Answer:
x=-4,1,2+5i,2-5i
Step-by-step explanation:
Given is an algebraic expression g(x) as product of two functions.
Hence solutions will be the combined solutions of two quadratic products
[tex]g(x) = (x^2 + 3x - 4)(x^2 - 4x + 29)\\[/tex]
I expression can be factorised as
[tex](x+4)(x-1)[/tex]
Hence one set of solutions are
x=-4,1
Next quadratic we cannot factorize
and hence use formulae
[tex]x=\frac{4+/-\sqrt{16-116} }{2} =2+5i, 2-5i[/tex]
Answer:
The answer above is correct:
B. 1
C. 4
E. 2+5i
F. 2-5i
Step-by-step explanation:
I got this right on Edg. 2021
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CC=\frac{5}{9}(F - 32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
If events A and B are mutually exclusive, find P(A/B)
A. P(A)
B. 1
C. 0
D. P(A)/P(B)
A plane left on time at noon on Monday. It arrived at its destination at 8:16PM the same day, which was 16 minutes late. On average, how many seconds did the plane fall behind every fifteen minutes?
To find the average delay per fifteen-minute interval, convert the total delay of 16 minutes into seconds, then divide by the number of fifteen-minute intervals between noon and 8:00 PM, yielding an average delay of 30 seconds per interval.
The question asks us to calculate how much time the plane fell behind schedule, on average, every fifteen minutes. Since the plane arrived 16 minutes late, we first need to convert this delay into seconds: 16 minutes is equal to 960 seconds (16 minutes imes 60 seconds/minute). To calculate the plane's average delay per fifteen-minute interval, we divide the total delay in seconds by the total number of fifteen-minute intervals between noon and the expected arrival time at 8:00 PM, which is 32 intervals (8 hours ×4 intervals/hour). Therefore, the average delay per interval is 960 seconds \/ 32 intervals = 30 seconds per interval.
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[tex] \displaystyle
|\Omega|=\binom{16}{2}=\dfrac{16!}{2!14!}=\dfrac{15\cdot16}{2}=120\\
|A|=4\cdot2=8\\\\
P(A)=\dfrac{8}{120}=\dfrac{1}{15}\approx7\% [/tex]
Let , 4 ,− 7 be a point on the terminal side of θ . find the exact values of cos θ , csc θ , and tan θ .
The exact values are [tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex], [tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex] and [tex]\tan \theta = -\frac{7}{4}[/tex], respectively.
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[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (1)
[tex]\csc \theta = \frac{\sqrt{x^{2}+y^{2}}}{y}[/tex] (2)
[tex]\tan \theta = \frac{y}{x}[/tex] (3)
If we know that [tex]x = 4[/tex] and [tex]y = -7[/tex], then the exact value of all the trigonometric relations are:
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex]
[tex]\cos \theta = \frac{4}{\sqrt{4^{2}+(-7)^{2}}}[/tex]
[tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex]
[tex]\csc \theta = \frac{\sqrt{x^{2}+y^{2}}}{y}[/tex]
[tex]\csc\theta = \frac{\sqrt{4^{2}+(-7)^{2}}}{4}[/tex]
[tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex]
[tex]\tan \theta = \frac{y}{x}[/tex]
[tex]\tan \theta = -\frac{7}{4}[/tex]
The exact values are [tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex], [tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex] and [tex]\tan \theta = -\frac{7}{4}[/tex], respectively.
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A cleaner recommends mixing 1 1/2 cup of cleaner for every 12 cups of water. What is the ratio of cleaner to water in simplest form?
The sides of a rectangle are in the ratio of 4:5. If the width is 28 in., find the length, the perimeter, and the area of this rectangle.
Suppose that 5 green balls and 12 purple balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a purple ball if the first ball is replaced before the second is drawn?
Uisng the concept of probability, the probability that the second ball drawn is purple is 12/17
Given the Parameters :
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Recall :
Probability = required outcome / Total possible outcomesSince selection is made with replacement :
P(purple) = number of purple balls / total number of balls
P(purple) = 12/17Therefore, the probability of drawing a purple ball is 12/17
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A rancher has 300 feet of fencing to enclose a pasture bordered on one side by a river. the river side of the pasture needs no fence. find the dimensions of the pasture that will produce a pasture with a maximum area.
A test is worth 50 points. Multiple-choice questions are worth 1 point, and short-answer questions are worth 3 points. If the test has 20 questions, how many multiple-choice questions are there?
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apex mcr
What is the area of this figure?
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Which of the following is the correct simplification of 7•4²÷ 8 -12
SCIENCE HELP 10 POINTS!!!!!
The greenhouse effect traps heat near earth's surface. Greenhouse gases in the atmosphere—carbon dioxide, water vapor, methane, and nitrous oxide—allow the shorter waves of ultraviolet radiation from the sun to enter earth's lower atmosphere. However, these gases do not allow the longer wavelengths of infrared radiation to pass back out to the outer atmosphere. The result is that the lower atmosphere heats up.This result happens naturally, but it can be accelerated by human activities. Since the late 1800s, human activity has greatly altered the amount of greenhouse gases that enter the atmosphere. Burning fossil fuels, farming, and clearing forests, as well as industry, have all contributed to increases of carbon dioxide (CO2), methane, nitrous oxide, and other greenhouse gases in the atmosphere.The result is that temperatures in the troposphere have gone up. Many scientists identify this increase in greenhouse gas emissions as contributing directly to global warming. This suggests that human activity has had an impact on the global climate.
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Which figure shows how a shape can be rotated about an axis to form the given object?
The answer is as shown in the attachment which is the first diagram (on the left) on the second row which is highlighted in the attachment
That is the only figure which when rotated about the axis will form a cylindrical form as required.
The top two will form into a solid sphere and the last would form into a solid cylinder and not the one as required.
Answer:
Option C.
Step-by-step explanation:
In this question we will go by every option.
Option A). When a circle showing in the figure is rotated then a hollow ring will be formed.
Option B). In this option when a circle like structure with two layers is rotated about an axis it will forms a ring with two layers. Inner part of the ring will be empty.
Option C). In this option when a vertical strip is rotated by the axis, it will form the cylinder similar to the object shown in the figure.
Option D). In this option when a strip attached to the axis is rotated, a sold cylinder is formed.
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