The expression given is:
[tex]2.5x+4.3x-5[/tex]We add like terms (if any) and then simplify.
There are two x's terms, so we add them up and keep "-5" as is.
Thus, we add
2.5x + 4.3x = 6.8x
So, the expression simplifies to:
[tex]\begin{gathered} 2.5x+4.3x-5 \\ =6.8x-5 \end{gathered}[/tex]The answer is:
6.8x - 5
help please! “find all points (x) where the function g(x)= |x+2| - |x-8| is not differentiable….”
A function is not differentiable at a point if the function has a "sharp/angled point''.
The solution will be resolved with the graph shown below
From the graph,
[tex]g(x)\text{ }is\text{ not differentiable at x =}-2,8[/tex]In a math class with 21 students, a test was given the same day that an assignment was due. There were 14 students who passed the test and 16 students who completed the assignment. There were 12 students who passed the test and also passed the test and also completed the assignment . What is the probability that a student chose randomly from the class passed the test or completed the homework? PLEASE HELP ME, WHOEVER ANSWERS I’ll MARK BRANLIEST!!
Passed test and did assignment: 12
Passed the test 14
Did assignment: 16
Then:
[tex]14-12=2[/tex][tex]16-12=4[/tex]Then:
[tex]2+4+12=18[/tex]There were 18 students who did something.
[tex]21-18=3[/tex]This leaves 3 people who did nothing. 12 out of the 16 who did the homework passed the test so:
[tex]\frac{12}{16}=0.75[/tex]The probability is 0.75.
solve question: 3^(2x-4) = 31
Solution
We want to solve
[tex]3^{2x-4}=31[/tex][tex]\begin{gathered} 3^{2x-4}=31 \\ \\ Taking\text{ the natural logarithm of both sides} \\ \\ ln(3^{2x-4})=ln(31) \\ \\ (2x-4)ln(3)=ln(31) \\ \\ (2x-4)=\frac{ln(31)}{ln(3)} \\ \\ 2x=\frac{ln(31)}{ln(3)}+4 \\ \\ x=\frac{ln(31)}{2ln(3)}+2 \\ \\ x=3.562874929 \\ \\ x=3.563\text{ \lparen to three decimal places\rparen} \end{gathered}[/tex]although samples are usually representative of the population from which they are selected you should not expect a sample statistic to be exactly equal to the corresponding population parameter. the natural difference that exist between statistic and theirparameters are known as
Recall that statistics are numerical values calculated over a set of data points, that are normal a smaller subset of a bigger dataset. The whole dataset is considered as the population, and the subset receives the name of the sample. This fact could be pictured as follows
The parameters, are numerical values that are calculated over the entire population, and in a way, they describe the population in different ways. One example could be the average height of males in the age range 10-15 (parameter), while a statistic woulde be the average of height of males in the age range 10-15 in the city of Washington D.C (sample).
Note that the parameters are normally unkno
Can someone check to see if my answer is correct
Hello there. To solve this question, we'll need to remember how to integrate a function over an interval.
The area under the curve y = y(x) in the interval [a, b] is given by the integral:
In this case, y(x) = 5x^6 and the interval is [0, 5]
The integral is:
To solve this integral, remember that:
The integral of the product between a constant and a function is equal to:
The integral of a power is given by:
Then, solving this integral:
Use the diagram of a section of the art museum shown to solve. 1'4 in. Mannerism Impressionism Art Art Baroque Art 11. in. Lobby 2 in. Key 1 in. = 20 ft Find the actual dimensions of the Baroque Art room.
Question:
Solution:
Notice that 1 in is equivalent to 20 ft, then using the appropriate conversion factors we have that:
[tex]2\text{ in (}\frac{20\text{ ft}}{1in}\text{) = 40 ft}[/tex]and
[tex]1\frac{1}{4}\text{ in (}\frac{20\text{ ft}}{1in}\text{) =}\frac{5}{4}in\text{ (}\frac{20\text{ ft}}{1in}\text{) = 25 ft}[/tex]then the actual dimensions of the Baroque Art room are:
[tex]40\text{ ft x 25 ft}[/tex]then, the correct answer is:
[tex]40\text{ ft x 25 ft}[/tex]Determine whether each sequence is an arithmetic sequence. If so, find the common difference and the next three terms. 1. -1, 2, -3, -4, ... 2. 1.25, 3.75, 6.25, 8.75, ...
1. it is not an arithmetic sequence
2.arithmetic sequence
[tex]\begin{gathered} \text{term}_5=11.25 \\ \text{term}_6=13.75 \\ \text{term}_7=16.25 \end{gathered}[/tex]Explanation
Step 1
find the common difference for the sequence.
[tex]\begin{gathered} -1,2,-3,4 \\ \text{term}_1=-1 \\ \text{term}_2=2 \\ \text{term}_3=-3 \\ term_4=-4 \\ term2-term1=2-(-1)=2+2=4 \\ \text{term}3-\text{term}2=-3-2=-5 \\ \text{term}4-\text{term}3=-4-(-3)=-4+3=-1 \end{gathered}[/tex]there is no common difference , so this is not an arithmetic sequence
Step 2
2.
find the common difference
[tex]\begin{gathered} 1.25,3.75,6.25,8,75 \\ \text{term}1=1.25 \\ \text{term}2=3.75 \\ \text{term}3=6.25 \\ \text{term}4=8.75 \\ \text{differences} \\ \text{term}2-\text{term}1=3.75-1.25=2.5 \\ \text{term}3-\text{term}2=6.25-3.75=2.5 \\ \text{term}4-\text{term}2=8.75-6.25=2.5 \end{gathered}[/tex]so, the common difference is 2.5, in other words, it means you have to add 2.5 to obtain the next term
Step 2.1
now, let's find the next three terms
[tex]\begin{gathered} \text{rule} \\ \text{term}_{n+1}=term_{n+2.5} \\ \text{then} \\ \text{term}5=\text{term}4+2.5 \\ \text{term}5=8.75+2.5=11.25 \\ term6=11.25+2.5=13.75 \\ \text{term}7=13.75+2.5=16.25 \end{gathered}[/tex]I hope this helps you
how could you find the combined area of all faces of a three-dimensional shape and give an example of why that would be a good measurement to know
The cuboid is a 3-dimensional shape formed from 6 rectangular faces
The surface area of it is the sum of the areas of its 6 faces
Every two opposite faces have the same areas
Its dimensions are length, width, and height
Its surface area = 2[length x width + length x height + width x height]
This means we multiply every two dimensions and add the answer then multiply the sum by 2
Let us take an example
If the dimensions of a cuboid are 2 cm, 3 cm, and 5 cm
Then let:
Length = 2 cm
Width = 3 cm
Height = 5 cm
The surface area = 2[2 x 3 +
Play | What is the perimeter of a triangle with sides 11 inches, 4 inches, and 12 inches in length? 4 11 12
The perimeter of a triangle is given as
P = a + b + c
where a, b, and c are the sides of the triangle
P = 11 + 4 + 12
P = 16 + 12
P = 28 inches
The perimeter of the triangle is 28 inches
The answer is 28 inches
Innovation the relationship between the dependent and independent variables is represented by
Answer:
[tex]\text{the relat}\imaginaryI\text{on between them }\imaginaryI\text{s represented by an equat}\imaginaryI\text{on}[/tex]Step-by-step explanation:
Independent variables are what we expect will influence dependent variables. A Dependent variable is what happens as a result of the independent variable. Then, its relation between them:
[tex]\text{ the relation between them is represented by an equation.}[/tex]can you help me with growth and Decay models
Of course, you can. Happy birthday, Keke!
Best wishes and blessings!
Can you read my messages here? Ok, Keke, Understood.
Let me review the image you uploaded, please.
Ok, Keke, let's solve the problem of depreciation.
Year 1: Cost of the car $ 30,000 - Depreciation = 0.18 * 30,000 = 5,400, Balance = 24,600 (30,000 - 5,400)
Part 1:
Therefore, the formula is:
• V = C − (1 − r)^t, ,where
,• V = Value of the car after t years
,• C = Cost of the car when it was purchased
,• r = Depreciation rate (0.18)
,• t = Years of usage of the car
Part 2:
Let's calculate the cost of the car after 10 years, using the formula we wrote above:
V = C * (1 − r)^t
V = 30,000 * (1 − 0.18)^10
V = 30,000 * 0.82^10
V = $ 4,123.44
Do you understand the solution?
The equation that I wrote above is the model. Highlighted and underlined.
Keke, remember you have two parts. Do you have it now?
Is it clear now?
If you don’t need any further explanation, I’ll go ahead and end our session. Feel free to let me know how I did by rating our session - all feedback is welcome and appreciated. Thanks for coming today!
Remember that the solutions from tutors are always available in your profile! Happy birthday!
Wendy is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, she spent a total of $100. Wendy will be earning a base salary of $70 per month from the gym, plus an additional $3 for every class she teaches. If Wendy teaches a certain number of classes during her first month as an instructor, she will earn back the amount she spent on certification. How much will Wendy's expenses and earnings be?
Write a system of equations, graph them, and type the solution.
In linear equation , 10 will Wendy's expenses and earnings be .
What are instances of linear equations?
Ax+By=C represents a two-variable linear equation in its standard form. A standard form linear equation is, for instance, 2x+3y=5.Finding both intercepts of an equation in this form is rather simple (x and y).When resolving systems of two linear equations, this form is also incredibly helpful.A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Let x represent the money she earn for every one class. Here I have this equation:
70(1) + 3x =100
70 + 3x = 100
3x = 100 -70
3x= 30
x= 30 ÷3
x= 10
Learn more about linear equation
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If a polynomial is divided by (x + 4), the quotient is x²-x+ 7, and the remainder is - 4. Find the original polynomial.
The original polynomial is.
(Simplify your answer. Do not factor.)
Step-by-step explanation:
similar to a number division of "z" divided by "a" resulting in "b" plus a remainder "r" divided by "a"
z/a = b + r/a
z = b×a + r
we have here
polynomial / (x + 4) = x² - x + 7 - 4/(x + 4)
polynomial = (x² - x + 7 - 4/(x + 4)) × (x + 4) =
= (x² - x + 7) × (x + 4) - 4 =
= x³ - x² + 7x + 4x² - 4x + 28 - 4 =
= x³ + 3x² + 3x + 24
Solve this for meIt says to simplify the answer where it’s cut off
Question:
[tex](3x^2-5x+7)(2x^2+x-2)[/tex]Step 1: Apply the distributive law
[tex]\begin{gathered} (a+b)(x+y+z)=a(x+y+z)+b(x+y+z) \\ =ax+ay+az+bx+by+bz \end{gathered}[/tex]Step 2: Apply the foil method of multiplication
[tex]\begin{gathered} (3x^2-5x+7)(2x^2+x-2) \\ =3x^2(2x^2+x-2)-5x(2x^2+x-2)+7(2x^2+x-2) \end{gathered}[/tex]Step 3: Expand the brackets
[tex]\begin{gathered} 3x^2(2x^2+x-2)-5x(2x^2+x-2)+7(2x^2+x-2) \\ 6x^4+3x^3-6x^2-10x^3-5x^2+10x+14x^2+7x-14 \\ \text{note: take note of the signs when expanding the brackets} \end{gathered}[/tex]Step 4: Collect similar terms
[tex]\begin{gathered} 6x^4+3x^3-6x^2-10x^3-5x^2+10x+14x^2+7x-14 \\ =6x^4+3x^3-10x^3-6x^2-5x^2+14x^2+10x+7x-14 \\ =6x^4-7x^3+3x^2+17x-14 \end{gathered}[/tex]Therefore,
The final answer is = 6x⁴ - 7x³ + 3x² + 17x - 14
The owner of a music store received a shipment of stereos at a cost of $160.00 each. What will the selling price be if he applies a 45% markup? $300 $205 $232 $88
The owner of a music store received a shipment of stereos at a cost of $160.00 each.
What will the selling price be if he applies a 45% markup?
Recall that the selling price is given by
[tex]S=C+M[/tex]Where C is the cost and M is the markup.
Let us first find the markup
The markup is found by multiplying the markup percentage with the cost
[tex]\begin{gathered} M=0.45\times\$160 \\ M=\$72 \end{gathered}[/tex]Now we can find the selling price
[tex]\begin{gathered} S=C+M \\ S=\$160+\$72 \\ S=\$232 \end{gathered}[/tex]So option C is correct.
Therefore, the selling price is $232
If a 54 gal hot water tank holds 450 lb of water, what weight of water will a 69 gal tank hold?A 69 gal tank hold will hold__ lb of water.(Round to the nearest whole number as needed.)
Given:
54 gal of hot water tank holds 450 lb of water.
Let's find the amount of water a 69 gal tank will hold.
Here, we have:
54 gal = 450 lb
69 gal = x lb
Now, apply the proportionality equation:
[tex]\frac{450}{54}=\frac{x}{69}[/tex]Cross multiply:
[tex]\begin{gathered} 54x=450*69 \\ \\ 54x=31050 \end{gathered}[/tex]Divide both sides by 54:
[tex]\begin{gathered} \frac{54x}{54}=\frac{31050}{54} \\ \\ x=575 \end{gathered}[/tex]Therefore, a 69 gal tank will hold 575 lb of water.
ANSWER:
575 lb of water
Which set of ordered pairs represents a function? What are functions?
Given:
The sets of ordered pairs are given.
To find:
The set of ordered pairs represents a function.
Explanation:
As we know,
The function is a relationship between inputs where each input is related to exactly one output.
That means,
No two different ordered pairs have the same x -coordinate.
Therefore, the set of ordered pairs represents a function is,
[tex]\lbrace(6,0),(5,0),(4,0)\rbrace[/tex]Final answer:
The correct option is (2).
You want to buy a $232,000 home. You plan to pay 15% as a down payment, and take out a 30 year loan for the rest.b) What will your monthly payments be if the interest rate is 6%?
EXPLANATION:
Given;
We are told that a mortgage loan of $232,000 with a 15% down payment has been taken. The loan tenure is 30 years. That means the initial payment based on a 15% of 232,000 will be $34,800.
Therefore, the following details;
[tex]\begin{gathered} Principal\text{ }amount=197200 \\ Rate=\frac{6}{12}=0.5\% \\ Period=30 \end{gathered}[/tex]Required;
We are required to calculate the monthly repayment amount if the loan repayment will be done monthly.
Step-by-step solution;
Note that the rate of interest is 6% per annum. However, since the repayment will be done monthly (that is 12 times each year), then the rate has been adjusted to (6/12)% as shown above.
Therefore using an online calculator, your input(s) will be;
[tex]\begin{gathered} Principal\text{ }amount=232000 \\ Down\text{ }payment=34800 \\ Rate=0.5 \\ Period\text{ }or\text{ }loan\text{ }term=30 \end{gathered}[/tex]With an online calculator, the monthly amount due would be;
[tex]Monthly\text{ }repayment=590[/tex]ANSWER:
If the interest rate is 6%, then the monthly repayment would be $590
what the GCF for 2x^3 + x^2
GCF = x²
Explanation:2x³ + x²
To find the greatest common factor (GCF), we need to factorise the expression.
x is common to both expression, so we factor it out
x(2x² + x)
When we check again, x is common to both so we factor it out again
2x² + x = x(2x + 1)
x(2x² + x) = x (x(2x + 1) = x² (2x + 1)
There is no other number we can factor out asides 1. As a result, the factor outside the parenthesis is the greatest common factor (GCF)
Hence, GCF = x²
1Suppose the probability of winning a particular lottery is 1 in 14C 9 or30,888If Juanita and Michelle each play the lottery on one particular evening, what is the probability thatboth will select the winning numbers if they make their selections independently of each other?The probability that both will select the winning numbers is approximately(Use scientific notation Use the multiplication symbol in the math palette as needed. Round to the nearest hundredth as needed)Help Me Solve ThisView an ExampleGet More HelpClear AllCheck Answer
The probability of each one of them selecting the winning numbers is:
[tex]\frac{1}{30888}[/tex]Now, since they make their choices independently, the probability of both selecting the winning numbers is the product of the probabilities for each one winning:
[tex]\frac{1}{30888}\cdot\frac{1}{30888}=\frac{1}{30888^2}[/tex]When we compute this division, we find the approximate value:
[tex]1.0481\cdot10^{-9}[/tex]Now, rounding this result to the nearest hundredth, the approximate probability that both will select the winning numbers is
[tex]1.05\cdot10^{-9}[/tex]Which of the following represents "next integer after the integer n"?n2nn + 1n - 1
The set of integers is generated by 1
The next integer after integer n is n + 1
y= 5x - 7-3x - 2y = -12Solve each system of equations using the substitution method Give the solution in (x,y) form
ANSWER:
[tex](2,3)[/tex]STEP-BY-STEP EXPLANATION:
We have the following system of equations:
[tex]\begin{gathered} y=5x-7 \\ -3x-2y=-12 \end{gathered}[/tex]Solving by Substitution
[tex]\begin{gathered} -3x-2\cdot(5x-7)=-12 \\ -3x-10x+14=-12 \\ -13x=-12-14 \\ x=\frac{-26}{-13} \\ x=2 \end{gathered}[/tex]Now, for y, replacing:
[tex]y=5\cdot2-7=10-7=3[/tex]The solution is:
[tex](2,3)[/tex]Need to learn how to solve these mixed fractions at least 1 subtraction, 1 multiplication and addition Please so I can do the restThanks
ANSWER:
[tex]\begin{gathered} 3\frac{1}{2}+4=7\frac{1}{2} \\ \frac{3}{8}+\frac{1}{4}=\frac{5}{8} \\ 9\frac{1}{4}-5\frac{1}{2}=3\frac{3}{4} \\ 3\frac{3}{5}-\frac{4}{5}=2\frac{4}{5} \\ 6\times4\frac{1}{2}=27 \\ 7\times2\frac{1}{8}=14\frac{7}{8} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
In the case of the sum for mixed numbers, both the integer part and the fractional part must be added when adding the fractions we must cross multiply and add in the numerator and the denominator is the product of the denominators, just like this:
[tex]\begin{gathered} 3\frac{1}{2}+4=\mleft(3+4\mright)\mleft(\frac{1}{2}+0\mright)=7\frac{1}{2} \\ \frac{3}{8}+\frac{1}{4}=\frac{3\cdot4+1\cdot8}{32}=\frac{12+8}{32}=\frac{20}{32}=\frac{5\cdot4}{8\cdot4}=\frac{5}{8} \end{gathered}[/tex]In the case of subtraction for mixed numbers, both the integer part and the fractional part must be subtracted. When subtracting fractions, we must cross multiply and subtract in the numerator and the denominator is the product of the denominators, just like this:
[tex]\begin{gathered} 9\frac{1}{4}-5\frac{1}{2}=\mleft(9-5\mright)\mleft(\frac{1}{4}-\frac{1}{2}\mright)=4\mleft(\frac{1\cdot2-1\cdot4}{8}\mright)=4\mleft(\frac{-2}{8}\mright)=4-\frac{1}{4}=3\mleft(1-\frac{1}{4}\mright)=3\mleft(\frac{4}{4}-\frac{1}{4}\mright)=3\frac{3}{4} \\ 3\frac{3}{5}-\frac{4}{5}=(3-1)\mleft(\frac{3}{5}+1-\frac{4}{5}\mright)=2\mleft(\frac{3}{5}+\frac{5}{5}-\frac{4}{5}\mright)=2\frac{4}{5} \end{gathered}[/tex]In the case of multiplication, both the whole part and the fractional part are multiplied and then added.
[tex]\begin{gathered} 6\times4\frac{1}{2}=\mleft(6\cdot4\mright)+\mleft(6\cdot\frac{1}{2}\mright)=24+3=27 \\ 7\times2\frac{1}{8}=\mleft(7\cdot2\mright)+\mleft(7\cdot\frac{1}{8}\mright)=14+\frac{7}{8}=14\frac{7}{8} \end{gathered}[/tex]Last year, there were n pies baked for the bake sale. This year, there were 215 pies baked. Using n, write an expression for the total number ofpies baked in the two years.
Given:
a.) Last year, there were n pies baked for the bake sale.
b.) This year, there were 215 pies baked.
Let,
T = The total number of pies baked in the two years.
The expression will be:
[tex]\text{ T = n + 215}[/tex]Need help with this problem
Solve each inequality:
[tex]\begin{gathered} \frac{1}{4}x>-1 \\ \\ \text{Multiply both sides of the inequality by 4:} \\ 4\cdot\frac{1}{4}x>4\cdot(-1) \\ \\ x>-4 \end{gathered}[/tex][tex]\begin{gathered} -2(x-1)\ge4 \\ \\ \text{Divide both sides of the inequality by -2 (change the inequality sign):} \\ \frac{-2(x-1)}{-2}\le\frac{4}{-2} \\ \\ x-1\le-2 \\ \\ Add\text{ 1 in both sides of the equation:} \\ x-1+1\le-2+1 \\ x\le-1 \end{gathered}[/tex]Then, the solution for the compound inequality is:
[tex]-4And the graph is:25What is the value of x in the equation below?6(x-8) = 7215o 20o24
the given expression is
6(x-8) = 72
6x - 48 = 72
6x = 72 + 48
6x = 120
x = 120/6
x = 20
thus, the answer is x = 20
Unit 3 Practice Worksheet 6 Radical Equations and Inequalities Solve each equation. Check your solution. 1. 14x + 9 - 3=5 2. √1-7y=3 3. V2x – 9 = 2 4. V7V + 5 =-3 5. V7+ X-5 = V6-X 6. V5+x-VX – 3 = 2 7. Vx+1=3-√4 - x x 8. x2 – 2x + 1 = 2x + 5HELP PLEASE
We are given set of equations in the question.
Question one
[tex]\sqrt[]{4x\text{ + 9}}\text{ - 3 = }5[/tex]Firstly, collect the like terms
The equation becomes
[tex]\sqrt[]{\text{4x + 9}}\text{ = 5+ 3}[/tex]Secondly, square the both sides
[tex]\sqrt[]{(4x+9)^2\text{ }}=(5+3)^2[/tex]Square will cancel the squareroot
(4x + 9) = (5 + 3)^2
Solve the expression inside the parenthesis
(4x + 9) = (8)^2
4x + 9 = 64
Collect the like terms
4x = 64 - 9
4x = 55
Divide both sides by 4
4x/4 = 55/4
x = 13 3/4
Second question
What is the probability of either event occurring when you spin a spinner with the numbers 1 through 4 which are all evenlyrepresented?Event A: Spinning an odd numberEvent B: Spinning a 4Express your answer as a simplified fraction.
Answer
Event A= 1/2
Event B= 1/4
Procedure
To get the probability of completely independent events you will need to divide the possibilities of getting a particular number over the total number of possibilities
Event A: 2/4 or 1/2 (The odd numbers are 1 and 3)
Event B: 1/4 (There is only one 4 in the range among 1 to 4)
i do not understand what i need to do and i'm having trouble.
We know that:
[tex]\begin{gathered} 6=\sqrt{6^2} \\ \\ \Rightarrow6=\sqrt{36} \end{gathered}[/tex]Then, the closest number to 6 must be:
[tex]\sqrt{37}[/tex]Jane walked for 3 km at a constant speed of x km/hr. She then jogged for a further x km at a constant speed of 8 km/hr. Her total time was 1/4 hr. Show that x2 - 10x + 24 = 0 Hence find the speed at which Jane walked, if her total distance was less than 8 km.
Given
Part 1
Jane walked for 3 km at a constant speed of x km/hr
speed x km/h and
distance is 3km
[tex]\begin{gathered} \text{Formula} \\ \\ \text{SPEED =}\frac{dis\tan ce}{\text{time}} \\ \\ \end{gathered}[/tex][tex]\begin{gathered} \text{make Time (T) the subject of the formula} \\ \\ \text{Time}=\frac{dis\tan ce}{S\text{ pe}ed} \end{gathered}[/tex][tex]T=\frac{3}{x}[/tex]
She then jogged for a further x km at a constant speed of 8 km/hr
Therefore, Distance is X km and
Speed is 8km/hr
[tex]\text{Time}=\frac{X}{8}[/tex]The total time is;
[tex]\frac{3}{x}+\frac{x}{8}=1\frac{1}{4}[/tex][tex]\begin{gathered} \frac{3}{x}+\frac{x}{8}=\frac{5}{4} \\ \\ \text{LCM is }8x \\ \end{gathered}[/tex]Multiply all through by the LCM
[tex]\begin{gathered} 8x\times\frac{3}{x}+8x\times\frac{x}{8}=8x\times\frac{5}{4} \\ simplify \\ 24+x^2=10x \\ \text{rearrange } \\ x^2-10x+24=0 \end{gathered}[/tex]Part 2
We have to solve the quadratic equation
[tex]\begin{gathered} x^2-10x+24=0 \\ By\text{ factorisation} \\ x^2-6x-4x+24=0 \\ x(x-6)-4(x-6)=0 \\ x-6=0 \\ x=6 \\ \text{and} \\ x-4=0 \\ x=4 \end{gathered}[/tex]Recall From the question
if her total distance was less than 8 km.
[tex]\begin{gathered} 3\operatorname{km}\text{ +6km = 9km} \\ It\text{ is greater than 8km, so it not 6} \\ \\ \text{Then} \\ 4\operatorname{km}\text{ +3km =7km} \\ \text{Then, it is 4} \end{gathered}[/tex]The speed X is 4km/h