Fill in the missing values to make the equations true.(a) log, 9-log, 11 = log5(b) log45 + log4 = log, 45(c) 5log72 = log7
Answers
(a)
[tex]\log _59-\log _511=\log _{5_{}}(\frac{9}{11})\text{ (}\because\log a-\log b=\log (\frac{a}{b})[/tex]Thus, the required value in the blank in 9/11/
(b)
[tex]\log _45+\log _4(9)=\log _445\text{ (}\because\log a+\log b=\log ab)[/tex]Thus, the required value in the blank is 9.
(c)
[tex]\begin{gathered} 5\log _72=\log _72^5(\because a\log b=\log b^a) \\ =\log _732 \end{gathered}[/tex]Thus, the requried value in the blank is 32.
Related Questions
evaluate B-( - 1/8) + c where b =2 and c=- 7/4
Answers
Answer: 3/8
Step-by-step explanation:
Given:
[tex]B-(-\frac{1}{8} )+c[/tex]
replace variables with their given values: b = 2 and C = 7/4
[tex]2-(-\frac{1}{8})+\frac{-7}{4}[/tex]
to make subtracting and addition easier, make each number has the same common denominator.
[tex]\frac{16}{8} -(-\frac{1}{8})+(\frac{-14}{8})[/tex]
Finally, solve equation.
***remember that subtracting a negative is the same as just adding and adding by a negative is the same as simply subtracting.
[tex]\frac{16}{8} -(-\frac{1}{8})+(\frac{-14}{8})=\frac{16}{8} +\frac{1}{8}-\frac{14}{8}[/tex]
= 3/8
Answer:
3/8
Step-by-step explanation:
2 - (-1/8) + (-7/4)
= 17/8 - 7/4
= 17/8 + -7/4
= 3/8
what is the driving distance between the police station and Art Museum
Answers
First, locate the coordinate points (x,y) of each place, by looking at the graph:
Police station = (0,-4)
Art museum = (6,1)
Apply the distance formula:
[tex]D=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Replacing:
[tex]D=\sqrt[]{(6-0)^2+(1-(-4))^2}=\sqrt[]{6^2+5^2}=\sqrt[]{36+25}=\sqrt[]{61}=7.81[/tex]perpendicular lines homework
Answers
all i need is for question 14 to be answered please help
Answers
Given
The path of particle 1 is,
[tex]x(t)=3t-6,\text{ }y(t)=t^2-2t[/tex]And, the path of second particle is,
[tex]x(t)=\sqrt{t+6},\text{ }y(t)=-3+2t[/tex]To model the path of the two particles in cartesian form and to find whether, the two particles collide.
Explanation:
It is given that,
The path of the first particle is,
[tex]x(t)=3t-6,\text{ }y(t)=t^2-2t[/tex]That implies,
[tex]x=2t-6,\text{ }y=t^2-2t[/tex]Consider,
[tex]\begin{gathered} x=2t-6 \\ 2t=x+6 \\ t=\frac{x+6}{2} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} y=(\frac{x+6}{2})^2-2(\frac{x+6}{2}) \\ y=\frac{x^2+12x+36}{4}-\frac{2x+12}{2} \\ y=\frac{x^2+12x+36-2(2x+12)}{4} \\ y=\frac{x^2+12x+36-4x-24}{4} \\ y=\frac{x^2+8x+12}{4}\text{ \_\_\_\_\_\_\_\_\_\_\lparen1\rparen} \end{gathered}[/tex]Also, the path of second particle is,
[tex]x(t)=\sqrt{t+6},\text{ }y(t)=-3+2t[/tex]That implies,
[tex]x=\sqrt{t+6},\text{ }y=-3+2t[/tex]Consider,
[tex]\begin{gathered} y=-3+2t \\ 2t=y+3 \\ t=\frac{y+3}{2} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} x=\sqrt{t+6} \\ \Rightarrow x^2=(t+6) \\ \Rightarrow x^2=(\frac{y+3}{2})+6 \\ \Rightarrow x^2=\frac{y+3+12}{2} \\ \Rightarrow2x^2=y+15 \\ \Rightarrow y=2x^2-15\text{ \_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]Hence, y=(x^2+8x+12)/4, y=2x^2-15 are the paths of the two particles respectively.
The graph of the path of the two particles are,
From, this it is clear that the particle collide at the points (-2.686, -0.568) and (3.829, 14.324).
need help with this problem, find the length of the darkened arc. C is the center of the circle
Answers
Notice that the central angle measures 138 degrees, We have a property of the circle that says that the measure of a central angle is equal to the arc between its sides.
Therefore, the arc measures 138 degrees
True or false if a set of points all lie on the same plane they are called collinear
Answers
We have that a group of points can be:
Coplanar: if they lie in the same plane
Collinear: if they lie in the same line
Answer- False: they are called coplanarAn asteroid is traveling at 32.0 kilometers per second. At this speed, how much time will it
take the asteroid to travel 1,040 kilometers?
Write your answer to the tenths place.
Answers
Answer:
1040 × 33.0 =
33,280
tenths= 33.3km\s
The long-distance calls made by South Africans are normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 minutes for 1500 south Africans what is the expected number of callers whose calls last less than 15 minutes?
Answers
The question provides the following parameters:
[tex]\begin{gathered} \mu=16.3 \\ \sigma=4.2 \end{gathered}[/tex]For 15 minutes, the z-score is calculated using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]At x = 15:
[tex]z=\frac{15-16.3}{4.2}=-0.3[/tex]The probability is calculated using the formula:
[tex]P(X<15)=Pr(z<-0.3)=Pr(z<0)-Pr(0From tables, we have:[tex]\begin{gathered} Pr(z<0)=0.5 \\ Pr(0Therefore, the probability is given to be:[tex]\begin{gathered} P(X<15)=0.5-0.1179 \\ P(X<15)=0.38 \end{gathered}[/tex]The expected number of callers will be calculated using the formula:
[tex]\begin{gathered} E=xP(x) \\ At\text{ }x=1500 \\ E=1500\times0.38 \\ E=570 \end{gathered}[/tex]Therefore, the expected number of callers whose calls last less than 15 minutes is 570 callers.
100 POINTS AND BRAINLY FOR THE CORRECT ONLY ANSWER IF U UNDERSTAND THE QUESTION!
A line includes the points (10,6) and (2,7). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
PLEASE AND THANK U
Answers
Answer:
[tex]y-6=-\dfrac{1}{8}(x-10)[/tex]
Step-by-step explanation:
To find the equation of a line that passes through two points, first find its slope by substituting the given points into the slope formula.
Define the points:
(x₁, y₁) = (10, 6)(x₂, y₂) = (2, 7)Substitute the points into the slope formula:
[tex]\implies m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-6}{2-10}=\dfrac{1}{-8}=-\dfrac{1}{8}[/tex]
Therefore, the slope of the line is -¹/₈.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:
[tex]\implies y-6=-\dfrac{1}{8}(x-10)[/tex]
a rectangular Garden has a length of 10 m and a width of 8 meters fill in the Box to show the perimeter and the area of the garden
Answers
Explanation
Step 1
Area,To find the area of a rectangle, multiply its height by its width
then
[tex]\text{Area}_{rec\tan gle}=length\cdot width[/tex]Let
length=10 m
width=8 m
replace,
[tex]\begin{gathered} \text{Area}_{rec\tan gle}=length\cdot width \\ \text{Area}_{rec\tan gle}=10\text{ m }\cdot\text{ 8 m} \\ \text{Area}_{rec\tan gle}=80m^2 \end{gathered}[/tex]Step 2
find the perimeter:
Perimeter is the distance around the outside of a shape,so for the garden the perimeter is
[tex]\text{Perimeter}_{rec\tan gle}=2(length+width)[/tex]replace,
[tex]\begin{gathered} \text{Perimeter}_{\text{garden}}=2(10m+8m) \\ \text{Perimeter}_{\text{garden}}=2(18\text{ m)} \\ \text{Perimeter}_{\text{garden}}=36\text{ m} \end{gathered}[/tex]I hope this helps you
A triangle has vertices P (4.1), Q (4, 5) and R (7,5) What is the area of ∆PQR? (Area= 1/12 basexheight)
Answers
First, plot the points on a graph and form the triangle:
By looking at the triangle we can see that:
Base: 2
Height: 4
Area : 1/2 x 2 x 4 = 4 units2
Select the correct answer from each drop-down menu.Glven: W(-1, 1), X(3, 4), Y(6, 0), and Z(2, -3) are the vertices of quadrilateral WXYZ.Prove: WXYZis a square.
Answers
ANSWER
all four sides have a length of 5
EXPLANATION
The distance between two points (x₁, y₁) and (x₂, y₂) is,
[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Let's find the distance between each pair of points, WX, XY, YX, and WZ,
[tex]WX=\sqrt{(3-(-1))^2+(4-1)^2}=\sqrt{(3+1)^2+(4-1)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex][tex]XY=\sqrt{(6-3)^2+(0-4)^2}=\sqrt{(3)^2+(-4)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex][tex]YZ=\sqrt{(2-6)^2+(-3-0)^2}=\sqrt{(-4)^2+(-3)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex][tex]WZ=\sqrt{(2-(-1))^2+(-3-1)^2}=\sqrt{(2+1)^2+(-4)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]Hence, using the distance formula we found that all four sides have a length of 5.
Find the average rate of change of the function in the graph shown below between x=−1 and x=1.
Answers
Answer:
Step-by-step explanation:
The last description actually clarifies the given equation. The equation should be written as: f(x) = 2ˣ +1. The x should be in the exponent's place.
The average rate of change, in other words, is the slope of the curve at certain points. In equation, the slope is equal to Δy/Δx. It means that the slope is the change in the y coordinates over the change in the x coordinate. So, we know the denominator to be: 2-0 = 2. To determine the numerator, we substitute x=0 and x=2 to the original equation to obtain their respective y-coordinate pairs.
f(0)= 2⁰+1 = 2
f(2) = 2² + 1 = 5
An online bookstore is having a sale. All paperback books are $6.00 with a flat shipping fee of $1.25. you purchase "b" booms and your total is "c". What is the independent variable?$6.00"c" cost"b" books$1.25
Answers
Let:
c = total
a = cost of each book
w = flat shipping fee
Therefore, the total is given by:
[tex]c=ab+w[/tex]where:
b = number of books
[tex]c=6x+1.25[/tex]The independent variable is:
"b" books
The solution to the equation4(x + 2) =3(5-x) is:
Answers
ANSWER:
The value of x is 1, that is, the solution of the equation is 1
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]4\cdot(x+2)=3\cdot(5-x)[/tex]Solving for x:
[tex]\begin{gathered} 4x+8=15-3x \\ 4x+3x=15-8 \\ 7x=7 \\ x=\frac{7}{7} \\ x=1 \end{gathered}[/tex]6. Diagram this statement. Then answer the questions (22) that follow. One third of the 60 questions on the test were true false. (a) How many of the questions on the test were true- false? (b) How many of the questions on the test were not true- false? (C) What percent of the questions were true-false?
Answers
3. Express the given integral as the limit of a Riemann sum but do not evaluate:
Answers
Expression of the integral [tex]\int\limits^3_0 {(x^{3}-6x) } \, dx[/tex] as the limit of a Riemann sum without any evaluation will be
Lim(n → ∞) ∑(n = 1 → ∞) [{(27i³/n³) - (18i/n)} * (3i/n)]
As per the question statement, we are provided with an integral [tex]\int\limits^3_0 {(x^{3}-6x) } \, dx[/tex] ,
And we are required to determine the expression of the above mentioned integral as the limit of a Riemann sum without any evaluation.
To start with, we need to know the formula [Δx = {(b - a)/n}]
And here, from our given integral [tex]\int\limits^3_0 {(x^{3}-6x) } \, dx[/tex], we get that, (a = 0) and
(b = 3). Therefore substituting the values of "a" and "b" in the formula to calculate Δx, we get,
[Δx = {(3 - 0)/n} = (3/n)]
Also, [(x[tex]_{i}[/tex]) = {a + (Δx)i} = {0 + (3/n)i) = (3i/n)],
Given, [ρ(x) = (x³ - 6x)], and thus, [ρ(x[tex]_{i}[/tex]) = ρ(3i/n)]
Or, [ρ(x[tex]_{i}[/tex]) = {(3i/n)³ - 6(3i/n)}]
Or, [ρ(x[tex]_{i}[/tex]) = {(27i³/n³) - (18i/n)}]
Then, Lim(n → ∞) ∑(n = 1 → ∞) ρ(x[tex]_{i}[/tex])Δx
= Lim(n → ∞) ∑(n = 1 → ∞) [{(27i³/n³) - (18i/n)} * (3i/n)]
Reimann Sum: In Mathematics, a Riemann sum is a certain kind of approximation method for an integral by a finite sum. Named after renowned German mathematician Bernhard Riemann, one very common application of the Reimann Sum is in approximating the area of functions or lines on a graph, and also the length of curve.To learn more about Integrals and Reimann Sum, click on the link below.
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A study shows that 28% of the population has high blood pressure. The study also shows that 86% of those who do not have high blood pressure exercise at least 90 minutes per week, while 32% of those with high blood pressure exercise at least 90 minutes per week. Which of the following relative frequency tables could the study provide?
Answers
The study can provide relative frequency table 2 (starting from the top)
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. The word per cent means per 100. It is denoted by the symbol “%”.
The total percentage of two or more ratios in a thesame entity is 100. For example, In a population, 28% has HBP (high blood pressure)
This means that number of those that do not have HBP will be 100 - 28 = 72%
86% of those who did not have HBP exercise at least 90 minute per week i.e
86% of no HBP ,exercise >or = 90 = (86/100) × 72 = 62%( nearest whole number)
Those that do exercise <90 minute per week = 72-62= 10%
32% of those with HBP exercise at least 90 minute( >or = 90 minutes) =( 32\100) × 28= 9%( nearest whole number)
Those with HBP and exercise <90= 28- 9= 19%
Therefore Table 2 starting from the top clearly shows this data.
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DEF is a right triangle. If FE= 12 and DE= 5, find DF.
Answers
Answer:
DF = 13
Explanation:
The Pythagoras theorem says that
[tex]FE^2+ED^2=DF^2[/tex]Now in our case,
FE = 12
ED =
Create three different proportions that can be used to find BC in the figure above. At least one proportion must include AC as one of the measures.
Answers
We are given two similar triangles which are;
[tex]\begin{gathered} \Delta AEB\text{ and }\Delta ADC \\ \end{gathered}[/tex]Note that the sides are not equal, but similar in the sense that the ratio of two sides in one triangle is equal to that of the two corresponding sides in the other triangle.
To calculate the length of side BC, we can use any of the following ratios (proportions);
[tex]\frac{AE}{ED}=\frac{AB}{BC}[/tex][tex]\frac{AB}{AC}=\frac{AE}{AD}[/tex][tex]\frac{AE}{AB}=\frac{AD}{AC}[/tex]Using the first ratio as stated above, we shall have;
[tex]\begin{gathered} \frac{AE}{ED}=\frac{AB}{BC} \\ \frac{8}{5}=\frac{6.5}{BC} \end{gathered}[/tex]Next we cross multiply and we have;
[tex]\begin{gathered} BC=\frac{6.5\times5}{8} \\ BC=4.0625 \end{gathered}[/tex]ANSWER:
[tex]BC=4.0625[/tex]What is the answer to 6x + =5
Answers
Answer:
x = 5/6 or x = 0.83
Step-by-step explanation:
6x + =5
6x + 0 = 5
6x = 5
6x/6 = 5/6
x = 5/6 or x = 0.83
Triangle ABC is inscribed in the circle with arcs shown. find X and the measures of angle A, angle B, Angle C
Answers
The total circumference of a circle = 360°
Therefore,
[tex]\text{arc AB + arc BC+ arc AC}=360^0[/tex]Where,
[tex]\begin{gathered} \text{arc AB=(6x+10)}^0 \\ \text{arc BC=(x+15)}^0 \\ \text{arc AC=((8x-40)}^0 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} (6x+10)^0+(x+15)^0+(8x-40)^0=360^0 \\ 6x^0+x^0+8x^0+10^0+15^0-40^0=360^0 \\ 15x^0-15^0=360^0 \\ 15x^0=360^0+15^0 \\ 15x^0=375^0 \\ \text{divide both sides by }15 \\ \frac{15x}{15}=\frac{375^0}{15} \\ x=25^0 \end{gathered}[/tex][tex]\begin{gathered} \text{arc AB=(6x+10)}^0=(6\times25+10)^0=150^0+10^0=160^0 \\ \text{arc BC=(x+15)}^0=(25^0+15^0)=40^0 \\ \text{arc AC=(8x-40)}^0=(8\times25^0-40^0)=200^0-40^0=160^0 \end{gathered}[/tex]To calculate
[tex]\begin{gathered} \angle A,B,\angle C \\ We\text{ will use the theorem,} \\ \text{The measure of an insribed angle in a circle equals half the measure of the intercepting arc} \\ \end{gathered}[/tex][tex]\begin{gathered} \angle A=\frac{arc\text{ BC}}{2} \\ \angle A=\frac{40^0}{2}=20^0 \end{gathered}[/tex][tex]\begin{gathered} \angle B=\frac{arc\text{ AC}}{2} \\ \angle B=\frac{160^0}{2}=80^0 \end{gathered}[/tex][tex]\begin{gathered} \angle C=\frac{arc\text{ AB}}{2} \\ \angle C=\frac{160^0}{2}=80^0 \end{gathered}[/tex]Hence,
x = 25°
∠ A=20°
∠ B=80°
∠ C=80°
Classify each Polynomial by degree and number of terms.1. X^3 + 5x 2. X^2 - 2x - 1 3. 5x^4 4. 6x^5 - 3x^2 + 7x + 9 5. -11x - 5 6. 4x^2 + 10 7. 128. 9x^3 - x^2 + 6x - 1]9. -3x^5 + 6x^4 v- 8THESE ARE THE OPTIONS Degree Name using degree 0 Constant 1 Linear 2 quadratic 3 Cubic 4 quartic 5 quintic 6 6th degreeTHESE ARE ALSO THE OTHER OPTIONSTerms NAME USING # OF TERMS1, monomial 2 , binomial3 trinomial4 or more polynomial
Answers
41 increased by 4 is what number ?
Answers
The statement
41 increased by 4
The word increase mean adding to the given number 41
Hence,
The statement can be expressed as
[tex]41+4[/tex]Simplifying the result gives
[tex]41+4=45[/tex]Therefore, the answer is
[tex]45[/tex]41 + 4 = (41-1+4=44+1=45)
41 + 4 = 45 (40+5=45)
(41-1=40 4 + 1 = 5 + 40 = 45)
Therefore, 41 increased by 4 (41+4) would be 45. Please correct me if I’m wrong.
Brian is looking to add tile to one wall in his kitchen, each tile is a rectangle that measures
14 inches by 2 inches. The wall that Brian wants to tile is a rectangle that measures
44.25inches by 51 inches. How many bie's will Brian need to cover the wall?
Answers
Using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.
What is a rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can also be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is an irregular shape with four equal sides.So, tiles needed to cover the wall:
The formula for the area of a rectangle: l × bCalculate the area of a tile as follows:
l × b14 × 228 in²Now, calculate the area of the wall as follows:
l × b44.25 × 512,256.75 in²Then, tiles needed to cover the wall:
2,256.75/2880.59Which means: 80½
Therefore, using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.
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{x|x ≤ - 6}
Write written interval motion and graph the interval
Answers
The inequality to interval notation. (−∞,−6) ( - ∞ , - 6 ).
What exactly is interval notation?
The number line's left to right location in the solution is indicated using interval notation (i.e., which part of the number line is shaded). Endpoints that are part of the solution are denoted by parentheses, while those that are not are denoted by brackets.For instance, the expressions -3x2, [-3,2], and xR|-3x2 denote that x is between -3 and 2 and might be either endpoint.Interval Notation x<-6. x<−6 x < - 6.
Convert the inequality to interval notation. (−∞,−6) ( - ∞ , - 6 ).
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Find an angle with θ with 0∘ < θ < 360∘ that has the same :
Sine as 220∘ : θ = _______ degrees
Cosine as 220∘ : θ = _______ degrees
Answers
The complete trigonometry ratios are sin(220) = -sin(40) and cos(220) = cos(140) and the angles are 40 and 220 degrees
How to determine the measure of the angles?Angle 1
The trigonometry ratio of the angle is given as
sin(220)
Expand the above expression
sin(220) = sin(180 + 40)
Apply the sine rule
sin(220) = sin(180)cos(40) + cos(180)sin(40)
Evaluate the ratios
sin(220) = 0 x cos(40) - sin(40)
So, we have
sin(220) = - sin(40)
So, the measure of the angle is 40 degrees
Angle 2
The trigonometry ratio of the angle is given as
cos(220)
Expand the above expression
cos(220) = cos(360 - 140)
Apply the cosine rule
cos(220) = cos(360)cos(140) + sin(140)sin(360)
Evaluate the ratios
cos(220) = 1 x cos(140) + sin(140) x 0
So, we have
cos(220) = cos(140)
So, the measure of the angle is 140 degrees
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x+y=22x+7y=9can u help me solve this equation
Answers
Keeping Od, this is the solution:
x + y = 2
2x + 7y = 9
___________
Step 1: Let's isolate x in equation 1, as follows:
x + y = 2
x = 2 - y
__________________
Step 2: Let's substitute x and solve for y in equation 2, this way:
2x + 7y = 9
2 (2 - y) + 7y = 9
4 - 2y + 7y = 9
4 + 5y = 9
Subtracting 4 at both sides:
4 + 5y - 4 = 9 - 4
5y = 5
Dividing by 5 at both sides:
5y/5 = 5/5
y = 1
_______________________
Step 3: Let's substitute y and solve for x in the first equation, as follows:
x + y = 2
x + 1 = 2
Subtracting 1 at both sides:
x + 1 - 1 = 2 - 1
x = 1
_____________________
Step 4: Let's write the solution as an ordered pair, this way:
(1, 1)
Segment EF is rotated 90° clockwise around the origin and then translated by (-6, y + 7).
The resulting segment E" F" has coordinates E" (-4, 5), F"(-1,-2).
What are the coordinates of the segment EF?
does anyone know this??
Answers
Answer:
E = 2,2 F = 5,-9
Step-by-step explanation:
First, you have to add (6, -7) to both coordinates (that being (-4,5)(-1,-2)
This results in E = 2,-2 and F = -5,-9
Next, you need to rotate both coordinates 90 counterclockwise, resulting in: E being (2,-2) and F being (5,-9)
Hope this helped!
Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible Through (15,5) and (5,15)
Answers
Given that the required linepasses through the points (15, 5)and (5, 15).
Find the slope of the line using teo-point formula.
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{15-5}{5-15} \\ =\frac{10}{-10} \\ =-1 \end{gathered}[/tex]Substitute the value of m into theslope-intercept form y = mx+c.
[tex]y=-x+c[/tex]Plug in the point (5, 15)to find c, the y-intercept.
[tex]\begin{gathered} 15=-5+c \\ c=20 \end{gathered}[/tex]Thus, y = -x + 20, which is the required equation of line.
