Determine whether the given function is linear. f(x) = 3 + 1/3x
Answers
you can either graph this or plug in values.
[tex]f(x)=3+\frac{1}{3}x[/tex]
[tex]f(-1)=3+\frac{1}{3}(-1)\\\\f(-1)=3-\frac{1}{3}\\\\f(-1)=2\ \frac{2}{3}\\\\f(0)=3\\\\f(1)=3\ \frac{1}{3}[/tex]
[tex]\therefore[/tex] we can conclude that this function is linear.
Also here is a graph
Related Questions
Write an equation of each line in point-slope form.
(-4,2) and (-3,5)
Answers
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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The directly proportional dependence is given by the formula y=3/8x
Answers
For the formula y = 3/8x , as x increases or decreases, the value of y increases or decrease by 3/8 times of x.
We have the following statement -
'The directly proportional dependence is given by the formula y = 3/8x '.
We have to analyze this statement.
What is the meaning of direct proportionality between variables ?Directly proportional means as the value of one variable increases, the value of another variable increases at the same rate.
According to the question, we have -
y = 3/8x
Here - y is directly proportional to x. This means that as x increases or decreases, the value of y increases or decrease by 3/8 times of x.
The graph of this equation is a straight line passing through origin. Therefore - Direct proportionality is represented by a straight line graphically.
Hence, for the equation y = 3/8x , as x increases or decreases, the value of y increases or decrease by 3/8 times of x.
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Write a function rule for the direct variation in the table.
Answers
The function rule for the direct variation in the table is [tex]y = 24/x[/tex] , indirect variation ; x = 2.4.
What is direct variation?Direct variation is the change in one quantity as a result of the change in another. This suggests that if one quantity rises or falls, the other must rise or fall correspondingly as well.
The formula y = kx is used to answer direct variation questions. If finding the proportionality constant is necessary, the answer is obtained by dividing y by x.
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Please help!!
1.The height of a projectile is a function of the time it is in the air. The height in feet for t seconds is given by the function h(t) = -16t2 + 96t . What is the domain of the function? What does the domain mean in the context of the problem?
2.Use the graph at right to answer the following question.
Solve for f(x) = -3
Answers
Problem 1
The domain is [tex]0 \le t \le 6[/tex] which in interval notation is [0, 6]
This is the set of t values where h(t) is positive or zero. Any other t values will make h(t) to be negative. So we ignore those t values. A negative height makes no sense.
The domain in the context of the problem means that the projectile is in the air from the time markers of t = 0 and t = 6. In short, the object is in the air for 6 seconds. It takes 6 seconds for it to hit the ground.
Here's how we can determine those t values. We plug in h(t) = 0 and solve for t.
h(t) = -16t^2 + 96t
-16t^2 + 96t = 0
-16t(t - 6) = 0
-16t = 0 or t - 6 = 0
t = 0/(-16) or t = 6
t = 0 or t = 6
======================================================
Problem 2
Draw a horizontal line through -3 on the y axis.
This horizontal line touches the blue graph at the points (-2,-3) and (2,3)
This means the inputs x = -2 and x = 2 lead to the output of y = -3
Therefore f(-2) = -3 and f(2) = -3
Answer: The solutions are x = -2 and x = 2
Which expressions are simplified? Pls help!!
Answers
Answer:
Only A
Step-by-step explanation:
[tex]b) \: \frac{1}{ {n}^{ - 5} } = {n}^{5} \\ \\ c) \: {n}^{6} \times {n}^{ - 8} = {n}^{ - 2} \\ \\ d) \: {n}^{7} \times {n}^{8} = {n}^{15} \\ \\ e) \: \frac{1}{ {n}^{3} } = {n}^{ - 3} [/tex]
please help. The question is attached. Do only C,D,E,F,G
Answers
Main Answer:
c. The value of x = 5 and y = 5.
d. The value of x = 1and y = 2.
e. The value of x = 10 and y = 2.
f. The value of x = 2 and y = 1.
g. The value of x=2 and y = 4.
Explanation for all parts:
A linear equation is an algebraic equation of the form y=mx+b involving a constant and a linear term.A square root of a number is a value that when multiplied by itself gives the number.Elimination method is a technique for solving a system of linear equation by eliminating the same variables.c. Given: 3y = x + 10
[tex]x^{2} +y^{2}=100[/tex]
To find: Solve the simultaneous equations.
[tex]x^{2} +y^{2}=100[/tex]
On taking square root from both sides of the equations, we get,
x + y = 10
3y = x + 10
x = 3y - 10
x - 3y = -10
By elimination method,
x - 3y = -10
x + y = 10
-----------------
-4y = -20
y = 5
On substituting the value of y = 5 in the equation x + y = 10 , we get,
x + y =10
x + 5 = 10
x = 5
Therefore, the required value of x = 5 and y = 5.
d. Given: y = 3x - 1
8[tex]x^{2}[/tex] - 2xy = 4
To find: Solve the simultaneous equations.
By substitution method,
We will substitute the value of y in equation 8[tex]x^{2}[/tex] - 2xy = 4 to get,
8[tex]x^{2}[/tex] - 2x(3x-1) = 4
8[tex]x^{2}[/tex] - 6[tex]x^{2}[/tex] +2x = 4
2[tex]x^{2}[/tex] + 2x = 4
By dividing the equation by 2 on both sides, we get,
[tex]x^{2}[/tex] + x = 2
[tex]x^{2}[/tex] + x - 2 = 0
[tex]x^{2}[/tex] + 2x - x - 2 = 0
x(x+2) -1(x+2) = 0
(x+2)(x-1) = 0
x+2 = 0 or x - 1= 0
x = -2 or x = 1
We will not consider the negative values of x.
So, x = 1.
y= 3x - 1
y = 3 × 1- 1
y = 3 - 1
y = 2
The value of x = 1and y = 2..
e. Given: x - 2y = 6
[tex]x^{2}[/tex] - 4xy = 20
To find: Solve the simultaneous equations
x - 2y = 6
x= 6 + 2y
By substitution method,
We will substitute the value of x= 6 + 2y in the equation
[tex]x^{2}[/tex] - 4xy = 20 to get,
[tex](6+2y)^{2}[/tex] - 4(6+2y)y = 20
36 + 4[tex]y^{2}[/tex] +24y - 24y - 8[tex]y^{2}[/tex] = 20
-4[tex]y^{2}[/tex] = 20 - 36
-4[tex]y^{2}[/tex] = -16
By dividing the equation by -4 on both sides, we get,
[tex]y^{2}[/tex] = 4
y = 2
So, x = 6 +2y
x = 6 + 2×2
x = 6+4
x=10
Therefore, the value of x = 10and y = 2.
f. Given: 4x - 3y = 5
[tex]x^{2} +3xy = 10[/tex]
To find: Solve the simultaneous equations.
4x - 3y = 5
4x= 5 + 3y
x = [tex]\frac{5+3y}{4}[/tex]
By substitution method,
We will substitute the value of x = [tex]\frac{5+3y}{4}[/tex] in the equation
[tex]x^{2} +3xy = 10[/tex] to get,
[tex](\frac{5+3y}{4} )^{2}[/tex] + 3[tex](\frac{5+3y}{4} )[/tex]y =10
[tex]\frac{25+9y^{2}+30y }{16}+ \frac{15y+9y^{2} }{4}[/tex] = 10
[tex]\frac{25+9y^{2}+30y+60y+36y^{2} }{16}[/tex]=10
25 + 45[tex]y^{2}[/tex] + 90y=160
By dividing the equation by 5 on both sides, we get,
5 + 9[tex]y^{2}[/tex] +18y= 32
[tex]9y^{2}[/tex] +18y - 27 = 0
By dividing the equation by 3 into both sides, we get,
[tex]y^{2}[/tex] +2y - 3 = 0
[tex]y^{2}[/tex] +3y -y - 3 = 0
y(y+3) - 1(y+3) = 0
(y+3)(y-1) = 0
y =-3 or y =1
We will not consider the negative values of x.
So, y=1.
x= [tex]\frac{5+3y}{4}[/tex]
x = [tex]\frac{5+3(1)}{4}[/tex]
x= [tex]\frac{5+3}{4}[/tex]
x= [tex]\frac{8}{4}[/tex]
x = 2
Therefore, the value of x=2 and y= 1.
g. Given: 2x+ y= 8
xy= 8
To find: Solve the simultaneous equations.
According to the equation,
2x+ y= 8
y = 8 - 2x
By substitution method,
We will substitute the value of y = 8 - 2x in the equation xy = 8 to get,
x(8-2x) = 8
8x - 2[tex]x^{2}[/tex] = 8
8x - 8 = 2[tex]x^{2}[/tex]
2[tex]x^{2}[/tex] - 8x + 8 = 0
2[tex]x^{2}[/tex] - 4x - 4x + 8 =0
2x(x - 2) - 4(x - 2) = 0
(x - 2)(2x - 4) = 0
x = 2 or 2x = 4
x= 2 or x =2
So, y = 8 - 2x
y = 8 - 2(2)
y = 8 - 4
y = 4
Therefore, the value of x = 2 and y= 4.
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State whether sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
A ₋trigonometric ratio is a ratio of the lengths of two sides of a right triangle.
Answers
Given statement 'A trigonometric ratio is a ratio of the lengths of two sides of a right triangle' is True.
In this question,
We have been given a statement 'A trigonometric ratio is a ratio of the lengths of two sides of a right triangle'
Sometimes, trigonometric ratios used to find the measures of acute angles in a right triangle.
To find the measures of acute angles in a right triangle, you need to know the measures of the two sides of the right triangle.
We determine which ratio to use depending on which sides are given. And we also use the inverse trigonometric functions to find the angle.
Trigonometric ratios are: sine, cosine, tangent, cotangent, secant, cosecant.
These ratios are abbreviated as, sin, cos, tan, cot, sec, cosec.
Therefore, given statement 'A trigonometric ratio is a ratio of the lengths of two sides of a right triangle' is True.
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OCPS Dashboard
Storyline Online W Race Now - 100% F
Jose has 13 1/4 cups of raspberries. He uses 7/8 cup of raspberries to make a smoothie. Jose uses the
remaining raspberries to make pancakes. If it takes 1 3/8 cups to make one pancake, how many pancakes can he make?
Answers
the number of pancakes that can be made using the remaining raspberries are 9 pancakes.
We are given that:
Total raspberries = 13 1/4 cups
Total raspberries = 53 / 4 cups
Now, he used 7 / 8 cups to make a smoothie.
So, Raspberries left = 53 / 4 - 7 / 8
Left = 99 / 8 cups
Now, for making 1 pancake Raspberries required = 1 3/8 sups
= 11 / 8 cups
So, the number of pancakes will be calculated by using division:
Number = 99 / 8 ÷ 11 / 8
Number = 99 / 11
Number = 9 pancakes
Therefore, we get that, the number of pancakes that can be made using the remaining raspberries are 9 pancakes.
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11) Each of Jeff's family, of four, buys a new phone. The total cost is $25 above or below $1200. Write
an equation that models the cost x, in dollars, of a single phone.
Answers
The equation that models the cost x in dollars of a single phone is given by 293.75 ≤ x ≤ 306.25.
What are inequalities ?
When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.
It is given that total cost of phone is $25 above or below $1200.
This is a case of inequality.
Let's assume the cost of one phone is $x.
So cost of 4 phones will be given by 4x.
and this will be equal to total cost which is given as $25 above or below $1200.
So , the inequality is given by ;
1200 - 25 ≤ 4x ≤ 1200 + 25
1175 ≤ 4x ≤ 1225
If we divide by 4 through this inequality then ;
(1175/4) ≤ (4x/ 4) ≤ (1225/ 4)
or
293.75 ≤ x ≤ 306.25
The cost of one phone will lie between $293.75 and $306.25.
Therefore , the equation that models the cost x in dollars of a single phone is given by 293.75 ≤ x ≤ 306.25.
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2 ___ =4
- _.
3. 9????
Answers
21. A scuba diver dives to a depth of 50 feet,
then rises 15 feet, then rises 20 feet. Write an
addition expression to describe this situation.
Then determine the sum and explain its
meaning.
Answers
Answer:
73
Step-by-step explanation:
Based on the given conditions, formulate: 20+50+15-12
Calculate the sum or difference:70+15-12
Calculate the sum or difference:85-12
Calculate the sum or difference:73
get the result:73
Answer:
50 - 15 = 35
35 + 20 = 55
Total amount of feet diven : 55 feet
Which set of ordered pairs (x,y)(x,y) could represent a linear function?{A}= A= {(-6, 6),(-3, 2),(0, -1),,\,(3, -5} {(−6,6),(−3,2),(0,−1),(3,−5)} {B}= B={(-9, 5),(-1, 3),(, 2),(7, 1) {(−9,5),(−1,3),(3,2),(7,1)} {C}= C= {(-9, -3),(-3, 0),(2, 3),(8, 6) {(−9,−3),(−3,0),(2,3),(8,6)} {D}= D= {(-4, -5),(0, -2),(5, 1) (9, 4)} {(−4,−5),(0,−2),(5,1),(9,4)}
Answers
From the given linear functions, the ordered pairs that represents a function is A= {(-6, 6),(-3, 2),(0, -1) (3, 5})
Linear functionsA set of ordered equation represents a linear function if the domain of the coordinates are not repeated.
For instance, the ordered pairs that is a function are the coordinates that do not have any repeated x-coordinates.
From the given linear functions, the ordered pairs that represents a function is A= {(-6, 6),(-3, 2),(0, -1) (3, 5})
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Find the greatest common factor of 24, 40 and 60.
Answers
Answer:
GCF of numbers 24, 40, 60 is 4
GCF(24, 40, 60) = 4
What is the equation 2n x 2m equal to?
Answers
Answer: 2n x 2m
Step-by-step explanation:
Since the variables are different, you cannot do anything.
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
Answers
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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Question below, please answer if you know :)
Answers
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 movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending c
Rewrite 99 + (88 +77) using the Associative Law of Addition.
O (99 +88) + 77
O (88+77) +99
O (99+77) +88
O 99 + (77 +88)
Answers
Step-by-step explanation:
The answer is 99+(77+88)
What are the domain and range of this relation? (-3,14),(0,7),(2,0),(9,-18),(23,-99)
Answers
The range and domain of the relation (-3,14),(0,7),(2,0),(9,-18),(23,-99) are {-3, 0, 2, 9, 23} and {14, 7, 0, -18, -99} respectively.
According to the given question.
We have a relation (-3,14),(0,7),(2,0),(9,-18),(23,-99).
As we know that, the set which contains all the first elements of all the ordered pairs of relation R is known as the domain of the relation.
And, the set which contains all the second elements of all the ordered pairs of relation R is known as the range of the relation.
Therefore, the domain of the given relation is {-3, 0, 2, 9, 23}.
And the range of the given relation is {14, 7, 0, -18, -99}.
Hence, the range and domain of the relation (-3,14),(0,7),(2,0),(9,-18),(23,-99) are {-3, 0, 2, 9, 23} and {14, 7, 0, -18, -99} respectively.
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Brian spent 14 minutes washing the dishes. That was 35% of the total number of minutes he spent doing chores.
How many minutes did Brian spend doing chores?
Answers
Answer: I got my answer by dividing 14 by 35, then multiplying by 100.
Answer: 250 minutes.
Step-by-step explanation: You make a fraction.
Actual time / Percentage
Then you multiply that by 100.
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?
Answers
[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]
How many solutions does the equation 12(2x+6)=6−x have?
Answers
Answer:x=0
Step-by-step explanation:
2x_____=2x10^=______ please help!!!!!!!!!!!!
Answers
We have the expression to be written as 2 × 10 = 2 x 10^ 1 = 20
What is index form?
The index form of a number can be defined as that number written as an exponential expression.
It is also said to be a single number that is raised to another number.
Given the expression;
2x _____ = 2 x 10^ 1 = ______
It is important to note that a number raised to the power 1 is that same number, so we have;
2 × 10
2 x 10^1 = 2 × 10
2 × 10 = 20
Thus, we have the expression to be written as 2 × 10 = 2 x 10^ 1 = 20
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There are 63 books on the bookshelf. There
are 9 books on each shelf. How many
shelves are there?
Answers
Answer:
there are 7 shelves. 9 x 7=63
Answer:
the answer is 7 shelves
Step-by-step explanation:
63÷9=7
The radius, diameter, or circumference of a circle is given. Find the missing measure to the nearest hundredth.
d = 8 1/2in., r=?, C=?
Answers
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 number of possible outcomes for following situation.
Perry chooses from 6 colors and 2 seat designs for his new mountain bike.
Answers
The number of possible outcomes is 12.
What do we mean by permutation and combination?A permutation is an act of arranging objects or numbers in a particular order. Combinations are a method of selecting objects or numbers from a collection or group of objects in such a way that the order of the objects is irrelevant. For example, we consist of four letters: P, Q, R, and S. Every possible arrangement is a combination. However, the combinations of P, Q, R, and S are permutations.To find the possible outcomes:
Given: 6 colors and 2 seat designs.
Therefore, the number of possible outcomes is 12.
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find the value of z.
Answers
Answer:
z = 14.4
Step-by-step explanation:
RX is an angle bisector and divide the opposite side that are proportional to the other 2 sides , that is
[tex]\frac{SX}{XT}[/tex] = [tex]\frac{RS}{RT}[/tex] ( substitute values )
[tex]\frac{5}{6}[/tex] = [tex]\frac{12}{z}[/tex] ( cross- multiply )
5z = 72 ( divide both sides by 5 )
z = 14.4
Solve and graph 3|2x+2|-2x=x+3
Answers
Answer: x= -1
Step-by-step explanation:
[tex]3\left|2x+2\right|-2x=x+3\\[/tex]
Next, we find Positive and Negative Intervals!
[tex]x < -1,\:\:x\ge \:-1[/tex]
Then Last we Solve The inequality for each interval.
No Solution or x= -1
Solve each equation. Check the solution. 3/b+2 = 6/b-1
Answers
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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The length of a pool is 5 more than the width. The perimeter is 96. Whats is the are of the pool.
Answers
Answer:
569,75
Step-by-step explanation:
(x+4) {2}+(y-6) {2} = 48 what is the radius
Answers
By interpreting the equation of the circle in standard form, we conclude that the circle (x + 4)² + (y - 6)² = 48 has a radius of approximately 6.928 units.
What is the radius of the equation of the circle?
In this question we find the equation of a circle in standard form, whose expression is described and explained below:
(x - h)² + (y - k)² = r²
Where:
(h, k) - Coordinates of the center of the circle.r - Radius of the circleAccording to the equation given in the statement, we find a circle with a center at (- 4, 6) and a radius of 6.928 units.
By interpreting the equation of the circle in standard form, we conclude that the circle (x + 4)² + (y - 6)² = 48 has a radius of approximately 6.928 units.
To learn more on equations of the circle: https://brainly.com/question/23799314
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