PLEASE READ BEFORE ANSWERING: ITS ALL ONE QUESTION HENCE "QUESTION 6" THEY ARE NOT INDIVIDUALLY DIFFERENT QUESTIONS.
Answers
First, lets note that the given functions are polynomials of degree 2. Since the domain of a polynomial is the entire set of real numbers, the domain for all cases is:
[tex](-\infty,\infty)[/tex]Now, lets find the range for all cases. In this regard, we will use the first derivative criteria in order to obtain the minimum (or maximim) point.
case 1)
In the first case, we have
[tex]\begin{gathered} 1)\text{ }\frac{d}{dx}f(x)=6x+6=0 \\ which\text{ gives} \\ x=-1 \end{gathered}[/tex]which corresponds to the point (-1,-8). Then the minimum y-value is -8 because the leading coefficient is positive, which means that the curve opens upwards. So the range is
[tex]\lbrack-8,\infty)[/tex]On the other hand, the horizontal intercept (or x-intercept) is the value of the variable x when the function value is zero, that is,
[tex]3x^2+6x-5=0[/tex]which gives
[tex]\begin{gathered} x_1=-1+\frac{2\sqrt{6}}{3} \\ and \\ x_2=-1-\frac{2\sqrt{6}}{3} \end{gathered}[/tex]Case 2)
In this case, the first derivative criteria give us
[tex]\begin{gathered} \frac{d}{dx}g(x)=2x+2=0 \\ then \\ x=-1 \end{gathered}[/tex]Since the leading coefficient is positive, the curve opens upwards so the point (-1,5) is the minimum values. Then, the range is
[tex]\lbrack5,\infty)[/tex][tex]\lbrack5,\infty)[/tex]and the horizontal intercepts do not exists.
Case 3)
In this case, the first derivative criteris gives
[tex]\begin{gathered} \frac{d}{dx}f(x)=-2x=0 \\ then \\ x=0 \end{gathered}[/tex]Since the leading coeffcient is negative the curve opens downwards and the maximum point is (0,9). So the range is
[tex](-\infty,9\rbrack[/tex]and the horizontal intercepts occur at
[tex]\begin{gathered} -x^2+9=0 \\ then \\ x=\pm3 \end{gathered}[/tex]Case 4)
In this case, the first derivative yields
[tex]\begin{gathered} \frac{d}{dx}p(t)=6t-12=0 \\ so \\ t=2 \end{gathered}[/tex]since the leading coefficient is postive the curve opens upwards and the point (2,-12) is the minimum point. Then the range is
[tex]\lbrack-12,\infty)[/tex]and the horizontal intercetps ocurr when
[tex]\begin{gathered} 3x^2-12x=0 \\ which\text{ gives} \\ x=4 \\ and \\ x=0 \end{gathered}[/tex]Case 5)
In this case, the leading coefficient is positive so the curve opens upwards and the minimum point ocurrs at x=0. Therefore, the range is
[tex]\lbrack0,\infty)[/tex]and thehorizontal intercept is ('0,0).
In summary, by rounding to the nearest tenth, the answers are:
Related Questions
My name is Nika and I need help in math I’m 73 and done with school but still don’t under algebra
Answers
The given equation is
[tex]2x-3=9[/tex]To solve this equation we have to isolate x on one side and put the numbers on the other side
To do that we will add 3 to each side to move 3 from the left side to the right side
[tex]2x-3+3=9+3[/tex]Simplify it
[tex]\begin{gathered} 2x+0=12 \\ 2x=12 \end{gathered}[/tex]Now we need to move 2 from the left side to the right side, then
Divide both sides by 2
[tex]\begin{gathered} \frac{2x}{2}=\frac{12}{2} \\ x=6 \end{gathered}[/tex]Then the solution of the equation is
x = 6
Gordin has 4.1 GB of data in one 4-week billing cycle on his cell phone. Any unused data will roll over to the next cycle. The table shows how much data Gordon uses each week before his next billing cycle. WEEK. DATA USAGE (IN GB) 1. 0.8 2. 1.3 3. 0.9 4. 1.1How much data does Gordon have left to roll over to the next billing cycle at the end of the four weeks?A. 0 GB of dataB. 0.8 GB of datac. 3 GB of data
Answers
Gordan have left 0 GB to roll over to the next billing cycle at the end of the four weeks.
What is Addition?
The sum of all the numbers are called the Addition of numbers.
Given that;
Gordin has 4.1 GB of data in one 4-week billing cycle on his cell phone.
And, The table shows how much data Gordon uses each week before his next billing cycle as;
WEEK = 1 2 3 4
DATA USAGE = 0.8 1.3 0.9 1.1
Now,
Since, Gordin has 4.1 GB of data in one 4-week billing cycle on his cell phone.
And, The table shows how much data Gordon uses each week before his next billing cycle.
So, We can add all the given data usage in 1 to 4 week as;
Data usage = 0.8 + 1.3 + 0.9 + 1.1
= 4.1 GB
Thus, Gordan have left 0 GB to roll over to the next billing cycle at the end of the four weeks.
Learn more about the addition visit:
https://brainly.com/question/24536701
#SPJ1
What is the image point of (-12, —8) after the transformation R270 oD ?
Answers
Answer
(-12, -8) after R270°.D¼ becomes (-2, 3)
Explanation
The first operation represented by R270° indicates a rotation of 270° counterclockwise about the origin.
When a rotation of 270° counterclockwise about the origin is done on some coordinate, A (x, y), it transforms this coordinates into A' (y, -x). That is, we switch y and x, then add negative sign to x.
Then, the second operation, D¼ represents a dilation of the coordinate about the origin by a scale factor of ¼ given.
The coordinates to start with is (-12, -8)
R270° changes A (x, y) into A' (y, -x)
So,
(-12, -8) = (-8, 12)
Then, the second operation dilates the new coordinates obtained after the first operation by ¼
D¼ changes A (x, y) into A' (¼x, ¼y)
So,
(-8, 12) = [¼(-8), ¼(12)] = (-2, 3)
Hope this Helps!!!
What is the area of a triangle that has a height of 10 feet and a base of 6 feet?A. 16 feet squaredO B. 30 feet squaredO C.35 feet squaredD. 60 feet squared
Answers
Th formula for the area of the triangle is as follows.
[tex]A=\frac{bh}{2}[/tex]where b is the base of the triangle and h is its height.
Substitute the given values into the formula and then simplify.
[tex]\begin{gathered} A=\frac{(6)(10)}{2} \\ =\frac{60}{2} \\ =30 \end{gathered}[/tex]Therefore, the area of the triangle is 30 square feet, which is option B.
Find the output, f, when the input, t, is 7 f = 2t - 3 f = Stuck? Watch a video or use a hint.
Answers
Answer:
f=11
Explanation:
Given the function:
[tex]f=2t-3[/tex]When the input, t=7
The value of the output, f will be gotten by substituting 7 for t.
[tex]\begin{gathered} f=2t-3 \\ =2(7)-3 \\ =14-3 \\ f=11 \end{gathered}[/tex]The output, f is 11.
Examine the graph and write a statement about the data. Use specific information from the graph.
Answers
This bar graph represents the percentage of the public's trust in the Federal Government from year 1960 to 2015. The public trust was highest in year 1960 at 74% and it was at its lowest in 2015 at 18%.
Find to the nearest degree the measure of the angle of elevation of the sun when a woman 150 cm tall casts a shadow 40 cm long.
Answers
The triangle formed is shown in the diagram below
The angle of elevation of the sun is represented by x. To determine x, we would apply the tangent trigonometric ratio which is expressed as
Tan# = opposite side/adjacent side
opposite side = 150
adjacent side = 40
Tan x = 150/40 = 3.75
x = Tan^-1(3.75)
x = 75.069
To the nearest degree, the measure of the angle of elevation of the sun is 75 degrees
Hello, I need help with this practice problem. Thank you so much.
Answers
Answer:
5 units
Explanation:
Given the points:
[tex]\begin{gathered} \mleft(x_1,y_1\mright)=K(-2,-1) \\ \mleft(x_2,y_2\mright)=N(2,2) \end{gathered}[/tex]We use the distance formula below:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute the given values:
[tex]\begin{gathered} KN=\sqrt[]{(2-(-2))^2+(2-(-1))^2} \\ =\sqrt[]{(2+2)^2+(2+1)^2} \\ =\sqrt[]{(4)^2+(3)^2} \\ =\sqrt[]{16+9} \\ =\sqrt[]{25} \\ =5\text{ units} \end{gathered}[/tex]The distance between the two points is 5 units.
Lena eats an apple every otherday. Suppose today is Monday,October 1. Lena eats an appletoday.When will Lena eat an appleon a Monday again?AnsLe
Answers
solve the following d. be sure to take into account whether a letter is capitalized or not .3y^3 ×m=5Qd
Answers
Step 1: Write out the equation.
[tex]3g^3+m=5Qd[/tex]Step 2: Divide both sides of the equation by 5Q, we have
[tex]\frac{3g^3+m}{5Q}=\frac{5Qd}{5Q}[/tex]this implies that
[tex]d=\frac{3g^3+m}{5Q}[/tex]What is the sequence that has a recursive formula A(n)= A(n-1)+4 where A(1)=3
Answers
1) Considering that, let's find each term:
[tex]\begin{gathered} a_1=3 \\ a_n=a_{n-1}+4 \\ a_2=a_1+4\Rightarrow a_2=3+4=7 \\ a_3=a_2+4\Rightarrow a_3=7+4\text{ =11} \\ a_4=11+4\text{ }\Rightarrow a_4=15 \end{gathered}[/tex]2) So the sequence is
[tex](3,7,11,15,\ldots)[/tex]As each term, from the 2nd one is 4 units more that's why we can make it using a recursive formula
the prompt is in the photo
Answers
By using the given box and whisker plot, the number of students that earned a score from 77 and 90 is: N. 13.
What is a box and whisker plot?A box and whisker plot is also referred to as boxplot and it can be defined as a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread.
In Mathematics, the five-number summary of any box and whisker plot include the following:
MinimumFirst quartileMedianThird quartileMaximumWhat is an interquartile range?IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.
Mathematically, interquartile range (IQR) is the difference between first quartile (Q₁) and third quartile (Q₃):
IQR = Q₃ - Q₁
Based on the given box and whisker plot, we can logically deduce the following quartile ranges:
Third quartile, Q₃ = 90
First quartile, Q₁ = 77
Now, we can calculate the interquartile range (IQR) is given by:
Interquartile range, IQR = Q₃ - Q₁
Interquartile range, IQR = 90 - 17
Interquartile range, IQR = 13
Read more on interquartile here: https://brainly.com/question/17083142
#SPJ1
Simplify this fraction: 30/36
Answers
To simplify this fraction, we will have to find the common factors of both the numerator and denominator, then divide.
Common factors of 30 and 36 are: 2, 3, and 6
Now both numerator and denominator by the highest common factor which is 6:
[tex]\frac{30}{36}\text{ = }\frac{5}{6}[/tex]
After simplifying the fraction, we have:
[tex]\frac{5}{6}[/tex]I need help with a 8th-grade math assignment:China has a population of approximately 1,382,323,332 people. The United States has a population of about 324,118,787 people.Part AUsing scientific notation, give the approximation for each population. Round the first factor to the nearest tenth.China: United States: Part BAbout how many more people live in China than in the United States? Express your answer using scientific notation. Round the first factor to the nearest hundredth.
Answers
We have the next given information:
China has a population of approximately 1,382,323,332 people.
The United States has a population of about 324,118,787 people.
a) We need to use scientific notation which is given by the next form:
[tex]ax10^n[/tex]Where a is the coefficient rounded to the nearest tenth.
and a is the terms moved to the decimal point.
For China:
1382323332.0, we moved the decimal point nine spaces to the right.
then
1.382323332
Expressed in scientific notation and rounded to the nearest tenth:
[tex]1.4x10^9[/tex]For the United States:
324,118,787 with the decimal point 324,118,787.0
then
324118787.0
Move the decimal point 8 spaces to the right, then:
3.24118787
Expressed in scientific notation and rounded to the nearest tenth:
[tex]3.2x10^8[/tex]
Part b:
To find how many more people live in China than in the United States, we need to subtract between China and the United States:
Then:
1,382,323,332 - 324,118,787 = 1,058,204,545
Now
1,058,204,545 equal to 1058204545.0
We need to move the decimal point 9 spaces:
1.058204545
Expressed as scientific notation and rounded to the nearest hundredth:
[tex]1.06x10^9[/tex]Sketch the graph of a function that has a local maximum value at x = a where f'(a) is undefined.
Answers
Derivative and Maximum Value of a Function
The critical points of a function are those where the first derivative is zero or does not exist.
Out of those points, we may find local maxima or minima or none of them.
One example of a function with a derivative that does not exist is:
[tex]y=-x^{\frac{2}{3}}[/tex]This function has a local maximum at x=0 where the derivative does not exist.
The graph of this function is shown below:
Choose which function is represented by the graph.111032-11-10 9 8 7 6 5 4-3-2-102 3 4 5 6 7 8 9 10 1110O A. 1(x) = (x − 1)(x +2)(x+4)(x+8)B. f(x) - (x-8)(x-4)(x-2)(x+1)C. f(x)=(x-1)(x+2)(x+4)D. f(x)=(x-4)(x-2)(x+1)876544 4 4 & & To-2X
Answers
The factors of a polynomial tell us the points where the graph intersects the x-axis.
From the graph provided in the question, the graph cuts the x-axis at the points:
[tex]x=-4,x=-2,x=1[/tex]Therefore, the factors will be:
[tex]\begin{gathered} x=-4,x+4=0 \\ x=-2,x+2=0 \\ x=1,x-1=0 \\ \therefore \\ factors\Rightarrow(x+4),(x+2),(x-1) \end{gathered}[/tex]Therefore, the polynomial will be:
[tex]f(x)=(x+4)(x+2)(x-1)[/tex]OPTION C is the correct option.
Please help me with this word problem quickly, work is needed thank you!
Answers
Given:
Sheila can wash her car in 15 minutes. Bob takes time twice as long to wash the same car.
Required:
Find the time they take both together.
Explanation:
Sheila can wash her car in 15 minutes.
Work done by sheila in a minute =
[tex]\frac{1}{15}\text{ }[/tex]Bob takes time twice as long to wash the same car. He washes the car in 30 minutes.
Work done by Bob in a minute
[tex]=\frac{1}{30}[/tex]If they work together let them take time x per minute.
[tex]\frac{1}{15}+\frac{1}{30}=\frac{1}{x}[/tex]Solve by taking L.C. M.
[tex]\begin{gathered} \frac{2+1}{30}=\frac{1}{x} \\ \frac{3}{30}=\frac{1}{x} \\ \frac{1}{10}=\frac{1}{x} \\ x=10\text{ minutes.} \end{gathered}[/tex]If they work together they will take 10 minutes.
Final Answer:
Sheila and Bob wash the car together in 10 minutes.
Can 37° 111° and 32° be measurements of a triangle?
Answers
Answer
The angles given can easily be the measurements of one triangle because they sum up to give 180°.
Explanation
The sum of angles in a triangle is known to be 180°
So, for the given angles to be to belong to one triangle, the sum of all the angles must be equal to 180°
So, we check by adding them
37° + 111° + 32° = 180°
Hope this Helps!!!
Write an equation that represents a vertical shrink by a factor of 1/4 of the graph of g(x)=|x|.
h(x)=?
Answers
an equation that represents a vertical shrink by a factor of 1/4 of the graph of g(x)=|x| is y = |x|/4
What is vertical stretch/vertical compression ?
• A vertical stretch is derived if the constant is greater than one while the vertical compression is derived if the constant is between 0 and 1.
• Vertical stretch means that the function is taller as a result of it being stretched while vertical compress is shorter due to it being compressed and is therefore the most appropriate answer.
The y-values are multiplied by a value between 0 and 1, which causes them to travel in the direction of the x-axis. This is known as a vertical shrink and tends to flatten the graph. A point (a,b) on the graph of y=f(x) y = f (x) shifts to a point (a,kb) (a, k b) on the graph of y=kf(x) y = k f (x) in both scenarios.
The function g(x) is defined as |x|.
To vertically shrink the graph of g(x) by a factor of 1/4, divide the function by 4.
g(x) = f(x)/3
f(x) is equal to (|x|)/4.
To learn more about this vertical shrink visit:
brainly.com/question/1447109
#SPJ1
1.The histogram (next page) summarizes the data on the body lengths of 143 wild bears. Write a fewsentences describing the distribution of body lengths.403020103035404570 7580 8550 55 60 65length in inchesBe sure to comment on the shape, center, and spread of the distribution.
Answers
The shape of the distribution is bell-shaped. This is because the distribution presents a normal distribution
The distribution is almost symmetrically skewed with no outlier
The center is about 60 inches(about 59 wild bears before the center and about 84 wild bears beyond the center)
The distribution is widely spread: The data range is the highest inches minus the lowest inches
Therefore, the spread of the distribution is 85 inches - 35 inches, which equals 50 inches.
the volume of a sphere is 2304pi in^3 the radius of the sphere is ___ inches.
Answers
Answer:
The radius = 12 inches.
Explanation:
Given a sphere with radius, r units:
[tex]\text{Volume}=\frac{4}{3}\pi r^3[/tex]If the volume of a sphere is 2304π in³, then:
[tex]\frac{4}{3}\pi r^3=2304\pi[/tex]We solve the equation for r:
[tex]\begin{gathered} \frac{4\pi r^3}{3}=2304\pi \\ 4\pi r^3=2304\pi\times3 \\ r^3=\frac{2304\pi\times3}{4\pi} \\ r^3=1728 \end{gathered}[/tex]Next. take cube roots of both sides.
[tex]\begin{gathered} r=\sqrt[3]{1728} \\ r=12\text{ inches} \end{gathered}[/tex]The radius of the sphere is 12 inches.
Referring to the figure, find the unknown measure of ABC.
Answers
According to the Inscribed Angle Theorem, the measure of an angle inscribed in a circle equals half the arc that it intercepts.
Then:
[tex]m\angle ABC=\frac{1}{2}m\overset{\frown}{AC}[/tex]Since the measure of the arc AC is equal to 84º, then:
[tex]m\angle ABC=\frac{1}{2}(84º)=42º[/tex]Therefore, the answer is:
The measure of ABC is 42º.
graph and label each figure and it's image under the given reflection. give the new coordinates. you don't have to graph it for me, could you just helps with the coordinates
Answers
Explanation
Step 1
Let the vertices
[tex]\begin{gathered} C(-4,7) \\ D(-2,4) \\ E(-4,1) \\ F(-6,4) \end{gathered}[/tex]When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed)
[tex]P(x,y)\rightarrow reflect\text{ across y a }\xi s\rightarrow P^{\prime}(-x,y)[/tex]then, apply the rule to find the new coordinates
[tex]\begin{gathered} C(-4,7)\rightarrow C^{\prime}(4,7) \\ D(-2,4)\rightarrow D^{\prime}(2,4) \\ E(-4,1)\rightarrow E^{\prime}(4,1) \\ F(-6,4)\rightarrow F^{\prime}(6,4) \end{gathered}[/tex]I hope this helps you
Find the probability of drawing a red ace and then a spade when two cards are dranw (without replacement) from a standard deck of cards.a. 1/102b. 31/102c. 1/2d. 31/64
Answers
a. probability of drawing a red ace (first draw)
In a standard deck, there are 52 cards. Out of these 52 cards, two are red aces. Hence, the probability of drawing a red ace is 2/52 or 1/26.
b. probability of drawing a spade (second draw)
On the second draw, 51 cards are left. Assuming that a red ace was taken on the first draw, 13 spades are left on the deck. Hence, the probability of drawing a spade is 13/51.
So, to get the probability of drawing a red ace AND a spade, simply multiply the two probabilities above.
[tex]\frac{1}{26}\times\frac{13}{51}=\frac{13}{1326}[/tex]Then, reduce 13/1326 into its simplest form by dividing both numerator and denominator by 13.
[tex]\frac{13\div13}{1326\div13}=\frac{1}{102}[/tex]Hence, the probability of drawing a red ace AND a spade is 1/102. (Option A)
Factor the common factor1) -36m + 16
Answers
Given:
-36m + 16
To factor out the common factor, let's find the Greatest Common Factor (GCF) of both values.
GCF of -36 and 16 = -4
Factor out -4 out of -36 and 16:
[tex]-4(9m)-4(-4)[/tex]Factor out -4 out of [-4(9m) - 4(-4)] :
[tex]-4(9m\text{ - 4)}[/tex]ANSWER:
[tex]-4(9m-4)[/tex]Given circle O with diameter AC, tangent AD, and the measure of arc BC is 74 degrees, find the measures of all other indicated angles.
Answers
We want to find the measure of the angles 1 to 8, given that the diameter is AC and the measure of the Arc BC is 74°.
The angle 5, ∡BOC is central and it is equal to the measure of the arc it intercepts, the arc BC. Thus the angle 5 is 74°.
The angle 4, ∡AOB also is central, and it is equal to the measure of the arc AB. As the line AC is the diameter of the circle O, the arc AC is equal to 180°, and thus, the sum of the angles 4 and 5 will be 180°:
[tex]\begin{gathered} \measuredangle4+\measuredangle5=180^{\circ} \\ \measuredangle4=180^{\circ}-\measuredangle5=180^{\circ}-74^{\circ}=106^{\circ} \end{gathered}[/tex]Thus, the angle 4 is 106°.
The angle 6 is an inscribed angle, and thus it is half of the arc it intersects, the arc AB. This means that the angle 6 is 106°/2=54°.
The angle 2 also is an inscribed angle, half of the arc BC, and thus, the angle 2 is 74°/2=37°.
Now, the triangle BOC has the angles 5, 6 and 7, and the sum of those angles is 180°. This means that:
[tex]\begin{gathered} \measuredangle5+\measuredangle6+\measuredangle7=180^{\circ} \\ 74^{\circ}+54^{\circ}+\measuredangle7=180^{\circ} \\ 128^{\circ}+\measuredangle7=180^{\circ} \\ \measuredangle7=180^{\circ}-128^{\circ}=52^{\circ} \end{gathered}[/tex]Thus, the angle 7 is 52°.
Following a same argument, we can get the angle 8, as being part of the triangle AOB.
[tex]\begin{gathered} \measuredangle2+\measuredangle4+\measuredangle8=180^{\circ} \\ \measuredangle8=180^{\circ}-37^{\circ}-106^{\circ}=37^{\circ} \end{gathered}[/tex]This means that the angle 8 is 37°.
As the line AD is tangent to the circle O, this means that the lines AC and AD are perpendicular, and thus, the angle 1 is 90°.
Lastly, as the angles 1, 2 and 3 are coplanar, their sum is 180°. This is:
[tex]\begin{gathered} \measuredangle1+\measuredangle2+\measuredangle3=180^{\circ} \\ \measuredangle3=180^{\circ}-\measuredangle1-\measuredangle2 \\ \measuredangle3=180^{\circ}-90^{\circ}-37^{\circ}=180^{\circ}-127^{\circ}=53^{\circ} \end{gathered}[/tex]Thus, the angle 3 is 53°.
Solve the inequality |3x+3| + 3 > 15Write the answer in interval notation
Answers
Solution:
Given the inequality:
[tex]|3x+3|+3>15[/tex]To solve the inequality,
step 1: Add -3 to both sides of the inequality.
Thus,
[tex]\begin{gathered} |3x+3|+3-3>-3+15 \\ \Rightarrow|3x+3|>12 \end{gathered}[/tex]Step 2: Apply the absolute rule.
According to the absolute rule:
[tex]\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad \mathrm{or}\quad \:u\:>\:a[/tex]Thus, from step 1, we have
[tex]\begin{gathered} 3x+3<-12\text{ or 3x+3>12} \\ \end{gathered}[/tex][tex]\begin{gathered} when \\ 3x+3<-12 \\ add\text{ -3 to both sides of the inequality} \\ 3x-3+3<-3-12 \\ \Rightarrow3x<-15 \\ divide\text{ both sides by the coefficient of x, which is 3} \\ \frac{3x}{3}<-\frac{15}{3} \\ \Rightarrow x<-5 \end{gathered}[/tex][tex]\begin{gathered} when \\ 3x+3>12 \\ add\text{ -3 to both sides of the inequality} \\ 3x+3-3>12-3 \\ \Rightarrow3x>9 \\ divide\text{ both sides by the coefficient of x, which is 3} \\ \frac{3x}{3}>\frac{9}{3} \\ \Rightarrow x>3 \end{gathered}[/tex]This implies that
[tex]x<-5\quad \mathrm{or}\quad \:x>3[/tex]Hence, in interval notation, we have:
[tex]\left(-\infty\:,\:-5\right)\cup\left(3,\:\infty\:\right)[/tex]Please tell me if these are correct if theyre not please help and tell me which ones are the right answers
Answers
Answer:
They're correct
Step-by-step explanation:
a plant is already 44 cm tall, and will grow one cm every month. let H be height in cm and M months. write and equation relating H to M . then use equation to find plants height after 32 months
Answers
H = height in cm
M = months
The plant is already 44 cm tall
GRowth every month = 1 cm
Equation:
H (m) = 44 + m
The height after m months, will be equal to the initial height (44) plus the number of months.
For 32 months, replace m by 32 and solve:
H (32) = 44+32
H (32) = 76 cm
After 32 months, the plant will be 76 cm tall
Which of the following measurements form a right triangle? Select all that apply.
Answers
We are asked to find which of the measurements form a right triangle.
A right triangle is a triangle that has an angle of 90°, and also we can use the Pythagorean theorem in them.
The Pythagorean theorem tells us that the sum of the two legs of the triangle squared is equal to the hypotenuse squared:
[tex]a^2+b^2=c^2[/tex]Where a and b are the legs of the triangle and c is the Hypotenuse. Also, in the right triangle, the hypotenuse is the longest side of the triangle.
We will use the Pythagorean theorem formula on all of the options using the first two given measures as a and b, and check that we the third measure as the value of c.
Option A. 7in, 24in, and 25 in.
We define:
[tex]\begin{gathered} a=7 \\ b=24 \end{gathered}[/tex]And apply the Pythagorean theorem:
[tex]7^2+24^2=c^2[/tex]And we solve for c. If the result for x is 25, the triangle will be a right triangle, if not, this will not be an answer.
-Solving for c:
[tex]\begin{gathered} 49+576=c^2 \\ 625=c^2 \end{gathered}[/tex]Taking the square root of both sides we find c:
[tex]\begin{gathered} \sqrt[]{625}=c \\ 25=c \end{gathered}[/tex]Since we get the third measure as the value of c option A is a right triangle.
Option B. 18ft, 23ft, and 29 ft.
we do the same as did with option A. First, define a and b:
[tex]\begin{gathered} a=18 \\ b=23 \end{gathered}[/tex]Apply the Pythagorean theorem:
[tex]18^2+23^2=c^2[/tex]And solve for c:
[tex]\begin{gathered} 324+529=c^2 \\ 853=c^2 \\ \sqrt[]{853}=c \\ 29.2=c \end{gathered}[/tex]We get 29.2 instead of just 29, thus option B is NOT a right triangle.
Option C. 10in, 24in, and 26 in.
Define a and b:
[tex]\begin{gathered} a=10 \\ b=24 \end{gathered}[/tex]Apply the Pythagorean theorem:
[tex]10^2+24^2=c^2[/tex]Solve for c:
[tex]\begin{gathered} 100+576=c^2 \\ 676=c^2 \\ \sqrt[]{676}=c \\ 26=c \end{gathered}[/tex]We get 26 which is the third measure given, thus, option C is a right triangle.
Option D. 10yd, 15yd, and 20yd.
Define a and b:
[tex]\begin{gathered} a=10 \\ b=15 \end{gathered}[/tex]Apply the Pythagorean theorem:
[tex]\begin{gathered} 10^2+15^2=c^2 \\ 100+225=c^2 \\ 325=c^2 \\ \sqrt[]{325}=c \\ 18.03=c \end{gathered}[/tex]We don't get 20yd as the value of c, thus, option D is NOT a right triangle.
Option E. 15mm, 18mm, and 24 mm
Define a and b:
[tex]\begin{gathered} a=15 \\ b=18 \end{gathered}[/tex]Apply the Pythagorean theorem
[tex]\begin{gathered} 15^2+18^2=c^2 \\ 225+324=c^2 \\ 549=c^2 \\ \sqrt[]{549}=c \\ 23.43=c \end{gathered}[/tex]We don't get 24 as the value of c, thus, option E is Not a right triangle.
Answer:
Option A and Option C are right triangles.