By definition, the area of a triangle is given by:
A = (1/2) * (b) * (h)
Where,
b: base
h: height
The area of the original triangle is 3 mm² and is dilated by a factor of 6. We have then
A = (1/2) * (6b) * (6h)
A = (1/2) * (b) * (h) * (6) * (6)
A = 3 * (6) * (6)
A = 108 mm²
answer
The area of the dilated triangle is 108 mm²
When a triangle with an original area of 3 mm squared is dilated by a factor of 6, the new area is found by multiplying the original area by the square of the dilation factor. This results in a new area of 108 mm squared.
The question asks about the effect of dilation on the area of a triangle. Specifically, it asks for the new area if a triangle with an original area of 3 mm² is dilated by a factor of 6. When dealing with dilation, the area of a shape changes by the square of the dilation factor. This means that if the dilation factor is 6, the new area will be 62 times the original area. This calculation can be performed as follows:
Original area = 3 mm²
Dilation factor = 6
New area = Original area × (Dilation factor)2 = 3 mm² × 62
New area = 3 mm² × 36 = 108 mm2
Therefore, the area of the dilated triangle is 108 mm²
if y varies directly as x, find the constant of variation if y= 32 when x= 8
Answer:
K = 4
Step-by-step explanation:
If y varies directly as x
y = k x
Divide both sides by by x
K = y/x
When y = 32 and
x = 8
K = 32/8
K = 4
I am 97 cm tall and my elder brother is 2m tall. How much taller is my elder brother than I?
Answer: 1.3 meters taller. so 103 cm.
Step-by-step explanation:
Answer:
103cm
Step-by-step explanation:
From the question given, we obtained the following data:
Height of the boy = 97cm
Height of the elder brother = 2m
First let us convert the height of the elder brother to cm. This is illustrated below:
1m = 100cm
2m = 2 x 100 = 200cm
So, the elder brother is 200cm tall. To know how much taller the elder brother is than the boy, subtract the height of the boy from that of the elder bother' as shown below:
200 — 97 = 103cm
Therefore, the elder brother is 103cm taller than the boy
What are zeros of the quadratic expression. A) x = 1 or x = 5 B) x = 1 or x = −5 C) x = −1 or x = 5 D) x = −1 or x = −5
Answer:whats the expression
Step-by-step explanation:
What is the volume of a cylinder With base radius 4 and height 5
Answer:
it's a base of 18 hope it works
Answer:80 pie
Step-by-step explanation:
Which answer choice states the range of the following
relation?
A) {-2, -5}
B) (-9,-8, -7, -6, -5}
C) {-2, -1, 0, 1, 2, -9,-8, -7, -6, -5}
D) {-2, -1, 0, 1, 2
Hello! Remember you have to write complete questions in order to get good and exact answers. Here you forgot to write the relation so I could help you providing my own relation.
Remember that for any relation, we have a set [tex]A[/tex] that matches the the domain (also called the set of inputs) of the function and the set [tex]B[/tex] that contains the range (also called the set of outputs).
Suppose our relation is:
[tex]y=-10+x \\ \\ For \ x=1,2,3,4,5[/tex]
So the x-values represents the set A and the y-values the set B. Therefore, by evaluating the x-values into our relation we get:
[tex]\text{If x=1} \\ \\ y=-10+1=-9 \\ \\ \\ \text{If x=2} \\ \\ y=-10+2=-8 \\ \\ \\ \text{If x=3} \\ \\ y=-10+3=-7 \\ \\ \\ \text{If x=4} \\ \\ y=-10+4=-6 \\ \\ \\ \text{If x=5} \\ \\ y=-10+5=-5[/tex]
So in this context, the correct option is:
B) (-9,-8, -7, -6, -5}
Answer:
the answer is b
Step-by-step explanation:
i took the test
Plot 12, -2, and 4 on the number line.
Answer:
that's easy just with your number line put then to least to greatest
The equation y = mx+b is used to express the equation of a line which solution is a quick way to solve this equation for x in terms of y?
Answer:
See Step-by-step explanation
Step-by-step explanation:
[tex]y=mx+b\\y-b=mx\\x=\frac{y-b}{m}[/tex]
Is 7/8 proportional or non proportional
Answer:
non-proportional
Step-by-step explanation:
7/8 is a fraction
A proportion is a relation that says two ratios are equal. A fraction is one ratio, so is not a proportion.
___
Something may be proportional to something else with a scale factor of 7/8. It seems some context may be missing from the question.
10 = 6 + e solve that
Answer:
4
Step-by-step explanation:
10= 6 + 4
Carry over the 6 to the 10 and make e the subject on the right hand side of the equation as shown below:
10 - 6 = e
4= e
Therefore e is 4.
Answer:
e = 4
Step-by-step explanation:
Check the answer by subtraction.
10 - 6 = 4
Or use fact families to check the answer
6 + 4 = 10
4 + 6 = 10
10 - 6 = 4
10 - 4 = 6
I need some help please I will give u a heart.
Answer:
Step-by-step explanation:
[tex]3\frac{1}{4}+2\frac{1}{6}=3+2+\frac{1}{4}+\frac{1}{6}\\\\=5+\frac{1}{4}+\frac{1}{6}\\\\LCM(4,6)=12\\\\\frac{1*3}{4*3}=\frac{3}{12}\\\\\frac{1*2}{6*2}=\frac{2}{12}\\\\5+\frac{1}{4}+\frac{1}{6}=5+\frac{3}{12}+\frac{2}{12}\\\\=5+\frac{3+2}{12}=5+\frac{5}{12}\\\\=5\frac{5}{12}[/tex]
Answer:
[tex]5\frac{5}{12}[/tex]
Step-by-step explanation:
Simplify the expression
Exact form: [tex]\frac{65}{12}[/tex]
Decimal Form: 5.416 (The six has a line on top indicating that it goes one forever basically)
Mixed Number form: [tex]5\frac{5}{12}[/tex]
Hopefully this helps
Also Give me your heart ;)
Yoryi bought an Apple Watch for $470. He paid $200 at the time of purchase and will make monthly payments of $30 to finish paying for the Apple Watch. He used the equation 200 + 30m = 470 to determine the number of months (m) he needs to make payments. For how many months will he make payments?
Answer:
9 months
Step-by-step explanation:200+30m=470
30m=270
m=9
He will pay for 9 months
Yoryi will make payments for 9 months.
Explanation:To determine the number of months (m) Yoryi needs to make payments, we can solve the equation 200 + 30m = 470. Here's how:
Subtract 200 from both sides of the equation: 30m = 270.Divide both sides of the equation by 30: m = 9.Therefore, Yoryi will make payments for 9 months.
Dylan scored a total of 48 points in first 4 games of the basketball season. Which equation can be used to find g, the average number of points he scores per game?
48 divided by 4 = g
4 divided by 48 = g
g divided by 4 = 48
4 divided by g = 48
Answer:
its The first one
Step-by-step explanation:
Ok so to do an average, you add all number together (48) then you Divide by the number of items added (4 games) then it's the first one. Hope this helps, sorry if someone then answer it.
Answer:
A
Step-by-step explanation:
I took the test
Which expression is equivalent to the following complex fraction?
2-1/y divided by 3+1/y
Answer: 2-1 / y times y/ 3+1
Step-by-step explanation:
In dividing fractions, it is possible to change the sign to multiplication sign by swapping positions of the numerator and denominator.
For example given,
a/b divided by c/d,
We can write this as
a/b times d/c
To simplify the given complex fraction [tex]\(\frac{{2 - \frac{1}{y}}}{{3 + \frac{1}{y}}}\),[/tex]we'll first rationalize the fractions in the numerator and denominator.
For the numerator:
[tex]\[2 - \frac{1}{y} = \frac{2y}{y} - \frac{1}{y} = \frac{2y - 1}{y}\][/tex]
For the denominator:
[tex]\[3 + \frac{1}{y} = \frac{3y}{y} + \frac{1}{y} = \frac{3y + 1}{y}\][/tex]
So, the original complex fraction becomes:
[tex]\[\frac{\frac{2y - 1}{y}}{\frac{3y + 1}{y}} = \frac{2y - 1}{3y + 1}\][/tex]
Therefore, the equivalent expression to the given complex fraction is option d. (2y-1)(3y+1).
The government of the Republic of Lemon Island plans to transform their lemon-based
economy into a tourism-based economy. They develop the following model to predict the
long-term effect of this transformation for the size of their economy y:
dy
dt = (A − Be−t/5
)y; A, B > 0.
(a) Find the general solution y(t) for this equation.
(b) The Republic of Lemon Island has a current economic growth of 2% per year and
the government expects the transformation to cause this growth rate to triple in
the long term. Explain why values A = 0.06 and B = 0.04 are a good choice to
approximate this behaviour.
(c) Using A = 0.06 and B = 0.04, find the particular solution y(t) assuming that the
size of the economy of Lemon Island before the transformation is $50 000 000, and
that the transformation causes the size of the economy to shrink by $10 000 000 at
t = 0.
(d) The size of the economy of Lemon Island without the transformation can be mod-
eled using the same equation with parameters A = 0.02 and B = 0.
In which year after the transformation will the size of the transformed economy
surpass the size of the economy without the transformation?
(e) Elections on Lemon Island are in five years time. The Lemon Island Polling In-
stitute (LIPI) predicts that the current government will only be re-elected, if the
growth rate of the economy is, by then, at least 4%. According to the first model,
can the current government expect to be re-elected?
Step-by-step explanation:
dy/dt = (A − Be^(-t/5)) y
(a) Find the general solution by separating the variables and integrating.
dy / y = (A − Be^(-t/5)) dt
dy / y = [A + 5B (-⅕ e^(-t/5))] dt
ln |y| = At + 5B e^(-t/5) + C
y = e^(At + 5B e^(-t/5) + C)
y = Ce^(At + 5B e^(-t/5))
(b) As t approaches infinity, dy/dt approaches Ay. The rate of growth, A, is triple the initial rate of growth 0.02, so A = 0.06.
When t = 0, dy/dt = (A − B)y. The rate of growth, A−B, is 0.02. We know A = 0.06, so B = 0.04.
(c) Given that A = 0.06, B = 0.04, and y(0) = 50×10⁶ − 10×10⁶ = 40×10⁶:
40×10⁶ = Ce^(0.06(0) + 5(0.04) e^(-0/5))
40×10⁶ = Ce^(0.2)
C = 40×10⁶ e^(-0.2)
y = 40×10⁶ e^(-0.2) e^(0.06t + 0.2 e^(-t/5))
y = 40×10⁶ e^(-0.2 + 0.06t + 0.2 e^(-t/5))
(d) If A = 0.02 and B = 0, and there is no transformation (y(0) = 50×10⁶), then:
50×10⁶ = Ce^(0.02(0) + 0)
50×10⁶ = C
y = 50×10⁶ e^(0.02t)
Comparing to the answer from part (c):
40×10⁶ e^(-0.2 + 0.06t + 0.2 e^(-t/5)) = 50×10⁶ e^(0.02t)
e^(-0.2 + 0.04t + 0.2 e^(-t/5)) = 5/4
-0.2 + 0.04t + 0.2 e^(-t/5) = ln(5/4)
-5 + t + 5e^(-t/5) = 25 ln(5/4)
t + 5e^(-t/5) = 5 + 25 ln(5/4)
Solve with a calculator:
t = 9.886
The transformed economy surpasses the untransformed economy in the 10th year.
(e) In year t=5, the size of the transformed economy is:
y = 40×10⁶ e^(-0.2 + 0.06(5) + 0.2 e^(-5/5))
y = 47.6×10⁶
The percent growth is:
(47.6×10⁶ − 40×10⁶) / 40×10⁶ × 100% = 19%
The growth rate is greater than 4%, so the current government can expect to be reelected.
How much money must be deposited now in an
account paying 7.25% annual interest, compounded
quarterly, to have a balance of $1000 after 10
years?
Answer:
[tex]\$487.48[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ A=\$1,000\\ r=7.25\%=7.25/100=0.0725\\n=4[/tex]
substitute in the formula above
[tex]1,000=P(1+\frac{0.0725}{4})^{4*10}[/tex]
[tex]1,000=P(\frac{4.0725}{4})^{40}[/tex]
[tex]P=1,000/(\frac{4.0725}{4})^{40}[/tex]
[tex]P=\$487.48[/tex]
How can you express 1/100 as a decimal
Answer:
0.01
Step-by-step explanation:
1/100=0.01
Answer: 0.01
Step-by-step explanation:
A town has a population of 5000 and
grows at 2% every year. What will be the
population after 5 years, to the nearest
whole number?
Final answer:
To calculate the population after 5 years at a 2% growth rate, you apply the formula for exponential growth, resulting in an estimated population of 5512 to the nearest whole number.
Explanation:
To calculate the population of a town after 5 years with a 2% annual growth rate, you would use the formula for exponential growth. In this case, the initial population is 5000 and the growth rate is 0.02 (2%). The population after n years is given by the formula P(n) = P(0) × (1 + r)ⁿ, where:
P(0) is the initial population,r is the growth rate,and n is the number of years.After 5 years, the formula will look like this:
P(5) = 5000 × (1 + 0.02)⁵
Calculating the above:
P(5) = 5000 × (1.02)⁵P(5) = 5000 × 1.10408P(5) = 5512.41To the nearest whole number, the population of the town after 5 years will be 5512.
EWE
YUIU Problems DV
A florist has 9 tulips and 18 carnations. If the florist wants to create identical bouquets
without any leftover flowers, what is the greatest number of bouquets the florist can make?
Answer:
9
Step-by-step explanation:
GCF of 9 and 18 is 9. I hope it helps. Srry of the last mishap and i hope you accept my apology.
Which of the following are aspects of the building and construction trades?
Carpentry
Plumbing
Lawn care
Masonry
Electrical work
Explanation:
All of the mentioned points are the aspects of building and construction trades.Carpenter performs carpentry and deals mainly with wood such as making of wooden cabinets, furniture etc.Electrician deals with electric work such as electrical wiring of the buildings and related equipment.Plumber deals with installing and maintaining drainage system or water availability.Mason are skilled in brick and blocklaying, concrete finishing etc.Answer:
Everything except lawn care.
What is the area of this figure?
Enter your answer in the box.
in²,
Answer:
400 in²
Step-by-step explanation:
(20×16) + (½×8×20)
320 + 80 = 400 in²
Make the number sentence true 5/10=blank/100
Answer:
50 = blank
Step-by-step explanation:
Step 1: Cross multiply
5/10 = ?/100
5*100 = 10?
500 / 10 = 10? / 10
50 = ?
Answer: 50 = blank
7. Hannah wants to rent a bike. Bike rentals
cost $15 per hour plus a one-time fee of $8.
Write an equation to represent the
relationship between the number of hours h
Hannah rents the bike and the total cost c.
Answer:
c=8+15h
Step-by-step explanation:
Josie and her brother, Sean both have a job after school. For every $5.50 José earns, her brother earns $6.50. On Tuesday, they earned a total of $30.00. How much did Josie earn? How much did her brother earn?
fill in the blanks
a ---÷48=-1
Ans is -48.
Hope this will help u..
As x approaches ∞, which statement is correct?
A) The linear function will eventually exceed the exponential function.
B) The exponential function will eventually exceed the linear function.
C) The exponential function will only exceed the linear function if it has a greater growth factor.
D) The linear function will only exceed the exponential function if it has a greater common difference.
Answer:
B
Step-by-step explanation:
This is very simple if we understand a point of linear and exponential functions.
First of all, a linear growing function increases.
An exponential growing function increases as well.
But, linear function, no matter what the slope is, grows at a CONSTANT RATE. But,
Exponential function grows at a COMPOUND RATE.
So, if there are 2 functions, linear and exponential, the exponential will always exceed the linear, AT SOME POINT EVENTUALLY because of the growth factor (no matter growth factor of linear and exponential -- whatever they are).
So,
B is the correct answer.
Growth factor of each (both) doesn't matter. Exponential will always win!
Answer:
b
Step-by-step explanation:
The exponential function will always exceed the linear function.A quantity increasing exponentially eventually exceeds a quantity increasing linearly.
With similar triangle, the ratios of all three paris of corresponding sides are equal
Answer:
TRUE
Step-by-step explanation:
If this is a True/False question, the answer is True.
__
One of the ways to define triangle similarity is by the ratios of the sides. If the ratios of corresponding sides are the same, the triangles are similar.
Another way to define triangle similarity is by the angle measures. If corresponding angles are congruent, the triangles are similar.
Both conditions will be met by similar triangles.
What is the following quotient 6-3(^3+6)/^379
Answer:
Quotient given:
\frac{6-3 \sqrt[3]{6} }{ \sqrt[3]{9} }
Answer:
2 \sqrt[3]{3} - \sqrt[3]{18}
Explanation:
1) Rationalize by multiplying numerator and denominator by \sqrt[3]{9}
2)
\frac{6-3 \sqrt[3]{6} }{ \sqrt[3]{9} } \frac{\sqrt[3]{9}}{\sqrt[3]{9}}
3) Due the operations
\frac{6 \sqrt[3]{3}-3 \sqrt[3]{6.3}}{ \sqrt[3]{27} }
\frac{6 \sqrt[3]{3}-3 \sqrt[3]{6.3}}{ 3 }=2 \sqrt[3]{3} - \sqrt[3]{18}
Step-by-step explanation:
Write the quadratic equation whose roots are 6 and -1 , and whose leading coefficient is 5.
X multiplied by 1/5 equals 6/3 what is x
Answer:
Step-by-step explanation:
x/5=6/3
3x=30
x=10
Answer:
x=10
Step-by-step explanation:
x*1/5 = 6/3
Simplify 6/3 =2
1/5x = 2
Multiply each side by 5
1/5x *5 = 2*5
x = 10
Factor this polynomial
2x²+19x+24