Graph paper recommended***
Quadrilateral MATH includes the points M(2,-4) and A(5,-2).
Part A: Find coordinates for T and H such that quadrilateral MATH is a rectangle.
Part B: Prove that the resulting quadrilateral is a rectangle.
18
Answers
a) The coordinates for T and H such that quadrillateral MATH is a rectangle are T(x, y) = (2, - 2) and H(x, y) = (5, - 4).
b) The quadrilateral MATH is a rectangle.
How to create and analyze quadrillateral on a Cartesian plane
Quadrilaterals are figures with four sides and whose internal angles sums a total of 360 degrees. A quadrilateral is a rectangle when each pair of opposite sides are parallel and have the same length to each others, each of the four angles are right angles and each pair of perpendicular sides.
a) Vectorially speaking, we can construct a rectangle by using the following definitions:
M(x, y) = (a, b), A(x, y) = (c, d), T(x, y) = (a, d), H(x, y) = (c, b)
If we know that a = 2, b = - 4, c = 5, d = - 2, then the points T and H are described below:
T(x, y) = (2, - 2), H(x, y) = (5, - 4)
The coordinates for T and H such that quadrillateral MATH is a rectangle are T(x, y) = (2, - 2) and H(x, y) = (5, - 4).
b) To prove that quadrilateral MATH, we need to prove that:
MT = HA
(2, - 2) - (2, - 4) = (5, - 2) - (5, - 4)
(0, 2) = (0, 2)
TA = MH
(5, - 2) - (2, - 2) = (5, - 4) - (2, - 4)
(3, 0) = (3, 0)
MT • TA = 0
(0, 2) • (3, 0) = 0 · 3 + 2 · 0 = 0
MH • HA = 0
(3, 0) • (0, 2) = 3 · 0 + 0 · 2 = 0
Therefore, the quadrilateral MATH is a rectangle.
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Related Questions
What is the sign of b/c
Answers
Answer:
Negative.
Step-by-step explanation:
b is above zero. So, it is positive.
c is below zero. So, it is negative.
A positive divided by negative number results in negative.
Answer:
B. negative
Step-by-step explanation:
-2 is negative. That's why.
Study island question below its 8th grade algebra
Answers
Answer:
376.8 [tex]units^{2}[/tex]
Step-by-step explanation:
There are a lot of moving parts. We need to find the area of the bottom of the circle the center and the top circle.
The top and the bottom will be the same.
The area of a circle:
a = [tex]\pi[/tex][tex]r^{2}[/tex]
a = 3.14([tex]5^{2}[/tex])
a = 3.14(25)
a =78.5
The center: Think of this as a label on soup can. If you tear the label off it would be a rectangle. To find the area we would multiply the height of the can by the circumference of the circle. They tell us the height is 7 and we can calculate the circumference.
C = [tex]\pi[/tex]d The d is the diameter it is 2 of the radiuses.
C = [tex]\pi[/tex]10
C = 3.14(10)
C = 31.4
Now we multiply 31.4 and 7 together to find the area of the center of the cylinder.
(31.4)(7) = 219.8
The total area:
top 78.5
center 219.8
bottom 78.5
Total 376.8
The lines shown below are perpendicular. If the green line has a slop of 2/5, what is the slope of the red line?
Answers
The slope of the red line that is perpendicular to the green line is: -5/2.
What are the Slope Values of Perpendicular Lines?When one line lies perpendicular to another line, the slope of one must be the negative reciprocal of the other line.
What is the Negative Reciprocal of a Number?If given a number, i.e. a/b, the negative reciprocal of a/b would the opposite value of the reciprocal of a/b.
Reciprocal of a/b is b/a. Negative reciprocal of a/b would therefore be: -b/a.
Given that the slope of the green line is: 2/5. And it is perpendicular to the red line. The slope of the red line would be the negative reciprocal of 2/5.
Negative reciprocal of 2/5 is -5/2.
Therefore, the slope of the red line is: -5/2.
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Planes X and Y are perpendicular. Points A, E, F, and G are points only in plane X. Points R and S are points in both planes X and Y. Lines EA and FG are parallel.
Planes X and Y are shown. Lines A E and F G are vertical and are on plane X. Line R S is at the intersection of the 2 planes.
Based on this information, which pair of lines, together, could be perpendicular to RS? Select two options.
Answers
The pair of the line together that could be perpendicular to RS and should be considered will be EA and FG.
What is a perpendicular line?It should be noted that in terms of elementary geometry, two geometric objects should be considered as perpendicular when they intersect at a right angle.
In such a case, a line is treated to be perpendicular to another line in the case when the two lines intersect at a right angle.
Therefore, based on the information, the pair of the line together that could be perpendicular to RS and should be EA and FG.
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1. Tanya determined that the dimensions of a painted barn quilt needed to be 1 1/3 ft by 2 1/4 ft. What will be the area of the barn quilt?
2. Mrs. Smith oatmeal cookie recipe calls for 2/5 of a cup of sugar. How much sugar would she need to make 1/2 of a batch of cookies?
3. At the park, 6 boys are practicing throwing, catching, andhitting a baseball. Of those 6 boys, 2/3 of them are working on hitting. How many boys are practicing hitting the ball.
4. Rachel works at a lemonade stand at the park. On Monday she used 1 2/5 bags of lemons. On tuesday she used 1 1/4 times as many lemons as on Monday. How many bags of lemons did Rachel use on Tuesday?
Answers
The area of the barn quilt is 3 sq.ft.
The amount of sugar needed to make 1/2 of a batch of cookies is 1/5 of a cup.
Number of boys are practicing hitting the ball = 4
Number of bags of lemons used by Rachel on Tuesday = 1[tex]\frac{3}{4}[/tex]
1. A painted barn blanket needed to be 1 1/3 feet by 2 1/4 feet in size.
Area of the barn quilt = 1 1/3*2 1/4
= 4/3*9/4
= 3 sq. ft.
2. The recipe for Mrs. Smith's oatmeal cookies asks for 2/5 cups of sugar.
Sugar needed for making 1/2 of a batch of cookies = 1/2*2/5
= 1/5 of a cup
3. Six boys are practicing baseball throwing, catching, and hitting in the park. Two thirds of those six youngsters are practicing hitting.
Number of boys practicing hitting the ball = 6*2/3 = 4
4. At the park's lemonade kiosk, Rachel works. She used 1 and 2/5 bags of lemons on Monday. She used 1 and 1/4 times as many lemons on Tuesday as she did on Monday.
Number of bags of lemon used on Tuesday = 7/5*5/4
= 7/4
= 1 and 3/4 bags
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The height of a soccer ball that is kicked from the ground can
be approximated by the function: y = -16x² + 48x, where y is the height of
the soccer ball in feet x seconds after it is kicked.
Find the time, in seconds, it takes from the moment the soccer ball is kicked until it
returns to the ground.
Answers
The time, in seconds, it takes from the moment the soccer ball is kicked until it returns to the ground is 3 seconds
How to determine the time to hit the ground?The function is given as:
y = -16x^2 + 48x
When the ball hits the ground, we have
y = 0
Substitute the known values in the above equation
-16x^2 + 48x = 0
Factor out -16x
-16x(x - 3) = 0
Divide through by -16x
x - 3 = 0
Add 3 to both sides
x = 3
Hence, the time, in seconds, it takes from the moment the soccer ball is kicked until it returns to the ground is 3 seconds
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If a right circular cone has a circular base with a diameter of length 16 cm and a volume of 320???? cm3, find its lateral area in square centimeters.
Answers
The lateral surface area of a right circular cone is 234.09 [tex]cm^2[/tex]
Given that volume = [tex]320cm^3[/tex]
Radius = 8cm
we know that
The volume of the right circular cone = [tex]V = \frac{\pi r^2h}{3}[/tex]
[tex]320 = \frac{22 \times 8^2h}{3 \times 7}[/tex]
after solving the equation we get
h = 4.77cm
now, the lateral surface area of the cone = [tex]A = \pi \times r \times \sqrt{h^2 + r^2}[/tex]
now putting the values in the above equation
[tex]A = \pi \times 8 \times \sqrt{4.77^2 + 8^2}[/tex]
A = 234.09 [tex]cm^2[/tex]
What is lateral surface area?All sides of an object, excluding its base and top, are considered its lateral surface (when they exist). The size of the lateral surface is referred to as its area.This must be distinguished from the total surface area, which consists of the base and top areas as well as the lateral surface area. In a broader sense, the total area of the sides of a prism makes up its lateral surface area.Calculating this lateral surface area requires multiplying the prism's height by the base's perimeter.To learn more about lateral surface area with the given link
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I have a list of five numbers, where the first number is 1 and the fifth number is 5. Each of the other numbers is equal to one more than the average of its two neighbors. What is the sum of all five numbers in the list?
Answers
The sum of all five numbers in the list is 25.
According to the question,
The first number on my list of five numbers is 1, and the fifth is 5. The other figures are all one more than their two nearest neighbors' averages.
Let the list of numbers be 1,x,y,z,5.
As each of the other numbers is equal to one more than the average of its two neighbors.
x=(1+y)/2+1
2x=3+y -(1)
Similarly,
y=(x+z)/2+1
2y=x+z+2 -(2)
z=(y+5)/2+1
2z=y+7 -(3)
Multiply equation (2) by 2 and then substitute equations (1) and (3),
4y=3+y+y+7+4
4y=2y+14
2y=14
y=14/2
y=7
From equation (1),
2x=3+7
2x=10
x=5
From equation (3),
2z=7+7
2z=14
z=14/2
z=7
The list is: 1,5,7,7,5
Sum of the numbers of list = 1+5+7+7+5 = 25
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Show the following linear expression. Show all of your work and identify any properities used.
7-6x-9-x+3
Answers
Answer:
-7x + 1
Associative Property can be used.
Step-by-step explanation:
Hello!
We can simply the expression by combining like terms.
Like terms are terms with the same variable and degree. They may have different coefficients.
Simplify7 - 6x - 9 - x + 37 - 9 + 3 - 6x - x1 - 7xThe simplified form is 1 - 7x, or -7x + 1.
We can also represent this using the Associative property, by grouping like terms:
7 - 6x - 9 - x + 3(7 - 9 + 3) + (-6 - x)1 + (-7x)-7x + 1HELP PLEASE !!!!!!!!!
Answers
The amount made per minute is $1.28 * 10^7
Ratio and proportionsFractions are written as a ratio of two numbers. For instance a/b is a fraction.
According to the question, a certain animated movie earned $1.1 * 10^9 every 9.1 * 10^1 minutes.
$1.1 * 10^9 = 9.1 * 10^1
In order to determine the amount earned per minute;
x = 1minute
Divide both expressions
1.1 * 10^9/x = 9.1 * 10^1
x = 1.1 * 10^9 /9.1 * 10^1
Divide the result
x = 1.1 * 10^9 /9.1 * 10^1
x = 0.12 *10^8
x = $1.28 * 10^7
Hence the amount made per minute is $1.28 * 10^7
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A force of 3 pounds is required to hold a spring stretched 0.6 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 0.7 feet beyond its natural length? answer exactly or round to 2 decimal places.
Answers
The work done (in foot-pounds) in stretching the spring from its natural length to 0.7 feet beyond its natural length is 1.23 foot-pound
Data obtained from the questionFrom the question given above, the following data were obtained:
Force (F) = 3 poundsExtension (e) = 0.6 feetWork done (Wd) =?How to determine the spring constantForce (F) = 3 poundsExtension (e) = 0.6 feetSpring constant (K) =?F = Ke
Divide both sides by e
K = F/ e
K = 3 / 0.6
K = 5 pound/foot
Thus, the spring constant of the spring is 5 pound/foot
How to determine the work doneSpring constant (K) = 5 pound/footExtention (e) = 0.7 feetWork done (Wd) =?Wd = ½Ke²
Wd = ½ × 5 × 0.7²
Wd = 2.5 × 0.49
Wd = 1.23 foot-pound
Therefore, the work done in stretching the spring 0.7 feet is 1.23 foot-pound
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Hold practice this with a piano in 2030 minute in 5 weeks at what rate did she practice in minutes per dayhold practice this with a piano in 2030 minute in 5 weeks at what rate did she practice in minutes per day
Answers
58 min/day rate did she practice in minutes per day.
What is time?
In math, time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through present, and to the future. Time is used to quantify, measure or compare the duration of events or the intervals between them, and even, sequence events.1 day = 2030 min ÷ (5 weeks × 7 days)
1 day = 2030 ÷ 35
1 day = 58 minutes
rate = 58 min/day
Therefore, 58 min/day rate did she practice in minutes per day.
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What is next year's expected cash flow if there is a 50/50 probability that it will be either $10 million or $60 million?
Answers
The next year's expected cash flow if there is a 50/50 probability that it will be either $10 million or $60 million is $35 million.
What is probability?Probability refers to possibilities. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. The probability formula states that the ratio of positive outcomes to all other outcomes determines how likely an event is to occur.
Sum of outcomes= 410+$60=$70 million
Number of outcomes=2
As the probability is 50/50, the next year’s expected cash flow will be
10+60/(2)
=70/2
=35 million dollars.
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Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
Answers
The line of best-fit that represents the relationship between velocity and time is:
v = 2.19t + 6.7.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (t,v) are given as follows:
(0, 6.1), (2.1, 12.2), (5.3, 17.4), (8.2, 26.4), (10, 28.1), (12.1, 32.8).
Hence, inserting these points into a calculator, the equation is given by:
v = 2.19t + 6.7.
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A train arrived at the station. If you count cars starting from the first one, the dining car is th 7th in the row. If you count cars starting from the last one, then the dining car is the 8th in a row. How many cars are there in this train?
Answers
Answer:
15
Step-by-step explanation:
from the first then it is 0+7=7
and from the last it is 0+8=8
then the number of cars available in the station is 8+7=15
A right circular cylinder has a diameter of 12 in and a height of 12 in. if water is flowing in at the rate of 4π in3 per minute, find the rate of change of the height when the height is 4 in?
Answers
The rate of change of the height is [tex]\frac{1}{9}[/tex] in/min.
What is a right circular cylinder?A right circular cylinder is a cylinder that has a closed circular surface having two parallel bases on both the ends and whose elements are perpendicular to its base. It is also called a right cylinder.
Volume of the cylinder = [tex]\pi r^{2}h[/tex]
Rate of change of height is [tex]\frac{dh}{dt}[/tex] = ?
At any time t,
Volume, V = [tex]\pi r^{2}h[/tex]
Since r does not change with time, then r is a constant, so,
V = [tex]\pi (6)^{2}h[/tex]
V = [tex]36\pi h[/tex]
Differentiate both sides with respect to time t,
[tex]\frac{dV}{dt} = 36\pi \frac{dh}{dt}[/tex] -------------(i)
Since [tex]\frac{dV}{dt}[/tex]is given as 4[tex]\pi[/tex] cu.in. per min,
[tex]4\pi = 36\pi \frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{4\pi }{36\pi }[/tex]
[tex]\frac{dh}{dt} = \frac{1 }{9 }[/tex] in/min.
Hence, The rate of change of the height is [tex]\frac{1}{9}[/tex] in/min.
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PLEASE HURRY ASAP I NEED IT ASAPP PLEASE SHOW YOUR WORKKK I WILL MAKE YOU BRAINLIEST
40 POINTS
PLEASE SHOW YOUR WORKKK I WILL MAKE YOU BRAINLIEST
In rectangle ABCD, what is the length of BD¯?
Answers
Answer:
BD = √97 cm ≈ 9.849 cm
Step-by-step explanation:
Diagonal BD of rectangle ABCD is the hypotenuse of right triangle ABD. Opposite sides of the rectangle are the same length, so we have ...
AB = 4 cm
AD = 9 cm
The sides are related to the diagonals by the Pythagorean theorem.
Pythagorean theoremThe Pythagorean theorem tells you the relation between sides and hypotenuse of a right triangle:
AB² +AD² = BD²
4² +9² = BD² = 16 +81 . . . . . evaluating the squares
BD = √97 . . . . . take the square root
The length of BD is √97 cm, about 9.849 cm.
Please help ASAP
A high school principal conducts a survey on whether or not students would be interested in an elective art course. The principal knows that it would be too time-consuming to survey all 482 students in the high school, so he decides to ask the 98 students currently in the cafeteria. One of the students states that this survey cannot be used to make an inference about the entire high school. Which of the following statements best justifies the student's interpretation of the survey?
The survey sample was too small.
B
An art teacher should have conducted the survey.
C
The survey method was flawed since the sample was not random.
D
An observational study, rather than a sample survey, should have been used.
Answers
The survey method was flawed since the sample was not random.
What is a survey?A survey is an investigation that is carried out on a sample of a population. However, for the sample to be representative of the population, care must be taken to pick the participants in the survey at random. The principal ought to have carefully crafted a method in which the sample can be selected in a randomized manner.
For instance, the principal could have decided to take the fifth student in every row in all the classes in the school. In that way, the sample would be adequately randomized hence the result of the survey would be adjudged as representative of the situation in the entire population and thus it will be reliable as a tool that can be used to make scientific inferences.
Thus, the survey method was flawed since the sample was not random.
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Answer: C
Step-by-step explanation:
The survey method was flawed since the sample was not random.
(4r-5r^2) - (r-2r^2)
Answers
Answer:[tex]3r-29r^2[/tex]
Step-by-step explanation:
The following Visual Image consists with the steps
|
|
|
|
|
4r - 5r^2 - r + 2r^2
-5r^2 + 2r^2 + 4r - r
-3r^2 + 3r
-3r(r - 1)
if 7 cosec^2 theta-9 cot^2theta=7 then what is the value of tantheta
Answers
The value of tanθ = ±∞ or tanθ = ±√(7/5)
The question is a trigonometric equation
What is a trigonometric equation?A trigonometric equation is an equation that has unknowns that contain trigonometric ratios.
How to find the value of tanθ?Given the trigonometric equation 7cosec²θ - 9cot²θ = 7, we require tanθ.
So, 7cosec²θ - 9cot²θ = 7
using the trigonometric identity 1 + cot²θ = cosec²θ.
Substituting this into the equation, we have
7cosec²θ - 9cot²θ = 7
7(1 + cot²θ)² - 9cot²θ = 7
7(1 + 2cot²θ + cot⁴θ) - 9cot²θ = 7
7 + 14cot²θ + 7cot⁴θ - 9cot²θ = 7
14cot²θ + 7cot⁴θ - 9cot²θ = 7 - 7
14cot²θ + 7cot⁴θ - 9cot²θ = 0
7cot⁴θ + 14cot²θ - 9cot²θ = 0
7cot⁴θ + 5cot²θ = 0
Factorizing out cot²θ, we have
cot²θ(7cot²θ - 5) = 0
⇒ cot²θ = 0 or 7cot²θ - 5 = 0
⇒ cotθ = ±√0 or 7cot²θ = 5
⇒ cotθ = ±0 or cot²θ = 5/7
⇒ cotθ = ±0 or cotθ = ±√(5/7)
⇒ 1/tanθ = ±0 or 1/tanθ = ±√(5/7)
⇒ tanθ = ±1/0 or tanθ = ±√(7/5)
⇒ tanθ = ±∞ or tanθ = ±√(7/5)
So, the value of tanθ = ±∞ or tanθ = ±√(7/5)
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Last night, the two dinner specials at Bob's favorite restaurant were salmon filet and filet mignon. The restaurant served 70 specials in all, 80% of which were salmon filets. How many filet mignon did the restaurant serve?
Answers
Based on the given parameters, the number of filet mignon the restaurant served is 14
How to determine the number of filet mignon the restaurant served?From the question, the given parameters are:
Dinner specials = salmon filet and filet mignon.
Dinner specials = 70 dinner specials
Salmon filets = 80%
This means that the proportion of filet mignon is
filet mignon = 100%- Salmon filets
This gives
filet mignon = 100%- 80%
Evaluate the difference
filet mignon = 20%
The number of filet mignon is calculated as:
filet mignon = 20% * Dinner specials
Substitute the known values in the above equation
filet mignon = 20% * 70
Express 20% as decimal
filet mignon = 0.20 * 70
Evaluate the product
filet mignon = 14
Hence, the number of filet mignon the restaurant served is 14
So, the complete parameters are:
Dinner specials = salmon filet and filet mignon.
Dinner specials = 70 dinner specials
Salmon filets = 80%
filet mignon = 14
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Kim purchased a dress that was originally $35. It was on sale for 30% off. She also bought a pair of shoes for 1/2 off the original price of $17. If the store added a 4% sales tax, how much would she pay for both items?
Answers
Answer: $34.32
Step-by-step explanation: We first calculate the price of the dress that was on sale. 30% of 35 is 35/10 x3. This is equal to 3.5x3 which is 7+3.5 = 10.5 We subtract this from 35 to get $24.5. So, the dress cost $24.5. Next 1/2 of 17 is 8.5. In total, the items cost $24.5+$8.5 = $33. Then, there is a 4% sales tax we have to add on to 33. 1% of 33 is 33/100 which is 0.33. This time 4 is 1.32. 33+1.32 is 34.32.
Volume= cm3
What is the volume?
Help me please asap! Thanks so much :)
Answers
The volume of the similar triangular prism is: 1,280 cm³.
What is the Volume of a Right Triangular Prism?Volume of a right triangular prism = 0.5 × b × h × altitude, where:
b is the base length of the triangular base
h is the height of the triangular base
Find the of the first triangular prism
Base length of the triangular base (b) = 4 cm
Height of the triangular base (h) = 4 cm
Altitude of the prism = 20 cm
Volume of the first triangular prism = 0.5 × 4 × 4 × 20 = 160 cm³.
Volume of the first prism/Volume of the second prism = (leg of first prism)³/(leg of second prism)³
160/Volume of the second prism = (4)³/(8)³
160/Volume of the second prism = 64/512
160/Volume of the second prism = 0.125
Volume of the second prism = 1,280 cm³.
Thus, applying the volume formula for a right triangular prism, the volume of the given similar prism is calculated as: 1,280 cm³.
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Which of the following steps were applied to ABCD to obtain A'B'C'D'?
A. shifted 3 units right and 4 units down
B. shifted 2 units right and 3 units down
C. shifted 3 units
right and 3 units down
D. shifted 2 units right and 4 units down
Answers
The answer is B.
To obtain A'B'C'D' from ABCD, we can clearly see that it has been shifted 2 units right and 3 units down.
PLEASE HELP IM BEGGINGGGGGGG ANSWERRRRRR
Answers
Answer:
Step-by-step explanation:
i'd say with the given info it will be the same
HELP: If you multiply both sides of an inequality by a negative number when should you reverse the inequality symbol?
A. Sometimes
B. Always
C. Never
D. Depends on if the number is a fraction of not
Answers
Based on the task content; If you multiply both sides of an inequality by a negative number, the inequality symbol should be reversed always. Option B
Multiplication of inequalityBased on the rule of inequality, whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.
For instance,
-4x > 12
divide both sides by -4
x < 12/-4
x < -3
If you multiply both sides of an inequality by a negative number, the inequality symbol should be reversed always.
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guys please help me
Answers
Answer:
-1 and 1
Step-by-step explanation:
Reflecting D over the y-axis maps it onto (1,2).
This is supposed to map onto F(0,3), so this is a shift 1 unit left and 1 unit up.
So, the blanks are -1 and 1, respectively.
Answer: (x + [-1], y + [1])
Step-by-step explanation:
See attached. We can draw, or picture it in our heads, what the reflection would look like. Then we can pick one (or multiple to test) points and see the translation.
We can also test with a set of points. B', (2, 4) becomes G in the transformation. G is at (1, 5)
(1 - 2, 5 - 4) -> (-1, 1)
Tanya is training a turtle for a turtle race. For every 1/3 of an hour that the turtle is crawling, he can travel 2/23 of a mile. At what unit rate is the turtle crawling?
Answers
The unit rate with the turtle crawling is 6/23 mile per hour.
According to the statement
we have given that the every 1/3 of an hour that the turtle is crawling, he can travel 2/23 of a mile. and
we have to find the unit rate with the turtle crawling
So, For this purpose,
we know that the
The unit rate of speed in miles per hour the number of miles in one hour.
So, to find the unit rate:
Divide distance in miles with the time which is in hours.
So,
unit rate of speed = distance / time
unit rate of speed = (2/23) / (1/3)
unit rate of speed = 6/23 mile per hour.
So, The unit rate with the turtle crawling is 6/23 mile per hour.
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A whole number is 6 more than 2 times another number. The sum of the two numbers is less than 50. This can be written in an inequality as x + 2x + 6 < 50, where x represents the smaller number.
Answers
The smaller number, x from the inequality x + 2x + 6 < 50 is x < 14.67
Inequalityx + 2x + 6 < 50
3x + 6 < 50
collect like terms3x < 50 - 6
3x < 44
divide both sides by 3x < 44/3
x < 14.6666666666666
Approximately,
x < 14.67
Therefore, the smaller number, x is approximately x < 14.67
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14. The price of a sofa is Sx. A man buys the sofa on hire purchase according to the following terms:
a downpayment of 25 % and the remaining to be paid in monthly instalments over 30 months at a
simple interest rate of 12 % per annum. Given that his monthly instalment is $52, find the value of x.
Answers
Question The price of a sofa is Sx. A man buys the sofa on hire purchase according to the following terms:
a downpayment of 25 % and the remaining to be paid in monthly instalments over 30 months at a
simple interest rate of 12 % per annum. Given that his monthly instalment is $52, find the value of x.