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Solve by factoring
x2 + 6.9. Hint. This is a double root.
3
9
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Answers
Answer:
–3 and –3
Step-by-step explanation:
x² + 6x = – 9
Rearrange
x² + 6x + 9 = 0
Multiply the first term i.e x² and last term i.e 9 together. The result is 9x².
Next, we shall find two factors of 9x² such that when we add them together, the result will be the same as the 2nd term i.e 6x in the expression above.
The factors are 3x and 3x.
Next, we shall replace 6x with 3x and 3x in the equation above as shown below:
x² + 6x + 9 = 0
x² + 3x + 3x + 9 =0
Factorise
x(x + 3) + 3(x + 3) = 0
(x + 3)(x +3) = 0
x + 3 = 0 or x + 3 =
x = – 3 or x = – 3
Therefore, the solutions are –3 and –3
Related Questions
In its first year of operations, Roma Company reports the following. Earned revenues of $53,000 ($45,000 cash received from customers). Incurred expenses of $29,500 ($23,050 cash paid toward them). Prepaid $8,750 cash for costs that will not be expensed until next year.
Answers
Complete question :
In its first year of operations, Roma Company reports the following. Earned revenues of $53,000 ($45,000 cash received from customers). Incurred expenses of $29,500 ($23,050 cash paid toward them). Prepaid $8,750 cash for costs that will not be expensed until next year. calculate the first year's net income under both the cash basis and the accrual basis of accounting.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Earned revenue = $53,000
Cash received from customers = $45000
Incurred expenses = $29,500
Cash paid towards incurred expenses = $23,050
Cash which will not be expensed till next year = $8,750
Cash Accounting:
Cash received $45,000
Expenses ($23,050 + $8750) = $31,800
Net Income $(45,000 - 31,800) = $13,200
Accrual Accounting :
Revenue earned $53,000
Expenses incurred $29,500
Net income $(53,000 - 29,500) = $23500
Which is the factorization of x3 + 8? (x + 2)(x2 – 2x + 4) (x – 2)(x2 + 2x + 4) (x + 2)(x2 – 2x + 8) (x – 2)(x2 + 2x + 8)
Answers
Answer:
here the answer is down below
Step-by-step explanation:
Answer:
A (x+2)(x^2-2x+4)
Step-by-step explanation:
just took test
What is the approximate area of the shaded sector in the circle shown below? O A. 25 in2 4.3 in 155 B. 5.82 in2 IC O C. 11.63 in2 D. 50 in2 SUBMIT
Answers
Answer:
D. 25 inch²
Step-by-step explanation:
Area of sector of a circle =(r^2∅) /2
where,
r = radius of the circle
∅= angle subtended by the arc at the center of circle in radians.
Given :
∅ =155°
radius =4.3 in
Convert 155° to radian
πradian=180°
155°=π / 180°*155°
=2.705 radians
Area of sector of a circle =(r^2∅) /2
=(4.3^2 * 2.705) / 2
=(18.49 * 2.705) / 2
=50.01545 / 2
=25.007725 inch²
Approximately 25 inch²
25in^2
hope this helpsss ✓✓✓
Chad washes windows after school to make some extra money. He charges $5.50 to wash each window. If the customer provides the supplies, Chad deducts $3.25 from the total cost. One customer paid a total of $27.50 and did not provide supplies. Which equation could be used to find the number of windows, w , that Chad washed for this customer? A) 5.5 w + 3.25 = 27.5 B) 5.5 w - 3.25 = 27.5 C) 5.5 w = 27.5 D) 5.5 - 3.25 w = 27.5
Answers
Answer:
C. 5.5 = 27.5
Step-by-step explanation:
The customer did not provide any supplies which means that the number 3.25 should not even be apart of the answer choice because it is not being deducted.
5.50 multiplied by how many widows (w) are washed should equal 27.50
Therefore C. 5.5 = 27.5 is the answer
Answer:
C) 5.5 w = 27.5
For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
Answers
Answer:
Step-by-step explanation:
Pythagorean Theorem: a^2+b^2=c^2.
15^2+ b^2=25^2
225+b^2= 625
b^2=400
b= 20 or x=20
Answer:
x = 20
Step-by-step explanation:
This is a right triangle and we know 2 of the points so we can use the Pythagorean Theorem to solve. The formula for the Pythagoreom Theroem is a^2 + b^2 = c^2. Side a is 15 and Side b is x. Side c or the hypotenuse is 25. Let's solve for side b:
a^2 + b^2 = c^2
15^2 + b^2 = 25^2
225 + b^2 = 625
Subtract 225 from both sides to get b^2 alone.
b^2 = 625 - 225
b^2 = 400
Find the square root of both sides.
b = 20 or x = 20
Would appreciate it if you gave me brainliest answer :)
For what values of a the following expressions are true: |a−5|=5−a
Answers
Answer:
Whenever [tex]a\leq 5[/tex].
Step-by-step explanation:
We can play around with some numbers and develop some rules for this equation.
Note that the number 5 and -5 are used here, so let's try using 5 as a.
[tex]|5-5| = 5-5\\|0| = 0\\0 = 0[/tex]
So 5 works. Let's try a random number like 3.
[tex]|3-5| = 5-3\\|-2| = 2\\2 = 2[/tex]
Okay, with this info we know that we might be able to develop one rule that [tex]a<5[/tex]. Just to test, let's try 0, -3, and -5.
[tex]|0-5| = 5-0\\|-5| = 5\\5 = 5[/tex]
Zero works.
[tex]|-3 - 5| = 5-(-3)\\|-8| = 8\\8 = 8[/tex]
-3 works.
[tex]|-5 -5| = 5-(-5)\\|-10| = 10\\10 = 10[/tex]
-5 works. Now, this might stop here making the equation [tex]-5 \geq a \leq 5[/tex], so let's test a number outside of -5 - say -20.
[tex]|-20 - 5| = 5-(-20)\\|-25| = 25\\25 = 25[/tex]
Yes! This works, so a works for this equation as long as [tex]a \leq 5[/tex].
Hope this helped!
Write h(x) = x2 - 6x + 3 in vertex form by following these
steps:
Step 1: Model x2 - 6x + 3 by placing tiles in the Product
section. First place the x2 and -x tiles along the left
and top borders to form two sides of a square. Then
place the + tiles along the ends of the -x tiles.
Answers
The vertex form of the quadratic equation is:
[tex]h(x) = (x - 3)^2 - 6[/tex]
How to write the quadratic equation in vertex form?
For a quadratic equation:
[tex]y = a*x^2 + b*x +c[/tex]
With vertex (h, k), the vertex form is:
[tex]y = a*(x - h)^2 + k[/tex]
In this case, we have the equation:
[tex]h(x) = x^2 - 6x + 3[/tex]
To get the x-value of the vertex we use the general formula:
[tex]h = -(-6)/(2*1) = 6/2 = 3[/tex]
To get the y-value, we evaluate the function in x = 3, so we get:
[tex]h(3) = k = (3)^2 - 6*3 + 3 = -6[/tex]
So the vertex is (3, -6).
Then the vertex form is:
[tex]h(x) = (x - 3)^2 - 6[/tex]
If you want to learn more about quadratic equations:
https://brainly.com/question/1214333
#SPJ1
Copying figures 6b
Can anyone help me with this? If so can you better explain it to me on paper. I’m really confused.
Answers
Answer: see Steps 1 - 5 (attached)
Step-by-step explanation:
I completed #1 for you. Each image shows one of the steps.
Follow the exact same steps to complete #2 - #5
#6 asks for a double angle.
Add an extra item to step 3: Draw an arc from vertex through the line
--> then draw another arc from B' to the other side of your line (away from the dot) and label that intersection as B''. Use the measure of the vertex to B'' for the remaining steps.
If you need step-by-step images, you will need to post #6 separately as I can only upload 5 images per question.
PLEASE HELP Draw the reflection of the figure over the line shown.
Answers
The answer is in the picture
Which of the following exponential functions is represented by the graph? Question 15 options: A) ƒ(x) = (1∕2)x B) ƒ(x) = 2x C) ƒ(x) = −2x D) ƒ(x) = (1∕2)−x
Answers
Answer:
Option (A)Step-by-step explanation:
Let the equation of the exponential function is f(x) = a(b)ˣ
Two points (-2, 4) and (-1, 2) lie on the graph,
For (-2, 4),
By substituting the values in the given function,
[tex]4=a(b)^{(-2)}[/tex]
[tex]4=\frac{a}{b^{2} }[/tex] ------(1)
For second point (-1, 2),
[tex]2=a(b)^{-1}[/tex]
[tex]2=\frac{a}{b}[/tex] -----(2)
Dividing equation (1) by equation (2),
[tex]\frac{4}{2}=\frac{\frac{a}{b^2}}{\frac{a}{b} }[/tex]
[tex]2=\frac{a}{b^{2}}\times \frac{b}{a}[/tex]
[tex]2=\frac{1}{b}[/tex]
b = [tex]\frac{1}{2}[/tex]
From equation (1),
[tex]4=\frac{a}{(\frac{1}{2} )^2}[/tex]
4 = 4a
a = 1
Therefore, equation of the exponential function will be,
f(x) = [tex]1.(\frac{1}{2})^{x}[/tex]
[tex]f(x)=(\frac{1}{2})^x[/tex]
Option (A) will be the answer.
Answer:Answer:
Option (A)
Step-by-step explanation:
Let the equation of the exponential function is f(x) = a(b)ˣ
Two points (-2, 4) and (-1, 2) lie on the graph,
For (-2, 4),
By substituting the values in the given function,
------(1)
For second point (-1, 2),
-----(2)
Dividing equation (1) by equation (2),
b =
From equation (1),
4 = 4a
a = 1
Therefore, equation of the exponential function will be,
f(x) =
Option (A) will be the answer.
Step-by-step explanation:
What is the equation of the line that is parallel to y = negative two-thirds x + 4 and that passes through (–2,–2)? On a coordinate plane, a line goes through (3, 2), and (6, 0). A point is at (negative 2, negative 2). y = negative two-thirds x minus four-thirds y = negative two-thirds x minus StartFraction 10 Over 3 EndFraction y = negative two-thirds x minus two-thirds y = negative two-thirds x minus StartFraction 17 Over 4 EndFraction
Answers
Answer:
Option B.
Step-by-step explanation:
If equation of a line is y=mx+c, then m is the slope of line.
The given equation is
[tex]y=-\dfrac{2}{3}x+4[/tex]
Here, slope of line is [tex]m=-\dfrac{2}{3}[/tex].
We need to find the equation of line that is parallel to given equation and passes through (–2,–2).
We know that, slope of parallel lines are same. So, slope of required line is [tex]m=-\dfrac{2}{3}[/tex]. So, equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-2)=-\dfrac{2}{3}(x-(-2))[/tex]
[tex]3(y+2)=-2(x+2)[/tex]
[tex]3y+6=-2x-4[/tex]
[tex]3y=-2x-4-6[/tex]
[tex]3y=-2x-10[/tex]
Divide both sides by 3.
[tex]y=\dfrac{-2x-10}{3}[/tex]
[tex]y=-\dfrac{2}{3}x-\dfrac{10}{3}[/tex]
Therefore, the correct option is B.
Answer:
B.) y = negative two-thirds x minus StartFraction 10 Over 3 EndFraction
Step-by-step explanation:
State the domain of the glven relation.
Answers
Answer:
x ≤ -1
Step-by-step explanation:
The domain is the x-values. Since the graph shows all numbers up to -1, the domain would be all numbers less than or equal to -1:
x ≤ -1
What is the absolute value of -47
Answers
Answer:
47
Step-by-step explanation:
If a number x < 0, |x| = -x, in this case, x = -47, therefore |-47| = -(-47) = 47.
Your class is measuring the heights of plants in different locations in the classroom.
The table gives the heights of each plant over 3 weeks. Use the drop-down menus to
complete each statement below about this data,
Answers
Answer:
First part) measuring each plant at the same time each week
Second part) centimeters and the same
Step-by-step explanation:
Answer:
These heights could have been measured by measuring each plant at the same time each week.
The unit of measure for the heights is centimeters. The units must be the same for each data point in order to compare the rates of growth.
Write 5 3/7 as an improper fraction.
Answers
Answer:
The answer is option A
Step-by-step explanation:
[tex]5 \frac{3}{7} [/tex]
Can be written as
[tex] \frac{38}{7} [/tex]
Hope this helps you
Answer:
38/7
Step-by-step explanation:
question: 5*3/7
we should first cross multiply 5 with 7 and add the 3 to the product.
the formula for solving any question like this is :-
( whole no. multiplied with denominator ) + numerator
denominator
here: (5*7)+3
7
Please help
simplify the expression
a²b⁴-b²a⁴/ab(a+b)
Answers
Answer:
ab² - a²b
Step-by-step explanation:
a²b⁴ - b²a⁴ can be factored as a²b²(b² - a²) which becomes a²b²(b + a)(b - a). Since the numerator and denominator both have (a + b) and ab the final answer is ab(b - a) = ab² - a²b.
1) Assume that Mike can walk 3 km per hour. If he had been walking for 5 hours away from the trail, create a table
of values to express how far he walked and graph his progress.
Answers
Answer:
see below for a table; see second attachment for a graph
Step-by-step explanation:
Each of the distance values in km in the table will be 3 times the time value in hours.
The slope of the line on the graph is 3. The practical domain of the distance function is 0 to 5 hours.
Find the angle between the given vectors to the nearest tenth of a
degree.
U = 13i - 8j V = 2i + 9j
Answers
Answer: 109.1 degrees
Step-by-step explanation:
To find the angle between the given vectors, we will use the formula below:
Cos(θ) = (U.V)/ |U|.|V|
Where
U = 13i - 8j
V = 2i + 9j
U.V = (2x13) + (-8×9)
U.V = 26 - 72
U.V = - 46
|U| = sqrt ( 13^2 + 8^2)
= sqrt ( 233) = 15.264
|V| = sqrt( 2^2 + 9^2)
= sqrt ( 85 ) = 9.22
Substitute all the value of the parameters into the formula
Cos ø = -46 / (15.3 × 9.2)
Cos ø = - 46 / 140.72
Cos Ø = - 32687
Find the cos inverse of the value
Ø = cos^-1( -32687)
Ø = 109.079 degrees
Therefore, the angle between the given vectors to the nearest tenth of a degree is 109.1 degrees
Community Theater Owner A community theater currently sells 200 season tickets at $50 each. In order to increase its season-ticket revenue, the theater surveys its season ticket holders to see if they would be willing to pay more. The survey finds that for every $5 increase in the price of a season ticket, the theater would lose 10 season-ticket holders. What action, if any, should the theater owner take to increase revenue? a. Let n be the number of $5 price increases in the cost of a season ticket. Write an expression for the cost of a season ticket after n price increases, and an expression for the number of season-ticket holders after n price increases. b. Use the expressions from part a to create a revenue function, R (n) , from the survey information. c. Graph the revenue function. Be sure to label the axes with the quantities they represent and indicate the axis scales by showing numbers for some grid lines.
Answers
Answer:
the owner should increase prices to increase revenue (up to n=5)a) c(n) = 50+5n; q(n) = 200-10nb) R(n) =50(10+n)(20-n)c) see below for a graphStep-by-step explanation:
a. The cost of a ticket after n price increases of $5 each will be ...
c(n) = 50 +5n
The number of season-ticket holders (q) after n price increases will be ...
q(n) = 200 -10n
__
b. The revenue after n price increases will be ...
R(n) = c(n)·q(n) = (50 +5n)(200 -10n)
R(n) = 50(10 +n)(20 -n)
__
c. See the attachment for a graph
__
d. The theater owner should raise the price of a season ticket to increase revenue. The number of $5 price increases should not exceed 5 if revenue is to increase. Above that number, revenue will decrease.
suppose y varies inversely with x, and y = 6 when x = 3. Find x when y = 12.
Answers
Answer:
1.5
Step-by-step explanation:
[tex]y \: \alpha \: \frac{1}{x} [/tex]
y = k ÷ x
yx = k
y = 6 , x = 3
6 • 3 = k
18 = k
when y = 12 , x = ?
yx = k
12x = 18
x = 18÷12
x = 3/2
x = 1.5
A train traveling at 100 km an hour takes 3 seconds to enter a tunnel and an additional thirty seconds to pass completely through it. Find the length, in kilometers, of the train. Express your answer as a common fraction
Answers
is 4(x+2)+3x+7 equivalent to 7x+14
Answers
Answer:
No equal
Step-by-step explanation:
If you multiply through you get
4x+8+3x+7 which equals
7x+15 which is not equal to 7x+14
Answer:
NoStep-by-step explanation:
Let's solve:
[tex]4(x + 2) + 3x + 7[/tex]
Distribute 4 through the parentheses
[tex] = 4x + 8 + 3x + 7[/tex]
Collect like terms
[tex] = 7x + 8 + 7[/tex]
Add the numbers
[tex] = 7x + 15[/tex]
Hope this helps..
best regards!
Lincy is standing 20 feet from the circular wall of an above ground swimming pool and 49 feet from a point of tangency. Find the radius of the pool.
Answers
Answer:
the radius of the pool is 50.025 feet
Step-by-step explanation:
From the information given:
We can have a schematic view of a diagrammatic illustration in our mind where the distance of the pool to Lincy is (20 + r ) and the distance to the tangent is 49.
So; by using pythagoras theorem, since the radius meets the tangent at a right angle; we have:
[tex]r^2 + 49^2 = ( r + 20 )^2[/tex]
[tex]r^2 +2401 = r^2 + 40r + 400[/tex]
[tex]2401 = 40r + 400[/tex]
[tex]2401- 400 = 40r[/tex]
2001 = 40 r
r = 2001/40
r = 50.025 feet
Help ASAP in this picture
Answers
Answer:
the first choice
Step-by-step explanation:
0.25= 0.25
2/3= 0.3333333
56%= 0.56
0.25<0.33<0.56
0.25=0.25
2/3= 0.333
%56= 0.56
We can calculate E the amount of euros that has the same value as D u.s dollars using the equation E=17/20D. How many euros have the same value as 1 US dollar? How many US dollars have the same value as 1 euro?
Answers
Answer:
You can try substituting the 1's for different variables (E, D) in the formula , to get answers for each.
The value of 2^3 + 4^2 = ___.
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
24
▹ Step-by-Step Explanation
2³ + 4²
= 2 * 2 * 2 → 8
= 4 * 4 → 16
8 + 16 = 24
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
24
Step-by-step explanation:
2³ + 4²
Solve for exponents first.
2³ = 2 × 2 × 2 = 8
4² = 4 × 4 = 16
8 + 16
Addition.
= 24
If tanx = 1, and 0< x < 90 degrees, find cos(x/2)? a. [tex]-\frac{\sqrt{2+\sqrt{2} } }{2}[/tex] b. [tex]\frac{\sqrt{2+\sqrt{2} } }{2}[/tex] c. [tex]\frac{\sqrt{2-\sqrt{2} } }{2}[/tex] d. [tex]-\frac{\sqrt{2}-\sqrt{2} }{2}[/tex]
Answers
Answer:
B is the correct answer.
Step-by-step explanation: If tanx=1, then cosx=√2/2. Use your half angle formulas to plug cosx in, and you should get B as your answer.
IF YOU GET ALL OF THESE CORRECT I WILL MARK YOU BRAINIEST:
-What is an ordered pair?
-What is first in an ordered pair, the x-value or the y-value?
-How do you find the distance between two points in a coordinate plane? -What is the distance between (4,3) and (4, -2)?
Answers
Answer:
1. an ordered pair is a pair or numbers in a specific order. It's a set of points.
2. The x-value is always first in an ordered pair, y-value second
3. The distance between the points is 5 units
Step-by-step explanation:
1. For example, (x,y)
2. no explanation needed
3.You can find the distance of two points by using the distance formula [tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]. To find the distance between (4,3) and (4,-2), we can plug the points into the distance equation. When solved, we get d=5, so the distance between the two points is 5 units.
hope this helps! please give brainliest!!
An ordered pair is a pair of values. The order in which the values appear is very important, since (x, y) is a whole different thing from (y, x).
The first in an ordered pair is the x-value, since mathematics usually goes by the order of the alphabet: a before b, and x before y.
The distance between two points in a coordinate plane is [tex]d = \sqrt{(x1 - x2)^2 + (y1 - y2)^2}[/tex], which is the distance formula.
The distance between (4, 3) and (4, -2)...
d = [tex]\sqrt{(4 - 4)^2 + (3 - (-2))^2}[/tex] = [tex]\sqrt{0^2 + 5^2}[/tex] = [tex]\sqrt{5^2}[/tex] = plus or minus 5.
Since distance can't be negative, the distance between the coordinates is 5 units.
Hope this helps!The sum of two numbers is 20 more than one of the numbers and 18 more than the other number. What are the two numbers?
Answers
Answer:
18 , 20Step-by-step explanation:
Let the numbers be x and y
Sum = x + y
Sum = one number + 20
[tex]x + y = x + 20[/tex]
Cancel equal terms on both sides of the equation.
[tex]y = 20[/tex]
Again,
Finding another number
Sum = other number + 18
[tex]x + y = y + 18[/tex]
Cancel equal terms on both sides of the equation
[tex]x = 18[/tex]
Hence, The two numbers are 18 and 20.
Hope this helps..
Best regards!
Please Answer ASAP: As storm clouds gathered, the temperature fell 4 degrees in 3/4 of an hour. At what rate was the temperature falling? Simplify your answer and write it as a proper fraction, mixed number, or whole number.
Answers
Answer:
[tex]5 \frac{1}{3}[/tex] degrees per hour.
Step-by-step explanation:
If we know that the temperature fell 4 degrees in [tex]\frac{3}{4}[/tex] of an hour, we can set up a proportion to see how much fell in an hour.
[tex]\frac{4}{0.75} = \frac{x}{1}[/tex]
[tex]4 \cdot 1 = 4\\4 \div 0.75 = 5.\overline{33}[/tex]
[tex]5.\overline{33}[/tex] as a fraction is [tex]5 \frac{1}{3}[/tex].
So, the temperature fell at a rate of [tex]5 \frac{1}{3}[/tex] degrees per hour.
Hope this helped!
Answer:
5 1/3
Step-by-step explanation: