I'm having some problems with this logarithmic question I will upload a photo
Answers
The Solution.
[tex]Let\log _{\frac{1}{9}}(\frac{1}{9})=x[/tex]Writing the above equation in index form, we have
[tex]\begin{gathered} (\frac{1}{9})^1=(\frac{1}{9})^x \\ Then\text{ it follows that} \\ 1=x \\ x=1 \end{gathered}[/tex][tex]\begin{gathered} \text{Let }\log _749=x \\ So\text{ we have} \\ 49=7^x \\ \text{Making the base of both sides equal, we have} \\ 7^2=7^x \\ x=2 \end{gathered}[/tex][tex]\begin{gathered} \text{Let }\log _{\frac{1}{4}}16=x \\ \\ 16=(\frac{1}{4})^x \\ 16=4^{-1\times x} \\ 4^2=4^{-x} \\ -x=2 \\ x=-2 \end{gathered}[/tex][tex]\begin{gathered} \text{Let }\log _{125}5=x \\ \text{cross multiplying, we have} \\ 5=125^x \\ 5^1=5^{3x} \\ 3x=1 \\ \text{Dividing both sides by 3, we get} \\ x=\frac{1}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{ Let }\log _8(\frac{1}{8})=x \\ \\ \frac{1}{8}=8^x \\ \\ 8^{-1}=8^x \\ -1=x \\ x=-1 \end{gathered}[/tex][tex]\begin{gathered} \text{ Let }\log _9(1)=x \\ 1=9^x \\ 9^0=9^x \\ x=0 \end{gathered}[/tex][tex]\begin{gathered} \text{ Let }\log _{\frac{1}{9}}(-1)=x \\ \\ -1=(\frac{1}{9})^x \\ \\ No\text{ solution because it has no real value.} \end{gathered}[/tex]Related Questions
what's the answer
find m<2ifm
Answers
The m∠2 is m∠2 = 14°.
What is degree measure?
Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.
As given in the figure,
m ∠WHI = 160°,
m ∠EHI = 104°
m ∠THE = 42°
We have to find the m ∠2
From figure,
m ∠WHI = m ∠WHT + m ∠THE + m ∠EHI
m ∠WHT = m ∠WHI - m ∠THE - m ∠EHI
m ∠WHT = 160° - 42° - 104°
m ∠WHT = 14°
Hence the measure of angle 2 is, m ∠2 = 14°.
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Divide f(x) = x^3 - x^2 - 2x + 8 by (x-1) then find f(1)
Answers
Division of f(x) = x³ - x² - 2x + 8 by (x-1) will have a quotient of x² - 2 and a remainder of 6.
What is the remainder theoremThe remainder theorem states that if f(x) is divides by x - a, the remainder is f(a).
We shall divide the f(x) = x³ - x² - 2x + 8 by x - 1 as follows;
x³ divided by x equals x²
x - 1 multiplied by x² equals x³ - x²
subtract x³ - x² from x³ - x² - 2x + 8 will result to -2x + 8.
-2x² divided by x equals -2
x - 1 multiplied by -2 equals -2x + 2
subtract -2x + 2 from -2x + 8 will result to a remainder of 6, and a quotient of x² - 2.
f(1) = (1)³ - (1)² - 2(1) + 8
f(1) = 1 - 1 - 2 + 8
f(1) = 6
Therefore, f(1) is a remainder of as x - 1 divides f(x) = x³ - x² - 2x + 8 resulting to a quotient of x² - 2 and a remainder of 6
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Directions: Find the missing number in each question, then identify the property used.4. 10* ( 2 + 6 )= ( 10 * 2 ) + ( 10 * x )
Answers
Answer:
The missing number: 6
The property used: Distributive Property of Multiplication
Explanation:
Given the below;
[tex]10\cdot(2+6)=(10\cdot2)+(10\cdot x)[/tex]The below shows an example of the distributive property of multiplication;
[tex]a(b+c)=(a\cdot b)+(a\cdot c)[/tex]Applying the distributive property in the given equation, we can see that;
[tex]x=6[/tex]So the missing number is 6 and the equation can be written as;
[tex]10*(2+6)=(10\cdot2)+(10\cdot6)[/tex]Determine the range of the following graph:
Answers
Answer:
R: {y | -11 ≤ y < 11}
Step-by-step explanation:
Range is going to include the possible output values in regards to the Y-axis on the graph. As far as when to use equal to and not, the open circle means it does NOT include that number, since the circle is not colored in on that number, while the full circle DOES include that number, and that is when you would introduce the equal than.
Hope this helps.
Radiation machines used to treat tumors produce an intensity of radiation that variesinversely as the square of the distance from the machine. At 3 meters, the radiationintensity is 62.5 milliroentgens per hour. What is the intensity at a distance of 2.6 meters?The intensity is(Round to the nearest tenth as needed.)
Answers
Answer: Intenisy = 83.2 milliroentgens per hour
Let the intensity from the radiation = I
Let the distance = d
The intensity is inversely proportional to the square of its distance
[tex]\begin{gathered} I\text{ }\propto\text{ }\frac{1}{d^2} \\ \text{Introducing a proportionality constant} \\ I\text{ = }\frac{k\text{ x 1}}{d^2} \\ I\text{ = }\frac{k}{d^2} \\ \text{When I = 62.5 , d = 3} \\ \text{From the above equation} \\ K=I\cdot d^2 \\ K\text{ = 62.5 }\cdot(3)^2 \\ K\text{ = 62.5 x 9} \\ K\text{ = 562.5 } \\ \text{ Find the intensity wen D = 2.6 meters} \\ I\text{ = }\frac{k}{d^2} \\ I\text{ = }\frac{562.5}{(2.6)^2} \\ I\text{ = }\frac{562.5}{6.76} \\ I\text{ = 83. 2 milliroentgens per our} \end{gathered}[/tex]Select the correct difference.-325 - (-725)4 z4 25-10 25-45
Answers
Given:
-325 - (-725)
We know that negative negative equals positive
(- -) = +
Therefore, we have:
-325 - (-725)
= -325 - -725
= -325 + 725 = 400
ANSWER:
400
Write the equation in standard form for the circle passing through (-7,7) centered at theorigin.
Answers
Step 1
State the equation of a circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where
h= -7
k= 7
Step 2
Find r
r is the distance between the origin and (-7,7)
Distance between 2 points is
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2^{}}[/tex][tex]\begin{gathered} \text{where} \\ x_2=0 \\ x_1=-7 \\ y_2=0 \\ y_1=7 \end{gathered}[/tex]Hence the distance is given as
[tex]\begin{gathered} d=\sqrt[]{(0-(-7))^2+(0-7)^2} \\ d\text{ =}\sqrt[]{49+49} \\ d=\sqrt[]{98} \\ d=7\sqrt[]{2} \end{gathered}[/tex]Hence r =7√2
Step 3
Write the equation in standard form after substitution.
[tex]\begin{gathered} (x-(-7))^2+(y-7)^2=(7\sqrt[]{2})^2 \\ (x+7)^2+(y-7)^2=(7\sqrt[]{2})^2 \end{gathered}[/tex]Which of the following lines is not perpendicular to y = –1.5x + 11?A. y =2/3x + 5B. 3y = 2x – 9C. 2y = 3x + 10D. –2x + 3y = 7
Answers
B. 3y = 2x – 9
is not perpendicular to the given line.
Explanation:The slopes of perpendicular lines are negative reciprocals
Given the line
y = -1.5x + 11
The slope is -1.5 or -3/2
Any line perpendicular to the one above must have its slope as 2/3
A. The slope is 2/3 . CORRECT
B. The slope is 2/3. CORRECT
C. The slope is 3/2. WRONG
D. The slope is 2/3. CORRECT
George shot the basketball 20 times in his game on Saturday. Of those 20 shots, he made 15.
What percentage of the shots did George make?
Answers
George made 75 percent of the shots.
First, let us understand the percentage:
A percentage is a fraction of a whole expressed as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.
To determine a percentage, we need to divide the portion of the whole by the whole itself and multiply by 100.
We are given the following:
George shot the basketball 20 times in his game on Saturday.
Of those 20 shots, he made 15.
We need to find the percentage of the shots George made.
The percentage of shots George made is given by:
Percentage = 15 / 20 * 100 = 15 * 5 = 75 %
So, 75 % of the shots did George make.
Thus, George made 75 percent of the shots.
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Factorise 49n^3 -- 25m^3
Answers
Factorization of 49n^3 -- 25m^3 is (5m + 7n) × (5m - 7n)
A difference of two perfect squares, A2 - B2 can be factored into (A+B×(A-B)
(A+B) • (A-B)
= A2 - AB + BA - B2
= A2 - AB + AB - B2
= A2 - B2
AB = BA is the commutative property of multiplication.
- AB + AB equals zero and is therefore eliminated from the expression.
⇒ 25 is the square of 5
⇒ 49 is the square of 7
⇒ m2 is the square of m1
⇒ n2 is the square of n1
Hence, The Factorization is (5m + 7n) × (5m - 7n)
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PLEASE HELP WILL GIVE BRAINLIEST URGENTTTTT. AM I RIGHT?
Answers
Answer 3rd one
Step-by-step explanation:
A file that is 273 megabytes is being downloaded. If the download is 15.6% complete, how many megabytes have been downloaded? round your answer to the nearest tenth.
Answers
1750 megabytes has been downloaded.
What do you mean by percentage?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If you need to calculate the percentage of a number, divide the number by the whole number and multiply by 100. Percentages therefore mean 1 in 100. The word percent means around 100. Represented by the symbol '%'.Percentages have no dimension. Hence it is called a dimensionless number.
It is given that 273 megabytes has been downloaded and it is 15.6% of complete.
Let x be the complete storage
15.6% of x = (15.6/100) × x
(15.6/100) × x = 273
x = (273/15.6) × 100 = 2730/15.6 = 1750
Therefore, 1750 megabytes has been downloaded.
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Math To Do, -ReadyHome Jefferson County School X+/student/dashboard/homeWhich unit would you most likely use to measure the capacity of a mug?
Answers
Although both fluid ounces and quarts are measurements for volume, the mug would be a very small fraction of a quart.
Thereby, the most likely unit of measurement used for the capacity of a mug would be fluid ounces.
Find an equation of the line that satisfies the conditionPasses through (-1,-3) and (4,2)
Answers
The points given are:
(-1, -3) and (4, 2)
Coordinates are:
x₁ =-1 y₁=-3 x₂ = 4 y₂ = 2
First, let's find the slope(m) of the equation using the formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]=\frac{2+3}{4+1}=\frac{5}{5}=1[/tex]Next, find the inetercept of the equation by substituting x =-1 y=-3 m = 1 into y=mx+ b
-3 = 1(-1) + b
-4 = -1 + b
Add 1 to bothside
-4+1 = b
-3 = b
b = -3
We can now form the equation of the line by simply substituting the value of m and b into y=mx+ b
y = x - 3
Therefore, the equation of the line that satisfies the condition is y = x - 3
Use<, >, or = to compare each pair of
expressions.
(-5)², -5² (-5)³, -53
Answers
Using <, >, or = to compare each pair of expressions, we get:
(A) (-5)² > -5² (-5)³(B) -5² (-5)³ < -53(C) (-5)² > -53What are expressions?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
It's possible to multiply, divide, add, or subtract with this mathematical operation.
So, using <, >, or = to compare each pair of expression:
Given expressions: (-5)², -5² (-5)³, -53
Then,
(A) (-5)²__-5² (-5)³
(B) -5² (-5)³ __ -53
(C) (-5)² __ -53
Now calculate as follows:
(A) (-5)²__-5² (-5)³
25 __ 25(-125)
25 > -3,125
(B) -5² (-5)³ __ -53
-3,125 < -53
(C) (-5)² __ -53
25 > -53
Therefore, using <, >, or = to compare each pair of expressions, we get:
(A) (-5)² > -5² (-5)³(B) -5² (-5)³ < -53(C) (-5)² > -53Know more about expressions here:
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4.5x + 5 = (if x = 4)
Answers
Answer:
23
Step-by-step explanation:
There is a population of 205 tigers in a national park. They are being illegally poached at the rate of 7tigers per year.Assume the population is otherwise unchanging, write a linear model using "P" for population and "t" fortime.What does the t-intercept signify?NOTE: This answer will NOT be automatically graded and will appear as a 0 until the instructor hasgraded it.Question Help: Message instructorSubmit Question
Answers
Solution.
Initial population = 205
After 1 year, population = 205 - 7 = 198
After 2 years , population = 198 - 7 = 191
After 3 years , population = 191 - 7 = 184
We can generate a table of value for the changes
[tex]\begin{gathered} Slope\text{ of the line, m = }\frac{198-205}{1-0} \\ m=-\frac{7}{1} \\ m=-7 \end{gathered}[/tex]One point on the line = (0, 205)
[tex]\begin{gathered} The\text{ equation of the linear model can be gotten using the formula} \\ y-y_1=m(x-x_1) \\ y-205=-7(x-0) \\ y-205=-7x \\ y=-7x+205 \\ Replacing\text{ y with P and x with t} \\ The\text{ linear model is P = -7t + 205} \end{gathered}[/tex]The t-intercept signifies the time when the population of the tiger will be zero. That is the time when there will be no more tigers in the park
Answer:
Step-by-step explanation:
bbbbbbbbbbb
Kyle can wash the car in 30 minutes. Michael can wash the car in 40 minutes. Working together, can they wash the car in less than 16 minutes?
Answers
Step-by-step explanation:
Kyle can do in 1 minute 1/30 of the work.
Michael can do in 1 minute 1/40 of the work.
the whole work is 1.
how much can they do together in 16 minutes ?
16×1/30 + 16×1/40 = 8/15 + 2/5 = 8/15 + 3/3 × 2/5 =
= 8/15 + 6/15 = 14/15
which is less than 1 = 15/15.
so, as they cannot even do the whole work in 16 minutes, they cannot do it in less than 16 minutes either.
find the counterexample to show that the statement is incorrect the difference of any two counting numbers will be a counting numbera: 7-4=3 which is not a counting number b: 10-2=8 which is a counting numberc: 3-5= -2 which is not a counting number d: there is no counterexample they statement is correct.
Answers
The right answer to your question is b: 10-2=8 which is a counting number
Nicolas drinks 2/3 liters of water in the morning and three 1/2 liters of water at lunch . during basketball practice, he drinks another 2/5 liter of water. what is the total amount of water in liters, that Nicolas drinks.
Answers
The total amount of water Nicholas drank is 47/ 30 liters of water.
Given : Amount of water Nicholas drinks in the morning = 2/3 liters
Amount of water he drinks at lunch = 1/2 liters
Amount of water he drinks during his basketball practice = 2/5 liters
Thus to calculate the total amount of water he drank in the whole we would you the operation of addition in which we will add all the above mentioned value.
The value which comes after adding all of the above mentioned numbers is called sum .
Thus the total amount of water Nicholas drank = 2/3 + 1/2 + 2/5
On taking the LCM we will get
= [tex]\frac{20 + 15 + 12}{30}[/tex]
= 47 / 30
Thus the total amount of water Nicholas drank is 47/ 30 liters of water.
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una persona olvido su paraguas en un autobuses pero se acordó que la suma de los digitos del l camion eran 11 si su producto son 24 que numeros eran del camion
Answers
Ecuaciones
Llamemos x al primer número del camión y y al segundo número.
Tenemos que su suma es 11, así que:
x+y=11
También sabemos que su producto es 24:
xy=24
De esta forma, tenemos un sistema de ecuaciones. Vamos a despejar la x de la primera ecuación:
x=11-y
Y la reemplazamos en la segunda:
(11-y)y=24
Operamos y ordenamos el poninomio para formar la ecuación cuadrática:
[tex]\begin{gathered} 11y-y^2=24 \\ y^2-11y+24=0 \end{gathered}[/tex]Para hallar las soluciones de esta ecuación, tomemos los coeficientes de la ecuación de segundo grado:
a=1, b=-11, c=24
Y aplicamos la fórmula resolvente
[tex]\begin{gathered} y=\frac{-\text{b}\pm\sqrt[]{b^2-4ac}\text{ }}{2a} \\ y=\frac{11\pm\sqrt[]{(-11)^2-4(1)(24)}\text{ }}{2(1)} \\ y=\frac{11\pm\sqrt[]{121-96}\text{ }}{2} \\ y=\frac{11\pm\sqrt[]{25}\text{ }}{2} \\ y=\frac{11\pm5\text{ }}{2} \end{gathered}[/tex]Tenemos dos posibles respuetas:
y=16/2=8
y=6/2=3
Sustituimos ambas respuestas para hallar x:
x=11-y
x=11-8=3
x=11-3=8
En cualquier orden que los tomemos, los números del camón eran 3 y 8
Nate's age is six years more than twice Connor's age. If the sum of their ages is 24 find each age
Answers
Answer:
12
Step-by-step explanation:
nate's age=6
connor's age =6+6=12
Nate's age +connor's age =24
Nate's age=24÷3=8
connor's age=8+8=16
the sum of thier ages =24
For the expression, which of the following is the coefficient of the term involving the variable x. x^3/2 + 4y + 5z²1. 3/22. 23. 34. 1/2
Answers
Given the expression:
[tex]\text{ }\frac{x^3}{2}+4y+5z^2[/tex]The term that involves the variable x is x^3/2.
Let's determine its coefficient:
[tex]\text{ }\frac{x^3}{2}\text{ = }\frac{1}{2}x^3[/tex]Therefore, the coefficient of the term that involves the variable x is 1/2.
GG is considering two websites for downloading music. The costs are detailed here.
Website 1: a yearly fee of $15 and $5 for each download
Website 2: $7 for each download
Select the equation for Website 1.
Responses
y=15x+5
y=5x+15
y=−7x
y=7x
Answers
The equation for Website 1 is y = 15 + 5x option (A) is correct if yearly fee of $15 and $5 for each download
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
GG is considering two websites for downloading music.
Website 1: a yearly fee of $15 and $5 for each download
Let x be the number of downloads
Equation for the website 1:
Total cost is y
y = 15 + 5x
Thus, the equation for Website 1 is y = 15 + 5x option (A) is correct if yearly fee of $15 and $5 for each download
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two cards are drawn without replacement from a standard deck of 52 playing cards what is the probability of choosing a club and then without replacement a spade
Answers
occurringGiven a total of 52 playing cards, comprising of Club, Spade, Heart, and Spade.
[tex]\begin{gathered} n(\text{club) = 13} \\ n(\text{spade) =13} \\ n(\text{Heart) = 13} \\ n(Diamond)=\text{ 13} \\ \text{Total = 52} \end{gathered}[/tex]Probability of an event is given as
[tex]Pr=\frac{Number\text{ of }desirable\text{ outcome}}{Number\text{ of total outcome}}[/tex]Probability of choosing a club is evaluated as
[tex]\begin{gathered} Pr(\text{club) = }\frac{Number\text{ of club cards}}{Total\text{ number of playing cards}} \\ Pr(\text{club)}=\frac{13}{52}=\frac{1}{4} \\ \Rightarrow Pr(\text{club) = }\frac{1}{4} \end{gathered}[/tex]Probability of choosing a spade, without replacement
[tex]\begin{gathered} Pr(\text{spade without replacement})\text{ = }\frac{Number\text{ of spade cards}}{Total\text{ number of playing cards - 1}} \\ =\frac{13}{51} \\ \Rightarrow Pr(\text{spade without replacement})=\frac{13}{51} \end{gathered}[/tex]Thus, the probability of both events occuring (choosing a club, and then without replacement a spade) is given as
[tex]\begin{gathered} Pr(\text{club) }\times\text{ }Pr(\text{spade without replacement}) \\ =\frac{1}{4}\text{ }\times\text{ }\frac{13}{51} \\ =\frac{13}{204} \end{gathered}[/tex]Hence, the probability of choosing a club, and then without replacement a spade is
[tex]\frac{13}{204}[/tex]Isabelle read a total of 20 books over 2 months. If Isabelle has read 30 books so far, how many months has she been with her book club? Assume the relationship is directly proportional.
Answers
Answer: she has been in book club for 3 months
Step-by-step explanation:
The reason is that she can read 10 books in one months than you would multiply it by three.
Answer:
3 months
Step-by-step explanation:
20:2/2=
10:1
10:1 x 3 = 30:3
30 books= 3 months.
How do you do it further problems.1. Find the Unit Rate2. Find the scale factor.3. Use the scale factor to get your answer.I NEED HELP WITH THIS
Answers
Answer:
see explanation
Step-by-step explanation:
given that W varies jointly with l and d² then the equation relating them is
W = kld² ← k is the constant of variation
(a)
to find k use the condition W = 6 when l = 6 and d = 3 , then
6 = k × 6 × 3² = 6k × 9 = 54k ( divide both sides by 54 )
[tex]\frac{6}{54}[/tex] = k , then
k = [tex]\frac{1}{9}[/tex]
W = [tex]\frac{1}{9}[/tex]ld² ← equation of variation
(b)
when W = 10 and d = 2 , then
10 = [tex]\frac{1}{9}[/tex] × l × 2² ( multiply both sides by 9 to clear the fraction )
90 = 4l ( divide both sides by 4 )
22.5 = l
(c)
when d = 6 and l = 1.4 , then
W = [tex]\frac{1}{9}[/tex] × 1.4 × 6² = [tex]\frac{1}{9}[/tex] × 1.4 × 36 = 1.4 × 4 = 5.6
ow 3. Hto What is the surface area of this triangular prism? 15 in. 12 in. 7 21 in 18 in. A. 846 in. B. 909 in. C. 1,062 in. D. 1,224 in. 2
Answers
To obtain the surface area of a triangular prism, the formula to employ is:
[tex]\begin{gathered} A_{triangular\text{ prism}}=2A_B+(a+b+c)h \\ \text{where A}_B=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where s=}\frac{a+b+c}{2} \\ a,b\text{ and c are sides of the triangular prism and h is the height} \end{gathered}[/tex]From the image, a=18in, b=21in, c =15in and h=12in
We have to obtain the value of 's' first, from the equation:
[tex]\begin{gathered} s=\frac{a+b+c}{2} \\ s=\frac{18+21+15}{2} \\ s=\frac{54}{2} \\ s=27in \end{gathered}[/tex][tex]\begin{gathered} \text{Then, we obtain the value of A}_B \\ A_B=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A_B=\sqrt[]{27(27-18)(27-21)(27-15)} \\ A_B=\sqrt[]{27(9)(6)(12)} \\ A_B=\sqrt[]{17496} \\ A_B=132.27in^2 \end{gathered}[/tex]The final step is to obtain the area of the triangular, having gotten the values needed to be inputted in the formula;
[tex]\begin{gathered} A_{triangular\text{ prism}}=2A_B+(a+b+c)h \\ A_{triangular\text{ prism}}=(2\times132.27)+(18+21+15)12 \\ A_{triangular\text{ prism}}=264.54+(54)12 \\ A_{triangular\text{ prism}}=264.54+648 \\ A_{triangular\text{ prism}}=912.54in^2 \end{gathered}[/tex]Hence, the surface area of the triangular prism is 912.54 square inches
Given AABC with vertices A(7, 7) B(-5, 3) and C(3,-5),
1) If BE is a median, then point E is located at what coordinate?
2) If AL is a median, at what coordinate would L be located?
3) If LP is a perpendicular bisector, what would be the slope of LP?
4) An altitude is always.
to the side of the triangle.
Answers
ABC's vertices are points A, B, and C. ABC's sides are made up of the AB, BC, and CA segments.
How to calculate vertices of ABC?Determine the length of the median across vertex A of triangle ABC, which has vertices A (7,3), B (5,3), and C.
Assume M(x,y) represents the ABC median from A to BC.
M will be the point at which BC splits in half.
x 1 =5, y1 =3
x 2 =3,y2 =−1
Using the midpoint formula, x=(x 1 + x 2)/2
∴x=(5+3)/2=8/2=4
Using the midpoint formula, y=(y 1 + y 2 )/2
∴y=(3+(−2))/2=2/2=1
Consequently, M's coordinates are (4,1).
The distance formula reads d(AM)=
By distance formula, d(AM)= √[(x2 - x1)² + (y2 -y1)²]
x1 = 7,y1 = -3
x2 = 4,y2 = 1
∴d(AM) = √[(4- 7)² + (1 - (-3)²]
∴d(AM) = √(-3)² + (4)² = √9 + 16
∴d(AM) = √25 = 5
As a result, the median AM is 5 units long.
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Mr. Newman packed 16 large - size ornaments and 29 medium - size ornaments into a box. He packed 13 boxers like this. Mr.Newman used this this equation to find x, the number of ornaments he packed into all the boxes x = (16+29)13how many ornaments did Mr.Newman pack into the boxes
Answers
We were told that Mr. Newman packed 16 large - size ornaments and 29 medium - size ornaments into a box. This means that the number of large and medium ornaments in each box is 16 + 29. Given that there were 13 boxes and x represents the total number of ornaments, the equation would be
x = (16 + 29)13
x = 45 * 13
x = 585
Option F is correct