What is an equation of the line that passes through the points (-6, 5) and (6, 7)?
Answers
Answer:
[tex]y=\frac{1}{6}x+6[/tex]
Step-by-step explanation:
Let [tex](x_1,y_1)\rightarrow(-6,5)[/tex] and [tex](x_2,y_2)\rightarrow(6,7)[/tex]
Determine slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\ \\m=\frac{7-5}{6-(-6)}\\ \\m=\frac{2}{6+6}\\ \\m=\frac{2}{12}\\ \\m=\frac{1}{6}[/tex]
Use either ordered pair to find the y-intercept
[tex]y=mx+b\\\\7=\frac{1}{6}(6)+b\\\\7=1+b\\\\6=b[/tex]
Final equation
[tex]y=\frac{1}{6}x+6[/tex]
Related Questions
Find the value of b.
A 57
B 50
C 123
D 61.5
Answers
Answer: The answer is 50
Step-by-step explanation:
I did the test
Which expression is equivalent to
Answers
Answer:
10³⁰
Step-by-step explanation:
firstly working out without the power of 3
[tex]( \frac{10 {}^{15} }{10 {}^{5} } )[/tex]
this is the same as 10¹⁵ ÷ 10⁵
here the bases are the same and it's division so we subtract the powers
15 - 5 = 10
10¹⁵ ÷ 10⁵ = 10¹⁰
we are left with (10¹⁰)³, multiply the powers
10 × 3 = 30
final answer = 10³⁰
Hey there!
(10^15/10^5)^3
10^15
= 1,000,000,000,000,000
10^5
= 10 * 10 * 10 * 10 * 10
= 100 * 100 * 10
= 10,000 * 10
= 100,000
(1,000,000,000,000,000/100,000)^3
= (10,000,000,000)^3
= 10,000,000,000 * 10,000,000 * 10,000,000
= 100,000,000,000,000,000 * 10,000,000
= 10^30
Therefore, your answer is: 10^30
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Polynomials help me please
Answers
Answer:
(x³+2x²-2x)-(-3x³+4x²-x)
(x³+2x²-2x)+(3x³-4x²+x)
(x³+3x³)+(2x²-4x²)+(-2x+x)
4x³-2x²-x ----you may write till here.
But, if not satisfied, factorize it
x(4x²-2x-1)
please mark brainliest
A swimming pool is to be constructed in a 1,408-ft2 backyard. There is to be a fence that will surround a 12-by-24-foot pool. The pool builder wants to build a concrete paver deck of a uniform width, x, surrounding the pool and filling the entire area of the backyard. What is the width of the pool deck?
9 ft
10 ft
11 ft
12 ft
Answers
Answer:
B. 10 ftStep-by-step explanation:
Let the width of the pool deck be x.
Dimensions of the pool are 12 + 2x and 24 + 2x.Total area is 1408 ft².We have equation:
(12 + 2x)(24 + 2x) = 140812*24 + 12*2x + 24*2x + (2x)² = 1408288 + 72x + 4x² = 14084x² + 72x + 288 - 1408 = 04x² + 72x - 1120 = 0x² + 18x - 280 = 0x² - 10x + 28x - 280 = 0x(x - 10) + 28(x - 10) = 0(x - 10)(x + 28) = 01)
x - 10 = 0x = 102)
x + 28 = 0x = - 28 (discarded as negative)Correct choice is B
The width of the pool deck is 10 feet (x = 10).
So, the answer is option B: 10 ft.
Here, we have to find the width of the pool deck, we need to calculate the total area occupied by the pool and the deck and then find the value of x that makes the total area equal to 1,408 square feet.
First, let's calculate the area of the pool.
The pool is 12 feet by 24 feet:
Area of the pool = Length × Width
Area of the pool = 12 ft × 24 ft
Area of the pool = 288 ft²
Now, we want to add the deck around the pool.
The length and width of the entire area (pool + deck) will be (12 + 2x) feet and (24 + 2x) feet, respectively, because we add x feet to both sides of the pool.
Area of the entire area (pool + deck) = (12 + 2x) ft × (24 + 2x) ft
We want this area to equal 1,408 square feet:
(12 + 2x) ft × (24 + 2x) ft = 1,408 ft²
Now, we can solve for x:
(12 + 2x) × (24 + 2x) = 1,408
Expand the equation:
288 + 48x + 24x + 4x² = 1,408
Combine like terms:
4x² + 72x - 1,120 = 0
Now, let's solve this quadratic equation for x.
We can either factor it or use the quadratic formula:
Using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
where a = 4, b = 72, and c = -1,120.
x = (-(72) ± √(72² - 4 * 4 * -1,120)) / 2 * 4
x = (-72 ± √(5,184 + 17,920)) / 8
x = (-72 ± √23,104) / 8
x = (-72 ± 152) / 8
Now, we have two possible solutions:
x = (-72 + 152) / 8
x = 80 / 8
x = 10
x = (-72 - 152) / 8
x = -224 / 8
x = -28
Since we are interested in a positive width for the deck, the width of the pool deck is 10 feet (x = 10).
So, the answer is option B: 10 ft.
To learn more on Area click:
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In a chess club, 75% of the members are boys. Of these boys, 8% have hazel eyes. If 6 boys have hazel eyes, how many people are in the chess club.
Define a variable for the unknown quantity.
Answers
Percentage
8% x 75%.x = 6
0.06x = 6
x = 100
Find the measure of AB.
A 21
B 14
C 20
D 22
Answers
Your cell phone costs $50 a month plus $0.25 for each text message, (t). How much would your monthly bill be if you sent 40 text messages?
Your total monthly bill would be $____
if you sent 40 text messages.
Answers
Answer:
$60
Step-by-step explanation:
40 text messages × .25 each = $10. Plus the $50 per month is $60.
Answer:
it should be $60 a month
What is the distance between (-4, 2) and (-4, -4)
Answers
Answer:
use Pythagoras theorem and a graph to be fluent in this
Step-by-step explanation:
answer is 2sqr(7)
10
Given the function f(x) = x + 1 and the linear function g(x), which function has a greater value when x = 2?
f(x) is greater.
g(x) is greater.
f(x) and g(x) are the same when x = 2.
g(x) is undefined when x = 2.
Answers
Answer:
F(x) is greater.
Step-by-step explanation:
f(2) = 2 + 1
(2,3)
Have a good day!
Answer:
F(x) is greater.
Step-by-step explanation:
Solve the following recurrence relation:
[tex]A_{n}=a_{n-1}+n; a_{1} = 0[/tex]
Answers
By iteratively substituting, we have
[tex]a_n = a_{n-1} + n[/tex]
[tex]a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)[/tex]
[tex]a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)[/tex]
and the pattern continues down to the first term [tex]a_1=0[/tex],
[tex]a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))[/tex]
[tex]\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)[/tex]
[tex]\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k[/tex]
Recall the formulas
[tex]\displaystyle \sum_{n=1}^N 1 = N[/tex]
[tex]\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2[/tex]
It follows that
[tex]a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2[/tex]
[tex]\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1[/tex]
[tex]\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}[/tex]
Use the figure to solve the inequality
Answers
Answer:a hope this helps
Step-by-step explanation:
Help need because i´m stuck
Answers
Answer:
594 in²
Step-by-step explanation:
There are several ways to do this.
divide the shaded region into rectangles, and add their areasdivide the shaded region into trapezoids and add their areassubtract the white space from a bounding rectangle.Given the way the figure is dimensioned, the last strategy is the easiest.
A rectangle that surrounds the entire figure will be 36 inches wide and 22 inches high. The white space rectangle in the lower right corner is shown to be 18 inches wide and 11 inches high.
The area of a rectangle is the product of its length and width:
A = LW
So the difference in area between the "bounding" rectangle and the whitespace rectangle is ...
shaded area = (36 in)(22 in) -(18 in)(11 in) = 792 in² -198 in²
shaded area = 594 in²
_____
Additional comment
You can also recognize that the dimensions of the cut out corner are each half the overall dimensions. That means the shaded area is 3/4 of the overall "bounding" rectangle. There are several ways you can make use of that fact.
Dan has a board that is
8 3/4
feet long. He cuts off
4 5/6
feet and says he has
4 1/12
feet left. Which of the following explains whether Dan is correct?
Answers
Answer:
He is wrong.The answer is 3 11/12.Step-by-step explanation:
Given equation:
8 3/4 - 4 5/6Simplify:
8 9/12 - 4 10/12Solve:
8 - 4 = 4= 9/12 - 10/12= 21/12 - 10/12= 11/12= 3 + 11/12= 3 11/12.He is wrong.
He was off by 3 digits.
The area of a parallelogram is 48 ft. If the base of the parallelogram is 8 feet, what is its height?
8 feet
6 feet.
5 feet
7 feet
Answers
[tex]\textit{area of a parallelogram}\\\\ A=bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ A=48\\ b=8 \end{cases}\implies 48=8h\implies \cfrac{48}{8}=h\implies 6=h[/tex]
What do I supposed to do ?
Answers
Answer:
Just add the 2 fractions that were mentioned
Step-by-step explanation:
turn 6 1/2 into an improper fraction and then add it to 5/8 by finding a common denominator
so it would be like -
13/2 + 5/8 = 52/8 + 5/8 = 57/8 = 7 1/8
Answer:
6 1/2 + 5/8 = 57/8 = 7 1/8 = 7.125
Step-by-step explanation:
Conversion a mixed number 6 1/2
to a improper fraction: 6 1/2 = 6 1/2 = 6 · 2 + 1/2 = 12 + 1/2 = 13/2
To find a new numerator:
a) Multiply the whole number 6 by the denominator 2. Whole number 6 equally 6 * 2/2 = 12/2
b) Add the answer from previous step 12 to the numerator 1. New numerator is 12 + 1 = 13
c) Write a previous answer (new numerator 13) over the denominator 2.
Six and one half is thirteen halfs
Add: 13/2 + 5/8 = 13 · 4/2 · 4 + 5/8 = 52/8 + 5/8 = 52 + 5/8= 57/8
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 8 = 16. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - thirteen halves plus five-eighths = fifty-seven eighths.
Could you please list all 6 answers below? 30 points and Brainliest if you answer. You have to put them in simplest form.
1. 3/8 x 4/11
2. 8/15 x 5/6
3. 7/12 x 3/14
4. 9/20 x 4/5
5. 7/10 x 20/21
6. 8/18 x 9/20
Answers
Answer:
[1] [tex]\frac{3}{22}[/tex]
[2] [tex]\frac{4}{9}[/tex]
[3] [tex]\frac{1}{8}[/tex]
[4] [tex]\frac{9}{25}[/tex]
[5] [tex]\frac{2}{3}[/tex]
[6] [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
[1] Using the given fractions,
3/8×4/11
Applying the fractions formula for multiplication,
=3×4/8×11
=12/88
Simplifying 12/88, the answer is
=3/22
ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋ
[2] Using the given fractions,
8/15×5/6
Applying the fractions formula for multiplication,
=8×5/15×6
=40/90
Simplifying 40/90, the answer is
=4/9
ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊ
[3] Using the given fractions,
7/12×3/14
Applying the fractions formula for multiplication,
=7×3/12×14
=21/168
Simplifying 21/168, the answer is
=1/8
ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊ
[4] Using the given fractions,
9/20×4/5
Applying the fractions formula for multiplication,
=9×4/20×5
=36/100
Simplifying 36/100, the answer is
=9/25
ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊ
[5] Using the given fractions,
7/10×20/21
Applying the fractions formula for multiplication,
=7×20/10×21
=140/210
Simplifying 140/210, the answer is
=2/3
ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊ
[6] First:
Reduce fractions where possible.
Then your initial equation becomes:
4/9×9/20
Applying the fractions formula for multiplication,
=4×9/9×20
=36/180
Simplifying 36/180, the answer is
=1/5
[RevyBreeze]
Your most trustful answer
How do we find the equivalent ratio of 8/20 PLS HELP ITS RLLY IMPORTANT!!!!
Answers
Answer:
2/5, 4/10, 6/15, 8/20, 10/25, 12/30, 14/35, 16/40, 18/45, 20/50, 22/55, 24/60, 26/65, 28/70, 30/75, 32/80, 34/85, 36/90, 38/95, 40/100 ...
make L and h the subject of formula
[tex]V = \frac{1}{2} LBH[/tex]
Answers
Answer:
[tex]V = \frac{1}{2} LBH \\ \\ \\ LH =V \div ( \frac{1}{2} B) \\ \\ LH =V \times \frac{2}{B} \\ \\ \\LH = \frac{2V}{B} [/tex]
A number of runners enter a race. The times that each runner finished is based on every hour. Five runners finished the race in 5 hours, 11 finished in 4 hours, 7 finished in 3 hours, 14 finished in 2 hours, and 21 finished the race in an hour.
1) Construct a histogram from the data below:
Answers
The histogram for the data is given at the end of this answer.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
In this problem:
The elements of x are given by the time in hours.The histogram shows the number of runners that finished the race in x hours.Hence, the graph given at the end of this answer is the histogram.
You can learn more about histogram at https://brainly.com/question/2962546
what is 1+1
prove me why
Answers
Answer:
1+1=2
Step-by-step explanation:
as we know that one is made up of 1/2+1/2=1
so 1/2+1/2+1/2+1/2=2
hope this helps you
have a great day :)
What is the width and height of this triangle?
Answers
Answer:
The base is 6.69 and the height is 6.02 (these are rounded to the nearest hundredth)
Step-by-step explanation:
soh-cah-toa
cos 42 = adjacent/9
adjacent = cos 42 x 9
adjacent = 6.69
sin 42 = opposite/9
opposite = sin 42 x 9
opposite = 6.02
Determine f(-a) where f(x) = x2 - 6x and simplify.
Answers
Answer:
6a
Step-by-step explanation:
replace x with -a
-2a -6(-a)
-2a +8a
6a
help me its hard for me and brainleist because I only have 2 minutes
Answers
Answer:
y=x+14
Step-by-step explanation:
Let us check if this is the answer:
the first numbers in the table are 0 and 14
0 plus 14 equals 14.
Now the next two numbers on the table:
1 plus 14 equals 15
And one more: the third numbers on the table:
2 plus 14 equals 16
-----does this make sense? need more explination? then let me know
If f(x) = 2x + 1 and g(x) = x^2, the function (gοf)(x) is:
Answers
Answer:
4x² + 4x + 1
Step-by-step explanation:
to evaluate (g ￮ f)(x) , substitute x = f(x) into g(x)
g(f(x))
= g(2x + 1)
= (2x + 1)² ← expand using FOIL
= 4x² + 4x + 1
Suppose that X stands for a temperature in degrees Celsium, Y the same temperature in degrees Fahrenheit. So: Y = (9/5)*X + 32
Let E(X)=10 and Var(X)=2, Find E(Y) and Var(Y).
Answers
The value of E(Y) and Var(Y) are 50 and 178/5 respectively
Temperatures measurementGiven the formula for temperature conversion expressed as:
Y = (9/5)*X + 32
where:
X stands for a temperature in degrees Celsius,
Y the same temperature in degrees
If E(X) = 10, then;
Y = (9/5) * 10 + 32
Y = (9*2) + 32
Y = 18 + 32
Y = 50
Hence E(Y) = 50
If Var(X) = 2
Y = (9/5) * 2 + 32
Y = 18/5 + 32
Y = 178/5
Hence Var(Y) = 50
The value of E(Y) and Var(Y) are 50 and 178/5 respectively
Learn more on temperature here: https://brainly.com/question/894531
What solution value satisfies the compound inequality x - 1 < -7 or x/4 > 1?
Answers
Answer:
x > -6 or x > 4
Answer: B. x = –8
Step-by-step explanation:
Write an equation of the circle with center (6,7) and radius 9.
Please help thanks.
Answers
Answer:
6,16
Step-by-step explanation:
What is the value of x ? (Make sure you give the value of x !!!!)
A 20 degrees
B 50 degrees
C 30 degrees
D. 40 degrees
Answers
Answer:
The value of x is 20 degrees.
Step-by-step explanation:
The three angles of a triangle must equal 180 degrees.
100 + 40 + 2x = 140 + 2x
180 - 140 = 40 (goal)
2(x) = 40
2(20) = 40
A) 20 degrees
Ed hiked 3 kilmometers on Saturday and swam 2 kilometers on sunday. How many total meters did ed hike and swim on saturday and sunday ?
Answers
Answer:
5000 meters
Step-by-step explanation:
kilometers to meters=1km to 1000m
so 5km to 5000m
The total meters did ed hike and swim on Saturday and Sunday 5000 meters.
We have given,
Ed hiked 3 kilometers on Saturday and
Swam 2 kilometers on Sunday.
What is the value of one kilometer?Kilometers to meters
1km = 1000m
We have to find the total distance Ed hiked and swam on Sunday and Saturday,
Total distance=3km +2km
=3km +2km
=5km
1km=1000m.
So 5km to 5000m.
To learn more about the distance visit:
https://brainly.com/question/17273444
im really struggling to finish this asap. help would rlly be appreciated :)
Answers
(43 + 4x) / 2 = 32
43 + 4x = 64
4x = 21
x = 21 / 4
x = 5.25