the radius to the y coordinate gives us 6 so the only point with a y coordinate on the circle is ( 2,6)
( 6,6) is outside the circle
HELP ASAP
The points $(-3,2)$ and $(-2,3)$ lie on a circle whose center is on the $x$-axis. What is the radius of the circle?
Answer:
[tex]radius = \sqrt{13}[/tex] or [tex]radius = 3.61[/tex]
Step-by-step explanation:
Given
Points:
A(-3,2) and B(-2,3)
Required
Determine the radius of the circle
First, we have to determine the center of the circle;
Since the circle has its center on the x axis; the coordinates of the center is;
[tex]Center = (x,0)[/tex]
Next is to determine the value of x through the formula of radius;
[tex]radius = \sqrt{(x_1 - x)^2 + (y_1 - y)^2} = \sqrt{(x_2 - x)^2 + (y_2 - y)^2}[/tex]
Considering the given points
[tex]A(x_1,y_1) = A(-3,2)[/tex]
[tex]B(x_2,y_2) = B(-2,3)[/tex]
[tex]Center(x,y) =Center (x,0)[/tex]
Substitute values for [tex]x,y,x_1,y_1,x_2,y_2[/tex] in the above formula
We have:
[tex]\sqrt{(-3 - x)^2 + (2 - 0)^2} = \sqrt{(-2 - x)^2 + (3 - 0)^2}[/tex]
Evaluate the brackets
[tex]\sqrt{(-(3 + x))^2 + 2^2} = \sqrt{(-(2 + x))^2 + 3 ^2}[/tex]
[tex]\sqrt{(-(3 + x))^2 + 4} = \sqrt{(-(2 + x))^2 + 9}[/tex]
Eva;uate all squares
[tex]\sqrt{(-(3 + x))(-(3 + x)) + 4} = \sqrt{(-(2 + x))(-(2 + x)) + 9}[/tex]
[tex]\sqrt{(3 + x)(3 + x) + 4} = \sqrt{(2 + x)(2 + x) + 9}[/tex]
Take square of both sides
[tex](3 + x)(3 + x) + 4 = (2 + x)(2 + x) + 9[/tex]
Evaluate the brackets
[tex]3(3 + x) +x(3 + x) + 4 = 2(2 + x) +x(2 + x) + 9[/tex]
[tex]9 + 3x +3x + x^2 + 4 = 4 + 2x +2x + x^2 + 9[/tex]
[tex]9 + 6x + x^2 + 4 = 4 + 4x + x^2 + 9[/tex]
Collect Like Terms
[tex]6x -4x + x^2 -x^2 = 4 -4 + 9 - 9[/tex]
[tex]2x = 0[/tex]
Divide both sides by 2
[tex]x = 0[/tex]
This implies the the center of the circle is
[tex]Center = (x,0)[/tex]
Substitute 0 for x
[tex]Center = (0,0)[/tex]
Substitute 0 for x and y in any of the radius formula
[tex]radius = \sqrt{(x_1 - 0)^2 + (y_1 - 0)^2}[/tex]
[tex]radius = \sqrt{(x_1)^2 + (y_1)^2}[/tex]
Considering that we used x1 and y1;
In this case we have that; [tex]A(x_1,y_1) = A(-3,2)[/tex]
Substitute -3 for x1 and 2 for y1
[tex]radius = \sqrt{(-3)^2 + (2)^2}[/tex]
[tex]radius = \sqrt{13}[/tex]
[tex]radius = 3.61[/tex] ---Approximated
help..!!! Why do i ask so many questions
Answer:
Hey there!
-4/3-4/5
-20/15-12/15
-32/15
Let me know if this helps :)
Point E is on line segment DF. Given DE=9 and DF=11, determine the length EF.
Answer:
EF = 2 units
Step-by-step explanation:
Given:
Line segment DF and point E on it.
DF = 11 unit
DE = 9 Unit
Find:
EF
Computation:
We know that,
DF = DE + EF
11 = 9 + EF
EF = 11-9
EF = 2 units
The number of patients treated at Dr. Jason's dentist office each day was recorded for seven days: 3, 8, 11, 22, 17, 5, 4. Using the given data, find the mean, median, and mode for this sample. A. mean: 10, median: 8, mode: none B. mean: none, median: 8, mode: 10 C. mean: 8, median: 10, mode: none D. mean: 14, median: 10, mode: 8
Answer: A. mean: 10, median: 8, mode: none
Step-by-step explanation:
Given : The number of patients treated at Dr. Jason's dentist office each day was recorded for seven days: 3, 8, 11, 22, 17, 5, 4.
First we arrange it order.
3, 4, 5, 8, 11, 17, 22
Mean = (Sum of observations) ÷ (Number of observations)
Number of observations = 7
Sum of observations = 3+4+5+8+11+17+22 =70
Mean = 70 ÷7 = 10
Median = Middle-most value
= 8
Mode = Most repeatted value
= none
Hence, the mean, median, and mode for this sample = A. mean: 10, median: 8, mode: none
Please help what are the slope and the y intercept of the linear function that is represented by the table?
Answer:
The slope is -2, the y-intercept is 12
Step-by-step explanation:
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Chose any two coordinates pair. Let's make use of:
[tex] (0, 12) = (x_1, y_1) [/tex]
[tex] (3, 6) = (x_2, y_2) [/tex]
Thus,
[tex] slope (m) = \frac{6 - 12}{3 - 0} [/tex]
[tex] slope (m) = \frac{-6}{3} [/tex]
[tex] slope (m) = -2 [/tex]
Using the slope-intercept equation, find the y-intercept, b, as follows:
[tex] y = mx + b [/tex]
Use any coordinate pair as x and y, then solve for b.
Let's use (3, 6)
[tex] 6 = (-2)(3) + b [/tex]
[tex] 6 = -6 + b [/tex]
Add 6 to both sides
[tex] 6 + 6 = - 6 + b + 6 [/tex]
[tex] 12 = b [/tex]
The slope (m) of the linear function that is represented by the table is -2, while the y-intercept (b), is 12.
Answer:
The slope is –2, and the y-intercept is 12.
Step-by-step explanation:
I used it and got it right
PLEASE HELP!!! What is factoring? Why is it useful to try to factor out the GCF first when factoring? Explain the relationship between factoring and multiplying polynomials. Give an example to help explain. Factor x^2-25, 3x^2-12x-15, and x^3+2x^2+3x+6 . What are the key features needed to graph a polynomial function? Explain how to find these key features to sketch a rough graph of a polynomial function. Why would someone want to factor a polynomial? Provide real world examples of different questions we can answer or facts we can determine from factoring a polynomial.
Answer:
What is factoring?Factoring is finding what to multiply to find an expression. It is like splitting expression into a multiplication of simplified expression.
Why is it useful to try to factor out the GCF first when factoring?Greatest common factor or GCF of two numbers is the largest number that divides evenly in both numbers, GCF works the same in polynomials, which divide the expression evenly .
Explain the relationship between factoring and multiplying polynomials. Give an example to help explainFactoring take away the multiplication, to factorize a polynomial it means take apart what is multiplied. the best example is a²+b²+2ab ( multiplied)
factorize :(a+b)(a+b) take apart what is multiplied
Factor x^2-25, 3x^2-12x-15, and x^3+2x^2+3x+6x²-25 =(x+5)(x-5)
3x²-12x-15 = 3(x²-4x-5) GCF=3
3(x-5)(x+1)
x³+2x²+3x+6 (x+2) common factor
(x+2)(x²+3)
What are the key features needed to graph a polynomial function?the key features are the vertex, axis of symmetry, x and y intercept
Explain how to find these key features to sketch a rough graph of a polynomial functionparabola : y=ax²+bx+c
ex: 3x²-12x-15
find vertex (h,k)
h=-b/2a =-(-12)/2(3)=2
k=f(h)=f(2)=3(2)²-12(2)-15
k=12-24-15=-27
vertex=(2,-27)
x intercept is when the graph =0 (y=0)
y intercept when x=0 then y= the constant c and where the graph cross the y axis
axis of symmetry is the x of the vertex: is a line about which a parabola is symmetrical and vertical when the axis of symmetric is vertical.
Why would someone want to factor a polynomial? Provide real world examples of different questions we can answer or facts we can determine from factoring a polynomial.factor a polynomial helps us understand more about equations,factoring helps us rewrite the polynomial into simpler expression.
example from real life:
A homeowner has a back yard and wants to turn it to garden beds so he can plant his vegetables, he wants to fill it with dirt he needs 240 cubic feet to fill it the length is 4 feet than the width , and the height is 4
solve:
length=W+4
height=1/3 w
V=length* width* height
240=(w+4)(w)(4)
351= 4w²+16w
4w²+16w-240=0
take 4 as common factor
4(w²+4w-60)
now factorize:
4(w-6)(w+10)=0
Factor completely, then place the answer in the proper location on the grid. 6x2 - 3x - 30
Answer:
3(2x-5)(x+2)
Step-by-step explanation:
Factor out the 3.
3(2x²-x-10)
Factor the remaining.
3(2x-5)(x+2)
(I don‘t know what grid they’re talking about.)
Christine, Dale, and Michael sent a total of 71 messages during the weekend. Dale sent 9 fewer messages than Christine. Michael sent 2 times as many messages as Christine. How many messages did they each send?
Answer:
Micheal sent 40 messages, Christine sent 20, and Dave sent 11.
Step-by-step explanation:
Christine, Dale, and Michael sent a total of 71 messages
C + D + M = 71
Dale sent 9 fewer messages than Christine
D = C - 9
Michael sent 2 times as many messages as Christine
M = 2C
Plug-in the numbers.
C + C - 9 + 2C = 71
4C - 9 = 71
4C = 80
C = 20
Now, plug in to other equations for other results.
D = (20) - 9
D = 11
M = 2(20)
M = 40
Micheal sent 40 messages, Christine sent 20, and Dave sent 11.
Verify?
40 + 20 + 11 = 71.
Write the equation 5x − 2y = 10 in the form y = mx + b. y equals start fraction five over two end fraction x minus 10 y equals start fraction five over two end fraction x minus five y equals start fraction five over two end fraction x plus five y equals negative start fraction five over two end fraction x minus five
Answer:
y = 5/2x - 5
Step-by-step explanation:
You have to rearrange the equation so that it is equal to y.
5x - 2y = 10
(5x - 2y) - 5x = -5x + 10
-2y = -5x + 10
(-2y)/-2 = (-5x)/-2 + (10)/-2
y = 5/2x - 5
A certain forest covers an area of 2600 km^2. Suppose that each year this area decreases by 4.75%. What will the area be after 11 years? Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
1522km^2
Step-by-step explanation:
To solve this, first convert the percentage to a decimal. That would be .0475.
Now subtract that from 1.0 to get the factor it decreases by. This would be 1-.0475 = .9525
Multiply 2600 x (.9525)^11 = 1522.258 which rounds to 1522 km^2
Answer:
The area will be 1292.98 km² after 11 years.
Step-by-step explanation:
To find what decreases by 4.57% each year in kilometers:
2600 × 4.57/100 = 26 × 4.57
= 118.82 km²
To find the area after 11 years:
118.82 × 11 = 1307.02
2600 - 1307.02 = 1292.98 km²
1292.98 km² is the answer.
in the equation x=c-b/a, find the value of x when c=10, b=2, and a=2
Answer:
9
Step-by-step explanation:
x = c - b/a
x = 10 - 2/2
x = 10 - 1
x = 9
Answer:
x = c - b (divided by) a
Step-by-step explanation:
x = 10 - 2over2
x = 10 - 1
x = 9
try 18/2 since that part is a fraction.
Maurice needs 45 exam review books for the students in his math class. The local bookseller will sell him the books at $3 each. He can also purchase them over the internet for $2 each plus $35 for postage. How much does he save by accepting the better offer?
Answer: he will save $42.50
Step-by-step explanation:
45÷3=15
45÷2+35=57.50
57.50-15= $42.50
Initial Knowledge Check
Question 2
Suppose that $4000 is placed in an account that pays 11% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year
sc
(b) Find the amount in the account at the end of 2 years.
?
Answer:
Step-by-step explanation:
We first need to figure out what the equation is for this set of circumstances before we can answer any questions. We will use the equation
[tex]A(t)=P(1+r)^t[/tex] which is just another form of an exponential equation where
(1 + r) is the growth rate, P is the initial investment, and t is the time in years. We will fill in the values we know first to create the equation:
[tex]A(t)=4000(1+.11)^t[/tex] which simplifies to
[tex]A(t)=4000(1.11)^t[/tex]
Now we'll just sub in a 1 for t and solve, then a 2 for t and solve.
When t = 1:
A(t) = 4000(1.11) so
A(t) = 4440
When t = 2:
[tex]A(t)=4000(1.11)^2[/tex] which simplifies to
A(t) = 4000(1.2321) so
A(t) = 4928.40
Given the sequence 4, 8, 16, 32, 64, ..., find the explicit formula. A. an=10(2n−1) B. an=5(2n−1) C. an=4(2n−1) D. an=20(2n−1)
Answer:
. an=4(2n−1)
Step-by-step explanation:
2x - 3y = -5
5x - 22 = -4y
Solve In Multiplication Method
Answer:
(2, 3 )
Step-by-step explanation:
Given the 2 equations
2x - 3y = - 5 → (1)
5x + 4y = 22 → (2) [ rearranged equation ]
Multiplying (1) by 4 and (2) by 3 and adding will eliminate the term in y
8x - 12y = - 20 → (3)
15x + 12y = 66 → (4)
Add (3) and (4) term by term to eliminate y, that is
23x = 46 ( divide both sides by 23 )
x = 2
Substitute x = 2 in either of the 2 equations and evaluate for y
Substituting into (2)
5)2) + 4y = 22
10 + 4y = 22 ( subtract 10 from both sides )
4y = 12 ( divide both sides by 4 )
y = 3
Solution is (2, 3 )
Given quadrilateral ABCD, where the diagonals AC and BD intersect at point E. AE≅EC and BE≅DE Can you prove can you prove that the figure is a parallelogram? Explain. A. Yes; two opposite sides are both parallel and congruent. B. Yes; diagonals of a parallelogram bisect each other. C. Yes; opposite sides are congruent. D. No; you cannot determine that the quadrilateral is a parallelogram.
Answer:
B. Yes; diagonals of a parallelogram bisect each other.
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.
Answer: B. Yes; diagonals of a parallelogram bisect each other.
If AE=EC and BE=DE then quadrilateral ABCD is a parallelogram because diagonals of parallelogram bisect each other.
What is parallelogram?A parallelogram is a 2 dimensional figure whose opposite sides are equal to each other and parallel to each other. Area of parallelogram is base*height.
How to prove quadrilateral a parallelogram?To be parallelogram ΔAEB and ΔEDC should be congruent.
Angle AEB= Angle DEC
AE=EC
DE=EB
so both triangles are congruent by side, side, angle.
Similarly AE=EC , DE=EB and vertical angles AED= Vertical angle BEC.
Therefore triangle AED and BEC are congruent and that makes all their corresponding sides are also congruent.
And AB=DC.
Hence both pairs of opposite sides of a quadrilateral are congruent ,then the quadrilateral is a parallelogram.
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HELP ME PLZZzzzzzzzz
Answer:
5 cm
Step-by-step explanation:
The volume (V) of milk in the container is calculated as
V = 8 × 15 × 12 = 480 cm³
After change of position with depth d then
8 × 15 × d = 480
120d = 480 ( divide both sides by 120 )
d = 4 cm
Find the value of x. Your answer must be exact.
X
12.
600
X=
Answer:
x = 6√3Step-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find x
To find x we use sine
sin ∅ = opposite / hypotenuse
From the question
The hypotenuse is 12
The opposite is x
Substitute the values into the above formula and solve for x
That's
[tex] \sin(60) = \frac{x}{12} [/tex]
[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]
[tex]x = \frac{ \sqrt{3} }{2} \times 12[/tex]
We have the final answer as
x = 6√3Hope this helps you
Write the equation of the line that is parallel to the line y=−14x−3 through the point (4,4). A. y=x+5 B. y=−14x+5 C. y=5x+1 D. y=5x−14
Answer:
None of the answers seem to be correct.
Step-by-step explanation:
The given equation is of the form y = mx + b where m is the slope and b is the y-intercept.
Here, m = -14
Two parallel lines have the same slope. So, the slope of the new line will be -14.
To calculate the y-intercept substitute x=4 and y=4 in the equation.
4 = (-14)(4) + b
Solving for b, we get b = 60.
So, the new equation will be y = -14x + 60
The equation of the line parallel to the given line is y =-14x+60, none of the given options is correct.
What is the equation of a straight line ?The equation of the straight line is given by y = mx +c , Where m is the slope of the line and c is the y-intercept.
The equation of the line is y = -14x -3
The slope of the line parallel to this will be the same as the given line.
m = -14 for both the lines
The line equation parallel to the given line is
y = -14x +c
The line passes through the points (4,4)
4 = -14 * 4 + c
c = 60
y = -14x +60
Therefore, the equation of the line parallel to the given line is y =-14x+60.
To know more about Equation of a straight line
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determine the equation for the quadratic relationship graphed below.
Answer:
[tex]\large \boxed{\sf \bf \ \ y=3x^2-6x-1 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
We can read from the graph that the vertex is (1,-4) , it means that the equation is, a being a real number.
[tex]y=a(x-1)^2-4[/tex]
And the point (0,-1) is on the graph so we can write.
[tex]a\cdot 1^2-4=-1 \\\\a-4+4=-1+4\\\\a = 3[/tex]
So the equation is.
[tex]y=3(x-1)^2-4\\\\=3(x^2-2x+1)-4\\\\=3x^2-6x+3-4\\\\=3x^2-6x-1\\\\=\boxed{3}x^2\boxed{-6}x\boxed{-1}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
[tex]y=3x^{2} -6x-1[/tex]
Step-by-step explanation:
A. 115
B. 167
C. 126
D. 96
Answer:
126
Step-by-step explanation:
Let x be the missing length
The triangles are similar:
● UE/140 = 45/x
From the graph we deduce that:
● UE = 140 - 90 = 50
Replace UE by its value
● 50/ 140 = 45/x
Switch x and 50
● x / 140 = 45/50
45/50 is 9/10 wich is 0.9
● x/140 = 0.9
Multiply 0.9 by 140
● x = 140 × 0.9
● x = 126
Answer:
I think its c 126
Step-by-step explanation:
Questions attached below (❁´◡`❁)
Problem 2
Josh forgot to apply the square root to 16 when he went from [tex](x-3)^2 = 16[/tex] to [tex]x-3 = 16[/tex]
Also, he forgot about the plus/minus.
This is what his steps should look like
[tex]x^2 - 6x - 7 = 0\\\\x^2 - 6x = 7\\\\x^2 - 6x +9= 7+9\\\\(x-3)^2= 16\\\\x-3= \pm\sqrt{16}\\\\x-3= 4 \text{ or } x-3= -4\\\\x= 7 \text{ or } x= -1\\\\[/tex]
There are two solutions and they are x = 7 or x = -1. To check each solution, you plug it back into the original equation
Let's try out x = 7
x^2 - 6x - 7 = 0
7^2 - 6(7) - 7 = 0
49 - 42 - 7 = 0
0 = 0 ... solution x = 7 is confirmed. I'll let you check x = -1
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Problem 3
We will have
a = 1, b = -4, c = 3
plugged into the quadratic formula below to get...
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-4)\pm\sqrt{(-4)^2-4(1)(3)}}{2(1)}\\\\x = \frac{4\pm\sqrt{4}}{2}\\\\x = \frac{4\pm2}{2}\\\\x = \frac{4+2}{2} \ \text{ or } \ x = \frac{4-2}{2}\\\\x = \frac{6}{2} \ \text{ or } \ x = \frac{2}{2}\\\\x = 3 \ \text{ or } \ x = 1\\\\[/tex]
The two solutions are x = 3 or x = 1. You would check this by plugging x = 3 back into the original expression x^2 - 4x + 3. The result should be zero. The same applies to x = 1 as well.
