Step-by-step explanation:
Equation of the given line is :
[tex] 2x +12y= - 1\\
\therefore 12y = - 2x - 1\\
\therefore y = \frac {- 2}{12}x - \frac {1}{12}\\
\therefore y = - \frac {1}{6}x - \frac {1}{12}\\[/tex]
Equating above equation with [tex] y= m_1x + c
[/tex] we find:
[tex] m_1 = - \frac{1}{6}[/tex]
Where [tex] m_1[/tex] is the slope of given line:
Let the slope of required line be [tex] m_2.[/tex]
Since lines are perpendicular
[tex] \therefore m_1 \times m_2= - 1\\
\\\therefore - \frac{1}{6} \times m_2= - 1\therefore m_2= 6\\[/tex]
Equation of required line in slope point form is given as:
[tex] y-y_1 =m_2(x-x_1) \\
\therefore y-9 =6(x-0)\\
\therefore y-9 =6x\\
\huge\orange {\boxed {\therefore y =6x+9}} \\[/tex]
Answer: A. Y= -6x+9
Step-by-step explanation:
300% of what number is 51
Answer:
17
Step-by-step explanation:
Let the number be x.
We know that 3x=51
If we divide both sides by three, we get x=17
17
act like there is a variable in there and youll get 17
Solve the proportional equation below:
10/2=a/a-9
a. 11.25
b. 7
c. 2
d. 1.125
To solve the given proportional equation, it simplifies to 5 = a/(a-9), leading to 4a = 45 after simplification and solving, with the solution being a = 11.25.
Explanation:To solve the proportional equation 10/2 = a/(a-9), we first simplify and then solve for a. The equation simplifies to 5 = a/(a-9). By cross-multiplication, we get 5(a - 9) = a, which simplifies to 5a - 45 = a. Bringing all terms to one side gives 4a = 45, and dividing both sides by 4 gives a = 11.25. Therefore, the correct answer is a. 11.25.
Step 2 - Identify which formula we use to prove certain properties of polygons.
Below are the properties of triangles/quadrilaterals you’ve been working with closely. Look at the properties given, then match it with the formula you would use to prove it. ( Hint: think about the type of answers we expect from each of the formulas listed - use your answers from Step 1 to help!)
**You could use each choice more than once!
_____ 1.) Both pairs of opposite sides are congruent.
_____ 2.) Both pairs of opposite sides are parallel.
_____ 3.) Diagonals are congruent.
_____ 4.) Diagonals bisect each other.
_____ 5.) Diagonals are perpendicular.
_____ 6.) Sides of polygon create a right angle.
_____ 7.) A triangle is isosceles/equilateral.
a.) Midpoint Formula
b.) Slope Formula
c.) Distance Formula
Properties of polygons.
Step-by-step explanation:
(1) Both pair of opposite sides are congruent. Distance Formula
(2) Both pairs of opposite sides are parallel. Slope Formula
(3) Diagonals are congruent . Distance Formula
(4) Diagonals bisect to each other. Midpoint Formula
(5) Diagonals are perpendicular. Slope Formula
(6) Sides of polygon create a right angle. Slope Formula
(7) A triangle is isosceles /equilateral. Distance Formula
I really need Help with this equation Please!!!!
Answer:
Option D: - 6; [tex]$ \textbf{-5}\frac{\textbf{5}}{\textbf{2}} $[/tex]; [tex]$ \textbf{-4}\frac{\textbf{1}}{\textbf{5}} $[/tex].
Step-by-step explanation:
The sequence is defined by:
[tex]$ A(n) = -6 + (n - 1)\bigg( \frac{1}{5} \bigg ) $[/tex]
To find the first term of the sequence simply substitute n = 1.
First term of the sequence:
[tex]$ A(1) = -6 + (1 - 1)\bigg( \frac{1}{5} \bigg ) $[/tex]
[tex]$ = - 6 $[/tex]
Fourth term of the sequence:
[tex]$ A(2) = -6 + (4 - 1) \bigg ( \frac{1}{5} \bigg) $[/tex]
[tex]$ = - 6 + 3\bigg( \frac{1}{5} \bigg) $[/tex]
[tex]$ = \frac{- 30 + 3}{5} $[/tex]
[tex]$ = \frac{-27}{5} $[/tex]
[tex]$ = \frac{-25 - 2}{5} $[/tex]
[tex]$ = - 5 - \frac{2}{5} $[/tex]
[tex]$ = -5\frac{2}{5} $[/tex] is the required answer.
Tenth term of the sequence:
[tex]$ A(10) = - 6 + (10 - 1) \bigg( \frac{1}{5} \bigg) $[/tex]
[tex]$ = - 6 + 9\bigg( \frac{1}{5} \bigg) $[/tex]
[tex]$ = \frac{-30 + 9}{5} $[/tex]
[tex]$ = \frac{-21}{5} $[/tex]
[tex]$ = \frac{-20 - 1}{5} $[/tex]
[tex]$ = - 4 - \frac{1}{5} $[/tex]
[tex]$ = -4\frac{1}{5} $[/tex] is the required answer.
On the calculator, click on the graph of y = 3x and trace to view the coordinates. When the x-coordinate is 4, what is the y-coordinate?
the y-coordinate corresponding to x=4 is 12.
the equation y=3x represents a linear function. A linear function is a type of mathematical relationship where the graph of the function forms a straight line.
The equation y=3x is in slope-intercept form, where y represents the dependent variable (usually plotted on the vertical axis),
x represents the independent variable (usually plotted on the horizontal axis), and 3 represents the slope of the line.
To find the y-coordinate when the x-coordinate is 4 in the equation y=3x, we need to substitute x=4 into the equation and solve for y.
Substituting x=4 into the equation y=3x,
we get: y=3×4=12
So, when x=4, y=12.
Therefore, the y-coordinate corresponding to x=4 is 12.
This means that the point on the graph of y=3x where the x-coordinate is 4 has a y-coordinate of 12.
a scientist has a bottle that is 5/8 full of solution. he used 2/5 of the solution in the bottle for an experiment. how much of a full bottle of solution does he use?
Final answer:
The scientist used 9/40 of a full bottle of solution.
Explanation:
To find out how much of a full bottle of solution the scientist used, we first need to calculate the amount that is left in the bottle. The bottle is currently 5/8 full, and the scientist used 2/5 of the solution. To calculate the amount left, we subtract the amount used from the initial amount:
Amount Left = Initial Amount - Amount Used
To subtract fractions, we need a common denominator. The common denominator for 8 and 5 is 40:
Amount Left = 5/8 - 2/5
To subtract the fractions, we need to have the same denominator, which is 40:
Amount Left = (5/8) * (5/5) - (2/5) * (8/8)
Amount Left = 25/40 - 16/40
Amount Left = 9/40
Therefore, the scientist used 9/40 of a full bottle of solution.
If $1800 is invested at 2% interest compounded annually find the total amount in 3 years.
Answer:
$1910.1744
Step-by-step explanation:
To start we have to calculate how much the total will give us in one year, for this we divide the number by 100 and multiply it by 102, so we will get that 2% in one year
(1800 / 100) * (100 + 2) =
18 * 102
1836
Now we will repeat the procedure but instead of using the 1800 we will use the 1836 which will be what we will have when the first year ends.
(1836 / 100) * (100 + 2) =
18.36 * 102
1872.72
Finally we do the same with the new number
(1872.72 / 100) * (100 + 2) =
18.7272 * 102
1910.1744
So in conclusion putting $1800 at the end of the 3 years we will get $1910.1744
$1910.1744 - $1800 = $110.1744
that is the exact amount of the profit that we will obtain.
Triangle ABC has verrocktes A (2,-1) B ( -3,0) and C ( -1,4) . Find the vertices of the image of triangle and after a translation of 2 units up
Answer:
A(2,1) , B(-3,2) , C(-1,6)
Step-by-step explanation:
A translation of 2 units up means the y values will be shifted up 2 units
A (2,-1) -> A(2,1)
B (-3,0) -> B(-3,2)
C (-1,4) -> C(-1,6)
The vertices of the image of triangle ABC after a translation of 2 units up are A' (2, 1), B' (-3, 2), and C' (-1, 6), found by adding 2 to the y-coordinate of each original vertex.
The student has asked how to find the vertices of the image of triangle ABC after a translation of 2 units up. To do this, we simply add 2 to the y-coordinate of each vertex of the triangle. Here are the steps for the translation:
For vertex A (2, -1), the new position after translation is A' (2, -1 + 2) or A' (2, 1).
For vertex B (-3, 0), the new position after translation is B' (-3, 0 + 2) or B' (-3, 2).
For vertex C (-1, 4), the new position after translation is C' (-1, 4 + 2) or C' (-1, 6).
Therefore, the vertices of the image of triangle ABC after the translation are A' (2, 1), B' (-3, 2), and C' (-1, 6).
You have decided to purchase a new Toyota 4Runner for $25,635. You have promised your daughter that the SUV will be hers when the car is worth $10,000. According to your car dealer, the SUV will depreciate in value approximately $3000 per year.
a) Write a linear equation in which y represents the total value of the car and x represents the age of the car,
The linear equation representing the value of the car as it depreciates over time is y = -3,000x + 25,635, where y is the value of the car and x is the age of the car in years.
To write a linear equation that describes the depreciation of the SUV over time, we define two variables: y represents the total value of the car at any time x, where x represents the age of the car in years.
The car is purchased for $25,635 and depreciates at a rate of $3,000 per year, which means that the value of the car decreases by a constant amount each year. We can write this situation as a linear function:
Linear Depreciation Equation:
y = -3,000x + 25,635
Here, the y-intercept is $25,635 (the value of the car at the time of purchase when x is zero), and the slope is -$3,000 (the rate at which the value of the car decreases per year).
-3t-8+7t =34 +9t -2
Solve for t
Please give an exposition
Answer:
t = -8
Step-by-step explanation:
combine like terms, so -3t + 7t = 4t and 34 - 2 = 32
so 4t - 8 = 32 + 9t
then subtract 4t from both sides and subtract 32 from both sides. You will get: -40 = 5t.
Then divide both sides by 5 so you will get -8 = t
Answer: t= -8
Step-by-step explanation:
3t-8+7t=34+9t-2-3t+7t-8=9t+32-24t-8=9t+32t= -8A grocer has two kinds of candies, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
Answer: 55 lbs of $0.40 and 45 lbs of $1.40
Step-by-step explanation:
Let's say that we have two buckets, one that weighs x pounds and the candies in it are $0.40 per pound and another that weighs 100-x pounds (because we know the two added together must be 100 pounds) and the candies in it are $1.40 per pound.
There is a third bucket that is made when you combine the two, it weighs 100 pounds and the candies in it are $0.85. Multiply the cents per pound by the pounds of the candy for each bucket and you get this equation:
0.4 * x + 1.4 (100-x) = 0.85 * 100
Solve!
0.4x + 140 - 1.4x = 85
-x + 140 = 85
-x = -55
x = 55
From this we get that 100 - x = 45.
So, the answer is 55 lbs of $0.40 and 45 lbs of $1.40
ANSWER: 55 lbs of $0.40 and 45 lbs of $1.40
Step-by-step explanation:
Let's say that we have two buckets, one that weighs x pounds and the candies in it are $0.40 per pound and another that weighs 100-x pounds (because we know the two added together must be 100 pounds) and the candies in it are $1.40 per pound.
There is a third bucket that is made when you combine the two, it weighs 100 pounds and the candies in it are $0.85. Multiply the cents per pound by the pounds of the candy for each bucket and you get this equation:
0.4 * x + 1.4 (100-x) = 0.85 * 100
Solve!
0.4x + 140 - 1.4x = 85
-x + 140 = 85 .
-x = -55
x = 55
From this we get that 100 - x = 45.
So, the answer is 55 lbs of $0.40 and 45 lbs of $1.40
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pronouns:she/they
What is the value of x?
Answer:
9
Step-by-step explanation:
The two triangles [tex]\triangle MNP\sim \triangle RST[/tex].
Therefore the corresponding sides are proportional.
[tex]\frac{|ST|}{|PN|} =\frac{|TR|}{|MP|}[/tex]
From the diagram |MP|=4, |PN|=3, |MN|=5 |ST|=x and |TR|=12.
Let us substitute the values and solve for x.
[tex]\frac{12}{4}=\frac{x}{3}[/tex]
Multiply both sides by 3 to get:
[tex]3*\frac{12}{4}=\frac{x}{3}*3[/tex]
This implies that:
[tex]9=x[/tex]
Therefore x=9
Vocabulary How can you tell if
a
fraction is a unit fraction?
A unit fraction is a fraction with a numerator of 1 and a positive integer denominator. Identifying unit fractions involves ensuring the numerator is 1. Examples include 1/2, 1/3, and 1/5.
A unit fraction is a fraction where the numerator is always 1, and the denominator is a positive integer. This means that a fraction of the form 1/b, where b is a positive integer, qualifies as a unit fraction. For example, 1/2, 1/3, and 1/5 are unit fractions because the numerators are all 1.
When working with fractions, it's important to understand their components. The numerator (top number) represents how many parts you have, while the denominator (bottom number) tells you into how many equal parts the whole is divided. This rule helps identify unit fractions, as the numerator must always be 1.
To summarize, determining unit fractions is straightforward: check if the numerator is 1 and the denominator is a positive integer. If both conditions are met, you have a unit fraction.
What is -1/4(×+2)+5=-×
THIS IS URGENTE I AM BEING TIMED PLZ HELP, if you answer correct i will mark you brainlyist
Mr. Anderson had $40.95 that he wanted to divide evenly among his seven children. How much should each child receive? Don't forget to include the $ sign.
Answer:
5.85
Step-by-step explanation:
$40.95 / 7 =5.85
Write 10+0.06+0.008 in word form
Answer:
Ten plus six hundredth plus 8 thousandth equals ten and sixty-eight thousandths
Step-by-step explanation:
0.06 is in the hundredth place
0.008 is in the thousandth place
Answer:
ten plus zero point zero six plus zero point zero zero eight
Step-by-step explanation:
The ten is 10 then plus + and then 0.06 plus + 0.008
Which describes the relationship between
A. adjacent angles
B. complementary angles
C. supplementary angles
D. vertical angles
Answer:
d
Step-by-step explanation:
The graph shows the number of Internet downloads of a song compared to the number of times it is played on the radio.
What can you conclude from the data? Check all that apply.
A)The number of times a song is played on the radio affects its number of downloads.
B)Increased radio play affects the download demand for all songs equally.
C)Even though there was very high radio play, the downloads of one song remained very low.
D)In general, increased radio play does not affect the number of downloads.
Answer: a,c
Step-by-step explanation:
Answer:
A .. C
Step-by-step explanation:
Does anyone know this?
Answer: yes
Step-by-step explanation:
Answer:
10 degrees
Step-by-step explanation:
Divide 360 by however many sides or angles are within the polygon.
360/x
360/36
10
Solve for e and f please
Answer:
Step-by-step explanation:
180-78=102
102÷2=51
E=51
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
i have no clue
Step-by-step explanation:
ask someone else
A weather forecast states that there is a 20% probability of rain in the next three days. Describe a simulation you could perform using random numbers to find the experimental probability that it will not rain on any of the next 3 days.
To simulate the 20% probability of rain over three days, generate a random number between 1 and 100 for each day. Count the trials where all three numbers are between 21 to 100 as 'non-rainy' days. The experimental probability of no rain in three days is the ratio of 'non-rainy' trials to total trials.
Explanation:Probability is a branch of mathematics that studies randomness and the chance of an event occurring. In this case, we can perform a simulation to experimentally determine the probability that it will not rain on the next 3 days even though there is a forecast of a 20% chance of rain.
One way to perform the said simulation is by using random numbers from 1 to 100. Why? Because probability can be expressed as a percentage, and the range from 1 to 100 encompasses all percentage possibilities (0% to 100%). So, for each day, we can generate a random number in this range. If the generated number falls in the range 1-20 (which represents the 20% predicted chance of rain), we consider that day as a 'rainy day'. If it falls in the range 21-100, we consider it a 'non-rainy day'.
We repeat this process for three days. The experimental probability of it not raining on all three days will be the ratio of favorable outcomes (all three numbers landing in the 'non-rainy day' range) to the total number of trials.
If we perform a large number of these three-day simulations, we'll have a good estimate of the experimental probability. The Law of Large Numbers ensures that as more trials are conducted, the experimental probability will approach the theoretical probability.
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which doesn't round to 4.7 4.746, 4.733, 4.647, or 4.680
Answer: 4.647
Step-by-step explanation:
The 4 in the hundredths place, or before the 6, is less than 5 so it will not round the 6 to a 7, therefore making it not round to 4.7
A 10 metre length of Wood is marked out into 10 equal lengths. How many metres from one end is the third mark?
3 metres from one end to the third mark
Solution:
Total length of wood = 10 metre
Wood is marked into 10 equal length.
[tex]$\text{Length of each marking}=\frac{\text{Total length}}{\text{Number of marking}}[/tex]
[tex]$=\frac{10}{10}[/tex]
= 1 metre
Length of each marking = 1 metre
Number of metres from one end to third mark = 1 + 1 + 1 = 3 metre
The image of the marking is attached below.
Hence 3 metres from one end to the third mark.
y=2x – 3
4x – 3y = 7
Answer:
4x - 3(2x - 3)= 7
4x - 6x + 9 = 7
-2x + 9 = 7
-2x = -2
x = 1
y = 2(1)-3= -1
(1,-1)
Determine if the ordered pair (-2, 1) is a solution
of 2x – y=-3.
Answer: no because 2 times -2 equals -4 and -4 - 1 = -5 not -3.
which is the product of 7/9 and 6?
Answer:
14/3
Step-by-step explanation:
7 x 6
9 1
7x6=42
9X1=9
42/9 or 14/3
The product of 7/9 and 6 is 14/3.
Explanation:To find the product of 7/9 and 6, multiply the numerator (7) by the number (6) and keep the denominator (9) the same.
The calculation is as follows:
(7/9) * 6
= (7 * 6)/9
= 42/9
To simplify the fraction, divide both the numerator and the denominator by their greatest common factor, which is 3.
The simplified answer is: 14/3
Alonso stands 8 yards west of Gregory. He then walks 10 yards north and discovers an arrowhead. How far is the arrowhead from Gregory’s position?
Answer:
Distance [tex]=\sqrt{164}\ \approx12.80\ yards[/tex]
Step-by-step explanation
Pythagorean theorem :
In a right triangle
[tex](Hypotenuse)^2=(Perpendicular)^2+(base)^2[/tex]
From the diagram
[tex]perpendicular = 10\ yards\\\\Base = 8\ yards \\\\Hypotenuse = distance\ (d)\\\\(d)^2=(10)^2+(8)^2\\(d)^2=100+64\\(d)^2=164\\d=\sqrt{164}\ \approx12.80\ yards[/tex]
what is 8.7
7 reapeating forever
as a fraction
also answer fast and the explanation Is not needed
THANKS
Answer:
55
Step-by-step explanation:
There are 3 feet in 1 yard. during the first play of a football game, one player runs the ball 10 yards before stepping out of bounds. the coach records the distance in feet and yards
Answer:
30 feet
Step-by-step explanation:
3 feet times 10 years would be 30. This is because for each yard, the player travels 3 feet.
Answer:
30 feet or 10 yards
Step-by-step explanation:
feet is 1 yard so
to get 10 yards
do 3 feet times 10 to make 30 feet
split 30 feet into yards
1 yard for every 3 feet
30 divided by 3 is 10 yards