Given the number :
[tex]0.000471[/tex]The scientific notation is a method to the write the numbers as two parts
The first part is the number as between 1 and 9
the second part as 10 to powers
so,
[tex]0.000471=\frac{471}{100000}=\frac{471}{10}\cdot\frac{1}{10000}=4.71\cdot10^{-4}[/tex]
Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0, 28t).Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution."- 15csc?(x) - 1 = -32cot(x)yea
To solve the equation:
[tex]-15\csc ^2x-1=-32\cot x[/tex]We meed to remember the identity:
[tex]\csc ^2x=\cot ^2x+1[/tex]Plugging this identity in the equation we have:
[tex]\begin{gathered} -15(\cot ^2x+1)-1=-32\cot x \\ -15\cot ^2x-15-1=-32\cot x \\ 15\cot ^2x-32\cot x+16=0 \end{gathered}[/tex]Hence we have the quadratic equation in the cotangent:
[tex]15\cot ^2x-32\cot x+16=0[/tex]To solve it let:
[tex]w=\cot x[/tex]Then we have the quadratic equation:
[tex]15w^2-32w+16=0[/tex]let's use the general formula to solve it:
[tex]\begin{gathered} w=\frac{-(-32)\pm\sqrt[]{(-32)^2-4(15)(16)}}{2(15)} \\ =\frac{32\pm\sqrt[]{1024-960}}{30} \\ =\frac{32\pm\sqrt[]{64}}{30} \\ =\frac{32\pm8}{30} \\ \text{then} \\ w=\frac{32+8}{30}=\frac{40}{30}=\frac{4}{3} \\ \text{ or } \\ w=\frac{32-8}{30}=\frac{24}{30}=\frac{4}{5} \end{gathered}[/tex]Once we know the value of w we can find the value of x, remember the definition of w, then we have:
[tex]\begin{gathered} \cot x=\frac{4}{3} \\ \text{ and} \\ \cot x=\frac{4}{5} \end{gathered}[/tex]Since it is easier to work with the tangent function we will use the fact that:
[tex]\tan x=\frac{1}{\cot x}[/tex]Hence our equations take the form:
[tex]\begin{gathered} \tan x=\frac{3}{4} \\ \text{and} \\ \tan x=\frac{5}{4} \end{gathered}[/tex]Finally to solve the equations we need to remember that the tangent function has a period of pi, therefore we have that:
[tex]\begin{gathered} x=\tan ^{-1}(\frac{3}{4})+\pi n \\ \text{and} \\ x=\tan ^{-1}(\frac{5}{4})+\pi n \end{gathered}[/tex]where n is any integer number. To find the solutions in the interval given we plug n=0 and n=1 in each expression for x; therefore, the solutions in the interval are:
[tex]\begin{gathered} x=0.6435 \\ x=0.8961 \\ x=3.7851 \\ x=4.0376 \end{gathered}[/tex]You have (12,-6) that dilates to (9,-4.5), what is the dilation?
The dilation is a reduction.
Lets the origin O(0,0) as a common point.
Let A be the point (12,-6) and B be the point (9,-4.5)
Distance formula = [tex]\sqrt{(x1-x2)^{2}+(y1-y2)^{2} }[/tex]
Therefore,
Distance between A and O = AO = [tex]\sqrt{(12-0)^{2}+(6-0)^{2} }[/tex]
= [tex]\sqrt{12^{2} +6^{2} }[/tex]
= [tex]\sqrt{144 + 36}[/tex]
= [tex]\sqrt{180}[/tex]
= 13.42
Distance between B and O = BO = [tex]\sqrt{(9-0)^{2}+(-4.5-0)^{2} }[/tex]
= [tex]\sqrt{9^{2} +(4.5)^{2} }[/tex]
= [tex]\sqrt{81 + 20.25}[/tex]
= [tex]\sqrt{101.25}[/tex]
= 10.06
As we can see, OA > OB
Therefore, it is a reduction.
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Which BEST describes the system of equations? 3x = 5 - 4y 6x + 8y = 7 A) Consistent B) Inconsistent Consistent and Dependent D) Consistent and Independent
The given set of equations is,
[tex]\begin{gathered} 3x=5-4y \\ \Rightarrow3x+4y-5=0\ldots\text{.}(1) \\ 6x+8y=7 \\ \Rightarrow6x+8y-7=0\ldots\ldots(2) \end{gathered}[/tex]The ratio of coefficient can be determined as,
[tex]\begin{gathered} \frac{a_1}{a_2}=\frac{3}{6}=\frac{1}{2}_{} \\ \frac{b_1}{b_2}=\frac{4}{8}=\frac{1}{2} \\ \frac{c_1}{c_2}=\frac{-5}{-7}=\frac{5}{7} \\ \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2} \end{gathered}[/tex]Thus, the solution is inconsistent as there is no solution.
Thus, option (B) is the correct solution.
263747_+'('-+'++'+58"-
report student again
Solve the right triangle ABC for all missing parts. Express angles in decimal degreesA=23°23', c= 47.25 mRound to the nearest hundredth please
The first step is to convert angle A = 23°23' to degrees. Recall, the interpretation of angle A is 23 degree 23 minutes. Also,
1 degree = 60 minutes
Let x = 23 minutes. Thus, we have these equations
1 = 60
x = 23
By crossmultiplying,
60x = 23
x = 23/60 = 0.3833
Thus,
angle A = 23 degrees + 0.3833 degrees = 23.3833 degrees
The triangle is shown below
Taking angle A as the reference angle,
hypotenuse = 42.75
opposite side = a
adjacent side = b
To find a, we would apply the sine trigonometric ratio which is expressed as
Sin# = opposite side/hypotenuse
Sin 23.3833 = a/47.25
By crossmultiplying,
a = 47.25Sin 23.3833
a = 18.75
To find b, we would apply the cosine trigonometric ratio which is expressed as
Cos# = adjacent side/hypotenuse
Cos 23.3833 = b/47.25
By crossmultiplying,
b = 47.25Cos 23.3833
b = 43.37
The given triangle is a right triangle. This means that one of its angles is 90 degrees. Thus,
angle C = 90 degrees
The sum of the angles in a traingle is 180 degrees. This means that
angle A + angle B + angle C = 180
23.3833 + angle B + 90 = 180
angle B + 113.3833 = 180
angle B = 180 - 113.3833
angle B = 66.62 degrees
60.60 increased by 60%
The answer is 96.96
From the question, we have
60.60 increased by 60%
= 60.60 + 60.60 * 60/100
= 96.96
Percentage:
Use the percentage formula to express a number or percentage in terms of 100. % simply indicates one out of one hundred. An expression for a number between 0 and 1 can be made using the percentage formula. It is a number that is represented as a fraction of 100. The sign % is used to denote it and it is mostly used to compare and calculate ratios. The formula for percentage increases is the ratio of the increased value to the original value multiplied by 100. It is described in percentage form. If anything is valued more highly, both its value and proportion will rise.
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4. A rectangular garage has a volume of 480 m, a length of 12 m and a width of 8 m. What isthe height of the garage?
Answer:
5 m
Explanation:
The volume of the rectangular garage can be calculated as:
[tex]\text{Volume }=\text{Length }\times\text{ Width }\times\text{ Height}[/tex]If we replace Volume by 480, Lenght by 12, and Width by 8, we get:
[tex]480=12\times8\times\text{ Height}[/tex]Now, we can solve the equation for the Height as:
[tex]\begin{gathered} 480=96\times\text{ Height } \\ \frac{480}{96}=\frac{96\text{ }\times Height}{96} \\ 5=\text{Height} \end{gathered}[/tex]Therefore, the height of the garage is 5 m
Question 2 Part C (2.02, 2.05): The linear function f(x) represents the average test score in your language arts class, where x is the number of the test taken. The linear function g(x) represents the average test score in your social studies class, where x is the number of the test taken.
Answer:
f(x)
Step-by-step explanation:
[tex]f(4)=0.3(4)+80=81.2 \\ \\ \\ \frac{g(3)-g(2)}{3-2}=\frac{81-83}{1}=-2 \\ \\ \therefore g(x)-85=-2(x-1) \\ \\ g(x)=-2x+2+85=-2x+87 \\ \\ g(4)=-2(4)+87=79 \\ \\ \therefore f(4)>g(4) \implies \boxed{f(x)}[/tex]
Find the area of the following figure with the indicated dimensions. Note that the figure represents a geometric shape with a hole.
13 cm
4 cm
8 cm
6 cm
Answer:
Step-by-step explanation:
pls help, this is too hard for me
The value that will be included in section D is C option 0.
The number that could not be included in the section B is D option [tex]\sqrt{32}[/tex].
An example of a value that could be represented by C is -10.
As we can observe from the figure, we can write the following:-
E is the set of natural numbers.
D is the set of whole numbers.
C is the set of integers.
D is the set of rational numbers.
A is the set of irrational numbers.
The biggest rectangle is the set of real numbers comprising of rational and irrational numbers.
Hence,
The value that will be included in section D is C option 0 as it is whole number.
The number that could not be included in the section B is D option [tex]\sqrt{32}[/tex] as it is an irrational number and will be included at A.
An example of a value that could be represented by C is -10 as C represents the set of integers.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 2.5, 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]
In a high school, 20% of the students own a supercharged Greased Lightning 409 car while the other 80% own a feeble Milquetoast car. Last year the students owning a 409 received 60 speeding tickets while the students owning a Milquetoast received 10 speeding tickets. That means that a student owning a 409 was k times more likely to receive a ticket than a student owning a Milquetoast. What is the value of k?
The value of k is 6
In this question, we have been given In a high school, 20% of the students own a supercharged Greased Lightning 409 car while the other 80% own a feeble Milquetoast car. Last year the students owning a 409 received 60 speeding tickets while the students owning a Milquetoast received 10 speeding tickets.
A student owning a 409 was k times more likely to receive a ticket than a student owning a Milquetoast.
We write this statement in mathematical expression form as,
60 = 10 * k
We need to find the value of k
Consider above equation,
60 = 10 * k
k = 60/10
k = 6
Therefore, the value of k is 6
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based only on the information given in the diagram which congruence theorems or postulates could be given as reasons why △ABC=△DEF
The triangle congruence theorem that give reason for △ABC ≅ △DEF is HL.
What is a congruent triangle?Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.
Triangles are congruent when they have exactly the same three sides and exactly the same three angles.
Triangle ABC is congruent to triangle DEF as follows:
The triangles are congruent by HL because it has same length of hypotenuse and the same length for one of the other two legs.
The HL(Hypotenuse and leg) rules applies only to right angle triangles.
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I actually have the answer it just says it’s wrong when I try to submit it. It says that I need to enter the correct number and units. Can anyone help with this?
Input
[tex]36.2\text{ yards}[/tex]Not
[tex]b=36.2[/tex]Show that each statement is false by providing a counterexample.
(a) If the measures of
a) Counterexample: [tex]m\angle{P}=90^{\circ}, m\angle{Q}=45^{\circ}, m\angle{R}=45^{\circ},[/tex]
b) Counterexample:[tex]m\angle{1}=45^{\circ}, m\angle{2}=45^{\circ},[/tex]
c) Counterexample: length=16, width=4
d) Counter example: angle ABD= 50 degree, angle CBD=10 degree
What is the interior?
Something's interior or related to its interior; inward.
a) An acute angle is one that measures less than 90 degrees.
Counterexample: [tex]m\angle{P}=90^{\circ}, m\angle{Q}=45^{\circ}, m\angle{R}=45^{\circ},[/tex]
(90 degrees is not an acute angle)
b) When the sum of two angles is 90°, then the angles are known as complementary angles
Counterexample:[tex]m\angle{1}=45^{\circ}, m\angle{2}=45^{\circ},[/tex]
( None of the angles is greater than 45 degrees )
c) Area of rectangle = length*width=16*4
Counterexample: length=16, width=4
d) Since C is the interior of the angle ABD, then, angle ABD+angle CBD=60 degrees
Counterexample: angle ABD= 50 degree, angle CBD=10 degree
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Franco is evenly dividing 3 and 1/3 pounds of flour into five containers and would like to know how many pounds of flour will be in each container. Franco sets up the following division problem to find his answer 3 and 1/3 divided by 5Convert Franco’s division problem into a product involving two fractions and find out how many pounds of flour each container will hold
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
3 and 1/3 pounds = flour
5 = containers
Step 02:
We must apply the algebraic rules to find the solution.
[tex]\begin{gathered} \text{flour:} \\ 3\text{ + }\frac{1}{3}\text{ = }\frac{9\text{ + 1}}{3}\text{ = }\frac{10}{3} \\ \end{gathered}[/tex][tex]\begin{gathered} \frac{10}{3}\cdot\text{ }\frac{1}{5}\text{ = }\frac{10}{15}\text{ = }\frac{2}{3\text{ }}\text{ (division =}==>\text{ product)} \\ \\ \end{gathered}[/tex]The answer is:
2/3 pounds of flour
how to check 9x - 11 = -38 ( x equals 7/2)
Answer:
Multiply 9 and 7/2 to check the answer.
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].
[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]
1. 2x + 7 + 3x + 5 =5x+12
2. 3x + 9 + 4x + 3 =7x+12
3. 5x - x = 4x
4. 5y + 7y = 12y
5. 7 + 6y + 5 =6y+12
6.2 + 6x + 4 + x = 6+7x
7.4 + 5y + 6 + 2y = 10+7y
8. 3x + 9 + 4x - 5 =4+7x
9.8+y-5+ 2y = 13+1y
10. 6y + 4 + 8y + 9 =14y+13
11. 2+x-1 + 4x=1+5x
12. 8y + 4y = 12+
pls i need the answers like now!!
Answer:are you fr bro??
1.true
2.true
3.true
4.true
5.true
6.true
7.true
8.true
9.y=2
10.true
11.true
12.y=1
Step-by-step explanation:
1. 5x+12=5x+12
2.7x+12=7x+12
3.5x=5x
4.12y=12y
5.6y+12=6y+12
6.7x+6=7x+6
7.7y+10=7y+10
8.7x+4=7x+4
9.3+3y=13+y
2y=10
y=2
10.14y+13=14y+13
11.5x+1=5x+1
12.12y=12
y=1
1. Tanisha drove 120 miles on 5 gallons of gas. How many miles can she drive if she has 12 gallons of gas?
Which is the graph of the inverse sine function?
On a coordinate plane, a graph starts at (negative 1, negative StartFraction pi over 2) and increases through (0, 0) to (1, StartFraction pi Over 2 EndFraction).
On a coordinate plane, a graph starts at (negative 1, pi) and decreases through (0, StartFraction pi Over 2 EndFraction) to (1, 0).
On a coordinate plane, a graph starts at (negative StartFraction pi Over 2 EndFraction, 0) and increases through (0, 0) to (StartFraction pi Over 2 Endfraction, 1).
a) is the graph of inverse sine function.
Define inverse sine function.The inverse of the sine function, also known as the arcsine function, returns the angle's value when the sine function's opposite side and hypotenuse ratio are equal. It produces the angle's value.
When the opposing side and hypotenuse of a right triangle are known, the angles can be determined using the inverse sine function. That is, angle = sin-1. The inverse sine function, which is represented as sin-1 or arcsine, is one of the inverse trigonometric functions that calculates the inverse of the sine function. Each restricted domain inverse of a trigonometric function, such as cosine, tangent, cosecant, or cotangent, exists. The trigonometric ratios from the right-angle triangle are utilized to compute the angles using the inverse function formulas.
Given,
a) is the graph of inverse sine function.
Function - inverse sine
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Answer:
A
Step-by-step explanation:
determine the length of . question 15 options: a) 9.17 units b) 6.32 units c) 3.74 units d) 10.77 units
The length of CD is 6.32 units.
From the question, we have
CB / AB = DB / CB
CB / 14 = 10 / CB
CB² = 14 × 10
CB = √140
using the Pythagorean theorem,
AB² = CB² + AC²
14² = (√140)² + AC²
196 - 140 = AC²
AC = √56
Using the ratio of the similar triangle,
CD / AC = DB / CB
CD / √56 = 10 / √140
CD = (√56 × 10)/√140
CD = 6.32 units
the length of CD is 6.32 units.
Divide:
Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.
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In the diagram, AABD is equiangular. What additional information is needed to provethat ABAE = AABC?АBEDсZBAE ZABC and ZABEZBACZABEZBAC and ZAEB ZBCAZAEB ZBCA and DE DCZBAE ZABC and DE DC
In my opinion is the first choice the correct answer, because it is proving that 2 angles are equal so the third angle will also have the same measure.
Frank reads at least 24 pages but not more than 36 pages of a book. He reads 12 pages per hour. The number of hours Frank reads p pages is modeled by a function. t(p)=p12 What is the practical range of the function?
all real numbers from 2 to 3, inclusive
all real numbers
all real numbers from 24 to 36, inclusive
all multiples of 12 between 24 and 36, inclusive
Answer:
as practical range of function is 2 to 3 so we have
12(2) = 24
12(3) = 36
i think this is it
Step-by-step explanation:
i don't really know how to explain it but:
12 x 2 = 24and
12 x 3 = 36Practice 5
In Richmond, Virginia, the average daily high temperature was 90°F for July. The average daily low temperature for the same month was 69°F. If a day's temperature change is measured by comparing the morning/low temperature to the afternoon/high temperature, what is the percent of increase between the average low and high temperatures in July? Round your answer to the tenths place. Do not include the % symbol in your answer.
26°F in July would be the percent of increase between the average low and high temperatures.
What is the temperature range?The difference between how hot and how cold two locations are is known as the temperature range.So, the month's typical daily maximum temperature is 90°F.
The month's typical low temperature is 69°F.The difference in temperature between the two ranges is 21°F or 90-69°F.When comparing the two temperatures, the result is:
79.5°F = 90+69/2 = 159/2The daily low-temperature increase as a percentage:
= 21/79.5 × 100/1= 2100/79.5= 26.4= 26°F ( nearest to the tenth place)Therefore, 26°F in July would be the percent of increase between the average low and high temperatures.
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A set of tires for your car cost 435.00 what is the cost for one tire?
Answer: Provided that the car has four tires, the cost per tire would be $ 108.75
Step-by-step explanation:
435 (Total tire cost) / 4 (number of tires) = 108.75 (the cost per tire)
**Cost model used does not include taxes or applicable other fees.
Answer:
108.75 each tire
Step-by-step explanation:
because 435.00 dividEd by 4 equals 108.75
use the commutative property to write an expression equivalent to -5 d + 1/2
We are asked to use the commutative property in the following expression:
[tex]-5d+\frac{1}{2}[/tex]Let's remember that the commutative property states the following:
[tex]a+b=b+a[/tex]In this case, we can swap the order of the terms and they will remain equivalent, like this:
[tex]-5d+\frac{1}{2}=\frac{1}{2}-5d[/tex]And thus we have rewritten the expression using the commutative property
The flu virus
is 8.0 x 10-6
cm in diameter. The
diameter of the plush
version is 1,250,000
times larger than the
microbe. What's the
diameter of the plush flu virus?
Diameter of the plush flu virus = 10 cm.
What is multiplication?Multiplication is the repeated addition of a number up to given number of times.
Given,
Diameter of the flu virus = 8.0 x [tex]10^{-6}[/tex]
Diameter of the plush flu virus = 1,250,000 × (Diameter of the flu virus)
Diameter of the plush flu virus = 1,250,000 × (8.0 x [tex]10^{-6}[/tex])
= 10 cm
Hence, Diameter of the plush flu virus = 10 cm.
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In a local election, Marshall received 682 votes and Emilio received 366 votes. Which option shows the ratio of Emilio's number of votes to Marshall's number of votes?
Given data:
The votes got by Marshall are M=682.
The votes got by Emilio are E=366.
The expression for the ratio of Emilio's number of votes to Marshall's number of votes is,
[tex]\begin{gathered} \frac{E}{M}=\frac{366}{682} \\ =\frac{183}{341} \end{gathered}[/tex]Rewrite in simplest terms: -5a – 8(-8a + 1)
The expression is given as
[tex]-5a-8(-8a+1)[/tex]Step 1: Expand the parenthesis (-8a+1) by multiplying through by -8:
[tex]\begin{gathered} -5a\lbrack+64a-8\rbrack \\ \therefore-5a+64a-8 \end{gathered}[/tex]Simplify the expression by collecting and solving like terms:
[tex]\begin{gathered} -5a+64a-8\text{ } \\ =59a-8 \end{gathered}[/tex]Thus, the simplest term is 59a - 8