Let's say x is going to be the number meters of the width of the room:
x: width
Since its lenght is 1.8 as it is width, then it will be 1.8 · x long:
1.8x: lenght
Step 2: relating the expressions for each side to its perimeterWe know that the perimeter of a rectangle is given by
Perimeter = 2· (width + lenght)
We know that the perimeter is 29 meters, then
Perimeter = 29
↓
29 = 2· (width + lenght)
We do know an expression for its width and lenght, we replace them:
29 = 2· (width + lenght)
↓
29 = 2· (x + 1.8x)
Step 3: finding xSince x + 1.8x = 2.8x:
29 = 2· (x + 1.8x)
↓
29 = 2· (2.8x)
↓ 2· 2.8 = 5.6
29 = 5.6x
↓ dividing both sides by 5.6
29/5.6 = 5.6x/5.6
5.2 = x
Final step: finding its dimensionsSince
x: width
then
Width = 5.2 meters
Since
1.8x: lenght
then
Lenght = 1.8 · 5.2 meters = 9.36 meters
Answer: the dimensions of the room are Width = 5.2 meters and Lenght = 9.36 meters
Consider the function f(x)= square root 5x-10 for the domain [2, +infinity). find f^-1(x), where f^-1 is the inverse of f. also state the domain of f^-1 in interval notation.edit: PLEASE DOUBLE CHECK ANSWERS.
let f(x) = y
To find the inverse of f(x), we would interchange x and y:
[tex]\begin{gathered} y\text{ = }\sqrt[]{5x\text{ - 10}} \\ \text{Interchanging:} \\ x\text{ = }\sqrt[]{5y\text{ - 10}} \end{gathered}[/tex]Then we would make the subject of formula:
[tex]\begin{gathered} \text{square both sides:} \\ x^2\text{ = (}\sqrt[]{5y-10)^2} \\ x^2\text{ = 5y - 10} \end{gathered}[/tex][tex]\begin{gathered} \text{Add 5 to both sides:} \\ x^2+10\text{ = 5y} \\ y\text{ = }\frac{x^2+10}{5} \\ \text{The result above is }f^{\mleft\{-1\mright\}}\mleft(x\mright) \end{gathered}[/tex][tex]\begin{gathered} f^{\mleft\{-1\mright\}}\mleft(x\mright)\text{ = }\frac{x^2+10}{5} \\ The\text{ domain of the inverse is all real numbers} \\ \text{That is from negative infinity to positive infinity} \end{gathered}[/tex]In interval notation:
[tex]\begin{gathered} \text{Domain = (-}\infty,\text{ }\infty) \\ f^{\{-1\}}(x)\text{ = }\frac{x^2+10}{5}\text{for domain (-}\infty,\text{ }\infty) \end{gathered}[/tex]Write the decimal as a quotient of two integers in reduced form.
0.513
The given decimal can be written as a quotient of 513/1000.
What is quotient?
In maths, the result of dividing a number by any divisor is known as the quotient. It refers to how many times the dividend contains the divisor. The statement of division, which identifies the dividend, quotient, and divisor, is shown in the accompanying figure. The dividend 12 contains the divisor 2 six times. The quotient is always less than the dividend, whether it is larger or smaller than the divisor.
we can write the decimal given 0.513 as a answer of of 513 divided by 1000.
I.e.
[tex]0.513 = \frac{513}{1000}[/tex]
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there are approximately 1.2 x 10^8 households in the U.S. If the average household uses 400 gallons of water each day what is the total number of gallons of water used by households in the US each day ? Please Answer this im scientific notation
According to the given data we have the following:
total households in the US=1.2*10^8. hence:
[tex]1.2*10^8=120000000[/tex]average household uses 400 gallons of water each day
let x=total number of gallons of water used by households in the US each day
Therefore x=total households in the US*average gallons of water households uses each day
x=120,000,000*400
x=48,000,000,000
The total number of gallons of water used by households in the US each day is 48,000,000,000
The linear regressionequation andcorrelation coefficientfrom the above datawas calculated to be:Predicted y = 16.2+2.45(x) with r = 0.98What is the coefficientof determination?Answer Choices:A. Coefficient of determination = 0.98B. Coefficient of determination = 0.96C. Coefficient of determination = 0.99D. Coefficient of determination cannot be determined with only the given information.
Given:
[tex]\text{ coefficient of correlation \lparen r\rparen = 0.98}[/tex]To find:
Coefficient of determination
Explanation:
The coefficient of determination is also known as the R squared value, which is the output of the regression analysis method.
If the value of R square is zero, the dependent variable cannot be predicted from the independent variable.
So, here the required coefficient of determination is:
[tex]r^2=(0.98)^2=0.9604\approx0.96[/tex]Final answer:
Hence, the required coefficient of determination is (B) 0.96.
In the scoring for a game, points can be negative and positive. There were - 3.25 points scored 4 times, -2.75 points scored 5 times, 3 points scored 2 times, and 5.5 points scored 4 times. How many more times would 5.5 points need to be scored to have a total gain greater than 15 points?
A. 1
C. 3
B. 2
D. 4
The number of times that 5.5 points is need to be scored to have a total gain greater than 15 points is A. 1
How to calculate the value?From the information, it was stated that there were - 3.25 points scored 4 times, -2.75 points scored 5 times, 3 points scored 2 times, and 5.5 points scored 4 times.
In this case, the entire score will be:
= (-3.25 × 4) + (-2.75 × 5) + (3 × 2) + (5.5 ×4)
= -13 - 13.75 + 6 + 22
= 11.25
Therefore, the times that 5.5 points is needed to be scored to have a total gain greater than 15 will be 1 time since 11.25 + 5.5 = 16.75. This is more than 15.
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Plot Points & Graph Function (Table Given)
We have the next function
[tex]y=-\sqrt[]{x}+3[/tex]We need to calculate some points
x y
0 3
1 2
4 1
9 0
Let's plot the points and then we connect them in order to obtain the graph
I thought of a number. from ²/₇ parts of that number I subtracted 0,4 and got ⅗. The number is: A: ²⁄₇ B: ⅖ C: 3,5D: 4,5
Note : The use of comma as number separator represent point in this solution
Step 1: Let the number be x, thus, 2/7 parts of the number means
[tex]\frac{2}{7}x[/tex]Step 2: Subtract 0,4 from 2/7 parts of x
[tex]\frac{2}{7}x-0,4\Rightarrow\frac{2}{7}x-\frac{4}{10}[/tex]Step 3: Equate the expression above to 3/5
[tex]\frac{2}{7}x-\frac{4}{10}=\frac{3}{5}[/tex]Step 4: Simplify the equation above
[tex]\begin{gathered} \frac{2}{7}x-\frac{4}{10}=\frac{3}{5} \\ \frac{20x-28}{70}=\frac{3}{5}(\text{cross multiply)} \\ 5(20x-28)=70(3) \\ 100x-140=210 \\ 100x=210+140 \\ 100x=350 \\ \frac{100x}{100}=\frac{350}{100}(\text{Divide both side by 100)} \\ x=3,5 \end{gathered}[/tex]Hence, the number is 3,5
Option C is correct
The function f(x) = 40(0.9)^x represents the deer population in a forest x years after it was first studied. What was the deer population when it was first studied?a. 44b.40c. 36d.49
We are given the function that models a deer population:
[tex]f(x)=40(0.9)^x[/tex]Where x is the years since the study started. If we want to know the initial population, we want to find the population at x = 0 years.
Thus:
[tex]f(0)=40(0.9)^0=40\cdot1=40[/tex]The correct answer is option b. 40
An equation that can be used to determine the total
The equation that we have to build has the following form:
[tex]y=mx+b[/tex]• The fixed cost of the phone is $88, which will be represented by ,b,.
,• The variable cost per month is $116.43, which will be represented by ,m,.
,• y ,is the dependent variable that we want to know (, C(t) ,)
,• x ,is the independent variable, in our case, ,t,.
Replacing the values given in the problem we get:
[tex]C(t)=116.93t+88[/tex]The cost for 22 months will be:
[tex]C(22)=116.93\cdot22+88[/tex][tex]C(22)=2660.46[/tex]Answer:
• Equation
[tex]C(t)=116.93t+88[/tex]• Cost in 22 months: $2660.46
Determine the angle relationship. Drag the correct answer to the blank. what is the angle relationship of < 3 & <7
we have that
between m<3 and m<7 -----> no relationship (because q and p are not parallel)
Part 2
the relationship between m<12 and m<10
is
vertical angles
m<12=m<10 ------> by vertical angles
Let f(x) = 2x-1 and g(x) = x2 - 1. Find (f o g)(-7).
Answer: (f o g)(-7) = 95
Step by step solution:
We have the two functions:
[tex]\begin{gathered} f(x)=2x-1 \\ g(x)=x^2-1 \end{gathered}[/tex]We need to find (f o g)(-7) or f(g(-7)), first we evaluate g(-7):
[tex](f\circ g)(-7)=f(g(-7))[/tex][tex]g(-7)=-7^2-1=49-1=48[/tex]Now we evaluate f(48):
[tex]f(48)=2\cdot48-1=96-1=95[/tex]what is the slope for the following points?(-1,1) and(3,3)
To find the slope for a line that connects the given points, use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are the given points.
Use:
(x1,y1) = (-1,1)
(x2,y2) = (3,3)
replace the values of the previous parameters in the formula for m:
[tex]m\text{ = }\frac{3-1}{3-(-1)}=\frac{2}{3+1}=\frac{2}{4}=\frac{1}{2}[/tex]Hence, the slope is 1/2
Determine the common ratio for each of the following geometric series and determine which one(s) have an infinite sum.
I. 4+5+25/4+…
II. -7+7/4-7/9+…
III. 1/2-1+2…
IV. 4- ++...
A. III only
B. II, IV only
C. I, Ill only
D. I, II, IV only
The correct answer is Option A ( III Only). I . -16 sum cannot be negative, II. Not a G.P, III. Sum = 1/4, and IV. Not a G.P.
Solution:Given geometric series,
I. 4 +5 +25 /4 ….
The common ratio(r) is (5/1)/(4/1) = 5/4.
S∞ = a / ( 1 - r)
= 4 / ( 1 - 5/4)
= 4 / -1/4
S∞ = -16.
Since sum cannot be negative.
II . -7 + 7/3 - 7/9+ ....
Here common ratio = -7 / (7/3) = -1/3
but - 7/9 / 7 /3 = 7/9
Here there is no common ratio so this not a G.P.
iii. 1/2 -1 + 2.....
Common ratio = -1 / (1/2) = -2
S∞ = a / ( 1 - r)
= 1/2 / (1 -(-2))
S∞ = 1/4.
iv 4 - 8/5 +16/5.....
Here there is no common ratio.
So this is not a G.P.
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C) 1) if Z1 and 22 are complementary angles, and mZ1 = 74°; find m22.
Answer:
16
Explanation:
The angles ∠1 and ∠2 are complementary, meaning
[tex]\angle1+\angle2=90^o[/tex]Visually,
Now, ∠1 = 74; therefore,
[tex]74^o+\angle2=90^o[/tex]subtracting 74 from both sides gives
[tex]\angle2=90^o-74^o[/tex][tex]\angle2=16^o[/tex]which is our answer!
What is the measure of the base of the rectangle if the area of the triangle is 32 ft2 ?A) 8 ftB) 16 ft C) 32 ftD) 64 ft
Answer:
B) 16 ft
Explanation:
The area of a triangle is equal to
[tex]Area\text{ =}\frac{Base\times Height}{2}[/tex]We know that the area is 32 ft² and the height is 4 ft, so replacing these values, we get
[tex]32=\frac{\text{Base}\times4}{2}[/tex]Now, we can solve for the base. So multiply both sides by 2
[tex]\begin{gathered} 32\times2=\frac{\text{Base }\times4}{2}\times2 \\ 64=\text{Base }\times4 \end{gathered}[/tex]Then divide both sides by 4
[tex]\begin{gathered} \frac{64}{4}=\frac{Base\times4}{4} \\ 16=\text{Base} \end{gathered}[/tex]Therefore, the measure of the base is 16 ft
The data shows the total number of employee medical leave days taken for on-the-job accidents in the first six months of the year: 12, 6, 15, 9, 28, 12. Use the data for the exercise. Find the standard deviation.
ANSWER:
The standard deviation is 7
STEP-BY-STEP EXPLANATION:
The standard deviation formula is as follows
[tex]\sigma=\sqrt[]{\frac{\sum^N_i(x_i-\mu)^2_{}}{N}}[/tex]The first thing is to calculate the average of the sample like this:
[tex]\begin{gathered} \mu=\frac{12+6+15+9+28+12}{6} \\ \mu=\frac{82}{6}=13.67 \end{gathered}[/tex]Replacing and calculate the standard deviation:
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{(12_{}-13.67)^2_{}+(6_{}-13.67)^2_{}+(15_{}-13.67)^2_{}+(9_{}-13.67)^2_{}+(28-13.67)^2_{}+(12_{}-13.67)^2_{}}{6}} \\ \sigma=\sqrt[]{\frac{293.33}{6}} \\ \sigma=6.99\cong7 \end{gathered}[/tex]21. Juanita is packing a box that is 18 inches long and 9 inches high. The total volume of the box.1,944 cubic inches. Use the formula V = lwh to find the width of the box. Show your work
The width of the box is 12 inches
Explanations:
The formula for calculating the volume of a rectangular box is expressed as:
[tex]V=\text{lwh}[/tex]where:
• l is the ,length ,of the box
,• w is the ,width, of the box
,• h is the ,height ,of the box
Given the following parameters
• length = 18 inches
,• heigh = 9 inches
,• volume = 1,944 cubic inches
Substitute the given parameters into the formula to calculate the width of the box as shown:
[tex]\begin{gathered} 1944=18\times w\times9 \\ 1944=162w \end{gathered}[/tex]Divide both sides by 162 to have:
[tex]\begin{gathered} 162w=1944 \\ \frac{\cancel{162}w}{\cancel{162}}=\frac{1944}{162} \\ w=12\text{inches} \end{gathered}[/tex]Hence the width of the box is 12 inches
The product two consequences positive even numbers is 728. Find the smaller of the two numbers. The smaller number is
Let the first number = n
So second number = n+2
the product of number is 728.
That mean:
[tex]n(n+2)=728[/tex]Solve the equation:
[tex]\begin{gathered} n(n+2)=728 \\ n^2+2n=728 \\ n^2+2n-728=0 \end{gathered}[/tex][tex]\begin{gathered} n^2+2n-728=0 \\ n^2+28n-26n-728=0 \\ n(n+28)-26(n+28)=0 \\ (n+28)(n-26)=0 \\ n=-28;n=26 \end{gathered}[/tex]For positive number is n=26.
scond number is:
[tex]\begin{gathered} =n+2 \\ =26+2 \\ =28 \end{gathered}[/tex]So smaller number is 26.
The following distribution represents the number of credit cards that customers of a bank have. Find the mean number of credit cards.Number of cards X01234Probability P(X)0.140.40.210.160.09
To solve this problem we have a formula at hand: the mean (m) number of credits cards is
[tex]m=\sum ^{}_XX\cdot P(X)[/tex]Then,
[tex]m=0\cdot0.14+1\cdot0.4+2\cdot0.21+3\cdot0.16+4\cdot0.09=1.66[/tex]Pour subtracted from the product of 10 and a number is at most-20,
we have
four subtracted from the product of 10 and a number is at most-20
Let
n ----> the number
so
[tex]10n-4\leq-20[/tex]solve for n
[tex]\begin{gathered} 10n\leq-20+4 \\ 10n\leq-16 \\ n\leq-1.6 \end{gathered}[/tex]the solution for n is the interval (-infinite, -1.6]
All real numbers less than or equal to negative 1.6
Find an equation of the line. Write the equation using function notation.
Through (4, -1); perpendicular to 4y=x-8
The equation of the line is f(x) =
The equation of line perpendicular to 4y = x-8 passing through (4,-1) is:
[tex]y = -4x+15[/tex].
What is a equation of line?These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.
Given equation of line is:
4y=x-8
We have to convert the given line in slope-intercept form to find the slope of the line
Dividing both sides by 4.
[tex]y = \frac{1}{4}x-2[/tex]
Let [tex]m_{1}[/tex] be the slope of given line
Then,
[tex]m_{1}[/tex] = [tex]\frac{1}{4}[/tex]
Let [tex]m_{2}[/tex] be the slope of line perpendicular to given line
As we know that product of slopes of two perpendicular lines is -1.
[tex]m_{1}*m_{2} = -1\\\frac{1}{4}*m_{2}=-1\\ m_{2} = -4[/tex]
The slope intercept form of line is given by
[tex]y = m_{2}x+c[/tex]
[tex]y = -4x+c[/tex]
to find the value of c, putting (4,-1) in equation
[tex]-1 = -4*4+c\\-1+16 = c\\c = 15[/tex]
Putting the value of c in the equation
[tex]y=-4x+15[/tex]
Hence, The equation of line perpendicular to 4y = x-8 passing through (4,-1) is [tex]y = -4x+15[/tex].
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I need a math tutor asap .
For this exercise you need to remember that a Cube is a solid whose volume can be calculated using the following formula:
[tex]V=s^3[/tex]Where "V" is the volume of the cube and "s" is the length of any edge of the cube (because all the edges of a cube have the same length).
For example, if you have a cube and you know that:
[tex]s=5\operatorname{cm}[/tex]You can substitute this value into the formula and then evaluate, in order to find the volume of the cube. This would be:
[tex]\begin{gathered} V=(5\operatorname{cm})^3 \\ V=125\operatorname{cm}^3 \end{gathered}[/tex]The answer is:
You can find it using the formula
[tex]V=s^3[/tex]Where "s" is the length of any edge of the cube
Given two functions f(x) and g(x):f(x) = 8x - 5,8(x) = 2x2 + 8Step 1 of 2 Form the composition f(g(x)).Answer 2 PointsKeypadKeyboard Shortcutsf(g(x)) =>Next
we have the functions
[tex]\begin{gathered} f(x)=8x-5 \\ g(x)=2x^2+8 \end{gathered}[/tex]Find out f(g(x))
Substitute the variable x in the function f(x) by the function g(x)
so
[tex]\begin{gathered} f\mleft(g\mleft(x\mright)\mright)=8(2x^2+8)-5 \\ f(g(x))=16x^2+64-5 \\ f(g(x))=16x^2+59 \end{gathered}[/tex]Which 3 pairs of side lengths are possible measurements for the triangle?
SOLUTION
From the right triangle with two interior angles of 45 degrees, the two legs are equal in length, that is AB = BC
And from Pythagoras, the square of the hypotenuse (AC) is equal to the square of the other two legs or sides (AB and AC)
So this means
[tex]\begin{gathered} |AC|^2=|AB|^2+|BC|^2 \\ since\text{ AB = BC} \\ |AC|^2=2|AB|^2,\text{ also } \\ |AC|^2=2|BC|^2 \end{gathered}[/tex]So from the first option
[tex]\begin{gathered} BC=10,AC=10\sqrt{2} \\ |AC|^2=(10\sqrt{2})^2=100\times2=200 \\ 2|BC|^2=2\times10^2=2\times100=200 \end{gathered}[/tex]Hence the 1st option is correct, so its possible
The second option
[tex]\begin{gathered} AB=9,AC=18 \\ |AC|^2=18^2=324 \\ 2|AB|^2=2\times9^2=2\times81=162 \\ 324\ne162 \end{gathered}[/tex]Hence the 2nd option is wrong, hence not possible
The 3rd option
[tex]\begin{gathered} BC=10\sqrt{3},AC=20 \\ |AC|^2=20^2=400 \\ 2|BC|^2=2\times(10\sqrt{3})^2=2\times100\times3=600 \\ 400\ne600 \end{gathered}[/tex]Hence the 3rd option is wrong, not possible
The 4th option
[tex]\begin{gathered} AB=9\sqrt{2},AC=18 \\ |AC|^2=18^2=324 \\ 2|AB|^2=2\times(9\sqrt{2})^2=2\times81\times2=324 \\ 324=324 \end{gathered}[/tex]Hence the 4th option is correct, it is possible
The 5th option
AB = BC
This is correct, and its possible
The last option
[tex]\begin{gathered} AB=7,BC=7\sqrt{3} \\ 7\ne7\sqrt{3} \end{gathered}[/tex]This is wrong and not possible because AB should be equal to BC
Hence the correct options are the options bolded, which are
1st, 4th and 5th
Alexa claims that the product of 2.3 and 10^2 is 0.23. Do you agree or disagree? Explain why or why not?
Answer:
disagree
Step-by-step explanation:
product = 2.3 * 10²
= 2.3 * 100
= 230
thus, the answer is different from the one acclaimed by Alexa.
The House of Pizza say that their pizzas are 14 inches wide, but when you measured it, the pizza was 12 inches. What is your percent error? Make sure to include your percent sign! (Round to 2 decimals)
The percent error of the house of the pizza would be 2.
The difference between the estimated and actual values in comparison to the actual value is expressed as a percentage. In other words, the relative error multiplied by 100 equals the percent error.
How to calculate the percent error?Percent errors indicate the magnitude of our errors when measuring something in an analysis process. Lower percentage errors indicate that we are getting close to the accepted or original value.
Suppose the actual value and the estimated values after the measurement are obtained. Then we have:
Error = Actual value - Estimated value
To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.
We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.
WE know that Error = Actual value - Estimated value
Then Error = 14 - 12 = 2
Therefore, the percent error would be 2.
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What is the value of 3-(-2) how can I solve this questions
Explanation:
[tex]\text{Given: }3-\mleft(-2\mright)[/tex]To find the value od 3-(-2), we will multiply the sign at the outer with the inner
[tex]undefined[/tex]help meeeeeeeeee pleaseee !!!!!
Because x is continuous, we should use interval notation, the domain is:
D: [1, ∞)
How to find the domain?For a function y = f(x), we define the domain as the set of possible inputs of the function (possible values of x).
To identify the domain, we need to look at the horizontal axis. The minimum value is the one we can see in the left side, and the maximum is the one we could see on the right side.
There we can see that the domain starts at x = 1 and extends to the left, so the notation we can use for the domain is:
D: x ≥ 1
We know that the value x =1 belongs because there is a closed dot there.
The correct option is A, because the domain is continuous (as we can see in the graph), we should use interval notation. In this case the domain can be written as:
D: [1, ∞)
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The graph of function f is shown. The graph of an exponential function passes through (minus 0.25, 10), (0, 6), (5, minus 2) also intercepts the x-axis at 1 unit. Function g is represented by the table. x -1 0 1 2 3 g(x) 15 3 0 - 3 4 - 15 16 Which statement correctly compares the two functions? A. They have the same y-intercept and the same end behavior as x approaches ∞. B. They have the same x-intercept but different end behavior as x approaches ∞. C. They have the same x- and y-intercepts. D. They have different x- and y-intercepts but the same end behavior as x approaches ∞.
The given data points from the graph of the exponential function, f, and the, values from the table of the function g, gives the statement that correctly compares the two functions as the option;
B. They have the same x–intercept but different end behaviours as x approaches ∞What is the end behaviour of a graph?The end behaviour of a function is the description of how the function behaves towards the boundaries of the x–axis.
The given points on the exponential function, f, are;
(-0.25, 10), (0, 6), (5, -2) and also the x–intercept (1, 0)
The points on the function g, obtained from the table of the values for g(x), expressed as ordered pairs are;
(-1, 15), (0, 3), (1, 0), (2, -34), (3, -16)
The coordinates of the x–intercept is given by the point where the y–value is zero.
The x–intercept for the exponential function, f, is therefore (1, 0)
Similarly, the x–intercept for the function, g, is (1, 0)
Therefore, both functions have the same x–intercept
However, the end behaviour of the function, f, as the x approaches infinity is that f(x) approaches negative infinity, while the end behaviour of the function, g, as the the value of x approaches infinity is g(x) is increasing towards positive infinity.
The correct option is therefore;
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name the three congruent parts shown by the marks on each drawing
In this case the aswer is very simple. .
The congruent parts are the equal parts in the 2 triangles.
Therefore, the congruent parts would be:
1. side AB and side XY
2. ∠ A and ∠ X
3. side AC and side XZ
That is the solution. .