Answer:
quadratic formula, completing the square, factorisation
Step-by-step explanation:
Quadratic formula:
x = (-b ± √(b² - 4ac) ÷ 2a)
where a is the value of the first coefficient, b is value of the second and c is value of the constant.
x = ((-b ± √(b² - 4ac)) ÷ 2a)
= (( -16± √((-16)² - 4(8)(3)) ÷ 2(8))
= ((-16 ± √(256 - 96)) ÷ 16)
= (-16 ± √(160)) ÷ 16
= -1 ± (√10)/4
Completing the square:
divide through by 8
x² + 2x + 3/8 = 0
1) put the x, not ^2, in parenthesis.
(x + ) = 0
2) half the coefficient (2) of x. that is 1. Put that into same parenthesis.
(x + 1) = 0
3) we have (x + 1)
4) square this and multiply out. (x + 1)² = x² + x + x +4 = x² +2x + 1
5) this looks just like the original equation (x² + 2x + 3/8) except for +1. What do we have to do to get back to original? 1 – (3/8) = 5/8. We have to subtract 5/8
6) now we have (x + 1)² – 5/8 =0
7) (x + 1)² = 5/8
8) (x + 1) = ± √(5/8)
9) x = ± √(5/8) - 1
= -1 ± (√10)/4
Factorisation:
(8x (- (2√10)) + 8) = 0,
8x = -8 + (2√10)),
x = -1 + (√10)/4
(x ( + (√10)/4 + 1) = 0
x = -1 - (√10)/4
A company is making concrete blocks. The blocks are in the form of right trapezoidal prisms and have the dimensions shown. What is the volume of one block? Show your work
Please help I give 40 brainly
Answer:
9180 (cm³)
Step-by-step explanation:
area of cross-section (trapezium) = 0.5 X (12 + 22) X 9
= 0.5 X 34 X 9 = 153 cm²
then multiply that by the length (60)
153 X 60 = 9180 (cm³)
Which of the following algebraic steps will solve the equation 3x/4=7/3 what is the solution
The solution to the equation is x = 28/9
Given data ,
To solve the equation 3x/4 = 7/3, you can follow these algebraic steps:
Step 1 :
Multiply both sides of the equation by 4 to eliminate the fraction in the denominator of the left side:
(4) (3x/4) = (4) (7/3)
3x = (4/1) (7/3)
Step 2:
Simplify the right side of the equation:
3x = 28/3
Step 3 :
Divide both sides of the equation by 3 to isolate x:
(1/3) (3x) = (1/3)(28/3)
x = (28/3) / 3
Step 4 :
Simplify the right side of the equation:
x = 28/9
Hence , the solution to the equation 3x/4 = 7/3 is x = 28/9
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el area de la base de un cilindro es de 40 pi m2. expresa el volumen en funcion de la altura
The volume of the cylinder, when expressed as a function of the height of same cylinder, is V ( h ) = 40 h ft ³.
How to express the volume of the cylinder ?The volume V of a cylinder is given by the formula:
V = Area of the base of the cylinder x height of the cylinder
Given that the area of the base A is 40 ft², you can substitute this into the formula to express the volume as a function of height:
V ( h ) = 40 ft ² x h
V ( h ) = 40h ft ³
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#11) Determine the period of the following trigonometric function y =
a) 360 b) 180°
c) 360
c) 120
d) 60*
The solution is: the period for the graph of y = cos (0) is:
c.360
We have the following equation:
y = cos (0)
The first thing you should know is that the period of a function is that value for which the function repeats itself.
We have then:
y = cos (0) = 1
y = cos (360) = 1
Therefore, the period is 360.
Answer:
the period for the graph of y = cos (0) is:
c.360
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complete question:
What is the period for the graph of y=cos(0)? (Sketch a graph to help determine the answer.)
a.180
b.90
c.360
d.270
Solids Applied Problem
Find the volume of 1 coin from the stack below. Each coin has a radius of 0.5 in and the coins
are offset by 1 in. The slant is 7in long. Show your work.
The amount of volume of 1 coin in the stack underneath is 0.433 cm³. The distance between the coins is 1 in, and each coin having a radius approximately 0.5 in. 7 inches make up the tilt.
Any three-dimensional solid's volume is the area it takes up. The volume of these solids include cubes, cuboids, cones, cylinders, and spheres. Different shapes have different volumes. We have looked at a variety of three-dimensional solids and shapes, including cubes, cuboids, cylindrical objects, cones, and and more.
V= πD²×h/4
=π0.5²×7/4
= 0.433 cm³
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For f(x) = √(x+4) , what is the value of the function when x = 8 ? Round to the nearest hundredth.
NEED ANSWER ASAP!!
Answer:
exact form : 2√3
decimal form : 3.46410161… or 3.46
hope this helps you!
Answer:
The value of the function is [tex]\sqrt{12}[/tex]. Rounded to the nearest hundredth, the answer is 3.46
Step-by-step explanation:
We are given the value of x, so we simply have to evaluate the function:
[tex]f(x)=\sqrt{x+4}[/tex]
Substitute 8
[tex]f(8)=\sqrt{8+4}[/tex]
Add in the radical
[tex]\sqrt{12}[/tex]
The value of the function is sqrt(12).
Rounded to the nearest hundredth: [tex]3.46[/tex]
A researcher wants to know the mean weight of all garbage being discarded per household in Gallup, NM. A random sample of n = 9 households is selected and the garbage weighed. The following data is obtained: 10.8, 17.2, 23.1, 27.8, 27.9, 31.0, 33.3, 37.6, 44.5.
Find a) the sample mean________. b) the sample median ________. c) the sample mode ________. d. the sample standard deviation (hint: divide by n -1) __________e) the sample variance _________. f) the sample range ______
Operating at the 90% confidence level:
g) what is the Margin of Error E (show work)
h) Find the 90% confidence interval for the mean weight of all garbage discarded per household in Gallup, NM. (show work)
i) What is the probability that the true population mean lies outside the interval in h) ______.
Operating at the 98% Confidence Level
k) What is the Margin of Error E (show work)
m) Find a 98% confidence interval for the mean weight of all garbage discarded per household in Gallup, NM.
o)What is the probability that the true population mean lies outside the interval in m) _____
Answer: what subject, and i got you.
Step-by-step explanation:
HELP ASAP/ Given line `t` on the graph provided, choose all points that lie on the line that passes through point `P` and is perpendicular to line ' t'
(choose all that apply)
All points that lie on the line that passes through point `P` and is perpendicular to line ' t' are: (4, -1) and (6, -5)
What is the equation of the line?The equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
Using two coordinates on line t as: (-4, 1) and (2, 4), the slope of the line t is:
Slope = (4 - 1)/(2 + 4)
Slope = 3/6
Slope = 1/2
Equation of line t is:
(y - 1)/(x + 4) = 1/2
y - 1 = x/2 + 2
y = ¹/₂x + 3
Thus, slope of line passing through P and perpendicular to t is: -1/(1/2) = -2
Now, coordinates of point P is (3, 1). Thus:
Equation passing through point P and perpendicular to line t is:
(y - 1)/(x - 3) = -2
y - 1 = -2x + 6
y = -2x + 7
The only coordinates that fits into this are (4, -1) and (6, -5)
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HELP ME QUICK. paul is thinking of a number. ⅖ of this number is 14 what is the number??
Answer:
Step-by-step explanation:
If we know that 2/5 of the number is 14, 5/5 must be the answer Paul is thinking of.
= (14/2) x 5 <---- This is 1/5 of the number
= 35
∴, the number Paul is thinking of if 35
Tanya has captured many purple-footed bog frogs. She weighs each one and
then counts the number of yellow spots on its back. This trend line is a. fit for these data.
O A weak
B. strong
C. parabolic
D. negative
Answer:
B) strong
Step-by-step explanation:
The correlation coefficient is close to 1, meaning it is both a strong correlation and a positive correlation.
Help with te question pls.P.S. got reward
The amount of water that flows into the tank each minute is given as follows:
0.56 cm.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:
Volume = length x width x height.
The dimensions for this problem are given as follows:
45 cm, 50 cm and 38 cm.
Hence the volume of the tank is given as follows:
V = 45 x 50 x 38
V = 85,500 cm³.
Three-fifths of the volume is given as follows:
3 x 85500/5 = 51300 cm³.
The height associated with 3/5 of the volume is given as follows:
50 x 38 x h = 51300
h = 51300/(50 x 38)
h = 27 cm.
This means that 27 - 13 = 14 cm flew into the tank in 25 minutes, hence the minute rate is given as follows:
14/25 = 0.56 cm.
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Can someone help me please
After using Gauss-Jordon elimination method, the solution for the system of equation is as follows;
[tex]\left[\begin{array}{cccc}1&0&0&-1\\0&1&0&-3\\0&0&1&-2\end{array}\right][/tex]
How do you find the solution for the system of equation using the elimination method by Gauss-Jordon?To solve the system of equation, its needs us to use the Gauss-Jordon elimination method. Therefore, the matrix
- 5 7 7 -30
1 -4 4 3
2 -4 6 -2 will be reduced to its echelon form as follows;
R₁ ÷ 5 R₂ - R₁ R₃ - 2× R₁
1 −1.4 −1.4 6 1 −1.4 −1.4 6 1 −1.4 −1.4 6
1 −4 4 3 0 2.6 5.4 -3 0 2.6 5.4 -3
2 −4 6 −2 2 −4 6 −2 0 −1.2 8.8 −14
R₂ ÷ -2.6 R₃ - 1.2 R₂
1 −1.4 −1.4 6 1 −1.4 −1.4 6
0 1 -2.077 1.154 0 1 -2.077 1.154
0 −1.2 8.8 −14 0 0 1 -2
R₁ - 1.4R₃ R₂ - 2.077R₃ R₁ - 1.4R₂
1 -1.4 0 3.2 1 -1.4 0 3.2 1 0 0 -1
0 1 -2.077 1.154 0 1 0 -3 0 1 0 -3
0 0 1 -2 0 0 1 -2 0 0 1 -2
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Annabel's water bottle holds 6 cups of water. How many fluid
ounces does it hold?
The amount of fluid ounces of water the water bottle can hold is 48 fluid ounces.
How to find the volume of water in fluid ounces?Annabel's water bottle holds 6 cups of water. Therefore, the amount in fluid ounces the bottle water can hold can be calculated as follows:
Therefore,
1 cup = 8 fluid ounces
6 cups = ?
cross multiply
Hence,
number of fluid ounces of water the water bottle can hold = 8 × 6
number of fluid ounces of water the water bottle can hold = 48 fluid ounces.
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The First Chicago Bank is reviewing its service charges and interest-paying policies on checking accounts. The daily balance of a checking account is defined to be the balance in the checking account at 2:00pm.
The bank has found that for all personal checking accounts the mean of all the daily balances is $ 900 and the standard deviation is $175.
In addition, the distribution of personal checking account daily balances can be approximated very well with a normal model.
Enter a positive value for n that makes this statement true: 1 x n is greater than 1 but less than 2
A positive value for n that makes the statement true is n = 1.5.
We need to find a positive value for n that satisfies the given inequality: 1 < 1 x n < 2.
Step 1: Choose a value of n such that it's greater than 1 when multiplied by 1.
Step 2: Ensure the chosen value also makes the product less than 2 when multiplied by 1.
Let's try n = 1.5:
1 x 1.5 = 1.5
Now, let's check if it satisfies the inequality:
1 < 1.5 < 2
Yes, it does. So, a positive value for n that makes the statement true is n = 1.5.
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What is the area of the composite figure
Answer:
34 units²
Step-by-step explanation:
triangle=1/2×5×2=5
other triangle at the right=5
square 6 ×5= 30
unshaded square= 3×2=6
30-6=24
total=5+5+24=34units²
Question 1
Find the volume of the prism, Round your answer to the nearest tenth, if necessary.
13 m
3m
5m
Need help with this question?
The volume of the prism is 195 cubic meters.
To find the volume of the prism, we need to multiply the length, width, and height of the prism.
Length = 13 m
Width = 3 m
Height = 5 m
Volume = Length x Width x Height
Volume = 13 m x 3 m x 5 m
Volume = 195 cubic meters
Help pleaseee is just one problem
The matrices after the row operations are given as follows:
a) [tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]
b) [tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\-6&-5&-2&-3\end{array}\right][/tex]
How to obtain the resultant matrices?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\2&5&-6&-4\end{array}\right][/tex]
When we multiply a matrix row by a constant, each element of the row is multiplied by the constant.
Hence the resulting matrix after we multiply row 3 by 2 is given as follows:
[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]
We can also exchange rows of the matrix, hence the resulting matrix after rows 1 and 3 are exchanged is given as follows:
[tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\-6&-5&-2&-3\end{array}\right][/tex]
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For the following stock investment, find (a) the total
purchase price, (b) the total dividend amount, (c) the
capital gain or loss, (d) the total return, and (e) the
percentage return. Ignore broker and SEC fees.
(a) What is the total purchase price?
4
Number of shares
Purchase price per share
Dividend per share
Sale price per share
60
$40
$2
$87
Answer:
can you be more clear
Step-by-step explanation:
what exactly does question need
name the leading coefficient and degree of the polynomial 4xy^8
(a) The leading coefficient is 4
(b) The degree is 8
How to determine the leading coefficient and the degree of the expressionFrom the question, we have the following parameters that can be used in our computation:
4xy⁸
Consider an expression ax where the variable is x
The leading coefficient of the variable in the expression is a
Using the above as a guide, we have the following:
The leading coefficient is 4
Consider an expression axⁿ where the variable is x
The degree of the variable in the expression is n
Using the above as a guide, we have the following:
The degree is 8
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(When a side has a measurement that is a mixed number, what do you need to do to use it in the formula: area = length x width?)
The sides of the rectangle should be in improper fractions, to calculate the area.
When a side has a measurement that is a mixed number, it's recommended to convert it to an improper fraction before using it in the formula for area.
To convert a mixed number to an improper fraction, you multiply the whole number by the denominator of the fraction part and add the numerator.
Then, you put the result over the original denominator.
Once you have the sides of the rectangle as improper fractions, you can proceed to calculate the area using the formula: area = length x width.
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Use the drawing tool(s) to form correct answer on the provided plot
Shawna oversees tour guides at a community college.each week she selects one day to record the number of tours each guide leads for prospective students. The results from last week are presented in the box plot below.
The data for this week is shown below and gives the number of tours led by each tour guide
{ 3,5,3,4,9,7,10,7,3,6,2,5}
Complete the box plot based on the data given above.
A construction of the box-and-whisker plot based on the data is shown below.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is also known as a box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the data (information) provided above, the five-number summary for the given data set include the following:
Minimum (Min) = 2.First quartile (Q₁) = 3.Median (Med) = 5.Third quartile (Q₃) = 7.Maximum (Max) = 10.In conclusion, we can reasonably infer and logically deduce that the maximum number is 10 while the minimum number is 2, and the median is equal to 5.
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what is the radius of the circle shown below x^2+y^2-8x-10y-8=0
Answer:
r = 7
Step-by-step explanation:
equation of circle is (x - a)² + (y - b)² = r²
where a is x-coordinate of centre of circle, b is y-coordinate of centre of circle, r is the radius. radius = half of diameter.
x² - 8x + y² - 10y = 8
we need to complete the sqaure for both x and y
x² - 8x = (x - 4)² = x² - 8x + 16, which is 16 more than x² - 8x. so we need to subtract that 16.
we now have (x - 4)² - 16.
now do the same with y
(y - 5)² = y² - 10y + 25, which is 25 more than y² - 10y. so we need to subtract 25.
we now have (y - 5)² - 25.
back to our full equation.
(x - 4)² -16 + (y - 5)² - 25 = 8
(x - 4)² + (y - 5)² - 41 = 8
(x - 4)² + (y + 5)² = 49 = r²
radius r = √49 = 7
The triangular prism below has a height of 13.4 units3 and a volume of 536 units
Find the area of one of its bases.
Answer: 40
Step-by-step explanation:
A, B & C form the vertices of a triangle.
∠
CAB = 90°,
∠
ABC = 58° and AB = 9.3.
Calculate the length of BC rounded to 3 SF.
Answer:
To calculate the length of BC in the triangle ABC, we can use the trigonometric functions sine and cosine.
Given that ∠CAB = 90° and ∠ABC = 58°, we can determine that ∠BCA = 180° - 90° - 58° = 32°.
Using the sine function, we can find the length of BC:
sin(∠BCA) = BC / AB
Rearranging the formula, we have:
BC = AB * sin(∠BCA)
Substituting the given values:
BC = 9.3 * sin(32°)
Using a calculator or trigonometric table, we find:
BC ≈ 9.3 * 0.529 = 4.917
Rounding to three significant figures (SF), the length of BC is approximately 4.92 units.
Step-by-step explanation:
If Richard's monthly deposit fee is R69, 95 per R100 what would be the total bank charges for R4200?
what the answer for this?
Shantae's living room is 20.2 metres long and its width half the size of its length. What is the difference between the length and width of her living room?
6th grade of a school with a total of 90 students. In the year-end summary, the number of good students is equal to 1/6 of the students in the whole grade, the number of good students is equal to 40 of the students in the whole block, the average number of students is equal to 1/3 of the number of students in the whole grade. is the weak student again, calculate the number of students in each category
There are a total of 15 good students, 35 weak and 40 in bad shape if number of good students are fraction of 1/6th of total students.
As we know that the total number of students are 90.
Good students are fraction of 1/6th of total students.
Good students= 1/6x90
Good students=15
There are 40 good students in a whole block, so X = 40.
In the whole grade, average number of students is 1/3 of students in whole grade.
Students in each class = 1/3x90
Students in each class = 30
Students who are not good in economics and government = 90-40
Students who are not good in economics and government = 50
As the total number of students is sum of good students and weak students.
15+Weak students =90-40
15+Weak students=50
Weak students=50-15
Weak students=35
So, total of 15 good students, 35 weak and 40 in bad shape.
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a. If this trend continues, predict the percent of U.S.house- holds with an Internet subscription in 2025. graph it
b.Explain any issues with your answer to part c.
The requried, predicted percentage of U.S. households with an Internet subscription in 2020 is approximately 88.3%.
To find the number of subscriptions in the year 2020, we need to find the value of y when x = 10 (since x is the number of years after 2010).
Substituting x = 10 into the equation y = 1.56x + 72.7, we get:
y = 1.56(10) + 72.7
y = 15.6 + 72.7
y = 88.3
Therefore, the predicted percentage of U.S. households with an Internet subscription in 2020 is approximately 88.3%.
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