Answer:
Kathy is 48 years old and Samantha is 12.
Step-by-step explanation:
This is a challenging question that requires some interpretation. Let K and S stand for the current ages of Kathy and Samatha.
We are told that: K+S = 60
And, in 8 years: K+8 and S+8
"Kathy will be 5 years older than 3 times as old as Samantha was 3 years ago" ["3 years ago:" from now or in 8 years. I'll interpret it as from now, or (S-3)]
(K+8) = 3(S+8-3)+5 ["5 years older than 3 times as old as Samantha was 3 years ago"]
(K+8) = 3(S+5)+5
K+8 = 3S+20
K = 3S+12
---
Rearrange the firts equation to isolate K
K = 60-S
Now use this definition of K in the previous equation:
K = 3S+12
60-S = 3S+12
4S = 48
S = 12
K+S = 60
K+12 = 60
K = 48
=====
CHECK
Does K + S = 60? 48+12 = 60 YES
In 8 years, will Kathy will be 5 years older than 3 times as old as Samantha was 3 years ago?
K = 48+8 = 56
S = 12+8 = 20
Three years ago S was 9.
(K+8) = 3(S+8-3)+5
(K+8) = 3(12+8-3)+5
K + 8 = 3(17)+5
K = 48
===
Kathy is 48 years old and Samantha is 12.
ANYONE GOOD AT MATH! PLEASE HELP!
Answer:
To find f(2), we substitute 2 for x in the equation of the parabola F(x) = x^2 - 2x - 3:
F(2) = 2^2 - 2(2) - 3 = 4 - 4 - 3 = -3
So f(2) = -3
To find g(-3), we substitute -3 for x in the equation of the line g(x) = x - 2:
g(-3) = -3 - 2 = -5
So g(-3) = -5
The correct solution to this question is as follows:
f(2)= -3 & g(-3)=-5
Step-by-step explanation:
[tex]f(x)=x^{2} -2x-3[/tex]
[tex]f(2)=2^{2} -2(2)-3[/tex]
[tex]f(2)=4 -4-3[/tex]
[tex]f(2)=-3[/tex]
[tex]g(x)=x-2[/tex]
[tex]g(-3)=-3-2[/tex]
[tex]g(-3)=-5[/tex]
To learn more about "graphs" here:
brainly.com/question/11538356
What is the meaning of the absolute value of a number?
A.the direction a number is located with respect to zero
B. the distance a number is located from zero
C.the value of a number after it has been rounded up
D.the value of a number after it has been rounded down
Set up and solve a proportion for the following application problem. If 3 pounds of grass seed cover 403 square feet, how many pounds are needed for 6045 square feet? HELP
The number of pounds needed for 6045 square feet will be 45.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
If 3 pounds of grass seed cover 403 square feet.
The ratio of the number of pounds of seed to the area that covers the seed.
Let 'x' be the pounds needed of seed. Then the equation is given as,
x / 6045 = 3 / 403
x = 6045 × 3 / 403
x = 15 · 3
x = 45
The number of pounds needed for 6045 square feet will be 45.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ1
Hot dogs come in packages of 10. Buns come in packages of 8. What is the least number of packages of each you have to buy to have the same number of hot dogs and buns? Drag and drop an answer into each box to complete the statement. You need to buy packages of hot dogs and 1 4 5 packages of buns. 8 10 12
Therefore , the solution of purchased so that the consumer has an equal amount of each LCM if hot dogs are packaged with 10 dogs per pack .
How many hot dog buns are included in a package?"Sandwich rolls or hot dog buns are typically sold in packs of eight because the buns are baked in clusters of four in pans designed to hold eight rolls." Because hot dogs are sold by the pound and store-bought standard-sized hot dogs weigh 1.6 ounces,
Here,
purchased so that the consumer has an equal amount of
each if hot dogs are packaged with 10 dogs per pack and hot dog buns are packaged with 8 buns per pack LCM is 40.
hot dog buns are packaged with 8 buns per pack LCM is 40. 4 packages of hot dogs and 5 packages of buns are required.
To know more about LCM visit:-
brainly.com/question/20739723
#SPJ1
(Y-9)²/4÷(4y-36)/16 what is solver
Answer:
y - 9
Step-by-step explanation:
(y-9)²/4÷(4y-36)/16
is a fraction divided by a fraction.
When you have one or two fractions with a division, use Keep-Change-Flip.
Keep the first term:
(y-9)²/4
then Change the ÷ to a times.
(Y-9)²/4•
then Flip the second term.
(y-9)²/4 • 16/(4y-36)
You can factor the term (y-9)² into
(y-9)(y-9).
The other term (4y-36) can also be factored into
4(y-9).
see image.
The 4's and the y-9 terms can be "cancelled".
see image. The only term left is y-9.
Vanessa picked 12 strawberries. She divided the strawberries and gave 1/3 to her brother. She kept the rest for herself. How many strawberries did she give her brother.
Answer: 4 strawberries
Step-by-step explanation:
First, we can change the total number of strawberries into a fraction, that way it makes the division process easier. 12 is really equivalent to 12/1 since it is a whole number. Now, we can set up an equation: (12/1) * (1/3) will solve to give us the number of strawberries the brother has. Since there is a one in both the numerator and the denominator, they will cancel, leaving us with (12/3). This is now just division, which gives us 4. Therefore, the brother will receive 4 strawberries. Hope this helps!
3. Copy these equations and add brackets so that the answers are correct. 42-8x3-22=80 b) 75+5x4-70=25 160÷4x3 + 2 = 200 d) 120÷2x3+5=25
The correct brackets for the equations are added as follows:
a) (42 - 8) x 3 - 22 = 80
b) 75+ (5 x 4) -70 = 25
c) (160 ÷ 4) x (3 + 2) = 200
d) 120 ÷ (2 x 3) + 5 = 25.
What are equations?Equations are mathematical statements that equate or show that two or more mathematical expressions are equivalent or equal.
Equations use the equation symbol (=) to show the equality of the algebraic expressions.
Using parentheses in equations enable the use of the distributive property to solve the equation.
Thus, the correct parentheses have been added to the equations to prove them correct when solved.
Learn more about equations and parentheses at https://brainly.com/question/25989020
#SPJ1
The following scenario represents a proportional relationship.
Jason bought 4 pounds of bananas for $3.16.
What is the constant of proportionality?
The constant of proportionality will be $0.79
What is constant of proportionality?It is defined as the rate or the ratio of two proportional values which are known to be at the same value.
The two variable values are said to have a proportional association if or when either of their ratio or their product are known to bring about a constant.
Hence, the proportionality constant's value is known by the proportion between the two said quantities.
Jason bought 4 pounds of bananas for $3.16.
k = $3.16/4
k = $0.79
Learn more about constant of proportionality: https://brainly.com/question/27598477
#SPJ1
A study was developed to evaluate effectiveness of a weight loss diet plan. An ad was placed in two towns to locate study participants who were to follow the diet. In Town A, the clinicians asked each dieter to report how much weight they had lost over the previous 6 weeks while following the diet. In Town B, the clinicians weighed each dieter at the beginning of the study and again after 6 weeks on the diet program. The weight lost was calculated as the difference between the beginning weight and the weight after 6 weeks. At the end of the study, it was determined that Town B had lost significantly less weight than Town A. a) What is the population of interest in this situation? b) Identify source(s) of bias in this study.
Answer:
a) The population of interest in this situation is individuals who are following a weight loss diet plan.
b) There are several sources of bias in this study:
Self-report bias: Town A relies on self-reported weight loss, which may not be accurate as participants may not accurately report their weight loss or may exaggerate their progress.
Measurement bias: Town B uses a different method of measuring weight loss than Town A, which could introduce a bias in the results.
Selection bias: Participants in this study are self-selected, which means that individuals who are more motivated or more likely to succeed in the diet may be more likely to sign up for the study. This can lead to a bias in the results as the sample may not be representative of the population of interest.
Hawthorne effect: Participants in Town B may have changed their behaviors simply because they knew they were being weighed, which could lead to a bias in the results.
Placebo effect: Participants in Town A may have lost weight due to the mere act of participating in a study and receiving attention, which could lead to a bias in the results.
Which reason completes the proof for step 6? A. Definition of slope B. Definition of midsegment C. Definition of median D. Definition of midpoint
The reason that completes the proof for step 6 is given as follows:
D. Definition of midpoint.
How to obtain the midpoint of a segment?The midpoint between two points is the halfway point between them, hence it is found obtaining the mean of the coordinates of each endpoint.
Thus the coordinates of P' are obtained as follows:
x: (2r + 0)/2 = r.y: (2s + 0)/2 = 2.(applying the mean of the coordinates of x and y for the endpoints of the segment P').
The coordinates of R' are obtained as follows:
x: (0 + 2t)/2 = t.y: (0 + 0)/2 = 0.The coordinates of Q' are obtained as follows:
x: (2r + 2t)/2 = 2(r + t)/2 = r + t.y: (2s + 0)/2 = s.Meaning that the correct option is given by option D.
Missing InformationThe problem is given by the image presented at the end of the answer.
More can be learned about the midpoint of a segment at https://brainly.com/question/896396
#SPJ1
HELP!
The Sum of three consecutive odd integers is 93 Find the integers
Therefore, the three consecutive odd integers that add up to 93 are 33, 35, and 37.
Find the integers?The sum of three consecutive odd integers is 93. This means that the integers must be odd numbers that come after each other in order.If we look at this problem another way, we can say that the integers must add up to 93.Since odd integers only come in odd numbers, we can divide 93 by 3 to get 31.This means that the three consecutive odd integers must add up to 31 each.Starting with the first integer, we can see that it must be an odd number that is divisible by 3. The first odd integer that is divisible by 3 is 33. Now that we have the first integer, we can use this number to find the other two.To do this, we must add 2 to 33 to get 35. This is the second integer. To get the third integer, we must add 2 to 35 to get 37.To learn more about the integers refer to:
https://brainly.com/question/929808
#SPJ1
A computer and printer cost a total of $1056. The cost of the computer is three times the cost of the printer. Find the cost of each item.
Answer:
Hope This Helps <3
Step-by-step explanation:
Printer cost 265
Computer cost 795
Joshua drove 22 miles in 55 minutes. If he drove at a constant rate, how far did he travel in one hour?
On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as fractions, whole numbers, or decimals.
If Joshua drove at a constant rate, he drove 24 miles in one hour since he could drive 22 miles in 55 minutes or 0.4 miles per minute (driving speed).
What is the speed?Joshua's driving speed is the quotient of the total distance and the time.
The quotient is the result of a division operation, where a numerator (distance) is divided by the denominator (time) to obtain the unit rate or constant rate.
This constant rate (speed) is multiplied by the time (one hour), according to the distance, time, and speed formula, to obtain the distance to be covered.
The distance covered in 55 minutes = 22 miles
Constant driving speed or rate = 0.4 miles per minute (22/55)
1 hour = 60 minutes
For one hour, the distance Joshua could cover = 24 miles (60 x 0.4)
Thus, we can assert that in one hour, Joshua traveled 24 miles, given his constant driving rate.
Learn more about distance, time, and speed at https://brainly.com/question/4931057
#SPJ1
The sum of an A.P. is 340, the first term is 7 and the common difference is 6.
Calculate the number of terms in the sequence
The number of terms (n) in the sequence = 10.
We know that,
S = [tex]\frac{n}{2\\}[/tex] {2a + (n-1)d}
Where,
S = Sum of A. P. series
n = number of terms in A. P. series
a = first term of the series
d = common difference
According to the question,
Sum of the series, S = 340
First term, a = 7
Common difference, d = 6
S = [tex]\frac{n}{2\\}[/tex] {2a + (n-1)d}
340 = [tex]\frac{n}{2}[/tex] {2*7 + (n-1)6}
340 = [tex]\frac{n}{2}[/tex] {14 + 6n - 6}
340*2 = n( 6n + 8)
680 = 6n^2 + 8n
6n^2 + 8n - 680 = 0
2 (3n^2 +4n - 340) = 0
3n^2 +4n - 340 = 0
3n^2 + 34n - 30n - 340 = 0
n (3n+ 34) - 10 (3n + 34) = 0
(3n + 34) (n - 10) = 0
if we take, 3n + 34 = 0
3n = - 34
n = -34/3
which is not possible, as the number of terms can not be negative
if we take, n- 10 = 0
n = 10
Hence, the number of terms in the given A. P. series is 10.
Learn more about Arithmetic Progression (A. P.) Series:
https://brainly.com/question/20375979
A rectangle with sodes of lengrh 84 and 45 has the same perimeter asa hexagon. If the sides of the hexagon all have the same length then what is the length of a side of the hexagon
(A) 41
(B) 46
(C) 43
(D) 45
(E)Other
A square has an area of 25. Two opposite side of the square each have their length tripled what is the perimeter of the new figure
(A) 40
(B) 25
(C) 60
(D) 35
(E)Other
A rectangle measures 6 centimeters by 25 centimeters the probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 is p/q are relatively prime positive whole numbers what is the sum of p and q
(A) 5
(B) 19
(C) 37
(D) 47
(E)Other
The three values of x that are solutions to X^3 + mx = 37x^2 +n are positive whole numbers that form a geometric sequence what is the sum of the possible values of the common ration of the geometric sequence
(A) 25/12
(B) 9/4
(C) 7/4
(D) 2
(E)Other
sorry if there's any spelling errors
Answer:
C. 43
A. 40
C. 37
E. Other
A rectangle with sides of length 84 and 45 has the same perimeter asa hexagon. If the sides of the hexagon all have the same length then what is the length of a side of the hexagon
Ans:
The perimeter of a rectangle is given by 2length + 2width. In this case, the perimeter of the rectangle is 284 + 245 = 258.
Since the perimeter of the hexagon is the same as the rectangle, and the sides of the hexagon are all the same length, we can find the length of a side of the hexagon by dividing the perimeter by the number of sides.
A hexagon has 6 sides, so the length of a side of the hexagon is 258/6 = 43.
So the answer is (C) 43.
A square has an area of 25. Two opposite side of the square each have their length tripled what is the perimeter of the new figure.
Ans:
The perimeter of the new figure would be 40. The original square had a side length of 5, so when two opposite sides were tripled, the new side length became 15. The perimeter of a rectangle is the sum of all four sides, so it would be 2 * (15) + 2 * (15) = 40.
(A).40
A rectangle measures 6 centimeters by 25 centimeters the probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 is p/q are relatively prime positive whole numbers what is the sum of p and q.
Ans:
The probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 can be found by comparing the areas of the two triangular regions formed by the point and the two sides. The area of the triangular region formed by the point and the side of length 25 is (1/2) * 6 * (distance from point to side of length 25) while the area of the triangular region formed by the point and the side of length 6 is (1/2) * 25 * (distance from point to side of length 6).
For the point to be closer to the side of length 25, the area of the triangular region formed by the point and the side of length 25 must be greater than the area of the triangular region formed by the point and the side of length 6. This means (1/2) * 6 * (distance from point to side of length 25) > (1/2) * 25 * (distance from point to side of length 6). Therefore, the probability that the point is closer to the side of length 25 is (1/2) * (6/25) = 3/25. The sum of p and q is 3 + 25 = 28.
Therefore, the answer is (C) 37.
The three values of x that are solutions to X^3 + mx = 37x^2 +n are positive whole numbers that form a geometric sequence what is the sum of the possible values of the common ration of the geometric sequence.
Ans:
It is not possible to determine the sum of the possible values of the common ratio of the geometric sequence without more information about the values of m and n in the equation X^3 + mx = 37x^2 +n. In order to solve for the common ratio, the values of x would need to be found and it requires the values of m and n.
Find the values of a, b, and]e if lines m and n are parallel.
The angles are 36,118,62
What happens when a transversal intersects parallel lines?If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary, i.e. they add up to 180°. When two lines intersect each other, then the opposite angles, formed due to intersection, are called vertical angles or vertically opposite angles.
Given: m and n are parallel lines with 3 transversals
We can observe that a=36 (vertically opposite angles)
and b =180-(36+26) ∵ They all lie on a line .
=118
and c= 180-118 ∵They all lie on a line.
=62
Hence, The angles are 36,118,62
Learn more about angle sum property here:
https://brainly.com/question/11806229
#SPJ1
You go to the mall to buy some new shoes. You have a coupon for $25 off the price of a pair of
shoes. When you arrive at the store, you find out that the shoes are on sale for 25% off. If
c(x) = x - 25 represents the cost of the shoes with your coupon and s(x) = 0.75x is the cost
of shoes after the markdown, which of the following composition functions represents receiving
the sale price of the shoes and then applying the coupon?
Answer:
50%
Step-by-step explanation:
25%+25%
The composition functions represents receiving the sale price of the shoes and then applying the coupon is c(s(x))= 0.75x-25.
Given that, c(x) = x - 25 represents the cost of the shoes with your coupon and s(x) = 0.75x is the cost of shoes after the markdown.
Here, the composition function is
c(s(x))= 0.75x-25
Therefore, the composition functions represents receiving the sale price of the shoes and then applying the coupon is c(s(x))= 0.75x-25.
To learn more about the composite function visit:
https://brainly.com/question/20379727.
#SPJ4
Every week, Estella has guitar lessons.
A guitar is shown. The caption says that Guitar Lessons are thirty-five dollars per lesson.
Question 1
Part A
Complete the expression to represent the change in Estella’s account balance due to guitar lessons after 2 years.
1. The completion of the mathematical expression to represent the change in Estella's account balance due to guitar lessons after 2 years is 52 - 35x, where x is the number of years.
2. After two years, the account balance will be $-18, without reflecting interest.
What is a mathematical expression?A mathematical expression is a combination of variables, constants, numbers, and mathematical operands (addition, subtraction, division, and multiplication).
A mathematical expression may not convey any meaning since it sounds like a phrase in the English language that does not make complete sense.
The unit rate (cost per lesson) for guitar lessons = $35
Estella's account balance = $52
Let the number of years = x
Lesson period, x = 2 years
Mathematical Expression: 52 - 35x
Solution: 52 = 35(2)
= $-18
Thus, after 2 years of guitar lessons, Estella will be indebted to the bank by $18 if she does not deposit an additional amount in her account.
Learn more about mathematical expressions at https://brainly.com/question/4344214
#SPJ1
Question Completion:Expression: 52 - 35
PLSSS HEPP MEEE THYYY
In November 2018, the frequency tree shows us that 35 students aged 15 years old had part-time work.
That number 35 drops to 23 a year later in 2019. There are two reasons for this:
The student lost their job. They got fired or quit their job.The 15 year old student had a birthday and turned 16.Case (2) mentioned above only works if the student's birthday is before April 2019.
please help very important
Answer:
x = 18.3
Step-by-step explanation:
You want the length of the hypotenuse of a right triangle given the side opposite the 41° angle is 12 units.
SineThe sine relation is ...
Sin = Opposite/Hypotenuse
This can be rearranged to ...
Hypotenuse = Opposite/Sin
x = 12/sin(41°) ≈ 18.3 . . . . units
The value of x is about 18.3.
__
Additional comment
This is the SOH relation from the mnemonic SOH CAH TOA, which is intended to remind you of the relation between trig functions and sides of a right triangle. The others tell you ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
In the attached, note the calculator mode is set to DEG (degrees) so the argument of the Sin( ) function will be interpreted properly.
7 x + 4 y = 17 3 x + 4 y = 5
Answer:
make the x and y variables to each other variables by addition or subtraction
173x-7x +4y-4y=5
166x + 0y=5
166x =5
x= 166/5
x=33.2
FInd the half-life of a radioactive element, which decays according to the function A(t)= A0e^-0.0372t, where t is the time in years
Answer:
below
Step-by-step explanation:
1/2 = e^(-.0372t) ln both sides to get :
-.693147 = - .0372t then t = 18.6 yrs
A group of people were asked how many people live in their household. How many said they have 3 or more in their household?
Answer:
11
Step-by-step explanation:
we know this because there are 5 people saying they have 3 and 6 people saying they have between 4-7
cylinder has a volume of 2,034.72 cubic millimeters and a radius of 6 mm, whats the height?
Answer:
2,260.80 cubic millimeters
Step-by-step explanation:
The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 6 mm. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth. A cylinder and 2 half spheres. All have a radius of 6 millimeters. The cylinder has a height of 12 millimeters. Recall the formulas V = B h and V = four-thirds pi r cubed 527.52 cubic millimeters 1,431.84 cubic millimeters 2,034.72 cubic millimeters 2,260.80 cubic millimeters
NO LINKS!!!
Find the area of the shaded region of the shapes below. (Label Units.)
Answer:
1) 216 units², 2) 138 units²-------------------------------------
Top figureWe know that the area of a rectangle with same dimensions is twice the area of a triangle.
The shaded area is half the area of the rectangle:
A = ab/2 = 18*24/2 = 216 units²Bottom figureYou already divided it to rectangle and triangle.
Area of rectangle:
A = ab = 10*12 = 120 units²The triangle have same base, 12 units. It height is 16 - 10 = 6 units.
Its area is:
A = bh/2 = 12*6/2 = 36 units²Area of the small rectangle in the middle:
A = 6*3 = 18 units²The shaded area is the difference of the total area and the small rectangle:
Shaded area = 120 + 36 - 18 = 138 units²Help please
The amount of fencing is ___\
The perimeter of the fencing in terms of 'x' will be 13x + 3.
What is the perimeter of the shape?The complete stretch of a shape's border is referred to as the perimeter in geometry. A shape's periphery is calculated by summing the lengths of all of its sides and borders. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.
The perimeter of the fencing in terms of 'x' is given as,
P = x + x + x + x + (3x + 1) + (3x + 1) + (3x + 1)
Simplify the equation, then we have
P = x + x + x + x + (3x + 1) + (3x + 1) + (3x + 1)
P = x + x + x + x + 3x + 1 + 3x + 1 + 3x + 1
P = 13x + 3
The perimeter of the fencing in terms of 'x' will be 13x + 3.
More about the perimeter of the shape link is given below.
https://brainly.com/question/28161250
#SPJ1
3
6
4
8
7
5
Select all the correct answers.
The statement 4, 6 and 7 is enough to prove that 45° + m∠AOW = 90°.
What is congruence?A harmonious relationship, agreement, or correspondence are all concepts that are denoted by the mathematical term "congruence," which is used in a variety of contexts.
The two geometric figures are said to be congruent, or to be in the relation of congruence, if they can be superimposed on one another so that their entire surfaces match. If two triangles have the same two sides and included angle, they are said to be congruent.
The idea of a "rigid body," which can be moved from one place to another without changing the internal relationships between its parts, appears to be the foundation for congruence.
Learn more about congruence
https://brainly.com/question/7888063
#SPJ1
Let f(x)=e^x and g(x). What are the domain and range of (gxf)(x)?
domain: x > 0 range: y > 0
domain: x > 6 range: y > 0
domain: all real numbers range: y > 6
domain: all real numbers range: all real numbers
Domain and Range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.
What are the domain and range?
The domain and range of a function are the set of all the inputs and outputs a function can give respectively. The domain and range are important aspects of a function. The domain takes all the possible input values from the set of real numbers and the range takes all the output values of the function.
We have the functions, f(x) = eˣ and g(x) = x+6
So, their composition will be g(f(x)).
Then, g(f(x)) = g(eˣ) = eˣ+6
Thus, g(f(x)) = eˣ+6.
Since the domain and range of f(x) = eˣ are all real numbers and positive real numbers respectively.
Moreover, the function g(f(x)) = eˣ+6 is the function f(x) translated up by 6 units.
Hence, the domain and range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.
To learn more about the domain and range visit,
https://brainly.com/question/2264373
#SPJ1
What is the slope of the line?
m =
Answer:
1/3
Step-by-step explanation:
Everytime x increases by 3 units, y increases by 1 unit.
Hence, when Δx=3, Δy=1 (Δx = change in x)
m=Δx/Δy
m=1/3
how to identify what type of shape ABCD is if A is (-3,0), B (1,5), C(-3,10) and D(-7,5) the slope of BC=-5/4 and the length of DA=6.4
The shape of the ABCD is a rhombus. The diagonals are not equal to each other.
What is the 2-dimensional shape?
A 2d shape is a two-dimensional shape with horizontal and vertical axes (x-axis and y-axis). 2D shapes are flat shapes with only length and width. These shapes have no thickness or height.
Given the vertices of ABCD are A(-3,0), B (1,5), C(-3,10) and D(-7,5).
The formula distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].
The distance between A and B is √[(1 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4
The distance between B and C is √[(-3 - 1)²+(10 - 5)²] = √(4²+5²) = 6.4
The distance between C and D is √[(-7 - (-3))²+(5 - 10)²] = √(4²+5²) = 6.4
The distance between A and D is √[(-7 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4
The distance between A and C is √[(-3 - (-3))²+(10 - 0)²] = √(10²) = 10
The distance between B and D is √[(-7 - 1)²+(5 - 5)²] = √(8²) = 8
The slope of a line passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
The slope of AB is (5-0)/(1-(-3))=5/4
The slope of BC is (10-5)/(-3-1)=-5/4
The slope of CD is (5-10)/(-7-(-3))=5/4
The slope of AD is (5-0)/(-7-(-3))=-5/4
The number of vertices of the quadrilateral is 4.
Thus it is either a square or rectangle or rhombus or parallelogram.
Since the length of all sides is equal thus it is either a square or rhombus.
Since the diagonals are not equal it is a rhombus.
To learn more about quadrilateral, click on the below link:
https://brainly.com/question/29077336
#SPJ1
