Answer:
14:46= 0.3
Step-by-step explanation:
Ratios can be expressed as a decimal, fraction or a math expression as above. (2 weeks is 14 days.)
Verify that the given point is on the curve and find the lines that are a. tangent and b. normal to the curve at the given point.
Answer:
4, -4, 16, 16, truetangent: x - y = 8normal: y = -xStep-by-step explanation:
You want to show that the point (4, -4) is on the graph of x² +y² = 32, and you want the tangent and normal lines at that point.
PointThe point is on the curve because when x = 4 and y = -4 the resulting statement is 16 +16 = 32, which is a true statement.
(a) TangentThe tangent to a circle is most easily found by first considering the normal. The normal line will be the line through the point on the circle and the center of the circle. Here, the center is (0, 0). The slope of the normal line is ...
m = y/x = -4/4 = -1
The tangent line's slope is the opposite reciprocal of this:
m = -1/(-1) = 1
The point-slope form of the equation for the tangent line is ...
y -k = m(x -h) . . . . . equation for line with slope m through point (h, k)
y -(-4) = 1(x -4) . . . . . equation for line with slope 1 through point (4, -4)
x -y = 8 . . . . . . . . . . add 4-y to put in standard form
The equation of the tangent line is x - y = 8.
(b) NormalIn the section above, we found the slope of the normal line is -1. We also noted that the normal line goes through the point (0, 0). Then the point-slope form of the normal line is ...
y -0 = -1(x -0)
y = -x
The equation of the normal line is y = -x.
__
Additional comment
The normal line can also be written as x + y = 0.
The tangent line can also be written as y = x -8.
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If AABC= AMNO, then what corresponding angle is congruent to angle N?
Answer:
.aabc=amn0#1211
Step-by-step explanation:
nosascoOsasco n=12.8
An auditorium has 50 rows of seats. The first row has 20 seats, the second row has 21 seats, the third row has 22 seats, and so on, each row having one more seat than the previous row. How many seats are there altogether?
Answer:
1050
Step-by-step explanation:
I'm pretty positive it would be 1050 by multiplying 50 and 20 and adding 50
The total number of seats in the auditorium are 2225.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that an auditorium has 50 rows of seats. The first row has 20 seats, the second row has 21 seats, the third row has 22 seats.
We can write the sequence as -
20, 21, 22, 23, 24, .......,
It is a arithmetic sequence. We can write the total number of seats in the auditorium as the sum of the terms of the sequence. We can write -
S{n} = (50/2)(2 x 20 + 49 x 1)
S{n} = 25(40 + 49)
S{n} = 25 x 89
S{n} = 2225
Therefore, the total number of seats in the auditorium are 2225.
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From the equation, find the axis of symmetry of the parabola.
y=-4x² + 24x-35
a. X=1
b. x=-1
PD
Ο Α
OB
O C
OD
C.
d.
x=3
X=-3
Please select the best answer from the choices provided
The equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.
We know that the method to find the axis of the symmetry of the parabola is given by:
x = - b / 2 a
We have the general equation of the parabola as:
y = a x² + b x + c
We have the equation of the parabola as:
y = - 4 x² + 24 x - 35
Comparing from this equation, we get that:
a = - 4
b = 24
c = - 35
Now, substituting the values, we get that:
x = - 24 / 2 (- 4)
x = - 24 / - 8
x = 24 / 8
x = 3
Therefore, the equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.
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–h2 – 4h + 5 = 0 solve quadratic equation
Answer:
\(x=-5, 1\)
General Formulas and Concepts:
Order of Operations: BPEMDAS
Standard Form: ax² + bx + c = 0
Quadratic Formula: \(x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}\)
Step-by-step explanation:
Step 1: Define
-h² - 4h + 5 = 0
a = -1
b = -4
c = 5
Step 2: Solve for x
Substitute: \(x=\frac{-(-4)\pm\sqrt{(-4)^2-4(-1)(5)} }{2(-1)}\)Simplify: \(x=\frac{4\pm\sqrt{(-4)^2-4(-1)(5)} }{2(-1)}\)Exponents: \(x=\frac{4\pm\sqrt{16-4(-1)(5)} }{2(-1)}\)Multiply: \(x=\frac{4\pm\sqrt{16+20} }{-2}\)Add: \(x=\frac{4\pm\sqrt{36} }{-2}\)Evaluate: \(x=\frac{4\pm6 }{-2}\)Evaluate: \(x=-5, 1\)Which of the following statements describes a rhombus?A. all sides are equalB. the opposite angles are equalC. the diagonals bisect each other at right anglesD. the adjacent angles are not supplementary
The Option B statement "the opposite angles are equal" accurately describes a rhombus, as each of the four angles of a rhombus are equal to each other. This means that the opposite sides of the rhombus have the same measure.
Which statement describes a rhombus?B. the opposite angles are equalA rhombus is a four-sided shape with all sides equal in length. It is also known as a diamond shape. The most important thing to remember about a rhombus is that the opposite angles are equal.
This means that the two angles across from each other on the rhombus have the same measure. This is what is meant by the statement "the opposite angles are equal," and it accurately describes a rhombus.
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10. The set of prime numbers greater than 11 with the cardinality of 5.
The set of prime numbers greater than 11 with the cardinality of 5 is {13, 17, 19, 23, 29}
How to determine the setFrom the question, we have the following parametes that can be used in our computation:
Set = prime numbers
Cardinality = 5
The cardinality implies that the number of elements in the set is 5
5 prime numbers greater than 11 are 13, 17, 19, 23, 29
Hence, the set is {13, 17, 19, 23, 29}
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please help me and hope you have a great day :)
1.5 times 19.5x
Answer:
29.25x
1.5 x 19.5 = 29.25
Answer:
1.5×19.5x=29.25xis required answer.
All of the following represent the same expression except _____.
19 less than 25
25 less than 19
19 subtracted from 25
25 minus 19
Answer:
25 less than 19
Step-by-step explanation:
Required
Determine the odd one among the list of options
Start by taking the options one after the other;
1. 19 less than 25:
This implies 25 - 19
2. 25 less than 19
This implies 19 - 25
3. 19 subtracted from 25
This implies 25 - 19
4. 25 minus 19
This implies 25 - 19
From the above analysis, the off option is option (2);
Answer:
25 less than 19
Step-by-step explanation:
Required
Determine the odd one among the list of options
Start by taking the options one after the other;
1. 19 less than 25:
This implies 25 - 19
2. 25 less than 19
This implies 19 - 25
3. 19 subtracted from 25
This implies 25 - 19
4. 25 minus 19
This implies 25 - 19
From the above analysis, the off option is option (2);
\((3x^{3} y^{2} z)(2xy^{5} z^{5}\)
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An NBA trainer wants to know if his stretching routine is helping the players on his team jump higher. He records the average height jumped for 8 players before completing his stretching routine, and then again after they have stretched. What is the parameter? Group of answer choices dbar = the true sample mean difference in jump height mu_d = the true sample mean difference in jump height dbar = the true population mean difference in jump height mu_d = the true population mean difference in jump height
Answer:
a. mu_d = the true population mean difference in jump height
Step-by-step explanation:
In statistical parlance, observations used for a study could either be randomly chosen points or members of a large group or population, this small chosen observation obtained from a larger group is called the sample, the statistical measures or characteristic of such group is called statistic; while statistical characteristic, computations or measurement of the entire group of observations is called the parameter.
Mean of sample are usually represented with a bar sign on top such as (xbar) ; while mean of a population is represented as μ.
Twice a number is 14. What is the number .
Answer: 7
Step-by-step explanation: 7+7=14
PLEASE HELP!
Identify the y-intercept and zeros of
y = x^4 - 9x^2 - 36
Algebraically
Answer:
Our y-intercept is (0, -36).
Our real zeros are: (-2√3, 0) and (2√3, 0)
And our imaginary zeros are: (i√3, 0) and (-i√3, 0)
Step-by-step explanation:
We have the function:
\(y=x^4-9x^2-36\)
Let's identify the y- and x-intercepts.
Y-Intercept:
To determine the y-intercept, we will substitute 0 for x and solve for y. So:
\(y=(0)^4-9(0)^2-36\)
Evaluate:
\(y=-36\)
Therefore, our y-intercept is at (0, -36).
X-Intercepts:
To determine our x-intercepts, we need to substitute 0 for y and solve for x. So:
\(0=x^4-9x^2-36\)
Now, we can factor. Before doing so, we can make the factored easier to see by converting this into quadratic form. Let's let u=x². Then:
\(0=(u^2)^2-9(x^2)-36\)
Substitute:
\(0=u^2-9u-36\)
Now, let's factor. We can use -12 and 3. So:
\(0=u^2+3u-12u-36 \\ 0=(u(u+3)-12(u+3)) \\ 0=(u-12)(u+3)\)
Now, we can substitute back u:
\(0=(x^2-12)(x^2+3)\)
Zero Product Property:
\(x^2-12=0\text{ or } x^2+3=0\)
Solve for x in each case:
\(x^2=12 \text{ or } x^2=-3\)
Take the square root of both sides. Since we're taking an even root, we will need plus/minus. Therefore:
\(x=\pm\sqrt{12}=\pm2\sqrt{3}\text{ or } x=\pm\sqrt{-3}=\pm i\sqrt{3}\)
Therefore, our zeros (both real and imaginary) are: (2√3, 0), (-2√3, 0), (i√3, 0), and (-i√3, 0)
Questions 16. Santhosh and Co. Chennai, opened a branch at Trichy on 1.1.2018. The following Information relate to the branch for the year 2018.
40,000
36,000
9,000
7200
3,600
30,000
16,200
300
3,000
Prepare branch account to find out the profit or loss of branch. Santosh & Co, Chennai opened its branch in Trichy on 1.1.2018. The action for 2018 is as follows
Credit sales at branch
Office expenses by Head office
Cash remittance to branch for petty cash Stock 31.12.2018
Goods sent to Branch
Salaries paid by head office
Debtors 31.12.2018
Petty cash on 31.12.2018
Cash sales at branch
of
The preparation of the branch's income statement for Santosh & Co. Chennai is as follows:
Branch of Santosh & Co. Chennai
Income StatementFor the year ended December 31, 2018
Sales revenue $40,300
Cost of goods sold 4,200
Gross profit $36,100
Expenses:
Office expenses $36,000
Salaries 3,600
Total expenses $39,600
Loss $3,500
What is an income statement?An income statement is a financial statement prepared at the end of an accounting period to determine the profit or loss generated by a business or branch.
The profit or loss is the difference between the total revenue and the total expenses for the accounting period.
Credit sales at branch 40,000
Office expenses by Head office 36,000
Cash remittance to branch for petty cash 9,000
Goods sent to Branch 7,200
Salaries paid by head office 3,600
Debtors 31.12.2018 30,000
Petty cash on 31.12.2018 16,200
Cash sales at branch 300
Stock of 31.12.2018 3,000
Sales revenue $40,300 ($40,000 + $300)
Cost of goods sold $4,200 ($7,200 - $3,000)
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12 students need to drink a total of 3 litres of water over the course of an activity.
How much water would be needed for 20 students during the same activity?
Give your answer in litres.
[2 ma
Answer
litres
Answer:
5 liters!
Step-by-step explanation:
For every 4 students, there's 1 liter of water needed.
S = Students - L = Liters
4S = 1L
8S = 2L
12S = 3L
16S = 4L
20S = 5L
Raina picks 20 flowers
1/4 are roses 2/5
are daisies
How many flowes are lilies?
Answer:
7 of the flowers were lilies.
Step-by-step explanation:
8 daises and 5 roses were picked. 8 + 5 = 13 20 - 13 = 7
7 of the flowers were lilies
What is the radius?
What is the diameter?
What it the circumference? Use 3.14 for pi.
What is the area?
Use 3.14 for pi.
Answer:
Step-by-step explanation:
radius = 3mm
diameter = 6mm
circumference = 6 x 3,14 = 18.84 mm
area = 3^2 x 3,14 = 28.26 mm^2
Corey buys chicken wings at a rate of $10 for 40 wings. He sells 10 wings for $5.
How much does Corey pay for each chicken wing he purchases?
Answer:
20
Step-by-step explanation:
Find the derivative of g(t)=3t^2+2t at t=-1 algebraically
Answer:
8.
Step-by-step explanation:
If y = ax^n then the derivative y' = anx^(n-1)
g(t) = 3t^2 + 2t so the derivative g'(t)
2*3 t^(2-1) + 2t(1-1)
= 6t + 2
At t =1 its value is 6 + 2 = 8.
. It takes 11 widgets to assemble one motor. Your team can assemble four motors in one day. If you need to order parts for next week (5 working days), how many widgets should you order?
Number of widgets needed to make one motor = 11
Number of motors made each day = 4
Number of widgets used per day :-
= 4 × 11
= 44 widgets
Number of widgets I need to order for the next five days of the upcoming week :-
= 44 × 5
= 220 widgets
Therefore , my team should order 220 widgets for the next week ( 5 working days ) .
Answer:
Your answer should be 220 widgets
Step-by-step explanation:
Becasue if you have 11 in one motor and you build four a day then multiply 4 and 11 to get 44. Then you see that you get 44 widgets in a day you multiply 44 by the number of working days which is 5. So after multiplying you get 220 widgets per week.
Tell me if this is the correct answer
Select the correct answer. Sarah wants to print copies of her artwork. At the local print shop, it costs her $1 to make 5 copies and $5 to make 25 copies. How much would it cost Sarah to make 100 copies? A. $15 B. $20 C. $25 D. $30
$1 = 5copies means
$5 = 25 copies obviously
then
$x = 100 copies
100 / 5 = $x
so she needs
$20
The cost of printing 100 copies of artwork is $20.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Suppose 2 pens cost $10, So the cost of 1 pen is (10/2) = $5.
From this unitary cost of pens, we can determine the cost of any no. of pens by multiplying the unit cost by the no. of pens.
Given, The cost of printing 5 artworks is $1.
∴ The cost of printing 100 copies is $(100/5),
= $20.
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5.
Jenny had to increase her gas budget from $300 per month to $350 per
month. What is the percentage increase in Jenny's budget?
Answer:
16.66667% increase
Step-by-step explanation:
100 x 350 - 300/ 300 = 50/3 = 16.66667% increase
Formula for percent increase is below↓
what is the distance between J(5.4,-3.2) and K(4,-1.2)
Answer:
The answer is
2.44 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ \)
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
J(5.4,-3.2) and K(4,-1.2)
The distance between them is
\( |JK| = \sqrt{ ({5.4 - 4})^{2} + ({ - 3.2 + 1.2})^{2} } \\ = \sqrt{( {1.4})^{2} + ({ - 2})^{2} } \\ = \sqrt{1.96 + 4} \\ = \sqrt{5.96} \: \: \: \: \: \: \: \: \\ = 2.44131112\)
We have the final answer as
2.44 unitsHope this helps you
Look at the figure. How many different labeled rays are shown?
A.)2
B.)10
C.)20
D.)8
The question is one the picture
Answer:
y=-1/2x+4
Step-by-step explanation:
The line is going down, which means it's negative. You then do rise over run, go up by 1 and go to the left by 2. To find the y intercept, it's 4 since the coordinate is (0,4).
Decide which of the two given prices is the better deal and explain why. You can fill a 12-gallon tank of gas for $39.43 or buy gas for $3.20/gallon.
Answer:
$3.20/gallon
Step-by-step explanation:
to fill up your tank at $3.20/gallon only costs $38.40
4tan(x)-7=0 for 0<=x<360
Answer:
x = 65.26 degrees or x = 245.26 degrees.
Step-by-step explanation:
To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:
4tan(x) = 7
Then, we can divide both sides by 4 to get:
tan(x) = 7/4
Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:
x = tan^-1(7/4)
Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).
However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).
To find the solution in the first quadrant, we can simply use the value we just calculated:
x = 65.26 degrees (rounded to two decimal places)
To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:
x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)
So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:
x = 65.26 degrees or x = 245.26 degrees.
Michaela plans on installing heated tile in her kitchen. A diagram of the kitchen floor plan is shown below.
Calculate the area of the floor, to the nearest 10th, to determine how many square metres of tile Michaela will need to buy.
*Hint: Divide the shape into 2! You will need to use trig!
Check the picture below.
so hmm we have a 6x6 square atop and a triangle with base of 6 and a height of "h", let's get "h".
\(\sin( 42^o )=\cfrac{\stackrel{opposite}{h}}{\underset{hypotenuse}{2}} \implies 2\sin(42^o)=h \implies 1.34\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{6})(\underset{h}{1.34})}~~ + ~~\stackrel{ square }{(6)(6)}} ~~ \approx ~~ 4.02+36~~ \approx ~~ \text{\LARGE 40.0}\)
1. Choose the trig expression equal to the one below 2cos^2 x - 1
Answer:
cos(2x) = 2cos²(x)-1
Step-by-step explanation:
We know the trigonometry identity as follows :
cos(2x) = cos²(x) – sin²(x) ....(1)
Also, sin²(x)+cos²(x) = 1
or
sin²(x) = 1-cos²(x)
Put the value of sin²(x) in equation (1)
cos(2x) = cos²(x) – (1-cos²(x))
= cos²(x) –1+cos²(x)
cos(2x) = 2cos²(x)-1
Hence, 2cos²(x)-1 is equal to cos(2x).
Find the sum or difference (I will give you brainlist :D)
To find the sum or difference we must know what k is however you can simplify the expression by rewriting and removing the parenthesis furthermore collecting the like terms to get the solution.
Attached photo shows the steps to the solution :P