Answer:
Acute
Step-by-step explanation:
For each graph, f(x) is the parent function and g(x) is a transformation of f(x). Use the graph to determine the equation of g(x).
The equation of g(x) when the parent function f(x) = 3^x is transformed is g(x) = 3^{x - 4} + 5.
The equation of g(x) when the parent function f(x) = 2^x is transformed is g(x) = 4(2)^{x - 3}.
The equation of g(x) when the parent function f(x) = 4^x is transformed is g(x) = -2(4)^{x + 1} + 3.
How to determine the equation of g(x) by using the graph?By critically observing the graph of the exponential function f(x) = 3^x, we can reasonably and logically deduce that f(x) is vertically translated (k) by 5 units up and horizontally translated (h) by 4 units to the right. Therefore, the equation of g(x) is given by:
g(x) = 3^{x - h} + k
g(x) = 3^{x - 4} + 5.
Based on the graph of the exponential function f(x) = 2^x, we can reasonably and logically deduce that f(x) is compressed by a scale factor (a) of 4 units and horizontally translated (h) by 3 units to the right. Therefore, the equation of g(x) is given by:
g(x) = a(b)^x - h}
g(x) = 4(2)^{x - 3}
Based on the graph of the exponential function f(x) = 4^x, we can reasonably and logically deduce that f(x) is reflected across the x-axis and expanded by a scale factor (a) of 2 units, followed by a translation of 1 units left and 3 units up:
where; a = -2, h = -1, and k = 3.
g(x) = a(b)^x - h} + k
g(x) = -2(4)^{x - (-1)} + 3
g(x) = -2(4)^{x + 1} + 3
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Multiplying a whole number by a proper fraction, results in a ___ product.
A. larger
B. smaller
Answer:
The answer to your problem is, A. Larger
Step-by-step explanation:
First in order to know to the answer lets learn about different types of fractions:
For example, 1/4, 3/4, 3/8, are all proper fractions.
4/3, 5/2, are all improper fractions.
When we have to multiply a whole number with fractions less than 1, then the resulting number will be less the number originally
Example; 3 x \(\frac{3}{4}\)
If we then multiplying numerators together and the denominators together.
3 x \(\frac{3}{4}\) = \(\frac{3}{1}\) x \(\frac{3}{4}\) = \(\frac{9}{4}\) = 2\(\frac{1}{4}\) < 3
Example /\
Thus the answer to your problem is, A. Larger OR Multiply.
The overall market for wheat is perfectly competitive. The market demand curve is given by QD- 1400-50P All farmers in the market are identical and each have a cost function of C(q)-0.5q +10q +18 with MC q+10 AVC 0.5q +10 ATC 0.5q+10+18/q Calculate the long run equilibrium price in this market
Since the cost function provided does not explicitly state the quantity of output (q), it is not possible to calculate the exact equilibrium price without additional information.
To calculate the long-run equilibrium price in this perfectly competitive wheat market, we need to find the point where the market demand curve intersects with the average total cost (ATC) curve of the farmers, as this is the point of minimum average total cost.
The market demand curve is given by QD = 1400 - 50P.
The cost function for each farmer is C(q) = 0.5q + 10q + 18, where MC = q + 10, AVC = 0.5q + 10, and ATC = 0.5q + 10 + 18/q.
In the long run, firms in a perfectly competitive market operate at their minimum average total cost, implying that price is equal to average total cost (P = ATC).
Setting the market demand equal to the average total cost:
1400 - 50P = 0.5q + 10 + 18/q
To solve for the equilibrium price, we need to find the quantity q at which this equation holds.
However, Since the cost function provided does not explicitly state the quantity of output (q), it is not possible to calculate the exact equilibrium price without additional information.
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What is the volume of the pyramid shown below?
Height = 21 cm
5 cm
5 cm
A 35 cubic centimeters
B 70 cubic centimeters
C 175 cubic centimeters
D 210 cubic centimeters
Volume of a square pyramid = 1/3 x length x width x height
Volume = 1/3 x 5 x 5 x 21 = 175 cubic centimeters.
The answer is C
Q1. Anurag's office is 12 km away from his house. He takes an auto to travel 1/6 of the total distance, covers 4/5 of the remaining by bus and walks the rest. 5 i. If he repeats the same on the way back, then find the distance he walk every day ii. If he goes to office 5 days in a week, how much distance does he walk every week iii. Why do you think does he walk some distance daily?
Anurag walks 2 km every day on his way back.
i. To find the distance Anurag walks every day on his way back, we need to calculate the distance covered by walking.
Given that Anurag takes an auto to travel 1/6 of the total distance and covers 4/5 of the remaining distance by bus, the remaining distance he has to walk can be found by subtracting the distance covered by the auto and bus from the total distance.
Total distance = 12 km
Distance covered by auto = 1/6 * 12 km = 2 km
Remaining distance = Total distance - Distance covered by auto = 12 km - 2 km = 10 km
Distance covered by bus = 4/5 * 10 km = 8 km
Distance walked = Remaining distance - Distance covered by bus = 10 km - 8 km = 2 km
Therefore, Anurag walks 2 km every day on his way back.
ii. If Anurag goes to the office 5 days in a week, the total distance he walks every week can be calculated by multiplying the distance walked every day by the number of days he goes to the office.
Distance walked every week = Distance walked every day * Number of days
Distance walked every week = 2 km/day * 5 days/week = 10 km/week
Therefore, Anurag walks 10 km every week.
iii. Anurag walks some distance daily because the office is not directly accessible by auto or bus. Walking the remaining distance is necessary to reach his destination. Walking provides physical exercise and can also be a convenient and cost-effective mode of transportation for shorter distances. It allows Anurag to maintain an active lifestyle and may have additional benefits such as reducing carbon emissions and contributing to his overall health and well-being.
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A 77-inch candle burns down in 44 hours. How far has it burned after 2\frac{1}{2}2
2
1
hours? Use the dropdown menu to state your answer as a decimal, mixed number, or improper fraction.
The length after 2 1/2 hours will be 72.625 inches.
How to calculate the amount burned?The question relates to a fraction. A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
Since the 77-inch candle burns down in 44 hours, the rate will be:
= 77/44
= 1.75 inch per hour.
Therefore, the length after 2 1/2 hours will be:
= 77 - 1.75(2.5)
= 77 - 4.375
= 72.625 inches.
The length is 72.625 inches.
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2. Find the general relation of the equation cos3A+cos5A=0
\(A=\frac{\pi}{8}+\frac{n\pi}{4}or\ A=\frac{\pi}{2}+n\pi\)
Step-by-step explanation:Find angles\(cos3A+cos5A=0\)
________________________________________________________
Transform the expression using the sum-to-product formula\(2cos(\frac{3A+5A}{2})cos(\frac{3A-5A}{2})=0\)
________________________________________________________
Combine like terms\(2cos(\frac{8A}{2})cos(\frac{3A-5A}{2})=0\\\\ 2cos(\frac{8A}{2})cos(\frac{-2A}{2})=0\)
________________________________________________________
Divide both sides of the equation by the coefficient of variable\(cos(\frac{8A}{2})cos(\frac{-2A}{2})=0\)
________________________________________________________
Apply zero product property that at least one factor is zero\(cos(\frac{8A}{2})=0\ or\ cos(\frac{-2A}{2})=0\)
________________________________________________________
Cos (8A/2) = 0:Cross out the common factor\(cos\ 4A=0\)
________________________________________________________
Solve the trigonometric equation to find a particular solution\(4A=\frac{\pi}{2}or\ 4A=\frac{3\pi}{2}\)
________________________________________________________
Solve the trigonometric equation to find a general solution\(4A=\frac{\pi}{2}+2n\pi \ or\\ \\ 4A=\frac{3 \pi}{2}+2n \pi\\ \\A=\frac{\pi}{8}+\frac{n \pi}{4\\}\)
________________________________________________________
cos(-2A/2) = 0Reduce the fraction\(cos(-A)=0\)
________________________________________________________
Simplify the expression using the symmetry of trigonometric function\(cosA=0\)
________________________________________________________
Solve the trigonometric equation to find a particular solution\(A=\frac{\pi }{2}\ or\ A=\frac{3 \pi}{2}\)
________________________________________________________
Solve the trigonometric equation to find a general solution\(A=\frac{\pi}{2}+2n\pi\ or\ A=\frac{3\pi}{2}+2n\pi,n\in\ Z\)
________________________________________________________
Find the union of solution sets\(A=\frac{\pi}{2}+n\pi\)
________________________________________________________
A = π/8 + nπ/4 or A = π/2 + nπ, n ∈ ZFind the union of solution sets\(A=\frac{\pi}{8}+\frac{n\pi}{4}\ or\ A=\frac{\pi}{2}+n\pi ,n\in Z\)
I hope this helps you
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A spinner with 10 equally sized slices has 2 red slices, 4 yellow slices, and 4 blue slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a red slice?
Answer: 5
Step-by-step explanation: with these problems you're supposed to add all the numbers and then you divide it by the number you're asking to find the probability of so 10/2=5
The probability that the dial stops on a red slice, when it is spun and stops on a slice at random is 1/5.
How to get probability of an event?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
A spinner with 10 equally sized slices has 2 red slices, 4 yellow slices, and 4 blue slices.
The total number of slices is 10 and the total number of favorable outcome to get a red slice is 2. Thus, the probability that the dial stops on a red slice is,
\(P=\dfrac{2}{10}\\P=\dfrac{1}{5}\)
Thus, the probability that the dial stops on a red slice, when it is spun and stops on a slice at random is 1/5.
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You buy 6 apples at $0.49/apple, 1 gallon of milk at $3.48/gallon, and 2 loaves of bread at $1.49/loaf. How much was your total purchase?
Answer:
Your total purchase was $9.40
Step-by-step explanation:
6 x 0.49 = 2.94
1 x 3.48 = 3.48
2 x 1.49 = 2.98
2.94 + 3.48 + 2.98 = 9.4
Evaluate yz + x² x=3.2, y=6.1, z=0.2
Answer:
Step-by-step explanation:
To evaluate the given expression, we need to substitute the given values for x, y, and z. The expression becomes:
yz + x²
Substituting the given values, we get:
(6.1 * 0.2) + (3.2^2)
This simplifies to:
1.22 + 10.24
Therefore, the value of the expression is approximately 11.46.
11.46
gimme brainlyest gang
the second term of this sequence is 20 and the third term is 50 the rule for finding the next term in this sequence is subtract y then multiply by 5 find the value of the first term
Answer:
1st -> 14
Step-by-step explanation:
Two numbers have a product of −24 and a difference of 11. What are the two numbers?
Answer:
-8 and 3, or -3 and 8
Step-by-step explanation:
xy = -24
x - y = 11
x = y + 11
y(y + 11) = -24
y^2 + 11x + 24 = 0
(y + 8)(y + 3) = 0
y = -8 or y = -3
x = 3 or x = 8
the numbers are -8 and 3, or -3 and 8
Which of he following is the solution to the differential equation dy/dx= 5y^2 with the initial condition y(0)= 3?
A. y= square root of 9e^5x
B. y= square root of 1/9e^5x
C. y= square root of e^5x+9
D. y= 3/1-15x
E. 3/1+15x
None of the above option is the correct answer. The correct answer is option f.
To solve this differential equation, we separate the variables and integrate both sides with respect to their respective variables:
\(dy/dx = 5y^2dy/y^2 = 5dx\)
Integrating both sides:
\(∫dy/y^2 = ∫5dx\)
-1/y = 5x + C
where C is a constant of integration.
Using the initial condition y(0) = 3, we can solve for C:
-1/3 = 5(0) + C
C = -1/3
Substituting the value of C in the equation above, we get:
-1/y = 5x - 1/3
Solving for y, we have:
y = -1 / (5x - 1/3)
Therefore, the solution to the differential equation with the initial condition y(0) = 3 is y = -1 / (5x - 1/3), which is equivalent to:
y = -1 / (15x - 1)
Hence, the answer is none of the given options. The correct answer is option f.
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Complete question
Which of he following is the solution to the differential equation dy/dx= 5y^2 with the initial condition y(0)= 3?
A. y= square root of 9e^5x
B. y= square root of 1/9e^5x
C. y= square root of e^5x+9
D. y= 3/1-15x
E. 3/1+15x
F. none of the above
PLEASE HELP URGENT!!! A relay race is 1 3 4 miles long. Each relay team has 4 runners. If each runner runs the same distance in the race, how far will each runner run? Choose the correct answer. StartFraction 7 Over 4 EndFraction times StartFraction 4 Over 1 EndFraction = 7, so each runner runs 7 miles. StartFraction 7 Over 4 EndFraction times StartFraction 4 Over 1 EndFraction = 28, so each runner runs 28 miles. StartFraction 7 Over 4 EndFraction times StartFraction 4 Over 1 EndFraction = StartFraction 7 over 16 EndFraction, so each runner runs StartFraction 7 Over 16 EndFraction miles. StartFraction 7 Over 4 EndFraction times StartFraction 4 Over 1 EndFraction = StartFraction 7 over 8 EndFraction, so each runner runs StartFraction 7 Over 8 EndFractionmiles.
Answer:
Each runner runs 7/16 miles
Step-by-step explanation:
Total distance = 1 3/4 miles
Runners per team = 4
If each runner runs the same distance in the race, how far will each runner run?
Distance covered by each runner = Total distance / runners per team
= 1 3/4 ÷ 4
= 7/4 ÷ 4
= 7/4 × 1/4
= 7/16 miles
StartFraction 7 Over 4 EndFraction times StartFraction 4 Over 1 EndFraction = StartFraction 7 over 16 EndFraction, so each runner runs StartFraction 7 Over 16 EndFraction miles.
Answer:
7/16
Step-by-step explanation:
Find c if m A = 70.6°, b = 10.4 in
Answer:
its 7.8
Step-by-step explanation:
Find the distance between c(-6,5)and D(-3,1)
Answer:
7
Step-by-step explanation:
The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72 and 84? (a) 0.683 (b) 0.954 (c) 0.271 (d) 0.340
The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .
In the question ,
it is given that ,
The random variable X is said to be normally distributed ,
the mean is given as , μ = 70 , and
standard deviation of normal distribution is (σ) = 10
probability that X is between 72 and 84 is written as P(72 < X < 84)
= P((72 - 70)/10 \(<\) Z \(<\) (84 - 70)/10)
= P(0.2 < Z < 1.4)
= P(0 \(<\) Z \(<\) 1.4) – P(0 \(<\) Z \(<\) 0.2)
From the z table , we get the values as
= 0.4192 – 0.0793
= 0.3399
≈ 0.340
Therefore , The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .
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An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 36 inches, and the length of the base is 12 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch. Were using the prothagrum therum. PLEASE NO LINKS OR RANDOM COMMENTS.
Using the principle of Pythagoras and the perimeter formular, the perimeter of the triangle is 85 inches.
Recall : Since the triangle is congruent :
Altitude = 36 inches Base = 12 inches Half of the base = 12/2 = 6 inchesUsing the principle of Pythagoras, we can obtain the hypotenus of the triangle :
Hypotenus = √(36² + 6²)
Hypotenus = √(1296 + 36) = √1332 = 36.496 = 36.5 inches
The perimeter of a triangle can is the sum of the side lengths of the triangle :
(base + side 1 + side 2) = (12 + 36.5 + 36.5) = 85 inchesTherefore, the perimeter of the triangle is 85 inches.
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Answer: 85 perimeter
Step-by-step explanation:
Erika is 12 years older than her friend Nick. She is also 3 times as old as Nick. Let x represent Nick’s current age.
Answer:
Nick is 6 years old.
Erica is 18 years old.
Step-by-step explanation:
Hello!
We know that Erica is 12 years older than Nick, which also means she is 3 times older than Nick. We can represent this situation as two equations.
Let E be Erica's age, and x be Nick's age.
E = x + 12, and E = x* 3
Since E is equal to E, we can say that x + 12 = 3x.
Solve for xx + 12 = 3x12 = 2x6 = xThe value of x is 6. Nick is 6 years old, and Erica is 18 years old.
6% of what number is 21?
a
1.26
b
12.6
c
350
can i get some help pls
Answer:
216
Step-by-step explanation:
Since a=-6,b=-4 and c= 3,we have to multiply them including the extra three
Which of the following functions has an amplitude of 2 and a phase shift of pi over 3 question mark
The trigonometric function with an amplitude of 2 and a phase shift of π/3 is given as follows:
h(x) = 2cos(3x - π/3) + 2.
How to define a cosine function?The standard definition of the cosine function is given as follows:
y = Acos(B(x - C)) + D.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.The required parameters for this problem are given as follows:
A = 2, C = π/3.
Hence the function is given as follows:
h(x) = 2cos(3x - π/3) + 2.
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Find the area under the standard normal distribution represented by each probability. (Round your answers to 4 decimal places.) (a) P(Z<0.32) : (b) P(Z>1.37) : (c) P(−0.68
(a) The area under the standard normal distribution for P(Z < 0.32) is approximately 0.6255. (b) The area for P(Z > 1.37) is approximately 0.0853. (c) The area for P(-0.68 < Z < 1.73) is approximately 0.7085.
To find the area under the standard normal distribution represented by each probability, we can use the standard normal distribution table or a calculator.
(a) P(Z < 0.32):
Using the standard normal distribution table or a calculator, we find that P(Z < 0.32) is approximately 0.6255.
(b) P(Z > 1.37):
Since the standard normal distribution is symmetric, P(Z > 1.37) is equal to 1 – P(Z < 1.37). Using the standard normal distribution table or a calculator, we find that P(Z < 1.37) is approximately 0.9147. Therefore, P(Z > 1.37) is approximately 1 – 0.9147 = 0.0853.
(c) P(-0.68 < Z < 1.73):
To find P(-0.68 < Z < 1.73), we need to calculate the difference between the cumulative probabilities P(Z < 1.73) and P(Z < -0.68). Using the standard normal distribution table or a calculator, we find that P(Z < 1.73) is approximately 0.9571 and P(Z < -0.68) is approximately 0.2486. Therefore, P(-0.68 < Z < 1.73) is approximately 0.9571 – 0.2486 = 0.7085.
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What's the quotient and the remainder of 17÷7
Answer:
The quotient is equal to 2
The remainder is equal to 3
Explanation:
We want to find the quotient and the remaider of the given expression.
\(\begin{gathered} \frac{17}{7}=\frac{14+3}{7}=\frac{14}{7}+\frac{3}{7} \\ =2+\frac{3}{7} \end{gathered}\)Therefore;
The quotient is equal to 2
The remainder is equal to 3
PLEASE HELP!! look at the image below
Answer:
A right 4 down 5
Step-by-step explanation:
counting the grid spaces from any point for example R and going to the point R' (R prime) will give you the translation
Evaluate ∫ ∫ (x² + y²)dx dy over the region in the positive quadrant which x+y≤1.
The given double integral is ∫ ∫ (x² + y²)dx dy, and we need to evaluate it over the region in the positive quadrant where x+y≤1.
To evaluate this double integral, we can first determine the limits of integration for both x and y based on the given region. In the positive quadrant, x and y both range from 0 to 1.
Now, integrating the inner integral with respect to x, we get:
∫ (x² + y²)dx = (1/3)x³ + y²x + C1,
where C1 is the constant of integration.
Next, we integrate the resulting expression with respect to y:
∫ [(1/3)x³ + y²x + C1] dy = (1/3)x³y + (1/3)y³x + C1y + C2,
where C2 is another constant of integration.
Finally, we evaluate this double integral over the given region by substituting the limits of integration:
∫∫ (x² + y²)dx dy = ∫[0 to 1] ∫[0 to 1-x] (x² + y²)dy dx.
Performing the integration, we can find the numerical value of the double integral within the given region.
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A landscape gardener wishes to spread fertiliser on a semicircular garden bed that has a diameter of 4.7 m. How much fertiliser is required if the fertiliser is applied at the rate of 20 g per square metre? Give your answer to the nearest gram.
Answer:
Step-by-step explanation:
radius of semicircle =4.7/2 m
area of semicircle=1/2 πr²
=1/2 ×π×(4.7)²
≈8.67 m²
fertiliser=8.67×20
=173.4
≈173 gm
») If 5y = 25, which property of equality was used to
keep the equation 5y - 7 = 25 - 7 equal?
») Convince Me!
What other properties of equality could you apply to
keep the equation 5y = 25 equal? Give an example of
each.
Answer:
a. Subtraction property
b. Addition property and Multiplication property
Step-by-step explanation:
Given
\(5y = 25\)
Solving (a): Which property is applied to \(5y-7 = 25-7\)
The property applied is the subtraction property of inequality, and it states that:
If \(a = b\)
Then
\(a - x = b - x\)
So, in this case:
\(a = 5y, b = 25\ and\ x=7\)
Solving (b): Other properties
1. The additive property of equality
If \(a = b\)
Then
\(a + x = b + x\)
So, the expression can be written as:
\(5y + 12 = 25 + 12\)
When 12 is subtracted from both sides, the equation returns to the original
i.e.
\(5y + 12 - 12 = 25 + 12 - 12\)
\(5y = 25\)
2. The multiplication property of equality
If \(a = b\)
Then
\(a * x = b * x\)
So, the expression can be written as:
\(5y* 2 = 25 * 2\)
\(10y = 50\)
When both sides are divided by 2, the equation returns to the original
i.e.
\(\frac{10y}{2} = \frac{50}{2}\)
\(5y = 25\)
Answer:
I Have the same question
Step-by-step explanation:
solve the equation 4+3x-1/2=9 .Explain the reasons why you chose your solution method.
Answer:
x = 5
Step-by-step explanation:
that would look like this:
\(\frac{4+3x-1}{2}=9\)
first, to remove the denominator (2), we should multiply both sides by 2. therefore, we get:
4 + 3x - 1 = 18.
now, we transpose 4 and -1 to the other side, in order to isolate 3x.
3x = 18 + 1 - 4
3x = 15
to find x, we divide both sides by 3. therefore, we get:
x = 5
Answer:
Step-by-step explanation:
\(4 + 3x - \frac{1}{2}=9\)
Subtract 4 from both the sides
\(3x - \frac{1}{2}=9 - 4\\\\3x - \frac{1}{2}= 5\)
Add (1/2) to both sides
\(3x = 5 + \frac{1}{2}\\\\3x = \frac{5*2}{1*2}+\frac{1}{2}\\\\3x=\frac{10}{2}+\frac{1}{2}\\\\3x=\frac{10+1}{2}\\\\3x=\frac{11}{2}\\\\x=\frac{11}{2*3}\\\\x=\frac{11}{6}\)
Kate is always reminding her younger brother Tony that she is taller Than he is. Kate is 63 inches tall and is growing at a rate of 1/3 inch per year. tony is 60 inches tall and is growing at a rate of 2 1/3 inches per year. How long will it take for Tony to catch up with Kate's height?
Answer:
between 1 and 2 years
Step-by-step explanation:
if you need a whole number, 2 years is the answer. if you need the exact answer, it would be 1.5 years