Math 7 until 2 test.
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Directions - Answer all the parts regarding the following scenario:
An Internet service provider charges $18 per month plus an initial set-up fee of $45.
A) Create a linear equation to model the situation. Equation:
B) Find the cost of the plan after the following intervals:
After 1 month =
dollars.
After 6 months =
dollars.
fter 1 year
dollars.
Answer:1.--63 dollars
6 months-108
1 year=216
Step-by-step explanation:18 times 6 is 108 and 108 times 2 is 216
If it exists, solve for the inverse function of each of the following:
1. f(x) = 25x - 18
6. gala? +84 - 7
7. 10) = (b + 6) (6-2)
3. A(7)=-=-
4. f(x)=x
9. h(c) = V2c +2
+30
10. f(x) =
5. f(a) = a +8
ox-1
2. 9(x) = -1
2x+17
8. () - 2*
Answer:
The solution is too long. So, I included them in the explanation
Step-by-step explanation:
This question has missing details. However, I've corrected each question before solving them
Required: Determine the inverse
1:
[tex]f(x) = 25x - 18[/tex]
Replace f(x) with y
[tex]y = 25x - 18[/tex]
Swap y & x
[tex]x = 25y - 18[/tex]
[tex]x + 18 = 25y - 18 + 18[/tex]
[tex]x + 18 = 25y[/tex]
Divide through by 25
[tex]\frac{x + 18}{25} = y[/tex]
[tex]y = \frac{x + 18}{25}[/tex]
Replace y with f'(x)
[tex]f'(x) = \frac{x + 18}{25}[/tex]
2. [tex]g(x) = \frac{12x - 1}{7}[/tex]
Replace g(x) with y
[tex]y = \frac{12x - 1}{7}[/tex]
Swap y & x
[tex]x = \frac{12y - 1}{7}[/tex]
[tex]7x = 12y - 1[/tex]
Add 1 to both sides
[tex]7x +1 = 12y - 1 + 1[/tex]
[tex]7x +1 = 12y[/tex]
Make y the subject
[tex]y = \frac{7x + 1}{12}[/tex]
[tex]g'(x) = \frac{7x + 1}{12}[/tex]
3: [tex]h(x) = -\frac{9x}{4} - \frac{1}{3}[/tex]
Replace h(x) with y
[tex]y = -\frac{9x}{4} - \frac{1}{3}[/tex]
Swap y & x
[tex]x = -\frac{9y}{4} - \frac{1}{3}[/tex]
Add [tex]\frac{1}{3}[/tex] to both sides
[tex]x + \frac{1}{3}= -\frac{9y}{4} - \frac{1}{3} + \frac{1}{3}[/tex]
[tex]x + \frac{1}{3}= -\frac{9y}{4}[/tex]
Multiply through by -4
[tex]-4(x + \frac{1}{3})= -4(-\frac{9y}{4})[/tex]
[tex]-4x - \frac{4}{3}= 9y[/tex]
Divide through by 9
[tex](-4x - \frac{4}{3})/9= y[/tex]
[tex]-4x * \frac{1}{9} - \frac{4}{3} * \frac{1}{9} = y[/tex]
[tex]\frac{-4x}{9} - \frac{4}{27}= y[/tex]
[tex]y = \frac{-4x}{9} - \frac{4}{27}[/tex]
[tex]h'(x) = \frac{-4x}{9} - \frac{4}{27}[/tex]
4:
[tex]f(x) = x^9[/tex]
Replace f(x) with y
[tex]y = x^9[/tex]
Swap y with x
[tex]x = y^9[/tex]
Take 9th root
[tex]x^{\frac{1}{9}} = y[/tex]
[tex]y = x^{\frac{1}{9}}[/tex]
Replace y with f'(x)
[tex]f'(x) = x^{\frac{1}{9}}[/tex]
5:
[tex]f(a) = a^3 + 8[/tex]
Replace f(a) with y
[tex]y = a^3 + 8[/tex]
Swap a with y
[tex]a = y^3 + 8[/tex]
Subtract 8
[tex]a - 8 = y^3 + 8 - 8[/tex]
[tex]a - 8 = y^3[/tex]
Take cube root
[tex]\sqrt[3]{a-8} = y[/tex]
[tex]y = \sqrt[3]{a-8}[/tex]
Replace y with f'(a)
[tex]f'(a) = \sqrt[3]{a-8}[/tex]
6:
[tex]g(a) = a^2 + 8a- 7[/tex]
Replace g(a) with y
[tex]y = a^2 + 8a - 7[/tex]
Swap positions of y and a
[tex]a = y^2 + 8y - 7[/tex]
[tex]y^2 + 8y - 7 - a = 0[/tex]
Solve using quadratic formula:
[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]a = 1[/tex] ; [tex]b = 8[/tex]; [tex]c = -7 - a[/tex]
[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex] becomes
[tex]y = \frac{-8 \±\sqrt{8^2 - 4 * 1 * (-7-a)}}{2 * 1}[/tex]
[tex]y = \frac{-8 \±\sqrt{64 + 28 + 4a}}{2 * 1}[/tex]
[tex]y = \frac{-8 \±\sqrt{92 + 4a}}{2 * 1}[/tex]
[tex]y = \frac{-8 \±\sqrt{92 + 4a}}{2 }[/tex]
Factorize
[tex]y = \frac{-8 \±\sqrt{4(23 + a)}}{2 }[/tex]
[tex]y = \frac{-8 \±2\sqrt{(23 + a)}}{2 }[/tex]
[tex]y = -4 \±\sqrt{(23 + a)}[/tex]
[tex]g'(a) = -4 \±\sqrt{(23 + a)}[/tex]
7:
[tex]f(b) = (b + 6)(b - 2)[/tex]
Replace f(b) with y
[tex]y = (b + 6)(b - 2)[/tex]
Swap y and b
[tex]b = (y + 6)(y - 2)[/tex]
Open Brackets
[tex]b = y^2 + 6y - 2y - 12[/tex]
[tex]b = y^2 + 4y - 12[/tex]
[tex]y^2 + 4y - 12 - b = 0[/tex]
Solve using quadratic formula:
[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]a = 1[/tex] ; [tex]b = 4[/tex]; [tex]c = -12 - b[/tex]
[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex] becomes
[tex]y = \frac{-4\±\sqrt{4^2 - 4 * 1 * (-12-b)}}{2*1}[/tex]
[tex]y = \frac{-4\±\sqrt{4^2 - 4 *(-12-b)}}{2}[/tex]
Factorize:
[tex]y = \frac{-4\±\sqrt{4(4 - (-12-b))}}{2}[/tex]
[tex]y = \frac{-4\±2\sqrt{(4 - (-12-b))}}{2}[/tex]
[tex]y = \frac{-4\±2\sqrt{(4 +12+b)}}{2}[/tex]
[tex]y = \frac{-4\±2\sqrt{16+b}}{2}[/tex]
[tex]y = -2\±\sqrt{16+b}[/tex]
Replace y with f'(b)
[tex]f'(b) = -2\±\sqrt{16+b}[/tex]
8:
[tex]h(x) = \frac{2x+17}{3x+1}[/tex]
Replace h(x) with y
[tex]y = \frac{2x+17}{3x+1}[/tex]
Swap x and y
[tex]x = \frac{2y+17}{3y+1}[/tex]
Cross Multiply
[tex](3y + 1)x = 2y + 17[/tex]
[tex]3yx + x = 2y + 17[/tex]
Subtract x from both sides:
[tex]3yx + x -x= 2y + 17-x[/tex]
[tex]3yx = 2y + 17-x[/tex]
Subtract 2y from both sides
[tex]3yx-2y =17-x[/tex]
Factorize:
[tex]y(3x-2) =17-x[/tex]
Make y the subject
[tex]y = \frac{17 - x}{3x - 2}[/tex]
Replace y with h'(x)
[tex]h'(x) = \frac{17 - x}{3x - 2}[/tex]
9:
[tex]h(c) = \sqrt{2c + 2}[/tex]
Replace h(c) with y
[tex]y = \sqrt{2c + 2}[/tex]
Swap positions of y and c
[tex]c = \sqrt{2y + 2}[/tex]
Square both sides
[tex]c^2 = 2y + 2[/tex]
Subtract 2 from both sides
[tex]c^2 - 2= 2y[/tex]
Make y the subject
[tex]y = \frac{c^2 - 2}{2}[/tex]
[tex]h'(c) = \frac{c^2 - 2}{2}[/tex]
10:
[tex]f(x) = \frac{x + 10}{9x - 1}[/tex]
Replace f(x) with y
[tex]y = \frac{x + 10}{9x - 1}[/tex]
Swap positions of x and y
[tex]x = \frac{y + 10}{9y - 1}[/tex]
Cross Multiply
[tex]x(9y - 1) = y + 10[/tex]
[tex]9xy - x = y + 10[/tex]
Subtract y from both sides
[tex]9xy - y - x = y - y+ 10[/tex]
[tex]9xy - y - x = 10[/tex]
Add x to both sides
[tex]9xy - y - x + x= 10 + x[/tex]
[tex]9xy - y = 10 + x[/tex]
Factorize
[tex]y(9x - 1) = 10 + x[/tex]
Make y the subject
[tex]y = \frac{10 + x}{9x - 1}[/tex]
Replace y with f'(x)
[tex]f'(x) = \frac{10 + x}{9x -1}[/tex]
The volume of a right circular cone is 300 cubic inches. What is the volume, in cubic inches, of
a right cylinder that has the same base and height as the cone?
Answer:
900 cubic inches.
Step-by-step explanation:
Given the following data
Volume of right circular cone = 300in³
We know that the volume of a right circular cone is given by the formula;
[tex] V = \frac{1}{3} \pi r^{2}h[/tex]
Where;
V is the volume of right circular cone.r is the radius of the base of the right circular cone.h is the height of the right circular cone.The volume of a right circular cylinder is given by the formula;
[tex] V = \pi r^{2}h[/tex]
Thus, multiplying the volume of the right circular cone by 3 would give us the volume of the right circular cylinder.
[tex] V = \frac{1}{3} \pi r^{2}h * 3[/tex]
Substituting into the equation, we have;
V = 300 * 3
V = 900in³
Therefore, the volume of a right cylinder that has the same base and height as the cone is 900 cubic inches.
The scatterplot shows the average monthly outside temperature and the monthly electricity cost.
Based on the scatterplot, what is the best prediction for the electricity cost if the temperature for the month is 21 degrees celsius
A) $450
B) $500
C) $600
D) $700
Answer: 600
Step-by-step explanation:
I just took the test
Help please, thanks.
Follow riderty on twitch
okay???i guess sooooo??
Blake records the amount of daily rainfall along with the average daily temperature for several days. The scatterplot shows his data.
A graph titled Rainfall and Temperature has rainfall (inches) on the x-axis and average daily temperature (degrees Fahrenheit) on the y-axis. Points are grouped closely together. Point (2.5, 98) is above the cluster.
Which statement about the outlier in the data set is true?
Answer:
I think its C (I think..im doing the test so ill tell u if its right or wrong)
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Blake should not include the outlier because it overstates the effect of rainfall on temperature.
what is 15% of 140? solve for x
Answer:
21
Step-by-step explanation:
140*0.15 is 21
Answer:
21
Step-by-step explanation:
What is the slope of the line?
Answer:
( -8 , 3 ) 8 Down 3 Across
Jeremy is on the planning committee for the rock climbing club. He is putting together a trip where members can go outdoor rock climbing. He is trying to determine how high the group should climb and how long the trip should last. He calls multiple parks in the area that offer rock climbing and collects data on the height of the rock formations and the average time it takes people to reach the top and come back down. The data he found is shown.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Daniels mom started a college savings account for him when he was born.she opened the account with $5 and planned to deposit $100 each month.the equation represents the balance in the account,y,based on the number of months since the account was opened,x.write the equation
Answer:
m(x) = 5 + 100x
Step-by-step explanation:
Let m(x) be the balance of the account after x months.
m(x) = 5 + 100x
Solve for x
(x/b)-y=3
Answer:
x = by + 3b
Step-by-step explanation:
I hope this helps ya!
what’s the equation show work
Answer:
hi
Step-by-step explanation:
A farmer has 30 boxes of eggs.
There are 6 eggs in each box.
Write, as a ratio, the number of eggs in three boxes to the total number of eggs.
Give your answer in its simplest form.
The ratio of the number of eggs in three boxes to the total number of eggs is 1: 15 in its simplest terms.
How to obtain real measurements from the ratio of two measurements?Suppose the real measurements were "a" and "b". Then their ratio will be formed as;
[tex]\dfrac{a}{b} = \dfrac{p \times x}{q \times x} = \dfrac{p}{q}[/tex]
where is a common factor (not 1)? This shows that to get the real measurements from the given ratio, we need to assume to have some factor possibly canceled from both the numerator and the denominator.
Thus, a = px, b = qx
We have given that farmer 30 boxes of eggs. and there are 6 eggs in each box.
Thus, we know that the total number of eggs is the same as the number of eggs given in 30 boxes.
Hence, the ratio will be;
2: 30,
then divide both sides by 2 ;
1: 15
Therefore, the ratio of the number of eggs in three boxes to the total number of eggs is 1: 15 in its simplest terms.
Learn more about ratios here:
brainly.com/question/186659
#SPJ2
Please sol
ve this real quick
Answer:
for question two: 12
for question four: 1/3
for question six: 25.75 (rounded to two decimal places)
What is the value of the expression below when z=6 and w= 7
8z + 7w?
Answer:
look below.
Step-by-step explanation:
as z= 7
3z -3
3(7) -3 =21-3 =18
Antonio ran 1/4 of The way from his house to school. She ran 1/10 mile. How far is it between his home and school
Answer:
2/5 mile
Step-by-step explanation:
Let's give the total distance the variable x.
1/4x = 1/10
x = 4/10
x = 2/5
Antonio writes the equation 80.4÷d+0.0804
What value of d makes the equation true?
a. 10^2
b. 10^3
c. 10^4
d. 10^5
Answer
I think you meant to wtite
80.4/d = 0.0804
the answer is d = 1000 or 10^3
Step-by-step explanation:
Can someone help me please
Answer:
-31 F = -35 C
-45 C = -49 F
-40 C = -40 F
City Y is coldest
Fahrenheit to Celsius conversion (°F to °C)
Write the equation of a line that is parallel to y = 2+2 and goes
through the point (8, 1).
Answer:
y = 2x + 1
Step-by-step explanation:
With parallel lines, the slope is always the same, only the y-intercept changes.
y = mx + b
m = slope
b = y-intercept
18 / x equals negative 2
Answer:
x = -1/9
Step-by-step explanation:
[tex]\frac{18}{x} = -2[/tex] multiply by 1/18 to cancel out
[tex]x = -2(\frac{1}{18} )\\x = -\frac{2}{18} \\x = -\frac{1}{9}[/tex]
Hey there!
18/x = -2
Multiply both sides by x
-2x = 18
Divide both of your sides by -2
-2x/-2 = 18/-2
Cancel out: -2x/-2 because it gives you 1
Keep: 18/-2 because it helps us solve for our answer
x = 18/-2
18/-2 = 18 divided by -2 ➡️ -9
Thus your answer is: x = -9 ✅
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Find the 22nd term of the arithmetic sequence whose common difference is d=4 and whose first term is a, = 3
Answer:
Step-by-step explanation:
t22 = a + (n- 1)d
t22 = 3 + 21*4
t22 = 3 + 84
t22 = 87
4/6 = 9/12 is a proportion.
true false
Answer:
The answer is False 9/12 simplified equals 3/4
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
What is the solution to the equation 3x + 2(x − 9) = 8x + x − 14? (1 point)
a. −8
b. −1
c. 1
d. 8
Answer:
B. -1
Step-by-step explanation:
STEP 1: Simplify 3x+2(x−9).
[tex]5x-18=8x+x-14[/tex]
STEP 2: Add 8x and x.
[tex]5x-18=9x=-14[/tex]
STEP 3: Move all terms containing x to the left side of the equation.
[tex]-4x-18=-14[/tex]
STEP 3: Move all terms not containing x to the right side of the equation.
[tex]-4x=4[/tex]
STEP 4: Divide each term by −4 and simplify.
[tex]x=-1[/tex]
[tex]3x-4=14\\[/tex]
[tex]\text {Hello! Let's Solve this Problem!}[/tex]
[tex]\text {\underline {The First Step is to Add 4}}[/tex]
[tex]\text {3x-4+4=14+4}[/tex]
[tex]\text {3x=18}[/tex]
[tex]\text {\underline {The Final Step is to Divide 3}}[/tex]
[tex]\text {3x/3=18/3}[/tex]
[tex]\text {Your Answer Would Be:}[/tex]
[tex]\Huge\boxed {x=6}[/tex]
[tex]\text {Best of Luck!}[/tex]
[tex]\huge\text{$x=\boxed{6}$}[/tex]
We can solve for the variable [tex]x[/tex] by isolating it on one side of the equals sign.
Start by adding [tex]4[/tex] to both sides to cancel out the [tex]-4[/tex] on the left side of the equation.
[tex]\begin{aligned}3x-4+4&=14+4\\3x&=18\end{aligned}[/tex]
Now divide both sides of the equation by [tex]3[/tex] since [tex]3x[/tex] is the same as [tex]3*x[/tex] and we want to isolate [tex]x[/tex], keeping in mind that anything multiplied by [tex]1[/tex] is itself.
[tex]\begin{aligned}3x&=18\\3*x&=18\\3*x\div3&=18\div3\\x*3\div3&=18\div3\\x*1&=6\\x&=\boxed{6}\end{aligned}[/tex]
A police car is approaching a right-angled intersection from the north at 35 mph, and a speeding car is heading east at 30 mph. When the police car is 0.75 miles north of the intersection and the speeding car is 1 mile to the east, what is the rate that the distance between the police car and car is changing?
Answer:
The rate that the distance between the police car and car is changing = 3 m/s
Step-by-step explanation:
The given speed of the police car = 35 mph
The speed of the speeding car = 30 mph
The position of the police car = 0.75 miles north
The position of the speeding car = 1 miles east
The distance of the police car from the speeding car, d = √(0.75² + 1²) = 1.25
d² = x² + y²
2d·dd/dt = 2x·dx/dt + 2·y·dy/dt
Where;
dx/dt = 30 mph
dy/dt = -35 mph
x = 1
y = 0.75
Substituting gives;
2×1.25 ×dd/dt = 2×1×30 - 2×0.75×35
2×1.25 ×dd/dt = 7.5
dd/dt = 7.5/2.5 = 3
dd/dt = 3 m/s
The rate that the distance between the police car and car is changing = dd/dt = 3 m/s
Answer:
The answer is increasing by 3 mph
Step-by-step explanation:
119+a=99.7 what is the answer
Answer: 19.3
Step-by-step explanation:
Find the value of x when 6-2x=5x-9x+2
Answer:
x = -2
Step-by-step explanation:
10
A bag contains 5 milk and 9 dark chocolates.
A sweet is selected at random.
What is the probability of choosing:
P(milk)
=
Answer:
5/14
Step-by-step explanation:
5 + 9 = 14- so our denominator is 14
Theres 5 milk chocolates, so the probability is 5/14
I hope this helped, please mark Brainliest, thank you !!