identifying equation in point slope form for the line perpendicular to y equals negative 1 / 3x - 6 that passes through -1,5
Answer:
y = 3x +8
Step-by-step explanation:
The slope of the given line is -1/3. The slope of a perpendicular line is the opposite of the reciprocal of that: -1/(-1/3) = 3.
Then, in point-slope form, the equation of the line is ...
... y - k = m(x - h) . . . . . for slope m through point (h, k)
... y - 5 = 3(x -(-1)) . . . . . for line of slope 3 through (-1, 5)
... y = 3x +8 . . . . . . . . . simplify
if a polynomial function f(x)has root -2 + square root 8 and 9 what must be a factor of f(x)
The polynomial function f(x) having roots [tex]-2 + \sqrt(8)[/tex] and 9 would have factors [tex](x + 2 - 2\times \sqrt(2))[/tex] and (x - 9). These roots can be determined by setting the known values equal to x and subtracting from x.
Explanation:In mathematics, specifically in polynomial functions, the roots of a function are values that make the function equal to zero. These roots correspond to the factors of the polynomial function. If a function f(x) has roots -2 + square root 8 and 9, then the factors of f(x) will be those values set equal to x and then subtracted from x.
Therefore, the corresponding factors would be [tex]x - (-2 + \sqrt{8})[/tex] and (x - 9). When you simplify these, they become [tex](x + 2 - \sqrt(8))[/tex] and (x - 9). To further simplify, we know that [tex]\sqrt(8) = 2\times \sqrt(2),[/tex] therefore we get [tex](x + 2 - 2\times \sqrt(2))[/tex] and (x - 9).
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If a polynomial function has roots -2 + Square root 8 and 9, then x - (-2 + Square root 8) and x - 9 must be factors of the polynomial.
Explanation:Polynomial functions are mathematical expressions comprising variables, coefficients, and non-negative integer exponents. They are used in various fields, including mathematics, physics, engineering, and computer science. They model relationships between variables, aiding in solving equations, analyzing data, and predicting outcomes in diverse applications.
If the polynomial function f(x) has roots -2 + Square root 8 and 9, then x - (-2 + Square root 8) and x - 9 must be factors of f(x). This is because if a number is a root of a polynomial, then the polynomial can be divided evenly by the corresponding linear factor.
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As Jupiter revolves around the sun, it travels at a speed of approximately 8 miles per second. Convert this speed to miles per minute. At this speed, how many miles will Jupiter travel in 6 minutes? Do not round your answers.
1 minute = 60 seconds.
Multiply the speed per second by 60 to get speed per minute:
8 * 60 = 480 miles per minute.
Multiply speed per minute by number of minutes to get total miles traveled:
480 * 6 = 2,880 total miles.
Find the volume of the figure
Answer:
1920 cm^3
Step-by-step explanation:
Divide into the rectangular prism on top, and the one on the bottom. Whole = sum of parts, so you find the volumes of those two separately and add them together to get the total.
V of rectangular prism = l x w x h (length x width x height)
Top:
l = 10
w = 8
h = 14 - 10 = 4
10 x 8 x 4 = 320
Bottom:
l = 10 + 10 = 20
w = 8
h = 10
20 x 8 x 10 = 1600
1600 + 320 = 1920
The volume of the rectangular prism together with subparts is 1920 cubic meters.
What is the volume of the rectangular prism?The volume of the rectangular prism is the product of the length, breadth, and height of the given prism.
Volume of rectangular prism = (length x width x height)
Divide into the rectangular prism on top, and the one on the bottom.
total volume = sum of parts, so we need to find the volumes of those two separately and add them together to get the total.
Top
l = 10
w = 8
h = 14 - 10 = 4
The volume of the rectangular prism = length x width x height
= 10 x 8 x 4 = 320
Bottom
l = 10 + 10 = 20
w = 8
h = 10
The volume of the rectangular prism = length x width x height
= 20 x 8 x 10 = 1600
The total volume of the shape = 1600 + 320 = 1920
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analyze the following pattern 1,2,5,10,17..... describe the pattern can someone help me with my apex
First differences start at 1 and increase by 2.
Step-by-step explanation:Whenever analyzing any sort of sequence, it is usually helpful to look at the differences between terms. Here, they are ...
... 1, 3, 5, 7
This set of numbers clearly increases by 2 from one to the next. That is, second differences are 2.
_____
When 2nd differences are constant, the pattern can be described by a 2nd-degree polynomial. In this case, that is
... n² -2n +2 . . . . for n = 1, 2, 3, ...
Answer:
Quadratic sequence with
nth term = n^2 - 2n + 2.
Step-by-step explanation:
1,2,5,10,17
The differences between terms are
1,3,5,7
and the second differences are
2,2,2
This is a quadratic sequence with first term n^2 ( where n = sequence number).
List the original sequence and the values of n^2:-
1 2 5 10 17
1 4 9 16 25
If we subtract the first list from the second we get
0 2 4 6 8 which is arithmetic with common difference 2 and first term 0
The nth term of this is 2(n - 1)
So the explicit formula for the nth term of the original sequence is
n^2 - 2(n - 1)
= n^2 - 2n + 2
If 11 key chains cost $53.35, then 4 key chains cost $
Answer:
(53.35/11)*4=19.40
Step-by-step explanation:
The cost of 4 key chains is $19.40.
Cost per key chain = Total cost / Number of key chains
= $53.35 / 11
≈ $4.85
Cost for 4 key chains = Cost per key chain * 4
= $4.85 * 4
= $19.40
So, 4 key chains cost $19.40.
What is the exact value of x?
Answer:
B
Step-by-step explanation:
[tex]5\cdot 21^{5x} = 16 \\\ 21^{5x} = \frac{16}{5} \\\\ 21^{5x} = 3.2 \\\ log 21^{5x} = log 3.2 \\\ 5x\cdot log 21 = log 3.2 \\\ 5x = \frac{log 3.2}{log 21} \\\\\ x = \frac{log 3.2}{5\cdot log 21}[/tex]
I hope I helped you.
The average age of six children is 13 years and 5 months. a seventh child joins the group, increasing the average age by two months. how old is this seventh child
idk
Answer:
14 years 7 months
Step-by-step explanation:
If the average age was increased by 2 months by adding a 7th child, the total age was increased by 2·7 months = 14 months more than the previous average. That is, the added child's age is 14 months more than the previous average, so is ...
... (13 years + 5 months) + (1 year + 2 months) = 14 years + 7 months
_____
For the non-believers:
The previous total of all ages was ...
... 6 × (13 years 5 months) = 80 years 6 months
The new total of all ages is ...
... 7 × (13 years 7 months) = 95 years 1 month
The amount added to the previous total is ...
... (95 1/12 - 80 6/12) years = 14 7/12 years = 14 years 7 months
To find the age of the seventh child, calculate the total age of the six children and the total age of all seven children.
Explanation:To solve this problem, we can use the concept of the average. Step 1: Calculate the total age of the six children by multiplying the average age (13 years and 5 months) by the number of children (6). Step 2: Calculate the total age of all seven children by multiplying the new average age (13 years and 7 months) by the total number of children (7). Step 3: Subtract the total age of the six children from the total age of all seven children to find the age of the seventh child.
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Explain your answer.
C. None of the above
Step-by-step explanation:It appears to me the average times for Ravens backs are lower (< 4.44 s) than those of Chiefs backs (< 4.48 s), so the Ravens are faster on average.
The spread of Ravens times is 4.30–4.57 s, whereas the spread of Chiefs times is 4.42–4.56. The Ravens clearly show a greater variation.
The offered choices suggest the Chiefs are faster on average (not true) and that the Chiefs have a greater variation (not true). Since both of these choices are incorrect, the only remaining suitable choice is None of the above.
find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale
14.4
Step-by-step explanation:This is a special case of the situation where two secant lines intersect a circle. The product of the near distance to the circle and the far distance to the circle from their point of intersection is a constant. A tangent is a degenerate case, where the near and far intersection points with the circle are the same point.
So, ...
... x · x = 9 · (9+14)
... x = 3√23 ≈ 14.4 . . . . . taking the square root
_____
Additional note on the geometry
This rule for the product of segments of secant lines also applies when the secants intersect inside the circle.
Answer:
14.39
Step-by-step explanation:
Theorem 12-15 III
(y+z) y=t squared
(9+14)9=x squared
23•9=x squared
207 =x squared
Square root of 207 is 14.39
Between 2005 and 2010, the average rate of inflation was about 2.7% per year. If a cart of groceries cost $190 in 2005. What did it cost in 2010?
Answer:
$217.07
Step-by-step explanation:
Each year, the cost of the groceries was multiplied by 100% +2.7% = 1.027. Doing this multiplication for 5 years result in a multiplying facor of ...
... 1.027^5
so the cost of the groceries after 5 years is ...
... $190.00 × 1.027^5 ≈ $217.07
Identify the sampling method.
You want to determine the number of text messages students at your school send in a month. You randomly ask 10 students from each grade.
A.) random
B.) systematic
C.) stratified
D.) none of these
You want to determine the number of text messages students at your school send in a month. You randomly ask 10 students from each grade.
This is a random sampling method.
This sampling method is a basic sampling method where we select a group of subjects (a sample) for study from a larger group or population. Each individual is chosen entirely by chance. Each member of the population has an equal chance of being included in the sample.
Answer:
answer is pretty much in the last sentance lol. random
Step-by-step explanation:
Translate this phrase into an algebraic expression. 45 decreased by twice a number Use the variable n to represent the unknown number.
The sum of my digits is an even number. My first digit is 6 less than my second digit. 12 is the number you get when you add my digits. What number am I?
Answer:
39
Step-by-step explanation:
Let a and b represent the first and second digits, respectively.
... a = b -6 . . . . . . the first digit is 6 less than the second
... a + b = 12 . . . . .the sum of digits is 12 (an even number)
Using the expression in the first equation, we can substitute for a in the second equation:
... (b -6) +b = 12
... 2b = 18 . . . . . . add 6, simplify
... b = 9 . . . . . . . . .divide by 2
... a = 9 -6 = 3 . . . . from the first equation
The number is 39.
15 POINTS!!!
Determine the function which corresponds to the given graph.
The asymptote is x = 5.
Answer:
y = ln(x -5)
Step-by-step explanation:
The log function has a vertical asymptote at x=0 and goes through the point (1, 0). This looks like that function translated 5 units to the right. When f(x) is translated right 5 units, x is replaced by x-5. The graph seems to be of the function ...
... y = ln(x -5)
_____
The natural log function will go through the points (2.718, 1) and (7.389, 2), as this curve appears to do.
I NEED HELP!! PLEASE!!!!
See the attachment
Step-by-step explanation:In this context, "x" stands for "a number". Then 1/2x is "one-half of a number" and 3/4x is "three-fourths of a number."
3/4 - ( ) means "three-fourths minus ..."
( ) + 1/2 means "one-half more than ..." or "the sum of ... and one-half."
Putting these ideas together lets you choose the phrases as indicated below.
At the produce counter, 71⁄5 pounds of seedless grapes cost $12.89. How much would 3 pounds cost? A. $3.58 B. $5.16 C. $1.79 D. $5.37
Answer:
D. $5.37
Step-by-step explanation:
We need to figure out how much grapes cost per pound
Change the mixed number to an improper fraction
7 1/5 = (5*7+1) /5 = 36/5
$12.89 / 36/5
Copy dot flip
12.89 * 5/36 = 1.79 per lb
If we are purchasing 3 pounds, we will multiply by 3
3 lbs * $1.79 / lb = $5.37
Last year, Mark designed a square-shaped banner for culture events at his school. This year, he is designing a similar banner for his school's sporting events. The sports banner is 12 inches longer than the length of the banner for the culture events. The area of the sporting events banner is given by the expression below, where x represents the side length, in inches, of the culture banner. Match each part of the expression with what it represents. the length of the sports banner the area of the culture banner the increase in area of the culture banner to make the sports banner the width of the sports banner the second degree term of the expression x2 + 12x arrowRight the first degree term of the expression x2 + 12x arrowRight the monomial, x, a factor of the expression x2 + 12x arrowRight the binomial, (x + 12), a factor of the expression x2 + 12x arrowRight
the second degree term of the expression x^2 + 12x arrowRight the area of the culture banner
the first degree term of the expression x^2 + 12x arrowRight the increase in area of the culture banner to make the sports banner
the monomial, x, a factor of the expression x^2 + 12x arrowRight the width of the sports banner
the binomial, (x + 12), a factor of the expression x^2 + 12x arrowRight the length of the sports banner
Explanation:The problem statement tells you x is the side length of the culture banner, and also the side length of the sports banner. It also tells you the length of the sports banner is 12 (inches) more than that of the culture banner, a value that can be written as x+12.
Of course, the area of a rectangle is the product of its length and width dimensions. Since the culture banner is a square of side length x, its area will be x^2. Since the sports banner is 12 inches longer and still x inches wide, the increase in area that represents will be 12x.
Question 11 options:
m∥n, m∠1 = 65°, m∠2 = 60°, and m∠6 = 85°. What is m∠DBC?
Answer:
∠DBC = 40°
Step-by-step explanation:
∠5 = ∠3 + ∠4 = 180° - ∠6 . . . . relationship of angles at a transversal, vertical angles
∠3 = 180° - ∠1 - ∠2 . . . . . . sum of angles of a triangle
Then
∠4 = 180° - ∠6 - (180° - ∠1 - ∠2) = ∠1 +∠2 -∠6 . . . . substitute for ∠3
∠4 = 65° +60° -85° = 40°
∠4 = ∠DBC = 40°
Using the rule of 72, t=72/r, how long will it take for the principal to double with an annual compound interest rate of 6%?
Answer:
12 years
Step-by-step explanation:
r = compound interest rate in percent
t = doubling time in years
t = (72percent years)/(6 percent) = 12 years
As a curious cultural fact, there is a connection between the 72 and the fact that ln(2) = 0.69314718055. The constant is 69.3 for continuous compounding...
Answer:
12 years
Step-by-step explanation:
Given: y varies directly as x. If y = 5 when x = 4, what is the value of y when x = 12? A) 9.6 B) 10 C) 12 D) 15
Answer:
D) 15
Step-by-step explanation:
We know the formula for direct variation is
y=kx
Substituting y=5 and x=4 we can calculate k
5=k4
Divide each side by 4
5/4 =k
Now y= 5/4 x
If x =12
y =5/4*12
y = 15
Write 3.19 as a ratio of two integers
Answer with explanation:
3.19 =There are two digits after decimals.
An integer is set of numbers which includes both positive natural number, Negative Natural number and Zero.
[tex]3.19=\frac{319}{100}[/tex]
Here, 319 and 100 , both are integers.
You can write equivalent form of
[tex]\frac{319}{100}=\frac{319 \times 2}{100 \times 2}=\frac{319 \times 3}{100 \times 3}=........[/tex]
The value 3.19 expressed as a ratio of two integers is :
[tex] \frac{319}{100} [/tex]
Integers are whole number values which may be positive or negativeGiven the decimal :
3.19 which can be expressed as an integer by multiplying with the Number of decimal places after the decimal Point.
Since there are two decimal places, we multiply 3.19 by 100 ; 3.19 × 100 = 319To express 3.19 as a combination of two integer values, we divide 319 by 100
Hence, 3.19 = 319 ÷ 100
[tex] \frac{319}{100} [/tex]
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Which expression below gives the average rate of change of the function g(x) = -x2 - 4x on the interval 6 ≤ x ≤ 8 ?
plsss
Answer:
the first selection (see below)
Step-by-step explanation:
The average rate of change (m) on the interval [x1, x2] is given by ...
... m = (g(x2) -g(x1))/(x2 -x1)
For g(x) = -x²-4x and (x1, x2) = (6, 8), the expression is the one attached.
Answer:
[tex]\frac{[-8^2 - 4(8)]- [-6^2 - 4(6)]}{8-6}[/tex]
Step-by-step explanation:
average rate of change of the function g(x) = -x^2 - 4x on the interval 6 ≤ x ≤ 8
To find average rate of change we use formula
Average =[tex]\frac{g(x_2)-g(x_1)}{x^2-x_1}[/tex]
use the given interval 6<=-x<=8
x2=8 and x1= 6
we replace the value in the given formula
g(x) = -x^2 - 4x
[tex]g(8) = -8^2 - 4(8)[/tex]
[tex]g(6) = -6^2 - 4(6)[/tex]
x2-x1 is 8-6
So equation becomes
[tex]\frac{[-8^2 - 4(8)]- [-6^2 - 4(6)]}{8-6}[/tex]
Help Now 5 points and will mark brainliest!!! On a trip to his grandparents, Donny drove 60 miles per hour for 45 minutes and 50 miles per hour for 30 minutes. How many miles did Donny drive? A) 55 miles B) 65 miles C) 70 miles D) 90 miles
If you travel at a constant speed, you follow this equation:
[tex] d = st [/tex]
where d is the distance, s is the speed and t is the time.
In this example, you first travel 60 miles per hour for 45 minutes. Since 45 minutes are 3/4 of a hour, you will cover a distance of
[tex] d_1 = 60\cdot\dfrac{3}{4} = 45 [/tex]
In the second part, since 30 minutes is half a hour, you will cover a distance of
[tex] d_2 = 50\cdot\dfrac{1}{2}=25 [/tex]
So, in total, you travel
[tex] d=d_1+d_2=45+25 = 70 [/tex] miles
Answer:
C-70 miles
Hope this helped :)
Algebra 2 help!
What are the x and y intercepts of the equation?
Round the answers to the nearest hundredth.
y = log(12x + 7) - 3
To find the x-intercept, set y=0 and solve.
... 0 = log(12x +7) -3
... 3 = log(12x +7) . . . . add 3
... 1000 = 12x +7 . . . . take the antilog. (10^3 = 1000)
... 993 = 12x . . . . . . . .subtract 7
... 82.75 = x . . . . . . . . divide by 12
To find the y-intercept, set x=0 and solve.
... y = log(12·0 +7) -3
... y = log(7) -3 . . . . . . simplify
... y ≈ 0.85 -3 = -2.15 . . . . use a calculator for the log function
Complete the point slope equation of the line through (3,6) (5,-8)
Answer:
-7(x-5)= y+9
Its kind of hard to explian but...
Hope this helped!! Have a good day c;
Answer:y-6=-7(x-3)
Step-by-step explanation:(3,6) and 5,-8)
Slope= -8-6/5-3
= -14/2
= -7
If your equation started out like this: y-6= then you need to use the point (3,6):
y-6=-7(x-3)
A man bought 8 boxes highlighter, each with 24 highlighter pens inside for $9 each box.He sold the highlighter for$1 each.Did he earn or lose.
Answer:
"earn"
Step-by-step explanation:
He paid $9 for a box of 24 pens. Selling those 24 pens for $1 each, he sold them for $24. Thus he earned $24 -9 = $15 on each of the 8 boxes he bought.
PLEASE HELP I HAVE 20 MINS!!! FIND EACH MISSING MEASURE
Answer:
33
Step-by-step explanation:
I think it would be 33 bc if you subtract 90-66 its 33 but
how did i get 90 bc 90 is a right angel.
0.5x+7/8=5 solve for x
[tex]0.5x+\dfrac{7}{8}=5\qquad\text{multiply both sides by 8}\\\\4x+7=40\qquad\text{subtract 7 from both sides}\\\\4x=33\qquad\text{divide both sides by 4}\\\\\boxed{x=\dfrac{33}{4}\to x=8\dfrac{1}{4}}[/tex]
pls help w/ algebra
the graphs of each group of equations have at least one characteristic in common. name the characteristic (s) and then graph each group of equations on the same axes.
a: y=x, y=3x, y=5x
b: y=2x, y=2x+1, y=2x-3
c: y=1/3x, y=2/5x, y=3/4x
d: 2y=6x, 4y-12x=0, 3x-y=0
e: 2x-4y=12, 3y+2x=-2, x+y=0
how would I go about finding the answer to this?
See attached graphs.
Step-by-step explanation:You are being asked to observe the graphs of the various equations and identify something they have in common. To answer the question, it usually works well to do exactly what the question asks you to do.
a: All three lines have a slope of at least 1 and pass through the origin.
b: These lines all have the same slope. They are parallel.
c: All three lines have a slope less than 1 and pass through the origin.
d: These are all the same line.
e: All of these lines intersect at the point (2, -2).
_____
Comment on the graphs
The number of attachments allowed here is limited, so some graphs have been combined. Where there are 3 lines, the first is red, the second is blue, the third is green.
Graphs for (a) and (c) appear on the same page. The graphs for (c) are shown as dashed lines.
Graphs for (b) and (d) appear on the same page. The graph for (d) is shown in orange (as a dashed line). All threee lines look exactly like this.
_____
Comment on the graphing program
These are graphed using the Desmos on-line graphing calculator. It has a tutorial available and is not difficult to learn for most simple graphing applications. (It prefers the variables x and y.) Graphs can be saved for later. (Here, screen shots are used because Brainly doesn't like external links.)