To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step.
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ANSWER:
Separate the quotient in two terms
STEP-BY-STEP EXPLANATION:
We have the following:
[tex]\begin{gathered} \tan x=\frac{\sin x}{\cos x} \\ \tan x=\frac{1}{\cos x}\cdot\sin x \end{gathered}[/tex]Therefore, the step shown in the image is to separate the quotient in two terms
Related Questions
Find the coordinates of the center, vertices, covertices, foci, length of transverse and conjugate axis and the equation of the asymptotes. Then graph the hyperbola.
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The given equation is,
[tex]\frac{x^2}{36}-\frac{y^2}{16}=1\text{ ---(1)}[/tex]It can be rewritten as,
[tex]\frac{x^2}{6^2}-\frac{y^2}{4^2}=1\text{ ---(2)}[/tex]The above equation is similar to the standard equation of left-right facing a hyperbola given by,
the top ten medal winning nations in a in a particular year are shown in the table. use the given information and calculate the median number of bronze medals for all nations round to the nearest tenth as needed
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We have the following:
We know that to calculate the average we must add the corresponding values of bronze medals of each nation and then divide by the number of nations like this
[tex]\begin{gathered} m=\frac{11+7+9+5+5+3+8+4+6+0}{10} \\ m=\frac{58}{10} \\ m=5.8 \end{gathered}[/tex]the median number of bronze medals for all nations is 5.8
Mr. and Mrs. Hill hope to send their son to college in fourteen years. How much money should they invest now at an interest rate of 9.5% per year, compounded continuously, in order to be able to contribute $8500 to his education?Round your answer to the nearest cent.
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continuouslyUsing the formula for a compounded continously
[tex]P=P_0\cdot e^{r\cdot t}[/tex]where P is the amount on the account after t years compounded at an interest rate r when Po is invested in an account.
then,
[tex]\begin{gathered} 8500=P_0\cdot e^{0.095\cdot14} \\ 8500=P_{0^{}}\cdot e^{1.33} \\ P_0=\frac{8500}{e^{1.33}} \\ P_0=2248.056\approx2248.06 \end{gathered}[/tex]We need to know how to Convert the fraction into its decimal representation on level seven using step by step instructions. We especially need to know how to solve 1/7 in level seven
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We want to convert our fractions in a way the denominators are potencys of 10. Let's start with the first one.
[tex]\frac{32}{40}[/tex]If we multiply both the numerator and denominator by 25, we're going to have
[tex]\frac{32\times25}{40\times25}=\frac{800}{1000}=0.8[/tex]Now, with the next fraction
[tex]\frac{12}{48}[/tex]Dividing both numerator and denominator by 12, we have
[tex]\frac{12}{48}=\frac{1}{4}[/tex]Again, If we multiply both the numerator and denominator by 25, we're going to have
[tex]\frac{1}{4}=\frac{25}{100}=0.25[/tex]For the next fraction, it is enough to multiply both numerator and denominator by 4
[tex]\frac{3}{25}=\frac{12}{100}=0.12[/tex]For the next one, we can again multiply both the numerator and denominator by 25
[tex]\frac{18}{40}=\frac{450}{1000}=0.45[/tex]Nancy plans to take her cousins to an amusement park. She has a total of $100 to pay for 2 different charges. • $5 admission per person • $3 per ticket for rides Which inequality could Nancy use to determine y, the number of tickets for rides she can buy if she pays the admission for herself and x cousins? A. 5y + 3(x + 1) >= 100 B. 5(x + 1) + 3y > 100 C. 5(x + 1) + 3y =< 100 D. 5y + 3(x + 1) < 100
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ANSWER
[tex]C.5(x\text{ + 1) + 3y }\leq100[/tex]EXPLANATION
Nancy has $100.
The charges are:
=> $5 admission per person. She has x cousins and herself to pay for, this means that she pays $5 for (x + 1) persons.
The admission charge is therefore:
$5 * (x + 1) = $5(x + 1)
=> $3 per ticket for rides. The number of rides she can pay for is y. So the charge for rides is:
$3 * y = $3y
Since she only has $100, everything she pays for can only be less than $100 or equal to $100.
This means that, if we add all the charges, they must be either less than or equal to $100.
That is:
[tex]5(x\text{ + 1) + 3y }\leq100[/tex]That is Option C.
Describe the relationship between average velocity of a car in motion versus the instantaneous velocity of the same car in motion. Which one matters more if you get pulled over on the freeway for speeding and why?
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Answer:
During a typical trip to school, your car will undergo a series of changes in its speed. If you were to inspect the speedometer readings at regular intervals, you would notice that it changes often. The speedometer of a car reveals information about the instantaneous speed of your car. It shows your speed at a particular instant in time.
Step-by-step explanation:
The instantaneous speed of an object is not to be confused with the average speed. Average speed is a measure of the distance traveled in a given period of time; it is sometimes referred to as the distance per time ratio. Suppose that during your trip to school, you traveled a distance of 5 miles and the trip lasted 0.2 hours (12 minutes). The average speed of your car could be determined as
On the average, your car was moving with a speed of 25 miles per hour. During your trip, there may have been times that you were stopped and other times that your speedometer was reading 50 miles per hour. Yet, on average, you were moving with a speed of 25 miles per hour.
hope this helps might not be the answer your looking for but a better explanation on how too figure it out :))
c. Where would the line y = - 2x + 1 lie? Again, justify your prediction and add the graph of this lineto your graph from part (b).
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Given:
b) First the two lines are graphed,
[tex]\begin{gathered} y=2x+3 \\ y=2x-2 \end{gathered}[/tex]Now, yoshi wants to add one more equation,
[tex]y=2x+1[/tex]The graph is represented as,
In the above graph the green line represents the y=2x+1 and it lies between the line y= 2x+3 and y= 2x-2.
c) The graph of the line y = -2x +1
It is observed that the green line y= -2x+1 intersects both the lines y= 2x+3 and y= 2x-2.
Mariana, who rents properties for a living, measures all the offices in a building she is renting. Size (square meters) Number of offices 60 3 70 2 98 5 X is the size of a randomly chosen office. What is the expected value of X? Write your answer as a decimal.
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The expected value formula is
[tex]E=\Sigma x\cdot P(x)[/tex][tex]\begin{gathered} E=60\cdot\frac{3}{10}+70\cdot\frac{2}{10}+98\cdot\frac{5}{10} \\ E=18+14+49 \\ E=81 \end{gathered}[/tex]Hence, the expected value is 81.Question 2 write an expression to represent the perimeter of Melissa‘s garden in the terms of X type the correct answer in each box use numerals instead of words
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From the given statement in part A,
There are given that square patch for the tomatoes
Now,
Let x is the length of the tomato patch, w is the width of the garden and L is the length of the garden
So,
[tex]\begin{gathered} L=3x+2 \\ W=x+5 \end{gathered}[/tex]Then,
From the perimeter of the vegetable garden:
[tex]\begin{gathered} P=2(L+W) \\ P=2(3x+2+x+5) \\ P=2(4x+7) \\ P=8x+14 \end{gathered}[/tex]Hence, the perimeter is, 8x + 14.
Can I please just have the answer I’m in a hurry to complete this lol
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By rearranging the triangles side by side and making sure the triangles vertices touches each other. The image below is formed
What you notice : The image formed by placing the triangle side by side with the vertices touching each other is that, the shape formed is a trapezium.
a) If the triangles are cut out at equal proportion, then the angles are equal and the the triangles are equiangular; the angles are 60 degrees each
b) If the triangles are not cut out equally, then the greatest number of right angle that we can get in a triangle is one (1) and the greatest number of obstuse angle in a triangle is one (1)
Reason:
The sum of the three angles of a triangle is 180 degrees, of which if one angle is 90 degrees (right angle) then the other two angles will be less than 90 degrees each, as their sum will give 90 degrees
Also if one of the three angles is an obtuse angle ( say 115 degrees) then the other two angles will be acute angles each.
The two-way table shows the number of students that do or do not do chores at home and whether they receive an allowance or not. I Allowance No Allowance 13 3 Do Chores Do Not Do Chores 5 a. How many total students do chores? b. What is the relative frequency of students that do chores and get an allowance to the number of students that do chores? Round to the nearest hundredth if necessary. chores nor get an allowance to the total number of What is the relative frequency of students that do not students? Round to the nearest hundredth if necessary, d. Of those that do not do chores what percentage still receive an allowance?
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a) do chores 13 + 3 = 16
answer: 16 students
b) this is
[tex]\frac{chores\text{ and allowance}}{\text{chores}}=\frac{13}{16}=0.8125[/tex]answer: 0.81
c) this is
[tex]\frac{\text{no chores and no allowance}}{total}=\frac{4}{25}=0.16[/tex]answer: 0.16
d) this is
[tex]\frac{no\text{ chores and allowance}}{no\text{ chores}}\times100=\frac{5}{9}\times100=\frac{500}{9}=55.55[/tex]answer: 55.55%
In the xy-plane, line n passes through point (0,0) and has a slope of 4. If line n also passes through point (3,a), what is the value of a?
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Is this a right triangle?Use the Pythagorean Theorem to find out!20 cm12 cm16 cmYesNo
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If this is a right triangle, then the Pythagorean theorem has to be valid.
This means that the sum of the squares of the legs has to be equal to the square of the hypotenuse (NOTE: we can identify the potential hypotenuse by finding the side with the most length).
Then, we calculate:
[tex]\begin{gathered} 12^2+16^2=20^2 \\ 144+256=400 \\ 400=400\longrightarrow\text{True} \end{gathered}[/tex]As the Pythagorean theorem is valid for this side's lengths, we know that this triangle is a right triangle.
Answer: Yes.
Find the average rate of change over the interval 0, 1 for the quadratic function graphed.
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the average rate of the change is ,
[tex]=\frac{3-5}{1-0}[/tex][tex]=\frac{-2}{1}=-2[/tex]A rectangular field is nine times as long as it is wide. If the perimeter of the field is 1100 feet, whatare the dimensions of the field?The width of the field isfeet.The length of the field isfeet.
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Given:
The perimeter of the rectangular field is 1100 feet.
According to the question,
l=9w
To find the dimensions:
Substitute l=9w in the perimeter formula,
[tex]\begin{gathered} 2(l+w)=1100 \\ 2(9w+w)=1100 \\ 20w=1100 \\ w=55\text{ f}eet \end{gathered}[/tex]Since the width of the rectangle is 55 feet.
The length of a rectangle is,
[tex]55\times9=495\text{ f}eet[/tex]Hence,
The width of the rectangle is 55 feet.
The length of a rectangle is 495 feet.
What is the volume of this sphere? Use a ~ 3.14 and round your answer to the nearest! hundredth. 5 m cubic meters
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We will have the following:
[tex]V=\frac{4}{3}\pi r^3[/tex]Now, we replace the values and solve:
[tex]V=\frac{4}{3}(3.14)(5)^3\Rightarrow V\approx523.33[/tex]So, the volume of the sphere is approximately 523.33 cubic meters.
***Example with an 8 m radius***
If the radius of the sphere were of 8 meters, we would have:
[tex]V=\frac{4}{3}(3.14)(8)^3\Rightarrow V\approx2143.57[/tex]So, the volume of such a sphere would be approximately 2143.57 cubic meters.
5 cm5 cmThe surface area of the above figure isA. 208.1 cm2B. 225.6 cm2C. 314.2 cm2D. none of the above
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It is a cylinder.
1.- Calculate the area of the base and the top
Area = 2*pi*r^2
Area = 2*3.14*5^2
Area = 157 cm^2
Total area of the base and top = 2 x 157 = 314 cm^2
2.- Calculate the perimeter of the circle.
Perimeter = 2*pi*r
Perimeter = 2*3.14*5
Perimeter = 31.4 cm
3.- Calculate the lateral area
Lateral area = 5 x 31.4
Lateral area = 157 cm^2
4.- Calculate the total area = 157 + 314
= 471 cm^2
5.- Result
D. None of the above
y=6/5x+9 how would I graph it
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To graph this linear function, we can find both intercepts of the function. To achieve this, we need to solve the equation when y = 0 (for this function) (this will be the x-intercept), and then we need to solve the resulting equation for this function when x = 0 (this will be the y-intercept). Then, we will have two points for which we can graph the function - we need to remember that a line is defined by two points.
Then, we can proceed as follows:
1. Finding the x-intercept[tex]y=\frac{6}{5}x+9,y=0\Rightarrow0=\frac{6}{5}x+9[/tex]Then, we have:
a. Add -9 to both sides of the equation:
[tex]\frac{6}{5}x=-9[/tex]b. Multiply both sides of the equation by 5/6:
[tex]\frac{5}{6}\frac{6}{5}x=-9\cdot\frac{5}{6}\Rightarrow x=-\frac{45}{6}=-\frac{15}{2}=-7.5[/tex]Therefore, the x-intercept is (-7.5, 0).
2. Finding the y-interceptWe have that x = 0 in this case. Then, we have:
[tex]y=\frac{6}{5}x+9\Rightarrow y=\frac{6}{5}(0)+9\Rightarrow y=9[/tex]Therefore, the y-intercept is (0, 9).
Now, we have the points (-7.5, 0) and (0, 9), and we can draw both points on the coordinate plane. The line will pass through these two points:
The from y=mx passes through the points (2, - 15) and (6, - 45)
Answers
y = -7.5x
Explanation:The given points: (2, -15) and (6, -45)
The equation of the proportional relationship given:
y = mx
m = slope
We apply slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} x_1=2,y_1=-15,x_2=6,y_2\text{ = }-45 \\ m\text{ = }\frac{-45\text{ - (-15)}}{6\text{ - 2}} \\ m\text{ = }\frac{-45+15}{4} \end{gathered}[/tex][tex]\begin{gathered} m\text{ = }\frac{-30}{4} \\ m\text{ = -15/2} \\ m\text{ = -7.5} \end{gathered}[/tex]The relationship of the equation becomes:
y = -7.5x
Select the correct product of (x + 3)(x - 5). CX - 15 X5 + 3x - 5x2 - 15 X - 15 C x + 3x - 5x - 15
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Distributive property:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]Multiplication of powers with the same base:
[tex]a^m\cdot a^n=a^{m+n}[/tex]For the given expression:
[tex]\begin{gathered} (x^2+3)(x^3-5)=x^2\cdot x^3+x^2\cdot(-5)+3\cdot x^3+3\cdot(-5) \\ \\ =x^{2+3}-5x^2+3x^3-15 \\ =x^5-5x^2+3x^3-15 \\ =x^5+3x^3-5x^2-15 \end{gathered}[/tex]Answer is the second option
Two balls are drawn in succession without replacement from an urn containing 5 red balls and 6 blue balls. Let Z be the random variable representing the number of blue balls. Construct the probability distribution and histogram of the random variable Z.
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ANSWER and EXPLANATION
Let R represent the number of red balls.
Let B represent the number of blue balls.
There are four possible outcomes when the balls are picked:
[tex]\lbrace RR,RB,BR,BB\rbrace[/tex]We have that Z is the random variable that represents the number of blue balls.
This implies that the possible values of Z are:
To construct the probability distribution, we have to find the probabilities of each of the outcomes:
[tex]\begin{gathered} P(RR)=\frac{5}{11}*\frac{4}{10}=\frac{2}{11} \\ P(RB)=\frac{5}{11}*\frac{6}{10}=\frac{3}{11} \\ P(BR)=\frac{5}{11}*\frac{6}{10}=\frac{3}{11} \\ P(BB)=\frac{6}{11}*\frac{5}{10}=\frac{3}{11} \end{gathered}[/tex]Hence, the probabilities for the possible outcomes of the random variable are:
[tex]\begin{gathered} P(Z=0)=\frac{2}{11} \\ P(Z=1)=\frac{3}{11}+\frac{3}{11}=\frac{6}{11} \\ P(Z=2)=\frac{3}{11} \end{gathered}[/tex]Therefore, the probability distribution is:
Now, let us plot the histogram:
That is the answer.
Solve for u-6u+3(u-3)=12
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Answer: u=7
Given:
[tex]-6u+3(u-3)=12[/tex]- Distribute 3(u-3):
[tex]\begin{gathered} -6u+3(u-3)=12 \\ \Rightarrow-6u+3u-9=12 \end{gathered}[/tex]- Combine like terms:
[tex]\begin{gathered} \begin{equation*} -6u+3u-9=12 \end{equation*} \\ \Rightarrow-6u+3u=12+9 \\ \Rightarrow-3u=21 \end{gathered}[/tex]- Divide both sides by -3:
[tex]\begin{gathered} \begin{equation*} -3u=21 \end{equation*} \\ \Rightarrow\frac{-3u}{-3}=\frac{21}{-3} \\ \Rightarrow u=7 \end{gathered}[/tex]Therefore, u=7.
I need help part two and three of this question:A line passes through the following points: (6,3) and (2,9)1. Write the equation of the lineWhich I got y=-3/2 x+122. Write an equation of a line that is perpendicular to the original form. 3. Write the equation of a line that is parallel to the original form.
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Part 2:
To determine an equation that is perpendicular to the line equation y = -3/2x + 12, get the negative reciprocal of the slope of the line equation.
[tex]\begin{gathered} \text{Given slope: }m=-\frac{3}{2} \\ \\ \text{The negative reciprocal is} \\ -\Big(-\frac{3}{2}\Big)^{-1}=\frac{2}{3} \\ \\ \text{We can now assume that any line in the form} \\ y=\frac{2}{3}x+b \\ \text{where }b\text{ is the y-intercept} \\ \text{is perpendicular to the line }y=-\frac{3}{2}x+12 \end{gathered}[/tex]Part 3:
An equation that is parallel to the line y = -3/2x + 12, is a line equation that will have the same slope as the original line.
Given that the slope of the line is m = -3/2, then any line equation in the form
[tex]\begin{gathered} y=-\frac{3}{2}x+b \\ \text{where} \\ b\text{ is the y-intercept} \end{gathered}[/tex]hi can someone help me
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This type of function is non linear.
Define function.A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output. You can tell if a relation is a function by looking at the inputs (the x-coordinates) and outputs (the y-coordinates). Keep in mind that each input has only one output in a function. A function is an equation with a single solution for y for each value of x. Each input of a particular type receives exactly one output when using a function.
Given,
f(x) = x²
This type of function is non linear.
The end behavior is:
as x ⇒ ∞ , y ⇒ ∞
x ⇒ -∞ , y ⇒ -∞
The function graphed is f(x) = (x -3)²
To learn more about function, visit:
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Convert the fraction to a decimal. Round the quotient to hundredths when necessary70 over 45
Answers
Given:
[tex]\frac{70}{45}[/tex]Required:
We need to convert the given fraction to a decimal.
Explanation:
Divide the number 70 by 45.
[tex]\frac{70}{45}=1.555...[/tex]Round off to the nearest hundredth.
[tex]\frac{70}{45}=1.56[/tex]Final answer:
[tex]\frac{70}{45}=1.56[/tex]Given:
[tex]\frac{70}{45}[/tex]Required:
We need to convert the given fraction to a decimal.
Explanation:
Divide the number 70 by 45.
[tex]\frac{70}{45}=1.555...[/tex]Round off to the nearest hundredth.
[tex]\frac{70}{45}=1.56[/tex]Final answer:
[tex]\frac{70}{45}=1.56[/tex]- 9 = 12 what is the value of K?
Answers
For this case we have the following expression given:
k/3 -9 = 12
We can add 9 in both sides and we got:
k/3 = 12+9
k/3= 21
And if we multiply in both sides by 3 we got:
k = 21*3 = 63
Order the following integers from least to greatest.-41, -53, -73, -78 A. -78, -53, -73, -41 B. -78, -73, -41, -53 C. -73, -78, -53, -41 D. -78, -73, -53, -41
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The value of negative integers decreases the further we get from the 0 point on the number line.
Therefore, if we arrange the numbers in ascending order ignoring the negative sign, the numbers will be in descending order when the negative sign is included.
By the definition above, we can say that the smallest number of the lot is -78 and the largest one is -41.
The numbers can be ordered from least to greatest as shown below:
[tex]-78,-73,-53,-41[/tex]OPTION D is the correct answer.
New York City mayor Michael made it his mission to reduce smoking in New York City. New York city’s adult smoking rate is 13.2%. In a random sample of 3932 New York City residents, how many of those people smoke? Round to the nearest integer
Answers
519 people smoked
Explanation
to figure out this we need to find teh 13.2 % of 3932
so
Step 1
Convert 13.2% to a decimal by removing the percent sign and dividing by 100
then
[tex]13.2\text{ \%}\rightarrow\frac{13.2}{100}\rightarrow0.132[/tex]Step 2
now, multyply the number by the percentage ( in decimal form),so
[tex]\begin{gathered} 13.2\text{ \% of 3932=0.132}\cdot3932=519.04 \\ \text{rounded} \\ 519 \end{gathered}[/tex]therefore, the answer is
519 people smoked
I hope this helps you
The day's high temperature in Detroit, Michigan was recorded as 50°F. Use the formula C=59(F−32) to write 50°F as degrees Celsius.
Answers
Given:
The day's high temperature in Detroit, Michigan was recorded as 50°F.
[tex]C=\frac{5}{9}(F-32)[/tex]Required:
To convert the 50°F as degrees Celsius.
Explanation:
Consider
[tex]C=\frac{5}{9}(F-32)[/tex]For F=50,
[tex]\begin{gathered} C=\frac{5}{9}(50-32) \\ \\ =\frac{5}{9}(18) \\ \\ =5\times2 \\ \\ =10\degree C \end{gathered}[/tex]Final Answer:
[tex]C=10\degree C[/tex]The sum of two numbers is 51. One number is 15 more than the other. What is the smaller number. Try solving this by writing a system of equations and substitution.
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Let's convert the given relationships into an equation.
Let's name the two number x and y.
The sum of the two numbers is 51: x + y = 51
One number is 15 more than the other: x = y + 15
Using the equations that we generated from the given relationships, let's determine the value of the two numbers by substitution.
Let's substitute x = y + 15 to x + y = 51.
[tex]\text{ x + y = 51 }\rightarrow\text{ (y + 15) + y = 51}[/tex][tex]\text{ y + 15 + y = 51 }\rightarrow\text{ 2y = 51 - 15}[/tex][tex]\text{ 2y = 36 }\rightarrow\text{ y = }\frac{36}{2}[/tex][tex]\text{ y = 18}[/tex]Since we now get the value of y, y = 18, let's determine the value of x.
[tex]\text{ x = y + 15 }\rightarrow\text{ x = 18 + 15}[/tex][tex]\text{ x = 33}[/tex]Therefore, the value of the two numbers is 18 and 33.