The slopes are different, and the y-intercepts are different. The slopes are different, and the y-intercepts are the same. The slopes are the same, and the y-intercepts are different. The slopes are the same, and the y-intercepts are the same.
Answers
Answer:
The slopes are the same and the y-intercepts are different.
Explanation:
Given:
[tex]\begin{gathered} x+2y=8 \\ 2x+4y=12 \end{gathered}[/tex]Recall that the slope-intercept equation of a line is generally given as;
[tex]y=mx+b[/tex]where;
m = slope of the line
b = y-intercept of the line
Let's go ahead and rewrite the first equation in slope-intercept form as seen below;
[tex]\begin{gathered} x+2y=8 \\ 2y=-x+8 \\ y=-\frac{1}{2}x+\frac{8}{2} \\ y=-\frac{1}{2}x+4 \end{gathered}[/tex]We can see from the above that the slope(m) of the first equation is -1/2 and the y-intercept(b) is 4.
Let's go ahead and rewrite the second equation in slope-intercept form as seen below;
[tex]\begin{gathered} 2x+4y=12 \\ 4y=-2x+12 \\ y=-\frac{2}{4}x+\frac{12}{4} \\ y=-\frac{1}{2}x+3 \end{gathered}[/tex]We can see from the above that the slope(m) of the second equation is -1/2 and the y-intercept(b) is 3.
We can see from the above that, for the two equations, the slopes are the same, and the y-intercepts are different.
Related Questions
Find the y-intercept of the line on the graph.
Answers
The y-intercept of the line on the graph is -2.
What is termed as the y-intercept?The point at which the graph intersects a y-axis is known as the y-intercept. Finding the intercepts of any function of the form y = f(x) is critical when graphing. A function can have one of two types of intercepts. They are known as the x and y intercepts. An intercept of a function is the point at which the function's graph intersects the axis. A graph's y intercept is the point at which the graph intersects the y-axis. We know that any point just on y-axis has an x-coordinate of 0. As a result, the x-coordinate of the a y-intercept is 0.For the given question;
The graph of the straight line is given.
The y-intercept of the line is the point on y axis where the value of the x becomes zero.
At x = 0, y = -2.
Thus, he y-intercept of the line on the graph is -2.
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actual distance=14 miles 35 miles 56 miles map distance=2 inches 5 inches 8 incheshow many miles does the actual distance measure if the distance on the map measures 14 inches?
Answers
According to the given information, the scale factor is 7 since the actual distance numbers are seven times greater than the map distance numbers.
That means, 14 inches on the map would represent 98 feet of actual distance since 14 times 7 is 98.
Therefore, the answer is 98 feet.if k is the midpoint of CT , CK =3x+23,and KT =5x+7,then find x and CT
Answers
Given:
CK = 3x + 23
KT = 5x + 7
If K is the midpoint of CT, then CK = KT. Then,
[tex]3x+23=5x+7[/tex]Finding x:
Subtracting 3x from both sides:
[tex]\begin{gathered} 3x+23-3x=5x+7-3x \\ 23=2x+7 \end{gathered}[/tex]Subtracting 7 from both sides:
[tex]\begin{gathered} 23-7=2x+7-7 \\ 16=2x \end{gathered}[/tex]And dividing both sides by 2:
[tex]\begin{gathered} \frac{16}{2}=\frac{2x}{2} \\ 8=x \end{gathered}[/tex]x = 8.
Finding CT:
K is the midpoint of CT, then CT = CK + KT
[tex]\begin{gathered} CT=3x+23+5x+7 \\ CT=3*8+23+5*8+7 \\ CT=24+23+40+7 \\ CT=94 \end{gathered}[/tex]CT = 94.
Answer:
x = 8
CT = 94
Skill plansTX StandaScienceRecommendationsA Math49 Language artsSocial studiesAlgebra 1> 0.11 Solve a system of equations using elimination: word problems NHRYou have prizes to reveal! GotWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanks.Kaylee is selling her handmade jewelry online. Yesterday, she sold 9 bracelets and 3necklaces, for a profit of $144. Today, she made a profit of $279 by selling 10 bracelets and 9necklaces. How much profit does Kaylee earn from each piece?Kaylee earns a profit of $|| from every bracelet and $from every necklace.Submit
Answers
Let x be the profit of a bracelet and y the profit of a necklace.
Yesterday she sold: 9 bracelets and 3 necklaces, for a profit of $144:
[tex]9x+3y=144[/tex]Today, she made a profit of $279 by selling 10 bracelets and 9 necklaces:
[tex]10x+9y=279[/tex]System of equations:
[tex]\begin{gathered} 9x+3y=144 \\ 10x+9y=279 \end{gathered}[/tex]To solve by elimination:
1. Multiply the first equation by -3:
[tex]\begin{gathered} -3(9x+3y=144 \\ \\ -27x-9y=-432 \end{gathered}[/tex]2. Add equation you get in step 1 and the second equation in the system:
[tex]-17x=-153[/tex]3. Use the equation you get in step 2 to solve x:
[tex]\begin{gathered} \text{Divide both sides of the equation into -17} \\ \\ \frac{-17}{-17}x=\frac{-153}{-17} \\ \\ x=9 \end{gathered}[/tex]4. Use the value of x to solve y:
[tex]\begin{gathered} 9x+3y=144 \\ \\ 9(9)+3y=144 \\ 81+3y=144 \\ \\ \text{Subtract 81 in both sides of the equation:} \\ 81-81+3y=144-81 \\ 3y=63 \\ \\ \text{Divide both sides of the equation into 3:} \\ \frac{3}{3}y=\frac{63}{3} \\ \\ y=21 \end{gathered}[/tex]Then, the solution for the system is :
[tex]\begin{gathered} x=9 \\ y=21 \end{gathered}[/tex]Kaylee earns a profit of $9 from every bracelet and $21 from every necklace
The captain of a ship at sea sights a lighthouse which is 100 feet tall. The captain measures the the angle of elevation to the top of the lighthouse to be 26°. How far is the ship from the base of the lighthouse? How many feet?
Answers
Answer:
Explanation;
The set will be a right angled triangle as shown;
7. The graph was made to compare the costs of renting copy machinesfrom Ames Business Product to those from Beck's Office Supply. Whatinformation is given by the point of intersection of the two lines? *
Answers
Notice that the y-axis of the given graph represents the total cost per month, and the x-axis represents the number of copies made in that month, therefore, the x-entry of the intersection of the graphs represents the number of copies for which the total cost per month is the same for both companies.
Answer: Last option.
Determine the slope and the y interception from the table of values
Answers
Slope = -2
y-intercept is 6
Explanation:To get the slope, we pick any two points in the table and apply the slope formula:
Picking points: (-2, 10) and (1, 4)
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} x_1=-2,y_1=10,x_2=1,y_2\text{ = }4 \\ \text{slope = m = }\frac{4\text{ - 10}}{1\text{ - (-2)}} \\ \text{slope = }\frac{4\text{ - 10}}{1\text{ + 2}} \end{gathered}[/tex][tex]\begin{gathered} \text{slope = -6/3} \\ \text{slope = -2} \end{gathered}[/tex]To get the y-intercept, we find the value of y when x = 0 on the table:
when x = 0, y = 6
Hence, the y-intercept is 6
Antonio buys persian rugs and then resells them for 150%
of his cost. If he bought a 4' by 9' rug $120, for how much
will he resell it?
Answers
Answer:
$180
Step-by-step explanation:
So first we need to know that 100% would be $120 because that was 100% of the price. Selling it for half the price is the same as selling it for 50%. So what we will be doing is we are going to sell the whole carpet - we are just going to sell it for half of $120. Now we need to thinking what would half the price be because half the price is the same as 50%. So 120/2 = $60 so if we have 100 percent (so $120) plus 50% (which is $60) the total we sold it for would be $180. Therefore our final answer would be $180.
What is 3/8×3/8×3/8 written as a power
Answers
I need help!!!! Please I'm not good at this:(
Answers
The values of the numbers will be:
1. 162
2. 162
3. 1 99/100.
4. 11.4
5. 72
How to calculate the values?1. 6³ - 8² + 300 ÷ ( 5 + 5)²
It should be noted that this will follow the rules or PEDMAS. This implies that the parentheses will be solved first and that subtraction comes last.
6³ - 8² + 300 ÷ ( 5 + 5²)
= 216 - 64 + 300 ÷ 30
= 216 - 64 + 10
= 216 - 54
= 162
2. 6³ - 8² + 300 ÷ ( 5 + 5²)
= 216 - 64 + 300 ÷ 30
= 216 - 64 + 10
= 216 - 54
= 162
3. (1/5 + 1/2)² + 3/10 × 5
= (7/10)² + 3/10 × 5
= 49/100 + 1 1/2
= 1 99/100
4. 8.1 ÷ 0.9 + 0.4³ ÷ 0.8 × 30
= 9 + 0.064 ÷ 0.8 × 30
= 9 + 0.08 × 30
= 9 + 2.4
= 11.4
5. (18 - 4² + 2)² / (1 ÷ 4 1/2)
= 4² / 2/9
= 16 × 9/2
= 72
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a wheelchair ramp is 4.2 meters long. It rises of 0.7 meter. What is the angle of elevation to the nearest tenth of a degree
Answers
Given :
A wheelchair ramp is 4.2 meters long.
It rises 0.7 meters
So, let the angle of elevation = x
so,
[tex]\begin{gathered} \tan x=\frac{0.7}{4.2}=\frac{1}{6} \\ \\ x=\tan ^{-1}\frac{1}{6}=9.462 \end{gathered}[/tex]Rounding the answer to the nearest tenth
So, the answer is : the angle = 9.5
pplications: Quadratic Equations
The height of a triangle is 5 m less than its base. The area of the triangle is 42 m².
What is the length of the base?
Enter your answer in the box.
m.
Answers
The length of the base of the triangle of found is 12 m.
What is meant by the term triangle?A triangle is a 2-dimensional closed shape with three sides, three angles, and three vertices. A triangle is indeed a type of polygon.Triangle CharacteristicsThe sum of a triangle's three interior angles is always 1800.The sum of any two triangle sides is always longer than the maximum of the third side.A triangle's area is equal to half the product of the its base and height.For the given question;
Let the height of triangle be 'h'.
Let the base of the triangle be 'b'.
The height of a triangle is 5 m less than its base.
h = b - 5
The area of the triangle is given as 42 m².
The formula for the area of the triangle is-
Area = ¹/₂ base × height
Put the values;
42 = ¹/₂ b × (b - 5)
b² - 5b = 84
b² - 5b - 84 = 0.
Find the factors of the quadratic equation.
(b - 12)(b + 7) = 0
b = +12, -7 (neglecting negative values)
b = 12 m.
Thus, the length of the base of the triangle of found is 12 m.
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A line passes through the points (2,18) and (7,23). Write a linear function rule in terms of x and y forthis line.The linear function rule is y=[
Answers
Answer::
[tex]y=x+16[/tex]Explanation:
Given two points on a line:
[tex]\begin{gathered} (x_1,y_1)=(2,18) \\ \left(x_2,y_2\right)=\left(7,23\right) \end{gathered}[/tex]We use the two-point formula below to find the linear function rule.
[tex]$$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$$[/tex]Substitute the values:
[tex]\begin{gathered} \frac{y-18}{x-2}=\frac{23-18}{7-2} \\ \frac{y-18}{x-2}=\frac{5}{5} \\ \frac{y-18}{x-2}=1 \end{gathered}[/tex]Next, make y the subject:
[tex]\begin{gathered} y-18=x-2 \\ y=x-2+18 \\ y=x+16 \end{gathered}[/tex]The linear function rule is:
[tex]y=x+16[/tex]Solve each equation Show steps for credit4. 5+y=75.8=2+q6.6=n-4
Answers
Answer:
• y=2
,• q=6
Explanation:
Number 4
Given the equation:
[tex]5+y=7[/tex]To solve for y, subtract 5 from both sides:
[tex]\begin{gathered} 5+y-5=7-5 \\ y=2 \end{gathered}[/tex]The value of y is 2.
Number 5
Given the equation:
[tex]8=2+q[/tex]To solve for q, subtract 2 from both sides:
[tex]\begin{gathered} 8-2=2-2+q \\ q=6 \end{gathered}[/tex]The value of q is 6.
Take a guess: A student takes a multiple-choice test that has 9 questions. Each question has four choices. The student guesses randomly at each answer. Round the answers to three decimal places. (a) Find P(3). (b) Find P (More than 1).
Answers
The probability that the student guesses 3 question correctly is 0.234 and the probability that the student guess more than one correctly is 0.7.
Using the property of binomial distribution we can calculate that the probability that a answer is correct is 0.25
As there are 4 options , hence we will see that probability that an option picked is correct is 1/4 = 0.25
Now we have to find the probability for 3 answers to be correct .
We will use the formula
[tex]P(X=x) = \frac{n!} {x! (n - x)!} \cdot p^x \cdot (1 - p)^{n - x}[/tex]
Now putting the values of x = 3 and the value of p = 0.25 we get
P(X = 3) = 0.234
therefore the value of P(3) = 0.234
Now we have to find the value of P(x>1)
Using the same formula we calculate the occurrence of the event
P(x>1)=1-P(x≤1)
or, P(x>1) = 0.7
Hence the required probability is 0.7.
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Find the sum. Enter your answer in the box below as a fraction, using theslash mark (/) for the fraction bar.2 413 13+Answer here
Answers
SOLUTION
We want to solve the fraction
[tex]\begin{gathered} \frac{2}{13}+\frac{4}{13} \\ \text{the two fractions has the same denominator, which is 13} \\ so\text{ we write the 13 and add the numerators 2 and 4} \\ we\text{ have } \\ \frac{2+4}{13} \\ =\frac{6}{13} \end{gathered}[/tex]Hence, the answer is 6/13
Identify the number as prime Kompass it or neither if the number is comp is it rated as the product of prime factors 133
Answers
Given the number 133, we list the first prime numbers and then look for a possible factor of 133:
Prime_list = {2, 3, 5, 7, 11, ...}
133 is not an even number, so we discard 2. 133 does not end with 0 or 5, so 5 can not be a factor. We evaluate 3, 7, and 11:
The only division with no rest is 133/7 = 19, and we know that 7 and 19 are prime numbers. We conclude that 133 is composite and can be represented as a product of 7 and 19:
[tex]133=7\cdot19[/tex]Can someone help explain this to me? Please and thank you!
Answers
Given the points on the line:
[tex]\mleft(-5,-2\mright),\mleft(3,-4\mright)[/tex]You can find the slope of the line using this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where these two points are on the line:
[tex](x_1,y_1),(x_2,y_2)[/tex]In this case, you can set up that:
[tex]\begin{gathered} y_2=-2 \\ y_1=-4 \\ x_2=-5 \\ x_1=3 \end{gathered}[/tex]Then, substituting values into the formula and evaluating, you get:
[tex]m=\frac{-2-(-4)}{-5-3}=\frac{-2+4}{-8}=-\frac{2}{8}=-0.25[/tex]• By definition, the Point-Slope Form of the equation of a line is:
[tex]y-y_1=m\mleft(x-x_1\mright)[/tex]Where "m" is the slope and this is a point on the line:
[tex](x_1,y_1)[/tex]In this case, having the two points on the line shown in the exercise, you can substitute their coordinates into the equation and simplify, in order to get two equations for the line in Point-Slope Form:
- Using the point:
[tex]\mleft(-5,-2\mright)[/tex]You get:
[tex]\begin{gathered} y-(-2)=-0.25(x-(-5)_{}) \\ \\ y+2=-0.25(x+5) \end{gathered}[/tex]- Using the point:
[tex]\mleft(3,-4\mright)[/tex]You get:
[tex]\begin{gathered} y-(-4)=-0.25(x-3_{}) \\ \\ y+4=-0.25(x-3_{}) \end{gathered}[/tex]• By definition the Slope-Intercept Form of the equation of a line is:
[tex]undefined[/tex]Find the horizontal asymptote of the graph of the rational function. y = x^2 + 6 ———— 4^2 - 7 Identify the horizontal asymptote for the graph of the function.
Answers
Given:
[tex]y\text{ = }\frac{x^2\text{ + 6}}{4x^2\text{ -7}}[/tex]The rule for horizontal asymptote is shown below:
For the given rational function, the degree of the numerator is equal to the degree of the denominator.
Hence, the horizontal asymptote is:
[tex]\begin{gathered} y\text{ = }\frac{1}{4} \\ \\ 1\text{ is the leading coefficient of the numerator} \\ and\text{ 4 is the leading coefficient of the denominator} \end{gathered}[/tex]Answer:
[tex]y\text{ = }\frac{1}{4}\text{ \lparen Option A\rparen}[/tex]3. Given: BAM is a right angle. If m BAM=4x+22, then solve for the value of x.
Answers
Right angle means that the angle is equal to 90 degrees
We will thus proceed by equating BAM = 90 degrees, we have:
[tex]\begin{gathered} 4x+22=90 \\ \text{Subtract 22 from both sides, we have:} \\ 4x+22-22=90-22 \\ 4x=68 \\ \text{divide through both sides by 4, we have:} \\ \frac{4x}{4}=\frac{68}{4} \\ x=17^{\circ} \end{gathered}[/tex]x = 17
Answer: 17 degrees
Step-by-step explanation:
<BAM is a right angle. A right angle is defined to be 90 degrees.
So...
<BAM = 4x + 22 is transformed to 90 = 4x + 22
90 = 4x + 22
4x = 90 - 22
4x = 68
x = 17 degrees
R is perpendicular to U. S is parallel to T. m <1 = 39° . Find the remaining angles.
Answers
First, notice that angle 1 and angle 4 are vertical angles, therefore:
[tex]\measuredangle1=39\text{ = }\measuredangle4[/tex]then, we have that angle 1 and angle 2 are supplemetary angles, then:
[tex]\begin{gathered} \measuredangle1+\measuredangle2=180 \\ \Rightarrow\measuredangle2=180-\measuredangle1=180-39=141 \\ \measuredangle2=141 \end{gathered}[/tex]Since angle 3 and angle 2 are vertical, we have the first measures of the diagram:
[tex]\begin{gathered} \measuredangle1=39 \\ \measuredangle2=141 \\ \measuredangle3=141 \\ \measuredangle4=39 \end{gathered}[/tex]Then, angle 1 and angle 5 are corresponding angles, then, we have the following:
[tex]\measuredangle1=39=\measuredangle5[/tex]Now, angle 5 and angle 6 are complementary angles, therefore:
[tex]\begin{gathered} \measuredangle5+\measuredangle6=90 \\ \Rightarrow\measuredangle6=90-\measuredangle5=90-39=51 \\ \measuredangle6=51 \end{gathered}[/tex]Angle 5 is vertical with angle 7, and angle 6 is vertical with angle 8. Also, we can see that angle 9 is a right angle, then, we have the next measures:
[tex]\begin{gathered} \measuredangle5=39 \\ \measuredangle6=51 \\ \measuredangle7=39 \\ \measuredangle8=51 \\ \measuredangle9=90 \end{gathered}[/tex]Finally, notice that angles 4, 9 and 10 are the angles of a right triangle, then, we would have the following:
[tex]\begin{gathered} \measuredangle4+\measuredangle9+\measuredangle10=180 \\ \Rightarrow\measuredangle10=180-\measuredangle9-\measuredangle4=180-90-39=51 \\ \measuredangle10=51 \end{gathered}[/tex]then, angle 10 and angle 11 are supplemetary, then:
[tex]\begin{gathered} \measuredangle10+\measuredangle11=180 \\ \Rightarrow\measuredangle11=180-\measuredangle10=180-51=129 \\ \measuredangle11=129 \end{gathered}[/tex]angle 10 is vertical with angle 13 and angle 11 is vertical with angle 12, then:
[tex]\begin{gathered} \measuredangle10=51 \\ \measuredangle11=129 \\ \measuredangle12=129 \\ \measuredangle13=51 \end{gathered}[/tex]I’m in major need of help for this question I honestly do not understand it
Answers
Answer
Explanation
Given the figure, we can deduce the following information:
a and b cut by transversal lines
To determine the value of x, we redraw the figure as shown below:
Since a and b are parallel lines, y must be equal to 36°. We also note that the angles on a straight add up to 180°. So,
[tex]\begin{gathered} 36+65+x=180 \\ \text{Simplify and rearrange} \\ x=180-65-36 \end{gathered}[/tex]Therefore, the equation that can be used to solve for x is:
[tex]x=180-65-36[/tex]Now, we get the value of x:
[tex]\begin{gathered} x=180-65-36 \\ \text{Calculate} \\ x=79\degree \end{gathered}[/tex]Therefore, the value of x is 79°.
Find the y intercept of the line on the graph.
Answers
Answer: the y-intercept is -3
Step-by-step explanation:
if you ever need to find the y-intercept, here is how to do it:
the y-axis is the line that goes up and down. wherever the line from the equation crosses that y-axis line, that is going to be the y-intercept. as you can see here, they intercept at -3.
19. Sally has $35 and earns $15 for each batch of cake balls she sells. Kristen has $52 and earns $12 for each batch of cookies she sells. How many batches of cake balls does Sally need to sell to have more money than Kristen?
Answers
ANSWER
6 batches
EXPLANATION
Let the number of batches of cake balls or batches of cookies be x.
Sally has $35 and earns $15 for every batch of cake she sells.
This means that the total amount of money that she has after selling x batches of cake balls is:
35 + 15x
Kristen has $52 and earns $12 for every batch of cookies she sells.
This means that the total amount of money that she has after selling x batches of cookies is:
52 + 12x
To find the number of batches of cake balls that Sandy must sell to have more money than Kristen, we have to write the inequality:
35 + 15x > 52 + 12x
Now, collect like terms:
15x - 12x > 52 - 35
3x > 17
Divide through by 3:
x > 17/3
x > 5.7
We have to round up to whole number since batches of cake balls must be whole.
So, Sandy must sell 6 batches of cake balls to have more money than Kristen.
Use the intermediate value theorem to determine whether f(x)=8x^4-9x^2-9 has a real zero between 1 and 2
Answers
ANSWER:
There is a real zero in this interval
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f\mleft(x\mright)=8x^4-9x^2-9[/tex]To determine if there is a real zero between 1 and 2, we must evaluate the function at these points, if there is a change from positive to negative or vice versa, by the intermediate value theorem we can say that it has a real zero in that interval.
[tex]\begin{gathered} f(1)=8\left(1\right)^4-9\left(1\right)^2-9 \\ \\ f(1)=8\cdot1-9\cdot1-9 \\ \\ f(1)=8-9-9 \\ \\ f(1)=-10 \\ \\ \\ f(2)=8\left(2\right)^4-9\left(2\right)^2-9 \\ \\ f(2)=8\cdot16-9\cdot4-9 \\ \\ f(2)=128-36-9 \\ \\ f(2)=83 \end{gathered}[/tex]We can observe that it goes from a negative value to a positive value in this small interval, which by means of the theorem we can say that if there is a real zero in this interval
How do I solve and what would the answer be?
Answers
SOLUTION
Given the question in the image, the following are the solution steps to get the inverse of the function
STEP 1: Write the given function
[tex]f(x)=\frac{2}{x-5}[/tex]STEP 2: Define an inverse of a function
[tex]\mathrm{A\: function\: g\: is\: the\: inverse\: of\: function\: f\: if\: for}\: y=f\mleft(x\mright),\: \: x=g\mleft(y\mright)\: [/tex]STEP 3: Find the inverse of the given function
[tex]\begin{gathered} f(x)=\frac{2}{x-5} \\ \text{Set the function f(x) to y} \\ y=f(x)=\frac{2}{x-5} \\ y=\frac{2}{x-5} \\ \text{Swap x with y} \\ x=\frac{2}{y-5} \\ \text{solve for y} \\ By\text{ cross multiplication,} \\ x(y-5)=2 \\ xy-5x=2 \\ \text{Add 5x to both sides} \\ xy-5x+5x_{}=2+5x \\ xy=2+5x \\ \text{Divide both sides by x} \\ \frac{xy}{x}=\frac{2+5x}{x} \\ y=\frac{2+5x}{x}=\frac{2}{x}+\frac{5x}{x} \\ y=\frac{2}{x}+5 \\ \text{Set the inverse to y} \\ f^{-1}(x)=_{}\frac{2}{x}+5 \end{gathered}[/tex]Hence, the inverse of the function is;
[tex]\frac{2}{x}+5[/tex]XB is the angle bisector of ZAXC. MZAXB23А.BVхC с
Answers
To obtain x, we can sum the angles < AQB and < BQC
=> 5X + 8X - 24
=> 13X -24
we are also told that that the sum of their angles is 80
13X - 24 = 80
13 X = 24 + 80
13X = 104
Divide both sides by 13
x = 104/13
x = 8
A group of students is playing a game of El Repollo, which involves passing a ball made of layers of paper. After catching the ball, a player peels off a layer of paper, answers a question that has been written on the paper, and then tosses the ball to the next player. . Sara tosses the ball to Alex from a height of 1.5 meters. • The ball reaches its highest point about 1 second later. • Alex misses the ball, and it hits the ground 2 seconds after Sara tosses it to him. Which function approximates the height of the ball, in meters, a seconds after Sara tosses it to Alex? f(x) = -5z²+9.25z + 1.5 f(x) = 5(x-1.5)(x-2) f(x) = -5x(x - 2) f(z) = 5x² -10.75z + 1.5
Answers
The quadratic function that approximates the height of the ball, in meters, seconds after Sara tosses it to Alex is:
y = ax² + bx + 1.5.
What is a quadratic function?A quadratic function is defined according to the following rule:
y = ax² + bx + c.
Considering the context of this problem, we will use equations to find the coefficients.
Sara tosses the ball to Alex from a height of 1.5 meters, meaning that the initial height is of 1.5 meters, thus the coefficient c has a value of 1.5, and:
y = ax² + bx + 1.5.
The ball reaches its highest point about 1 second later, hence the x-coordinate of the vertex is calculated as follows:
xv = -b/2a = 1
-b = 2a
b = -2a
The ball hits the ground 2 seconds after Sara tosses it to him, hence y(2) = 0, that is:
0 = 4a + 2b + 1.5
4a + 2b = -1.5.
2a + b = -1.5.
2a - 2a = -1.5.
(undefined function, there is a small typo in the problem but the procedure is shown in this problem, we just have to solve the system of equations for a and b).
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find the missing value so that the line passing through the 2 points has the given slope:
Answers
The foruma for calculating the slope of a line passing through two points is expresses as;
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]Given the coordinates (-20, y) and (-11, 15) with slope m = 0
Substitute the given parameters into the formula above and find y;
[tex]\begin{gathered} 0\text{ = }\frac{15-y}{-11-(-20)} \\ 0\text{ = }\frac{15-y}{-11+20} \\ 0\text{ = }\frac{15-y}{9} \\ \text{cross multiply} \\ 0\text{ = 15-y} \\ y\text{ = 15} \end{gathered}[/tex]Hence the value of y is 15. Option C is correct
what is the solution set?
Answers
Answer:
the answer is either 20 or 4 ..
