Answers
The function rule for each are:
f(x) = -2x - 6
g(x) = 5x - 4
f(x) is less than g(x), in terms of slope, while in terms of y-intercept, f(x) is greater than g(x).
How to Write the Rule of a Function?The rule of a function can be written in slope intercept form as, f(x) = mx + b, where the slope is m and the y-intercept is the value of b.
To write the function rule for f(x), substitute m = -2 and b = -6 into f(x) = mx + b:
f(x) = -2x - 6
Find the slope of the function g(x) whose graph is given:
Slope of g(x) = rise/run = 5/1 = 5
m = 5
The y-intercept is at y = -4, therefore b = -4.
To write the function rule for g(x), substitute m = 5 and b = -4 into g(x) = mx + b:
g(x) = 5x - 4
In terms of slope, f(x) is less than g(x)
In terms of y-intercept, f(x) is greater than g(x).
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Related Questions
bob can do a job in 5 hours while bill can do the same job in 8 hours. how many hours would it take them, working together, to do this job?
Answers
Hours taken by Bob and Bill if they work together is 3 1/13.
Here it is given that Bob can do a job in 5 hours and Bill can do the job in 8 hours.
We have to find the time taken by both to do the work if done together.
Time ratio of Bob and Bill = 5: 8
Efficiency of Bob and Bill = 8: 5
Total amount of work done = 5× 8 = 8× 5 = 40
The total efficiency of Bob and Bill = 13
Hours took by both bob and bill to do the work if done together = 40/13
= 3 [tex]\frac{1}{13}[/tex]
Therefore the work done together is 3 [tex]\frac{1}{13}[/tex] hours.
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divide and find quotient
(a⁴-b⁴) ÷ (a+b)
(step by step explanation)
Answers
Answer:
Step-by-step explanation:
(a⁴-b⁴)/(a-b)
using..(a+b²)=(a+b)(a-b)
=(a²+b²)(a²-b²)/(a-b)
=(a²+b²)(a+b)(a-b)/(a-b)
=(a²+b²)(a+b)
Three students ran for class president. lisa got 36 votes for class president. she got six times more votes than lauren. chandler got seven times more than lauren. how many votes did lauren get?
Answers
Lauren got 5 votes in class president election.
Number of votes Lisa got = 36
Let the number of votes of Lauren be x. So, forming the equation between the number of votes of Lisa and Lauren.
36 = x + 6x
Calculating the value of x from mentioned equation
36 = 7x
Rewriting the equation with 7 as denominator
x = 36/7
Performing division on Right Hand Side of the equation
x = 5.14
Rounding off the digits as number of votes will be whole number
x = 5
Based on the mentioned information, Lauren got 5 votes.
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relative maxima and relative minima of the function f(x) = x^5 - 4x^3 + 3x^2 - 8x - 6
Answers
The relative maxima and relative minima of the function
f(x) = x^5 - 4x^3 + 3x^2 - 8x - 6
the relative maxima is -1.871the relative minima is 1.518How to fine the relative maxima and minimaThe relative minima and maxima is calculated
by differentiating the given function find the critical values or roots of the equationdifferentiate the second tiesubstitute the critical value that are real numbersthe critical value that gave a negative value is the maximathe critical value that gave a positive value is minimaThe procedure is done as follows
x^5 - 4x^3 + 3x^2 - 8x - 6
differentiating gives
5x^4 - 12x^2 + 6x - 8
solving the equation for the critical values are
x₁ = 0.176 + 0.73i
x₂ = 0.176 - 0.73i
x₃ = 1.518
x₄ = -1.871
The second derivative
5x^4 - 12x^2 + 6x - 8
differentiating gives
20x^3 - 24x + 6
substituting x = 1.58
20 * 1.58^3 - 24 * 1.58 + 6
= 46.966 (positive hence minima)
substituting x = -1.871
20 * -1.871^3 - 24 * -1.871 + 6
= -169.9 (negative hence maxima)
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an insurance company won't repair a car when the cost of the repair is 25% or more of the car's value. if a repair costs $1400, what is the value of the car (in interval notation)?
Answers
The interval of the cost of the car is [5600, ∞).
Here we have to find the cost of the car.
Let x be the cost of the car.
So from the question, we have that the cost of the repair is 25% or more of the car's value.
So we have to find the interval notation of the cost of the car.
x ×25% ≥ 1400
x × 25/100 ≥ 1400
x ≥ 1400× 100/25
x≥ 5600
So we get that the cost of the car is greater than $5600.
Therefore the cost of the car in an interval is [5600, ∞)
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a campus radio station surveyed 500 students to determine the types of music they like. the survey revealed that 206 like rock, 161 like country, and 118 like jazz. moreover, 30 like rock and country, 27 like rock and jazz, 22 like country and jazz, and 11 like all three types of music. what is the probability that a randomly selected student likes jazz or country but not rock? note: a venn diagram may be useful here. a) 0.400 b) 0.300 c) 0.522 d) 0.262 e) 0.422 f) none of the above.
Answers
The probability that a randomly selected student likes neither rock nor country is taken as;
P(R' ∩ C') = 0.326
Let us denote them as follows;
Number that like to be rock music be - R
Number that like to be Country music be - C
Number that like to be Jazz music be - J
Thus, as we are given and we have;
R is equal to 206
C is equal to 161
J is equal to 118
P(R') =206
P(C') =161
P(R' ∩ C') = 0.326
So, now P is removed
R ∩ C = 30 - 11 = 1
Hence the answer is none of the above
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By the triangle sum theorem, the sum of the angles in a triangle is equal to Response area. Therefore, m∠A+m∠B+m∠C=180°. Using the Substitution Property, (4x)°+90°+(x+10)°=180°. To solve for x, first combine like terms to get 5x + 100 = 180. Using the Response area, 5x = 80. Then, using the division property of equality, x = 16. To find the measure of angle A, use the Response area to get m∠A=4(16)°. Finally, simplifying the expression gets m∠A=64°.
Answers
The required measure of the angle is m∠A=64°.
orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
,
Here,
Angles are represented by an algebraic expression, and the sum of the angle is 180°.
According to the question,
m∠A+m∠B+m∠C=180°
Substitute the value in the equation,
4x+90°+x+10=180°
5x = 180 - 100
5x = 80
x = 16°
Thus, the required measure of the angle is m∠A=64°.
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Use the remainder theorem to find P(-1) for P(x) = −x³ – 2x² −9. Specifically, give the quotient and the remainder for the associated division and the value of P(-1).
Answers
Using remainder theorem, Quotient = x-9 and Remainder = x² - x.
According to the remainder theorem, the remainder equals f when a polynomial, p(x), is divided by (x - a) (a). Euclid's Division Lemma can be used to demonstrate this. Using this, p(x) = q(x) (x - a) + r, where q(x) is the quotient and 'r' is the remainder.Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that when a polynomial P(x) is divided by a factor (x - a), which isn't really an element of the polynomial, a smaller polynomial is produced along with a remainder.P(x) = −x³ – 2x² −9
P(-1) = −(-1)³ – (-1)x² −9
P(-1) = −(-1) – 2(1) −9
= 1 -2 -9
= -10
Remainder of P(-1) = −(-1)³ – (-1)x² −9 is -10.
Remainder of P(x+1)
= −x³ – 2x² −9 / x+1
Quotient = x-9 and Remainder = x² - x
Hence, using remainder theorem, Quotient = x-9 and Remainder = x² - x.
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Select the correct answer. Solve the following equation for x. x2 - 36 = 0
Answers
Answer:
Step-by-step explanation:
x2-36=0
+36 +36
x2=36
/2 /2
x=18
in november's math meet, the little monsters of beast academy solved $\frac{1}{5}$ of the problems. in march's math meet, they solved $\frac 23$ of the problems. (there might be different numbers of problems asked in november and march.) in total, the little monsters solved $13$ of $30$ problems over both math meets. how many problems were asked at march's math meet?
Answers
The little monsters solved 15 problems in March's Math meet
Given, that in November's math meet, the little monsters of beast academy solved 1/5 of the problems.
In March's math meet, they solved 2/3 of the problems.
In total, the little monsters solved 13 of 30 problems over both math meets.
Let, the number of problems in November be n,
and the number of problems in March be m
According to the question,
n + m = 30 as, the total problems be 30
Now, (1/5)n + (2/3)m = 13 as, they solved total 13 problems
n + m = 30 ... (1)
n/5 + 2m/3 = 13 ... (2)
On simplifying Eq (2) becomes
3n + 10m = 195 ... (2)
On multiplying Eq (1) by 3, we get
3n + 3m = 90
3n + 10m = 195
On subtracting, we get
- 7m = - 105
m = 105/7
m = 15
So, the problems asked in March's Math meet be 15.
Hence, 15 problems were asked at March's Math meet.
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suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. how many times would we have to flip the coin in order to obtain a 99% confidence interval of width of at most .18 for the probability of flipping a head? (note that the z-score was rounded to three decimal places in the calculation) a) 164 b) 205 c) 167 d) 212 e) 202 f) none of the above
Answers
The coin is flipped at least 52 times in order to obtain a 99% confidence interval of width of at most . 18 for the probability of flipping a head.
Hence, Option F is correct answer.
In a sample with a number n of people surveyed with a probability of a success of π , and a confidence level of (1-α), we have the following confidence interval of proportions.
[tex]\pi[/tex] ± z[tex]\sqrt{\frac{\pi \p(1-\pi )}{n} }[/tex]
z is the z-score that has a pvalue of [tex]1-\frac{\alpha }{2}[/tex]
Since, the coin is fair, so [tex]\pi =0.5[/tex].
The margin of error is:
[tex]M=z\sqrt{(\frac{\pi (1-\pi )}{n} )}[/tex]
99% confidence level:
So [tex]\alpha =0.01[/tex] ,z is the value of Z that has a p value of 1-[tex]\frac{0.01}{2}[/tex]=0.995,
so Z= 2.575
How many times would we have to flip the coin ?
We have to flip the coin in order to obtain a 99% confidence interval of width of at most 18 for the probability of flipping a head at least n times.
n is found when M=0.18 .
So
M=[tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
[tex]0.18=2.575\sqrt{\frac{0.5*0.5}{n} }[/tex]
[tex]0.18\sqrt{n} =2.575*0.5[/tex]
[tex]\sqrt{n}=\frac{2.575*0.5}{0.18}[/tex]
[tex]\sqrt{n} ^{2} =(\frac{2.575*0.5}{0.18} )^{2}[/tex]
n = 51.16
Thus, we have to flip the coin at least 52 times.
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Two cyclists are 7 miles apart when they begin biking away from each other in
opposite directions. The speed of the first cyclist is 12 miles
per hour. The speed of
the second cyclist is b miles per hour greater than the speed of the first cyclist.
How many
miles does the second cyclist bike in 45 minutes?
Answers
The distance covered by second cyclist is, 9 + (3/4)b miles.
What is speed?
Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be meters per second (m/s) in this example since the distance is measured in meters (m) and the time is measured in seconds (s).
Given: Two cyclists are 7 miles apart when they begin biking away from each other in opposite directions.
The speed of the first cyclist is 12 miles per hour. The speed of the second cyclist is b miles per hour greater than the speed of the first cyclist.
Speed of first cyclist = 12 miles per hour.
Speed of second cyclist = 12 + b miles per hour.
Since, distance = speed x time
The distance covered by the second cyclist in 45 minutes is,
45 minutes = 45/60 = 3/4 hour.
Therefore, distance covered by second cyclist is,
= (12 + b) x 3/4 = 9 + 3b/4 miles.
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what could be the maximum number of deaths if only 27% of the people in a population of eighteen million is susceptible?
Answers
The maximum number of deaths could be 5840000.
What is susceptible?Being prone to something indicates you are more likely to get sick from it, such as an infection or an earache.Has something ever been given to you that you didn't want? Well, that is probably going to be the case since the word "susceptible" means "likely to be influenced or affected by." If you're easily swayed by flattery, all someone needs to do to get what they want from you is to pay you one or two compliments. Crack-prone materials won't last very long in good condition.acc to our question-
total popuation= 8000000susceptinlr percentage= 278000000 * 27/10021600008000000 - 21600005840000.hence,The maximum number of deaths could be 5840000.
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I need help like asap !!!
only numbers and decimal points
Answers
Now we have to,
→ find the required value of b.
Formula we use,
→ (AC)² = (BC)² + (AB)²
Then the value of b will be,
→ (10)² = b² + (6)²
→ 100 = b² + 36
→ b² = 100 - 36
→ b = √64
→ [ b = 8 ft ]
Hence, value of b is 8 ft.
Multiply 2.9x and 5x.
(Multiplying Linear Expressions LC)
14.5x2
7.9x2
14.5x
7.9x
Answers
Multiplication of 2.9x and 5x gives 14.5x²
How to multiply algebraic expressions?The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants
Given: 2.9x and 5x
To multiply 2.9x and 5x, multiply the numbers and multiply the letters:
2.9x × 5x = 2.9 × 5 × x × x = 14.5x²
Therefore, 2.9x multiplied by 5x is 14.5x²
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In 2001 there were 6680 electric-powered vehicles in use in the United States. In 1998 only 4760 electric vehicles were being used. (Source: U. S. Energy Information Administration)
a. Assume that the relationship between time, x, and number of electric-powered vehicles, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (years past 1998 comma number of vehicles).
Answers
An equation of slope-intercept form describing this relationship. Use ordered pairs of the form the equation, y = 640x + 4760
Since there were 4760 electric vehicles in 1998, when x=0 (indicating 0 years have passed since 1998), y=4760. There were 1,920 more electric vehicles on the road after three years. 1920 / 3 = 640 is the average rate of change every year. Between 1998 and 2001, there were 640 more automobiles every year.Our slope measures m=640. By dividing the change in y by 4760, or 1920, we can determine the slope.The y-intercept is just the starting point, or x=0. At this point, x=0. The y-intercept is shown here: (0, 4760). Equation of slope intercept: y = 640x + 4760 where b=4760.
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Exercice 1 On remplit le réservoir d’eau. Voici la
quantité d’eau notée en fonction du temps écoulé :
Durée (min) 5 15 20 30
Volume (L) 36 108 142 210
1. a. Représenter graphiquement les données de ce tableau en mettant :
• en abscisses les durées : 1 cm pour 5 min.
• en ordonnées les quantités d’eau : 1 cm pour 24 L.
Answers
Answer:
55 L
Step-by-step explanation:
Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $35 to come to his house and $60 for every hour they work. If the plumber charges Jerald a total of $305, how many hours did the plumber work?
Write and solve an equation to determine the number of hours worked by the plumber.
35x + 60 = 305; x = 7 hours
35x − 60 = 305; x = 10.4 hours
60x + 35 = 305; x = 4.5 hours
60x − 35 = 305; x = 5.7 hours
Answers
Answer:
60x + 35; x = 4.5 hours
(x is not actually equal to 4.5, it is equal to 4.67)
Step-by-step explanation:
The description says that the plumber charges a one time fee of 35 dollars to come to someones house, and then 60 dollars an hour. The total pay is 305 dollars. x will be the number of hours that the plumber works.
60x + 35 = 305
Subtract 35 from both sides: 60x = 280
Divide by 60: x = 280/60
Simplify: x=14/3
Fraction to decimal: x=4.67
Answer: C (60x + 35 = 305; x = 4.5 hours)
It's right trust me! Wish you luck!
Brainliest?
Help me find one possible solution to the inequality and show how it makes sense in the situation.
A yearbook company promises to give the junior class a picnic if they spend at least $28,000 on yearbooks and class rings. Each yearbook costs $35, and each class ring costs $140. How many yearbooks and class rings must the junior class buy to get their picnic?
here is the inequality: 35x + 140y ≥ 2800
Answers
Answer:A - 200
B - 1 Class Ring and 796 yearbooks
C - No, they would come up short 2800 dollars
Step-by-step explanation:
a car is traveling at 57 mi/h before it enters into a skid. the drag factor of the road surface is 1.1, and the braking efficiency is 100%. how long might the average skid mark be to the nearest tenth of a foot?
Answers
The average skid mark for the car is 98.5 feet.
The average skid mark can be calculated by the formula -
S = ✓30Dfn, where s is speed of car, D is skid distance, f is drag factor and n is braking efficiency. Keep the values in formula to calculate the value of D.
57 = ✓30 × D × 1.1 × 1
Performing multiplication on Right Hand Side of the equation
57 = ✓D × 33
Taking square on both sides of the equation
D = 57² ÷ 33
Taking square on numerator on Right Hand Side of the equation
D = 3249 ÷ 33
Performing division on Right Hand Side of the equation
D = 98.45 feet
Rounding to the nearest tenth of a foot
D = 98.5 feet
Hence, the average skid mark is 98.5 feet.
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The largest U.S. flag in the world is 225 feet by 505 feet.
------------------------
If a square yard of the flag weighs about 3.8 ounces, how much does the entire flag weigh in pounds?
Answers
The weight of the U.S. flag in pounds is 2,998.44 pounds.
What is the weight of the flag?The dimension of the U.S. flag is in feet. The dimensions have to be converted to yards.
1 foot = 1/3 yards
225 / 3 = 75 yards
505 / 3= 168.33 yards
The next step is to determine the area of the U.S. flag.
Area = length x width
75 x 168.33 = 12,625 yards²
Weight of the U.S. flag in ounces = 12,625 yards² x 3.8 = 47,975 ounces
1 ounce = 1/16 pounds
Weight of the U.S. flag in pounds = 47,975 / 16 = 2,998.44 pounds
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Can anyone write the equation of the graph?
Answers
The function of the graph is f(x) = |x - 3| + 5
How to find the equation of the graph line?From the question, we have the graph that can be used in our computation:
Given that the graph is an absolute value graph
We start by calculating the vertex of the graph
In this case, the minimum point on the graph is located at the point (3, 5)
This means that
Vertex = (3, 5) i.e. (h, k) = (3, 5)
Recall that the general form of an absolute value function is f(x) = |x - h| + k
Substitute the known values in the above equation
So, we have the following equation
f(x) = |x - 3| + 5
On the graph, we have
(x, f(x)) = (2, 6)
So, we have
6 = a|2 - 3| + 5
This gives
a = 1
So, we have
f(x) = 1 * |x - 3| + 5
Evaluate
f(x) = |x - 3| + 5
Hence, the equation of the graph represented by the figure is f(x) = |x - 3| + 5
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6. The supplement of an angle is 8 less than three times the measure of the angle. Find
the measure of both angles.
X =180
m/1=
m/2 =
Answers
By using the concept of supplementary angle, it can be calculated that
The two angles are 47° and 133°
What are supplementary angles?
At first it is important to know about angle.
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.
Two angles are said to be supplementary if the sum of the angles is 180°
Let one angle be x
Other angle = 180 - x
The supplement of an angle is 8 less than three times the measure of the angle
By the problem
180 - x = 3x - 8
3x + x = 180 + 8
4x = 188
x = [tex]\frac{188}{4}[/tex]
x = 47°
Other angle = 180 - 47 = 133°
The two angles are 47° and 133°
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How can the dimensions of algebra tile rectangles and area models be used to represent expressions and multiplication?
Answers
The dimensions of algebra tile rectangles and area models can be used to represent expressions and multiplication by measuring the length and breadth of the tiles and multiplying them.
What is a Rectangle?This is a plane figure which is referred to as a quadrilateral and has four right angles. The area is calculated by the following below:
Area = Length × breadth.
In cases where the algebra tile rectangles is used , it is ideal to first measure the length and the breadth after which they are then multiplied to give the appropriate answer. For example if the length is 7cm and the breadth is 6cm then the area will be 7cm × 6cm = 42cm²
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5. A rectangular 52 inch flat screen TV has a length of 42 inches. The salesman explains that all TV's are sold by the length of the diagonal. So, a 52 inch flat screen TV actually has a diagonal measure of 52 inches. To the nearest whole inch, what is the height of the TV?
Answers
The height of the TV is 31 inches . This can be calculated using Pythagoras theorem.
What is Pythagoras theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
Main Body:
according to the question --
hypotenuse = 52 in
base = 42 in
height =?
Pythagoras theorem = [tex]{P^{2} +B^{2} }[/tex] = [tex]H^{2}[/tex]
inserting the values --
52² = 42² +H²
H² = 2704- 1764
H² = 940
H≈31 inches
Hence the height of TV is 31 inches
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Question 1 of 10
Which of the following is the solution to | x1-2 ≤-3?
O A. All values are solutions
OB. xs-1 and x 25
OC. xs-1
OD. No solution
Answers
x = -1 is the solution to the given inequality |x| - 2 ≤ -3.
The five steps to resolving inequalities are as follows?
When addressing an inequality, we can:
Equal numbers are added to both sides.Take the same amount away from both sides.Add the same positive number to both sides.Subtract the same positive value from both sides.Reverse the sign and multiply both sides by the same negative value.Isolate the variable on one side of the inequality and place all other constants on the other. To achieve this, alter the inequality by performing opposing procedures. First, multiply each side by two to isolate the x. Any action you take toward one side must also be taken toward the other.
C) If x = -1,
|x| - 2 ≤ -3
|-1| - 2 ≤ -3.
1 - 2 ≤ -3.
-1 ≤ -3 which is true.
Hence, x = -1 is the solution to the given inequality |x| - 2 ≤ -3.
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help meeeeeeeeeee pleaseeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
The perfect square trinomial is x² + 10x + [tex] \boxed{\sf 25} [/tex]The factored perfect square trinomial is [tex] \boxed{\sf (x + 5)(x + 5) \ or \ {(x + 5)}^2} [/tex]Step-by-step explanation:
Given:
Binomial: x² + 10x
To Find:
Constant that should be added to the binomial so that it becomes a perfect square trinomial.Factor the trinomial.Solution:
To find the constant we would compare the binomial with (a + b)² i.e. a² + 2ab + b² as it is the formula for perfect square.
By comparing we get:
a² = x²
2ab = 10x
b² = constant (To find out)
From this we can make out:
a = x
[tex] \therefore[/tex]
[tex] \rm \implies 2 \times x \times b = 10x \\ \\ \rm \implies b = \frac{10x}{2x} \\ \\ \rm \implies b = 5 \\ \\ \therefore \\ \\ \rm \implies {b}^{2} = 25[/tex]
So, constant that should be added to the binomial so that it becomes a perfect square trinomial is [tex] \boxed{\rm 25} [/tex].
Perfect square trinomial is x² + 10x + 25
Factorisation of the trinomial:
[tex] \rm \implies {x}^{2} + 10x + 25 \\ \\ \rm \implies {x}^{2} + 10x + {5}^{2} \\ \\ \rm \implies {x}^{2} + 5x + 5x + {5}^{2} \\ \\ \rm \implies x(x + 5) + 5(x + 5) \\ \\ \rm \implies (x + 5)(x + 5) \\ \\ \rm \implies {(x + 5)}^{2} [/tex]
Question 4 (10 points)
(02.07 MC)
The figure shows triangle PQR and line segment AB, which is parallel to QR:
Triangle PQR has a point A on side PQ and point B on side PR. The line AB is parallel to the line QR.
Part A: Is triangle PQR similar to triangle PAB? Explain using what you know about triangle similarity. (5 points)
Part B: Which line segment on triangle PAB corresponds to line segment QR? Explain your answer. (3 points)
Part C: Which angle on triangle PAB corresponds to angle Q? Explain your answer. (2 points)
Answers
The location of the points A and B on side PQ and PR, and the information that segment AB is parallel to QR indicates;
Part A: Triangle ΔPQR is similar to ΔPAB by AA similarity postulate
Part B: The line segment on triangle ΔPAB that corresponds to line segment QR is segment AB
Part C: The angle on triangle ΔPAB that corresponds to angle ∠Q is angle ∠A
What makes two triangles similar?Two triangles are similar if two angles in one triangle are congruent to two angles in the other triangleThe lengths of all three sides of one triangle that is similar to other another triangle are proportional to the three sides of the other triangleTwo triangles are similar if two sides of on triangle are proportional to two sides of the other or second triangle and if the included angle between the two sides are congruent.Please find attached the drawing of triangles ΔPQR and ΔPAB created with MS Word
The in formation in the question are;
Line [tex]\overline{AB}{[/tex] is parallel to [tex]\overline{QR}[/tex], [tex]\left(\overline{AB} \parallel \overline{QR}\right)[/tex]
ΔPQR and ΔPAB overlap
Part A: Angle ∠PQR is congruent to angle ∠PAB (corresponding angles to parallel lines having a common transversal)
∠PRQ is congruent to ∠PBA (Corresponding angles formed by a common transversal to parallel lines)
ΔPQA is similar to ΔPAB (Angle-Angle, AA similarity postulate)
Part B: Corresponding sides of triangles are located on the same relative position within the triangle
Segment QR is the included segment to ∠PQR and ∠PRQ, which are each congruent to ∠PAB and ∠PBA, respectively in ΔPAB and segment AB is the included side to ∠PAB and ∠PBA, therefore, the line segment on triangle ΔPAB that corresponds to line segment QR is segment AB
Part C: Angle ∠Q on triangle ΔPQR is adjacent to segment QR on the right and angle ∠P on the left, while angle ∠A is adjacent segment AB on the right and ∠P on the right, segment AB in ΔPAB corresponds to segment QR on triangle ΔPQR, therefore, by the relative position of angle ∠A on triangle ΔPAB, it is the angle that corresponds to angle ∠Q
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A textbook store sold a combined total of 423 psychology and math textbooks in a week. The number of psychology textbooks sold was two times the number of math textbooks sold. How many textbooks of each type were sold?
Answers
Taking into account the definition of a system of linear equations, the textbook store sold 141 math textbooks and 282 psychology textbooks.
System of linear equationsA system of linear equations is a set of linear equations (that is, a system of equations in which each equation is of the first degree) in which more than one unknown appears.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.
This caseIn this case, a system of linear equations must be proposed taking into account that:
"p" is the number of psychology textbooks sold."m" is the number of math textbooks sold.You know:
A textbook store sold a combined total of 423 psychology and math textbooks in a week. The number of psychology textbooks sold was two times the number of math textbooks sold.The system of equations to be solved is
p + m= 423
p=2m
It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, substituting the second equation in the first one you get:
2m + m= 423
3m=423
m= 141
Substituting this value in the second equation you get:
p= 2m
p= 2×141
p= 282
Finally, 141 math textbooks and 282 psychology textbooks were sold by the textbook store.
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A vehicle purchased for $32500 depreciates at a constant rate of 6%. Determine the approximate value of the vehicle 15 years after purchase.
Answers
The value of vehicle after 15 years is $12,846.98 when purchased at $32500 and with rate of depreciation 6%.
What is rate of depreciation?The depreciation rate is the percentage at which an asset depreciates over its anticipated useful life. It can also be described as the portion of an organization's long-term investment in an asset that the organization claims as a tax-deductible expense over the course of the asset's useful life.
Here,
The value of vehicle=$32500
rate of depreciation=6% per year
time period=15 years
The percent value of vehicle=100-6=94%
Therefore to find the value in 15 years we multiply 32500 by 0.94 raised to the 15th power.
The value of vehicle after 15 years=$12,846.98
After 15 years, a vehicle that cost $32,500 and had a 6% depreciation rate is worth $12,846.98.
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