Answer:
b = 9
Step-by-step explanation:
All the steps are correct. This final step in finding the value of "b" is to take the square root of both sides. This gets rid of the power that "b" is raised to. Once you do this, you are just left with the variable and the answer of 9.
b² = 81
√b² =√81
b = 9
Which line is perpendicular to the line: y − 4 = 25(x +1)?
Please help!
The price of products may increase due to inflation and decrease due to depreciation. Derek is studying the change in the price of two products, A and B, over time.
The price f(x), in dollars, of product A after x years is represented by the function below:
f(x) = 72(1.25)x
Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below shows the price f(t), in dollars, of product B after t years:
t (number of years)
1 2 3 4
f(t) (price in dollars)
65 84.5 109.85 142.81
Which product recorded a greater percentage change in price over the previous year? Justify your answer. (5 points)
Answer:
A)25% B)Product B
Step-by-step explanation:
A) To find whether product A price is increasing or decreasing, we will find the difference in price between year 0 and 1 year after.
When x = 0,
f(0) [tex]72(1.25)^{0}\\= 72*1\\= 72[/tex]
when x = 1,
f(1) = [tex]72(1.25)^{1}\\= 72*1.25\\= 90[/tex]
From here we can already see the price is increasing.
% increase = (Difference in price / Original Price) * 100
= [tex]\frac{90-72}{72} *100\\=\frac{18}{72} *100\\=0.25*100\\=25percent[/tex]
Therefore the price is increasing by 25% per year.
B) Same concept as Part A, we will find the price difference between year 1 and 2.
% increase = (Difference in price / Original Price) * 100
[tex]\frac{84.5-65}{65} * 100\\= \frac{19.5}{65} * 100\\= 0.3*100\\= 30 percent[/tex]
Therefore we can see here Product B has a higher increase than Product A.
Step-by-step explanation:
A
f(x) = 72 × 1.25 × x
so, the price is $90 after 1 year (72×1.25×1).
$180 after 2 years (72×1.25×2)
$270 after 3 years (72×1.25×3)
and so on.
or did you mean
f(x) = 72 × (1.25)^x
so, still, the price is $90 after 1 year (72×1.25^1).
$112.50 after 2 years (72×1.25^2).
$140.625 = $140.63 after 3 years (72×1.25^3)
that makes more sense. I will continue with that assumption.
so, the price is increasing, as every factor of the multiplication is positive and larger than 1. therefore, it only goes up.
and due to the formula, the price of every year is the price of the previous year multiplied by 1.25.
a multiplication by 1.25 is an increase of 25% (compared to a constant multiplication by 1).
so, the price increases every year by 25%.
B
year 1
price $65
year 2
price $84.50 difference $19.50
100% = 65
1% = 65/100 = 0.65
19.5/0.65 = 30% difference
year 3
price $109.85 difference $25.35
100% = 84.5
1% = 84.5/100 = 0.845
25.35/0.845 = 30% difference
year 4
price $142.81 difference $32.96
100% = 109.85
1% = 109.85/100 = 1.0985
32.96/1.0985 = 30% difference
so, product B has the greater percentage increase in the price (30% vs. 25%).
(-2,4) on cordinate plane
The coordinate -2, 4 implies -2 is the value on the x or horizontal axis and 4 is the value on the y or vertical axis.
What is a coordinate plane?This a plane used for graphs or points that is based on a vertical axis (y) and a horizontal axis (x).
How does -2,4 look on a coordinate plate?The first number, -2 indicates the value in x or the horizontal axis, while the second number 4 indicates the position on y or the vertical axis. You can see this in the imaged attached (red dot).
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The coordinate -2, 4 implies -2 is the value on the x or horizontal axis and 4 is the value on the y or vertical axis.
What is a coordinate plane?
This a plane used for graphs or points that is based on a vertical axis (y) and a horizontal axis (x).
How does -2,4 look on a coordinate plate?
The first number, -2 indicates the value in x or the horizontal axis, while the second number 4 indicates the position on y or the vertical axis. You can see this in the imaged attached (red dot).
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Julia surveyed twenty households on her street to determine the average number of children living in each household. the tables below represent the collected data and a randomly selected sample from the population. compare the mean of the population with the mean of the sample. population data 0 3 3 1 3 2 2 2 5 4 3 3 3 0 1 2 0 2 3 3 sample data 5 3 0 2 4 what is the difference between the mean of the sample and the mean of the population? 0.55 1.25 2.25 2.80
The difference between the mean of the sample and the mean of the population is A. 0.55
Calculations and Parameters:Given the population data is:
0 3 3 1 3 2 2 2 5 4 3 3 3 0 1 2 0 2 3 3
The sample data is:
5 3 0 2 4
The mean of the population data is:
45/20= 2.25
The mean of the sample data is:
14/5= 2.8
Therefore, the difference between the mean of the sample and the population is:
2.8-2.25= 0.55
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For some △MNP: P = 38°, N = 90°, and m = 12 cm. Solve the triangle. Hint: Sketch the
triangle and label all unknown parameters.
Angle M = 52°, n = 15.2cm, p = 9.4cm
What is a triangle?A triangle is a plane shape with three sides and three angles.
To define the triangle completely we have to know the measure of the three angles and three sides.
Analysis:
The triangle is a right-angled triangle
we need to find the remaining angle M and two sides n and p
M + N + P = 180
M + 90 + 38 = 180
M = 180 - 128 = 52°
sin 52 = m/n
m = n sin 52
n = m/sin 52 where m = 12cm
n = 12/0.788 = 15.2cm
sin 38 = p/n
p = n sin 38
p = 15.2 x 0.615 = 9.4cm
In conclusion, solving the triangle means finding M, n and p which are 52°, 15.2cm and 9.4cm respectively.
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GRADE 11 MATH
PLEASE HELP!
Nelson received $10,000 on his 17th birthday. This is the accumulated amount of an
investment his parents made on the day he was born. The investment earned 9.5%/a,
compounded semi-annually.
a) Determine the amount that Danny’s parents invested 17 years ago. [3 marks]
b) How much interest did the investment earn? [1 mark]
The amount that was invested 17 years ago is $2064.25.
The interest earned is $7935.75.
What is the amount invested 17 years ago?The formula that would used to determine the amount that was invested 17 years ago is:
P = FV / (1 + r)^nm
Where:
FV = Future value = 10,000P = Present value R = interest rate = 9.5 / 2 = 4.75%m = number of compounding = 2 N = number of years = 1710,000 / (1.0475)^(17 x 2) = $2064.25
Interest earned = 10,000 - 2064.25 = $7935.75
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A car used of a gallon of gas to drive of a mile. At this rate, how many miles
can the car travel using 1 gallon of gas?
Find the volume of the rectangular prism using the formula v = bh.
the area of the base, b, equals
___ cm2.
the volume of the prism is
___cm3.
Answer:
v=bh cm3 cm2 is not answer is 903cm2 23
The graph below shows the function f(x)=
x-3
+3
-2x-3•
The true statement about the graph is that there is a hole at x = 3 and an asymptote at x = -1.
How to explain the graph?The expression in the denominator is x^2-2x-3
x² - 2x-3 ≠0
-3 = +1 -4
(x²-2x+1)-4 ≠0
(x²-2x+1)=(x-1)²
(x-1)² - (2)² ≠0
∴a²-b² =(a-b)(a+b)
(x-1-2)(x-1+2) ≠0
(x-3)(x+1) ≠0
x≠3 for all x≠ -1
There is a hole at x=3 and an asymptote at x= -1, so Option B is wrong
Asymptote:
x-3/x^2-2x-3
We know that denominator is equal to (x-3)(x+1)
x-3/(x-3)(x+1)
x-3 will be cancelled out by x-3
1/x+1
We have asymptote at x=-1 and hole at x=3, therefore the correct option is A.
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Martin wants to use coordinate geometry to prove that the opposite sides of
a rectangle are congruent. He places parallelogram ABCD in the coordinate
plane so that A is (0, 0), B is (a,0), C is (a, b), and D is (0, b).
What formula can he use to determine the distance from point D to point A?
A. 0-0)2+(b-0)² = √√b² = b
B. (a-a)2+(b-0)² = 6²
C. (0-0)² + (b-0)² = 6²
OD. √(-a)2+(b-0)²-√√b² = b
The correct answer is option A which is the distance between A and D will be AD = [tex]\sqrt{(0-0)^2-(b-0)^2}=\sqrt{b^2}=b[/tex].
What is coordinate geometry?A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
The formula utilised to find the distance between two points is;-
X = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
We have the coordinates of the point A = (0, 0) and D is (0, b).By applying the formula to find the distance between A and D.
AD = [tex]\sqrt{(0-0)^2-(b-0)^2}=\sqrt{b^2}=b[/tex].
Therefore the correct answer is option A which is the distance between A and D will be AD = [tex]\sqrt{(0-0)^2-(b-0)^2}=\sqrt{b^2}=b[/tex].
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Table for a linear equation
Fill in the table using this function rule.
y = -10x + 1
x y
-5
-1
0
1
Answer:
x: y :
-5 | 51
-1 | 11
0 | 1
1 | 11
Step-by-step explanation:
y = 10x + 1
(Table)
x: y:
-5 |
-1 |
0 |
1 |
Lets begin plugging in our (x) into the function(x = -5)y = -10(-5) + 1
y = 50 + 1 (if you multiply a negative by a negative it will be positive)
y = 51
(x = -1)y = -10(-1) + 1
y = 10 + 1
y = 11
(x = 0)y = -10(0) + 1
y = 0 + 1
y = 1
(x = 1)y = -10(1) + 1
y = 10 + 1
y = 11
Plug into the table
(table)
x: y :
-5 | 51
-1 | 11
0 | 1
1 | 11
If you have any questions feel free to ask:)Regina’s work to find the surface area of a square pyramid from its net is shown below.
A square pyramid. The square base has side lengths of 9.4 inches. The triangular sides have a height of 11.9 inches.
Surface area of the pyramid = 4 (one-half (9.4) (12.8)) + 9.4 squared = 329 square inches
What error did Regina make?
She should have used One-half (9.4) (11.9) to represent the area of a single triangle.
She should have multiplied all the terms inside the parentheses by 4 when she simplified.
She should have used One-half (4.7) (12.8) to represent the area of a single triangle.
She should have used a different collection of shapes as the net of the pyramid.
She put 12.8 in place of 11.9 in the formula of the triangle. Then the correct option is A.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Regina’s work to find the surface area of a square pyramid from its net is shown below.
A square pyramid. The square base has side lengths of 9.4 inches. The triangular sides have a height of 11.9 inches.
Surface area of the pyramid = 4 [one-half (9.4) (12.8)] + 9.4² = 329 square inches
Then the error done by Regina will be
She should have used One-half (9.4) (11.9) to represent the area of a single triangle.
Then the correct option is A.
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Answer:
A
Step-by-step explanation:
which of the following is the equation of a line in sloep intercept form for a line with slope = 1/3 and y intercept at 0,-4
Answer:
Step-by-step explanation:
y + 4 = 1/3(x - 0)
y + 4 = 1/3x - 0
y = 1/3x - 4
I need help to find this number in scientific notation form pls.
Answer:
the answer is ( -0 ) ok?
Step-by-step explanation:
also my name ifs kris ik you from somewhere
i am very embarrest to say this but u are very pretty
are u single? im sorry if its freakish
are u mexican? of Philippians? im from la pearla tapatia mx hbu?
Given that p(x) = 2(x - 12)2 + 5, what is the value p(3)
Answer:
p(3) = 25
Step-by-step explanation:
p(3) = 2(3 - 12)2+5
p(3) = 6 - 24 + 2 + 5
p(3) = 25
What is the area of the following circle
Answer:
Area = 153.86
Step-by-step explanation:
Formula: A = [tex]\pi r^{2}[/tex]
diameter (d) = 14
radius = d / 2
radius is 14 / 2 = 7
A = [tex]\pi (7)^{2}\\\pi 49\\49\pi \\49(3.14) = 153.86[/tex]
Find the x-intercept and y-intercept of each linear function
Jamal has run 7 miles from point a to point b of a race. the entire race from point a to point c is 26 miles. how many
more miles will he run to complete the race?
The number of more miles he needs to run to complete the race is 19 miles.
How to find distance in miles?He has run 7 miles from point a to point b of a race.
The entire race from point a to point c is 26 miles.
Therefore, the number of more miles he needs to run to complete the race is as follows:
let
x = the more miles he needs to run
Hence,
x = 26 - 7
x = 19 miles
Therefore, he needs to run 19 more miles to complete the race.
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does someone mind helping me with this question? Thank you!
Answer:
70
Step-by-step explanation:
ok so we just plug 4 for x in the expression:
5 (2*4 + 6 )
5 ( 8 + 6 )
5*14 = 70
Have a good day! :)
PLEASE HELP!!! 50 POINTS!!!
Answer:
Part A:
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
Part B:Simply put, coterminal angles start at 0° and end at the same place, though in different directions and multiple times around (you're probably going to want to make that sound a little more formal). Since each time around is 360°, boom
Part C: 75° is in Quadrant II, right? If I go one more time around, 75 + 360 = 435°. I can also go "backward. Starting at 0 and going clockwise, I'm going 75 fewer degrees than all the way around, so 360-75 = 285° but since I'm going "backward" 75 - 360 = -285°. One more is on you.
Step-by-step explanation:
temp change -4.2 and 9.1
Subtraction is a mathematical operation that reflects the removal of things from a collection. The temperature change from -4.2 to 9.1 is 13.3.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
The temperature change from -4.2 to 9.1 is,
ΔT = 9.1 - (-4.2) = 9.1 + 4.2 = 13.3
Hence, the temperature change from -4.2 to 9.1 is 13.3.
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A number cube is rolled 14 times and the results are recorded in the table.
what, in simplest form, is the experimental probability that the number 4?
Answer:
2.3333 ≈ 2
Step-by-step explanation:
The first step is the 1/6 because you are only counting the value 4 not the other ones like 1,2,3,5,6. So then that is 0.1666666. Then you multiply it by 14 which is rounded to 2. I can tell you are a 6th grader.
DISCLAIMER: THIS ANSWER MAY BE FALSE BECAUSE THERE IS NO PICTURE ATTACHED TO THIS POST. THUS, NEXT TIME YOU SHOULD UPLOAD A PICTURE. THIS IS ONLY A GUESS NOT A REAL ANSWER.
Keiko surveyed people with cell phones.
Age in years=a
Texts they send per day=t
He drew a best-fit line and determined its equation.
Student
Keiko
Trend Line
t -1.63a + 92.14
Evaluate how many texts a 15 year old would send each day according to Keiko's trend line equation.
Using the line of best fit, the amount of texts a 15-year old would send in a day is of 67.69.
What does the line of best fit gives?It gives the expected number of texts a person of an age a would send in a day, according to the following function:
t = -1.63a + 92.14.
For a person that is 15 years old, we have that a = 15, hence the expected number is given by:
t = -1.63 x 15 + 92.14 = 67.69 texts.
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help solve these algebraic fractions please, with explanation would be great
Step-by-step explanation:
i answered it , and tried to give explanation too...
hope its helpful ,
the picture below illustrates a special type of comic section called a circle. which of the following offers the best description of how a circle is formed?
From the diagram, a circle is formed because D. The plane passes through only one nappe of a circular one and is parallel to its base.
How does the diagram show the formation of a circle?The plane given only passes through one nappe instead of the two nappes.
The angle that the plane passes the nappe is parallel and not perpendicular to the base of the nappe as shown in the diagram.
The plane does not pass through the vertex which is the point where the planes.
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Use the vectors to determine two dot products: u•v and u•w
u=9i-6j
v=-3i-2j
w=19i+15j
A
Take the product of corresponding components, then take the total:
u • v = (9i - 6j) • (-3i - 2j) = 9 (-3) + (-6) (-2) = -15
u • w = (9i - 6j) • (19i + 15j) = 9 × 19 + (-6) 15 = 81
Alternatively, use the definition and algebraic properties of the dot product.
• For any vector x,
x • x = ||x||²
where ||x|| is the magnitude of x.
• i • i = j • j = k • k = 1
• i • j = j • k = k • i = 0
• For any scalar c and any two vectors x and y,
cx • y = x • cy = c (x • y)
• For any vectors x, y, and z,
(x + y) • z = z • (x + y) = x • z + y • z
Then the products you want are
u • v = (9i - 6j) • (-3i - 2j)
… = -27 (i • i) + 18 (j • i) - 18 (i • j) + 12 (j • j)
… = -27 + 12 = -15
u • w = (9i - 6j) • (19i + 15j)
… = 171 (i • i) - 114 (j • i) + 135 (i • j) - 90 (j • j)
… = 171 - 90 = 81
Find the volume of the rectangular prism in cubic feet. 3.4 ft 0.8ft 0.6ft "these are not the answers these are the ft of the prism
Answer:
A
Step-by-step explanation:
becaauss im smart and trust me im smart
2. Mr. Walters starts preparing breakfast at
6:45 AM. He finishes at 7:50 AM. How long
does it take for him to prepare breakfast?
explanation/proof why the lines are parallel and insights
Answer:
The lines are parallel is the will never touch.
Step-by-step explanation:
As one of the grade 9 top performing students competing for the “Boy Scout of the Year” award, you are assigned by your scoutmaster to design a camping site for the coming Boy Scout in-door camping. You have to maximize the area at which the 20 scouts can assemble their own tents. The tents should be equally spaced and must be situated at the same distance of 20 m from the tent of the scout master, which is located at the center of the scouts. The angle at which the tents are positioned from the scoutmaster should be approximately the same. Would you know how far apart the tents of the scouts are from each other?
Answer:
Yes you would know
Step-by-step explanation:
We can view these tents as sides on a shape that is 30 sided, with lines connecting each tents together.
After this we calculate the interior angle of each side, and use our given 20m to calculate it.