Find the constant rate of change for each linear function and interpret their meaning.
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Related Questions
an internet company charges a one time setup fee of 44.99 and a monthly fee of 29.99 for internet service the company is offering a 25 percent discount on the monthly fee for the first year
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yark
Write a polynomial function of f of least degree with rational coefficients a leading coefficient of 1 and the given zeros -5 2i
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y = (x + 5)(x + 2i)(x - 2i) = (x - 5)(x^2 + 4)
which expands to
y = x^3 + 5x^2 + 4x + 20
find the nonpermissible replacement for y in this expression Y+7/Y-3
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Final answer:
The nonpermissible value for y in the expression (Y+7)/(Y-3) is 3, because it would make the denominator zero, resulting in an undefined expression.
Explanation:
The question is asking to find the nonpermissible value for y in the expression (Y+7)/(Y-3). In algebra, nonpermissible values are values for the variable that would make the denominator of a fraction equal to zero. We set the denominator of our expression equal to zero and solve for y.
Steps to find the nonpermissible value:
Identify the denominator of the expression, which is (Y-3).
Set the denominator equal to zero: Y - 3 = 0.
Solve for y: Y = 3.
Therefore, the nonpermissible replacement for y is 3, as substituting this value into the denominator would create a division by zero, which is undefined in mathematics.
Evaluate the expression. If necessary, round to the nearest hundredth.
log 1,000
3
103
1/3
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3 is the correct answer.
[tex] log(1000) = log_{10}( {10}^{3} ) = 3 [/tex]
So the answer to your question is 3.
helpppppppppppppppppppppp
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Explanation:
1) given:
y = (x + 3)^2 + (x + 4)^2
2) expand the binomials:
y = x^2 + 6x + 9 + x^2 + 8x + 16
3) add like terms:
y = 2x^2 + 14x + 25
4) take common factor 2 of the first two terms:
y = 2 (x^2 + 7x) + 25
5) complete squares for x^2 + 7x
x^2 + 7x = [x +(7/2)x ]^2 - 49/4
6) substitue x^2 + 7x = (x + 7/2)^2 - 49/4 in the equation for y:
y = 2 [ (x + 7/2)^2 - 49/4] + 25
7) take -49/4 out of the square brackets.
y = 2 (x + 7/2)^2 - 49/2 + 25
8) add like terms:
y = 2(x + 7/2)^2 + 1/2
And that is the vertex for of the given expression.
What is the solution to the system of equations below? Y=-4/5x-6 & y=-30
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-30=-4/5x-6
And then solve for x:
Add 6 on both sides.
-24=-4/5x
Then multiply by the reciprocal of -4/5.
-5/4*-24=-5/4*-4/5x
x=30
But then you are gonna want to plug 30 in for x in y=-4/5x-6 to make sure that it is the same as y=-30.
The solution of the system is y = -30 and x = 30.
How to solve the system of equations?Here we have two equations:
y = -(4/5)*x - 6
y = -30
The second equation can be replaced in the first one, so we get:
-30 = -(4/5)*x - 6
Now we can solve that for x.
-30 + 6 = -(4/5)*x
24*(5/4) = x = 30
So the solution of the system is y = -30 and x = 30.
If you want to learn more about system of equations:
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What is the circumference of the circle in terms of pi? The radius is 2.2 and I got 13.82 but the choices are 1.1, 1.21, 2.2 and 4.4 im so confused so could someone please explain what i did wrong?
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C = 2 π (2.2)
C = 4.4 π (in term of pi)
answer
4.4π
While training for a marathon, Sean runs at least 28 miles a week. He has already ran 6 miles this week. The inequality shown can be used to find m, the number of miles Sean still needs to run this week. m + 6 ≥ 28 Which inequality represents the solution set for this situation? A) m ≥ 22 B) m ≤ 22 C) m ≤ 34 D) m ≥ 34
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Explanation : Just l like a normal equation , we need to isolate the variable to get its value. We can do that by simply substracting 6 from both sides of the equation :
m + 6 >= 28
m + 6 - 6 >= 28 - 6
6 - 6 cancel out so we end up with
m >= 22
I hope you understood my brief explanation. And please consider marking this awnser as Branliest if you think it deserves it. Thank you so :)
Answer: A) m ≥ 22
Step-by-step explanation:
Hi, to answer this question we simply have to solve the inequality given for m (miles ran per week).
m + 6 ≥ 28
Subtracting 6 from both sides:
m+6-6 ≥ 28 -6
m ≥ 22
Sean still needs to run 22 miles this week.
So, the correct option is A) m ≥ 22
Feel free to ask for more if needed or if you did not understand something.
Which unit should be studied to review symbols from set theory? Unit 1 Unit 3 Unit 5 Unit 7
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Write an equation that is perpendicular to y = -7x + 2 and passes through (7 , 5)
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The slope of a line perpendicular to another line is the negative reciprocal, that is, [tex]m_{perp} = \frac{-1}{m} [/tex].
For your equation, the slope is –7. That means the slope of its perpendicular line must be [tex]- \frac{-1}{7} = \frac{1}{7} [/tex].
Now, we must also find such a line that passes through (7, 5). It is easiest to write this in point-slope form, [tex]y-y_1=m(x-x_1)[/tex].
We get [tex]y-5= \frac{1}{7} (x-7)[/tex]. Technically, we are done, but it is customary to convert this into slope-intercept form, [tex]y=mx+b[/tex].
[tex]y-5= \frac{1}{7} (x-7)\\\\y= \frac{1}{7}x-1+5\\\\y= \frac{1}{7}x+4[/tex].
And that's our final answer. We can verify the solution graphically. See attached.
In general, our steps are:
1) Find the slope of the given line if it is not given directly.
2) Find the slope of the perpendicular line (the negative reciprocal).
3) Identify the point it must pass through.
4) Substitute the values into the point-slope form.
5) Write the equation in slope-intercept form.
Choose the option that correctly completes the statement.
The measure of an exterior angle of a triangle is _____ the sum of the measures of the remote interior angles.
less than
greater than
equal to
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The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
Explanation:The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
For any triangle, the sum of the measures of the three interior angles is always 180 degrees. An exterior angle is formed by extending one side of the triangle. The sum of the measures of the exterior angle and its corresponding remote interior angles is always 180 degrees. Therefore, the measure of an exterior angle is equal to the sum of the measures of the remote interior angles.
Final answer:
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
Explanation:
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
For example, if one of the remote interior angles of a triangle measures 40 degrees, then the corresponding exterior angle measures 40 degrees as well. The sum of the measures of the other two interior angles would be 140 degrees, making the exterior angle equal to 40 degrees.
Therefore, the correct option that completes the statement is equal to.
IMAGE ATTACHED
At an amusement park, the probability that a child eats a hot dog and drinks a soda pop is 0.38. The probability that a child eats a hot dog is 0.61, and the probability that a child drinks soda pop is 0.89. What is the probability (rounded to the nearest hundredth) that a child drinks soda pop given that the child has already eaten a hot dog? Hint: cap p left parenthesis cap a vertical line cap b right parenthesis equals start fraction cap p left parenthesis cap a intersection cap b right parenthesis over cap p left parenthesis cap b right parenthesis end fraction
A| 0.34
B| 0.43
C| 0.62
D| 0.69
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It's been estimated that if you consume an extra 3,500 calories, you will gain 1 pound of fat. one can of soda contains 40 grams of sugar. sugar has 4 calories per gram. if a person drinks a six-pack of soda every day, how many pounds will he or she gain in 1 year?
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1 can of soda---------------> 40 grams of sugar
if 1 gram sugar------------------------------------>has 4 calories
40 grams (1 can of soda)-----------------------> X
X=40*4=160 calories
then
1 can of soda--------------> has 160 calories
six-pack of soda every day--------------> 6*160=960 calories every day
in one year------------> 960*365=350400 calories in one year
if 3500 calories----------------> 1 pound of fat
350400 calories----------------X
X=350400/3500=100.11 pound
In one year she or he will gains 100.11 pound of fat
the answer is 100.11 pound
Every morning, a deli offers a “commuter special” in which customers can select a pastry, beverage, and a copy of one of the local papers and pay $1.00. Their options are listed in the table.
Last Tuesday, the deli did not have any muffins. How did that affect the number of possible combinations?
A. It decreased the number of combinations by 1.
B. It decreased the number of combinations by 4.
C. It decreased the number of combinations by 8.
D. It decreased the number of combinations by 10.
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Answer: C
c. It decreased the number of combinations by 8.
please help thank you
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When doing ratios, if you know the proportion of the length and width you just multiply that ratio to the origingal value
If a company is considering the purchase of a parcel of land that was acquired by the seller for $93,000 is offered for sale at $166,000, is assessed for tax purposes at $103,000, is recognized by the purchaser as easily being worth $156,000, and is purchased for $153,000, the land should be recorded in the purchaser's books at:
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Answer:
The land should be recorded in the purchaser's books at : $153,000.
Step-by-step explanation:
Since the parcel of land is purchased by the company for $153,000, hence the land should be recorded in the purchaser's books at : $153,000.
He perimeter of this pentagon is 280 cm. find the lengths of the sides.
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280 / 5 which equals 56 cm
What is the solution to 2h+8>3h-6
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2h-3h>-6-8
-h>-14
h<14
Answer h∈(-∞;14)
There's a 40% chance of rain on Tuesday and a 50% chance of rain Friday. What percent will it rain both Tuesday and Friday?
p.s. this is a probability question I think
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50% or 50/100 which is in decimal format 0.5.
P( tueday AND friday) <----- AND is a keyword, means product
P(tuesday) AND P(friday)
0.4 * 0.5
0.2 or 0.2 * 100 or 20% chance that it will rain on both days.
One reading list had a total of 12 fiction and nonfiction books. Compared to the first list, there are twice as many fiction books and 3 times as many nonfiction books making a total of 28 books on the second reading list. Write a system of linear equations and find the number of fiction and nonfiction books on the first list.
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x = fiction books
y = nonfiction books
We write the system of equations that best suits the problem.
We have then:
x + y = 12
2x + 3y = 28
Solving the system:
x = 8
y = 4
Answer:
x + y = 12
2x + 3y = 28
the number of fiction and nonfiction books on the first list are:
8 fiction books
4 nonfiction books
Answer:
(8,4)
Step-by-step explanation:
yes
The simplest form of square root of eighty can be written as a times square root of b, where a = and b = .
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The correct answer is:
A=4
B=5
hopes this helps you and future people!
Answer:
a = 4 and b = 5
Step-by-step explanation:
The simplest form of square root of eighty can be written as:
[tex]\sqrt{80}=\sqrt{2\times2\times2\times2\times5}[/tex]
Now as it is a square root function, we will pair up the four 2's in two pairs.
And will take out [tex]2\times2[/tex] outside the square root.
Making the answer = [tex]2\times2\sqrt{5}[/tex]
or [tex]4\sqrt{5}[/tex]
So, a = 4
and b = 5
Suppose we set θ0=−2,θ1=0.5 in the linear regression hypothesis from q1. what is hθ(6)?
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hθ(x) = -2 + 0.5x
hθ(6) = -2 + 0.5 * 6
hθ(6) = 1
HOW ARE RESTRICTIONS AND DISCONTINUITIES CREATED IN RATIONAL EXPRESSIONS? HOW CAN THEY BE ACCOUNTED FOR GRAPHICALLY?
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Graphically, this is usually represented by a dashed vertical line indicating a vertical asymptote.
In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator zero, as division by zero is undefined. Graphically, these are represented as vertical asymptotes or holes. They can be accounted for by noting the x-values where the denominator equals zero.
Explanation:In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator of the expression equal to zero, as division by zero is undefined. A rational expression is a ratio of two polynomials, typically written in the form P(x)/Q(x), where P(x) and Q(x) are polynomial expressions and x is a variable.
For example, in the rational expression (x+2)/(x-3), x-3 is the denominator. The restriction is determined by setting the denominator equal to zero. If x-3 equals zero, then the value of x that makes this true is 3. Therefore, x cannot be 3 as this would make the denominator zero, creating a discontinuity in the rational expression.
Graphically, discontinuities in rational expressions are represented as vertical asymptotes or holes. A vertical asymptote occurs when the denominator of the fraction is zero but the numerator is not. A hole occurs when both the numerator and the denominator are zero at the same point. These can be accounted for by noting the x-values where the denominator equals zero.
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Given the geometric sequence 100, 50, 25, ..., find the 7th term.
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T(7)=100(1/2)^6=1.5625
What is the x-intercepts of the graph of y = 12x-5x-2
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First, we see that it's already written in slope intercept, y = mx + b where m is the slope and b is the y intercept, we just need to simplify the like terms on the right. We have:
y = 12x-5x-2
y = 7x - 2
Now that we have it in slope intercept form, whenever we have an x intercept, since it is crossing the x axis, there's no y value. We plug in 0 for y:
0 = 7x - 2
2 = 7x
2/7 = x
The x intercept is (2/7, 0)
Hope this helps!
Jason is buying a home theater system on layaway for $349. If he makes a down payment of $25 and pays $54 each week will it take Jason to pay for the home theater system?
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First, you would take 349 and subtract 25 from it.(349-25=324) This gets rid of the down payment.
Next, you would divide 324 by 54. (324÷54=6)
It would take him 6 weeks!
Hope this helped! And make sure to check my calculations!
Godspeed
-Song
Jason will take 6 weeks to pay off the home theater system on layaway after making an initial down payment of $25 and weekly payments of $54.
The student's question is about how long it will take Jason to pay for a home theater system using a layaway plan. Jason has made an initial down payment of $25 and will make weekly payments of $54.
To calculate the time it will take to pay off the remaining balance, we subtract the down payment from the total cost: $349 - $25 = $324. Then, we divide the remaining balance by the weekly payment amount: $324 / $54 = 6. This means it will take Jason 6 weeks to pay off the home theater system on layaway.
Please help me !! Thank you!!
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2. yes. The cost is proportional to the number of tickets, hence a linear function of the number of tickets.
3. no. The population is modeled by an exponential function.
4. yes. Distance is proportional to time at a constant speed.
5. yes. (maybe) In the context of this question, "at a constant rate" is presumed to mean "by a constant amount". In that case, growth is linear.
If the rate expressed as a constant percentage (say, 3%) per year, then growth is exponential, not linear.
Fuel prices have increased by 9% this year. The smiths family’s fuel bill for this year is now £1956. How much was the bill likely to have been last year
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1956 times .09 equals 176.04, subtract 176.04 fro 1956 and you get 1779.96.
.hey can you help me I will crown you brainliest
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A rectangle has a length of 12 millimeters and a width of 17 millimeters.
What is the effect on the perimeter when the dimensions are multiplied by 12?
a. The perimeter is increased by a factor of 12.
b. The perimeter is increased by a factor of 48.
c. The perimeter is increased by a factor of 144.
d. The perimeter is increased by a factor of 576.
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ok so original perimeter = 12 +12 + 17 +17 = 58 mm
if dimensions are multiplied by 12:
12*12 = 144 and 17*12 = 204
new perimeter = 144 +144 +204 +204 = 696 mm
696 / 58 = 12
so the perimeter increased by a factor of 12, answer is A
Answer:
The perimeter is increased by a factor of 12.
Option (a) is correct .
Step-by-step explanation:
Formula
Perimeter of a rectangle = 2 (Length + Breadth)
As given
A rectangle has a length of 12 millimeters and a width of 17 millimeters.
Perimeter of a rectangle = 2 × (12 + 17)
= 2 × 29
= 58 millimeters ²
As given
when the dimensions are multiplied by 12 .
New Length = 12 × 12
= 144 millimeter
New Breadth = 17 × 12
= 204 millimeter
Thus
New Perimeter of a rectangle = 2 × (144 + 204)
= 2 × 348
= 696 millimeter²
[tex]\frac{New\ perimeter\ of\ a\ rectangle}{Perimeter\ of\ a\ rectangle} = \frac{696}{58}[/tex]
[tex]\frac{New\ perimeter\ of\ a\ rectangle}{Perimeter\ of\ a\ rectangle} = 12[/tex]
Therefore the perimeter is increased by a factor of 12.
Option (a) is correct .