The boy goes to school by bus for 1 3/4km, then he walks 1/3 km.
To determine the total distance he traveled you have to add both distances:
[tex]1\frac{3}{4}+\frac{1}{3}[/tex]To solve this sum, add the fractions first and then add the result to the whole number:
- Add both fractions:
[tex]\frac{3}{4}+\frac{1}{3}[/tex]To add both fractions you have to express them using the same denominator first. A common multiple between the denominators "4" and "3" is "12". Multiply the first fraction by 3 and the second by 4 to express them as their equivalent fractions with denominator 12. Then proceed to add them:
[tex]\frac{3\cdot3}{4\cdot3}+\frac{1\cdot4}{3\cdot4}=\frac{9}{12}+\frac{4}{12}=\frac{9+4}{12}=\frac{13}{12}[/tex]The result is 13/12, as you can see the numerator is greater than the denominator, which indicates that this is an improper fraction, i.e. its value is greater than 1. You can write this fraction as a mixed number as follows:
- Solve the division:
[tex]13\div12=1.08\bar{3}[/tex]The mixed number will have the whole number "1".
- To express the decimal value as a fraction, multiply it by 12
[tex]0.08\bar{3}\cdot12=1[/tex]The result is the numerator of the fraction, and the denominator will be 12, so:
[tex]0.08\bar{3}=\frac{1}{12}[/tex]And the resulting mixed number is:
[tex]\frac{13}{12}=1\frac{1}{12}[/tex]Finally, add the remaining whole number from the first sum to determine the distance between his house and the school:
[tex]1+1\frac{1}{12}=2\frac{1}{12}[/tex]The distance he traveled from home to school is 2 1/12 km.
In a survey, 12 people were asked how much they spent on their child's last birthday gift. The results wereroughly bell-shaped with a mean of $39.1 and standard deviation of $17.4. Estimate how much a typical parentwould spend on their child's birthday gift (use a 99% confidence level). Give your answers to 3 decimal places.Express your answer in the format of ī + Error.$£ $
Given:
number of people (n) = 12
mean = 39.1
standard deviation = 17.4
99% confidence level
Using the confidence level formula, we can find the estimate of how much a typical parent would spend on their child's birthday:
[tex]\begin{gathered} CI\text{ = x }\pm\text{ }\frac{z\varphi}{\sqrt[]{n}} \\ \text{where x is the mean} \\ z\text{ is the z-score at 99\% confidence interval} \\ \varphi\text{ is the standard deviation} \\ n\text{ is the number of people asked} \end{gathered}[/tex]The z-score at 99% confidence level is 2.576
Substituting, we have:
[tex]\begin{gathered} CI\text{ = 39.1 }\pm\text{ }\frac{2.576\text{ }\times\text{ 17.4}}{\sqrt[]{12}} \\ =26.161\text{ and 52}.039 \end{gathered}[/tex]Hence, a typical parent would spend between $26.161 and $52.039 or :
[tex]39.1\text{ }\pm\text{ 12.939}[/tex]The volume of cylinder is 504 pi cm^(3) & height is 14cm Find the curved surface area 8 total surface area.
The Solution:
The correct answers are:
Curved surface area = 527.79 squared centimeters
Total surface area = 753.98 squared centimeters.
Given that the volume of a cylinder with height 14cm is
[tex]504\pi cm^3[/tex]We are required to find the curved surface area and the total surface area of the cylinder.
Step 1:
We shall find the radius (r) of the cylinder by using the formula below:
[tex]V=\pi r^2h[/tex]In this case,
[tex]\begin{gathered} V=\text{volume =504}\pi cm^3 \\ r=\text{ radius=?} \\ h=\text{ height =14cm} \end{gathered}[/tex]Substituting these values in the above formula, we get
[tex]504\pi=\pi r^2\times14[/tex]Finding the value of r by first dividing both sides, we get
[tex]\begin{gathered} \frac{504\pi}{14\pi}=r^2 \\ \\ r^2=36 \end{gathered}[/tex]Taking the square root of both sides, we get
[tex]\begin{gathered} \sqrt[]{r^2}\text{ =}\sqrt[]{36} \\ \\ r=6\operatorname{cm} \end{gathered}[/tex]Step 2:
We shall find the curved surface area by using the formula below:
[tex]\text{CSA}=2\pi rh[/tex]Where
[tex]\begin{gathered} \text{ CSA=curved surface area=?} \\ h=14\operatorname{cm} \\ r=6\operatorname{cm} \end{gathered}[/tex]Substituting these values in the formula above, we have
[tex]\text{CSA}=2\times6\times14\times\pi=168\pi=527.788\approx527.79cm^2[/tex]Step 3:
We shall find the total surface area by using the formula below:
[tex]\text{TSA}=\pi r^2+\pi r^2+2\pi rh=2\pi r^2+2\pi rh[/tex]Where
TSA= total surface area and all other parameters are as defined earlier on.
Substituting in the formula, we get
[tex]\text{TSA}=(2\pi\times6^2)+(2\pi\times6\times14)=72\pi+168\pi[/tex][tex]\text{TSA}=240\pi=753.982\approx753.98cm^2[/tex]Therefore, the correct answers are:
Curved surface area = 527.79 squared centimeters
Total surface area = 753.98 squared centimeters.
Rewrite 25% as a fraction in simplest form.
Answer:
1/4
Step-by-step explanation:
How to put 7^3/4 in radical form
Given:
[tex]7^{\frac{3}{4}}[/tex]Resolving it to its radical form can be gotten based on the general laws of indices.
We have:
[tex]A^{\frac{x}{y}}=\sqrt[y]{A^x}[/tex]I.e. the number is raised to the power of the numerator and then we get the denominator's root of the number obtained.
Thus:
[tex]\begin{gathered} 7^{\frac{3}{4}}=\sqrt[4]{7^3}=\sqrt[4]{343} \\ \sqrt[4]{343}=343^{\frac{1}{4}}=343^{(\frac{1}{2}\times\frac{1}{2})} \\ =343^{(\frac{1}{2}\times\frac{1}{2})}=\sqrt[]{343^{\frac{1}{2}}} \end{gathered}[/tex]Now, we have our value in the square root form as:
[tex]\sqrt[]{343^{\frac{1}{2}}}=\sqrt[]{7^{\frac{3}{2}}}[/tex]the length of a rectangle is 2 inches more than the width. The area is 24 square inches. Find the dimensions
Given:
length(l) = width(w) + 2
[tex]\text{Area}=24[/tex][tex]l\times w=24[/tex][tex](w+2)w=24[/tex][tex]w^2+2w-24=0[/tex][tex](w+6)(w-4)=0[/tex][tex]w=4\text{ or -6}[/tex]Negative not possible.
[tex]\text{width(w)}=4\text{ inches}[/tex][tex]\text{length(l)}=w+2[/tex][tex]\text{length of the rectangle=4+2}[/tex][tex]\text{length of the rectangle=}6\operatorname{cm}[/tex]Determine if the side lengths could form a triangle. Use an inequality to prove the answer. Inequality must be used.
The side lengths given form a triangle
Explanation:Let the lengths of the sides of the triangle be "a", "b" and "c"
For the length to form sides of a triangle, the sum of any two sides of the triangle must be greater than the third as shown:
[tex]\begin{gathered} a+b>c \\ a+c>b \\ b+c>a \end{gathered}[/tex]Given the sides of the triangle as 34km, 27km, and 58km
Let a = 34km, b = 27km and c = 58km
Substituting these values in the expression above to check if it is true:
[tex]\begin{gathered} 34+27=61>58 \\ 34+58=92>27 \\ 27+58=85>34 \end{gathered}[/tex]Since the inequality expression supports the theorem above, hence the side lengths given form a triangle
Determine the transformations that produce the graph of the functions g (T) = 0.2 log(x+14) +10 and h (2) = 5 log(x + 14) – 10 from the parent function f () = log 1. Then compare the similarities and differences between the two functions, including the domain and range. (4 points)
The transformation to get g(x) from f(x) are:
translate 14 units to the left and 10 unit upwards
[tex]h(x)=5\log (x+14)-10[/tex]the transformatio to get h(x) from f(x) are:
translate 14 units to the left and 10 units downwards
18. The weights of four puppies are shown in pounds. 9.5 9 9.125 9 Which list shows these weights in order from greatest to least F. 99.5 9 9.125 w 9.5 9 9.125 9.125 9 9.5 9 + J. 9 9 9.5 9.125
The correct list is
[tex]9\frac{3}{4},\text{ 9.5, 9}\frac{3}{8},9.125[/tex]This is option F
Suppose the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 17 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 112 million dollars? Round your answer to four decimal places.
0.8413 is the probability that a random selected firm will earn less than 112 million dollar
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
Let X be a random variable represents the income of the firm in the industry
Hence
X~ N (mean =u= 95 , standard deviation= d = 17 )
We must determine the likelihood that a randomly chosen company will make fewer than 112 million dollars in earnings ie.
P(X<112) = P(X-u/d < 112-95/17)
Z=X-u/d = 112 - 95/17 = 1
P(X<112) = P(Z-1)=0.8413
Using the standard normal probability table.
P(X<112) = 0.8413
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The function C(x) =17.5x-10 represents the cost (in dollars) of buying x tickets to the orchestra with a $10 coupon.
a) It represents the discount of $10 coupon
b) It repesetns the cost of each ticket
c) Five tickets cost is:
C(5) = 17.5(5) - 10 = 87.5 - 10 = 77.5
Five tickets cost $77.50
d) 130 = 17.5x - 10
130 + 10 = 17.5x
140 = 17.5x
x = 140/17.5 =8
x = 8
With $130 you can buy 8 tickets
LanaCharles almn on the coordinate plane what is the perimeter of a ALMN round to the nearest unit
The Solution:
Given the graph below:
We are required to find the perimeter of the triangle LMN rounded to the nearest unit.
Step 1:
Find the distance LM, where L(-3,2) and M(3,5)
By the formula for distance between two points, we have
[tex]LM=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where,
[tex]\begin{gathered} x_1=-3 \\ y_1=2 \\ x_2=3 \\ y_2=5 \end{gathered}[/tex]Substituting, we get
[tex]LM=\sqrt[]{(3--3)^2+(5-2)^2}=\text{ }\sqrt[]{6^2+7^2}=\text{ }\sqrt[]{85}=9.2195[/tex]Step 2:
Find the distance LN:
[tex]LN=12[/tex]Step 3:
Find the distance MN, where M(3,5) and N(9,2)
[tex]MN=\sqrt[]{(9-3)^2+(2-5)^2}=\text{ }\sqrt[]{6^2+(-3)^2}=\text{ }\sqrt[]{45}=6.7082[/tex]Step 4:
The perimeter is:
[tex]\text{ Perimeter=LM+MN+LN=9.2195+6.7082+12=27.9277}\approx28\text{ units}[/tex]Therefore, the correct answer is 28 units.
A certain drug dosage calls for 330 mg per kg per day and is divided into four doses (1 every 6 hours). If a person weighs 210 pounds, how many milligrams of the drug should he receive every 6 hours?Round your answer to the nearest milligram. Do not include units with your answer.
First, we convert the 210 pounds to kilograms as the dose is given in mg per kg.
Recall that:
[tex]1pound=0.453592\text{ kilograms.}[/tex]Therefore:
[tex]210\text{ pounds=95.2544 kilograms.}[/tex]The dose call for 330 mg per kg, therefore, to get the dose for 95.2544 kg, we multiply by 95.2544:
[tex]330*95.2544\text{ mg=31433.952mg.}[/tex]Finally, dividing by 4 we get the dose the person should receive every 6 hours:
[tex]7858.488mg\approx7858mg.[/tex]Answer: [tex]7858.[/tex]use the above diagram to answer the following questions.
Remember that the sum of the interior angles is 180. Then, we have the following equation:
[tex]55^{\circ}+65^{\circ}\text{ + }\angle M\text{ = 180}[/tex]This is equivalent to:
[tex]120^{\circ}\text{ + }\angle M=180^{\circ}[/tex]solve for M-angle:
[tex]\text{ }\angle M=180^{\circ}-\text{ 120}^{\circ}=60^{\circ}[/tex]Then, te correct answer is :
[tex]\text{ }\angle M^{}=60^{\circ}[/tex]If 16 is increased to 23, the increase is what percent of the original number? (This is known as the percent of change.)
Step 1
Given data
Old value = 16
New value = 23
Step 2
Write the percentage increase formula
[tex]\text{Percentage increase = }\frac{I\text{ncrease}}{\text{Old}}\text{ }\times\text{ 100\%}[/tex]Step 3
Increase = 23 - 16 = 7
[tex]\begin{gathered} \text{Percentage increase = }\frac{7}{16}\text{ }\times\text{ 100\%} \\ =\text{ 43.75\%} \end{gathered}[/tex]Use the Pythagorean Theorem to find the missing side length. *A. 12B. 144C. 10D. 24
We use the Pythagorean theorem formula to find the missing side length.
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where} \\ a\text{ and }b\text{ are the sides} \\ c\text{ is the hypotenuse} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} a=x \\ b=16 \\ c=20 \end{gathered}[/tex][tex]\begin{gathered} a^{2}+b^{2}=c^{2} \\ x^2+16^2=20^2 \\ x^2+256=400 \\ \text{ Subtract 256 from both sides} \\ x^2+256-256=400-256 \\ x^2=144 \\ $$\text{ Apply square root to both sides of the equation}$$ \\ \sqrt{x^2}=\sqrt{144} \\ x=12 \end{gathered}[/tex]AnswerThe length of the missing side is 12.
i need help please and thank youthere are 2 pictures bc i couldn’t get it all in 1!
we have the system
y < -2x^2+4x-2
The solution for this inequality is the shaded area below the vertical dashed parabola
and
[tex]y\ge\frac{2}{3}x-3[/tex]the solution for this inequality is the shaded area above the solid line y=(2/3)x-3
therefore
the solution for this system of inequalities
Is the shaded area below the vertical dashed parabola y=-2x^2+4x-2 and above the solid line y=(2/3)x-3
see the attached figure to better understand the problem
please help figure out this problem i’m trying to determine if the lines that appear to be tangent are tangent
Suppose that the two lines that form the missing angle are tangents to the circle. Then, the measure of the missing angle can be found using the following equation:
[tex]\measuredangle ABC=\frac{arc\text{ AEC - arc AGC}}{2}[/tex]Notice that we can complete the information about the arcs of the circle with the central angle:
then, we can find the angle x with the following expression:
[tex]\begin{gathered} \measuredangle x=\frac{243-117}{2}=\frac{126}{2}=63 \\ \Rightarrow\measuredangle x=63\degree \end{gathered}[/tex]therefore, the measure of the missing angle is 63 degrees.
Do 9 and 10 keep it 9th grade if you can Question 9-10
Given the formula for the volume of a cylinder:
[tex]V=\pi r^2h[/tex]You know that "r" is the radius of the cylinder and "h" is the height.
a. In order to solve the formula for "h", you can divide both sides of the formula by:
[tex]\pi r^2[/tex]As follows:
[tex]\frac{V}{\pi r^2}=\frac{\pi r^2h}{\pi r^2}[/tex][tex]h=\frac{V}{\pi r^2}[/tex]b. Having a cylindrical swimming pool, you know that:
[tex]\begin{gathered} r=12\text{ }ft \\ V=1810\text{ }ft^3 \end{gathered}[/tex]And, for this case:
[tex]\pi\approx3.14[/tex]Therefore, you can substitute values into the formula for the height of a cylinder found in Part "a" and evaluate:
[tex]\frac{V}{\pi r^2}=\frac{\pi r^2h}{\pi r^2}[/tex][tex]h=\frac{1810\text{ }ft^3}{(3.14)(12\text{ }ft)^2}[/tex][tex]h=\frac{1810\text{ }ft^3}{452.16\text{ }ft^2}[/tex][tex]h\approx4\text{ }ft[/tex]Hence, the answers are:
a.
[tex]h=\frac{V}{\pi r^2}[/tex]b.
[tex]h\approx4\text{ }ft[/tex]Match the following. Match the items in the left column to the items in the right column.1. divisor2. decimal fraction3. algorithm4. fraction5.quotient6. reminder7. doidonsa. the result of dividing two numbersb. the number being dividedc. a set of rules to be followed tosolve a problemd. the number of equal parts a number is being divided intoe. a fraction in which the denominator is 10 or a power of 10f. the amount left over after Chivisiong. a number that expresses the portiona whole
We can match as follows:
1. divisor ----> d. the number of equal parts a number is being divided into
2. decimal fraction ----> e. a fraction in which the denominator is 10 or a power of 10
3. algorithm ----> c. a set of rules to be followed to solve a problem
4. fraction ----> g. a number that expresses the portion
5. quotient ----> a. the result of dividing two numbers
6. reminder ----> f. the amount left over after Division
Why is it incorrect to write {∅} to denote a set with no elements?
Answer:
It's incorrect because {∅} is saying that the set contains empty sets, which is not the same as saying the set is empty (which can be denoted by { } or ∅
Step-by-step explanation: It's all in the answer.
A) Write an expression for the given number trick B) Simplify the expression you came up with
a)
Since we need an Expression, we also need a variablel for the "number".
Let's use "n".
We will translate each of the lines:
Pick a number : n
Mutiply that number by 12, so it becomes: n x 12
Add 15 to that, so we put parenthesis around that expression and add "15" to it:
(n x 12) + 15
Divide by 3, then we simply divide whole thing by 3, so we have:
[tex]\frac{(n\times12)+15}{3}[/tex]b)
To simplify, let's re-write:
[tex]\begin{gathered} \frac{(n\times12)+15}{3} \\ =\frac{12n+15}{3} \\ =\frac{12n}{3}+\frac{15}{3} \\ =4n+5 \end{gathered}[/tex]This is the simplified form.
Find the 11th term of the arithmetic sequence -5x- 1, -8x + 4, -11 x+ 9, ...
Recall that an arithmetic sequence is a sequence in which the next term is obtained by adding a constant term to the previous one. Let us consider a1 = -5x-1 as the first term and let d be the constant term that is added to get the next term of the sequence. Using this, we get that
[tex]a_2=a_1+d[/tex]so if we replace the values, we get that
[tex]-8x+4=-5x-1+d[/tex]so, by adding 5x+1 on both sides, we get
[tex]d=-8x+4+5x+1\text{ =(-8+5)x+5=-3x+5}[/tex]To check if this value of d is correct, lets add d to a2. We should get a3.
Note that
[tex]a_2+d=-8x+4+(-3x+5)=-11x+9=a_3[/tex]so the value of d is indeed correct.
Now, note the following
[tex]a_3=a_2+d=(a_1+d)+d=a_1+2d=a_1+d\cdot(3-1)[/tex]This suggest the following formula
[tex]a_n=a_1+d\cdot(n-1)[/tex]the question is asking for the 11th term of the sequence, that is, to replace the value of n=11 in this equation, so we get
[tex]a_{11}=a_1+d\cdot(10)=-5x-1+10\cdot(-3x+5)\text{ =-5x-1-30x+50 = -35x+49}[/tex]so the 11th term of the sequence is -35x+49
Find the slope, if it exists, of the line containing the pair of points. (−2,−6) and (−15,−7)
The linear regression for a given data set has the form
[tex]y=a+bx[/tex]where the values a and b can be solved using the equation
[tex]\begin{gathered} a=\frac{(\sum y)(\sum x^2)-(\sum x)(\sum xy)}{n(\sum x^2)-(\sum x)^2} \\ b=\frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2} \end{gathered}[/tex]Based on the given data set, we have n equals 5. We will solve for the values of the summation first. We have the following
[tex]\begin{gathered} \sum y=4+4+6+6+8=28 \\ \sum x=1+3+5+7+9=25 \\ \sum xy=(1\cdot4)+(3\cdot4)+(5\cdot6)+(7\cdot6)+(8\cdot9)=160 \\ \sum x^2=1^2+3^2+5^2+7^2+9^2=165^{} \\ (\sum x)^2=25^2=625 \end{gathered}[/tex]Using these values to compute for the values of a and b, we get
[tex]\begin{gathered} a=\frac{(28\cdot165)-(25\cdot160)}{5(165)-625}=\frac{31}{10}=3.1 \\ b=\frac{5(160)-(28\cdot25)}{5(165)-625}=\frac{1}{2}=0.5 \end{gathered}[/tex]Take note that the problem wants us to reduce the numbers to the nearest tenth. Hence, the linear regression for the given data set is written as
[tex]y=3.1+0.5x[/tex]1) find the value of AC
2) find the measure of
1) The value of AC = 116
2) The measure of ∠BEF = 53°
What is Bisector?
When anything is divided into two equal or congruent portions, usually by a line, it is said to have been bisected in geometry. The line is then referred to as the bisector. Segment bisectors and angle bisectors are the sorts of bisectors that are most frequently taken into consideration.
Given,
BD is a perpendicular bisector
A is an angle bisector
BD is a perpendicular bisector then AD = DC
2n + 18 = 4n - 22
4n - 2n = 18 + 22
2n = 40
n = 40/2
n = 20
AD = 2(20) + 18
= 40 + 18
AD = 58
Now,
1) Length of AC
AC = 2AD
Here, AD = 58
AC = 2(58)
AC = 116
Hence, The value of AC is 116
2) A is an angle bisector
∠BAE = ∠DAE = 37°
∠DAE = 37°
Δ ADE is a right angle triangle
∠DEA = 90 - ∠DAE
= 90 - 37
= 53°
Since, ∠DEA = ∠BEF
∠BEF = 53°
Hence, The measure of ∠BEF = 53°
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You pick a card at random.
1 2 3 4
What is P(factor of 24)?
Write your answer as a percentage rounded to the nearest tenth
Answer:
100%
Step-by-step explanation:
All of the numbers are factors of 24. So, picking a factor of 24 is guaranteed, so the probability is 1.
This is equal to 100%.
A baker has 85 cups of flour to make bread. She uses 6 1/4 cups of flour for each loaf of bread. How many loaf of bread can she make
Answer;
The number of loaf of bread she can make is;
[tex]13\text{ loaves}[/tex]Explanation:
Given that a baker has 85 cups of flour to make bread.
[tex]A=85\text{ cups}[/tex]And for each bread she uses 6 1/4 cups of flour.
[tex]r=6\frac{1}{4}\text{ cups}[/tex]The number of loaf of bread she can make can be calculated by dividing the total amount of flour by the amount of flour per bread;
[tex]\begin{gathered} n=\frac{A}{r}=\frac{85}{6\frac{1}{4}}=\frac{85}{6.25} \\ n=13.6 \end{gathered}[/tex]Since it will not complete the 14th loaf of bread.
So, the number of loaf of bread she can make is;
[tex]13\text{ loaves}[/tex]A disk is in the form of square and measures 5.25inches on each side. Find the diagonal length of thedisk. I am taking geometry In the 8th grade and I am lost
Answer:
The diagonal length is 7.42 inches.
Explanation:
The disk with its diagonal is:
Then, we can look at the diagonal as the hypotenuse of a right triangle. Then, if we call D to the diagonal:
[tex]\begin{gathered} D^2=(5.25in)^2+(5.25)^2 \\ D=\sqrt{2(5.25in)^2}\approx7.42in \end{gathered}[/tex]A group of friends' dinner bill before tax is $122.75. The sales tax rate is 8%. They want to leave an 18% tip after tax. What is their total dinner bill,
including tax and tip, rounded to the nearest cent?
O $150.57
O $154.29
o $154.67
O $156.43
Their total dinner bill including sales tax rate is 8% and 18% tip will be $156.43 by using the concept of percentages and addition.
What is percent?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.
What is sales tax?A sales tax is a fee that is paid to the government when certain goods and services are sold. Typically, laws permit the seller to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing body.
Here,
$122.75 dollars to be paid without tax and tip,
=8% of $122.75
=$9.82.
=122.75+9.82
=$132.57
=18% of 132.57
=$23.86
=132.57+23.86
=$156.43
Using the addition and percentages concepts, they can calculate their total dinner bill, which is $156.43 after adding the 8% sales tax and 18% gratuity.
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13х-17y+16z= 73
-11x + 15y + 17z= 61
46x+10y-30z = -18
The solution of the linear system of three simultaneous equations is presented as follows; x = 2, y = 1 and z = 4
What is a set of simultaneous equation?Simultaneous system of equations consists of a finite set of equations for which a solution to the equation system is required.
The linear system of three equations can be presented as follows;
13•x - 17•y + 16•z = 73...(1)
-11•x + 15•y + 17•z = 61...(2)
46•x + 10•y - 30•z = -18...(3)
The above system of equations can be solved using common multiples of the coefficients as follows;
Multiply equation (2) by 2 and equation (3) by 3 to get;
2 × (-11•x + 15•y + 17•z) = 2 × 61 = 122
-22•x + 30•y + 34•z = 122...(4)3 × (46•x + 10•y - 30•z) = 3 × (-18) = -54
138•x + 30•y - 90•y = -54...(5)Subtracting equation (4) from equation (5) gives;
138•x + 30•y - 90•z - (-22•x + 30•y + 34•z) = -54 - 122 = -176
138•x - (-22•x) + 30•y - 30•y - 90•z - 34•z = -176
160•x - 124•z = -176
40•x - 31•z = 44
[tex] \displaystyle {z = \frac{(44 + 40\cdot x)}{31}}[/tex]
Plugging in the value of z in equation (1) and (2) gives;
1043•x - 527•y + 704 = 73 × 31 = 2236...(6)
Which gives;
[tex] \displaystyle {y = \frac{(1043\cdot x - 1559)}{527}}[/tex]
339•x + 465•y + 748 = 61 × 31 = 1891...(7)
Which gives; [tex] \displaystyle {y = \frac{(381 - 113\cdot x )}{155}}[/tex] which gives;
[tex] \displaystyle { \frac{(1043\cdot x - 1559)}{527}= \frac{(381 - 113\cdot x )}{155}}[/tex]
Therefore; 221216•x - 442432 = 0
x = 442432 ÷ 221216 = 2
x = 2
y = (1043×2 - 1559)÷527 = 1
y = 1
z = (44 + 40×2) ÷ 31 = 4
z = 4
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Answer:
√52
Step-by-step explanation:
[tex] \sqrt{ {(4 - ( - 2))}^{2} + {(1 - ( - 3))}^{2} } [/tex]
[tex] \sqrt{ {6}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} [/tex]
