Answer:
(x + 3)² = 15
Step-by-step explanation:
Given
x² + 6x - 6 = 0 ( add 6 to both sides )
x² + 6x = 6
To complete the square
add (half the coefficient of the x- term )² to both sides
x² + 2(3)x + 9 = 6 + 9
(x + 3)² = 15
Follow below steps:
The question asks about rewriting the quadratic equation x^2+6x-6=0 by completing the square. To complete the square for an equation of the form ax^2+bx+c=0, we need to add and subtract the square of half the coefficient of x, which is (b/2)^2, to make it a perfect square trinomial.
Here are the steps for completing the square for the given equation:
Divide all terms by the coefficient of x^2 if it is not 1 (in this case, it is already 1).
Move the constant term to the other side of the equation: x^2 + 6x = 6.
Find (b/2)^2, where b is the coefficient of x, which is 6 in this case. So, (6/2)^2 = 9.
Add and subtract this value inside the equation: x^2 + 6x + 9 - 9 = 6.
Write the left-hand side as a perfect square and simplify the right-hand side: (x+3)^2 - 9 = 6.Finish by repositioning: (x+3)^2 = 15.
The equation x^2+6x-6=0 rewritten by completing the square is (x+3)^2 = 15.
What is the area of a circle with a diameter of 16.2 inches?
3.14 for pi
Answer:
Area= 206.202 cm squared
Step-by-step explanation:
Formula for area of Circle=
[tex]\pi r ^{2} [/tex]
Now we will input the value:
[tex]\pi (8.1)^{2} [/tex]
And, calculate the answer
[tex]3.14 \: \times 65.61[/tex]
[tex] = 206.0154[/tex]
Answer:
[tex]area = 206.0154[/tex]
I'm not sure if you need the rounded up answer or not, so I kept the answer in exact form.
The algebra tiles represent the perfect square trinomial x2 + 10x + c.
What is the value of c?
Answer:
c=25
Step-by-step explanation:
x^2 + 10x+c
To find the value of c, take the coefficient of the x term, divide it by 2, then square it
10/2 =5
Then square it
5^2 =25
c=25
3.
A hardware store sells three types of shovels, spade, flat, and square. The spade costs $16.00, the flat costs $9.60, and the square costs $12.80 each. The store keeps an inventory of 80 shovels. They always buy twice as many spade shovels as square. One day, after selling out of shovels, the store had receipts totaling $1,072.00. Find how many of each type of shovel were sold that day.
a. Write a system of equations to represent the information given.
b. Put the system into a matrix. Name the matrix using dimensions.
c. What is the determinant of the coefficients?
d. Use Cramer’s rule to solve the system.
e. If the store doubled all prices and inventory, what would the new matrix be?
Answer:
See explanation
Step-by-step explanation:
Let x be the number of spade shovels, y -the number of flat shovels and z - the number of square showels sold that day.
The store keeps an inventory of 80 shovels, then
x+y+z=80
The store always buy twice as many spade shovels as square, so
x=2z
The total cost of all shovels is
16x+9.60y+12.80z=1,072
a) The system of three equations is
[tex]\left\{\begin{array}{l}x+y+z=80\\ \\x=2z\\ \\16x+9.60y+12.80z=1,072\end{array}\right.[/tex]
b) In matrix form this is
[tex]\left(\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 16&9.60&12.80\end{array}\right)\cdot \left(\begin{array}{c}x\\y\\z\end{array}\right)=\left(\begin{array}{c}80\\0\\1,072\end{array}\right)[/tex]
c) The determinant is
[tex]\left\|\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 16&9.60&12.80\end{array}\right\|=0-32+9.60-0+19.20-12.80=-16[/tex]
d) Find three determinants:
[tex]\left\|\begin{array}{ccc}80&1&1\\ 0&0&-2\\ 1,072&9.60&12.80\end{array}\right\|=0-2,144+0-0+1,536-0=-608[/tex]
[tex]\left\|\begin{array}{ccc}1&80&1\\ 1&0&-2\\ 16&1,072&12.80\end{array}\right\|=0-2,560+1,072-0+2,144-1,024=-368[/tex]
[tex]\left\|\begin{array}{ccc}1&1&80\\ 1&0&0\\ 16&9.60&1,072\end{array}\right\|=0+0+768-0-0-1,072=-304[/tex]
So,
[tex]x=\dfrac{-608}{-16}=38\\ \\y=\dfrac{-368}{-16}=23\\ \\z=\dfrac{-304}{-16}=19[/tex]
e) If the store doubled all prices and inventory, then the new matrix is
[tex]\left(\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 32&19.20&25.60\end{array}\right)\cdot \left(\begin{array}{c}x\\y\\z\end{array}\right)=\left(\begin{array}{c}160\\0\\2,144\end{array}\right)[/tex]
The summer after sophomore year, Haley nannied for a family and earned $2000. She
decided to save it all and deposit it into an account earning 5.8% interest compounded
monthly. When Haley finished college, 6 years later, she decided to use the money to put
deposit on a car. How much money did Haley have?
Answer:
$2,830.09
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 5.8/100
r = 0.058 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 2,000.00(1 + 0.058/12)(12)(6)
A = 2,000.00(1 + 0.004833333)(72)
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $2,000.00 at a rate of 5.8% per year compounded 12 times per year over 6 years is $2,830.09.
The question asks about the amount of money Haley would have after 6 years, saving $2000 in an account earning 5.8% interest compounded monthly. Using the compound interest formula, she would have approximately $2780.73.
Explanation:This question deals with a financial concept known as compound interest. The formula for compound interest is A = P(1+r/n)^(nt), where A is the amount that the principal P has grown to after n number of times compounded over t periods at an interest rate of r. To calculate how much money Haley has, plug in the values: P=$2000, r=5.8/100=0.058, n=12 (since interest is compounded monthly), and t=6 years.
Therefore, the money Haley has is A=$2000 (1+0.058/12)^(12×6) ≈ $2780.73. Thus, after 6 years, Haley has approximately $2780.73, due to the monthly compounded interest of her savings.
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Question 27 of 28
1 Point
What is the slope of the line shown below?
(3,-2)
(2,-4)
Answer:
The slope is 2
Step-by-step explanation:
To find the slope given two points, we use the formula
m = (y2-y1)/(x2-x1)
= (-4--2)/(2-3)
= (-4+2)/(2-3)
= -2/-1
= 2
A. Billy should choose 1/3 of 3/4; he’ll earn 1/15 more.
B. Billy should choose 1/3 of 3/4; he’ll earn 1/20 more.
Answer:ANS.B
Step-by-step explanation:1/3*3/4=3/12=.25 THE BETTER DEAL
3/12-2/10=30/120-24/120=6/120=1/20 ANS.B
PLEASE HELP
if AD=2/3AB, the ratio of the length BC to the length of DE is what?
A. 1/6
B. 1/4
C. 3/2
D. 3/4
Answer:
c
Step-by-step explanation:
Answer:
C.) 3/2
Explanation:
PLATO
y=12x + 18
If the value of x increases by 1, what happens to the value of y?
Answer:
Hello everyone, the answer is 2, edge 2022. Hoped I helped :)
Step-by-step explanation:
The parking rates @ the hospital's parking garage are 50 cents for the first hour and 25 cents for each additional hour. If juan parks in the garage for 8 hours, how much will the total charge for parking be?
Answer:
$2.25Step-by-step explanation:
[tex]n-number\ of\ hours\\\\\text{The equation of the function:}\\\\f(n)=0.25(n-1)+0.50\\\\\text{for n = 8:}\\\\f(8)=0.25(8-1)+0.50=0.25(7)+0.50=1.75+0.50=2.25[/tex]
I need help please.
Answer:
31 / 12
Step-by-step explanation:
To get the perimeter, just add up all the sides of the parallelogram, so 5/8 + 5/8 + 2/3 + 2/3 = 31/12
What is the solution set for the open sentence, using the given replacement set ? 5x−7=8 ; {1, 2, 3, 4} ? x = 1 x = 2 x = 3 x = 4
Answer:
x = 3
Step-by-step explanation:
5x−7=8
Add 7 to each side
5x-7+7 = 8+7
5x = 15
Divide by 5
5x/5 = 15/5
x=3
Eduardo’s average speed on his commute to work was 55 miles per hour. On the way home, he hit traffic and only averaged 40 miles per hour. If the round trip took him 1.25 hours, which expression represents the distance, in miles, for his trip home that is missing from the table?
t – 1.25
1.25 – t
40(1.25 – t)
40(t – 1.25)
Answer:
40(1.25-t)
Step-by-step explanation:
There are 3 components to consider; time, speed and distance
Time and Speed are given.
The distance has to be calculated.
Speed to work = 55 miles per hourTime to work = 1.25-TSpeed to home = 40 miles per hourTime to home = 1.25-t Total Time = T + t = 1.25Distance for trip to home
Speed = Distance/Time
40 = Total Distance/1.25-t
Total Distance = 40(1.25-t)
Therefore, 40(1.25-t) is the correct answer.
!!
Answer:
Option C. 40(1.25 - t)
Step-by-step explanation:
Eduardo's average speed on his commute to work = 55 miles per hour
On the way home his average speed was = 40 miles per hour
Round trip took him 1.25 hours.
Let t be the total time taken by Eduardo for the trip to work.
Then time taken on the way home = Total time for round trip - Time taken from work to home
= (1.25 - t) hours
Average speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]
40 = [tex]\frac{\text{Distance}}{(1.25-t)}[/tex]
Now the distance for his trip home can be represented by
Distance = 40(1.25 - t)
Option C. 40(1.25 - t) will be he answer.
What is the average rate of change between:
x = 1 and x = 2? 2
x = 2 and x = 3? 4
x = 3 and x = 4? 8
Answer:
2
4
8
increases
Step-by-step explanation:
The average rate of change between x-values can be calculated by using the formula [tex](f(x2) - f(x1))/(x2 - x1).[/tex]. For x = 1 and x = 2, the rate is 2; for x = 2 and x = 3, the rate is -4; and for x = 3 and x = 4, the rate is 8.
Explanation:The question asks about the average rate of change between certain points on an x-axis. In mathematics, the average rate of change is calculated by dividing the change in the output by the change in the input. In other words, it reflects how much the function's value (y-coordinate) changes when the input (x-coordinate) moves 1 unit.
To find the average rate of change, use the formula [tex](f(x2) - f(x1))/(x2 - x1).[/tex] In this case:
The average rate of change between x = 1 (value 2) and x = 2 (value 4) would be [tex](4 - 2) / (2 - 1) = 2.[/tex]Between x = 2 (value 4) and x = 3 (value 0), it would be ([tex]0 - 4) / (3 - 2) = -4.[/tex]Lastly, between x = 3 (value 0) and x = 4 (value 8) it would be [tex](8 - 0) / (4 - 3) = 8.[/tex]Learn more about Average Rate of Change here:https://brainly.com/question/34745120
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Which graph shows the solution to the inequality -3x-7 <20?
-
105
10
-10
The solution to the inequality is [tex]\(x > -9\)[/tex]. Therefore, the option b is correct.
To solve the inequality [tex]\(-3x - 7 < 20\)[/tex], we'll isolate the variable [tex]\(x\)[/tex] step by step.
Given inequality:
[tex]\[ -3x - 7 < 20 \][/tex]
Add 7 to both sides of the inequality:
[tex]\[ -3x < 20 + 7 \ \\\\\\[ -3x < 27 \][/tex]
Now, divide both sides by [tex]\(-3\)[/tex]. Remember, when dividing or multiplying by a negative number, we need to reverse the inequality sign:
[tex]\[ x > \frac{27}{-3} \ \\\\\\[ x > -9 \][/tex]
The solution to the inequality is [tex]\(x > -9\)[/tex]. This means that any value of [tex]\(x\)[/tex] that is greater than -9 satisfies the inequality [tex]\(-3x - 7 < 20\)[/tex].
Multiply these polynomials and simplify. Enter your response in standard form (-6y + 8y4 – 5)(y2 – 11y)
Answer: The required simplified answer in standard form is [tex]8y^6-88y^5-6y^3+61y^2+55y.[/tex]
Step-by-step explanation: We are given to multiply the following polynomials and write the answer is standard form :
[tex]M=(-6y+8y^4-5)(y^2-11y)~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To multiply the given polynomials, we need to multiply each term of one polynomial to each term of the other polynomial.
From (i), we have
[tex]M\\\\=(-6y+8y^4-5)(y^2-11y)\\\\=y^2(-6y+8y^4-5)-11y(-6y+8y^4-5)\\\\=-6y^3+8y^6-5y^2+66y^2-88y^5+55y\\\\=8y^6-88y^5-6y^3+61y^2+55y.[/tex]
Thus, the required simplified answer in standard form is [tex]8y^6-88y^5-6y^3+61y^2+55y.[/tex]
Answer: 8y^6- 88y^5- 6y^3 +61y^2 +55y
Put the following steps for calculating net worth in the correct order
Step-by-step explanation:
1.List your assets (what you own), estimate the value of each, and add up the total.
2.List your liabilities (what you owe) and add up the outstanding balances.
3.Subtract your liabilities from your assets to determine your personal net worth.
If f(x) = 2x - 8 and g(x) = x4, what is (gºf)(5)?
Answer:
(g°f)x =16 when x = 5
Step-by-step explanation:
It might be easier to understand if you wrote this the other acceptable way.
g(x) = x^4
f(x) = 2x - 8
g(f(x)) means that in g(x) wherever you see and x you put f(x)
g(f(x)) = (f(x) ) ^ 4 Now put in the general value for f(x)
g(2x - 8) = (2x - 8)^4
You really don't want to expand this (although it would give you the right answer eventually).
g(2*5 - 8) = (2 * 5 - 8)^4
g(2*5 - 8) = (10 - 8)^4
g(2*5 - 8) = 2^4
Answer 16
A color printer prints 10 pages in 6 minutes.
How many minutes does it take per page?
Answer:
1 2/3 pages per minute
Step-by-step explanation:
1) 10/6 = 1.6666666666666 = 1 2/3
Final answer:
To calculate the printing time per page for a color printer, divide the total printing time by the number of pages. In this case, it takes 0.6 minutes to print one page.
Explanation:
To find out how many minutes it takes to print one page on a color printer that prints 10 pages in 6 minutes, we can use time quantification. We divide the total time taken to print the pages by the number of pages printed. So, performing the calculation:
Identify the total time taken for a known number of pages: 6 minutes for 10 pages.
Divide the total time by the number of pages to find the time per page: 6 minutes \/ 10 pages = 0.6 minutes per page.
Hence, the printer takes 0.6 minutes to print one page.
Need help on inequality.
10 less than or equal to - 2/3 (9+12b)
Answer:
b less than or equal to -2.
Step-by-step explanation:
- 2/3 (9+12b) ≥ 10
-6 - 8b ≥ 10
-8b ≥ 16
b ≤ -2. ( Note the inequality sign flips as we are dividing by a negative).
Simplify this expression.
3w+7-5r+2-r
Answer:
[tex]\displaystyle 3w+9-6r[/tex]
Step-by-step explanation:
Distributive property: A(B+C)=AB+AC
Group like terms.
[tex]\displaystyle-5r-r+3w+7+2[/tex]
Add the numbers from left to right.
[tex]\displaystyle-5r-r=-6r[/tex]
[tex]\displaystyle -6r+3w+7+2[/tex]
Finally, add the numbers from left to right, to find the answer.
[tex]2+7=9[/tex]
[tex]\displaystyle 3w+9-6r[/tex], is the correct answer.
Hope this helps!
Answer:
3w - 6r +9
Step-by-step explanation:
3w+7-5r+2-r
Combine like terms
3w -5r-r +7+2
3w - 6r +9
What is the perimeter of an equilateral triangle if each side is (x+3)? Write as a simplified expression
Answer:
3x + 9
Step-by-step explanation:
An equilateral triangle has all sides equal
Perimeter = 3 × (x + 3)
3x + 9
Multiply the polynomials.
(x + 4)(x^2 - 5x+3)
Answer:
x^3 - x^2 - 17x + 12
Step-by-step explanation:
To multiply two polynomials together, first multiply each term of one polynomial by each term of the other polynomial. Then, collect like terms.
(x + 4)(x^2 - 5x + 3) =
Multiply x by each term of x^2 - 5x + 3. Multiply 4 by each term of x^2 - 5x + 3.
= x^3 - 5x^2 + 3x + 4x^2 - 20x + 12
Now collect like terms and write them in descending order of degree.
= x^3 - x^2 - 17x + 12
Answer:
x^3-x^2-17x+12
Step-by-step explanation:
There are 2 cups in 1 half quart of milk. How many cups are in 1 quart of milk?
There are
cups in 1 quart of milk.
Final answer:
There are 4 cups in 1 quart of milk.
Explanation:
In 1 half quart of milk, there are 2 cups. To find out how many cups are in 1 quart of milk, we can set up a proportion:
2 cups / 1 half quart = x cups / 1 quart
Cross multiplying, we get:
2 * 1 quart = 1 half quart * x cups
2 quarts = 0.5 quarts * x cups
Dividing both sides by 0.5 quart, we find that:
x = 2 * 2 = 4
Therefore, there are 4 cups in 1 quart of milk.
A camper attaches a rope from the top of her tent, 4 feet above the ground, to give it more support. If she stakes the rope to the ground 6 feet from the middle of her tent, about how long is the rope from the ground to the tent?
Answer: 7.2
Step-by-step explanation:
Use pythag. here: a(a)+b(b)=c(c)
4(4)=16
6(6)=36
16+36= 52
The square root of 52 is your answer: 7.21110255093. You can round this to 7.2
Given A = {(1, 3)(-1, 5)(6,4)}, B = {(2,0)(4, 6)(-4,5)(0, 0)) and C = {(1, 1)(0, 2)(0, 3)(0, 4)(-3,5)}, answer the following multiple
choice question:
From the list of sets A, B, and C, state the domain of set B.
Domain of set B: {0, 6,5}
Domain of set B: {2, 4,-4, 0}
Set B does not have a domain
Answer:
"Domain of set B: {2, 4,-4, 0}"
Step-by-step explanation:
When it the set A,B,C (and others) are given in this form it means that the coordinate pairs are the domain and range of each set, respectively.
The first coordinate is part of the domain (x) and the second coordinate is part of the range (y).
For example, the domain of A is all the numbers that are the first in each coordinate pair, so domain of A would be 1, -1, and 6.
Likewise, the domain of B would be 2, 4, -4, and 0.
Hence,
Domain of set B: {2, 4,-4, 0} -- is the correct answer.
How many terms are in the binomial expansion of (3x + 5)9? 8 9 10 11
Answer: 10
Step-by-step explanation:
We know that in the binomial expansion of [tex](a+b)^n[/tex], the total number of terms = n+1
For the binomial expansion of [tex](3x + 5)^9[/tex] , n= 9
Then, the total number of terms in binomial expansion of [tex](3x + 5)^9[/tex] will be :-
[tex]n+1=9+1=10[/tex]
Hence, there are 10 terms are in the binomial expansion of [tex](3x +5)^9[/tex].
which best describes how to add 9.73 and 21.6?
A. align the digits on the left digit.
add from left to right, regrouping as necessary.
B. Align the digits on the right digit.
add from right to left, regrouping as necessary.
C. align the digits on the decimal point.
add from left to right, regrouping as necessary.
D. align the digits on the decimal point.
add from right to left, regrouping as necessary.
In order to add the numbers 9.73 and 21.6 correctly, follow the steps below:
Step 1: Write the numbers so that the decimal points are aligned. If the numbers have a different number of decimal places, you can add zeros to the end of one of the numbers so that they both have the same number of decimal places. This doesn't change the value of the number, but it makes them easier to add.
```
9.73
+21.60
```
Step 2: You begin adding from the rightmost digit and move to the left, regrouping (carrying over) as necessary.
Starting with the rightmost decimal digits, you have:
```
3 (from 9.73)
+ 0 (from 21.60 because we added a zero to match the number of decimal places)
```
Adding these together, you simply get 3 since 3 + 0 = 3.
Step 3: Now add the second rightmost decimal digits:
```
7 (from 9.73)
+ 6 (from 21.60)
```
Adding these together, 7 + 6 = 13, so you write down the 3 and carry over the 1 to the next higher place value.
Step 4: Add the digits to the left of the decimal point next, remembering to add any carried over value:
```
1 (carried over from the previous step)
+ 9 (from 9.73)
+ 1 (from 21.60, there's no decimal here but we align based on the decimal point)
```
This gives us 1 + 9 + 1 = 11. So we place the 1 right to the left of the decimal point and carry over the other 1.
Step 5: Continue to the next highest place value:
Since there is no other digit in 9.73 at this place value, we can simply add what we have:
```
1 (carried over from the previous step)
+ 0 (since there is no other digit in 9.73)
+ 2 (from 21.60)
```
This gives us 1 + 0 + 2 = 3.
Now, combine all of the numbers we've placed:
```
31.33
```
So, the correct way to add 9.73 and 21.6 is to align the digits on the decimal point and add from right to left, regrouping as necessary. This corresponds to answer choice D.
Which is an equation for the nth term of the sequence?
12, 15, 18, 21, ...
Question 1 options:
a)
= 12n + 3
b)
= 3n + 9
c)
= n + 3
d)
= 9n + 3
Answer: The correct option is (B) [tex]a_n=3n+9.[/tex]
Step-by-step explanation: We are given to select the equation that represents the nth term of the following sequence :
12, 15, 18, 21, . . .
We see that
the given sequence is an arithmetic one with first term a = 12 and common difference d given by
d = 15 - 12 = 18 - 15 = 21 - 18 = . . . =3.
We know that
the nth term of an arithmetic sequence with first term a and common difference d is given by
[tex]a_n=a+(n-1)d.[/tex]
Therefore, the nth term of the given sequence is
[tex]a_n=a+(n-1)d=12+(n-1)\times3=12+3n-3=3n+9.[/tex]
Thus, the required nth term of the given sequence is [tex]a_n=3n+9.[/tex]
Option (B) is CORRECT.
Help me... :/
Find the measure of each exterior angle of a regular 45-gon.
Answer:
7740° / 45
Step-by-step explanation:
The sum of the interior angles is given by this formula: (n - 2) * 180°. So a regular 45-gon would have interior angles that add up to: (45 - 2) * 180°. = 43 * 180°. = 7740°. Now divide that by the 45 angles to find the measure of one interior angle
hope that helped :(
The measure of each exterior angle of a regular 45-gon is calculated using the formula: Exterior Angle = 360° / Number of Sides. Hence, each exterior angle of a 45-gon measures 8°.
Explanation:In mathematics, the measure of each exterior angle of a regular polygon can be found using the formula: Exterior Angle = 360° / Number of Sides. So, to find the measure of an exterior angle in a 45-sided shape, or 45-gon, you would perform the calculation: 360° / 45 = 8°.
This indicates that each exterior angle of a regular 45-gon measures 8 degrees. This is a key concept to remember when working with regular polygons, as it can be used to determine other characteristics of the shape such as the sum of the exterior angles, which in any polygon is always 360°.
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A tree that is 14 feet tall casts a shadow that is 30 feet long. Find the angle of the elevation from the top of the shadow to the top of the tree. Round to the nearest degree.
Let x = angle we must find
tan x = 14/30
arctan(tan x) = arctan(14/30)
x = 25.0168934781
Answer: 25 degrees