[tex]\textsf{Let's calculate the slope of the line passing thought the points (-4, 4) and (-6, 6) } \\ \textsf{using the following formula: }\mathsf{m = \frac{\Delta y}{\Delta x}} \textsf{ where m is the slope of the line.}[/tex][tex]\textsf{So:}[/tex]
[tex]\mathsf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{4 - 6}{-4 - (-6)} = \dfrac{-2}{2} = -1}[/tex]
[tex]\textsf{Hence the slope is -1.}[/tex]
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
70 POINTS PLEASE HELP. WILL MARK BRAINLIEST
Mrs. Ashe is planning to take her study group on a field trip to an amusement park. The regular cost is $50 per person. There is a party special that costs $35 per person with an additional $300 fee for a private room where students can eat lunch. Mrs. Ashe is trying to decide if she should use the regular price or the party special.
Part 1:
A) Write an equation in slope-intercept form (y=mx+b) to show the total cost of the regular price with x people, where x = number of students in the study group and y = the total cost. (10 points)
B) Write an equation in slope-intercept form (y=mx+b) to show the total cost of the party special with x people, where x = number of students in the study group and y = the total cost. (10 points)
Answer:
a) y = 50x + 0
b) y = 35x + 300
Step-by-step explanation:
a) The price is $50 (per person), so you multiply 50 by the number of people going (which is x).
b) The price is $35 dollars (per person), so you multiply 35 by the number of people (which again would be x). There is also an extra cost of $300.
Hope this helps! :)
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.
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.
A mug is 2/3 full. The mug contains 5/6 of a cup of water. Find the capacity of the mug.
We want to find the total capacity of the mug given that we know how much liquid there is in a 2/3 full mug.
We will find that the capacity of the mug is 1.25 cups.
We know that when the mug is 2/3 full, it has 5/6 cups.
Then if we define C as the total capacity of the mug, we can write:
(2/3)*C = 5/6 cups.
Now we can solve the above equation for C:
C = (3/2)*(5/6) cups = 1.25 cups.
The capacity of the mug is 1.25 cups.
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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
Of 140 seventh graders, 15% earn the presidential fitness award. How many students earn the award?
Answer:
119
Step-by-step explanation:
Hope this helps! Brainliest is appreciated.
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.
Algebra 1, Section 7.08
Answer:
=2x^3+5x+2
Step-by-step explanation:
hope this helps
what is the perimeter?
Answer:
18 yards
Step-by-step explanation:
6+5+3+4= 18
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
Factor these completely. -a^2-2a+80
Answer:
-(a-8)*(a+10)
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.
Use the equation to answer the question.
12a+9b=k(2a+32b)
Which value of k makes the equation true?
a.6
b.2
c.4
d.3
To find the value of k that makes the equation true, we can start by expanding both sides of the equation. Then, rearrange the equation to isolate the terms with a on one side and the terms with b on the other side. Finally, solve for k to find the value that makes the equation true.
Explanation:To find the value of k that makes the equation true, we can start by expanding both sides of the equation:
12a + 9b = k(2a + 32b)
12a + 9b = 2ka + 32kb
Next, we can rearrange the equation to isolate the terms with a on one side and the terms with b on the other side:
12a - 2ka = 32kb - 9b
This simplifies to:
(12 - 2k)a = (32k - 9)b
To make this equation true, the coefficient of a must be equal to the coefficient of b. Therefore, we can set up an equation:
12 - 2k = 32k - 9
Solving for k:
12 + 9 = 32k + 2k
21 = 34k
k = 21/34
Therefore, the value of k that makes the equation true is 21/34.
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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).
What does 5.9E4 mean?
Answer:
59,000
Step-by-step explanation:
That is scientific notation, as used in a calculator, for example, to mean
5.9 * 10^4
5.9 * 10^4 = 5.9 * 10,000 = 59,000
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 ;)
3 4/6 - 2 1/4 please help me
Answer:1 5/12
Step-by-step explanation:
3 4/6 - 2 1/4
Change to improper fraction we have
22/6 - 9/4
(2x22-3x9)/12
(44-27)/12
17/12=1 5/12
Answer:
1 5/12
Step-by-step explanation:
3 4/6 - 2 1/4
3 2/3 - 2 1/4
11/3 - 9/4
Lcm is 12
(11×4 - 9×3)/12
(44 - 27)/12
17/12
1 5/12
George is playing cards what is probability of pulling an ace or Jack from the deck
Answer: 4/52 or 1/13 (simplified)
Step-by-step explanation: There are 52 cards in a deck and 4 aces
Answer:
1/13
Step-by-step explanation:
There are 13 types of cards in a deck and there are 4 cards in each. So if you wanted to pull a ace or jack from the deck it would be 1/13
the box that contains the salt lick is 1 1/4 feet by 1 2/3 feet 5/6 feet.how many cubes of salt lick fit in the box?explain or show your reasoning.
Answer:
24
Step-by-step explanation:
24 cubes. Reasoning varies. Sample reasoning: The length of the box
can fit or 5/4 : 5/12 =3 cubes. The width of the box can fit or 5/3 : 5/12 = 4 cubes. The height of the box can fit 5/6 : 5/12 = 2 cubes. The box can fit
or 24 cubes.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Length of the box = 5/6 ft
Width of the box = 5/4 ft
Height of the box = 5/3 ft
Sides of the cube salt lick = 5/12 ft
Number of salt lick in the box (length) = 5/6 ÷ 5/12
= 2 cubes.
Number of salt lick in the box (width) = 5/4 ÷ 5/12
= 3 cubes.
Number of salt lick in the box (length) = 5/3 ÷ 5/12
= 4 cubes.
Total number of salt lick = 4 × 3 × 2
= 24 cubes.
Write the quadratic equation whose roots are 6 and -1 , and whose leading coefficient is 5.
Finding Side Lengths
2 in.
xin.
These two figures are the image and pre-image of a
dilation
Find the lengths of the missing sides.
4 in.
5 in.
Answer:
x = 2.5y = 5Step-by-step explanation:
As the two figure are the image and pre-image of a dilation.
Considering the left sided triangle is original and right sided triangle ( smaller one) is the image.
As one of the sides of the left triangle (original figure) is 4 in. And the corresponding length of the side on the right triangle (image of the figure) is 2 in.
It means the image of the side (2 in) is obtained when the side (4 in) of the original object is dilated by a scale factor of 1/2. In other words, the side of the image (2 in) is obtained multiplying the side (4 in) of original figure by 1/2. i.e. 4/2 = 2 in
Lets determine the missing side of the right side triangle by the same rule.
As the original object has one of the sides is 5 in and the corresponding side of the image has x in. As the original figure is dilated by a scale factor of 1/2. so the missing side of x will be: x = 5/2 = 2.5
So, the value of x will be 2.5
Similarly, the original object has one of the sides with length (y + 1 in). As the As the original figure is dilated by a scale factor of 1/2. As the corresponding length of the side of the image triangle is 3 in.
so
y + 1 = 2(3) ∵ 3 in (image side) is multiplied by 2
y + 1 = 6
y = 6 - 1
y = 5
So, the value of y = 5
Therefore,
x = 2.5y = 5Answer:5.5
6
Step-by-step explanation:
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.
Solve for x
3.5x=24.5
Answer:
8.166666666666666666666666666666666666666666
Step-by-step explanation:
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:
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
Which equation has real zeros corresponding to
the x-intercepts of the graph?
y = log3(x) – 1
y = 3x - 3
y=-3(x - 1) + 3
y = log3(2x) - 2
Answer:
A
Step-by-step explanation:
y = log3(x) – 1
I don't know why but this is the correct answer.
[tex]y = \log_{3}x - 1[/tex] is the equation with real zeros corresponding to the x-intercepts of the graph.
How to find a function based on a graphAccording to the statement, we must find a function such that all values of [tex]x[/tex] so that [tex]y(x) = 0[/tex] and are the same of the graph. A quick approach consists in solving on each expression:
Expression A
[tex]\log_{3}x-1 = 0[/tex]
[tex]\log_{3}x = 1[/tex]
[tex]x = 3[/tex]
Expression B
[tex]3\cdot x - 3 = 0[/tex]
[tex]3\cdot x = 3[/tex]
[tex]x = 1[/tex]
Expression C[tex]-3\cdot (x-1) + 3 = 0[/tex]
[tex]-3\cdot x +6 = 0[/tex]
[tex]x = 2[/tex]
Expression D[tex]\log_{3}2x - 2 = 0[/tex]
[tex]\log_{3}2x = 2[/tex]
[tex]2\cdot x = 9[/tex]
[tex]x = \frac{9}{2}[/tex]
Hence, we conclude that [tex]y = \log_{3}x - 1[/tex] is the equation with real zeros corresponding to the x-intercepts of the graph. [tex]\blacksquare[/tex]
Remarks
The graph is missing and all functions are poorly formatted. Correct statement is shown below:
Which equation has real zeros corresponding to the x-intercepts of the graph?
A. [tex]y = \log_{3} x - 1[/tex]
B. [tex]y = 3\cdot x -3[/tex]
C. [tex]y = -3\cdot (x-1) + 3[/tex]
D. [tex]y = \log_{3}2x -2[/tex]
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Six tenths of what number is 5.4? Write the equation that you would use to solve this problem and show steps that are needed to solve it.
Answer:
bruh bruh bruh bruh bruh
Step-by-step explanation:
cringe
Answer:9
Step-by-step explanation:
multiply the 5.4 by 10 and the 0.6 by ten, then divide the 54 by 6
You get 9, then multiply that by 0.6, and you get 5.4
you multiply because the statement includes "of" which means multiplication
Find the area of the circle with the center C (1, -2) and passes through the point (4, 2). Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
r=√((4-1)²+(2+2)²)=√(9+16)=5
area of circle=π r²=3.14×5²=78.50=78.5
The area of the circle is found by calculating the radius using the distance formula and then applying the formula A = πr². Using the common approximation of π as 3.14, the area is found to be approximately 78.5 square units when rounded to the nearest tenth.
The first step in finding the area of the circle is to determine its radius. The radius can be found by calculating the distance between the center of the circle, C (1, -2), and a point on the circle, (4, 2). Using the distance formula, we get the radius r = √((4-1)² + (2-(-2))²)} = √{(3)² + (4)²} = √{9 + 16} = √{25} = 5 units. Next, we use the formula for the area of a circle, which is A = πr². Substituting the radius in, we find A = π(5)² = 25π. The approximation on the circle for π is 3.14, thus the area of the circle is approximately A = 25 * 3.14 = 78.5 square units, which should be rounded to the nearest tenth.
It is also noteworthy that any approximation on the circle may vary slightly depending on the value chosen for π, but using 3.14 is commonly accepted for most calculations. So our final answer is, rounding to the nearest tenth, the area of the circle is approximately 78.5 square units.
The hypotenuse of a 30°-60°-90°
triangle has a length of 12 cm.
Which could be the length of a leg
of the triangle?
Answer: Below
Step-by-step explanation:
If you don't know Trigonometry, in a 30-60-90 triangle, the hypotenuse is always twice as long as the side opposite the 30° angle and the side opposite the 60° angle is √3 times as long as the side opposite the 30° angle.
So, since the hypotenuse has length 12 cm,
side opposite 30° angle (shorter leg) = 6 cm
side opposite 60° angle (longer leg) = 6√3 cm
The possible lengths of the legs are 6 and 6√3
How to determine the length of a leg?The triangle is given as:
30-60-90 triangle
And we have:
Hypotenuse = 12 cm
A 30-60-90 triangle is a unique triangle with the following parameters
Opposite = Hypotenuse/2
Adjacent = Hypotenuse/2 * √3
So, we have:
Opposite = 12/2
Adjacent = 12/2 * √3
Opposite = 6
Adjacent = 6√3
Hence, the possible lengths of the legs are 6 and 6√3
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