Answer:
1
Step-by-step explanation:
The numbers are mutually prime, so the GCF is 1.
Answer:
1
Step-by-step explanation:
n-1 and n are consecutive integers.
Examples of consecutive pairs:
(7,8)
(10,11)
(100,101)
and so on...
The remainder will always be 1 when doing n divided by n-1.
n=(n-1)(1)+1.
All this is here to try to convince you that n and n-1 will only have common factor of 1.
A camera is placed in front of a hyperbolic mirror. The equation of the hyperbola that models the mirror is , where x and y are in inches. The camera is pointed toward the vertex of the hyperbolic mirror and is positioned such that the lens is at the nearest focus to that vertex.
Answer:
The lens is 1 inch from the mirror
Step-by-step explanation:
* Lets revise the equation of the hyperbola with center (0 , 0) and
transverse axis parallel to the y-axis is y²/a² - x²/b² = 1
- The coordinates of the vertices are (0 , ± a)
- The coordinates of the co-vertices are (± b , 0)
- The coordinates of the foci are (0 , ± c) where c² = a² + b²
* Lets solve the problem
∵ The equation of the hyperbola is y²/16 - x²/9 = 1
∵ The form of the equation is y²/a² - x²/b² = 1
∴ a² = 16
∴ a = √16 = 4
∵ The coordinates of the vertices are (0 , ± a)
∴ The coordinates of the vertices are (0 , 4) , (0 , -4)
∴ b² = 9
∴ b = √9 = 3
∵ c² = a² + b²
∴ c² = 16 + 9 = 25
∴ c = √25 = 5
∵ The coordinates of the foci are (0 , ± c)
∴ The coordinates of the foci are (0 , 5) , (0 , -5)
∵ The camera is pointed towards the vertex of the hyperbolic mirror
which is (0 , 4) and is positioned such that the lens is at the nearest
focus to that vertex which is (0 , 5)
∴ The distance between the lens and the mirror equal the distance
between the vertex and the focus
∵ The vertex is (0 , 4) and the nearest focus is (0 , 5)
∴ The distance = 5 - 4 = 1 inch
* The lens is 1 inch from the mirror
You select a card at random from the cards that make up the word "replacement". Without replacing the card, you choose a second card. Find the probability of choosing a vowel and then not a vowel. There is 1 letter for each card.
Answer:
The probability is 14/55
Step-by-step explanation:
The word replacement contains 11 letters.
In which 4 letters are vowel = e,a,e,e
And 7 letters are not vowel = r,p,l,c,m,n,t
The probability of getting the vowel in the first try = 4/11
The probability of getting something that is not a vowel = 7/10.
The denominator is one less because the vowel card is not replaced, meaning there is one less card to choose from.
Multiply the values:
=4/11 * 7/10
=28/110
=14/55
The probability is 14/55....
MAJOORRRR HELPPPP!!!
A scientist running an experiment starts with 100 bacteria cells. These bacteria double their population every 15 hours. Find how long it takes for the bacteria cells to increase to 300. Use the formula , where is the original number of bacteria cells, is the number after t hours, and d is the time taken to double the number.
It takes hours for the number of bacteria to increase to 300.
It takes 24 hours for the number of bacteria to increase to 300.
We have given that,
A scientist running an experiment starts with 100 bacteria cells.
These bacteria double their population every 15 hours.
Find how long it takes for the bacteria cells to increase to 300.
Use the formula, where is the original number of bacteria cells, is the number after t hours, and d is the time taken to double the number.
[tex]P_0=100[/tex]
[tex]d=15[/tex]
What is the formula?[tex]P_t=P_02^{\frac{t}{d} }[/tex]
[tex]Pt=300=100\times2^{\frac{t}{15} }[/tex]
[tex]3=2^{\frac{t}{15}}[/tex]
[tex]\frac{t}{15} =1.6[/tex]
t=24
It takes 24 hours for the number of bacteria to increase to 300.
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What is the correct value of b?
Answer:
b = 6Step-by-step explanation:
[tex]cosecant=\dfrac{hypotenuse}{opposite}\\\\\text{We have}\ opposite=3b,\ \text{and}\ hypotenuse=22.5,\ \text{and}\ \csc x=\dfrac{5}{4}.\\\\\text{Substitute:}\\\\\dfrac{5}{4}=\dfrac{22.5}{3b}\qquad\text{cross multiply}\\\\(5)(3b)=(4)(22.5)\\\\15b=90\qquad\text{divide both sides by 15}\\\\b=6[/tex]
PLEASE HELP MEOWT!!!
Rewrite sin^(4)xtan^(2)x in terms of the first power of cosine.
Step-by-step explanation:
[tex] { \sin(x) }^{4} { \tan(x) }^{2} [/tex]
[tex] { \sin(x) }^{4} \frac{ { \sin(x) }^{2} }{ { \cos(x) }^{2} } [/tex]
[tex] \frac{ ({ {1 - \cos(x) }^{2} })^{3} }{ { \cos(x) }^{2} } [/tex]
hopefully this helps, I'm rusty with my trig identities
Answer:
sin⁴(x)tan²(x) = (10 -15cos(2x) +6cos(4x) -cos(6x))/(16(1 +cos(2x))
Step-by-step explanation:
The relevant identities are ...
[tex]\sin^4{x}=\dfrac{3-4\cos{(2x)}+\cos{(4x)}}{8}\\\\\tan^2{x}=\dfrac{1-\cos{(2x)}}{1+\cos{(2x)}}\\\\\cos{(a)}\cos{(b)}=\dfrac{\cos{(a+b)}+\cos{(a-b)}}{2}[/tex]
Then your product is ...
[tex]\sin^4{(x)}\tan^2{(x)}=\dfrac{3-4\cos{(2x)}+\cos{(4x)}}{8}\cdot\dfrac{1-\cos{(2x)}}{1+\cos{(2x)}}\\\\=\dfrac{3-4\cos{(2x)}+\cos{(4x)}-3\cos{(2x)}+4\cos^2{(2x)}-\cos{(4x)}\cos{(2x)}}{8(1+\cos{(2x)})}[/tex]
Collecting terms and using the identity for the product of cosines, we get ...
[tex]=\dfrac{3-7\cos{(2x)}+\cos{(4x)}+4\dfrac{1+\cos{(4x)}}{2}-\dfrac{\cos{(6x)}+\cos{(2x)}}{2}}{8(1+\cos{(2x)})}\\\\=\dfrac{10-15\cos{(2x)}+6\cos{(4x)}-\cos{(6x)}}{16(1+\cos{(2x)})}[/tex]
Geometry:
The vertices of triangle ABC are A(0, 0), B(8, 1), and C(5, 5). Find the coordinates of the image of triangle ABC after a rotation of 90 degrees counterclockwise about the origin, a reflection over the x-axis, and a translation using the rule (x, y) → (x + 6, y - 1).
Answer:
Step-by-step explanation:
The transformations you want are ...
90° CCW: (x, y) ⇒ (-y, x)reflection over x-axis: (x, y) ⇒ (x, -y)translation by your rule: (x, y) ⇒ (x+6, y-1)Taken together, these make the transformation ...
(x, y) ⇒ (-y+6, -x-1)
So, your points become ...
A(0, 0) ⇒ A'(6, -1)
B(8, 1) ⇒ B'(5, -9)
C(5, 5) ⇒ C'(1, -6)
___
The attachment shows the original triangle in red and the progression to the final triangle in blue.
n a bag there are two $20 bills, one $10 bill, four $5 bills, and three $1 bills. If Frank picks one bill from the bag, the expected value of the bill he chooses is ____$. If one more $20 bill and one more $10 bill are added to the bag, the expected value will change to _____$.
Answer:
Initial expected value = 7.3 $
If one more $20 bill and one more $10 bill are added to the bag expected value = 8.57 $
Step-by-step explanation:
a) Total number of bills = 2 + 1 + 4 + 3 = 10
[tex]\texttt{Probability of picking 20 dollar bill}=\frac{2}{10}=0.2\\\\\texttt{Probability of picking 10 dollar bill}=\frac{1}{10}=0.1\\\\\texttt{Probability of picking 5 dollar bill}=\frac{4}{10}=0.4\\\\\texttt{Probability of picking 1 dollar bill}=\frac{3}{10}=0.3[/tex]
Expected value = 20 x 0.2 + 10 x 0.1 + 5 x 0.4 + 1 x 0.3 = 7.3$
b)If one more $20 bill and one more $10 bill are added to the bag
Total number of bills = 3 + 2+ 4 + 3 = 12
[tex]\texttt{Probability of picking 20 dollar bill}=\frac{3}{12}=0.25\\\\\texttt{Probability of picking 10 dollar bill}=\frac{2}{12}=0.167\\\\\texttt{Probability of picking 5 dollar bill}=\frac{4}{12}=0.333\\\\\texttt{Probability of picking 1 dollar bill}=\frac{3}{12}=0.25[/tex]
Expected value = 20 x 0.25 + 10 x 0.167 + 5 x 0.333 + 1 x 0.25 = 8.57$
Answer:
$7.30 for the first one and $8.58 for the second one
Step-by-step explanation:
ANSWER FOR PLATO
You bought a new television that has a 92 in. 76 in. screen. It has a feature that splits the screen to allow you to watch 4 channels at once. What is the scale factor and size for each channel when this feature is turned on?
Answer:
1/4
23in * 19 in.
Step-by-step explanation:
The scale factor is 1/4 and the channel size is 92*1/4 * 76 * 1/4
= 23 in * 19 in screen.
Answer:
Scale factor = 1/2, New screen 46 in by 38 in.
Step-by-step explanation:
The dimensions of screen is 92 in. by 76 in.
It has a feature that splits the screen to allow you to watch 4 channels at once as shown in the below figure.
All four parts are equal.
Let the dimensions of new screen be x in. by y in.
[tex]2x=92[/tex] and [tex]2y=76[/tex]
Divide both sides by 2.
[tex]x=46[/tex] and [tex]y=38[/tex]
Scale factor is
[tex]\text{Scale factor}=\frac{\text{New dimension}}{\text{Corresponding original dimension}}[/tex]
[tex]\text{Scale factor}=\frac{46}{92}[/tex]
[tex]\text{Scale factor}=\frac{1}{2}[/tex]
Therefore, the scale factor is 1/2.
URGENT PLEASE HELP ME WITH THIS MATH QUESTION
Answer :
22.5 is the answer
MARK ME AS BRANILIST
Answer: 90
Step-by-step explanation:
Basically you reflect twice and then rotate it
For a Saturday matinee, adult tickets cost $4.50 and kids under 12 pay only $2.00. If 100 tickets are sold for a total of $350, how many of the tickets were adult tickets and how many were sold to kids under 12?
Answer:
60 ADULT TICKETS
40 KIDS UNDER 12 TICKETS
Step-by-step explanation:
By playing around with numbers, you can figure out what makes this situation true. By multiplying 4.50 by 60, you get 270. Then, by multiplying 2 by 40, you get 80. Finally, add 270 and 80, which results in 350, which satisfies the problem.
Hope this helps!
By setting up a system of equations, we find that 60 adult tickets and 40 kids tickets were sold for the Saturday matinee when 100 tickets are sold for a total of $350.
Let x be the number of adult tickets sold and y be the number of kids tickets sold. We then have the following system of equations:
x + y = 100 (Total number of tickets)
$4.50x + $2.00y = $350 (Total revenue)
2x + 2y = 200
4.5x + 2y = 350
2.5x = 150
x = 60
y = 100 - 60 = 40
So, 40 kids tickets were sold.
Todd Foley is applying for a $98,000 mortgage. He can get a $651 monthly payment for principal and interest and no points, or a $541 monthly payment with 2.075 points. Approximately, how many months will it take Todd to cover the cost of the discount points if he takes the lower monthly payment? (Round your answer to the nearest whole month.)
Answer:
18 months
Step-by-step explanation:
The difference in payments is $651 -541 = $110 per month. The cost of the points is ...
$98,000 × 0.02075 = $2033.50
So, it will take $2033.50/($110/mo) ≈ 18.48 mo to make up the cost.
It will take Todd 18 months to cover the cost of the discount points.
_____
Comment on rounding
The question asks for the answer to be rounded to the nearest whole month. Since the quotient is about 18.486, this rounds to 18. After 18 months, the cost of the points is not quite covered. $53.50 remains to be covered. It isn't until Todd's 19th payment that the cost of points has been fully covered. For "break even" problems such as this one, I prefer to round to the next higher integer, rather than the nearest integer.
PLEASE HELP ME WITH THIS MATH QUESTION
Answer:
Rx-axis (P) is (-4 , 1)
Step-by-step explanation:
* Lets revise the reflection
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) reflected across the line y = x
∴ Its image is (y , x)
- If point (x , y) reflected across the line y = -x
∴ Its image is (-y , -x)
* Lets solve the problem
∵ The point P is (-4 , -1)
∵ Rx-axis (P) means reflect point P across the x-axis
∵ The reflection of a point (x , y) across the x-axis is (x , -y)
- That means we will change the sign of the y-coordinate of point P
∵ P = (-4 , -1)
∴ The y-coordinate of point P is -1 will change to 1
∴ The image of point P after reflection is (-4 , 1)
* Rx-axis (P) is (-4 , 1)
Answer:
P is -4 , 1
Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Place the indicated product in the proper location on the grid.
-4x 3 y 2(7xy 4)
Answer:-28x^4y^2(-4x^3y^6)
Step-by-step explanation: Distribute and add exponents, put in parentheses to make it easier to understand but it's not necessary for the final answer.
Answer:
[tex]-28x^4y^6[/tex]
Step-by-step explanation:
The given expression is
[tex]-4x^3y^2(7xy^4)[/tex]
We need to place the indicated product in the proper location on the grid.
The given expression can be rewritten as
[tex](-4\times 7)(x^3x)(y^2y^4)[/tex]
[tex]-28(x^3x)(y^2y^4)[/tex]
Using the product property of exponent, we get
[tex]-28\times x^{3+1}\times y^{2+4}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]-28\times x^{4}\times y^{6}[/tex]
[tex]-28x^{4}y^{6}[/tex]
Therefore the answer of given product is [tex]-28x^{4}y^{6}[/tex].
Which graph shows an even function?
Answer:
A.Step-by-step explanation:
The graph of even function is symmetrical about the y-axis.
The graph of odd function is symmetrical about the origin.
A. even
B. odd
C. odd
D. neither
(look at the picture)
Answer:
I would be A
Step-by-step explanation:
It has symmetry across the y axis
TechWiz Electronics makes a profit of $35 for each MP3 player sold and $18 for each DVD player sold. Last week, TechWiz sold a combined total of 153 MP3 and DVD players. Let x be the number of MP3 players TechWiz sold last week. Write an expression for the combined total profit (in dollars) TechWiz made from MP3 and DVD players last week.
Final answer:
The expression for the combined total profit made by TechWiz Electronics from MP3 and DVD players last week is 17x + 2754.
Explanation:
The profit TechWiz Electronics made from selling MP3 players can be represented by the expression 35x, where x is the number of MP3 players sold.
The profit from selling DVD players can be represented by the expression 18(153-x), where 153 is the total number of players sold and x is the number of MP3 players sold.
To find the combined total profit, we can add these two expressions together:
Combined Total Profit = 35x + 18(153-x)
Using the distributive property, we can simplify as:
Combined Total Profit = 35x + 2754 - 18x
Combining like terms, we can simplify further:
Combined Total Profit = 17x + 2754
Therefore, the expression for the combined total profit TechWiz made from MP3 and DVD players last week is 17x + 2754.
Select all the exponential functions that have a percentage rate of change of 19%
A) f(x)=3182(0.9)^2x
B) f(x)=1.74(0.81)^3x
C) f(x)=0.2(0.38)^x/2
D) f(x)= 156(1-0.19)^x
Please Help
Answer:
B) f(x)=1.74(0.81)^3x
and
D) f(x)=156(1-0.19)^x
Step-by-step explanation:
The percentage will always be where the b is, or inside the parentheses. You just have to make sure that, when not greater than 1, you must find out WHAT SUBTRACTS FROM 1 TO GET THAT RESULT. So ask yourself, what decimal number subtracts from 1 to get 0.81?
0.81 is the equivalent to (1-0.19) because (1-0.19) = 0.81.
0.19 is 19%, which is what we're looking for!
The exponential function with a percentage rate of change of 19% is option D) f(x)= 156(1-0.19)ˣ, because it reflects a 19% decrease with the base 0.81 (which is equal to 1 - 0.19).
Exponential functions have a percentage rate of change of 19%, we need to identify the function where the base of the exponent reflects this rate of change. The percentage rate of change can be represented as a decimal where a 19% increase is 1.19 and a 19% decrease is 0.81 (since 1 - 0.19 = 0.81).
Now, let's analyze the given functions:
A) f(x) = 3182(0.9)²ˣ does not represent a 19% rate of change.
B) f(x) = 1.74(0.81)³ˣ does not represent a 19% rate of change as it involves 0.81 to the power of 3x, not x.
C) f(x) = 0.2(0.38)ˣ/² does not represent a 19% rate of change.
D) f(x) = 156(1-0.19)ˣ does represent a 19% rate of change because the base is 0.81 which is equivalent to 1 - 0.19.
Therefore, the correct answer is option D).
The isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of x if the shortest side
Answer:
(7.5-2.1) /2
If the shortest side measures 2.1 m.
7.5-2.1 =5.4. Then divide by 2 each side is 2.7m
Answer:
The equation for finding the value of x is 2x + 2.1 = 7.5 and the value of x is 2.7 m.
Step-by-step explanation:
Perimeter of the isosceles triangle = 7.5 m
Length of the shortest side = 2.1 m
Let the length of each of the other sides of the triangle = x meter
Then the equation for the perimeter of the triangle becomes:
Sum of 3 sides f the triangle = 7.5 m
=> 2*x + 2.1 = 7.5
=> 2*x = 7.5 - 2.1 = 5.4
=> x = 5.4/2 = 2.7 m
So the relevant equation for finding the value of x is 2x + 2.1 = 7.5 and the value of x is 2.7 m.
What is the square footage for this property described by the metes-and-bounds method? Beginning at the point of the southerly side of Smith Street, 200 feet easterly from the corner formed by the intersection of the southerly side of Smith Street and the easterly side of Johnson Street; then east 200 feet; then south 100 feet; then west 200 feet; then north 100 feet to the POB.
A. 20,000 square feetB. 10,000 square feetC. 5,000 square feetD. 15,000 square feet
Answer:
A. 20,000 square feet
Step-by-step explanation:
The description is that of a rectangle 200 ft long and 100 ft wide. The area is the product of those dimensions:
area = (200 ft)(100 ft) = 20,000 ft²
The correct option is option A.
Area of a rectangle:The area of a rectangle is the region covered by the rectangle in a two-dimensional plane.
The formula to finding the area of the rectangle is,
[tex]A=l\times b[/tex]
It is given that,
Length=100 ft
Breadth=200 ft
[tex]A=l\times b[/tex]
Now, substituting the given values into the above formula we get,
[tex]A=200 \times 100\\A=20000[/tex]
The required area is 20,000 square feet.
Learn more about the topic area of the rectangle:
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Solve the system of equations.
6d + 3f = 12
2d = 8 - f
a. d= 3, f = 2
b. d = 3, f = 14
c. no solution
d. infinite solutions
Answer:
c. no solution
Step-by-step explanation:
6d + 3f = 12
2d = 8 - f
Multiply the second equation by 3
3*2d = 3(8-f)
6d = 24-3f
Substitute into the first equation for 6d
(24-3f) +3f = 12
Combine like terms
24 =12
This is never true, so there are no solutions
Answer:
c. No Solution.
Step-by-step explanation:
6d + 3f = 12
2d = 8 - f
Rearranging the second equation:
2d + f = 8 Multiply this equation by 3:
6d + 3f = 24
Note that the left side of this equation = the left side of the first equation but the right sides are different. So this system does not make sense and there are No Solutions.
Factor a number, variable, or expression out of the trinomial shown below:
6x2 – 12x + 9
A. 2(3x2 – 9x + 6)
B. 2(3x2 – 4x)
C. 3(2x2 – 4x + 3)
D. 3(2x2 – 4x + 9)
Answer:
C. 3(2x2 – 4x + 3)
Step-by-step explanation:
6x^2 – 12x + 9
We can factor out a 3
3(2x^2 -4x+3)
Answer:
c. 3(2x^2-4x+3)
Step-by-step explanation:
The numbers 6, 12, and 9 are all multiples of 3. Divide everything by three, move it to the outside. There are no more common factors between all 3 terms so the trinomial is completely factored. Hope this helped, if not then I apologize.
4\sqrt(2)+10
Is this rational or not?
Answer:
not rational
Step-by-step explanation:
√2 is irrational. Any arithmetic operation (addition, subtraction, multiplication, division) performed on that number and any rational number will result in an irrational number (except for multiplication by 0).
Answer:
Step-by-step explanation:
Because of that sqrt, this expression is irrational. A rational expression is one that can be expressed as the ratio of two integers.
Sandra swims the 100-meter freestyle for her school’s swim team. Her state’s ranking system awards 3 points for first place, 2 points for second, 1 point for third, and 0 points if she does not place. Her coach used her statistics from last season to design a simulation using a random number generator to predict how many points she would receive in her first race this season.
What is Sandra’s expected value of points awarded for a race?
Integer Value Points Awarded Frequency
1-8 3 20
9-15 2 12
16-9 1 6
20 0 2
Answer:
2.25
Step-by-step explanation:
The total frequency is:
20 + 12 + 6 + 2 = 40
Calculate the probability of each score:
P(X=3) = 20/40 = 0.50
P(X=2) = 12/40 = 0.30
P(X=1) = 6/40 = 0.15
P(X=0) = 2/40 = 0.05
So the expected value is:
E = (3)(0.50) + (2)(0.30) + (1)(0.15) + (0)(0.05)
E = 2.25
BRAINLIEST HURRY!
the griffins bought a netbook for$250.if the small computer depreciates at a rate of 25%a year,what will it be worth afer 3 years
Answer:
[tex]\$105.47[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]V=P(1-r)^{x}[/tex]
where
V is the depreciated value
P is the original value
r is the rate of depreciation in decimal
x is Number of Time Periods
in this problem we have
[tex]P=\$250\\r=25\%=25/100=0.25\\x=3\ years[/tex]
substitute
[tex]V=250(1-0.25)^{3}[/tex]
[tex]V=250(0.75)^{3}[/tex]
[tex]V=\$105.47[/tex]
Answer and Step-by-step explanation:
After three years the worth of it will be [tex]$105.47[/tex]
We know that each year, it's worth 75% of what it was, giving us :
[tex]=0.75*W[/tex] (Note that "W" means "Worth")
Now we calculate it in three years time so,
The first year is :[tex]250*0.75 = $187.50[/tex]
The second year is :[tex]187.5*0.75 = $140.625[/tex]
The third year is :[tex]140.625*0.75 = $105.47[/tex]
Now, we have our answer :
After three years time the worth of it is [tex]$105.47[/tex]
f(x)=x^3−2x+6
g(x)=2x^3+3x^2−4x+2
Find (f−g)(x).
Select one:
a. x^3+3x^2−2x+4
b. x^3+3x^2−2x−4
c. 3x^3+3x^2−6x+8
d. −x^3−3x^2+2x+4
Answer:
d
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x)
= x³ - 2x + 6 - (2x³ + 3x² - 4x + 2) ← distribute parenthesis by - 1
= x³ - 2x + 6 - 2x³ - 3x² + 4x - 2 ← collect like terms
= - x³ - 3x² + 2x + 4 → d
What is the value of x in the following equation: x - 2 = 9?
(please and thank you!!!)
AnswEr:
Add the two, to both sides. -2+2=0
So, the equation would like like this
x -2= 9
+2 +2
Then solve, the 2’s cancel out leaving you with x by itself. Finishing the equation to look like this-> x=11
A person came to work at 8:30 AM, went out at 11:45 AM, had lunch, came in at 12:30 PM, and left work at 5:15 PM. The total number of hours worked by this person was
Final answer:
The total number of hours worked by the person is calculated by adding the working times from two segments of the day. The morning session contributes 3 hours and 15 minutes, and the afternoon session adds 4 hours and 45 minutes. The combined total working hours are 8 hours.
Explanation:
To calculate the total number of hours worked by the person, we need to break down their workday into segments and sum up the time they spent working.
Morning session: From 8:30 AM to 11:45 AM
Afternoon session: From 12:30 PM to 5:15 PM
Calculating each session separately, we get:
Morning session: 11:45 AM - 8:30 AM = 3 hours and 15 minutes
Afternoon session: 5:15 PM - 12:30 PM = 4 hours and 45 minutes
Adding both sessions together:
3 hours and 15 minutes + 4 hours and 45 minutes = 8 hours total
Final Calculation:
3 hours 15 minutes + 4 hours 45 minutes = 7 hours 60 minutes = 8 hours
Therefore, the total number of hours worked by this person was 8 hours.
What is the solution set of y = x2 + 2x + 7 and y = x + 7? A. {(0, 7), (-1, 6)} B. {(0, 7), (-7, 0)} C. {(0, 7), (1, 8)} D. {(-2, 0), (4, 0)}
Answer:
A.
Step-by-step explanation:
If
[tex]y=x^2+2x+7[/tex] AND
y = x + 7, then by the transitive property of equality:
[tex]x^2+2x+7=x+7[/tex]
We can solve for the values of x by getting everything on one side of the equals sign and then solving for x:
[tex]x^2+x=0[/tex]
We can factor out the common x to get:
x(x + 1) = 0
which tells us by the Zero Product Property that either
x = 0 and/or x + 1 = 0 and x = -1
We are expecting 2 solutions for x since this is a second degree polynomial. We will sub both -1 and 0 into y = x + 7 to solve for the corresponding values of y
y = 0 + 7 so
y = 7 and the coordinate is (0, 7)
y = -1 + 7 so
y = 6 and the coordinate is (-1, 6)
An elevator starts at the main floor and goes up 8 floors. It then goes back fown 5 floors. What integer represents elevator final position with respect to the main floor?
Answer:
integer 3 represents elevator final position with respect to the main floor.
Step-by-step explanation:
Given : An elevator starts at the main floor and goes up 8 floors. It then goes back down 5 floors.
To find : What integer represents elevator final position with respect to the main floor.
Solution : We have given
Elevator starts at the main floor and goes up floors = + 8 ( for up).
Then goes back down floor = - 5 ( - sign for down).
Final position : 8 - 5 = 3 .
It will reach at 3 floor from the main floor .
Therefore, integer 3 represents elevator final position with respect to the main floor.
CAN SOMEONE HELP ME WITH THIS MATH QUESTION ITS ABOUT TRANSLATION
Answer:
(- 4, 1 )
Step-by-step explanation:
A translation (x + 1), y - 3 ) means add 1 to the original x- coordinate and subtract 3 from the original y- coordinate.
B = (- 5, 4 ), thus
B' = (- 5 + 1, 4 - 3 ) = (- 4, 1 )
[tex]B=(-5,4)\\\\B'=(-5+1,4-3)\\B'=(-4,1)[/tex]
Verify sin(360º - θ)= -sin θ
Show your work
Answer:
A nice way to show it is through the unit circle.
In the unit circle, the point at angle theta from the origin has a y value of sin theta.
If you rotate a point 360-theta degrees from the origin, that is like rotating it theta degrees "backwards", or downwards, which is going to yield the same exact point, reflected through the x-axis. In other words, the y value, or sin(360-theta), is exactly -sin(theta).
Answer:
The verification is in the explanation.
Step-by-step explanation:
To solve this I'm going to use the difference identity for sine:
[tex]\sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a)[/tex].
[tex]\sin(360^\circ-\theta)=\sin(360^\circ)\cos(\theta)-\sin(\theta)\cos(360^\circ)[/tex]
We are going to apply that [tex]\sin(360^\circ)=0 \text{ while } \cos(360^\circ)=1[/tex]
[tex]\sin(360^\circ-\theta)=0 \cdot \cos(\theta)-\sin(\theta)\cdot 1[/tex]
[tex]\sin(360^\circ-\theta)=-\sin(\theta)[/tex]