Answer:
[tex]t = 23.10\ years[/tex]
Step-by-step explanation:
We have an exponential decay function:
[tex]A = A_0e ^{-0.03t}[/tex]
This function decreases as the years pass. That is, if A is the quantity for a time t and [tex]A_0[/tex] is the original quantity at time t = 0 then:
[tex]A <A_0[/tex]
We want to know for what value of t the value of A decreases by half of [tex]A_0[/tex]. That is, we want to know when [tex]A = \frac{A_0}{2}[/tex]
Then we do:
[tex]\frac{A_0}{2} = A_0e ^{-0.03t}\\\\\frac{1}{2} =e ^{-0.03t}\\\\ln(\frac{1}{2}) = -0.03t\\\\t = \frac{ln(\frac{1}{2})}{-0.03}[/tex]
[tex]t = 23.10\ years[/tex]
help me please asap!
4 · x^4 · x^4 · y
4 x^8 y
In words: four times x to the eighth times y
Write an equation that gives the proportional relationship of the graph.
A) y = 1/3 x
B) y = 2x
C) y = 3x
D) y = 6x
Answer:
C
Step-by-step explanation:
A proportional graph is a line. Every line has a slope. The slope is found by subtracting two points as a ratio. The line has points (0,0) and (2,6).
6-0 = 6
2 -0 = 2
The ratio is vertical over horizontal so 6/2 = 3.
The equation is y = 3x.
Answer:
C) [tex]y=3x[/tex]
Step-by-step explanation:
1) Checking the coordinate points (2,6), (4,12), (6,18), (8,24). And since the Proportionality Constant is given by
[tex]k=\frac{y}{x}[/tex]
[tex]k=\frac{y}{x}=\frac{6}{2}=\frac{12}{4}=\frac{18}{6}=\frac{24}{8}=3[/tex]
Then k=3
2) A Proportional Function is given by:
[tex]y=kx[/tex]
Thus we can state that proportional function rule as:
[tex]y=3x[/tex]
LMK ASAP 10 POINTS........
Answer:
20cm
Step-by-step explanation:
Answer:
The correct answer is option 2
45 cm
Step-by-step explanation:
It is given a circle with circumference C = 180 cm
To find the length of arc ABC
From the figure we can see that the central angle of arc ABC = 90°
Therefore the arc length = (90/360) * Circumference
Arc ABC = (90/360) * 180 = (1/4) * 180 = 45
Therefore arc length = 45 cm
The correct answer is option 2
can you please help me
Answer:
[tex]\large\boxed{f(-7b)=-35b+10}[/tex]
Step-by-step explanation:
[tex]\text{Put}\ v=-7b\ \text{to the function}\ f(v)=5v+10:\\\\f(-7b)=5(-7b)+10=-35b+10[/tex]
v2=17
(round to the nearest tenth as needed.Use a comma to separate answers as needed.)
Put the answer into a calculator;
-√17 = -4.123105626
√17 = 4.123105626
Round to the nearest tenth by looking at the 2nd digit after the decimal point. If it is 5 or greater, round up, otherwise round down.
-√17 = 4.123105626
2 is less than 5, so we leave it as it is.
-√17 ≈ -4.12
√17 = 4.123105626
2 is less than 5, so we leave it as it is.
√17 = 4.12
v ≈ -4.12, 4.12
what is the rule for the reflection?
Step-by-step explanation:
the y-axis is the point (-x,y). Reflect over the y = x: When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed).
Answer:
The rule for reflection on the x-axis is (x,y) -> (x,-y)
The rule for reflection on the y-axis is (x,y) -> (-y,y)
Step-by-step explanation:
A reflection is a transformation that represents a turn of a figure. The figures can be reflected in a point, a line, or a plane.
A reflection copies each point of a figure to an image through a fixed line. The fixed line is called the reflection line.
QUICK !!
What is the image point of (2,-7) after a translation right 4 units and up 3 units ?
Answer:
(6, - 4)
Step-by-step explanation:
A translation of 4 units right is equivalent to adding 4 to the x- coordinate
A translation of 3 units up is equivalent to adding 3 to the y- coordinate
(x, y) → (x + 4, y + 3) ← translation rule
Hence
(2, - 7) → (2 + 4, - 7 + 3) → (6, - 4)
Anwser: (−2,−7)→(−2+4,−7−2)=(2,−9)
Explanation: {right 4 units: add 4 to x-coordinate}
down 2 units: subtract 2 from y-coordinate
Find the area of the triangle, height=x, base=5/3x
Answer:
[tex]A=\frac{5x^{2}}{6}[/tex]
Step-by-step explanation:
Let's solve this by using the Area formula for a triangle:
[tex]A=\frac{1}{2}bh[/tex]
Base: [tex]\frac{5}{3}x[/tex]
Height: [tex]x[/tex]
Solve for A (Area)
[tex]A=\frac{1}{2}(\frac{5}{3}x)(x)[/tex]
[tex]A=\frac{5x^{2}}{6}[/tex]
Since we do not have a given value for [tex]x[/tex], this is as far as we can condense the equation.
The area would be 5x^2/ 6x
Step-by-step explanation:See the image
Can you help me on 34 and 35 please
-- #34 is choice-C .
-- See the picture attached to this answer, for both solutions.
Its the ratio one
If y'all can help that would be great
Answer:
9
Step-by-step explanation:
The 4 part of the ratio represents 12 girls
Divide 12 by 4 to find the value of one part of the ratio
[tex]\frac{12}{4}[/tex] = 3 ← value of 1 part of the ratio, hence
Multiply the 3 part of the ratio by 3 to obtain number of boys
3 × 3 = 9 ← number of boys
Answer:9
Step-by-step explanation: it is 3 to 4 so you multiply 4 by 3 you get 12 you multiply 3 by 3 you get 9
lorena’s backpack has a mass of 20,000 grams. what is the mass of lorena’s backpack in kilograms?
Answer:
20 kg
Step-by-step explanation:
If we want any value in grams to be in kilograms, we divide it by 1000
in this example: 20000/1000
=20 kg
A rock drops from a height of 60m. how long does it take for it to hit the ground?
Answer:
The answer is actually C. 3.5. I just answered this question on a quiz and I got it correct. I'm sorry for the late response but I hope this helps!
which choice is equivalent to the expression below? heLp!
Find the side of an equilateral traingle whose perimeter is 75 cm
Answer:
Each side is 25cm long.
Step-by-step explanation:
75/3=25 (This is because each side of an equilateral triangle is equal to each other.) (The perimeter is all sides added together.)
Answer:
equilateral traingle mean all sides are equal..so 75÷3
=25cm
Step-by-step explanation:
its equal....so we just simply just divide..
2. What’s the answer to this question please!
Answer:
D.
Your doing it for a week..5 days, his cases are 12, but how many cases(c) does he need to sell minus his rent vs what his goal is.
The total amount paid on a 35 year loan was $98,000. If the interest rate was 4.1% and compounded monthly, what was the principal? Round your answer to the nearest cent.
Answer:
The principal amount was $23,393.45
Step-by-step explanation:
The total amount paid on a 35 year loan was $98,000 at the rate of interest 4.1%
We will calculate Principal amount by this formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where A = amount (98,000)
P = Principal amount (P)
r = rate of interest 4.1% (0.041)
n = number of compounding interest monthly (12)
t = time (35 years)
[tex]98,000=P(1+\frac{0.041}{12})^{(12)(35)}[/tex]
[tex]98,000=P(1+0.003416)^{(420)}[/tex]
[tex]98,000=P(1.003416)^{(420)}[/tex]
98,000 = P(4.189386)
= 4.189386P = 98,000
P = [tex]\frac{98000}{4.189386}[/tex]
P = 23,392.4494 ≈ $23,392.45
The principal amount was $23,393.45
Answer:
$23,392
Step-by-step explanation:
Use the compound interest formula and substitute the values given: $98,000=P(1+.041/12)[tex]^{12(35)}[/tex]
Simplify using order of operations:
$98,000=P(1.003416667)[tex]^{420}[/tex]
P=$98,000(1.003416667)[tex]^{420}[/tex]
P≈$23,392
Find the slope of a line perpendicular to each given line x=3
Answer:
0 or undefined
Step-by-step explanation:
Answer:
The slope doesn't matter.
Step-by-step explanation:
Since the variable equals a constant, any y value would be perpendicular to x = 3.
So lines perpendicular to x = 3 would be,
y = 1y = 2y = 3And so on...Gerald was able to mow 1/2 of a lawn in 12 minutes how many lawns could he mow in 2 hours
Answer:
5
Step-by-step explanation:
he can mow one lawn in 24 min
2 hours=120 min
120÷24=5
Bonjour,
combien fait 87$ augmenté de 200% ?
Bonsoir,
Combien fait 87$ augmenté de 200% ?
87 $ x 200/100 = 174 $ d'augmentation,
174 + 87 = 261 $
simplify (2r^3)^2
a. 2r^5
b. 2r^6
c. 4r^5
d. 4r^6
Answer:
The answer is D. 4r^6.
<3
-Callie
Step-by-step explanation:
Answer:
D. 4r^6.
Step-by-step explanation:
The f(x)=2^x and g(x)=f(x+k). If k=-5, what can be concluded about the graph of g(x).
The graph of g(x) is shifted vertically :
a) 5 units above the graph of f(x)
b) 5 units below the graph of f(x)
c) the graph is not shifted vertically from the graph of f(x)
The graph of g(x) is shifted horizontally:
a) 5 units to the left of the graph of f(x)
b) 5 units to the right of the graph of f(x)
c) the graph is not shifted horizontally from the graph of f(x)
PLEASE I NEED HELP
I will give brainliest
[tex]\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}[/tex]
[tex]\bf ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\[/tex]
[tex]\bf \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]
now, with that template in mind, let's take a look
[tex]\bf \begin{cases} f(x)=&2^x\\ g(x)=&f(x+k)\\ & f(x-5)\\ &2^{x-5} \end{cases}~\hspace{10em}g(x)=2^{\stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{-5})}+\stackrel{D}{0} \\\\\\ \textit{horizontal shift by }\cfrac{C}{B}\implies \cfrac{-5}{1}\implies -5\qquad \qquad \textit{ of 5 units to the right}[/tex]
The graph of g(x) is shifted horizontally 5 units to the right of the graph of f(x).
The correct option is (b).
What is a Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
As per the given data:
We are given 2 functions, and we have to find out the shift in the graph.
f(x) = 2^x
g(x) = f(x+k)
When the value of k = -5 we have to find out the shift in the graph of g(x).
For finding out the shift in the graph of g(x):
g(x) = f(x+k)
By substituting the given value of f(x) = 2^x and k = -5:
g(x) = 2^(x-5)
When y = f(x) is changed to y = f(x - 5) the graph of f(x) shifts 5 units to the right horizontally.
Similarly, for g(x) = 2^(x-5) the graph will shift by 5 units to the right.
Hence, The graph of g(x) is shifted horizontally 5 units to the right of the graph of f(x).
To learn more about Function, click:
brainly.com/question/12431044
#SPJ3
Help here’s a few examples!!
QUESTION 1
The given expression is
2+8
The greatest common factor of 2 and 8 is 2.
We can rewrite as: [tex]2+8=2\times1+2\times4[/tex]
Factor to get: [tex]2+8=2(1+4)[/tex]
QUESTION 2
Given: 9-3
Greatest common factor of 9 and 3 is 3.
Rewrite as: [tex]9-3=3\times3-3\times1[/tex]
Factor: [tex]9-3=3(3-1)[/tex]
QUESTION 3
Given: 30+25
Greatest common factor of 30 and 25 is 5.
Rewrite as: [tex]30+25=5\times6+5\times4[/tex]
Factor: [tex]30+25=5(6+4))[/tex]
QUESTION 4.
Given: 35-14
The greatest common factor of 35 and 14 is 7.
Rewrite as: [tex]35-14=5\times7-2\times7[/tex]
Factor: [tex]35-14=7(5-2)[/tex]
QUESTION 5
The given expression is 81-18.
The greatest common factor of 81 and 18 is 9.
Rewrite as: [tex]81-18=9\times9-9\times2[/tex]
Factor: [tex]81-18=9(9-2)[/tex]
QUESTION 6
Given: 60+100
The greatest common factor of 60 and 100 is 20.
Rewrite as : [tex]60+100=20\times3+20\times5[/tex]
Factor: [tex]60+100=20(3+5)[/tex]
QUESTION 7
Given: 28-20
The greatest common factor of 28 and 20 is 4.
Rewrite as: [tex]28-20=4\times7-4\times5[/tex]
Factor: [tex]28-20=4(7-5)[/tex]
QUESTION 8
Given: 72+48
The greatest common factor of 72 and 48 is 24.
Rewrite as: [tex]72+48=24\times3+24\times2[/tex]
Factor: [tex]72+48=24(3+2)[/tex]
QUESTION 9
The given expression is [tex]12x+18[/tex].
The greatest common factor of [tex]12x[/tex] and 18 is 6.
Rewrite as; [tex]12x+18=6\times2x+6\times3[/tex]
Factor; [tex]12x+18=6(2x+3)[/tex]
QUESTION 10
Given: [tex]4y+10[/tex]
The greatest common factor of [tex]4y[/tex] and 10 is 2.
Rewrite the expression as; [tex]4y+10=2\times2y+2\times5[/tex]
Factor: [tex]4y+10=2(2y+5)[/tex]
I need some help, thanks!
Answer:
2 sections.
Step-by-step explanation:
Given that number of students that had homework last night = 8
Given that number of students that had not homework last night = 4
Then total number of students = 8+4= 12
Then fraction of students that had not homework last night = 4/12
Alaina used that data to design a spinner with 6 congruent sections.
Then number of sections of Alaina's spinner the represents students who did not have homework = ( 6 section) ( 4/12 fraction)
= 6(4/12)
=24/12
=2
Hence final answer is 2 sections.
What is the tangent of angle Z?
Answer:
C) 12/5
Step-by-step explanation:
Tan = Opposite / Adjacent
So
Tan(Z) = YX /YZ
Given: YZ = 5 and XZ = 13
so
(YZ)^2 = (XZ)^2 - (YZ)^2
= 13^2 - 5^2
= 169 - 25
= 144
YZ = 12
Tan(Z) = YX /YZ
Tan(Z) = 12/5
Someone please help ASAP will give brainliest
Answer:
jk(x) = -16x^2 -12x+10
Step-by-step explanation:
j(x) = -4x+2
k(x) = 5+4x
jk(x) = (-4x+2) (5+4x)
FOIL
-4x*5 +-4x*4x +2*5 +2*4x
Combine like terms
-20x-16x^2 +10+8x
-16x^2 -12x+10
jk(x) = -16x^2 -12x+10
What is the distance between points A and C
Answer:
Step-by-step explanation:
(- 4 - 2)² + (- 4 - 1)² = AC²
(- 6)² + (- 5)² = AC²
36 + 25 = AC²
AC² = 61
AC = √61
AC ~ 7.81 unitário
I hope I helped you.
The distance between points A and C is calculated using the displacement vector ĐAC, resulting in a distance of 4.5 km.
Explanation:The student's question, 'What is the distance between points A and C', pertains to the calculation of displacement in a vector context within the field of Mathematics. To determine the displacement vector ĐAC, we apply the given information that point C is located three-quarters of the distance from point A to point B. If the full displacement from A to B, denoted as ĐAB, has a magnitude of 6 km, the displacement vector from A to C, which is ĐAC, has a magnitude of 0.75 times 6 km, which equals 4.5 km.
The displacement vector ĐAC is parallel to ĐAB and in the same northeasterly direction, indicating that the distance from A to C is simply 4.5 km. The student can understand that the magnitude of displacement is different from the distance traveled if the path taken is not a straight line; however, in this instance, the path is straight, and therefore, the displacement coincides with the actual distance covered.
To summarize, the distance between points A and C is the magnitude of the displacement vector ĐAC, which is 4.5 km.
Type the correct answer in each box. The length of a rectangle is 3 inches more than its width. The perimeter of the rectangle is 34 inches. The length of the rectangle is inches, and its width is inches.
Answer: (Width x = 7) (Length 10)
Step-by-step explanation:
(x+3) + = 34/2
2x + 3 = 17
2x = 14
x = 7 -----------Width
10 ---------------Length
Answer: Width= 7 in.
Length= 10 in.
Step-by-step explanation:
[tex]l=w+3[/tex]
The perimeter of the rectangle is 34 inches.
[tex]2(w+l)=34[/tex]
substitute
[tex]2(w+w+3)=34[/tex]
[tex]2(2w+3)=34[/tex]
distributive property [tex]a(b+c)=ab+ac[/tex]
[tex]2\cdot 2w+2\cdot 3=34[/tex]
[tex]4w+6=34[/tex]
[tex]4w+6-6=34-6[/tex]
[tex]4w=28[/tex]
divide 4 on both sides
[tex]w=7[/tex]
Width is 7 inches
substitute w=7 in equation [tex]l=w+3[/tex]
[tex]l=7+3[/tex]
[tex]l=10[/tex]
Length is 10 inches
PLEASE HELP ASAP <333
What is the sum of the geometric series ?
Answer:
Step-by-step explanation:
There are a couple of ways to do this. You could figure all four terms out and add them, which is likely the simplest way.
One: 6^(1 - 1) = 6^0 = 1
Two: 6^(2 - 1) = 6^1 = 6
Three: 6^(3 - 1) = 6^2 = 36
Four: 6^(4 - 1) = 6^3 = 216
Sum = 259
Using 3.14 for p, what is the volume of a ball with a radius of 3 centimeters?
Answer: 113.1
Step-by-step explanation:
first you have to multiply 4/3*pie or 3.14 times 3
4/3 x 3.14 x 3 = 113.1
Solve. x2 + 10x = −24
➷ Add 24 to both sides:
x^2 + 10x + 24
Find two values that multiply to make 24 but add to make 10
As you will notice, this is 6 and 4
Now factorize it:
(x + 4)(x + 6)
The values of x would be the opposite of what is in the parenthesis
Therefore x = -4 or x = -6
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
x= -6 x=-4
Step-by-step explanation:
x2 + 10x = −24
Add 24 to each side
x2 + 10x+24 = −24+24
x2 + 10x +24=0
Factor
(x+6) (x+4) = 0
Using the zero product property
x+6 = 0 x+4 = 0
x+6-6 = 0-6 x+4-4 =0-4
x= -6 x=-4