Answers
Answer:
f(x) = -8 x + 34
Step-by-step explanation:
First, normalize the equation 8y = x-16 into y = ... form (divide by 8):
y = 1/8 x - 2
So the slope of this line is 1/8. The slope of a perpendicular line is the negative reciprocal, which means you swap numerator and denominator and add a minus sign. So the slope of our line is -8 and our function will look like f(x) = -8x + b
Now all we have to do is find b such that f(x) goes through (5,-6).
So f(5) = -8*5 + b = -6, and solve it for b:
-40 + b = -6 =>
b = 34.
So f(x) = -8x + 34
[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}.\\\\\text{We have}\ 8y=x-16\qquad\text{divide both sides by 8}\\\\y=\dfrac{1}{8}x-2\to m_1=\dfrac{1}{8}.\\\\\text{Let}\ y=mx+b.\ \text{It's perpendicular to given line. Therefore}\ m=-\dfrac{1}{\frac{1}{8}}=-8.\\\\y=-8x+b.\\\\\text{The line passes through point (5, -6)}.\ \text{Put the coordinates of the point}\\\text{to the equation of a line:}[/tex]
[tex]-6=-8(5)+b\\-6=-40+b\qquad\text{add 40 to both sides}\\34=b\to b=34\\\\Answer:\ \boxed{f(x)=-8x+34}[/tex]
Related Questions
if you are solving a system of equations and you came to a statement like for equals four, what do you know about the solution to the system?
Answers
Answer:
see explanation
Step-by-step explanation:
when solving an equation and the final statement reads
4 = 4
this means that there are an infinite number of solutions to the system
Evaluate the expression below, -0.25 -(-1/5)+0.2+(-1/4)
Answers
Answer:
0.4
Step-by-step explanation:
-1/5 = -2/10 = -0.2, -1/4 = -25/100 = -0.25
-0.25-(-1/5)+0.2+(-1/4) = -0.25+0.2+0.2+0.25 = -0.25+0.25+0.2+0.2 = 0.4
Answer:
0.0016
Step-by-step explanation:
The volume of a sphere is 36π in³. What is the radius of the sphere? Enter your answer in the box. in.
Answers
Answer:
3 inches
Step-by-step explanation:
⇒r3=36π×3/4π
or r3=27
Taking cube root of both sides
r=3 inch
Distinguish between the situations that can be modeled with a linear function, an exponential functions or neither
Answers
Answer:
Examples of linear functions would be relationships that represent a constant rate of change, such as 20 miles per gallon of gas. Exponential functions would be relationships that represent a growth or decay the increases or decreases by an exponential amount, such as a bacterial growth that doubles each hour. Examples of situations that would be neither linear or exponential would be absolute value functions or quadratic functions.
Step-by-step explanation:
Situations, or relationships between data, that can be modeled with a linear function must show a constant increase or decrease in rate. For example, we could control the rate of temperature in a water bath by two degrees every ten minutes. For exponential functions, these can be modeled in situations where there is a significant growth or decay of a material. For instance, the radioactivity of an element will decrease by one-half every year. This would represent an exponential decay. For other types of situations, such as changes in body temperature (absolute value) or the speed of a kayaker (quadratic), these would not be modeled using either linear or exponential functions.
A linear function can model constant rate of change, exponential function can model constant growth or decay, and some situations do not fit into these mathematical models.
Explanation:A linear function can model situations where there is a constant rate of change between two variables. For example, if the cost of a movie ticket increases by $2 for every additional hour of the movie, you can represent this relationship with a linear function.
An exponential function can model situations where there is constant growth or decay. For example, if the value of an investment doubles every year, you can represent this relationship with an exponential function.
There are situations that cannot be modeled with either a linear or exponential function. For example, unpredictable events or situations with multiple complex factors may not fit into these mathematical models.
Brainliest + Points! Need help and please show work :)
A target is made of a blue square inside of a red square. The blue square has an area of 64 square units, and the red square has an area of 196 square units.
Assuming it hits the target, what is the probability that a dart will land in the blue region?
A.
0,25
B.
0.33
C.
0.67
D.
0.75
Answers
Answer:
B. 0.33
Step-by-step explanation:
The probability will be given by the amount of space in the target area, blue, compared to the total amount of space, the red square.
The size of the blue square is 64 and the size of the red square is 196; this gives us a probability of
64/196 = 16/49 = 0.3265 ≈ 0.33.
The required probability that a dart will land in the blue region is 0.33. Option B is correct.
Given that,
A target is made of a blue square inside of a red square. The blue square has an area of 64 square units, and the red square has an area of 196 square units.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Total sample space = 196
Total favorable space = 64
The probability that a dart will land in the blue region is given as.
probability = 64 / 196 ≈ 0.33
Thus, the required probability that a dart will land in the blue region is 0.33. Option B is correct.
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I need help with this question please help
Answers
Middle right : 1/20
Bottom middle : 1/5
You can check by multiplying those rows, columns and diagonals if you're still not sure about the answer
What is the written form of the decimal number 0.954?
Answers
Answer:
nine hundred fifty-four thousandths
Step-by-step explanation:
If you mean written as in a form in words:
To the first decimal place means tenths because it is out of ten
To the second place, it's hundredths because 100 = 10^2
3rd is 1000, and so on
A fraction (as in two out of five), is expressed in words as "two fifths"
So 954 out of 1000 would be nine hundred fifty-four thousandths
you are making scarves for presents each scarf needs 3/4 yards of fabric how many yards of fabric do you need for 6 scarves
Answers
Answer: 8/1
Step-by-step explanation: 6/1 x 3/4= 24/3( divide both numbers by 3) and you get 8/1 yards of fabric.
Answer:
18/4
Step-by-step explanation:
3/4 per scarf
6 scarfs
6*(3/4)=(18/4)=4.5 yards
Equation in standard form
8x=-5y+3
Answers
Answer:
8x + 5y = 3
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
given 8x = - 5y + 3 ( add 5y to both sides )
8x + 5y = 3 ← in standard form
For a certain spinner, if we expect to win a prize four times in sixty tries, what is the theoretical probability of winning a prize?
Answers
Answer:1/15
Take 60/4=15
The theoretical probability of winning a prize is 1/15.
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, given data;
Total trials = 60
Expect to win = 4
Probability = favorable outcomes/total outcomes
= 4 / 60
= 1/15
Thus, The theoretical probability of winning a prize is 1/15.
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Suppose you have a 1/10 chance of winning with a scratch-off lottery ticket. If you buy 3 tickets, what is the probability of winning with all 3
Answers
Answer:
0.001
Step-by-step explanation:
We are given that
Suppose you have the probability of winning with a scratch -off lottery ticket,P(A) =[tex]\frac{1}{10}[/tex]
Probability:It is defined as the possibility of an event that is occurred or not.
It is obtained by dividing the number of favourable cases with total number of cases.
The formula of finding out the probability of an event
P(E)=[tex]\frac{Number\;of\;favourable\; cases}{Total\;number\;of\;cases}[/tex]
We have to find the probability of winning 3 lottery
The probability of winning all three tickets,[tex]P(A AA)=P(A)\cdotP(A)\cdotP(A)[/tex]
Therefore, the probability of winning all 3 lottery =[tex]\frac{1}{10}\times \frac{1}{10}\times \frac{1}{10}[/tex]
The probability of winning all three tickets,P(A AA)=[tex]\frac{1}{1000}[/tex]
The probability of winning all three tickets,P(A AA)
=0.001
Answer:0.001
if the domain of f(x) = x^2 + 1 is limuted to {0,1,2,3} what is the maximum value of the range?
Answers
Answer: 10
Plug in the given x values and see which result is the largest
Plug in x = 0 ---> x^2+1 = 0^2 + 1 = 1
Plug in x = 1 ----> x^2 + 1 = 1^2 + 1 = 2
Plug in x = 2 ----> x^2 + 1 = 2^2 + 1 = 5
Plug in x = 3 ---> x^2 + 1 = 3^2 + 1 = 10
The range is therefore {1, 2, 5, 10} which is just the set of possible outputs.
We see that y = f(x) = 10 is the largest output of the range if the domain is restricted to the set {0, 1, 2, 3}
What is the volume of this cylinder use 3.14 for pie
72
200.96
204.53
226.08
Answers
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
W have r = 3cm and H = 8cm. Substitute:
[tex]V=\pi(3)^2(8)=\pi(9)(8)=72\pi\ cm^3[/tex]
[tex]\pi\approx3.14\to V=72(3.14)=226.08\ cm^3[/tex]
Answer: 226.08 cm³.6.099 round each number to the place of the underlined digit. The underline number is 0
Answers
Answer:
6.1
Step-by-step explanation:
If we are rounding at the 0 digit, we look at the next digit, which is 9
9 >= 5 so we need to round the 0 up to 1
6.099 rounds to 6.1
Answer:
6.1 is your answer
Step-by-step explanation:
The underlined digit (the tenth place) is 0. Look at the number in the place value directly right to it (hundredth place). It is a 9. Because 9 is greater than 5, round up.
6.099 rounded to the nearest tenth place is 6.1
~
If 2/3 of the 600 seeds sprouted, how many seeds did not sprout?
Answers
By calculating 2/3 of 600, we find that 400 seeds sprouted, which means 200 seeds did not sprout.
Explanation:To determine how many seeds did not sprout, we start by calculating the number of seeds that did sprout. Given that 2/3 of the 600 seeds sprouted, we multiply 600 by 2/3:
600 × (2/3) = 400
So, 400 seeds sprouted. Next, we subtract this number from the total number of seeds to find out how many did not sprout:
600 - 400 = 200 seeds
Therefore, 200 seeds did not sprout.
Find the solutions of the form x=a,y=0and x=0 ,y=b for the following equations: 2x+5y=10 and 2x+3y=6. is there any common solution?
Answers
Answer:
x=0 and y=2
Step-by-step explanation:
We have been given system of equations:
2x+5y=10 (1)
And 2x+3y=6 (2)
Subtract equation (2) from(1) we get:
2y=4
y=2
Now, substitute y=2 in equation(2) we get:
2x+3(2)=6
2x+6=6
2x=0
x=0
Hence, x=0 and y=2
How do I find the perimeter of the shapes
Answers
Answer:Here is the answer
Step-by-step explanation: You first break the shape into two different shapes.Then add them side by side. Determine the length for each side. Then add them together. Add both of the perimeters of the shapes.
PLEASE HELP!!!!!!
Which number(s) below belong to the solution set of the inequality? Check all that apply.
“9x>117”
A. 13
B. 19
C. 6
D. 14
E. 8
F. 12
Answers
If I understand the question corrects it’s asking which numbers work in the inequality so you just plug in each number where x is.
B and D
Paws at play made a total of $1234 grooming 22 dogs. Paws at Play charges $43 to groom each small dog and $75 for each large dog.
a. Write a system of equations that can be used to determine the number of small and large dogs that were groomed.
b. How many large dogs did Paws at Play groom?
Answers
Answer:
Answer (a):
s + l = 22 ... (i)
43s + 75l = 1234 ... (ii)
Answer (b)
9 large dogs.
Step-by-step explanation:
Paws at Play made a total of $1234 grooming 22 dogs.
Paws at Play charges $43 to groom each small dog and;
$75 for each large dog.
Let the number of small dogs be 's'
And the number of large dogs be 'l'
A system of equations will be:
s + l = 22 ... (i)
43s + 75l = 1234 ... (ii)
Solving this set of simultaneous equations by elimination, we simply multiply (i) by 43 to get;
43s + 43l = 946 ... (i)
43s + 75l = 1234 ... (ii)
Subtracting (i) from (ii) we get;
32l = 288 , l = [tex]\frac{288}{32}[/tex] = 9
So there are 9 large dogs.
A recipe calls for 12 cups of blueberries to make 7 jars of blueberry jam.
What is true about the number of cups of blueberries in each jar?
Each jar has 7/12 cup of blueberries.
Each jar has 1/12 of 7 cups of blueberries.
Each jar has 12/7 cups of blueberries.
Each jar has 1 5/12 cups of blueberries.
Answers
Answer:
Each jar has 12/7 cups of blueberries.
Step-by-step explanation:
To find out how many cups of blueberries per jar, we take the number of cups of blue berries and divide by the number of jars
12 cups/7 jars
12/7 cups of blueberries per jar
Each jar has 12/7 cups of blueberries.
Answer:
Step-by-step explanation:
PLZ HELP ONE MORE TIME LAST QUESTION
Megan purchased a new gadget for her technology hobby. She plans to sell it sometime in the future, however, its value depreciates monthly. The expression below shows the depreciated sales value of the gadget: 2020 – 22m What does the second term of the expression represent?
A. The number of months Megan will wait to sell the gadget.
B. The original value of the gadget.
C. The monthly depreciation value of the gadget.
D. The total depreciation value of the gadget.
Answers
Answer: C
Step-by-step explanation: The word problem says that the value depreciates monthly, which means that -22m is how much Megan's gadget depreciates because m stands for months.
Options B and D are not true because the value has a variable, which indicates that it is decreasing by number of months according to the minus sign and not at a fixed amount.
Option A is not true because the word problem says that the expression shows the monthly depreciated sales value of the gadget, not the amount of time Megan will wait to sell the gadget.
18 - t/20= -9 what does t equal?
18 - t/20 = -9 what does t equal?
Answers
Answer:
t = 540
Step-by-step explanation:
18 - t/20 = -9
Subtract 18 from both sides.
-t/20 = -27
Multiply both sides by -20.
t = 540
What is the zero in the quadratic function f(x)= 9x^2-54x-19?
Answers
Answer:
6.33... and 0.333...
Step-by-step explanation:
The quadratic formula is
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].
It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions. Using the formula will require less work than finding the factors if factorable. We will substitute a=9, b=-54 and c=-19.
[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-(-54)+/-\sqrt{(-54)^2-4(9)(-19)} }{2(9)}\\x=\frac{54+/-\sqrt{2916+684} }{18}[/tex]
We will now solve for the plus and the minus.
The plus,,,
[tex]x=\frac{54+\sqrt{3600}}{18}\\x=\frac{54+60}{18}\\x=\frac{114}{18}\\x=6.3[/tex]
and the minus...
[tex]x=\frac{54-\sqrt{3600}}{18}\\x=\frac{54-60}{18}\\x=\frac{-6}{18}\\x=-0.333...[/tex]
Which equation represents a non-proportional situation? y = 6x y = –2x + 14 y = –3x y = 14x
Answers
The equation of proportional situation is y = ax.
Therefore your answer is y = -2x + 14
GEOMETRY HELP PLEASE!!!!!!! Josh is building an enclosure with recycled cardboard for his collection of model cars his design is as shown below:
What is the length of side BC in inches?
A) 14
B) 43
C) 49
D) 63
Answers
A third-grade gym class has 54 students. The gym teacher divides them into 9 groups. She then divides each group into 2 teams. How many students are on each team?
Answers
Answer:
Step-by-step explanation: I would say 3 because when you divide 54 by 9 you get 6. Then when you divide 6 by 2, you get 3. Hope this helps‼ ☺
The number of students gym teacher has putted in each team is, 3
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Given that,
A third-grade gym class has 54 students
The gym teacher divides them into 9 groups
Then divides each group into 2 teams
The number of students in each team = ?
Number of students in a group = 54/9
= 6 students
Then each group divided into two teams,
Number of students in each team = 6/2
= 3
Hence, the number of students is 3
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Which expressions are equivalent to (5⋅x)⋅3 ? Drag and drop the equivalent expressions into the box.
3⋅(5⋅x)
5⋅3+x⋅3
5⋅(x⋅3)
15x
5⋅3⋅x⋅3
Answers
Answer:
3⋅(5⋅x)
5⋅(x⋅3)
15x
Step-by-step explanation:
As the values are inside the brackets, it does not matter what side the (x3) is on, so 3⋅(5⋅x) is equivalent.
Multiplying the contents of the brackets in the third one (x * 3) by 5 gives the same value as 3 * (x * 5) so 5⋅(x⋅3) is also equivalent.
On multiplying the brackets out:
5 * x = 5x
5x * 3 = 15x
So 15x is also equivalent.
Hope this helps!
Answer:
B
Step-by-step explanation:
Slope 8/5;y-intercept(0,-9)
Answers
Answer:
y = 8/5x - 9
Step-by-step explanation:
That would be your equation.
Final answer:
The question pertains to finding the equation of a straight line with a given slope of 8/5 and a y-intercept of (0,-9), which can be represented in slope-intercept form as y = (8/5)x - 9.
Explanation:
The question involves constructing the equation of a line with a given slope and y-intercept.
To find the equation of a line, we use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Given the slope of 8/5 and a y-intercept of (0,-9), the equation of the line would be y = (8/5)x - 9.
The slope tells us that for every increase of 5 units in the horizontal direction (-axis), the line rises 8 units in the vertical direction (-axis). Meanwhile, the y-intercept indicates that the line crosses the y-axis at -9.
Yana and Amber play a word game using tile letters. Each person takes 7 tiles from a set of tiles. Points are earned by using the chosen letter tiles to make a word. Points are lost when tiles are returned to the set and new tiles are chosen. The table shows the points earned or lost by each girl in their first six turns of the game.
Answers
Answer:
A Yana's average number of points is 0.5 points greater than Amber's
Step-by-step explanation:
i added up all of Yana's points = 15
I added up all of Amber's points = 12
then i divided them both by 6 because there is 6 numbers total so then i got
Yana = 2.5 Amber = 2
2.5 - 2 = 0.5 so Yana's average number of points is 0.5 points greater than Amber's
:}
Answer:
A: Yana's average number of points is 0.5 points greater than Amber's
Step-by-step explanation:
I did this on my homework
HELP!!!!!!!!!!!!!!!!!!!!!!! CAN SOMEONE ANSWER ALL OF THESE.
Answers
1. -4 and 3/10 and 4.51010910921... are all rational numbers.
2. Yes 81 is a perfect square because its square root is 9 which is a real number.
3. 5
4. Well the closest perfect square to 52 is 49 and 64. 52 is closer to 49 and the square root of 49 is 7 so the estimated value of the square root of 52 is about 7.
False- every square root is not rational because some aren't perfect squares, meaning the result is a decimal that keeps going forever.
5. (x+6, y-5)