The equation y=−4(5)x y = − 4 ( 5 ) x can be simplified to y = -20x. This equation is a linear function with a slope of -20. As x increases, y decreases at a rate of 20 units for every one unit increase in x. Therefore, the value of y will decrease rapidly as x increases.
Consider a binomial experiment with n = 10 and p = 0.40.
In a binomial experiment with n = 10 and p = 0.40 there is a 57.0% chance of getting 5 or more successes in the 10 trials.
A binomial experiment is a statistical experiment that consists of a fixed number of independent trials, where each trial can have only two outcomes, typically called "success" or "failure." The probability of success for each trial is denoted by p, and the number of trials is denoted by n.
In this case, we are given n = 10 and p = 0.40. This means that we are conducting an experiment with 10 independent trials, where the probability of success for each trial is 0.40.
Using this information, we can answer questions about the probability of various outcomes. For example, we can calculate the probability of getting exactly 5 successes in the 10 trials:
P(X = 5) = (10 choose 5) * 0.40^5 * (1 - 0.40)⁽¹⁰⁻⁵⁾
P(X = 5) = 0.246
This means that there is a 24.6% chance of getting exactly 5 successes in the 10 trials.
We can also calculate the probability of getting 5 or more successes:
P(X >= 5) = P(X = 5) + P(X = 6) + ... + P(X = 10)
P(X >= 5) = 0.246 + 0.204 + 0.088 + 0.026 + 0.005 + 0.001
P(X >= 5) = 0.570
This means that there is a 57.0% chance of getting 5 or more successes in the 10 trials.
Overall, the binomial distribution is a useful tool for modeling situations where there are a fixed number of trials with a binary outcome, and the probability of success is known for each trial.
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16 students at a school were asked about their favorite pasta dish. A graph of the results is on the left.
Create a bar graph showing the possible results for all 400 students in the school. Be sure to number the vertical axis.
Answer:
Step-by-step explanation:
to solve this question, we need to use the graph on the left to find the proportions of students who prefer each pasta dish, and then multiply those proportions by 400 to get the estimated number of students in the whole school who prefer each pasta dish. Then we need to plot those numbers on a bar graph with the pasta dishes on the horizontal axis and the number of students on the vertical axis. The graph below shows one possible way to create the bar graph:
We can see that the vertical axis is numbered from 0 to 120 in increments of 20. The bars show the estimated number of students who prefer each pasta dish, based on the sample of 16 students. For example, since 4 out of 16 students prefer spaghetti, we can estimate that 4/16 x 400 = 100 students in the whole school prefer spaghetti. Similarly, since 3 out of 16 students prefer lasagna, we can estimate that 3/16 x 400 = 75 students in the whole school prefer lasagna. We can repeat this process for the other pasta dishes and plot them on the graph.
✧☆*: .｡. Hope this helps, happy learning! (*✧×✧*) .｡.:*☆
Determine o valor das letras para que a sequencia 4,8,a,18 seja inversamente proporcional a sequencia 54,b,24,c
Answer:
Step-by-step explanation:
The values of the letters are: a = k / (648b), b = k / (1296c), c = k / (1296b) and 24c = k / (576a).
To determine the value of the letters in the given sequences, we need to first recall the formula for inverse proportionality, which states that the product of the terms in one sequence is equal to the constant value of the product of the terms in the other sequence. Mathematically, we can represent this as:
4 x 8 x a x 18 = k = 54 x b x 24 x c
Here, k is the constant of proportionality. To find the value of the letters, we can solve for them algebraically. First, we can simplify the equation by dividing both sides by 4 x 18 x 24:
a = k / (4 x 8 x 18 x 24 / 54 x b x c)
a = k / (6b c)
Next, we can substitute the given values of the sequence into the equation and simplify:
a = k / (6b c) = k / (648b)
Multiplying both sides by 648b, we get:
648b a = k
Similarly, we can solve for the values of the other letters as follows:
b = k / (54 x 24 x c) = k / (1296c)
24c = k / (4 x 8 x a x 18) = k / (576a)
c = k / (54 x b x 24) = k / (1296b)
Therefore, the values of the letters are:
a = k / (648b)
b = k / (1296c)
c = k / (1296b)
24c = k / (576a)
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Make a number line and mark all the points that represent the following values of x. X < -1 and x > 1
To make a number line for the values of x that are less than -1 and greater than 1, we can start by drawing a horizontal line and marking a point at 0. Then, we can label the left side of the line with negative numbers and the right side with positive numbers.
Next, we need to mark all the points that represent the values of x that satisfy the condition X < -1 and x > 1. This means we are looking for all the numbers that are less than -1 and greater than 1 at the same time. However, there are no numbers that satisfy this condition since a number cannot be both less than -1 and greater than 1 simultaneously.
Therefore, there are no points to mark on the number line for this condition.
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this table shows incidence rates (per 100,000) of groups exposed to neither risk factors or to one or two risk factors for lung cancer. what is the expected value of incidence rate x on asbestos exposure group among smokers in multiplicative scale?
The correct response is 12, as finding the predicted smoking and asbestos exposure group requires finding x, and in that case, the ratios in the rows and columns are equal.
4/2 = x/6 Or 6/2= x/4
This suggests that x = 12.
Smoking refers to the act of inhaling and exhaling the smoke produced by burning tobacco or other substances such as marijuana or hookah. It is a highly addictive habit that poses significant health risks to both smokers and those exposed to secondhand smoke. Smoking can lead to a variety of illnesses and diseases, including lung cancer, heart disease, stroke, chronic obstructive pulmonary disease (COPD), and various other cancers. It is estimated that smoking is responsible for nearly 8 million deaths globally each year.
The chemicals in tobacco smoke can also harm the environment, contributing to air pollution and litter. Despite the well-known risks associated with smoking, many people continue to smoke due to addiction, peer pressure, or a lack of understanding about the long-term consequences.
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The number of fish in a lake is growing exponentially. The table shows the values, in thousands, after different numbers of years since the population was first measured.
years population
0 10
1
2 40
3
4
5
6
By what factor does the population grow every two years? Use this information to fill out the table for 4 years and 6 years.
By what factor does the population grow every year? Explain how you know, and use this information to complete the table
The population in 4 year is 160 and in 6 year is 320.
The population is grows by a factor of 2 every two years.
We can use the following formula to get the rate of population growth every two years:
Growth factor: (population after n years / (population after (n-2) years) ^ 1/2
This formula can be used to determine the growth factor as follows:
Growth factor is equal to (40/10)*(1/2) = 2
This indicates that every two years, the population increases by a factor of 2.
Then, for 4 year the population
= 10 x 2⁴
= 10 x 16
= 160
For 6 year the population is
= 10 x 2⁶
= 10 x 32
= 320
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Evaluate the following expression. Your answer must be in exact form: for example, type pi/6 for π/6 or DNE if the expression is undefined. 37 arcsin (sin(-3π/8))=
To evaluate the expression 37 * arcsin(sin(-3π/8)), follow these steps:
1. First, identify the expression: 37 * arcsin(sin(-3π/8))
2. Calculate the value of sin(-3π/8) using the sine function: sin(-3π/8)
3. Apply the arcsin function to the result from step 2: arcsin(sin(-3π/8))
4. Multiply the result from step 3 by 37: 37 * arcsin(sin(-3π/8))
Let's solve each step:
2. sin(-3π/8) = -0.3826834324 (rounded to 10 decimal places)
3. arcsin(-0.3826834324) = -π/8 (in exact form, since the input is the sine of a known angle)
4. 37 * (-π/8) = -37π/8
So, the expression 37 * arcsin(sin(-3π/8)) evaluates to -37π/8 in exact form.
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Your parents are buying a house for $187,500. They have a good credit rating, are making a 20% down payment, and expect to pay $1,575/month. The interest rate for the mortgage is 4.65%. What must their realized income be before each month?
Be sure to include the following in your response:
the answer to the original question
the mathematical steps for solving the problem demonstrating mathematical reasoning
Qn in attachment
.
..
Answer: d
Step-by-step explanation:
Answer:
pls mrk me brainliest
Step-by-step explanation:
(￣(ｴ)￣)ﾉ
For the function f(x) = x^2e^7x find the critical numbers and use the First Derivative Test to find the local
maximum and minimum values and where they occur. Enter exact answers in fraction form.
For the function f(x) = x^2e^7x the critical numbers are 0 and -2/7 and using the First Derivative Test local minima at x = 0 and -2/7.
The function f(x) = x²e⁷ˣ
Differentiate the function f(x) with respect to x
f'(x) = 2xe⁷ˣ + 7x²e⁷ˣ
f'(x) = xe⁷ˣ(2 + 7x)
Now put f'(x) = 0 for critical points.
xe⁷ˣ(2 + 7x) = 0
x = 0 2 + 7x = 0 e⁷ˣ ≠ 0
x = 0 x = -2/7 e⁷ˣ ≠ 0
Hence, 0 and -2/7 are the critical points.
f'(x) = 2xe⁷ˣ + 14x²e⁷ˣ
Now f''(x) = 2e⁷ˣ + 14xe⁷ˣ + 28xe⁷ˣ + 98x²e⁷ˣ
f''(x) = 2e⁷ˣ + 42xe⁷ˣ + 98x²e⁷ˣ
f''(x) = 2e⁷ˣ(1 + 21x + 49x²)
Now f''(x) at x = 0
f''(0) = 2e⁷⁽⁰⁾(1 + 21(0) + 49(0)²)
f''(0) = 2(1 + 0 + 0)
f''(0) = 2 > 0
So f(x) has minima at x = 0
Local minima at x = 0 and y = 0.
Now f''(x) at x = -2/7
f''(0) = 2e⁻²(1 + 21(-2/7) + 49(-2/7)²)
f''(0) = 2e⁻²(1 - 6 + 4)
f''(0) = -2e⁻² < 0
f(x) has local minima at x = -2/7
Now y at x = -2/7 is
y = f(-2/7)
y = (-2/7)² e⁻²
y = 4/49e²
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El mastil de un velero se halla unido a la proa y a la popa por dos cables que forman con la cubierta, angulo de 45 grados y 60 grados, respectivamente. si el barco tiene una longitud de 25m, ¿cual es la altura del mastil?
La altura del mástil es de aproximadamente 20.87 metros.
How to find mast height?Para resolver el problema, se puede utilizar la ley de cosenos para encontrar la longitud del mástil:
c² = a² + b² - 2ab cos C
Donde:
c es la longitud del mástil (lo que se busca)
a es la longitud de la parte delantera del barco (25m)
b es la longitud de la parte trasera del barco (también 25m)
C es el ángulo entre a y b, que se puede calcular utilizando la tangente: tan C = 1.5 (pues tan 60° = √3, y tan 45° = 1)
Resolviendo para c:
c² = 25² + 25² - 2(25)(25)cos(arctan 1.5)
c = √(25² + 25² - 2(25)(25)(1/√(1+(1.5)²)))
c ≈ 31.08 m
Por lo tanto, la altura del mástil es de aproximadamente 31.08 metros.
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Find an exponential function that passes through (2,8) and (4,128)
The final exponential function using the values of 'a' and 'b':
y = (1/2)(4^x)
To find an exponential function that passes through the points (2,8) and (4,128), follow these steps:
Step 1: Recall the general form of an exponential function: y = ab^x
Here, 'a' and 'b' are constants that need to be determined using the given points.
Step 2: Substitute the first point (2,8) into the equation:
8 = ab^2
Step 3: Substitute the second point (4,128) into the equation:
128 = ab^4
Step 4: Divide the second equation by the first equation to eliminate 'a':
(128 = ab^4) / (8 = ab^2)
16 = b^2
Step 5: Solve for 'b':
b = √16
b = 4
Step 6: Substitute the value of 'b' back into the first equation:
8 = a(4^2)
Step 7: Solve for 'a':
8 = 16a
a = 8/16
a = 1/2
Step 8: Write the final exponential function using the values of 'a' and 'b':
y = (1/2)(4^x)
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Talissa invested money into two different accounts. One at citibank which
she started her investment at $400 with an interest rate of 3% compounded
annually. She started at the same price at the second bank, however the
interest rate was 4. 2% compounded continuously. Set up an equation to show
the total amount.
To set up an equation to show the total amount, we can use the formula for compound interest:
A = P(1 + r/n)^nt
Where:
A = the total amount
P = the principal (initial investment)
r = the interest rate
n = the number of times the interest is compounded per year
t = the time period (in years)
For the investment at Citibank:
P = $400
r = 3%
n = 1 (compounded annually)
t = 1 (since it is compounded annually)
So, the equation would be:
A1 = $400(1 + 0.03/1)^(1*1)
A1 = $412
For the investment at the second bank:
P = $400
r = 4.2%
n = ∞ (compounded continuously)
t = 1 (since it is for 1 year)
So, the equation would be:
A2 = $400e^(0.042*1)
A2 = $416.99
To find the total amount, we can add the two amounts together:
Total amount = A1 + A2
Total amount = $412 + $416.99
Total amount = $828.99
Therefore, Talissa's total amount after one year with the two investments is $828.99.
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this is due soon. i dont know how to do it
The unit multiplier for the conversion is 24 ft/min = (24 ft² / 1 min) * (12 inch / ft) * (12 inch / ft) * (1 min / 60 sec)
What is an equation?An exponential equation is an expression that shows how numbers and variables using mathematical operators.
1 minutes = 60 seconds
1 foot = 12 inch
The unit multiplier for the conversion of 24 square feet per minute to square inches per second
24 ft/min = (24 ft² / 1 min) * (12 inch / ft) * (12 inch / ft) * (1 min / 60 sec)
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7. Membership at the local Sky Zone costs $189 per year and an hour costs $15 each.
Write an expression (make sure it looks like an expression, not an equation) to
represent the total cost of going to Sky Zone for the year. Evaluate the expression
(make it an equation) if you jump for 19 hours in a year. Write a "therefore"
statement. (4 marks)
189*365=68985
68985/15= $4599
Step-by-step explanation:
or $5000 if you round up
Nicholas cleans his room in 10 hour. Gloria
cleans her room for 3 minutes and 18 seconds. How many seconds longer does Nicholas clean his room than Gloria?
To determine how many seconds longer Nicholas cleans his room than Gloria, we first need to convert both their cleaning times into seconds.
1. Convert Nicholas's cleaning time to seconds:
Nicholas cleans his room in 10 hours. There are 60 minutes in an hour and 60 seconds in a minute. So, we multiply 10 hours by 60 minutes and then by 60 seconds:
10 hours * 60 minutes/hour * 60 seconds/minute = 36,000 seconds
2. Convert Gloria's cleaning time to seconds:
Gloria cleans her room for 3 minutes and 18 seconds. We convert 3 minutes into seconds by multiplying it by 60 seconds/minute:
3 minutes * 60 seconds/minute = 180 seconds
Now, add the 18 seconds to the 180 seconds:
180 seconds + 18 seconds = 198 seconds
3. Subtract Gloria's cleaning time from Nicholas's cleaning time:
36,000 seconds (Nicholas) - 198 seconds (Gloria) = 35,802 seconds
In conclusion, Nicholas cleans his room for 35,802 seconds longer than Gloria.
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What is the slope of the line represented by the equation y=4/5x - 3?
A).-3
B).-4/5
C).4/5
D).3
The equation y = (4/5)x - 3 is in slope-intercept form, y = mx + b, where m is the slope of the line. Therefore, the slope of the line represented by the equation is:
m = 4/5
So the answer is C) 4/5.
A solid is made by a hemisphere and cylinder having equal radii. The volume of the solid is 2707 cm'. If the height of the cylinder is 80 cm, find the total surface area of the solid
The total surface area of the solid is approximately 1818 [tex]cm^{2}[/tex]. Let's call the radius of the hemisphere and cylinder "r".
The volume of the solid is the sum of the volumes of the hemisphere and cylinder: V = (2/3)π[tex]r^{3}[/tex] + π[tex]r^{2}[/tex]h. Substituting in the given values, we get: 2707 = (2/3)π [tex]r^{3}[/tex] + π[tex]r^{2}[/tex](80)
To solve for r, we can rearrange the equation and use a numerical method or calculator. We get: r ≈ 11.6 cm
Now, we can use the radius to find the surface area of the solid. The surface area is the sum of the curved surface areas of the hemisphere and cylinder, plus the area of the circular base of the cylinder: A = 2π[tex]r^{2}[/tex] + 2πrh + π[tex]r^{2}[/tex].
Substituting in the given values and solving for A, we get: A ≈ 1818 [tex]cm^{2}[/tex]. Therefore, the total surface area of the solid is approximately 1818 [tex]cm^{2}[/tex].
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LT 18.1
The radius of Circle A below is 11 millimeters and the measure of < BAC is 60°.
What is the length of Arc BC, to the nearest millimeter?
A. 12 mm
B. 24 mm
C. 6 mm
D. 3 mm
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=11\\ \theta =60 \end{cases}\implies s=\cfrac{(60)\pi (11)}{180}\implies s=\cfrac{11\pi }{3}\implies s\approx 12~mm[/tex]
Answer: 12mm
Step-by-step explanation:
Basically, you will find the circumference of the entire circle and then using that find the length of the arc.
So the circumference of the circle is its radius (11) times pi multiplied by 2.
2(11 x 3.14) = 69.08
Now a circle is always 360 degrees and the angle of the sector is 60 degrees.
So we have our circumference and we only need that small portion, so you take and make it a fraction and multiply by the circumference to find the length of that small portion:
60/360 x 69.08 = 11.51
Rounded = 12
A magazine listed the number of calories and sodium content (in milligrams) for 13 brands of hot dogs. Examine the association, assuming that the data satisfy the conditions for inference. Complete parts a and b
Option B is correct. In this context, the meaning is: Among hot dogs with the same number of calories, the sodium content varies, with a standard deviation of about 75 milligrams
The calculated test statistic is 3.75
How to get the correct optionThe test statistics can be gotten from the data that we already have available in this question
The coefficient is given as 2.235
The Standard error of the coefficient is given as 0.596
The formula used is given as
Such that t = coefficient / Standard error
where the coefficient = 2.235
The standard error = 0.596
We have to apply the values to formula:
= 2.235 / 0.596
= 3.75
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The library is 14.5 miles due west of the park the courthouse is 21.7 miles north west from the park how many miles is the library from the courthouse
The library is about 26.1 miles from the courthouse.
To solve this problem, we will apply the Pythagorean theorem, which tells us that during a right triangle, the square of the period of the hypotenuse( the longest side) is same to the total of the places of the lengths of the different two sides.
In this instance, the park is on the right angle, and the library and courthouse are the opposite two factors. we can consider the distance among the library and the park because the length of 1 leg of the triangle, and the space among the courthouse and the park as the length of the other leg.
So, using the Pythagorean theorem, we're suitable to calculate the period of the hypotenuse( the distance among the library and the courthouse)
library- to- park distance2 courthouse- to- park distance2 = library- to- courthouse distance2
[tex](14.5)^2 + (21.7)^2 = library-to-courthouse distance^2[/tex]
[tex]210.25 + 471.29 = library-to-courthouse distance^2[/tex]
[tex]681.54 = library-to-courthouse distance^2[/tex]
Taking the square root of both aspects, we get
library- to- courthouse distance[tex]= sqrt(681.54) \approx26.1[/tex]
Accordingly, the library is about 26.1 miles from the courthouse.
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Solve the trigonometric equation in the interval [0, 2π). give the exact value, if possible; otherwise, round your answer to two decimal places. (enter your answers as a comma-separated list.) 2 cos2(x) + cos(2x) = 0 x =
To solve the trigonometric equation 2cos^2(x) + cos(2x) = 0 in the interval [0, 2π), we will first use the double angle formula for cos(2x) and then solve for x. Recall that cos(2x) = 2cos^2(x) - 1.
Substitute this into the equation: 2cos^2(x) + (2cos^2(x) - 1) = 0 Combine the terms: 4cos^2(x) - 1 = 0 Now, isolate cos^2(x): cos^2(x) = 1/4 Take the square root of both sides: cos(x) = ±√(1/4) = ±1/2 Now, find the values of x in the interval [0, 2π) that satisfy the equation: For cos(x) = 1/2: x = π/3, 5π/3 For cos(x) = -1/2: x = 2π/3, 4π/3 Combine the answers as a comma-separated list: x = π/3, 2π/3, 4π/3, 5π/3
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Find the length of the following parametric curve. x = 6 + it, y = 4 + 43/2, 03752. 0 << Enter your answer symbolically, as in these examples
To find the length of the parametric curve, we can use the formula:
L = ∫a^b √(dx/dt)² + (dy/dt)² dt
Substituting the given values, we get:
L = ∫0^1 √(6)² + (43/2, 03752)² dt
Simplifying:
L = ∫0^1 √(36 + (43/2, 03752)²) dt
Therefore, the length of the parametric curve is:
L = √(36 + (43/2, 03752)²)
In mathematics, substitution refers to the process of replacing a variable or expression in an equation or formula with another variable or expression that has the same value.
For example, if we have an equation: 2x + 3y = 7, and we want to substitute x with the value 4, we replace x with 4 to get:
2(4) + 3y = 7
8 + 3y = 7
We can then solve for y to find its value.
Substitution is a commonly used technique in algebra and calculus to simplify expressions, solve equations and evaluate functions.
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Help is extremely appreciated! :)
Answer:
To find the weighted mean, we need to multiply each delivery value by its corresponding frequency, add the products, and divide by the total frequency.
(3 x 7) + (6 x 6) + (9 x 1) + (12 x 0) = 21 + 36 + 9 + 0 = 66
Total frequency = 7 + 6 + 1 + 0 = 14
Weighted mean = 66 / 14 = 4.7 (rounded to the nearest tenth)
Therefore, the weighted mean is 4.7
A single number cube is rolled twice. The 36 equally-likely outcomes are shown to the right. What is the first step in finding the probability of getting two numbers whose sum is 12? Find the probability of getting two numbers whose sum is 12.
The probability of getting two numbers whose sum is 12 when rolling a single number cube twice is 1/36.
To find the probability of getting two numbers whose sum is 12 when a single number cube is rolled twice, we'll first need to identify the favorable outcomes.
A number cube has six faces, numbered from 1 to 6. When it is rolled twice, there are 6 x 6 = 36 equally-likely outcomes. To find the probability, we can use the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
The first step is to identify the favorable outcomes, which are the pairs of numbers that add up to 12. Since we are dealing with a number cube that has faces numbered 1 to 6, there is only one possible pair that satisfies this condition: (6,6).
Now that we have determined the favorable outcome, we can find the probability:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability = 1 (for the pair 6,6) / 36
Thus, the probability of getting two numbers whose sum is 12 when rolling a single number cube twice is 1/36.
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Problem 3: enter the value of c when the expression 12.2x + c is
equivalent to 6.1(2x - 3.4).
The value of c that makes the two expressions equivalent is -20.74.
Let's start by simplifying the expression 6.1(2x - 3.4). To do this, we use the distributive property of multiplication, which states that a(b + c) = ab + ac. Applying this to our expression, we get:
6.1(2x - 3.4) = 6.1(2x) - 6.1(3.4) = 12.2x - 20.74
Now we can rewrite the equation we want to solve as:
12.2x + c = 12.2x - 20.74
To solve for c, we need to isolate it on one side of the equation. We can do this by subtracting 12.2x from both sides:
c = -20.74
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What is the diameter of a sphere with a volume of
7483
m
3
,
7483 m
3
, to the nearest tenth of a meter?
The diameter of the sphere is approximately 20 meters to the nearest tenth of a meter.
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. Since we are given the volume of the sphere, we can solve for the radius as follows:
V = (4/3)π[tex]r^{3}[/tex]
[tex]r^{3}[/tex] = (3V) / (4π)
r = [tex](3V/4\pi )^{1/3}[/tex]
Substituting the given value of the volume, we get:
r = [tex](3*7483/4\pi )^{1/3}[/tex] ≈ 10.0
Therefore, the radius of the sphere is approximately 10 meters. The diameter of the sphere is twice the radius, so the diameter is approximately:
2 x 10 ≈ 20 meters
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how do i find the inverse
Step-by-step explanation:
To solve for inverse, utilize the following steps.
Step 1: let f(x)=y so we get
[tex]y = \sqrt{x - 6} + 5[/tex]
Step 2: Swap y and x
[tex]x = \sqrt{y - 6} + 5[/tex]
Solve for y.
[tex]x - 5 = \sqrt{y - 6} [/tex]
[tex](x - 5) { }^{2} + 6 = y[/tex]
Step 4: Let y =f^-1(x)
[tex](x - 5) {}^{2} + 6 = f {}^{ - 1} (x)[/tex]
Answer: [tex]f^{-1}(x) =[/tex] x²-10x+19
Step-by-step explanation:
Let's replace f(x) for y for now.
[tex]y=\sqrt{x-6}+5[/tex]
To find inverse. make your y into x, and your x into y
[tex]x=\sqrt{y-6}+5[/tex] >Now you solve for y. subtract 5 from both sides
[tex]x-5=\sqrt{y-6}[/tex] >Square both sides to get rid of root
[tex](x-5)^{2} =(\sqrt{y-6})^{2}[/tex] >drop root and square (x-5)
(x-5)(x-5) = y-6 >FOIL
x²-5x-5x+25 = y-6 > combine like terms
x²-10x+25 = y-6 >add 6 to both sides
x²-10x+19=y > this is your inverse now put the y into inverse form
[tex]f^{-1}(x) =[/tex] x²-10x+19
what are complementary angles and supplementary angles difference between them?
Answer:
Supplementary angles are angles that have a sum of 180°. When two angles are supplementary, we say that one angle is the supplement of the other.
Complementary angles are angles that add up to 90°. When two angles are complementary, we can say that one angle is the complement of the other
Step-by-step explanation:
gabriela is building wooden box that is 15 in. tall and has a rectangular base that is 18 in by 15 in
A open box without a top 1260 sq. in. wood will Gabriella use.
Since the top of the box is the same area as the base, calculate the base.
B = length × width
Length of the wooden box = 18 in.
Width of the wooden box = 15 in.
B = 18(15) = 270 in.
Calculate the surface area of the box.
Surface Area = 2(B + wh + hl)
h = 15
w × h = 15(15) = 225
h × l = 15(18) = 270
Surface Area of the wooden box = 2(270 + 225 + 270) = 2(765) = 1,530 sq. inches
Subtract the base from the surface area: 1,530 - 270 = 1,260sq. in.
Learn more about Surface area of box at:
https://brainly.com/question/22998786
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The given question is incomplete, complete question is:
Gabriella is beauty a wooden box with a rectangular base that is 18 in by 15 in and is 15 in tall if she wants a open box without a top how much wood will Gabriella use