Answer:
Option B.
Step-by-step explanation:
We have the equation:
x^2 + 6*x - 2 = 0
Remember that:
(a*x + b)^2 = (a*x)^2 + 2*a*b*x + b^2
Because the term with x^2 has a coefficient equal to 1, then a = 1.
(x + b)^2 = x^2 + 2*b*x + b^2
The ter with x is: 6*x
then:
2*b*x = 6*X
2*b = 6
b = 6/2 = 3
we have:
(x + 3)^2 = x^2 + 6*x + 9
Now, our equation is:
x^2 + 6*x - 2 = 0
Now we can add the term (11 - 11) = 0
x^2 + 6*x - 2 + (11 - 11) = 0
x^2 + 6*x - 2 + 11 - 11 = 0
x^2 + 6*x + (11 - 2) - 11 = 0
x^2 + 6*x + 9 - 11 = 0
And we know that:
x^2 + 6*x + 9 = (x + 3)^2
Then we can rewrite our equation as:
(x + 3)^2 - 11 = 0
Then the correct option is B.
The equation that matches our result is option B. (x+3)² - 11. Therefore, rewriting x² + 6x - 2 = 0 by completing the square gives us (x+3)² - 11 = 0.
To rewrite the equation x² + 6x - 2 = 0 by completing the square, we need to follow these steps:
Move the constant term (-2) to the other side of the equation:
x² + 6x = 2
Take half of the coefficient of x (which is 6) and square it. Add the result to both sides of the equation:
x² + 6x + (6/2)² = 2 + (6/2)²
x² + 6x + 9 = 2 + 9
x² + 6x + 9 = 11
Now, let's look at the answer choices:
A. (x+3)² = 18
B. (x+3)² - 11
C. (x+3)² - 2
D. (x+3)² - 9
Among the answer choices, the equation that matches our result is option B. (x+3)² - 11. Therefore, rewriting x² + 6x - 2 = 0 by completing the square gives us (x+3)² - 11 = 0.
To know more about equation:
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• A rope 75 meters long was cut into pieces that were each 1.5 meters long.
How many pieces resulted?
Help!!
Find Y.
Round to the nearest tenth.
Answer:
Y ≈ 59.0°
Step-by-step explanation:
Using the Cosine rule
cosY = [tex]\frac{x^2+z^2-y^2}{2xz}[/tex]
with x = 22, y = 20, z = 18
cosY = [tex]\frac{22^2+18^2-20^2}{2(22)(18)}[/tex]
= [tex]\frac{484+324-400}{792}[/tex]
= [tex]\frac{408}{792}[/tex] , then
Y = [tex]cos^{-1}[/tex] ( [tex]\frac{408}{792}[/tex] ) ≈ 59.0° ( to the nearest tenth )
Solve the right angle . Round decimal answers to the nearest tenth
9514 1404 393
Answer:
YZ = 8.5∠X = 70.5°∠Z = 19.5°Step-by-step explanation:
There are a couple of ways to do this. We can find YZ using the Pythagorean theorem, or we can find it using trig functions.
We know from SOH CAH TOA that ...
Cos = Adjacent/Hypotenuse
cos(X) = 3/9 = 1/3
X = arccos(1/3) ≈ 70.5°
Angle Z is the complement of this, so is ...
Z = 90° -70.5° = 19.5°
__
The length of side YZ can be found from ...
Sin = Opposite/Hypotenuse
sin(X) = YZ/XZ
YZ = XZ·sin(X) = 9·sin(70.5°) ≈ 8.485 ≈ 8.5
__
In summary, ...
YZ = 8.5; ∠X = 70.5°; ∠Z = 19.5°
Solve the system using a matrix,
3x – 2y = 2
6x - 5y = -1
9514 1404 393
Answer:
(x, y) = (4, 5)
Step-by-step explanation:
The solution to the matrix equation ...
[tex]\left[\begin{array}{cc}3&-2\\6&-5\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{c}2\\-1\end{array}\right][/tex]
is shown in the attachment. It is found by multiplying the equation on the left by the inverse of the coefficient matrix.
[tex]\left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{c}4\\5\end{array}\right][/tex]
Could I get some assistance with this one? I'm a little stuck. Thank you so much! C:
Answer:
$13.64
Step-by-step explanation:
you need about 1853 sheets of paper which is
1853 ÷ 500, or 3.706 reams
if 1 ream costs $3.68 then 3.706 reams costs 3.706 × 3.68 or $13.64
a sales clerk wants to make at least $519 . If he makes a base salary of $335 and $10.25 per hour at his part time job how many hours will he have to work?
Answer:
18 hours at least to reach the goal
Step-by-step explanation:
Well 519 is the lowest objective so lets aim for that
we can make an equation
since base pay is 335 that doesn’t change
We can make x for hours
335+10.25x ≥ 519
SO it can exactly equal or be greater
You’d get 17.95121... and you can’’t work 17.95121 hours so it has to be 18.
I NEED HELP ASAPPPPP
Answer:
y=55 degrees x=125 degrees
Step-by-step explanation:
What's the measure of X
Use the table to write each ratio Redbirds to blue socks
solve for x in the rectangle below
Answer:
There isnt a rectangle buddy
Step-by-step explanation:
State the cross section of the shape found in the picture
A baker has 6 pounds of sugar. He divides into 3 containers. He then uses 1 container to bake pies. Which expression shows how many pounds of sugar the baker used?
Step-by-step explanation:
You have 6 pounds of sugar, when you set it into 3 containers, you will get:
6:3=2 ( pounds per container)
And he used one container for pies it would be:
1 container contains 2 pounds of sugar, so he used 2 pounds of sugar.
What is the slope, m, of the line through (-7, -2) and (-6, 7)?
Answer:
Slope = 9
Step-by-step explanation:
(-7 , -2) ; x₁ = -7 and y₁ = -2
(-6 , 7) ; x₂ = -6 and y₂ = 7
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]=\frac{7-[-2]}{-6-[-7]}\\\\=\frac{7+2}{-6+7}\\\\=\frac{9}{1}\\\\= 9[/tex]
Can someone pls help with this
Answer: 4
Step-by-step explanation:
Marya has $146 in her checking account . She writes a check for $193 . What is the new balance in her checking account ?
Answer:
-$47
Step-by-step explanation:
If she has $146 in he account and we take away $193, we are left with -$47, making her in debt.
What is the value of the expression below when y=2 AND z=8?
8y-z
Answer:
Step-by-step explanation:
Please Help!!!
NO xtiny urls
Answer:
Step-by-step explanation:
Find the scale factor used to go from the actual picture to the scale drawing!
Answer:
1/3
Step-by-step explanation:
9:6
3:2
9/3 = 3
6/2 = 3
9 x (1/3) = 3
6 x (1/3) = 2
scale factor is 1/3
prove why 2,5,8,11 and 14 are not perfect squares?
Answer:
because there is an exact square number such as:4,9
Answer:
✓2=1.41421
✓5=2.23607
✓8=2.82842
✓11=3.31662
✓14=3.74166
Step-by-step explanation:
Therefore the numbers are increasing by three so they cant be perfect square
Convert 3y=-x + 5 into slope form
Answer:
y=-x/3+5/3
Step-by-step explanation:
slope form is y=mx+b
Vicky made some purchases at the
Sunflower Market. She bought strawberries
for $3.50, carrots for $2.25 and a bouquet of
flowers for $9.95. If sales tax is 5%, what will
Maria pay altogether?
1. $16.48
2. $15.70
3. $16.49
4. $16.50
Step-by-step explanation:
Vicky Bought:
Strawberries $3.50
Carrots $2.25
Flowers $9.95
Subtotal $3.50 + $2.25 + $9.95
= $15.70
5% Sales Tax (5% of Subtotal) = 5/100 x $15.70
= $0.785 (will not round off here as it is not the final answer.)
Total = Subtotal + 5% Sales Tax
= $15.70 + $0.785
= $16.485
= $16.49 (rounded off to nearest cent)
A rocking horse has a weight limit of 60 pounds. What percentage of the weight limit is 33 pounds?
Answer:
57 pounds weight is 95 percent of the limit i think
Step-by-step explanation:
Answer:
55%
Step-by-step explanation:
50% of 60 is 30
5% of 60 is 3
plsss help and please dont be scammer
Answer:
38 students
Step-by-step explanation:
because 19% of 205 is 38.95, but not fully 39 students, so about 38 students
pls show your work if possible
Answer:
32 in²
Step-by-step explanation:
A= ((a+b)/2)*h
A= ((6+10)/2)*4
A=32
Johnathan wants to paint the bottom of his swimming pool the color blue. the swimming pool has a diameter of 50 feet . How many square feet will Johnathan need to paint ?
Need the Answer for this, provide an explanation.
Answer:
D) -5x(x² + 2x + 3)
Step-by-step explanation:
-5x³ - 10x² - 15x
Common factor:
-5x
Factored:
-5x(x² + 2x + 3)
A can of juice has a radius of 4 inches and a height of 7 inches. What is the volume of the can?
Round your answer to the nearest tenths place.
Answer:
351.7
Step-by-step explanation:
Volume of a cylinder:
V = πr²h
V = 3.14(4²)(7)
V = 3.14(16)(7)
V = 50.24(7)
V = 351.68
Rounded to the nearest tenth:
351.7
where is -3 3/4 on a number line
Answer:
here lol https://imageshare.best/8R2I7D
Step-by-step explanation:
in a class of 38 students, 16 passed chemistry,
Answer:
what are you asking exaclty ???
Step-by-step explanation:
5/3 plus 11/4 I NEED IT FAST!!