To solve the equation 5x(x+6) = -50 by completing the square, we first isolate the quadratic term and then add the square of half the coefficient of x to both sides of the equation. Taking the square root gives us the solution x = -3 + i and x = -3 - i.
Explanation:
To solve the equation by completing the square, we first need to isolate the quadratic term on one side of the equation. So, let's distribute the 5x to get 5x^2 + 30x = -50. Next, we move the constant term to the other side and divide the equation throughout by the leading coefficient to get x^2 + 6x + 10 = 0.
Now, we can complete the square by adding the square of half the coefficient of x (which is 3) to both sides of the equation. This gives us (x + 3)^2 + 10 - 9 = 0, which simplifies to (x + 3)^2 + 1 = 0.
Taking the square root of both sides, we get x + 3 = ±√(-1), which means x = -3 ± i. Hence, the solution to the equation is x = -3 + i and x = -3 - i.
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tyler can shovel the driveway in 2 hours. dakota can complete the job in 90 minutes. if they work together, how long will it take
Write the expression for a number used as a factor fifteen times being multiplied by a number used as a factor ten times. Then, write the product as one power.
The expression for a number used as a factor fifteen times being multiplied by a number used as a factor ten times is: [tex]X^{15} \times X^{10} = X^{25}[/tex]
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.
We need to write the expression for a number used as a factor fifteen times being multiplied by a number used as a factor ten times.
Then, also write the product as one power.
This is exponents so, a number used as a factor fifteen times is X^15.
Then we have to multiplied by a number used as a factor ten times is X^10.
Therefore, the final expression form as;
[tex]X^{15} \times X^{10} = X^{25}[/tex]
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What can 16 over 49 be simplified to?
There is a special at the store: $34 for 7 roses. Harry is trying to figure out if it's a good deal. Help Harry figure out the unit price (round to 2 decimal places)
$6,285÷y=700 y is about
If a player always gets three cards, describe two different ways to recieve a score of 7.
Answer:
1 + 3 + 3 = 7
5 + 1 + 1 = 7
Step-by-step explanation:
If a player have the three cards. Each card will have a number and we have to find the numbers on each card that total 7.
Let card 1 gets 1
Then other two cards may have 3 and 3
So, 1 + 3 + 3 = 7
Now we take another combination which totals 7
5 + 1 + 1 = 7
Therefore, there may be two different ways are
1 + 3 + 3 = 7
5 + 1 + 1 = 7
math question down below
Which expression is equivalent to −2.6+(−2.9)+(−7.1) ?
Answer:
-12.6
Step-by-step explanation:
To evaluate the given expression
-2.6+(−2.9)+(−7.1, first we will open out the brackets and multiply the signs. Before that, we must take note of the following sign operations
-×- = +
-×+ = -
+×- = -
+×+ = +
The equation above becomes;
-2.6-2.9-7.1 (all the signs are now minus since the product of plus and minus sign gives a minus sign)
(-2.6-2.9)-7.1
= -5.5-7.1
= -12.6
Since all the values in the equation are negative values, our resulting answer will be a negative value.
During Tracy’s trip across the country , she traveled 2884 miles . Her trip took
What is the equation in point slope form of the line that passes through the point (2,6) and has slope of 5?
A: y+2=5(x+6)
B: y-6=5(x-2)
The equation of the line that passes through the point (2,6) and has slope of 5 is Option B:
y - 6 = 5 ( x - 2 )
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
Given data ,
Let the point be P( x₁ , y₁ ) = P( 2 , 6 )
Slope m = 5
Now , the equation of line is given by the equation
y - y₁ = m ( x - x₁ )
Substituting the values of x₁ , y₁ and m in the equation , we get
y - 6 = 5 ( x - 2 )
Therefore , the equation of the line is y - 6 = 5 ( x -2 )
Hence , equation of the line that passes through the point (2,6) and has slope of 5 is y - 6 = 5 ( x - 2 )
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GIVEN: ab perpendicular to BC AND DC PERPENDICULAR TO BC
AC = BD
PROVE:AB =DC
Proofs
Answer with Step-by-step explanation:
We are given that AB is perpendicular to BC and DC perpendicular to BC.
AC=BD
We have to prove that AB=DC
In triangle ABC and triangle DCB
AC=BD (Given)
[tex]\angle B=\angle C=90^{\circ}[/tex]
[tex]BC=BC[/tex]
Reason:Reflexive property
[tex]\triangle ABC\cong \triangle DCB[/tex]
Reason:RHL postulate
[tex]AB\cong DC[/tex]
Reason:CPCT
Therefore, AB=DC when two sides are congruent then the sides are equal.
Hence, proved.
Jason uses the polynomial identity (x−y)^2=x^2−2xy+y^2 to show that 6² = 36.
What is 156.16 divided by 8
Is 4.25 a rational number integer or whole number??
4.25 is a rational number
A rational number is a number that can be expressed as a fraction of two integers
Examples of rational numbers are , [tex]\frac{1}{4} \frac{2}{3}[/tex]
4.25 can be rewritten as [tex]4\frac{1}{4}[/tex]
An integer is a number without fractions or decimals
For example, integers are 2, - 1000
A whole number is a number that is a positive integer. It does not include negative numbers, fractions or decimals.
Examples are 1, 2, 10
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8439 divided by 245 with remainder
Answer:
The remainder of 8439 divided by 245 is 109.
Step-by-step explanation:
Given two numbers as 8439 and we have to divide it by 245.
That is , Dividend = 8439
Divisor = 245
Solution:
Using division algorithm,
Dividend = ( Divisor * Quotient )+Remainder
8439 = (245*34)+Remainder
8439 =8330+Remainder
Taking 8330 to other side to find the remainder, we have
8439 -8330 = Remainder
109 = Remainder
Thus The remainder of 8439÷245 is 109.
help me divide y over x??
Your office manager has given you a budget of $30,000 to replace the old computers in your office with new ones. Each new computer will cost $550. You make a quick count and determine that 15 computers will need to be replaced. How much money will be left (per week) for the next six weeks?
1) 550 x 15 = 8250 (First you want to get the total cost of the computers)
2) 30,000 - 8250 = 21,750 (Then you want to subtract that by 30,000 to see how much money is left over)
3) 21,750/6 = 3625 (Then divide by 6 ,by the weeks, and get your answer)
Answer: $3625
Danielle has a CD at crossland bank. she invest $22,350 for four years at 4.55% interest. compounded monthly. What is her ending balance? How much interest did she make?
Answer: Her ending balance is $26,703.837 and her interest is $4,353.837
Step-by-step explanation:
First year,
p =22350 R = 4.55 T = 1
Interest = PRT/100
= 22350 × 4.55 × 1 / 100
=$1016.925
P = $22350 + $1016.925 = $23366.925
For the 2nd year,
I = $23366.925 × 4.55 × 1 / 100
=$1063.195
p= $23366.925 + $1063.195 = $24,430.12
For the 3rd year,
I = $24,430.12 × 4.55 × 1 / 100
= $1111.57
p = $24,430.12 + $1111.57 = $25,541.68
For the 4th year;
I = $25541.68 × 4.55 × 1 / 100
= $1,162.147
P = $ 25541.69 + $1,162.147 = $26,703.837
Therefore th ending balance is $26,703.837
Her compound interest is , $26,703.837 - $22350 =$4,353.837
Which statement is true?
A)
0.4 is less than 0.07 because 4 is less than 7.
Eliminate
B)
0.4 is less than 0.07 because 40 is less than 70.
C)
0.4 is greater than 0.07 because 70 is greater than 40.
D)
0.4 is greater than 0.07 because 40 is greater than 7.
Rita ran 5 miles in 48 minutes .What was her time per mile?
Alice serote the prime factorization of 40 as 2x2x4x5. is she correct? if not what is the prime factorization of 40? explain
Answer:
2.2.2.5
Step-by-step explanation:
I need help on 4, 5, and 6
Part A: Using the graph above, create a system of inequalities that only contains points D and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)
Part B: Explain how to verify that the points D and F are solutions to the system of inequalities created in Part A. (3 points)
Part C: Chickens can only be raised in the area defined by y > 2x − 2. Explain how you can identify farms in which chickens can be raised. (2 points)
The following question has two parts. First, answer part A. Then, answer part B.
Part A
A high school athlete ran the 100 meter sprint in 13.245 seconds. Round the time to the nearest tenth. Enter the answer in the box.
Part B
Explain how you arrived at the answer. Include any rules that you followed.
8) It costs a band $8 per T-shirt produced. At a small festival the band gives away 10 T-shirts, and sells others for $20 each. Their total T-shirt-related profits (taking into account those they gave away) is $304, how many T-shirts did the band sell?
The table shows the distances and times that four rowboats traveled. Which rowboat was the fastest?
Answer:
Rowboat C traveled the fastest.
Step-by-step explanation:
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Which graph represents the solution set of the system of inequalities?
{3y≤2x+62x+y>0
we have
[tex]3y\leq 2x+6[/tex] ---> inequality A
[tex]2x+y > 0[/tex] ---> inequality B
using a graphing tool
see the attached figure
The solution is the shaded area
the answer in the attached figure
Find the product and explain the process and reasoning of $0.79*3.7
In a recent year, the population of California was about 2.52 x 10^7 people. Its land area is about 4.05 x 10^5 km^2. What was the average number of people per square kilometer? Write your answer in scientific notation.
PLEASE I NEED HELP ASAP!!!!!!!!!!!!
The average number of people per square kilometer in California is [tex]6.22 \times 10^1.[/tex]
To find the average number of people per square kilometer in California, we divide the total population by the land area.
Given:
Population of California = [tex]2.52 \times 10^7[/tex] people
Land area of California = [tex]4.05 \times 10^5 km^2[/tex]
Calculate the population density.
Population density = Population / Land area
Population density = [tex](2.52 \times 10^7) / (4.05 \times 10^5) people/km^2[/tex]
Divide the numbers and simplify.
Population density = (2.52 / 4.05) x 10^(7-5) people/km^2
Population density = [tex]0.622 \times 10^2 people/km^2[/tex]
Rewrite in scientific notation.
Population density = [tex]6.22 \times 10^1 people/km^2[/tex]
So, the average number of people per square kilometer in California is [tex]6.22 \times 10^1[/tex].
expand and simpilify
(3x-2)^2-(x+6)(x-8)