Answer:
A) [tex]y=\frac{1}{2}x+3[/tex] - Linear
B) [tex]y=4x+2[/tex] - Linear
C) [tex]xy=12[/tex] - Nonlinear
Step-by-step explanation:
To determine whether a function is linear or nonlinear.
The function of a straight line is given as :
[tex]y=mx+b[/tex]
where [tex]m[/tex] represents slope of line and [tex]b[/tex] represents the y-intercept.
Any function that can be represented as a function of straight line is called a linear function otherwise it is nonlinear.
We will check the equations given for linear or nonlinear.
A) [tex]y=\frac{1}{2}x+3[/tex]
The function is in the form [tex]y=mx+b[/tex] and hence it is a linear function with slope [tex]m=\frac{1}{2}[/tex] and y-intercept [tex]b=3[/tex].
B) [tex]y=4x+2[/tex]
The function is in the form [tex]y=mx+b[/tex] and hence it is a linear function with slope [tex]m=4[/tex] and y-intercept [tex]b=2[/tex].
C) [tex]xy=12[/tex]
On solving for [tex]y[/tex]
Dividing both sides by [tex]x[/tex]
[tex]\frac{xy}{x}=\frac{12}{x}[/tex]
[tex]y=\frac{12}{x}[/tex]
This function cannot be represented in the form [tex]y=mx+b[/tex], hence it is a nonlinear function.
What is the largest source of water on earth?
Answer:
Seawater
Step-by-step explanation:
I just took a quiz on this and it said the correct answer is sea water
Erik has $50 in a savings account that earns
5% annually. The interest is not compounded. How much will he have in 1 year?
Answer:
[tex]\$52.50[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=1\ year\\ P=\$50\\ A=?\\r=5\%=5/100=0.05[/tex]
substitute in the formula above
[tex]A=50(1+0.05*1)[/tex]
[tex]A=50(1.05)[/tex]
[tex]A=\$52.50[/tex]
The graph of g(x) = (x-h) + k is shown on the coordinate
grid. What must be true about the signs of h and K?
Both hand k must be positive
Answer:
The sign of h must be negative, and the sign of k must be positive.
Solve the system: x + 2 = y ,x2 − 10 = y
Answer:
If you wanted the intersecting points there is only one and It's (12, 14)
Hope that could help.
7x-7(x+6)=10
B=infinite
C=no solution
D=x=2/7
A=3/5/7
Answer:
No solution
Step-by-step explanation:
we have
[tex]7x-7(x+6)=10[/tex]
Solve for x
Apply distributive property left side
[tex]7x-7x-42=10[/tex]
Combine like terms left side
[tex]-42=10[/tex] ----> is not true
therefore
The equation has no solution
An advertisement consists of a rectangular printed region plus 5-cm margins on the sides and 6-cm margins at top and bottom. If the area of the printed region is to be 238 cm2, find the dimensions of the printed region that minimize the total area. Printed region: l = , w =
Answer:
Dimensions of printed area
x = 7.58 the length
y = 31.40 cm the height
Step-by-step explanation:
Printed region P(a) = 238 cm²
Let call x and y dimensions of printed area then:
A = 238 = x*y ⇒ y = 238/x
And the area of the advertisement is
A(a) = L * W where L = x + 6 and W = y + 5
A(x) = (x + 6 ) * ( y + 5 )
Area as a function of x y = 238/ x
A(x) = (x + 6 ) * ( 238/x + 5 )
A(x) = 238 + 5x + 1428/x + 30
A(x) = 268 + 5x + 1428/x
Taking derivatives on both sides of the equation
A´(x) = 5 - 1428/x²
A´(x) = 0 ⇒ 5x² = 1428 ⇒ x² = 57.12
x = 7.58 cm and y = 238/ 7.58 y = 31.40 cm
-3(v - 3) - 6 is greater than or equal to 12
Answer:
v<=-3
Step-by-step explanation:
-3(v-3)-6>=12
-3v+9-6>=12
-3v+3>=12
-3v>=12-3
-3v>=9
v>=9/-3
v>=-3
What is the following product? (Square root 14 - square root 3) (square root 12 + square root 7)
Answer:
Step-by-step explanation:
The product of this expression is option (A) (2√42 + 7√2 - 6 - √21) is the correct answer.
What is simplification of an expression?Simplification of an expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression. It involves, multiply out the brackets and then simplify the resulting expression by collecting the like terms.
For the given situation,
The expression is [tex](\sqrt{14} -\sqrt{3})( \sqrt{12} +\sqrt{7} )[/tex]
⇒ [tex]\sqrt{14}\sqrt{12} +\sqrt{14} \sqrt{7} -\sqrt{3} \sqrt{12} -\sqrt{3} \sqrt{7}[/tex]
⇒ [tex]\sqrt{168}+\sqrt{98}-\sqrt{36}-\sqrt{21}[/tex]
⇒ [tex]\sqrt{2^{2}(42) } +\sqrt{7^{2}(2) } -\sqrt{6^{2} }-\sqrt{21}[/tex]
⇒ [tex]2\sqrt{42 } +7\sqrt{2 } -6-\sqrt{21}[/tex]
Hence we conclude that the product of this expression is option (A) (2√42 + 7√2 - 6 - √21) is the correct answer.
Learn more about simplification of an expression here
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write an equation for a line parallel to 3x-6y=18
4/7 - -4/7
It’s confusing I calculated it but there’s no answer so I really need help
Answer:
Step-by-step explanation:
4/7 - (-4/7) = 4/7 + 4/7 = 8/7 or 1 1/7......a negative times a negative is a positive...so those two negatives turn into a positive...so ur basically just adding them
The recursive function for a sequence is given below.
f(1) = 200
f(n) = 2 · f(n − 1), for n = 2, 3, 4, ...
What is the 5th term of this sequence?
Answer:
f(5) = 3200
Step-by-step explanation:
Using the recursive formula to generate the terms, that is
f(2) = 2 × f(1) = 2 × 200 = 400
f(3) = 2 × f(2) = 2 × 400 = 800
f(4) = 2 × f(3) = 2 × 800 = 1600
f(5) = 2 × f(4) = 2 × 1600 = 3200
Answer: 6400
Step-by-step explanation:
Given :
f(1) = 200
f(n) = 2.f(n-1) , for n = 2 ,3 , 4 , ...
To find the 5th term
when n = 2 , the sequence becomes
f(2) = 2 .f(2-1)
f(2) = 2 f(1)
since f(1) = 200
therefore:
f(2) = 2 x 200
f(2) = 400
When n = 3
f(3) = 2f(2)
f(3) = 2 x 400
f(3) = 800
When n = 4
f(4) = 2 f(3)
f(4) = 1600
When n =5
f(5) = 2f(4)
f(5) = 3200
When n = 6
f(6) = 2f(5)
f(6) = 6400
Since n = 2 , 3 , 4 ... this means that the 5th term if f(6) , therefore ,the 5th term is 6400
Find the value of y for the following system of equations. x + y = 7 x + y = 7 7 2
The value of y is 28
y = 28
Alexis wants to figure out the price to charge friends for the blu-rays. She doesn’t want to make money at this point since it is a brand new business, but does want to cover her costs. Suppose Alexis created 50 blu-rays. What is the cost of producing those 50 blu-rays? How much is it for each blu-ray?
B(x) = 1250 +1.75x
Answer:
The cost of producing 50 blu-rays will be $1337.5
Each blu-rays must be sold of $26.75
Step-by-step explanation:
The cost of producing x number of blu-rays is given by the relation
B(x) = 1250 + 1.75x ........... (1)
Therefore, the total cost for producing 50 blu-rays will be
B(50) = 1250 + 1.75 × 50 = $1337.5 (Answer)
Now, Alexis does not want to make a profit by selling the blu-rays to her friends and wants just to cover her costs.
Therefore, the selling price of 50 blu-rays will be $1337.5.
Hence, each blu-rays must be sold of [tex]\frac{1337.5}{50} = 26.75[/tex] dollars. (Answer)
Find two consecutive integers whose
Sum is 93.
Answer:
46 and 47.
Step-by-step explanation:
If x is one of the integers then the other is x+1.
x + x + 1 = 93
2x = 92
x = 46.
Use substitution to solve the system of equations.
y + x = 3
y = 1.5x + 1
Answer:
x=0.8, y=2.2 (0.8, 2.2).
Step-by-step explanation:
y+x=3
y=1.5x+1
-------------
1.5x+1+x=3
2.5x=3-1
2.5x=2
x=2/2.5
x=0.8
y+0.8=3
y=3-0.8
y=2.2
To solve the given system of equations by substitution, we substitute the second equation into the first, solve for x, and then substitute x back into the second equation to solve for y, which yields x=0.8 and y=2.2 as the solution.
Explanation:To solve the system of equations using substitution, we start by isolating one variable in one of the equations. Here, the second equation already gives us y in terms of x: y = 1.5x + 1.
Next, we substitute this expression for y into the first equation y + x = 3. This gives us:
(1.5x + 1) + x = 3Combine like terms to solve for x:
2.5x + 1 = 32.5x = 2x = 0.8Now that we have the value of x, we can find the value of y by substituting x back into the equation y = 1.5x + 1:
y = 1.5(0.8) + 1y = 2.2Hence, the solution to the system of equations is x = 0.8 and y = 2.2.
As a final step, you may want to check your solution by plugging the values back into the original equations to confirm that they satisfy both equations.
Draw a picture to show the division. Express your answer as a fraction. 3÷5=
Answer:
your answer is down below
Step-by-step explanation:
Check the picture below.
Is Y=-3x-2 linear or no?
Yes!
This would be in-fact a linear equation!
How?This equation is set up in y=mx+b form, therefore we know it is a linear equation.
Example of a linear equation:y=12x+2
The 12 is the mx in the equation.
And the 2 is the B in the equation! :)
That is how we solve that.
Any questions?
Have a great day!
what is 85% written as a decimal and as a fraction
Answer:
.85 or 85/100
Step-by-step explanation:
Answer:
0.85 is your decimal. 85 / 100 - not simplified.
17 / 20 - simplified.
Step-by-step explanation:
For the decimal, all you gotta do is move your decimal to the left 2 times.
-Hope this helps.
For the fraction, 85% is per 100, so it's 85 / 100. To simplify, the answer is 17 / 20.
Select the four choices below that are equal to 2 × 3 × 4.
Final answer:
2 × 3 × 4, which equals 24.
Explanation:
To find equivalent expressions, we need to think about numbers that can multiply together to reach 24, while also keeping in mind the properties of operations and exponents.
One way is to use exponents. For instance, since 2 × 2 × 2 equals 23 or 8, and 3 × 4 equals 12, multiplying these two results gives us 8 × 12 which is also 24.We could also factor the number differently. Considering 2 × 2 × 2 × 3 can be rearranged to get (22 × 2) × 3 which simplifies to 4 × 2 × 3 and again equals 24.Another expression is taking multiples of 4 such as 4 × 6 which is the same as (2 × 2) × (2 × 3), resulting in the original 24.Last but not least, we can use the distributive property to create 2(3+9) since 3 + 9 equals 12, and 2 × 12 is 24.PLZ HELP!!! Katrina is solving the equation x-2(x+3)=4(2x+3)-x(x-4) . Which equivalent equations might Katrina use? Check all that apply.
Answer:
X2-13X-18=0
Step-by-step explanation:
x-2(x+3)=4(2x+3)-x(x-4)
Multiply through the equations
x-2x-6=8x+12-x2+4x
Equate all to zero
x-2x-6-8x-12+x2-4x=0
x2-4x+x-2x-8x-6-12
x2-13x-18=0
Answer:
A. x minus 2 x minus 6 = 8 x + 12 minus x minus 4
E. Negative x minus 6 = 7 x + 8
Step-by-step explanation:
i took the unit test review on edg
1. You have a 20 foot long ladder that you want to lean against a vertical wall. You want the top of the ladder to touch the wall 19 feet off the ground. What angle will the ladder form with the ground?
2. Using the same 20 foot ladder against the same vertical wall, you decide that it would be better if the ladder formed a 70 degree angle with the ground. How far up the wall will the top of the ladder reach?
3. You want to find the area of triangle BCD but all you have is the information provided in the image below. Then you realize you can use the special right triangle (30-60-90) to find the height of the triangle. Once you know the height and provided base measurement calculate the area.
What is the area of the triangle? Show all steps.
Answer:
1. The ladder forms 71.8° with the ground.
2. The top of the ladder will reach 18.79 feet up the wall.
3. Height = 8.66 cm and area = 21.65 sq. cm.
Step-by-step explanation:
1. If the angle of elevation of the ladder is [tex]\theta[/tex] then we can write
[tex]\sin \theta = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} = \frac{19}{20}[/tex]
⇒ [tex]\theta = \sin ^{-1}(\frac{19}{20}) = 71.8[/tex] Degrees.
Therefore, the ladder forms 71.8° with the ground. (Answer)
2. Now, if the ladder formed a 70 degree angle with the ground and the length of the ladder remains the same as 20 feet, then we can write
[tex]\sin 70 = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} = \frac{x}{20}[/tex]
⇒ x = 20 sin 70 = 18.79 feet.
Therefore, the top of the ladder will reach 18.79 feet up the wall.
3. See the attached figure.
We have, [tex]\tan 60 = \frac{BC}{CD} = \frac{BC}{5}[/tex]
⇒ Height = BC = 5 tan 60 = 8.66 cm.
Therefore, the area of the triangle BCD will be = [tex]\frac{1}{2} \times CD \times BC = \frac{1}{2} \times 5 \times 8.66 = 21.65[/tex] sq. cm. (Answer)
Write a polynomial equation with roots 5 and -9i. X^3-?x^2+?X-?=0
Answer:
x³ - 5x² + 81x - 405 = 0
Step-by-step explanation:
Complex roots occur in conjugate pairs.
Thus given x = - 9i is a root then x = 9i is also a root
The factors are then (x - 5), (x - 9i) and (x + 9i)
The polynomial is the the product of the roots, that is
f(x) = (x - 5)(x - 9i)(x + 9i) ← expand the complex factors
= (x - 5)(x² - 81i²) → note i² = - 1
= (x - 5)(x² + 81) ← distribute
= x³ + 81x - 5x² - 405, thus
x³ - 5x² + 81x - 405 = 0 ← is the polynomial equation
The required polynomial equation is x³ - 5x² + 81x - 405 = 0 with roots 5 and -9i.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
As we know that complex roots occur in conjugate pairs.
Thus given x = - 9i is a root then x = 9i is also a root
The factors are then (x - 5), (x - 9i) and (x + 9i)
The polynomial is the product of the roots, that is
f(x) = (x - 5)(x - 9i)(x + 9i)
Expand the complex factors in the above equation
f(x) = (x - 5)(x² - 81i²) [∵ i² = - 1]
f(x) = (x - 5)(x² + 81)
f(x) = x³ + 81x - 5x² - 405
This is equating to zero.
f(x) = 0
Thus, the required polynomial is x³ - 5x² + 81x - 405 = 0
Learn more about the polynomial here:
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Need help with number 6
Answer:
Step-by-step explanation:
Two fire hoses are used to extinguish a fire. Hose A, when turned on alone, can extinguish the fire in 7 minutes, while hose B takes "n" minutes more time than hose A. Find an expression (in terms of "n") for how much of the fire they will extinguish in 1 minute when both hoses are turned on together.
The expression in terms of "n" for how much of the fire they will extinguish in 1 minute when both hoses are turned on together is [tex]\frac{n + 14}{7n + 49}[/tex]
Solution:
Given that,
Hose A, when turned on alone, can extinguish the fire in 7 minutes
Hose B takes "n" minutes more time than hose A
Hose takes (n + 7) minutes to extinguish the fire
STEP 1: Calculate how much work (here work is to extinguish the fire) each person does in one minute
[tex]Hose A = \frac{1}{7}th \text{ of the work }\\\\Hose B = \frac{1}{n+7}th \text{ of the work }[/tex]
STEP 2: Add up the amount of work done by each person in one minute
Work done in one minute when both are working together:
[tex]\rightarrow \frac{1}{7} + \frac{1}{n + 7}\\\\\rightarrow \frac{n + 7 + 7}{7n + 49}\\\\\rightarrow \frac{n + 14}{7n + 49}[/tex]
Therefore, the expression in terms of "n" for how much of the fire they will extinguish in 1 minute when both hoses are turned on together is:
[tex]\frac{n + 14}{7n + 49}[/tex]
The total rate in 1 minute is [tex]\frac{1}{7} + \frac{1}{7+n}[/tex].
To find the expression for how much of the fire they will extinguish in 1 minute when both Hose A and Hose B are turned on together, we need to determine their individual rates first.
Hose A can extinguish the fire in 7 minutes, so its rate is:
⇒ Rate of Hose A = 1 fire ÷ 7 minutes = [tex]\frac{1}{7}[/tex].
Hose B takes 'n' minutes more than Hose A. Therefore, it takes (7 + n) minutes to extinguish the fire, so its rate is:
⇒ Rate of Hose B = 1 fire ÷ (7 + n) minutes = [tex]\frac{1}{7+n}[/tex].
When both hoses are operating together, their combined rate is the sum of their individual rates:
⇒ Combined Rate = [tex]\frac{1}{7} + \frac{1}{7+n}[/tex]
We need the combined rate per minute:
⇒ Combined Rate per Minute = [tex]\frac{1}{7} + \frac{1}{7+n}[/tex]
This fraction represents the portion of the fire they will extinguish in 1 minute when both hoses are used together.
Express your answer in scientific notation.
2.8\cdot10^{-3} -0.00065 =2.8⋅10
−3
−0.00065=2, point, 8, dot, 10, start superscript, minus, 3, end superscript, minus, 0, point, 00065, equals
Answer:
2.15
×
10
−
3
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Answer:
The answer is 2.15 * 10^-3
Step-by-step explanation:
I got this answer from Khan Academy.
Hope this helps! :)
Which of the following expressions are equivalent to 8 3/2
Answer:
19/2
Step-by-step explanation:
8 3/2=19/2
Answer:
19/2
Step-by-step explanation:
Use the table of net profits and losses to find the net profit for the week.
Bert's Catering Service
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
$200 –$130 –$25 $240 $225 –$100 $75
$485
–$485
$5
$335
Your answer is A. $485
200 – 130 = 70
70 – 25 = 45
45 + 240 = 285
285 + 225 = 510
510 – 100 = 410
410 + 75 = 485
Solve 3x + 6 = 34. need anwser asap
A.-2
B.4
C.6
D.10
The correct solution for the equation 3x + 6 = 34 is x = 9.33 (repeating). The provided options do not match this solution, indicating an error in the given choices.
Explanation:To solve the equation 3x + 6 = 34, start by subtracting 6 from both sides to isolate the term with the variable x on one side. You get 3x = 28. Next, divide both sides by 3 to solve for x, which gives you x = 28 / 3 or 9.33 (repeating). None of the provided options A, B, C, or D matches the solution, indicating a potential error in the question or the options provided.
A1.0 kg cart moving right at 5.0 -- on a frictionless track
collides with a second cart moving left at 2.0 m/s.
The 1.0 kg cart has a final speed of 4.0 m/s to the left, and the
second cart has a final speed of 1.0 m/s
to the right.
What is the mass of the second cart?
Consider rightward as the positive direction.
Answer:
3.0 kg
Step-by-step explanation:
Momentum before collision = momentum after collision
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
(1.0 kg) (5.0 m/s) + m (-2.0 m/s) = (1.0 kg) (-4.0 m/s) + m (1.0 m/s)
5.0 kg m/s + m (-2.0 m/s) = -4.0 kg m/s + m (1.0 m/s)
9.0 kg m/s = m (3.0 m/s)
m = 3.0 kg
. A friend opens a savings account by depositing $1000. He deposits an
additional $75 into the account each month.
a. What is a rule that represents the amount of money in the account as an
arithmetic sequence?
b. How much money is in the account after 18 months? Show your work.
Answer:
the rule is:
75x + 1000
Step-by-step explanation:
after 18 months
plug 18 in for x.
75(18) + 1000
= 1350
1350 + 1000
= 2350
$2350 after 18 months
Answer:
Part (A) 1000+(n-1)75
Part (B) 2,275
subtract the 1 it's not 2350
Step-by-step explanation: