Answers
The given equations are
[tex]-x+4y=7[/tex][tex]6x-3y=42[/tex]To find the answer we need to cancel out x or y.
so we have to find the LCM of the coefficients of the corresponding variable.
consider the coefficients of x is -1 in the first equation and 6 in the second equation .
Lcm of -1 and 6 is 6.
Multiplying the first equation by 6.
consider the coefficients of y is 4 in the first equation and -3 in the second equation .
Lcm of 4 and 3 is 12
Multiplying the first equation by 3 and the second equation by 4.
Either one of these is the first step to eliminate variables.
Amswer os
Related Questions
Tonya leaves home on her motorcycle and travels 12 miles east and 7 miles north. How far in Tonya from her original starting point?
Answers
The distance is 13.892 miles.
Given:
Distance travelled in east is 12 miles.
Distance travelled in north is 7 miles.
The objective is to find how far is tonya from the starting point.
The distance between starting point and ending point can be calculated using Pythagorean theorem.
Consider the given figure as,
By applying Pythagorean theorem,
[tex]AC^2=AB^2+BC^2[/tex]Now, substitute the given values in the above formula.
[tex]\begin{gathered} x^2=12^2+7^2 \\ x^2=144+49 \\ x^2=193 \\ x=\sqrt[]{193} \\ x=13.892 \end{gathered}[/tex]how do I know what exponent and base I use when I simplify an exponent, for example, 16^1/4 become (2^4)^1/4 which becomes 2. How do I know I have to use 2^4 instead of another number like 4^2 that is still equal to 16. Why can't I use a different number that is equal to the same thing?
Answers
Answer:
Reason:
16^1/4=(2^4)^1/4
Explanation:
You can use either 4^2 or 2^4 both gives the same answer.
In order to simplify the steps we use 2^4.
we get,
[tex]16^{\frac{1}{4}^{}^{}}=(2^4)^{\frac{1}{4}}[/tex][tex]=2^{4\times\frac{1}{4}}[/tex]4 in the power got cancelled and we get,
[tex]=2[/tex]Alternate method:
If we use 4^2 we get,
[tex]16^{\frac{1}{4}}=(4^2)^{\frac{1}{4}}[/tex][tex]=4^{2\times\frac{1}{4}}[/tex][tex]=4^{\frac{1}{2}}[/tex]we use 4=2^2,
[tex]=(2^2)^{\frac{1}{2}}=2[/tex]In order to get answer quicker we appropiately use 2^4=16 here.
Rules in exponent:
[tex]a^n\times a^m=a^{n+m}[/tex][tex]\frac{a^n}{a^m}=a^{n-m}[/tex][tex]\frac{1}{a^m}=a^{-m}[/tex][tex](a^n)^m=a^{n\times m}[/tex][tex]4^{3\times\frac{1}{2}}=4^{\frac{3}{2}}[/tex]use 4=2^2, we get
[tex]=2^{2\times\frac{3}{2}}[/tex]2 got cancelled in the power, we get
[tex]=2^3[/tex][tex]=8[/tex]we get,
[tex]4^{3\times\frac{1}{2}}=8[/tex]As a fraction in simplest terms, what would you multiply the first number by to get the second? First number: 56 Second number: 57
Answers
We're asked to find a number x such that by being multiplied by 36 becomes 57, so we need
[tex]\begin{gathered} 56x=57 \\ x=\frac{57}{56} \end{gathered}[/tex]then
[tex]56(\frac{57}{56})=57[/tex]Evaluate the expression. 2 13 21 The value of the expression is
Answers
To solve the exercise you can use the following property of powers
[tex](\frac{a}{b})^n=\frac{a^n}{b^n}[/tex]Then, you have
[tex]\begin{gathered} |(\frac{-1}{2})^3\div(\frac{1}{4})^2|=|\frac{(-1)^3}{(2)^3}^{}\div\frac{(1)^2}{(4)^2}^{}| \\ |(\frac{-1}{2})^3\div(\frac{1}{4})^2|=|\frac{-1^{}}{8}^{}\div\frac{1}{16}^{}| \end{gathered}[/tex]Now, apply the definition of fractional division, that is
[tex]\frac{a}{b}\div\frac{c}{d}=\frac{a\cdot d}{b\cdot c}[/tex][tex]\begin{gathered} |(\frac{-1}{2})^3\div(\frac{1}{4})^2|=|\frac{-1^{}\cdot16}{8\cdot1}^{}| \\ |(\frac{-1}{2})^3\div(\frac{1}{4})^2|=|\frac{-1^{}6}{8}^{}| \\ |(\frac{-1}{2})^3\div(\frac{1}{4})^2|=|-2| \end{gathered}[/tex]Finally, apply the definition of absolute value, that is, it is the distance between a number and zero. The distance between -2 and 0 is 2.
Therefore, the value of the expression is 2.
[tex]\begin{gathered} |(\frac{-1}{2})^3\div(\frac{1}{4})^2|=|-2| \\ |(\frac{-1}{2})^3\div(\frac{1}{4})^2|=2 \end{gathered}[/tex]15. A beekeeper estimates that his bee population will triple each year.
Answers
Answer:
[tex]P\mleft(x\mright)=150(3^x)[/tex]Explanation:
The initial number of bees = 150
[tex]P(0)=150[/tex]The beekeeper estimates that his bee population will triple each year. Thus, after 1 and 2 years:
[tex]\begin{gathered} P(1)=150\times3 \\ P(2)=150\times3\times3=150\times3^2 \end{gathered}[/tex]Continuing in like manner, after x years:
[tex]P(x)=150(3^x)[/tex]P(x) is the required function.
How does the value of 1 in Maisha’s time compare with the value of 1 in Patti’s time?
Answers
Please help me find the inverse of f(x) = 2^x. I think that will help me label these?
Answers
Given function:
[tex]f(x)=2^x[/tex]To obtain the inverse of the function f(x), we follow the steps outlined below:
Step 1: Replace f(x) with y:
[tex]y=2^x[/tex]Step 2: Interchange x and y
[tex]x=2^y[/tex]Step 3: Solve for y:
[tex]\begin{gathered} \text{Take logarithm of both sides} \\ \log x=log2^y \\ y\log 2\text{ = log x} \\ \text{Divide both sides by log2} \\ y\text{ = }\frac{\log x}{\log \text{ 2}} \\ y\text{ = }\log _2x \end{gathered}[/tex]Step 4: Replace y with f-1(x):
[tex]f^{-1}(x)\text{ = }\log _2x[/tex]Answer:
[tex]f^{-1}(x)\text{ = }\log _2x[/tex]PDonald has xxx twenty-dollar bills and 111 ten-dollar bill
Answers
the equation for this problem is
20x +10
where x is the number of bills with 20-dollars
You are choosing 4 of your 7 trophies and arranging them in a row on a shelfIn how many different ways can you choose and arrange the trophies?A. 840B. 28C. 24D. 5040
Answers
The formula to find how many different ways are there to choose a subgroup of r things from a group of n things is
[tex]\frac{n!}{(n-r)!}[/tex]Here, you have 7 trophies and you want to choose 4 of them, so you have
[tex]\frac{7!}{(7-4)!}\text{ = }\frac{5040}{6}=840[/tex]So there are 840 ways to choose your 4 trophies out of the 7 you have.
Write 3.6x10^-4 in standard form
Answers
In order to write the given number in standard form, you take into account that the factor 10^(-4) can be written as follow:
[tex]10^{-4}=\frac{1}{10^4}[/tex]Next, you consider that the number of the exponent in a 10 factor means the number of zeros right side number 1:
[tex]\frac{1}{10^4}=\frac{1}{10000}[/tex]that is, there are four zeros right side of number 1.
Finally, you write the complete number:
[tex]3.6\times10^{-4}=\frac{3.6}{10^4}=\frac{3.6}{10000}[/tex]What is 44.445 to the nearest hundredth
Answers
Answer:
44.45
Explanation:
Given 44.445
We are to convert to the nearest hundredth
Since the last value at the back is greater than 4, we will add 1 to the preceding value behind it to make it 5 as shown
44.445 = 44.4(4+1) [1 is added to the second value from the back
44.445 = 44.45
Hence the value to nearest hundredth is 44.45
Which products are greater than 2 5/6?A.1/8 × 2 5/6B.2 5/6 × 2 5/6C.2 5/6 × 1 5/8D.5/6 × 2 5/6E.6/5 × 2 5/6
Answers
First, we need to change the mixed number to an improper fraction:
[tex]2\frac{5}{6}=\frac{(6\cdot2)+5}{6}=\frac{17}{6}\approx2.83[/tex]Now let's evaluate each of the options:
A.
[tex]\frac{1}{8}\times2\frac{5}{6}=\frac{1}{8}\times\frac{17}{6}=\frac{1\cdot17}{8\cdot6}=\frac{17}{48}\approx0.354[/tex]B.
[tex]2\frac{5}{6}\times2\frac{5}{6}=\frac{17}{6}\times\frac{17}{6}=\frac{17\cdot17}{6\cdot6}=\frac{289}{36}\approx8.02[/tex]C.
[tex]2\frac{5}{6}\times1\frac{5}{8}=\frac{17}{6}\times\frac{13}{8}=\frac{17\cdot13}{6\cdot8}=\frac{221}{48}\approx4.60[/tex]D.
[tex]\frac{5}{6}\times2\frac{5}{6}=\frac{5}{6}\times\frac{17}{6}=\frac{5\cdot17}{6\cdot6}=\frac{85}{36}\approx2.36[/tex]E.
[tex]\frac{6}{5}\times2\frac{5}{6}=\frac{6}{5}\times\frac{17}{6}=\frac{6\cdot17}{5\cdot6}=\frac{17}{5}\approx3.4[/tex]Now, we can conclude that options B, C, and E are greater than 2 5/6.
what is the fill in for the diagram drop downs drop down 1: is it a reflexive property, equivalent equation or transitive property of equality.drop down 2: does it have subtraction property of equality, divison of equality or reflexive property and lastly drop down 3: is it a substitution, equivalent equation or subtraction property of equality
Answers
Remember the following properties of real numbers:
Reflexive property:
This property states that a number is always equal to itself.
This property is different from the equivalent equations property. In fact, two equations that have the same solution are called equivalent equations,
Division property of equality:
This property states that when we divide both sides of an equation by the same non-zero number, the two sides remain equal.
Substitution property of equality:
This property states that if x = y, then x can be substituted in for y in any equation.
We can conclude that the correct answer is:
Answer:Drop Down 1: reflexive property
Drop Down 2: division property of equality.
Drop Down 3: substitution
what are the consecutive perfect cubes which added to obtain a sum of 100?441?
Answers
Answer:add 341 more cubes and that shall be your answer
1,2, 3 and 4 are the consecutive perfect cubes which added to obtain a sum of 100.
What is Number system?A number system is defined as a system of writing to express numbers.
Consecutive perfect cubes which added to obtain a sum of 100
Perfect cubes are the numbers that are the triple product of the same number.
1³+2³+3³+4³
One cube plus two ube plus three cube plus four cube
1+8+27+64
One plus eight plus twenty seven plus sixty four.
100
1,2, 3 and 4 are the consecutive perfect cubes which added to obtain a sum of 100.
Hence, 1,2, 3 and 4 are the consecutive perfect cubes which added to obtain a sum of 100.
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ2
Find the distance between (-4, 2) and (10, 2) c. -14d. 14
Answers
The distance between two points (a, b) and (c, d) is given by:
[tex]\sqrt[]{(c-a)^2+(d-b)^2}[/tex]For points (-4, 2) and (10, 2), we have:
a = -4
b = 2
c = 10
d = 2
Thus, the distance between those points is
[tex]\sqrt[]{\lbrack10-(-4)\rbrack^2+(2-2)^2}=\sqrt[]{(10+4)^2+0}=\sqrt[]{14^2}=14[/tex]Therefore, the answer is 14.
I tried but immediately got confused on what to start with
Answers
Radius of the inscribed circle.
Given:
Side length of square = 8cm
From the diagram, the circumference of the inscribed circle touches the sides of the square. Hence, we can say that the diameter of the inscribed circle is equal to the side length of the square.
The diagram below shows this relationship
We know that the radius (r) is related to the diameter (d) as
=O REAL NUMBERSDistributive property: Integer coefficientsUse the distributive property to remove the parentheses.+(-5u-+*+4)INOPX 5 ?
Answers
The given expression is:
[tex]-(-5u-x+4)[/tex]Using the distributive property of multiplication over addition, we have
[tex]\begin{gathered} -(-5u-x+4)=-(-5u)-(-x)-(+4) \\ =+5u+x-4=5u+x-4 \end{gathered}[/tex]Therefore, removing the paranthesis gives:
5u + x - 4
.
Carolyn has a circular swimming pool with a diameter of 20 feet. She needs to know the area of the bottom of the pool so that she can find out how much paint to buy for it. What is the approximate area?
Answers
To find the area of the bottom we have to use the formula to find the area of a circle:
[tex]A=\pi r^2[/tex]Where A is the area and r is the radius.
The first step is to find the radius of the circle, which is half the diameter:
[tex]\begin{gathered} r=\frac{D}{2} \\ r=\frac{20ft}{2} \\ r=10ft \end{gathered}[/tex]Replace r in the given formula and use 3.14 as pi:
[tex]\begin{gathered} A=3.14\cdot(10ft)^2 \\ A=314ft^2 \end{gathered}[/tex]The answer is 314ft^2.
Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R(P) = -9p2 + 18,000p. What unitprice should be established for the dryer to maximize revenue? What is the maximum revenue?
Answers
Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R(P) = -9p2 + 18,000p. What unit
price should be established for the dryer to maximize revenue? What is the maximum revenue?
we have the quadratic equation
[tex]R(p)=-9p^2+18,000p[/tex]this is a vertical parabola, open downward
the vertex represents a maximum
Convert to factored form
Complete the square
factor -9
[tex]R(p)=-9(p^2-2,000p)[/tex][tex]R(p)=-9(p^2-2,000p+1,000^2-1,000^2^{})[/tex][tex]\begin{gathered} R(p)=-9(p^2-2,000p+1,000^2)+9,000,000 \\ R(p)=-9(p^{}-1,000)^2+9,000,000 \end{gathered}[/tex]the vertex is the point (1,000, 9,000,000)
therefore
the price is $1,000 and the maximum revenue is $9,000,000Problem N 2
we have the equation
[tex]C(x)=0.7x^2+26x-292+\frac{2800}{x}[/tex]using a graphing tool
the minimum is the point (8.58,308.95)
therefore
Part a
the average cost is minimized when approximately 9 lawnmowers ........
Part b
the minimum average cost is approximately $309 per mower
Given that the points (-2, 10), (5, 10), (5, 1), and (-2, 1) are vertices of a rectangle, how much longer is the length than the width? A) 1 unit B) 2 units 0) 3 units D) 4 units E) 5 units
Answers
The length of both sides is obtained by subtracting one coordinate from another sharing a similar coordinate.
(-2,10) - (5,10) = (-7,0)
These points are 7 units apart.
Let's compare the other length.
(5,10) - (5,1) = ( 0, -9)
These points are 9 units apart.
Therefore, the length is longer than the breadth by 9 - 7 = 2 units
Option B
I need help with statistical problem I have got the answer of 0.3354 because I subtracted 0.9991 - 0.146 I wanted to know if that was correct I kept getting the answer wron
Answers
From the quetion
We are given a normal distribution with mean = 0 and standard deviation = 1
The sketch of the distribution is as shown below
Therefore option C is the correct answer
We are to find the probability that a given score is between -2.18 and 3.74
The probability is
[tex]P\mleft(-2.18Therefore,The probability is 0.9853
Mr. Eric’s business class has 91 students, classified by academic year and gender, As illustrated in the following table. Mr. Eric randomly chooses one student to collect yesterday’s work. What is the probability that he selects a female, given that he chooses randomly from only the juniors? Express your answer as a fraction.
Answers
Given:
Eric’s business class has 91 students
Mr. Eric randomly chooses one student to collect yesterday’s work
We will find the probability that he selects a female, given that he chooses randomly from only the juniors
As shown from the table:
The number of females from the juniors = 6
The number of juniors = 6 +13 = 19
So, the probability will be =
[tex]\frac{6}{19}[/tex]Set B and Set C are grouped according to the Venn Diagram below. Set B is (9, 12, 14, 17, 18) and Set C is (6,9,11, 12, 18, 19). The sample space is (1, 6, 9, 11, 12, 14, 17, 18, 19, 20).
Answers
To get the probability of an event to occur, we have the following formula:
[tex]P=\frac{no.\text{ of favorable outcomes}}{\text{total no. of possible outcomes}}[/tex]According to the problem, the sample space is (1, 6, 9, 11, 12, 14, 17, 18, 19, 20) therefore, the total no. of possible outcomes is 10.
For Set B, the sample is (9, 12, 14, 17, 18), therefore, there are 5 possible outcomes that belong to set B.
Starting with the first question, what is the probability of Set B to occur?
[tex]P=\frac{no.\text{ of outcomes from B}}{\text{total no. of possible outcomes}}=\frac{5}{10}=\frac{1}{2}=0.50=50\text{ percent}[/tex]For Set C, the sample is (6,9,11, 12, 18, 19) therefore, there are 5 possible outcomes that belong to set C as well.
On the next question, what is the probability of Set C to occur?
[tex]P=\frac{no.\text{ of outcomes from C}}{\text{total no. of possible outcomes}}=\frac{5}{10}=\frac{1}{2}=0.50=50\text{ percent}[/tex]For the third question, what is the probability of Set B or C to occur?
Since the outcomes under B or C are (6, 9, 11, 12, 14, 17, 18, 19), the probability of the union of B and C is:
[tex]P=\frac{no.\text{ of outcomes from B or C}}{\text{total no. of possible outcomes}}=\frac{8}{10}=\frac{4}{5}=0.80=80\text{ percent}[/tex]On to the last question, what is the probability of the intersection of B and C to occur?
Since the outcomes that are found on both B and C are (9,12,18), the probability of the intersection of B and C is:
[tex]P=\frac{no.\text{ of outcomes found on both B and C}}{\text{total no. of possible outcomes}}=\frac{3}{10}=0.30=30\text{ percent}[/tex]Write an equation for the area and solve the equation for x.
Answers
Given the figure of a rectangle
The area = A = 26
Length = x + 6
width = x + 2
Area = length * Width
so, the equation of the area will be:
[tex]A=(x+6)(x+2)[/tex]so,
[tex](x+6)(x+2)=26[/tex]solve for x as follows:
[tex]\begin{gathered} x^2+8x+12=26 \\ x^2+8x+12-26=0 \\ x^2+8x-14=0 \\ \end{gathered}[/tex]Use the general rule to find the value of x
So,
[tex]\begin{gathered} a=1,b=8,c=-14 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{-8\pm\sqrt[]{64-4\cdot1\cdot-14}}{2\cdot1} \\ \\ x=\frac{-8\pm\sqrt[]{120}}{2}=\frac{-8\pm2\sqrt[]{30}}{2}=-4\pm\sqrt[]{30} \end{gathered}[/tex]So, the answer will be:
[tex]\begin{gathered} A=(x+6)(x+2)_{} \\ \\ x=-4+\sqrt[]{30},-4-\sqrt[]{30} \end{gathered}[/tex]THE GRAPH OF THIS SYSTEM OF LINEAR INEQUALITIES IS X-2Y< OR EQUAL 6 X> OR EQUAL TO 0 Y< OR EQUAL TO 2GRAPH
Answers
The graph of the system of linear inequalities x - 2y ≤ 6 , x ≥ 0 and y ≤ 2 is attached below.
The system of linear inequalities is x - 2y ≤ 6 , x ≥ 0 and y ≤ 2
The solution set of x ≥ 0 includes {x ∈ R , x ≥ 0 }
The solution set of y ≤ 2 includes {y ∈ R , y ≤ 2 }
The solution set of x - 2y ≤ 6 , shows the region of the graph that is below the straight line x - 2y = 6 .
Let us now plot the graph of the straight line x - 2y = 6 with the slope of -1/2 .
At x = 0 , y = - 3
At x = 2 , y = - 2
At x = -4 , y = - 5
hence the graph will pass through the points (0,-3) , (2,-2) and (-4,-5)
The line x = 0 indicates the x-axis and the line y=2 indicates the straight line parallel to x axis passing through (0,2) .
The shaded region of the graph indicates the solution set of the system of inequalities.
To learn more about inequality visit:
brainly.com/question/20383699
#SPJ9
What is the y intercept of this table?Х 0,3,6. y 5,11,17
Answers
We are given a table of x-values and their corresponding y values for a function. We are asked to express the y-intercept.
Since the table reads that for x= 0 the associated value id y = 5, then right from that info we can say that the function intercepts the y axis at the point y=5.
In coordinate pair point it reads like: (0, 5)
Recall that the y-intercept is the point at which the function crosses the y-axis, and that happens when x = 0.
Consider the line y=7x-7Find the equation of the line that is perpendicular to this line and passes through the point (-8,5) Find the equation of the line that is parallel to this line and passes through the point (-8,5)
Answers
Given:
The equation of a straight line is,
[tex]y=7x-7[/tex]The objective is to find,
a) The equation of perpendicular line passes throught the point (-8,5).
b) The equation of parallel line passes throught the point (-8,5).
Explanation:
The general equation of straight line is,
[tex]y=mx+c[/tex]Here, m represents the slope of the straight line and c represents the y intercept.
a)
For perpendicular lines, the prouct of slope of two lines will be (-1).
By comparing the general equation and the given equation the slope value will be,
[tex]m_1=7[/tex]Now, the slope value of perpendicular line can be calculated as,
[tex]\begin{gathered} m_1\times m_2=-1 \\ 7\times m_2=-1 \\ m_2=-\frac{1}{7} \end{gathered}[/tex]Since, the perpendicular line passes through the point (-8,5), the equation of line can be calculated using point slope formula.
[tex]\begin{gathered} y-y_1=m_2(x-x_1)_{} \\ y-5=-\frac{1}{7}(x-(-8)) \\ y-5=-\frac{1}{7}(x+8) \\ y-5=-\frac{x}{7}-\frac{8}{7} \\ y=-\frac{x}{7}-\frac{8}{7}+5 \\ y=-\frac{x}{7}-\frac{8}{7}+\frac{35}{7} \\ y=-\frac{x}{7}+\frac{27}{7} \end{gathered}[/tex]Hence, the equation of perpendicular line is obtained.
b)
For paralle lines the slope value will be equal for both lines.
[tex]m_1=m_3=7[/tex]Since, the parallal line passes through the point (-8,5), the equation of line can be calculated using point slope formula.
[tex]\begin{gathered} y-y_1=m_3(x-x_1) \\ y-5=7(x-(-8)) \\ y-5=7(x+8) \\ y-5=7x+56 \\ y=7x+56+5 \\ y=7x+61 \end{gathered}[/tex]Hence, the equation of parallel line is obtained.
Find the indicated values for the function f(x)= Answer all that is shown
Answers
For this problem, we are given a certain function and we need to evaluate it in various points.
The function is given below:
[tex]f(x)=\sqrt{5x-15}[/tex]The first value we need to calculate is f(4), we need to replace x with 4 and evaluate the expression.
[tex]f(4)=\sqrt{5\cdot4-15}=\sqrt{20-15}=\sqrt{5}=2.24[/tex]The second value we need to calculate is f(3), we need to replace x with 3 and evaluate the expression.
[tex]f(3)=\sqrt{5\cdot3-15}=\sqrt{15-15}=0[/tex]The third value we need to calculate is f(2), we need to replace x with 2 and evaluate the expression.
[tex]f(2)=\sqrt{5\cdot2-15}=\sqrt{10-15}=\sqrt{-5}[/tex]The value for this is not real.
Given that line AB is tangent to the circle, find m
Answers
Solution:
Given the figure below:
To solve for m∠CAB, we use the chord-tangent theorem which states that when a chord and a tangent intersect at a point, it makes angles that are half the intercepted arc.
Thus,
[tex]m\angle CAB=\frac{1}{2}\times arc\text{ CDB}[/tex]where
[tex]\begin{gathered} m\angle CAB=(4x+37)\degree \\ arc\text{ CDB=\lparen9x+53\rparen}\degree \end{gathered}[/tex]By substituting these values into the above equation, we have
[tex]4x+37=\frac{1}{2}(9x+53)[/tex]Multiplying through by 2, we have
[tex]\begin{gathered} 2(4x+37)=(9x+53) \\ open\text{ parentheses,} \\ 8x+74=9x+53 \end{gathered}[/tex]Collect like terms,
[tex]\begin{gathered} 8x-9x=53-74 \\ \Rightarrow-x=-21 \\ divide\text{ both sides by -1} \\ -\frac{x}{-1}=-\frac{21}{-1} \\ \Rightarrow x=21 \end{gathered}[/tex]Recall that
[tex]\begin{gathered} m\operatorname{\angle}CAB=(4x+37)\operatorname{\degree} \\ where \\ x=21 \\ thus, \\ m\operatorname{\angle}CAB=4(21)+37 \\ =84+37 \\ \Rightarrow m\operatorname{\angle}CAB=121\degree \end{gathered}[/tex]Hence, the measure of the angle CAB is
[tex]121\degree[/tex]which of the following is an even fonction?
g(x)=(x-1)² +1
9(x) = 2x² +1
9(x) = 4x+2
g(x) = 2x
Answers
Answer:
g(x)=2x^2 +1 would be the even function
Step-by-step explanation:
To find if a function is even, you substitute -x for every x in the function. If the function stays the exact same, the function is even. For the first one, (x-1)^2 +1, If -x is substituted, we get (-x-1)^2 +1, which is not the same as the original function.
2x^2 +1 = 2(-x)^2 +1 =2x^2 +1 This function is even
(a negative squared will be positive)
4x+2 = 4(-x)+2 =-4x +2 This function is not even
2x = 2(-x) = -2x This function is not even