Answer:
-4432.5 m
Step-by-step explanation:
Displacement is measured in meters, so will be the product of velocity in m/s and time in s.
(-98.5 m/s)×(45.0 s) = -4432.5 m
___
If you're concerned with significant figures, you can round this to -4430 m, which has the required 3 significant figures.
Answer:
-4432.5 m
Step-by-step explanation:
distance (or displacement) = rate times time.
Here, the displacement is
(-98.5 m/s)(45.0 s) = -4432.5 m
What is the first step in simplifying the expression
For this case we have the following expression:
[tex]\frac {11x-2-3 (1-7x) ^ 2} {(x + 1)}[/tex]
We must indicate the first step that allows to start the simplification of the expression.
It is observed that the first step to follow is to solve the square of the binomial that is in the numerator of the expression.
[tex](1-7x) ^ 2[/tex]
Answer:
Option A
Answer:
0
Step-by-step explanation:
11x-2-3(1-7x)^2/(1x+1)
11x-2-3-21x/1+1
-32x-2-3-1
-32x-1+1
-32=0
/-32 /-32
x=0
Is the pythagorean theorem only for right triangles
Yes, the Pythagorean Theorem only works with right triangles.
You can use it to solve for the hypotenuse, or either one of the sides depending on the information you are provided with.
Answer:
yes
Step-by-step explanation:
I am having a hard time with this proof of vertical angles. The choices for them are at the bottom.
Answer:
Angles 1 and 3 are verical: Given
Angles 1 and 3 are formed by ntersecting lines:
Definition of vertical angles.
Angles 1 and 2 are a linear pair and angles 2 and 3 are a linear pair:
Definition of linear pair.
1 and 2 are supplementary, and 2 and 3 are supplementary:
Linear Pair Theorem
Angles 1 and 3 are congruent:
Congruent Supplement Theorem
Step-by-step explanation:
The first is given because it tells you it is given.
The second is the definition of vertical angles. Vertical angles are angles formed by two intersecting lines.
The third statement is the definition of linear pair. Linear pair is a pair of adjacent angles formed by two lines that intersect.
The fourth statement comes from the theorem of linear pairs. Linear pair theorem states that if you have 2 angles that are a linear pair, then they are supplementary.
The fifth statement comes from the congruent supplement theorem. It says if 2 angles are supplementary to the same angle, then they are congruent to each other.
a baseball is thrown into the air with an upward velocity of 30 ft/s. its initial height was 6 ft, and its maximum height is 20.06 ft. how long will it take the ball to reach its maximum height? round to the nearest hundredth.
i've been stuck on this question for almost an hour so if anyone can help that would be greatly appreciated
Check the picture below.
where is the -16t² coming from? that's Earth's gravity pull in feet.
[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{30}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{6}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\\\ h(t)=-16t^2+30t+6 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+30}t\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\bf \left(-\cfrac{30}{2(-16)}~~,~~6-\cfrac{30^2}{4(-16)} \right)\implies \left( \cfrac{30}{32}~,~6+\cfrac{225}{16} \right)\implies \left(\cfrac{15}{16}~,~\cfrac{321}{16} \right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\stackrel{\stackrel{\textit{how many}}{\textit{seconds it took}}}{0.9375}~~,~~\stackrel{\stackrel{\textit{how many feet}}{\textit{up it went}}}{20.0625})~\hfill[/tex]
Answer:
Step-by-step explanation:
I'm not sure if this question is coming from a physics class or an algebra 2 or higher math class, but either way, the behavior of a parabola is the same in both subjects. If a parabola crosses the x axis, those 2 x values are called zeros of the polynomial. Those zeros translate to the time an object was initially launched and when it landed. The midpoint is dead center of where those x values are located. For example, if an object is launched at 0 seconds and lands on the ground 3 seconds later, it reached its max height at 2 seconds. So what we need to do is find the zeros of this particular quadratic, and the midpoint of those 2 values is where the object was at a max height of 20.06.
I used the physics equation representing parabolic motion for this, since it has an easier explanation. This equation is
[tex]x-x_{0}=v_{0}+\frac{1}{2}at^2[/tex]
where x is the max height, x₀ is the initial height, v₀ is the initial upwards velocity, t is time (our unknown as of right now), and a is the acceleration due to gravity (here, -32 ft/sec^2). Filling in our values gives us this quadratic equation:
[tex]20.06-6=30(t)+\frac{1}{2}(-32)t^2[/tex]
Simplifying that a bit gives us
[tex]14.06=30t-16t^2[/tex]
Rearranging into standard form looks like this:
[tex]0=-16t^2+30t-14.06[/tex]
If we factor that using the quadratic formula we find that the 2 times where the ball was launched and then where it came back down are
t = .925 and .95 (the ball wasn't in the air for very long!)
The midpoint occurs between those 2 t values, so we find the midpoint of those 2 values by adding them and dividing the sum in half:
[tex]\frac{.925+.95}{2}=.9375[/tex]
Therefore, the coordinates of the vertex (the max height) of this parabola are (.94, 20.06). That translates to: at a time of .94 seconds, the ball was at its max height of 20.06 feet
NEED HELP FAST!!!!!!!!!!!
John the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 3 clients who did Plan A and 5 who did Plan B. On Saturday there were 9 clients who did Plan A and 7 who did Plan B. John trained his Friday clients for a total of 6 hours and his Saturday clients for a total of 12hours. How long does each of the workout plans last?
Answer:
45 minutes each
Step-by-step explanation:
Set Plan A clients as x and Plan B clients as y to make a system of equations, the constant is the number of hours worked.
3x+5y=6
9x+7y=12
Now solve using substitution or elimination. I will use elimination.
-9x-15y=-18 I multiplied the whole first equation by -3 to eliminate x.
9x+7y=12, add the equations
-8y=-6 solve for y
y= 3/4 of an hour or 45 minutes
Next plug y into either equation
3x+5(3/4)=6 Solve for x.
3x+15/4=6
3x=2.25
x=0.75, also 45 minutes
To check plug in each variable value to each equation to see if they work if you need to.
PLEASE HELP ME WITH THIS MATH QUESTION
Answer:
The measure of arc EF = 146°
Step-by-step explanation:
From the figure we can see two circles with same center.
From the figure itself we get measure of arc AB is same as measure of arc EF, measure of arc Ac is same as measure of arc ED and measure of arc BC is same as arc FD.
The measure of arc AB = 146°
Therefore the measure of arc EF = 146°
Simplify. –2.2 – 3.1 A. 0.9 B. 5.3 C. –5.3 D. –0.9
Answer:
C. -5.3
Step-by-step explanation:
Simply add the negatives straight across to arrive at your answer.
I am joyous to assist you anytime.
Answer: C.-5.3
Step-by-step explanation: I could be wrong
Nick recently started a landscaping company. He began with 3 3 clients. Thanks to word-of-mouth referrals, his clients double each month. How many clients will Nick have after one year?
Answer:
6144 clients
Step-by-step explanation:
Number of clients in the beginning = 3
The number of clients doubled each month. This means for every month the number of clients was 2 times the previous month. This can be modeled by a geometric sequence, with first term as 3 and common ratio of 2.
The general formula for the geometric sequence is:
[tex]a_{n}=a_{1}(r)^{n-1}[/tex]
Here,
[tex]a_{1}[/tex] is the first term of the sequence which is 3
r is the common ratio which is 2 and n represents the number of term.
We need to calculate the number of clients after 1 year i.e. after 12 months. So here n will be 12. Using these values, we get:
[tex]a_{12}=3(2)^{12-1}=6144[/tex]
Thus, after 1 year the company started by Nick will have 6144 clients
Answer:
12,288
Step-by-step explanation:
all i did was multiple the previous outputs by 2.
3
6
12
24
48
96
192
384
768
1536
3072
6144
12288
Solving Quadratic Equations posttest
A.
B.
C.
D.
Answer:
D. [tex] x = 3 \pm \sqrt{10} [/tex]
Step-by-step explanation:
[tex] x^2 - 6x - 1 = 0 [/tex]
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
a = 1; b = -6; c = -1
[tex] x = \dfrac{-(-6) \pm \sqrt{(-6)^2 - 4(1)(-1)}}{2(1)} [/tex]
[tex] x = \dfrac{6 \pm \sqrt{36 + 4}}{2} [/tex]
[tex] x = \dfrac{6 \pm \sqrt{40}}{2} [/tex]
[tex] x = \dfrac{6 \pm \sqrt{4 \times 10}}{2} [/tex]
[tex] x = \dfrac{6 \pm 2 \sqrt{10}}{2} [/tex]
[tex] x = 3 \pm \sqrt{10} [/tex]
URGENT PLEASE HELP ME WITH THIS MATH QUESTION Should
Answer:
A composition of transformations is a combination of two or more transformations.A composition of reflections over parallel lines has the same effect as a translation (twice the distance between the parallel lines.
Step-by-step explanation:
Write a rational function that has the specified characteristics.
Answer:
a) f(x) = (x-5)/((x-3)(x-10))
b) f(x) = (x-4)/((x+4)(x^2+1))
c) f(x) = 2(x-1)(x+1)/((x+3)(x-4))
d) f(x) = -2(x+5)(x-3)/((x+2)(x-5))
e) f(x) = -3(x^2-1)(x-2)/(x(x^2-9))
Step-by-step explanation:
Ordinarily, we think of a horizontal (or slant) asymptote as a line that the function nears, but does not reach. Some of these questions ask for the horizontal asymptote to be zero and for a function zero at a specific place. That is, the actual value of the function must be the same as the asymptotic value, at least at one location.
There are several ways this can happen:
add a vertical asymptote on the same side of the zero as the required vertical asymptote. The function will cross the horizontal asymptote and then approach from the new direction.add a vertical asymptote on the other side of the zero from the required asymptote. The function zero will then be between the asymptotes, and the function will approach the asymptote in the expected way. (See the attachment)add complex zeros in the denominator. The function will cross the horizontal asymptote and approach it from the new direction. This does not add any asymptotes to the function.To make the horizontal asymptote be zero, the degree of the denominator must be greater than the degree of the numerator. That is, there must be additional real or complex zeros in the denominator beyond those for the required vertical asymptotes.
__
a) f(x) = (x-5)/((x-3)(x-10)) . . . . vertical asymptote added at x=10 to make the horizontal asymptote be zero
__
b) f(x) = (x-4)/((x+4)(x^2+1)) . . . . complex zero added to the denominator to make the horizontal asymptote be zero
__
c) f(x) = 2(x-1)(x+1)/((x+3)(x-4)) . . . . factor of 2 added to the numerator to make the horizontal asymptote be 2. Numerator and denominator degrees are the same. (See the second attachment.)
__
d) f(x) = -2(x+5)(x-3)/((x+2)(x-5)) . . . . similar to problem (c)
__
e) f(x) = -3(x^2-1)(x-2)/(x(x^2-9)) . . . . similar to the previous two problems (See the third attachment.)
_____
You remember that the difference of squares factors as ...
a² -b² = (a-b)(a+b)
so the factor that gives zeros at x=±3 can be written (x²-9).
To write a rational function with specific characteristics, define the characteristics and use factors to create the desired asymptotes and holes.
Explanation:To write a rational function with specific characteristics, we need to define the characteristics first. For example, let's say we want a function with a vertical asymptote at x = 2, a horizontal asymptote at y = 0, and a hole at x = -3. We can write the rational function as:
f(x) = (x + 3)(x - 2) / (x - 2)
In this function, the factor (x - 2) in both the numerator and denominator creates the vertical asymptote at x = 2. The (x + 3) factor in the numerator creates the hole at x = -3, and the horizontal asymptote at y = 0 is determined by the highest power of x in the numerator and the denominator being the same, which is x^1.
Learn more about Rational Functions here:https://brainly.com/question/27914791
#SPJ3
HELP ASAP Solve log7 b > 2. Question 18 options: b > 7 b > 49 b > 2–7 b > 14
Answer: Second Option
[tex]b > 49[/tex]
Step-by-step explanation:
We have the following expression:
[tex]log_7(b) > 2[/tex]
We have the following expression:
To solve the expression, apply the inverse of [tex]log_7[/tex] on both sides of the equality.
Remember that:[tex]b ^ {log_b (x)} = x[/tex]
So we have to:
[tex]7^{log_7(b)} > 7^2[/tex]
[tex]b > 7^2[/tex]
[tex]b > 49[/tex]
The answer is the second option
Find the angle between the given vectors to the nearest tenth of a degree. u = <6, 4>, v = <7, 5>
Answer: 1.8°
Step-by-step explanation:
To calculate the angle between the vectors u and v we use the formula of the dot product.
The dot product between two vecotores is:
[tex]u\ *\ v = |u||v|*cosx[/tex]
Where x is the angle between the vectors
As we know the components of both vectors, we calculate the dot product by multiplying the components of both vectors
[tex]u=6i + 4j\\v=7i +5j[/tex]
Then:
[tex]u\ *\ v = 6*7 + 4*5[/tex]
[tex]u\ *\ v = 42 + 20[/tex]
[tex]u\ *\ v =62[/tex]
Now we calculate the magnitudes of both vectors
[tex]|u|=\sqrt{6^2 + 4^2}\\\\|u|=2\sqrt{13}[/tex]
[tex]|v|=\sqrt{7^2 +5^2}\\\\|v|=\sqrt{74}[/tex]
Then:
[tex]62 = 2\sqrt{13}*\sqrt{74}*cosx[/tex]
Now we solve the equation for x
[tex]62 = [tex]cosx=\frac{62}{2\sqrt{13}*\sqrt{74}}\\\\x=arcos(\frac{62}{2\sqrt{13}*\sqrt{74}})\\\\x=1.8\°[/tex]
Find the value of x, if m arc FN = 5x – 10 and m= arc UN = 3x + 30.
Answer:
x=20
Step-by-step explanation:
we know that
Triangles YNF and YUN are congruent by SSS
Because
YN=YF=YU=r -----> the radius of the circle
FN=NU ----> given problem
therefore
∠FYN=∠NYU
and
arc FN=∠FYN -----> by central angle
arc NU=∠NYU -----> by central angle
so
arc FN=arc NU
substitute the given values
5x-10=3x+30
solve for x
5x-3x=30+10
2x=40
x=20
Use the unit circle to find the value of sin 3π/2 and cos 3π/2. Show work please!
Answer:
Step-by-step explanation:
3π/2 is equivalent to 270°. The "opposite side" for this angle is -2; the adjacent side is 0, and the hypotenuse is 2.
Thus, sin 3π/2 = opp/hyp = -2/2 = -1, and
cos 3π/2 = adj/hyp = 0/2 = 0.
Answer:
[tex]sin\frac{3\pi}{2}=-1[/tex] and [tex]cos\frac{3\pi}{2}=0[/tex]
Step-by-step explanation:
We are given that a unit circle
We have to find the value of [tex]sin\frac{3\pi}{2}[/tex] and [tex]cos\frac{3\pi}{2}[/tex] by using the unit circle
Radius of circle=r=1 unit
We know that
[tex]x=r cos\theta[/tex] and [tex]y=r sin\theta[/tex]
We [tex]\theta=\frac{3\pi}{2}[/tex]
Then x=[tex]1\cdot cos\frac{3\pi}{2}[/tex]
[tex]x=cos (2\pi-\frac{\pi}{2})[/tex]
[tex]x=cos \frac{\pi}{2}[/tex] ([tex]cos(2\pi-\theta)=cos\theta[/tex])
[tex]x=0 (cos\frac{\pi}{2}=0)[/tex]
[tex]y=1\cdot sin\frac{3\pi}{2}[/tex]
[tex]y=sin(2\pi-\frac{\pi}{2})[/tex]
[tex]y=-sin\frac{\pi}{2}[/tex] ([tex]sin(2\pi-\theta)=-sin\theta[/tex])
[tex]y=-1[/tex] ([tex]sin\frac{\pi}{2}=1[/tex])
Hence, [tex]sin\frac{3\pi}{2}=-1[/tex] and [tex]cos\frac{3\pi}{2}=0[/tex]
Janice is trying to earn $30 to buy a necklace. She has saved $5.25. She earns $2.25 per hour weeding her grandmother's garden and she earns $5.50 per hour selling seashells at the flea market. Will Janice have enough to buy the necklace if she works in the garden for 2 hours and at the flea market for 4 hours? Use the inequality 2.25y + 5.50z + 5.25 ? 30. Yes, because the total will be $26.50. Yes, because the total will be $31.75. No, because the total will be $25.25. No, because the total will be $46.50.
Answer:
Yes, because the total will be $31.75
Step-by-step explanation:
Let
x -----> number of hours weeding grandmother's garden
z ----> number of hours selling seashells at the flea market
we know that
The inequality that represent this situation is
[tex]2.25x+5.50z+5.25\geq30[/tex]
so
For x=2 hours, z=4 hours
substitute in the inequality
[tex]2.25(2)+5.50(4)+5.25\geq30[/tex]
[tex]4.50+22+5.25\geq30[/tex]
[tex]31.75\geq30[/tex] -----> is true
therefore
Janice will have enough to buy the necklace
Answer:
yes
Step-by-step explanation:
because the total will be $31.75.
Drag the tiles to the boxes to form correct pairs.
Multiply the pairs of numbers and match them to their products.
Answer:
Answer in the picture.
Answer:
[tex](-7)(-1.2)\leftrightarrow 8.4[/tex]
[tex](-2\frac{1}{2})(-2)\leftrightarrow 5[/tex]
[tex](2.5)(-2)\leftrightarrow -5[/tex]
[tex](7)(-1.2)\leftrightarrow -8.4[/tex]
Step-by-step explanation:
Product rule of signs:
(+)(+) = (+)
(+)(-) = (-)
(-)(+) = (-)
(-)(-) = (+)
Using these signs simplify the given expression.
[tex](-7)(-1.2)=8.4[/tex]
It means (-7)(-1.2) is equivalent to 8.4.
[tex](-2\frac{1}{2})(-2)=(-\frac{5}{2})(-2)=5[/tex]
It means [tex](-2\frac{1}{2})(-2)[/tex] is equivalent to 5.
[tex](2.5)(-2)=-5[/tex]
It means (2.5)(-2)- is equivalent to -5.
[tex](7)(-1.2)=-8.4[/tex]
It means (7)(-1.2) is equivalent to -8.4.
Line C: y = x + 12 Line D: y = 3x + 2 Which of the following shows the solution to the system of equations and explains why? (A) (4, 14), because one of the lines passes through this point.(B) (4, 14), because the point lies between the two axes(C) (5, 17), because both lines pass through this point(D) (5, 17), because the point does not lie on any axis
Answer:
C)
Step-by-step explanation:
We are given with a pair of linear equations,
y=x+12
y=3x+2
Let us solve them for x and y
In order to solve them we subtract first equation from the second ,
0=2x-10
Adding 2x on both sides we get
2x=10
Dividing both sides by 2 we get
x=5
Now replacing this value of x in first equation
y=5+12=17
Hence the solution of the two equations is (5,12)
And by solution of a linear pair of equations, we mean that both the lines passes through that point.
Can someone please help me with this transformation question
Answer:
x+(-2), y+(-3)
Step-by-step explanation:
Trapezoid ABCD has vertices A(-5,2), B(-3,4), C(-2,4) and D(-1,2).
The reflection across the y-axis has the rule
(x,y)→(-x,y),
so
A(-5,2)→A'(5,2)B(-3,4)→B'(3,4)C(-2,4)→C'(2,4)D(-1,2)→D'(1,2)The translation that maps points A', B', C' and D' to E, H, G, F is
A'(5,2)→E(3,-1)B'(3,4)→H(1,1)C'(2,4)→G(0,1)D'(1,2)→F(-1,-1)and has a rule
(x,y)→(x-2,y-3)
A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.)
Answer:y = 18(1.15)^x
Step-by-step explanation:
g o o g ; e
Answer:
The required equation is [tex]y = 18(1.15)^x[/tex].
Step-by-step explanation:
Consider the provided information.
The Initial value of poster = $ 18
After 1 year amount of increase = $ 20.70
With the rate of 15% = 0.15
Let future value is y and the number of years be x.
[tex]y = 18(1.15)^x[/tex]
Now verify this by substituting x=1 in above equation.
[tex]y = 18(1.15)^1=20.7[/tex]
Which is true.
Hence, the required equation is [tex]y = 18(1.15)^x[/tex].
the vertex of this parabola is at (5,-4). which of the following could be its equation?
Answer:
Option D
Step-by-step explanation:
The equation of a parabola in vertex form is
[tex]y = a(x - h)^{2} + k[/tex]
Where (h,k) is the vertex.
We were given the vertex as (5,-4). This implies that:
h=5, k=-4, we can see that a=2 is the leading coefficient of all the options.
We substitute the values to get:
[tex]y = 2(x - 5)^{2} + - 4[/tex]
Or
[tex]y =2( {x - 5)}^{2} - 4[/tex]
The value of an antique plate after x years can be modeled by f(x) = 18(1.05)x. Which graph can be used to approximate the number of years it will take for the plate’s value to be $30?
Answer:
The approximate number of years is 10
The graph in the attached figure
Step-by-step explanation:
Let
f(x) the value of an antique plate
x is the number of yeras
we know that
The system of equations that represented the problem is equal to
[tex]f(x)=18(1.05)^{x}[/tex] ----> equation A
[tex]f(x)=30[/tex] ----> equation B
Solve the system by graphing
The solution of the system of equations is the intersection point both graphs
using a graphing tool
The solution is the point (10.47,30)
see the attached figure
therefore
The approximate number of years is 10
Answer:
1st graph
Step-by-step explanation:
just did it in edge
Jane and Lee had dinner at The Palace The bill totaled $20 30 with tax The service
was good, so they decided to leave a 15% tip. What is 15% of $20 30. to the
nearest cent?
Answer:
$3.45
Step-by-step explanation:
$20.30 / 10 = $2.30 = 10%
$2.30 / 2 = $1.15 = 5%
$2.30 + $1.15 = $3.45 = 15%
In step one do you found the volume (in cubic feet) of the main tank(359,006.67). The maximum density of killer whales per cubic foot is 0.000011142, what is the maximum number of killer whales allowed on the main show tank at any given time? I must explain your answer using words and you must show all working calculations to receive credit
Answer:
4 killer whales
Step-by-step explanation:
The dimensional analysis is ...
(whales/ft³)(ft³/tank) = whales/tank
Putting the numbers with the units, we get ...
(1.1142·10^-5 whales/ft³)(3.5900667·10^5 ft³/tank) = 4.00005... whales/tank
The maximum number of killer whales allowed in the main show tank is 4.
The decimal form of 43% is
Answer:
.43
Step-by-step explanation:
If I see % in a number I like to think of it as times 1/100 or divided by 100 (those are the same thing).
So we are doing 43 divided by 100 (or 43/100) which gives you .43 .
Anytime you divide by 100 you have to move the decimal left twice. (43 is 43. so 43. divided by 100 is .43)
Example
23.5%=.235
Why?
23.5 divided by 100 is .235
Another example
4%=.04
Why?
4. divided by 100 is .04
Find the value of x if m arc ADC = (4x + 4)° and m angle ABC = 150°.
Answer:
The measure of angle x is 74°
Step-by-step explanation:
we know that
The inscribed angle measures half of the arc that comprises
so
∠ABC=(1/2)[arc ADC]
substitute the given values
150°=(1/2)[4x+4]
300°=[4x+4]
4x=300-4
4x=296
x=74°
If two lines l and m are parallel, then a reflection along the line l followed by a reflection along the line m is the same as a
A. translation.
B. reflection.
C. rotation.
D. composition of rotations.
If two lines l and m are parallel, then a reflection along line l followed by a reflection along line m is the same as a translation. Therefore, the correct answer is: A. translation.
If two lines l and m are parallel, a reflection along l followed by a reflection along m is equivalent to a translation. This can be understood geometrically: when a figure is reflected across parallel lines, it undergoes a displacement without changing its orientation.
The sequence of two reflections results in the figure being shifted along a path parallel to the original lines, akin to a translation. While reflections change orientation and translations shift position, the combination of two reflections across parallel lines maintains the figure's orientation while relocating it.
A growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. What is the population of the culture 6 days after inoculation? Y = 1,000(1.15)6 2,313 bacteria y = 1,000(1.15)7 y = 1,000(1.5)5 y = 1,000(1.5)6 11,391 bacteria
Answer:
The correct option is Y = 1,000(1.15)6 2,313 bacteria
Step-by-step explanation:
According to the given statement a growth medium is inoculated with 1,000 bacteria.
Bacteria grow at a rate of = 15% = 0.15
Add 1 to make it easier = 0.15+1 = 1.15
We have to find the population of the culture 6 days after inoculation.
= 1000(1.15)^6
=1000(2.313)
= 2313 bacteria
The population of the culture 6 days after inoculation = 2313 bacteria
Therefore the correct option is Y = 1,000(1.15)6 2,313 bacteria....
Answer:AAAAAAAAAAAAAAAAAAAA
Ancient paintings were found on cave walls in South America. The Carbon-14 in the paintings was measured and was found to be 19% of the original weight. How old were the paintings?
A. 3,839
B. 9,239
C. 13,839
D. 19,239
Answer: C. 13,839 (the answer is not among the given options, however the result is near this value)
Step-by-step explanation:
The exponential decay model for Carbon- 14 is given by the followig formula:
[tex]A=A_{o}e^{-0.0001211.t}[/tex] (1)
Where:
[tex]A[/tex] is the final amount of Carbon- 14
[tex]A_{o}=[/tex] is the initial amount of Carbon- 14
[tex]t[/tex] is the time elapsed (the value we want to find)
On the other hand, we are told the current amount of Carbon-14 [tex]A[/tex] is [tex]19\%=0.19[/tex], assuming the initial amount of Carbon-14 [tex]A_{o}=[/tex] is [tex]100\%[/tex]:
[tex]A=0.19A_{o}[/tex] (2)
This means: [tex]\frac{A}{A_{o}}=0.19[/tex] (2)
Now,finding [tex]t[/tex] from (1):
[tex]\frac{A}{A_{o}}=e^{-0.0001211.t}[/tex] (3)
Applying natural logarithm on both sides:
[tex]ln(\frac{A}{A_{o}})=ln(e^{-0.0001211.t})[/tex] (4)
[tex]ln(0.19)=-0.0001211.t[/tex] (5)
[tex]t=\frac{ln(0.19)}{-0.0001211}[/tex] (6)
Finally:
[tex]t=13713.717years[/tex] This is the age of the paintings and the option that is nearest to this value is C. 13839 years
Can someone help me please?
A rectangle with a perimeter of 92 inches has a length of 14 inches longer than its width. What is its width in inches.
Please explain step by step thank you.
Answer:
16 inches
Step-by-step explanation:
w = width of the rectangle
l = length of the rectangle
The perimeter of a rectangle is the length around it:
P = 2w + 2l
Given:
P = 92
l = w + 14
Substituting:
92 = 2w + 2(w + 14)
92 = 2w + 2w + 28
64 = 4w
w = 16
The width of the rectangle is 16 inches.
Final answer:
The width of the rectangle is 16 inches, deduced by using the perimeter formula for a rectangle and solving for width with given conditions.
Explanation:
To find the width of the rectangle given its perimeter and the fact that its length is 14 inches longer than its width, we start by listing what we know:
The perimeter of the rectangle is 92 inches.
The length (L) is 14 inches longer than the width (W).
Remember, the perimeter (P) of a rectangle is given by P = 2L + 2W. We can substitute L with W + 14, since the length is 14 inches more than the width. This gives us:
P = 2(W + 14) + 2W
Now we can plug in the value for P:
92 = 2(W + 14) + 2W
Then, distribute:
92 = 2W + 28 + 2W
Combine like terms:
92 = 4W + 28
Now, subtract 28 from both sides:
64 = 4W
Lastly, divide by 4 to solve for W:
16 = W
So, the width of the rectangle is 16 inches.