Answer:
C
Step-by-step explanation:
Here, we want to know what what the display on the calculator means.
Well, the expression has to do with how scientific calculators display powers of 10.
So what this means is that the value 3.456 is raised to the power of 14.
This is a way in which the screen of the scientific calculators maximizes the space on their screens.
Perhaps, we have the result of a multiplication to the powers of 27. It would be quite funny seeing 27 zeros lying on the screen of the calculator right? isn’t it?
So the calculator makes a better way of this by just printing E 27 and this automatically means 10 raised to the power of 27
This makes our answer C
Kindly note that the + sign indicates that the power of the 10 is positive 14.
Please prove this!!!!
Answer: see proof below
Step-by-step explanation:
Use the following Sum/Difference Identities:
sin(A + B) = sin A · cos B + sin B · cos A
sin(A - B) = sin A · cos B - sin B · cos A
Use the following Half-Angle Identities:
[tex]\sin\bigg(\dfrac{\theta}{2}\bigg)=\dfrac{\sqrt{1-\cos \theta}}{\sqrt2}\\\\\\\cos\bigg(\dfrac{\theta}{2}\bigg)=\dfrac{\sqrt{1+\cos \theta}}{\sqrt2}[/tex]
[tex]\text{Use the Unit circle to evaluate:}\ \cos\dfrac{\pi}{4} = \sin\dfrac{\pi}{4} = \dfrac{\sqrt2}{2}[/tex]
Use the following side work:
[tex]\sin\bigg(\dfrac{\pi}{8}\bigg)=\sin\bigg(\dfrac{\frac{\pi}{4}}{2}\bigg)=\dfrac{\sqrt{1-\cos \frac{\pi}{4}}}{\sqrt2}=\dfrac{\sqrt{2-\sqrt2}}{2}\\\\\\\cos\bigg(\dfrac{\pi}{8}\bigg)=\cos\bigg(\dfrac{\frac{\pi}{4}}{2}\bigg)=\dfrac{\sqrt{1+\cos \frac{\pi}{4}}}{\sqrt2}=\dfrac{\sqrt{2+\sqrt2}}{2}[/tex]
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \qquad \qquad \qquad \sin^2\bigg(\dfrac{\pi}{8}+\dfrac{A}{2}\bigg)-\sin^2\bigg(\dfrac{\pi}{8}-\dfrac{A}{2}\bigg)\\\\\text{Sum/Difference Identity:}\qquad \bigg(\sin\dfrac{\pi}{8}\cdot \cos \dfrac{A}{2}+\sin \dfrac{A}{2}\cdot \cos \dfrac{\pi}{8}\bigg)^2\\\\.\qquad \qquad \qquad\qquad \qquad \quad -\bigg(\sin\dfrac{\pi}{8}\cdot \cos \dfrac{A}{2}-\sin \dfrac{A}{2}\cdot \cos \dfrac{\pi}{8}\bigg)^2[/tex]
[tex]\text{Expand and Simplify:}\qquad \quad 4\sin \dfrac{\pi}{8}\cdot \cos\dfrac{A}{2}\cdot \sin \dfrac{A}{2}\cdot \cos \dfrac{A}{2}\\\\\\\text{Substitute:}\qquad \qquad \qquad 4\bigg(\dfrac{\sqrt{2-\sqrt2}}{2}\bigg)\cdot \cos \dfrac{A}{2}\cdot \sin \dfrac{A}{2}\bigg(\dfrac{\sqrt{2+\sqrt2}}{2}\bigg)\\\\\\\text{Simplify:}\qquad \qquad \qquad \sqrt2\cos \bigg(\dfrac{A}{2}\bigg)\cdot \sin \bigg(\dfrac{A}{2}\bigg)[/tex]
[tex]\text{Half-Angle Identity:} \quad \sqrt2\bigg(\dfrac{\sqrt{1+\cos A}}{\sqrt2}\bigg)\bigg(\dfrac{\sqrt{1-\cos A}}{\sqrt2}\bigg)\\\\\\\text{Simplify:}\qquad \qquad \qquad \dfrac{\sqrt{1-\cos^2 A}}{\sqrt2}\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{\sqrt{\sin^2 A}}{\sqrt2}\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{\sin A}{\sqrt2}[/tex]
[tex]\text{LHS = RHS:}\quad \dfrac{\sin A}{\sqrt2} = \dfrac{\sin A}{\sqrt2}\quad \checkmark[/tex]
A recipe for 2 loaves of banana bread calls for 3 bananas and 2 cups of flour. How many
bananas are needed to make 10 loaves of bread?
Answer:
15 bananas
Step-by-step explanation:
If two loaves of bread uses 3 bananas then multiply that by 5 because 10 divided by 2 is 5 and get 15 bananas.
q divided by 7 equals 6 have a nice day!
Answer:
q = 42
Step-by-step explanation:
[tex]\frac{q}{7}=6\\\\\frac{q}{7}*7=6*7\\\\ \boxed{q=42}[/tex]
Hope this helps.
4.89 gallons of milk is sold for $12.79. If you have $21.44 in your wallet. How many
gallons of milk you can buy?
Answer:
12.79/4.89 is $2.62 per gallon
2.62x<=21.44
Step-by-step explanation:
You could buy 8 because 21.44 divided by 2.62 is 8.1832...
What is an algebraic expression for 58 less than a number n?
Answer:
n-58
Step-by-step explanation:
Answer: n - 58
Step-by-step explanation:
The n goes first. You are subtracting 58 to find the missing value once n is determined.
What is the exact value of cos(-60°)?
Answer: 1/2
Step-by-step explanation:
cosine=adjacent/hypotenuse
Cos (-60)=1/2
This is a special triangle
see below as the ratio of each side
Hope this helps!! :)
Please let me know if you have any question
Mrs. Zhang's bee farm has a population that is about 1 tenth as large as Mr. Doyle's bee farm. If Mrs. Zhang's bee population is about 46,000, about how many bees does Mr. Doyle have?
Answer:
Mr. Doyle has 460000 bees
Step-by-step explanation:
We are told that Mrs. Zhang's bee farm has a population that is about 1 tenth as large as Mr. Doyle's bee farm.
Thus;
Population size of Mrs. Zhang's bee farm = 1/10 × population size of Mr. Doyle's bee farm
Now, we are given that Mrs. Zhang's bee population is about 46,000.
Thus, from the earlier equation, we have;
46000 = 1/10 × population size of Mr. Doyle's bee farm
Thus, when we multiply both sides by 10,we get;
population size of Mr. Doyle's bee farm = 46000 × 10 = 460000 bees
Find any 5 rational numbers between; a) -1 and 2 b) −3 8 −5 14
Answer:
Step-by-step explanation:
Hello,
You can list the following ones which are correct for a), b) and c)
[tex]\boxed{\sf \bf \ \ 1, \dfrac{1}{2}, \dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5} \ \ }[/tex]
Thanks
(6−3x
2
−8x
4
−2x
3
)+(6+7x
2
)+(2−7x
3
+3x
2
)
What is the constant?
Answer:
14
Step-by-step explanation:
I tried to put the problem together as best as I could and i got the problem as (6-3x^2-8x^4-2x^3)+(6+7x^2)+(2-7x^3+3x^2)
That means that the constants are 6+6+2.
6+6+2= 14
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after minutes of calls is , and the remaining credit after minutes of calls is . What is the remaining credit after minutes of calls?
Answer and Step-by-step explanation: Suppose remaining credit is y and time in minutes is x. To determine a value of y corresponding to a value of x, first find the equation for the function.
Since the function is linear, the equation is of the form: y = mx + b. To determine it:
1) Find slope, or inclination, of the line:
slope (m) = [tex]\frac{y_{b}-y_{a}}{x_{b}-x_{a}}[/tex]
where x's and y's are points of the function.
2) Determine the y-intercept, or b: Use a point of the function, replace them at the equation, y = mx + b, and find b.
3) The equation will be: y = mx + b
With the equation, replace x for the minutes the question is asking and calculate to find the remaining credit.
Th result will be a pair (x,y)
solve for x 4(2x+9)=-44+8
write this as a simplified expression. if you want to write the rules so that i could later figure out this problem later :)
Answer:
4x - 2
Step-by-step explanation:
Perimeter of triangle
[tex] =( 2x - 5) + (3x - 2) +( 5 - x) \\ = 2x + 3x - x - 5 - 2 + 5 \\ = 5x - x - 2 \\ = 4x - 2[/tex]
1
Is the value of -6 -6 POSITIVE, NEGATIVE, or ZERO?
Answer:
Negetive
Step-by-step explanation:
It helps to re-write.
-6 + -6 is the same as -6 -6
-6 + -6 = - 12
It would be different if these were multiplied together, but AS WRITTEN, they are subtracted. If it was (-6)(-6) or -6(-6) that would indicate multiplication as well.
The answer is negative.
$9.40 per hour times 22 hours round to the nearest cent
Answer:
The answer is 206.8. But you want me to round to the nearest cent so the real answer is $207.00
Step-by-step explanation:
Multiply.
(9√3+√5)(9√3+√5)
Simplify your answer as much as possible.
Answer:
[tex]248 + 18\sqrt{15}[/tex]
Step-by-step explanation:
[tex](9\sqrt{3}+\sqrt{5} )(9\sqrt{3}+\sqrt{5} )=(9\sqrt{3}+\sqrt{5} )^2[/tex]
[tex]81 \cdot 3 + 2\cdot 9\sqrt{3} \cdot \sqrt{5} + 5[/tex]
[tex]243 + 18\sqrt{15} + 5[/tex]
[tex]248 + 18\sqrt{15}[/tex]
there are (4 to the 9th power) to the 5th power times 4 to the 0 power books at the library. what is the total number of books?
Answer:
1310720
Step-by-step explanation:
you multiply (4^9) and get 262144 then multiply (262144)^5 and get 1310720*4^0 and multiply 4*0 and get 0 so 1310720 if that makes sense
See your levels
Brenna went on vacation and sent postcards to all of her family and friends. She needed 45
postcards, but the store only sold them in packs of 12. She bought 4 packs. How many
postcards did she have left over?
A swimming pool is a rectangular prism. The pool is 36 feet long and 20 feet wide. What is the total amount of water, in cubic feet, needed to fill the pool to a depth of 4feet?
Answer:
[tex]2880\ ft^{3}[/tex]
Step-by-step explanation:
The computation of the total amount of water needed could be determined by using the volume formula which is shown below:
[tex]Volume = L \times W \times D[/tex]
where
L = length,
W = width,
and D = depth.
Now putting the values to the above formula
[tex]Volume = (36\ ft) \times (20\ ft) \times (4\ ft) \\\\= 2880\ ft^{3}[/tex]
Therefore, the total amount of water needed is [tex]2880\ ft^{3}[/tex]
We simply applied the above formula
Answer:
280ft3
Step-by-step explanation:
how would one go about solving this graph?
Density = Mass / Volume, so you could use that information to solve for each value in the graph.
2. Mass = Density * Volume = 8.07 * 1.04 = 8.59 g
3. Volume = Mass / Density = 8.26 / 8.10 = 1.02 mL
4. Density = Mass / Volume = 7.91 / 0.99 = 7.99 g/mL
5. Mass = Density * Volume = 8.05 * 0.98 = 7.89 g
6. Volume = Mass / Density = 8.53 / 8.05 = 1.06 mL
Factoring the expression 20a^3b^3 – 24a^5b^2 + 4a^3b^2 gives a new expression of the form
Ua^xb^y (Wa^2 + Vb+ z), where U > 0.
What is the value of U?
What is the value of W?
What is the value of V?
What is the value of Z?
What is the value of x?
What is the value of y?
Answer:
[tex]U = 4\\W = -6\\V = 5\\Z = 1\\x = 3\\y = 2[/tex]
Step-by-step explanation:
Then given expression is:
[tex]20a^3b^3-24a^5b^2+4a^3b^2[/tex]
To express the given expression in the form:
[tex]Ua^xb^y(Wa^2+Vb+Z)[/tex]
and to find the values of [tex]U, W, V, Z, x, y[/tex].
First of all, let us check the maximum common powers of [tex]a, b[/tex] in each term from the given expression.
The maximum common power of [tex]a[/tex] is 3 and
The maximum common power of [tex]b[/tex] is 2.
So, we can take [tex]a^3b^2[/tex] common out of each term.
And maximum common coefficient that can be taken out common is 4.
Taking 4[tex]a^3b^2[/tex] common from each term of given expression, we get:
[tex]4a^3b^2(-6a^2+5b+1)[/tex]
Now, let us compare the given term with:
[tex]4a^3b^2(-6a^2+5b+1)[/tex] = [tex]Ua^xb^y(Wa^2+Vb+Z)[/tex]
Now, the values that we get the following values:
[tex]U = 4\\W = -6\\V = 5\\Z = 1\\x = 3\\y = 2[/tex]
which is our answer.
A test has five questions. To pass the test, at least three of the questions must be answered correctly. question ----> Find the probability that Mark guesses 4 questions correctly.
Answer:
1/5
Step-by-step explanation:
Total Question no. 5
Three must be answer correctly so 3/5 to pass
and 2/5 to fail
So 1/5 because to pass the test he can answer it correctly only one time
19x + 8 - 7x = 48 - 8x
Answer:
x = 2
Step-by-step explanation:
19x - 7x + 8x = 48 - 8
20x = 40
20x/20 = 40/20
x =2
Answer:
x=2
Step-by-step explanation:
[tex]19x + 8 - 7x = 48 - 8x \\ ⟹ 12x + 8 = 48 - 8x \\ ⟹ 12x + 8x = 48 - 8 \\ ⟹20x = 40 \\ ⟹ x = \frac{40}{20} \\ ⟹x = 2[/tex]
Susan plans to rent a bike in New Orleans to tour the city. The cost of the rental is $20 per day. The cost of a helmet is for as long as Susan needs the bike . Susan has 250 to rent a bike for 15 days. Does Susan have enough moneyExplain .
Susan does not have enough money.
20 times 15 will cost $300. Susan only have $250.
I'm not sure if this is correct.
It costs twelve dollars to get in to the fair. Tickets for rides cost extra and are d dollars each. If Tyra buys 20 tickets, how much would it cost her for the fair?
Answer:
12 + 20d
Step-by-step explanation:
OG fare = 12
Ticket price =d
20 Tickets =20d
The diagonal of a square is 4 cm. Find its ar
ea.
Answer:
Area of square= d²/2
= 4²/2
= 16/2
= 8cm²
Step-by-step explanation:
A=
[tex]a {?}^{2} [/tex]
d=
[tex] \sqrt{2a} [/tex]
we can find A.USE THIS FORMULA
A =1/2 d squared
so 1/2×4 squared=8
8 is the answer
Please help me if you can..
A cart starting from rest travels a distance of 12.7 meters in 3.6 seconds. The average speed of the cart is
Select one:
a. 3.5 m/s
b. 0.3 m/s
C. 45.7 m/s
d. 16.3 m/s
Answer:
A
Step-by-step explanation:
12.7 meters divided by 3.6 seconds is 3.527 round it up and it stays 3.5 m/s
The average speed of the cart is: 3.5 m/s
The correct option is (A).
What is Average speed?The average speed is the total distance traveled by the object in a particular time interval.
Given:
distance = 12.7m, time= 3.6 seconds
Average speed will be,
= Distance/time
=12.7/3.6
=3.522 m/s
Hence, the average speed is 3.522 m/s.
Learn more about average speed here:
https://brainly.com/question/12322912
#SPJ2
Which set of angle measures could be the measures of the interior angles of a triangle? 90°, 42°, and 58° 60°, 60°, and 60° 100°, 48°, and 42° 31°, 75°, and 70°
Answer:
60°, 60°, and 60° is the set of interior angles of triangle.
Step-by-step explanation:
Given:
Set of interior angles
90°, 42°, and 58° 60°, 60°, and 60° 100°, 48°, and 42° 31°, 75°, and 70°Find:
Set of interior angles of triangle
Computation:
We know that, sum of interior angles of triangle is 180°
So,
90° + 42° + 58° = 190°
60° + 60° + 60° = 180°
100° + 48° + 42° = 190°
31° + 75° + 70° = 176°
So,
60°, 60°, and 60° is the set of interior angles of triangle.
Answer:
60°, 60°, and 60°
Step-by-step explanation: I took the quiz
The sum of a number and 4 equals the same number times 3. What is the Number?
Answer:
2
Step-by-step explanation:
let the number be n, then sum of number and 4 is n + 4 and 3 times the number is 3n, thus
n + 4 = 3n ( subtract n from both sides )
4 = 2n ( divide both sides by 2 )
2 = n
That is the number is 2
Answer:
2
Step-by-step explanation:
1.form an equation
call the number x
x+4=3x
2.solve using inverse operations
x=2
A bag of chips contains 145 calories per serving. Each bag of chips contain 3 servings. How many calories are in 2 bags of chips?
Answer:
870
Step-by-step explanation:
you take the calories per serving, 145, and multiply it by the number of servings in the bag, 3. this gives you 435, the number of calories in a bag. then you take the number of calories in a bag times the number of bags. you get 870
Answer:
870
Step-by-step explanation: