In order to calculate the age of the father, you first consider that the average of the family is 30, then, you have:
(x1 + x2 + x3 + x4 + x5 + x6)/6 = 30
where x3, x4, x5 and x6 are the ages of the children, x1 is the age of the mother and x2 is the age of the father
You cn write the previous expression as:
(x1 + x2)/7 + (x3+x4+x5+x6)/7 = 30
The second term in the second expression is the average age of the children, which is 12. Furthermore, the mother is 4 years younger than the father, that is, x1 = x2 - 4. You replace this values in the expression above and you obtain:
(x1 + x2)/7 + (x3+x4+x5+x6)/7 = 30
(x2 - 4 + x2)/7 + 12 = 30
Next, you solve for x2:
(x2 - 4 + x2)/7 + 12 = 30
(2x2 - 4)/7 + 12 = 30
multiply the previous expression by 7:
2x2 - 4 + 12(7) = 30(7)
2x2 - 4 + 84 = 210
2x2 = 130
x2 = 65
Then, the age of the father is 65
What is the sum of the rational expressions below?3xХ+X+9 X-4O A.4x2-3xx2 +5X-36O B. 4x2-3x2x+5C.4x2x+5hosD.4xx2 +5x - 36
Given
[tex]\frac{3x}{x+9}+\frac{x}{x-4}[/tex]To find the sum of the rational expressions.
Explanation:
It is given that,
[tex]\frac{3x}{x+9}+\frac{x}{x-4}[/tex]Then,
[tex]\begin{gathered} \frac{3x}{x+9}+\frac{x}{x-4}=\frac{3x(x-4)+x(x+9)}{(x+9)(x-4)} \\ =\frac{3x^2-12x+x^2+9x}{x^2+9x-4x-36} \\ =\frac{4x^2-3x}{x^2+5x-36} \end{gathered}[/tex]Hence, the answer is option A).
Show me how do divided 6.345 ÷ 0.09 step by step.
70.5
1) To divide a decimal number by another one, we can turn them into fractions and simplify it, whenever possible:
[tex]\begin{gathered} 6.345=\frac{6345}{1000} \\ 0.09=\frac{9}{100} \end{gathered}[/tex]Each decimal place represents the number of zeros beside the 1 on the denominator, or each decimal place represents 1/10.
2) Dividing it as fractions, we need to multiply the first by its reciprocal:
[tex]\frac{\frac{6345}{1000}}{\frac{9}{100}}=\frac{6345}{1000}\times\frac{100}{9}=\frac{6345}{90}=\frac{141}{2}=70.5[/tex]Notice that we simplified 6345/90 by 45 then we got 141/2. In other words, 6345/100 and 141/2 are the same, Because 141/2 is the nonreducible fraction.
To divide 6.345 ÷ 0.09 using long division, let's multiply first both numbers by 100, doing this we'll keep the proportionality, and make our calculations easier.
6.345 x 100 = 634.5
0.09 x 100 = 9
1) First, let's divide 634 by 9. 70 x 9 = 630. The closest value.
2) Then let's bring down 4.5. 4.5 ÷ 9 = 0.5
3) 70.5 x 9 = 634.5.
Kris and Pat were born on the exact same day but not in the same year their ages are shown in the table When Pat was 30 how old was Chris
A ) 18 years old
B) 19 years old
C) 27 years old
add three to kris' age to find Pat's age
Explanation
Step 1
when Kris was 15 .how old was pat
find the rule
a) check if the difference between the ages is constant
[tex]\begin{gathered} \text{Pat's age - Kris' Age=} \\ 7-4=3 \\ 10-7=3 \\ 15-12=3 \\ y_4\text{-}15= \\ 22-x_5= \\ 26-23=3 \end{gathered}[/tex]it means Pat is 3 years older than Kriss
then
when Kris was .how old was pat
[tex]\begin{gathered} y_4\text{-}15=3 \\ y_4-15=3 \\ \text{add 15 in both sides} \\ y_4-15+15=3+15 \\ y_4=18 \end{gathered}[/tex]Step 2
when Pat was 22, How old was Kris
the difference between the ages is the same, 3
so
[tex]\begin{gathered} 22-x_1=3 \\ \text{subtract 22 in both sides} \\ 22-x_5-22=3-22 \\ -x_5=-19 \\ x_5=19 \end{gathered}[/tex]Step 3
when Pat was 30, How old was kris
replace
[tex]\begin{gathered} \text{Pat's age -Kris' age=3} \\ 30-\text{Kri's age=3} \\ \text{subtract 30 in both sides} \\ 30-\text{Kri's age-30=3-}30 \\ -\text{Kris'age =-27} \\ \text{Kris'age }=27 \end{gathered}[/tex]Step 4
wich choice best represents the rule
as we saw before,
add three to kris' age to find Pat's age
[tex]\text{Kris' age+3}=\text{Pat's age}[/tex]Last season, your favorite basketball teamwon 60 games. So far this season, yourfavorite basketball team has won 72 games.What is the percent change in the numberof games that your favorite team won fromlast season to this season?
In order to determine the percent change in the number of games, you first calculate the difference between the number of games won last season and current season.
current season = 70 games won
last season = 60 games won
70 - 60 = 10
next, you determine what is the associated percent of 10 games to 60 games from the last season. You proceed as follow:
(10/60)(100) = 16.66
that is, you calculate the quotient between increase of games won, the number of games won last season, and to the result you multiply by 100.
Hence, the increase in the percent of games won is of 16.66%
Compare each pair of rationals using a <, >, or =. 7. 3/4 ____ 7/10 8. -1.6 ____ 0.3 9. 2.8 ____ 5/2
EXPLANATION:
To know when a fraction is greater than another, the following procedure must be done, they must be multiplied by a cross and the result in whole number will determine which of the two is greater.
[tex]\begin{gathered} 7.\frac{3}{4}\text{ }>\frac{7}{10}=(3\times10)=30(4\times7)=28 \\ \\ \end{gathered}[/tex]7.You must first cross multiply the denominator of the first fraction with the number of the second fraction, then multiply the denominator of the second fraction with the numerator of the first fraction,So you will have the exact answer of which is the greatest.
[tex]8.\text{ -1.6 }<0.3[/tex]8.Every negative number that moves away from zero is always less than zero.
9.To compare or know which is greater if a decimal or a fraction we must divide the fraction between itself and this will give me a decimal, now if I can compare;
[tex]\begin{gathered} \frac{5}{2}=2.5_{} \\ \text{Now }compare\text{ the two decimals:} \\ 2.8>2.5; \end{gathered}[/tex]that is, 2.8 is greater than the fraction 5/2
find the real solution(s), if any, of the system by examining the graph
Given:
[tex]\begin{gathered} -6x-3y=18\ldots\ldots\ldots(1) \\ \frac{x^{2}}{9}+\frac{y^{2}}{36}=1\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]Let us consider the equation (1),
[tex]\begin{gathered} -6x-3y=18 \\ -2x-y=6 \\ -y=2x+6 \\ y=-(2x+6)\ldots\ldots\ldots(3) \end{gathered}[/tex]Substitute equation (3) in (2), we get
[tex]\begin{gathered} \frac{x^2}{9}+\frac{(-(2x+6))^2_{}}{36}=1 \\ \frac{4x^2}{36}+\frac{4x^2+36+24x}{36}=1 \\ \frac{4x^2+4x^2+36+24x}{36}=1 \\ 8x^2+36+24x=36 \\ 8x^2+24x=0 \\ 8x(x+3)=0 \\ x=0,x=-3 \end{gathered}[/tex]Substitute x=0 and x=-3 in equation (3) we get,
[tex]\begin{gathered} y=-(2(0)+6) \\ =-6 \\ y=-(2(-3)+6) \\ =0 \end{gathered}[/tex]Hence, the solutions are, (0,-6) and (-3,0).
Let us verify this, by substituting (0,-6) and (-3,0) in equation (1), we get
For (0, -6),
[tex]\begin{gathered} -6(0)-3(-6)=18 \\ 18=18 \end{gathered}[/tex]For (-3, 0)
[tex]\begin{gathered} -6(-3)-3(0)=18 \\ 18=18 \end{gathered}[/tex]Hence, it is verified.
f(x) = |×| g(x) = |×+9| – 5 We can think of g as a translated (shifted) version of f. Complete the description of the transformation. Use nonnegative numbers. To get the function g. shift f up/down by units and to the right/left v by units.
First we can check the value 9 that is added inside the absolute module operator.
This value is together with the variable x inside the operator, that is, from f(x) we can replace x by 'x + 9' in order to get the first part of g(x)
This addition of 9 to the value of x represents a horizontal translation of 9 units to the left.
Then, the subtraction of 5 units outside the absolute module operator is a addition/subtraction to the function, that is, we can subtract 5 units from f(x) in order to get this second part of f(x).
This subtraction of 5 units to the value of f(x) represents a vertical translation of 5 units down.
So the answer is:
To get the function g(x), shift f down by 5 units and to the left by 9 units.
Calculate the simple interest due on a 54-day loan of $3600 if the interest rate is 3%. (Round your answer to the nearest cent.)
Answer:
$5832.00cents
Step-by-step explanation:
PRT÷100
$3600 ×54 ×3 /100
= $5832.00cents.
Use the following information to fill out the entire two-way table.At PRHS, there are 450 students in the 9th and 10th grade taking geometry, and one third ofthem are 9th graders. The students were surveyed on which unit from quarter 4 they liked best.65 students said that unit 5 was their favorite, but only 25 of them were 9th graders. Unit 8 wasthe most popular for 9th graders, with 50 of them saying it was their favorite. Unit 7 was themost popular with 10th graders, with 100 of them saying it was their favorite. Unit 6 and Unit 8were equally popular for 10th grade students. A total of 125 students sald that Unit 6 was theirfavorite.Answer ALL 3 of the following questions.1. What is the probability that a randomly selected student will be a 9th grade student OR astudent that preferred unit 7? Show your work or explain how you know. Leave it insimplified fraction form.2. What is the probability that a randomly selected student will be a 10th grade student whoalso prefers unit 8? Show your work or explain how you know. Leave it in simplifiedfraction form.3. Given the student prefers Unit 5, what is the probability the student is in the 10th grade?Show your work and explain how you know. Leave it in simplified fraction form.
Here, we want to calculate probabilities;
We have this as follows;
1) We want to calculate the probability that a randomly selected student is a 9th grader or a student that preferred unit 7
From here, we need the number of students who are 9th graders and students that prefer unit 7
From the question, we have it that 1/3 of the total students are 9th graders
So, for a total of 450, the number of 9th graders will be 1/3 * 450 = 150 students
Secondly we need the number of students that prefers unit 7
Let us try and complete the table as follows;
From the completed table, the numbers that like unit 7 are 130
So the probability we want to calculate is the sum of the two divided by 450
We have this as;
[tex]\frac{130+150}{450}\text{ = }\frac{280}{450}\text{ = }\frac{28}{45}[/tex]2) Here, we want to calculate the probability that a randomly selected student is a 10th grader who also prefers unit 8
From the table, we can see that the number of students who are 10th graders and also prefer unit 8 is 80
So, we have the probability as;
[tex]\frac{80}{450}\text{ = }\frac{8}{45}[/tex]3) Here, we want to calculate the probability that given that a student prefers unit 5, what is the probability that he is a 10th grader
We use the conditional probability value here
Where event A is the probability that student is a 10th grader, while event B is the probability that a student prefers unit 5
We have the probability as;
[tex]\begin{gathered} P(A|B)\text{ = }\frac{P(AnB)}{P(B)} \\ \\ P(\text{AnB) = }\frac{40}{450};\text{ P(B) = }\frac{65}{450} \\ \\ P(A|B)\text{ = }\frac{40}{65} \end{gathered}[/tex]2. The following triangle is an isosceles triangle. What is the length of the missing side? ? 11 in. 37 ? 4 in. 11 in 37° 4 in 530
An ISOSCELES triangle has two sides equal, and two base angles are also equal.
The two sides on the left and the right are equal. The right side measures 11 inches, therefore the left side also measures 11 inches.
The correct answer option is 11 inches
Let and y be whole-number variables such that y is the greatest whole number less than or equal to the table below lists some valuesfor and y.xy79411 513 6Which of the following statements is true?A. y changes by a constant amount when r changes by 2.OB. z changes by a constant amount when y changes by 1.C. y changes by a constant amount when changes by 1.D. 2 changes by a constant amount when y changes by 2.
we have
Verify each statement
A -------> For (7,3) and (9,4) -----> x changes by 2 and y change by 1
(9,4) and (11,5) -------> x changes by 2 and y change by 1
(11,5) and (13,6) -----> x changes by 2 and y change by 1
option A is true
B ----> option B is true
C -----> is not true
D ----> (7,3) and (11,5) ------> y changes by 2 and x changes by 4
(9,4) and (13,6) ----> y changes by 2 and x changes by 4
option D is true
step 2
Verify A, B and D
For x=14 ------> y=7
For x=16 -------> y=8
For x=18 ------> y=9
the answer must be option AI need to know if A and B are CORRECT and I need HELP WITH C
The sum of all angles of a triangle is always equal to 180°. Therefore, looking at triangle A we have 3 angles, 53°, 68°, and x. The sum of them will be 180:
a)
[tex]x+53+68=180[/tex]Now we solve it for x
[tex]\begin{gathered} x=180-53-68 \\ \\ x=59\degree \end{gathered}[/tex]b)
Same thing here, the angles are 46°, 71°, and x, the sum is equal to 180°:
[tex]\begin{gathered} x+46+71=180 \\ \\ x=180-46-71 \\ \\ x=63\degree \end{gathered}[/tex]c)
Now for C, we have the angles x, x again, and 24°, therefore the sum will be
[tex]\begin{gathered} x+x+24=180 \\ \\ 2x+24=180 \\ \\ 2x=180-24 \\ \\ 2x=156 \\ \\ x=\frac{156}{2} \\ \\ x=78\degree \end{gathered}[/tex]Final answers:
a) x = 59°
b) x = 63°
c) x = 78°
a circle with radius 12 mm is rotated around a diameter what is the volume of the solid formed
We know that the radius of the sphere will be equal to the radius of the circle:
Since the equation for the volume of the sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]where r is the radius
r = 12 mm
and
π = 3.1416
We can replace it:
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \downarrow \\ V=\frac{4}{3}\pi\cdot(12\operatorname{mm})^3 \\ \downarrow\text{ since}(12\operatorname{mm})^3=1728\operatorname{mm}^3 \\ V=\frac{4}{3}\pi\cdot1728\operatorname{mm}^3 \\ \downarrow\text{ since }\frac{4}{3}\cdot1728=2304 \\ V=2304\pi\operatorname{mm}^3 \\ \downarrow\text{ since }\pi=3.1416 \\ V=7238.2\operatorname{mm}^3 \end{gathered}[/tex]AnswerThen, the volume is given by
2304π mm³
or
7238.2 mm³
Two-Variable inequalities from their graph. (0,0) and (4,3)
Points (0,0) (4,3)
Find slope m of line y= mx + b
m = 4/3. Positive
b= 0
Then equation is
y = (4/3)x
Now find inequality
y ≤ (4/3)x
Blue zone represents inequality searched
Answer is y≤ (4/3)x
If two lines intersect and one angle measures 25°, what are the measures of the other angles?1. 1252. 1553. 754. 25
When two lines intersect, four angles are created. Opposite angles are equal, therefore, we have two sets of angles with the same measure. Adjacent angles are supplementary.
By definition, supplementary angles add up to 180º. Since in our intersection we have an angle of 25º, the adjacent angles will be 180º minus 25º.
[tex]180-25=155[/tex]The measure of the other angles are 155º.
$5,500 how much money would be in the savingaccount after 5 years if the compounds interest monthly at a rate of 5% per year.
Answer:
There would be $7,058.47 in the saving account.
Step-by-step explanation:
The amount of money, after t years, with compound interest, is given by the following formula:
[tex]A(t)=P(1+\frac{r}{n})^{n\ast t}[/tex]In which:
P is the amount of the initial deposit.
r is the interest rate, as a decimal.
n is the number of compoundings per year.
t is the number of years.
In this question:
Deposit of $5,500, so P = 5500.
5 years, so t = 5.
Rate of 5%, so r = 0.05.
Monthly compounding, so 12 times a year, which means that n = 12.
Then
[tex]A(5)=5500(1+\frac{0.05}{12})^{12\ast5}=7058.47[/tex]There would be $7,058.47 in the saving account.
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC = 15 and DC = 6, what is the length of BC in simplest radical form? (Note: the figure is not drawn to scale.) B х A D 6 C с 15 Submit Answer Answer: I
Answer
BC = x = 3√10
Explanation
To answer this question, we will use the concept of similar triangles.
We know that the two triangles ABC and BDC are similar because they are right angle triangles with one common non-right angle angle too, Angle C.
Using angle C as a reference point, we can write the corresponding sides.
And we know that corresponding sides for similar triangles have the same ratio.
∆ABC = ∆BDC
AB is corresponding to BD
BC is corresponding to DC
CA is corresponding to CB
So,
(AB/BD) = (BC/DC) = (CA/CB)
The sides that we need include
BC, DC, CA and CB
BC = x
DC = 6
CA = 15
CB = x
(BC/DC) = (CA/CB)
(x/6) = (15/x)
Cross multiply
x² = (6)(15)
x² = 90
Take the square root of both sides
√(x²) = √(90)
x = √90
x = √[(9)(10)]
x = (√9) (√10)
x = 3√10
Hope this Helps!!!
Algebra 1 Question. Please View Attachment. Help needed ASAP :)
Recall that the graph of h(x) translated n units to the right is the graph of h(x-n).
Now, notice that the given graph is the graph of the function f(x)=x translated 1 unit to the right, therefore the given graph is the graph of f(x-1).
Setting f(x+k)=f(x-1), since the graph is a line we get that:
[tex]x+k=x-1.[/tex]Subtracting x from the above equation we get:
[tex]k=-1.[/tex]Answer: First option.
y=0.5x+3; what is the slope?
The given equation,
[tex]y=0.5x+3[/tex]Comparing it with the slope intercept equation
[tex]y=mx+c[/tex]where m is the slope.
Thus the slope is m=0.5.
2 A cognitive psychologist conducted a study of whether familiarity of words (X) predicts the time it takes (in seconds) to press a button indicating whether the word is singular or plural (I), with all participants being given the same words. Familiarity with these words was rated at a later time on a 7-point scale (with higher numbers indicating more farniliarity). The participants' scores were 6 2 5 3 7 Y 0.3 1.5 0.8 1.4 0.1 a Figure the Pearson correlation coefficient (25 pts.).
We will have the following:
*Firts: We have that the correlation coefficient is given by:
[tex]r=\frac{\sum ^n_{i=1}X_iY_i-\frac{1}{n}(\sum ^n_{i=1}X_i)(\sum ^n_{i=1}Y_i)}{\sqrt[]{\sum^n_{i=1}X^2_i-\frac{1}{n}(\sum^n_{i=1}X_i)^2}\sqrt[]{\sum ^n_{i=1}Y^2_i-\frac{1}{n}(\sum ^n_{i=1}Y_i)^2}}[/tex]*Second: We calculate the means, that is:
[tex]x_m=4.6[/tex]&
[tex]y_m=\text{0}.82[/tex]*Third: We calculate the sums:
[tex]\sum ^n_{i=1}X^2_i-\frac{1}{n}(\sum ^n_{i=1}X_i)^2=123-\frac{23^2}{5}=17.2[/tex][tex]\sum ^n_{i=1}Y^2_i-\frac{1}{n}(\sum ^n_{i=1}Y_i)^2=4.95-\frac{4.1^2}{5}=1.588[/tex][tex]\sum ^n_{i=1}X_iY_i-\frac{1}{n}(\sum ^n_{i=1}X_i)(\sum ^n_{i=1}Y_i)=13.7-\frac{23\cdot4.1}{5}=-5.16[/tex]Fourth: We replace the data:
[tex]r=\frac{-5.16}{\sqrt[]{17.2\cdot1.588}}\Rightarrow r=-0.987[/tex]Thus making the coefficient r = -0.987.
And this would be the scatterplot:
What is the lateral surface area of the of the following figure? A. 982.36B. 851.76C. 785.34D. 709.8
Given : a triangular prism
The lateral surface area is the sum of the rectangular sides
So, the lateral surface area =
[tex]\begin{gathered} 18.2\cdot13+18.2\cdot13+18.2\cdot20.8 \\ =851.76\operatorname{cm} \end{gathered}[/tex]Another method : Find the perimeter of the triangle then multiply by 18.2
[tex]\begin{gathered} 18.2\cdot(13+13+20.8)_{} \\ =18.2\cdot46.8 \\ =851.76\operatorname{cm} \end{gathered}[/tex]so, the answer is option B. 851.76
9. A gallon of lemonade calls for 2 scoops of sugar. If you want to make 5 gallons, how much sugar should you put in? (2 pts)
Answer:10
Step-by-step explanation: if you need 2 for 1 gallon multiply it by 5
you have 1 gallon with 2 scoops
2 for 5 gallons gives you 10 scoops total for 5 gallons
what is the domian of the graph
answer:
2 ≤ x ≤ 5
step-by-step explanation:
at the end of the piece-wise function (the short line), the circles are closed.
closed circles = ≤ or ≥
open circles = < or >
immediately, c and d are out of the equation.
the domain refers to what the range of x-values is (bottom line) so let's look. we have (2,5) and (5,3)
the x-values of those are 2 and 5, with x in between/including them.
(if we were to find the range it would be 5 and 3, with x in between/including them)
so, 2 ≤ x ≤ 5. we use ≤ because it is not smaller than 2, and not bigger than five. using ≥ would be all numbers except in between 2 and 5.
Will anyone be willing to help me with this? i’ll give 10 points
Only first table correctly represents y as a function of x where each value of x is mapped to a unique value of y.
What is a function?A function is defined from a set x to a set y where each element of x receives exactly one element of y. The set x is referred to as the function's domain, while the set y is referred to as the codomain of the function. A popular representation of this connection is y = f(x), which is pronounced "f of x."
Consider the first table:
Any value of x is mapped to a single value of y. Therefore first table represents a function.
Consider the second table:
For x = -50, there are 2 different values of y which are 50 and -50. Therefore second table does not represent a function.
Consider the third table:
For x = 21, there are 4 different values of y. Therefore third table does not represent a function.
Consider the fourth table:
For x = -25, there are 2 different values of y which are 30 and 20. Therefore fourth table does not represent a function.
To learn more about functions visit the below link:
https://brainly.com/question/22340031
#SPJ13
According to psychologists, IQs are normally distributed, with a mean of 100 and a standard deviation of 18.a. What percentage of the population has IQs between 82 and 100?
To solve this question, we will have to find the Z score.
[tex]Z=\frac{x-\bar{x}}{s.d}[/tex]Where x is the value of the IQ
X-bar is the mean.
s.d is the standard deviation
[tex]\begin{gathered} Z_1=\frac{82-100}{18} \\ =-\frac{18}{18} \\ =-1 \end{gathered}[/tex][tex]Z_2=\frac{100-100}{18}[/tex][tex]\begin{gathered} Z_2=\frac{0}{18} \\ =0 \end{gathered}[/tex]The percentage of the population with IQs between 82 and 100 will be calculated thus:
[tex]\begin{gathered} P(-1-1) \\ =0.5-0.1587 \\ =0.34134 \\ \text{The percentage is}\colon \\ =0.34134\times100=34.134\text{ \%} \end{gathered}[/tex]16. - 2y +5=-1Is 3 the solution?17. 1.3m -5.6 = -3Is-2 the solution?
To find out if a certain value of the variable is the solution of the equation we plug this value into the equation:
[tex]\begin{gathered} 1.3(-2)-5.6=-3 \\ -2.6-5.6=-3 \\ -8.2=-3 \end{gathered}[/tex]Since the last line is not true, then we conclude that -2 IS NOT the solution.
Can you please help me with the following equation
a(1.50) + b(0.50) = $7.00
Answer:
1.50a+0.50b=7.00
2.00ab=7.00
ab=3.1
Given the matrices A and B shown below, find – B – 1/3A[ -18 3]. [ -4 12][ -15 -6] [ 8 -12]
Answer:
[10 -13]
[-3 14]
Explanation:
First, we will calculate 1/3A, so:
[tex]\frac{1}{3}A=\frac{1}{3}\begin{bmatrix}{-18} & 3 & \\ {-15} & -6 & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{\frac{1}{3}(-18)} & {\frac{1}{3}(3)} & \\ {\frac{1}{3}(-15)} & {\frac{1}{3}(-6)} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-6} & {1} \\ {-5} & {-2} \\ & {}\end{bmatrix}[/tex]Because 1/3 multiply each value in the matrix. Now, adding the respective values in the same position, we can calculate -B - 1/3A as:
[tex]\begin{gathered} -B-\frac{1}{3}A=-\begin{bmatrix}{-4} & {12} & \\ {8} & {-12} & {}{}\end{bmatrix}-\begin{bmatrix}{-6} & {1} \\ {-5} & {-2}\end{bmatrix} \\ -B-\frac{1}{3}A=\begin{bmatrix}{4} & {-12} & \\ {-8} & {12} & {}{}\end{bmatrix}-\begin{bmatrix}{-6} & {1} \\ {-5} & {-2}\end{bmatrix} \\ -B-\frac{1}{3}A=\begin{bmatrix}{4-(-6)} & {-12-1} & \\ {-8-(-5)} & {12-(-2)} & {}{}\end{bmatrix} \\ -B-\frac{1}{3}A=\begin{bmatrix}{4+6} & {-12-1} & \\ {-8+5} & {12+2} & {}{}\end{bmatrix} \\ -B-\frac{1}{3}A=\begin{bmatrix}{10} & {-13} & \\ {-3} & {14} & {}{}\end{bmatrix} \end{gathered}[/tex]Therefore, the answer is:
[tex]-B-\frac{1}{3}A=\begin{bmatrix}{10} & {-13} & \\ {-3} & {14} & {}\end{bmatrix}[/tex]Find the equation of a line passing through the points (3,-4) and (1,2)
Explanation:
The equation of a line in slope-intercept form is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
The formula for the slope of a line with points (x1, y1) and (x2, y2) is:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]In this case the slope is:
[tex]m=\frac{-4-2}{3-1}=\frac{-6}{2}=-3[/tex]For now we have:
[tex]y=-3x+b[/tex]To find the y-intercept b, we have to replace (x,y) for one of the given points and solve for b. If we use point (1,2):
[tex]\begin{gathered} y=-3x+b \\ \text{ replacing x = 1 and y = 2} \\ 2=-3\cdot1+b \\ 2=-3+b \\ b=2+3=5 \end{gathered}[/tex]Answer:
The equation of the line is: y = -3x + 5
Answer:
y=\neg;[3]x+5
Step-by-step explanation:
Rearrange the equation so r is the independent variable q-10=6(r+1)