In general, the logarithmic function definition states that
[tex]y=log_b(x)\Leftrightarrow x=b^y[/tex]Therefore, in our case,
[tex]3^x=243\Leftrightarrow x=log_3(243)[/tex]Thus, the answer is log3(243)=x, the first option.there are four marbles in a vase blue blue red and green jenny pulls out two marbles without replacement list tge sample space
Let' begin by listing out the information given:
Number of marbles = 4; blue, blue, red, and green
Jenny pulls out two marbles without replacement. We have:
[tex]\begin{gathered} S=\mleft(Blue,Blue\mright),(Blue,Red),(Blue,Green) \\ S=(Red,Blue),(Red,Green) \\ S=(Green,Blue),(Green,Red) \\ \therefore S=\mleft\lbrace(BB),(BR),(BG),(RB),(RG),(GB),(GR)\mright\rbrace \end{gathered}[/tex]Avery flipped a coin 24 times and recorded the results in the box below. Which of the following best describes the difference between the experimental and theoretical probability of flipping heads?Heads= h Tails= th, t, t, h, t, t, t, h, t, t, h, t, t, t, h, t, t, t, t, h, t, t, t, t.A. According to theoretical probability, Avery would have expected to land on heads ten more times than she did experimentally.B. According the theoretical probability, Avery would have expected to land on heads half as many times as she did experimentally.C. According to theoretical probability, Avery would have expected to land on heads twite as many times as she did experimentally.D. According to theoretical probability, Avery would have expected to land on heads 12 more times than she did experimentally.
In order to determine the best description, first count the number of times for heads h and tails t.
Based on the given information, the number of heads was h = 6 and the number of tails was t = 18.
The theoretical probability in this case results in a 50% of probability for both events, that is, for 24 times at which the coin was flipped, 12 would be tail and 12 would be head.
Then, based on the previous explanation, you can conclude that:
C. According to theoretical probability, Avery would have expected to land on heads twite as many times as she did experimentally.
Can you please check 3 and 4 to see if I did them right?
We are given the following linear equation:
[tex]5x+15=45[/tex]The following problem is an example of a situation that can be modeled using the given equation.
Hayle did some chores this week, she got 5 dollars for each chore she did. Her dad forgot to pay her some days and gave her $15 dollars for the missing days. If she has a total of $45 dollars. How many chores did Hayle do?. The number of chores is represented by the variable "x".
Find the value of xa. 13 b. 14/5 c. 5 d. 8
Given that
There is a figure of the circle and we have to find the value of x.
Explanation -
Since the two chords of the circle are given and they are intersected making four parts. And we have to find the value of x.
So by using Intersecting Chords Theorem
If AC and BD are the chords intersecting at E. Then,
AE x EC = DE x EB
So in the given figure we have,
[tex]\begin{gathered} 4\times10=x\times8 \\ 40=x\times8 \\ x=\frac{40}{8} \\ x=5 \end{gathered}[/tex]
So C is the correct option.
Final answer -
Therefore the final answer is 5.55. Use the effective tax rate method to calculate the property tax on a $112,500 home. The assessment rate is 43%. The property tax rate is$32.89 per $1,000 of assessed value. Round the effective tax rate to threeplaces. What is the property tax?
Let's begin by listing out the given information:
Home (Property Value) = $112,500
Assessment rate = 43% = 0.43
Property tax rate = $32.89 per $1,000 of assessed value
The Property tax is calculated using the formula:
[tex]\begin{gathered} AssessedValue=112,500\times0.43=48,375 \\ PropertyTax=\frac{32.89}{1,000}\times48,375=1591.05375\approx1591.05 \\ PropertyTax=\text{ \$}1591.05 \end{gathered}[/tex]The effective tax is calculated using the formula:
[tex]\begin{gathered} ETR=\frac{TaxesPaid}{TaxableIncome} \\ ETR=\frac{PropertyTax}{AssessedValue}=\frac{1591.05}{48,375}=0.0329 \\ ETR=0.0329=3.29\text{ \%} \\ ETR=3.29\text{ \%} \end{gathered}[/tex]The graph below shows a company’s profit f(x) in dollars, depending on the price of goods x, in dollar’s, being sold by the company: Part A: What do the x-intercepts and maximum value of the graph represent in context of the disrobed situation?Part B: What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit for the company in the situation described?Part C: What is an approximate average rate of change of the graph from x=1 to x=3, and what does this rate represent in context of the described situation?
We will have the following:
Part A:
The x-intercepts represent the prices of the goods than wen sold represent no net gain or loss.
The maximum value represents the price at which there will be a maximum profit.
Part B:
We will have that the increasing and decreasing intervals are respectively:
[tex]I_{\text{increaing}}=(-\, \infty,3)[/tex][tex]I_{\text{decreasing}}=(3,\infty)[/tex]They tells us respectively that:
Increasing: The greater the price the greater the profit.
Decreasing: The greater the price the smaller the profit.
Part C:
We determine the equation of the parabola. We can see that it's vertex is located at (3, 120), we can also see that the parabola passes by the origin (0, 0); so:
[tex]f(x)=a(x-3)^2+120\Rightarrow0=a(0-3)^2+120[/tex][tex]\Rightarrow0=9a+120\Rightarrow9a=-120\Rightarrow a=-\frac{40}{3}[/tex]So, the equation that represents the parabola is:
[tex]f(x)=-\frac{40}{3}(x-3)^2+120[/tex]Then, we will determine the average rate of change as follows:
[tex]\text{average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]So:
[tex]\text{average rate of change}=\frac{(-40/3((3)-3)^2+120)-(-40/3((1)-3)^2+120)}{3-1}[/tex][tex]\text{average rate of change}=\frac{80}{3}\Rightarrow average\text{ rate of change}\approx26.67[/tex]So, the avereage rate of change for the graph from x = 1 to x = 3 is exactly 80/3, that is approximately 26.67.
Write the slope of the line in slope-intercept form using y=mx+b
In order to find the equation for this line in the slope-intercept form, let's use two points of the line in the equation.
Using the points (-3, 3) and (0, -3), we have:
[tex]\begin{gathered} y=mx+b \\ (0,-3)\colon \\ -3=0\cdot m+b \\ b=-3 \\ \\ (-3,3)\colon \\ 3=-3m-3 \\ -3m=6 \\ m=-2 \end{gathered}[/tex]So the slope of this line is m = -2, the y-intercept is b = -3 and the equation is y = -2x - 3.
Select the correct answer from each drop-down menu.y 10+816+4AETBBية1+60-8106A sequence of transformations maps AABCO ABC. The sequence of transformations that maps ABC onto ABC is a✓ followed by
Explanation:
To find the transformation
We will first have to write out the coordinates of ABC
The coordinates of ABC are:
[tex]\begin{gathered} A=(-4,4) \\ B=(-8,2) \\ C=(-6,6) \end{gathered}[/tex]Next, we will write the equation of the image
[tex]\begin{gathered} A^{\prime}=(4,-2) \\ B^{\prime}=(2,2) \\ C^{\prime}=(6,0) \end{gathered}[/tex]From the given coordinates of the image and pre-image
When we rotate a figure of 90 degrees counterclockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure.
To rotate the figure 90 degrees clockwise about a point, every point(x,y) will rotate to (y, -x)
Also, there was a
Solve for the missing side lengths.V1045°A. Ou = 10/2, vV =10./33B. Ou-20v2, v =1033c. Ou = 20v2, v =10D. Ou = 10v2, v = 10
We have a right triangle, where we know that one of the angles (besides the right angle) has a measure of 45°.
Then, the other angle measure can be calculated as:
[tex]\begin{gathered} \alpha+45+90=180 \\ \alpha=180-90-45 \\ \alpha=45\degree \end{gathered}[/tex]Then, as the other angle measure is equal, we have an isosceles triangle.
Then, length v has to be equal to the side with length 10.
With the value of v we can calculate u with the Pythagorean theorem:
[tex]\begin{gathered} u^2=v^2+10^2 \\ u^2=10^2+10^2 \\ u^2=2\cdot10^2 \\ u=\sqrt[]{2}\cdot10 \\ u=10\sqrt[]{2} \end{gathered}[/tex]Answer: u = 10√2, v = 10
It cost Kaylee $7.26 to send 66 text messages. How much does each text cost to send? On the double number line below, fill in the given values, then use multiplication or division to find the missing value. dollars o text messages Answer: $ Submit Answer
This situation is represented by the equation
[tex]7.26=66x[/tex]Where x is the cost for each text sent, to find it, clear x from the equation
[tex]\begin{gathered} 7.26=66x \\ \frac{7.26}{66}=x \\ 0.11=x \\ x=0.11 \end{gathered}[/tex]It costs $0.11 to send a text
The diagram shows two parallel lines cut by a transversal. One angle measure is shown.do8abº5499coFind the values of a, b, c, d, e, f, and g.
This question applies the rules of angles on a plane. The transversal that cuts the two parallel lines is a decisive one. From there you can determine which angles are opposite, alternate and so on.
Obeserve carefully that angle 54 and angle a lie on a straight line.
"Angles on a straight line sum up to 180 degrees."
Therefore,
Angle 54 + Angle A = 180
54 + A = 180
Subtract 54 from both sides of the equation
54 - 54 + A = 180 - 54
A = 126
Also note that;
"Opposite angles are equal in size."
Angle B is opposite to angle 54
Therefore angle B is 54 degrees.
Note also that angle C is opposite to angle A, therefore angle C equals angle A and that makes angle C = 126
If the two parallel lines are cut by a transversal, then it makes it easy to identify alternate angles. Alternate angles are formed on the inner sides of the two parallel lines but on the opposites sides of the tranversal. If you observe VERY CLOSELY, it usualltakes the form of a Z shape. You can equally determine alternate angles on the outer parts of the parallel lines in which case it becomes "exterior alternate angles."
"Alternate angles are equal."
Observe carefully and you'll see that angle B and angle D are interior alternate angles. That means B equals to D and therefore angle D = 54 degrees.
Similarly, angle A and angle G are alternate angles. Therefore angle G = 126 degrees.
Also angle F is opposite to angle D, and therefore angle F = 54 degrees.
Angle E is opposite to angle G, therefore angle E = 126 degrees
answer this for methe other to answers are c.the slope is 3/2,and the y-intercept is -2d.the slope is 3/2,and the y-intercept is 3
We are given a line that passes through the points (3,0) and (0,-2) (from the graph) from that information we can find the slope of the line using the following formula:
[tex]m=\frac{y_{2\text{ }}-y_1}{x_{2\text{ }}-x_1}[/tex]where
[tex]\begin{gathered} (x_1,y_1);\text{ } \\ (x_2,y_2) \end{gathered}[/tex]Are the points through which the line passes. Replacing
[tex]m=\frac{-2-0}{0-3}=\frac{2}{3}[/tex]Since the intercept is the point of the line when x = 0, and the line passes through (0,-2), the intercept is -2.
The slope is 2/3 and the intercept -2
M Find the range of possible diagonal lengths in a parallelogram with the given side lengths. 4. 3 and 12 5. x and 2x 6. x and x 812a, 25) F C12a + 2c, 25) The area of a parallelogram is given by the formula A=bh, where A is the area, b is the length of a base, and h is the height perpendicular to the base. ABCD is a parallelogram. E, F, G, and Hare the midpoints of the sides. 7. Show that the area of EFGH is half the area of ABCD. G A(0,0) D(200)
Here, we want to find the range of the diagonal length of a parallelogram measuring x by x units
From what we have, we can see that the sides are equal and what this mean is that we have a square with equal diagonal length from any of the sides
So to get the diagonal length, we use the Pythagoras' theorem since the dsigonal splits the square into two equal parts
Thus, we have;
[tex]\begin{gathered} d^2=x^2+x^2 \\ \\ d^2=2x^2 \\ \\ d\text{ = x}\sqrt[]{2} \end{gathered}[/tex]If you don’t need further explanation on this question, we can end the session. I’d really appreciate you letting me know how I did by rating our session after you exit. Thanks and have a great day!
What is the length of the side of an equilateral triangle if the height is 9√3
An equilateral triangle is a triangle were all the sides have the same measurement, and all the angles are the same(60º).
The height of an equilateral triangle divides the triangle into two equal right triangles. The height represents the oposite side of the angle of 60º, and the hypotenuse has the length of the side of the equilateral triangle, if we find the hypotenuse we have our answer.
Using trigonometric relations on the right triangle, we can find the value for the hypotenuse. The ratio between the opposite side to an angle and the hypotenuse is equal to the sine of this angle. If we call the hypotenuse as h, we have the following relation
[tex]\sin (60^o)=\frac{9\sqrt[]{3}}{h}[/tex]The sine of 60º is a known value
[tex]\sin (60^o)=\frac{\sqrt[]{3}}{2}[/tex]Then, combining both expressions, we have
[tex]\frac{9\sqrt[]{3}}{h}=\frac{\sqrt[]{3}}{2}[/tex]Solving for h
[tex]\begin{gathered} \frac{9\sqrt[]{3}}{h}=\frac{\sqrt[]{3}}{2} \\ \frac{9}{h}=\frac{1}{2} \\ \frac{h}{9}=2 \\ h=18 \end{gathered}[/tex]The length of the side of an equilateral triangle if the height is 9√3 is equal to 18.
helllllppppppppppppppppp
Graph the function f(x)=3(0.25)x.
How can features of the graph be described?
Select from the drop-down menus to correctly complete the statements.
The function is an example of exponential
Choose...
.
As x
Choose...
without bound, the function approaches y = 0. As x
Choose...
without bound, the function
Choose...
without bound.
The required graph of the given exponential function f(x) = 3(0.25)ˣ which has been attached below.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
The exponential function is given in the question following as:
f(x) = 3(0.25)ˣ
As per the attached graph, can see that the domain of the given function is all real numbers that are (-∞, ∞) in the interval notation. The range of the given function is (0, ∞) in the interval notation.
The required graph of the given exponential function f(x) = 3(0.25)ˣ which has been attached below.
Learn more about exponential function here:
brainly.com/question/11487261
#SPJ1
Given the point A(-3,-2) and B(6, 1),find the coordinates of the point Pon directed line segment ABthat partitions AB in the ratio 2:1.
1) Let's pick the points A(-3,-2) B(6,1)
2) Let's visualize it to better understand
Stretch or compress each linear function. Let g(x) be a vertical compression of f(x)=8x+6 by a factor of 1/4. Write the rule for g(x).
we have
f(x)=8x+6
we know that
The rule for a vertical compresion of f(x) is equal to
(x,y) -------> (x, ay)
where a is the factor
so
(x,f(x)) -------> (x,1/4f(x))
thet means
g(x)=1/4{8x+6}
g(x)=2x+1.5
Which of the following ordered pairs is a solution to the graph of the system of inequalities? Select all that apply(5, 2)(-3, -4)(0, -3)(0, 1)(-4, 1)
ANSWER
(5, -2) and (0, -3)
EXPLANATION
We want to find which of the ordered pairs is a solution to the system of inequalities.
Ordered pairs are written in the form (x, y), this means, whichever ordered pair is a solution, when inserted into the system of inequalities, should be true.
This means that the values of x and y must be true for both inequalities in the system.
The system of inequalities is:
[tex]\begin{cases}-2x-3\leq\text{ y} \\ y-1<\text{ }\frac{1}{2}x\end{cases}[/tex]A. (5, -2)
[tex]\begin{gathered} -2(5)\text{ - 3 }\leq-2\Rightarrow\text{ -10 - 3}\leq-2\Rightarrow\text{ -13 }\leq-2 \\ -2\text{ - 1 < }\frac{1}{2}(5)\Rightarrow\text{ -3 < }\frac{5}{2} \end{gathered}[/tex]Since both inequalities are correct, this is a solution.
B. (-3, -4)
[tex]-2(-3)\text{ - 3 }\leq-4\Rightarrow\text{ 6 - 3 }\leq-4\Rightarrow\text{ 3}\leq-4[/tex]Since the first inequality is already incorrect, we do not need to go further.
It is not a solution
C. (0, -3)
[tex]\begin{gathered} -2(0)\text{ - 3 }\leq\text{ -3 }\Rightarrow\text{ -3 }\leq\text{ -3} \\ -3\text{ - 1 < }\frac{1}{2}(0)\Rightarrow\text{ -4 < 0} \end{gathered}[/tex]Since both inequalities are correct, this is a solution.
D. (0, 1)
[tex]\begin{gathered} -2(0)\text{ - 3 }\leq\text{ 1 }\Rightarrow\text{ -3 }\leq\text{ 1} \\ 1\text{ - 1 < }\frac{1}{2}(0)\Rightarrow\text{ 0 < 0} \end{gathered}[/tex]Since 0 is not less than 0, this is not a solution.
E. (-4, 1)
[tex]-2(-4)\text{ - 3 }\leq\text{ 1}\Rightarrow\text{ 8 - 3 }\leq1\Rightarrow\text{ 5 }\leq1[/tex]Since 5 is not less than 1, this is not a solution.
Therefore, the solutions are (5, -2) and (0, -3)
Log5b=1.61 then log5b
The solution to the Logarithmic Expression Log ₅ 8 given that Log 5 = 1.61 And Log 8 = 2.08 is; 1.29
How to solve logarithmic expressions?Some of the rules of logarithm are as follows;
Rule 1; Log (M*N) = Log M + Log N
Rule 2; Log (M/N) = Log M - Log N
Rule 3; Log (M)ⁿ = nLog(M)
Rule 4; Log 1 = 0
Rule 5; Logₐ a = 1
Now, we are given that Log 5 = 1.61 And Log 8 = 2.08. We want to find Log ₅ 8.
From the rules of logarithm, we can say that;
Logₐ7 = (Log 7)/(Log a)
Thus;
Log ₅ 8 = (Log 8)/(Log 5)
= 2.08/1.61
= 1.29
Read more about Logarithmic Expressions at; https://brainly.com/question/237323
#SPJ1
Complete question is;
If Log 5 = 1.61 And Log, 8 = 2.08, Then Log ₅ 8 = O 3.25 O 3.35 10 0.47 O 2.69 O 1.29
A researcher is interested in whether using mental imagery can help people remember specific details when given information. To conduct the experiment, the researcher asks 100 volunteers to participate. The researcher places everyone’s name in a hat and randomly selects 50 names, making sure to sure to mix the names between each selection.
Which component is missing from the researcher’s process?
The researcher did not use enough randomization in the process.
The researcher used volunteers instead of randomly selected people from the population.
The researcher did not assign the 50 names to the treatment group or the control group.
The researcher should have used numbers instead of names for confidentiality reasons.
The 50 names were not allocated to either the treatment group or the control group by the researcher.
What is research?A problem must be thoroughly investigated in order to meet specific planned research objectives.
Research involves a certain process. The definition of the issue that will be studied during the research process is one of the crucial procedures.
After doing that, the researcher must decide whether there is enough knowledge about the issue that he or she plans to study.
Scientific research is research done with the intention of advancing science by the methodical collection, analysis, and evaluation of data—and that too in a planned manner: This research is being done by a researcher.
The instruments of observation, experimentation, and conclusion are essential components of the scientific method.
In this instance, the researcher should have randomly assigned the volunteers to the treatment group and the control group.
To know more about the Research, visit:
https://brainly.com/question/24174276
#SPJ1
There are 167 students taking a foreign language at North HighSchool. Based on the graphic above, how many students are takingSpanish?
59 (1st option)
Explanation:Given:
Total students taking the foreign language = 167
To find:
The number of students taking Spanish
To determine the number of students for Spanish, we will do an estimation:
The Spanish region is represented by the red region
The blue and red region is approximately half of the circle. This means half of the total students
Half of the students = 1/2(167) = about 83 students
The blue region in the half of the circle is about 1/3. The red represents the remaining part (2/3)
The Spanish region = 2/3 × 83
The Spanish region = 55.3
The closest number to this in the options is 59 (1st option)
Comparing Relationships with Tables1. Decide whether each table could represent a proportional relationship.If the relationship could be proportional, what would the constant ofproportionality be?a. How loud a sound is depending on how farDistance toaway you are.Listener (ft)Sound Level(dB)85791020407367Costb. The cost of fountain drinks at Hot Dog Hut.Volume(fluid ounces)($)$1.4920$1.59$1.8930
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where
k is the constant of proportionality
Verify each table
table a
Let
x ----> distance
y ----> sound level
For each ordered pair calculate the value of k
k=y/x
so
(5,85) -----> k=85/5=17
(10,79) ----> k=79/10=7.9
the values of k are differents
that means
the table nor represent a proportional relationship
table b
let
x ----> volume
y ----> cost
k=y/x
(16,1.49) ----> k=1.49/16=0.093125
(20,1.59) ----> k=1.59/20=0.0795
the values of k are differents
that means
the table nor represent a proportional relationship
Trying to use a model or number line for fractions for a 4th grader
Given:
[tex]\frac{76}{100}-\frac{50}{100}[/tex]Solve:
[tex]\begin{gathered} \frac{76}{100}-\frac{50}{100} \\ so\colon \\ =\frac{76-50}{100} \\ =\frac{26}{100} \end{gathered}[/tex][tex]\begin{gathered} =\frac{26}{100} \\ =0.26 \end{gathered}[/tex]In number line 0.26 lies in between 0 to 1.
Complete the following: 1, Jabomplete the squares for each quadratic, list the center and radius, then graph each circle (a labeling its translated center: (a) r2 + 2x + y2 - 4y = 4 (c) 2x2 + 2y2 + 3x - 5y = 2 (e) r2 + y2 + 3x = 4 (g) x² + y2 + 4x = 0 (1) r² + y2 + 2mx - 2ny = 0 (b) x2 + y2 - 4x = 0 (d) x2 + y2 - 2x - 8y = 8 4x + 4y? - 16x + 24y = -27 (h) x + y? - 7y = 0 (i) x + y2 - 2ax + 2by = c Determine which of the following equations represents a circle with a real non-zero radiu a) r? + y + 10x = -30 (b) 3x2 + 3y? - 11x = -91 4x + 4y + 18-8y = -85 (d) 36x* + 36y- 36x + 48y = -16 the equation of the circle which accen 2 and is concentric
3x² + 3y² - 11x = -91
Divide through by 3
x² + y² - 11/3 x = -91/3
x² - 11/3 x + y² = -91/3
(x² - 11/3 x ) + y² = -91/3
[x² - 11/3 x +(-11/6)² ] + y² = -91/3 + (- 11/6)²
(x - 11/6)² + y² = -91/3 + 121 / 36
[tex](x-\frac{11}{6})^2+y^2=\frac{-1092+\text{ 121}}{36}[/tex][tex](x\text{ - }\frac{11}{6})^2+y^2=\frac{-971}{36}[/tex]Comparing this with (x-a)² + (y-b)² = r²
r² = -971/36
Taking the square root will give an immaginary number
The radius is NOT a real number
This equation does not have a real radius
For each value of y,determine whether it is a solution to y<7
Y < 7 indicates that any value below 7 is included
therefore, 5 is a solution, 12 is NOT a solution, 7 is NOT a solution and 4 is a solution.
[tex]( - 4x + 2y \leqslant 4 )(x + 4y \ \textgreater \ - 10)[/tex]how do I graph this
Given the system of inequalities
[tex]\begin{gathered} -4x+2y\leq4 \\ x+4y>-10 \end{gathered}[/tex]We start by getting the plot of one of these inequalities. Let's start on -4x + 2y ≤ 4. This equation can be rewritten as
[tex]\begin{gathered} 2y\leq4+4x \\ y\leq2+2x \end{gathered}[/tex]Initially, we consider the equation
[tex]y=2+2x[/tex]Plotting the equation, we have
Considering the values of these function at
[tex]y\leq2+2x[/tex]Let's use the same steps implemented above for the second inequality. We have
[tex]\begin{gathered} 4y>-10+x \\ y>\frac{x-10}{4} \end{gathered}[/tex]Plotting this we have,
The dashed line represents the values that are not included in the equation, as a present for inequalities with less than or greater than. The shaded region represents the solution
After plotting the two inequalities individually, we now superimpose the two graphs. We get
where the darker region represents the solution of the inequalities.
What is an equation for each translation of y=|x|?1. 4 units up2. 7 units down
To find an equation for each translation, keep in mind this:
f(x); g(x)=f(x)+a, the function is translated a units up.
f(x); g(x)=f(x)-a, the function is translated a units down.
Use this information to find the equation for each translation.
4 units up - Add 4 units to the function:
[tex]y=\lvert x\rvert+4[/tex]7 units down - Substract 7 units to the function:
[tex]y=\lvert x\rvert-7[/tex]Those are the answers for each translation.
Can you help explain how to solve this for me?
SOLUTION:
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex][tex]\begin{gathered} d=\sqrt{(-4-8)^2+(5--6)^2} \\ d=\sqrt{-12^2+11^2} \\ d=\sqrt{265}=16.28 \end{gathered}[/tex]b.
[tex]\begin{gathered} m=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2} \\ m=(\frac{-6+5}{2},\frac{-4+8}{2}) \\ m=(-\frac{1}{2},2) \end{gathered}[/tex]Last week, Thor ran 30 laps around the lake. Shaq ran 5/9 as many laps around the lake as Thor did. How many laps around the lake did Shaq run?
Explanation:
Thor: 30 laps
Shaq: 5/9 Thor's laps.
To find how many laps Shaq did, we have to multiply Thor's laps by 5/9:
[tex]30\times\frac{5}{9}=\frac{30\times5}{9}=\frac{150}{9}[/tex]And simplify the fraction:
[tex]\frac{150}{9}=\frac{50}{3}[/tex]It's an improper fraction. Written as a mixed number:
[tex]\frac{50}{3}=16\frac{2}{3}[/tex]Answer:
Shaq did 16 2/3 laps around the lake
Halley's Comet appears in the sky once every 75 years it last appeared in 1986 two students wrote Expressions to find out which years after 1986, will appear.Julian says 75× Casey says 1986+75xWhose expression is correct and why?A) Neither expression is correct, because the correct expression is 75 + 1986x.B)Both expressions are correct because both show that appears every 75 years.D) Julian's expression is correct, because it shows that the comet appears every 75 years. The hear it last appeared it doesn't matter.
The expression that will tell us the years after 1986 is Casey's:
[tex]1986+75x[/tex]The reason being: every 75 years the comet will do another "pass by" and we will have to add 75 each new time.
So, the option is B) since each can be used to determine the values, but Casey's is more "practical".