y - 9.1x - 3.6 = 0 is an equation of the line y=9.1 x+3.6 in standard form
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
Standard form of an equation is given as ax + by + c = 0
Here is given
⇒ y = 9.1 x+3.6
⇒ y - 9.1x - 3.6 = 0
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Question below, please answer if you know :)
The final coordinates of the triangle are A''(x, y) = (3, 2), B''(x, y) = (- 1, 4) and C''(x, y) = (2, 0), respectively.
What are the coordinates of the vertices of the image derived from transformation rules?
In this question we know the coordinates of the three vertices of the triangle, whose image must be generated by combining reflection across y-axis and translation, two kinds of rigid transformations, whose formulas are summarized below:
Reflection across y-axis
P'(x, y) = P(x, y) + (- 2 · p, 0) (1)
Translation
P'(x, y) = P(x, y) + T(x, y) (2)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vectorp - x-Coordinate of the original point.If we know that A(x, y) = (1, - 3), B(x, y) = (5, - 1) and C(x, y) = (2, - 5), then the final coordinates are:
Reflection across y-axis
A'(x, y) = (1, - 3) + (- 2, 0)
A'(x, y) = (- 1, - 3)
B'(x, y) = (5, - 1) + (- 10, 0)
B'(x, y) = (- 5, - 1)
C'(x, y) = (2, - 5) + (- 4, 0)
C'(x, y) = (- 2, - 5)
Translation
A''(x, y) = (- 1, - 3) + (4, 5)
A''(x, y) = (3, 2)
B''(x, y) = (- 5, - 1) + (4, 5)
B''(x, y) = (- 1, 4)
C''(x, y) = (- 2, - 5) + (4, 5)
C''(x, y) = (2, 0)
The final coordinates of the triangle are A''(x, y) = (3, 2), B''(x, y) = (- 1, 4) and C''(x, y) = (2, 0), respectively.
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The price of a gallon of unleaded gas was 2.90 yesterday. Today, the price fell to 2.85 . Find the percentage decrease. Round your answer to the nearest tenth of a percent.
Answer:
it decreeased by 1.7% rounded to the nearest tenth
Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.) (-5,0)
The equation of the circle that passes through the point (-5 , 0) and has a center located at the origin is x^2 + y^2 = 25
Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-5 , 0).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(-5 - 0)^2 + (0 - 0)^2
radius= √25
radius = 5
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (0 , 0)
r = 5
(x - 0)^2 + (y - 0)^2 = 5^2
x^2 + y^2 = 25
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Use the given conditions to write an equation for the line in point-slope form and general form.
Passing through (7,−9) and perpendicular to the line whose equation is
The equation of the line in point-slope form is
The equation of the line in general form is
The equation of the line in point-slope form is y = -1/3 x + 20/3 and 3y + x = 20
Equation of a lineThe equation of line perpendicular to another line in point slope form is expressed as;
y-y₁ = -1/m(x-x₁)
Given the equation of a line x -3y - 8 = 0
x - 3y = 8
-3y = -x + 8
y = 1/3x - 8/3
Slope m = 1/3
Substitute the point (-7, 9) and slope 1/3 into the equation
y-9 = -1/3(x-(-7))
y-9 = -1/3(x+7)
3(y-9) = -(x+7)
3y-27 = -x -7
3y = -x + 20
y = -1/3 x + 20/3
Write in general form.
3y = -x + 20
3y + x = 20
Hence the equation of the line in point-slope form is y = -1/3 x + 20/3 and 3y + x = 20
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can you answer this?
(i) 6 litres = 6000 cm³
(ii) The rate at which the water is now flowing from the tap is 50cm³/second
Calculating rateFrom the question, we are to convert the given value in litres to cm³
(i) We are to determine the value of 6 litres in cm³
NOTE: 1 litre = 1000 cm³
Thus,
6 litres = 6 × 1000cm³
= 6000 cm³
(ii)
From the given information,
It takes 60 seconds to fill a 6 litre watering can from the tap
That is,
At a rate of 6000 cm³ per 60 seconds
Now,
The rate at which water flows from the tap is halved
Then,
The new rate will be
6000/2 cm³ per 60 seconds
= 3000 cm³ per 60 seconds
Thus,
The new rate is 3000/60 cm³/second
= 50 cm³/second
= 50cm³/second
Hence, the rate at which the water is now flowing from the tap is 50cm³/second
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The half-life of nickel-63 is 92 years. The amount of nickel-63 in a sample is .670 g. How much nickel-63
would be left after 460 years?
[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &\stackrel{grams}{0.67}\\ t=\textit{elapsed time}\dotfill &\stackrel{years}{460}\\ h=\textit{half-life}\dotfill &\stackrel{years}{92} \end{cases} \\\\\\ A=0.67\left( \frac{1}{2} \right)^{\frac{460}{92}}\implies A=0.67\left( \frac{1}{2} \right)^5\implies A\approx 0.021~grams[/tex]
Which of the choices shows the values arranged from least to greatest.
Answer:
C (Third one) -6, -10/3, 1/4, Sqr6, 3.9
Step-by-step explanation:
-6 = -6
-10/3 = -3.33333333
1/4 = 0.25
Sqr6 = 2.4494...
3.9 = 3.9
PLS HELP I NEED THIS ASAP
Answer:
Slope is -2/5
Step-by-step explanation:
m = (y2 - y1)/(x2 - x1)
I used points (5,-3) (-10,3)
A construction crew is lengthening a road that originally measured 12 miles. The crew is adding one mile to the road each day. Let L be the length (in miles) after D days of construction. Write an equation relating L to D.
The equation relating L to D will be L = 12 + D.
How to illustrate the equation?From the information, the construction crew is lengthening a road that originally measured 12 miles and the crew is adding one mile to the road each day.
Let L be the length (in miles) after D days of construction.
Therefore, the equation will be:
L = 12 + D
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PLEASE ANSWER THIS ASAP I NEED THE ANSWER ASAP!!
The relationship between 5 tablespoons of cocoa per 2 cups of milk is proportional(multiplicative). Let's represent the amount of tablespoons of cocoa we need for 1 cup of milk with x.
We can divide 5 by 2 in order to get x tablespoons for 1 cup of milk.
5 / 2 = 2.5
So, you need 2.5 tablespoons of cocoa for 1 cup of milk :)
For f(x)=-4 x+1 , what is the output for the given input?
a. -2
f (5) = -7 is the output for the given input .
How can you tell whether a function is linear or not?
Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.f(x)= -4 x+1
Put x = -2 ⇒ - 4 × -2 + 1
⇒ - 8 + 1
⇒ - 7
Therefore f (5) = - 7
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Write an equation of each line in standard form with integer coefficients.
the line through (2,3) and (4,5)
The equation of the line in standard form passing through the points (2 , 3) and (4 , 5) is x - y = -1.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant.
Given two points, (2 , 3) and (4 , 5), use the two-point form to generate the equation of the line.
y - y2 = [(y2 - y1)/(x2 - x1)] (x - x2)
y - 5 = [(5 - 3)/(4 - 2)](x - 4)
y - 5 = (2/2)(x - 4)
y - 5 = x - 4
To write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.
y - 5 = x - 4
x - y = -5 + 4
x - y = -1
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Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer.
44,46,91
The following set of numbers, 44, 46, and 91, cannot be the measures of the sides of a triangle.
A triangle is a polygon with three sides and three vertices.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 44, b = 46, and c = 91
a + b > c 44 + 46 > 91 90 > 91 False
a + c > b 44 + 91 > 46 135 > 46 True
b + c > a 46 + 91 > 44 137 > 44 True
If at least one of these three statements is not true, then the set of numbers is not a valid measure of the sides of a triangle.
Hence, the set of numbers 44, 46, and 91 can not be the measure of the sides of a triangle.
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please help me! This is really hard!
The set of numbers that are written in order from least to greatest is: 15.75, √250, 4², 50/3, 16.7 x 10³.
Which number goes from lowest to highest?You need to solve for the quantities given to see which numbers are the smallest and which are the largest.
15.75 = 15.75
√250 = 15.8
4² = 16
50 / 3 = 16.7
16.7 x 10³ = 16,700
The order from least to greatest is therefore:
15.75, √250, 4², 50/3, 16.7 x 10³.
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Write an equation of each line in point-slope form.
(-4,2) and (-3,5)
The equation of the line in point-slope form, which passes through the pair of points located at (-4 , 2) and (-3 , 5), is y - 2 = 3(x + 4).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (-4 , 2) and (-3 , 5).
m = (y2 - y1)/(x2 - x1)
m = (5 - 2)/(-3 - -4)
m = 3
Using the point slope form, plug in the values of the slope and Point A to set up the equation.
(y - y1) = m(x - x1)
where m = 3 and (x1 , y1) = (-4 , 2)
(y - 2) = 3(x - -4)
y - 2 = 3(x + 4)
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A data set includes the following numbers: 5/4, 1 3/4, 72% and 3.48.
Part A: What is the order of numbers from least to greatest? Write your answers using the numbers in their original form.
Part B: Did you use estimation or rewrite the numbers in equivalent form?
(Please use a step-by-step explanation)
The numbers from least to greatest is 72%, 5/4. 1 3/4. 3.48
What is the order of the numbers?To order a number from least to greatest, the numbers would be arranged in ascending order. The farther a positive number is from zero on the number line, the greater the number is. For example, 100 is greater than 1.
The numbers are not written in equivalent forms. Some are written as improper fractions, percentages, decimals and mixed fractions.
An improper fraction is a fraction where the numerator is greater than the denominator. A mixed fraction is a non-integer that is made up of a whole number and a proper fraction. Percentages are numbers written as a quantity out of 100. A decimal is a number that is made up of integers and non-integers.
To order the numbers, all the numbers would be converted to decimals:
5/4 = 1.25
1 3/4 = 1.75
72% = 72/100 = 0.72
The numbers from least to greatest is: 72%, 5/4. 1 3/4. 3.48
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How do you find and write y=x+17 in slope intercept form?
Answer:that is already in slope intercept form
Step-by-step explanation:
Answer:
y = x + 17
Step-by-step explanation:
Given equation,
→ y = x + 17
Now we have to,
→ write it in slope-intercept form.
The slope-intercept form,
→ y = mx + b
Let's solve the given problem,
→ y = mx + b
→ y = x + 17
(It's already in slope-intercept form)
Hence, the answer is y = x + 17.
Solve using Gaussian elimination.
−4x−2y−4z=−24
3x−2y+5z=31
2x+4y−3z=−9
A) 4 / -2 / 3
B) 4 / 2 / 3
C) -2 / 3 / 4
D) 2 / 3 / 4
Answer:
4 / -2 / 3
Step-by-step explanation:
Find the value of x to the nearest tenth. 1086/π = x
x = 345.54545454 is the value of x to the nearest tenth. 1086/π = x
What is π ?
The circumference to diameter ratio of any circle is known as pi, and it is represented by the Greek letter p, or. No matter how big the circle is, this ratio will always be equal to pi. The value of pi in decimal notation is around 3.14.Why is pi so important?
It is a number that is just a little bit larger than three and represents the ratio of a circle's circumference to its diameter. We can better comprehend our cosmos thanks to the constant. A new idea for measuring angles and a new unit of measurement were both inspired by the definition of.1086/π = x
Put value of π = 22/7
1086/22/7 = x
x = 49.363636 × 7
x = 345.54545454
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Every Saturday, 10 friends play dodgeball at a local park. To pick teams, they randomly draw cards with consecutive integers from 1 to 10 . Odd numbers are on Team A, and even numbers are Team B. What is the probability that a player on Team B has drawn the number 10 ?
rewrite (1)/(6)x^(3)y+(5)/(6)xy^(2) using a common factor.
The equivalent expression of the given expression is (x^3y + 5xy^2)/6
How to rewrite the expression?The expression is given as:
(1)/(6)x^(3)y+(5)/(6)xy^(2)
Rewrite properly as
1/6x^3y + 5/6xy^2
Take the LCM
So, we have
(x^3y + 5xy^2)/6
Hence, the equivalent expression of the given expression is (x^3y + 5xy^2)/6
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Solve each equation. Check the solution. 3/b+2 = 6/b-1
The solution of the given equation 3/b+2 = 6/b-1 is found to be (y = -5).
What is termed as cross multiplication?The numerator of the 1st fraction is multiplied by denominator of the 2nd fraction, and the numerator of the 2nd fraction is multiplied by denominator of the 1st fraction in cross-multiplication.
During cross multiplication, denominators are removed.It is used to compare fraction sizes and solve proportional as well as percentage problems.In proportion problems, it is common to have an absent value or variable.After having removed the denominators using cross multiplication, mathematics skills are used to solve for the missing variable once more.Proportion and percentage problems have been solved in the same way.Now, for the given equation in the question;
3/b+2 = 6/b-1
Cross multiplying the terms;
3(b - 1) = 6(b + 2)
Opening the brackets;
3b - 3 = 6b + 12
Bring the variables and constants on the different sides.
6b - 3b = -3 - 12
3b = -15
b = -5
Therefore, the solution of the stated equation 3/b+2 = 6/b-1 is found to be (b = -5).
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whats 8 3/4 as a decimal
Answer:8.75
Step-by-step explanation:
3/4=0.75
0.75+8=8.75
Pls help I'll mark brainliest and it's 20 points, very important!
Melanie wants to rent a bike on her vacation for less than $50. At Mike's Bike Shop, she can rent a bike for $8 per hour plus a $6 flat fee. Any portion of an hour is charged as a full hour.
The inequality that represents this situation is 8h+6<50, where h represents the number of hours Melanie rents the bike.
What does the solution for the inequality mean in relation to the situation
The solution h<5.5 means that Melanie can rent the bike for no more than 5.5 hours.
he solution h<7 means that Melanie can rent the bike for no more than 7 hours.
The solution h<5.5 means that Melanie can rent the bike for no more than 5 hours.
Answer:
The solution h < 5.5 means that Melanie can rent the bike for no more than 5.5 hours.
Hope this helps :)
Explanation and Check part below.
Step-by-step explanation:
1. Isolate the variable by doing the inverse operation which is in this case subtracting 6 on bothsides of the equation.
8h + 6 < 50
- 6 - 6
8h < 44
2. Dive both sides of the equation by 8.
8h < 44
--- ----- <--------- fraction bar, divide
8 8
h < 5.5
need help solving ToT
Answer:
Again the answer is D
Step-by-step explanation:
The radius, diameter, or circumference of a circle is given. Find the missing measure to the nearest hundredth.
d = 8 1/2in., r=?, C=?
The missing measure to the nearest hundredth is r = 2.25 in, C = 14.13 in.
What is circumference of circle?A circle's outside boundary is called the circumference and can be measured, or calculated, by using
Circumference = 2πr
where r is the radius of circle.
Now it is given that,
Diameter of circle, d = 8 1/2 in = 9/2 in
So, radius of circle, r = d/2 = 9/4 in
⇒ r = 2.25 in
Therefore,
∵ Circumference of circle, C = 2πr
∴ Circumference of circle, C = 2π*9/4
⇒ Circumference of circle, C = 14.130 in
Thus, the missing measure to the nearest hundredth is r = 2.25 in, C = 14.13 in.
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Find the eighth term of each geometric sequence. 10,5,2.5, . . . . .
The eighth term of the given geometric sequence is: [tex]\frac{5}{64}[/tex]
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: 10, 5, 2.5, ...
Here, [tex]\frac{5}{10}=\frac{2.5}{5}=\frac{1}{2}[/tex]
Thus, the given geometric sequence has a₁ = 10 and r = 1/2
The nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]
For n = 8, a₈ = [tex]\frac{10}{2^7}=\frac{5}{2^6} = \frac{5}{64}[/tex]
Hence, The eighth term of the given geometric sequence is: [tex]\frac{5}{64}[/tex]
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The length and width of a rectangle are consecutive odd integers. The perimeter of the rectangle is 96 centimeters. Find the length and width of the rectangle.
Width = centimeters Length = centimeters
Answer:
23 cm, 25 cm
Step-by-step explanation:
Let the Width be W cm.
Since the Length and Width are consecutive odd integers we know that the length:
Length = (W + 2) cm
Perimeter of Rectangle = Sum of all sides = 2 x Length + 2 x Width
So rewriting the perimeter , we have:
2W + 2(W+2) = 96 cm
Now lets solve for W to get the width.
2W + 2W + 4 = 96 cm
4W + 4 - 4 = 96 - 4
4W = 92 cm
W = 23 cm
Next, we know that the length = (W + 2) cm
Therefore the length = 23 + 2 = 25 cm
Can someone help me with this I don't understand this. :(
Answer:
See the attached photos for help!
Step-by-step explanation:
I also recommend looking up desmos graphing calculator to actually see the graphs!
If you need more in depth assistance on this, feel free to let me know :]
7. Sound travels through air at 330 meters per second. How long will it take a bat's cry to reach its prey and echo back if the prey is 1 meter away? Round to the nearest thousandth of a second. (please show how you got the answer)
It will take 0.006 seconds for bat's cry to reach its prey and echo back.
What is Sound?Sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
Given is the speed of sound which is 330 m/s. The prey is 1 meter away from the bat.
The time it takes a bat's cry to reach its prey and echo back can be calculated using the formula -
time = distance / speed
The distance covered by the sound as it reaches the prey and echo back is equal to 2 x 1 = 2 meters.
Speed of sound → 330 m/s.
So, the time taken will be -
t = 3/330
t = 0.006 s
Therefore, it will take 0.006 seconds for bat's cry to reach its prey and echo back.
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