Answer:
The slope of AB is - 2,
Slope of BC is \frac{1}{2}
2
1
Slope of CD is -\frac{3}{4}−
4
3
Slope of AD is \frac{1}{2}
2
1
,
ABCD is trapezoid because one pair of opposite sides is parallel.
Step-by-step explanation:
Given vertices of quadrilateral ABCD,
A(−1, −1) , B(−3, 3) , C(1, 5) , and D(5, 2),
∵ Slope of a line passes through two points (x_1, y_1)(x
1
,y
1
) and (x_2, y_2)(x
2
,y
2
) is,
m=\frac{y_2-y_1}{xc_2-x_1}m=
xc
2
−x
1
y
2
−y
1
Thus, the slope of AB = \frac{3+1}{-3+1}=\frac{4}{-2}=-2
−3+1
3+1
=
−2
4
=−2
Slope of BC = \frac{5-3}{1+3}=\frac{2}{4}=\frac{1}{2}
1+3
5−3
=
4
2
=
2
1
Slope of CD = \frac{2-5}{5-1}=-\frac{3}{4}
5−1
2−5
=−
4
3
Slope of DA = \frac{-1-2}{-1-5}=\frac{-3}{-6}=\frac{1}{2}
−1−5
−1−2
=
−6
−3
=
2
1
Since, when two line segment having the same slope then they are parallel to each other.
∴ BC ║ DA
A quadrilateral only having two parallel sides is called trapezoid,
Hence, ABCD is a trapezoid.
Given the graph of quadrilateral ABCD, the coordinates of A, B, C and D are (-3,-4), (1,4), (4,0) and (1,-4) respectively. The length of DA using distance formula is 4 units.
The coordinates of the points in the graph is given in the form of (x,y) where x is the abscissa and y is the ordinate.
The distance formula is used to find the length of the line given the endpoints of the line.
Given endpoints as [tex](x_1, y_1) \ and \ (x_2, y_2)[/tex],
[tex]d = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
The coordinates of vertices are given by:
A = (-3,-4)
B = (1,4)
C = (4,0)
D = (1,-4)
The length of DA can be found by distance formula :
DA = [tex]\sqrt{(1+3)^2+(-4+4)^2} = \sqrt{(1+3)^2} = \sqrt{4^2} = 4[/tex]
Learn more about distance formula here
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helphelphelphelphelphelp
Answer:
see image
Step-by-step explanation:
After two people answer one of my questions, how do I give brainlyist to one of them?
do what you want ok and choose
In a triangle, a segment connecting the midpoints of two sides of the triangle is
called:
Answer:
A.) Midsegment
Step-by-step explanation:
Trust me bro
What is the value of a? Round to the nearest tenth.
Answer:
50 percent?
Step-by-step explanation:
An 8 Foot ladder leans against a building. I'd the ladder makes an angle of 60° with the ground, how far up the wall does the ladder reach? Also, how far from the building is the base of the ladder? round to the nearest 10th
9514 1404 393
Answer:
up the wall: 4√3 ft ≈ 6.9 ftalong the ground: 4 ftStep-by-step explanation:
The side ratios in a 30°-60°-90° triangle are 1 : √3 : 2. Since the hypotenuse of this triangle is 8 feet, the multiplier of these ratio values is (8 ft)/2 = 4 ft.
The triangle sides are ...
4 ft : 4√3 ft : 8 ft
The ladder reaches 4√3 ≈ 6.9 ft up the wall. Its base is 4 ft from the building.
which is less full? A dump truck that is 1/10 full or one that is 7/10 full?
Answer:
Its the first one
Step-by-step explanation:
A dump truck that is 1/10 is less full than a 7/10 one.
One dozen cookies cost $5.50. At that rate, how much does one cookie cost?
Answer:
0,458$
Step-by-step explanation:
Someone please helppp
Answer:
Step-by-step explanation:
L = 2 + sqrt(2)
W = 4 - 2sqr(2)
Area = L * W
Area = (2 + sqrt(2) )* (4 - 2sqrt(2) )
Use Foil
F: 2*4 = 8O: 2*(-2sqrt(2) = - 4sqrt(2)I: 4*sqrt(2)L: sqrt(2)*(-2sqrt(2) = - 2*2= - 4Result
Area = 8 - 4 - 4sqrt(2) + 4sqrt(2)
Area = 4
35\40 = 7\?
a. 5
b. 8
c. 1
d. 4
Answer:
b. 8
Step-by-step explanation:
Simplify the left side by dividing the top and bottom by 5
35/5 = 7
40 /5 = 8
7/8
Hey there!
35/40 = 7/x
Cross Multiply the fraction
35(x) = (7)(40)
→ 35x = 280
DIVIDE 35 to BOTH SIDES
35x/35 = 280/35
CANCEL out: 35/35 because that gives you 1
KEEP: 280/35 because that helps solve for the x-value
→ x = 280/35
x = 8
Therefore, your answer is most likely: 8 (Option B)
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
How do I solve this
Answer:
x = -1 y = 3
Step-by-step explanation:
x = 2y-7
2x + 3y = 7
Substitute x =2y-7 in 2y + 3y = 7
2(2y-7) + 3y = 7
4y-14+3y = 7
7y - 14 = 7
7y = 7 + 14
7y = 21
7y/7 = 21/7
y = 3
Substitute 3 for y in x = 2y-7
x = 2(3) - 7
x = 6 -7
x = -1
Answered by Gauthmath
(8-16) + (8 + 6)
If the parentheses are removed from the above
expression, how will the value of the expression
change?
A. no change
B. increase of 3
C. increase of 7
D. increase of 12
E. increase of 16
Step-by-step explanation:
Right now, we would solve everything within the parenthesis first.
(8 - 16) + (8 + 6)
(-8) + (14)
14 - 8
6
But if we remove the parenthesis, it doesn't matter what order we do things in.
8 - 16 + 8 + 6
8 + 8 - 16 + 6
16 - 16 + 6
6
The reason why both of these are the same, is because the only calculations we're doing are addition and subtraction, which don't care about parenthesis.
Answer:
A
pls help me asap!!!!!!
Seena’s mother is 7 times as old as Seena. After 4 years
her mother will be 4 times as old as she will be then .Find
their present ages.
Seena’s mother is 4 times as old as Seena. After 5 years her mother will be 3 times as old as she will be then .Find their present ages.
Solution :✧ Let us assume :
Seena's age be x
Her mother's age be 4x
✧ After 5 years :
Seena's age = x + 5
Her mother's age = 4x + 5
✧ Ratio of age after 5 years :
Seena's mother = 3
Seena's ratio = 1
Hence, the equation is :
[tex] \looparrowright\frak{ \frac{4x + 5}{x + 5} = \frac{3}{1} }[/tex]
By cross multiplying we get
[tex] \looparrowright \frak{3(x + 5) = 4x + 5}[/tex]
[tex] \looparrowright \frak{3x + 15 = 4x + 5}[/tex]
[tex] \looparrowright \frak{x = 10}[/tex]
Hence, the ages are
Seena's age = x = 10 yrs
Her mother's age = 4x = 4 × 10 = 40 years
∴ Seena's age is 10 and her mother's is 40 respectively
What are the zeros of f(x) = x2 - 8x+16?
O A. x= 4 only
B. x = -4 and x = 4
C. X=-2 and x = 8
D. x=-4 only
Answer:
x=4
Step-by-step explanation:
f(x) = x^2 - 8x+16
Set equal to zero
0 = x^2 -8x +16
Factor
what 2 numbers multiply to 16 and add to -8
-4*-4 = 16
-4+-4 = -8
0= (x-4)(x-4)
Using the zero product property
x-4 = 0 x-4 =0
x=4 x=4
there are nickels, dimes, and quarters in a piggy bank. altogether, the coins are worth $3.65. the number of dimes is three times greater than the number of nickels, and the number of quarters is one greater than double the number of nickels. how many quarters, nickels, and dimes are there?
This question is solved using a system of equations, and doing this, we get that: There are 9 quarters, 4 nickels and 12 dimes.
I am going to say that:
x is the number of nickels.
y is the number of dimes.
z is the number of quarters.
In all, they are worth $3.65.
A nickel is worth $0.05, a dime is worth $0.1 and a quarter is worth $0.25, so:
[tex]0.05x + 0.1y + 0.25z = 3.65[/tex]
Dimes: 3 times greater than nickels:
This means that:
[tex]y = 3x[/tex]
Quarters: One greater than double the number of nickels:
This means that:
[tex]z = 2x + 1[/tex]
Value of x:
We have y and z as function of x, so we can replace into the equation and find the value of x, so:
[tex]0.05x + 0.1y + 0.25z = 3.65[/tex]
[tex]0.05x + 0.1(3x) + 0.25(2x+1) = 3.65[/tex]
[tex]0.05x + 0.3x + 0.5x + 0.25 = 3.65[/tex]
[tex]0.85x = 3.4[/tex]
[tex]x = \frac{3.4}{0.85}[/tex]
[tex]x = 4[/tex]
y and z:
[tex]y = 3x = 3(4) = 12[/tex]
[tex]z = 2x + 1 = 2(4) + 1 = 9[/tex]
There are 9 quarters, 4 nickels and 12 dimes.
A similar question is found at https://brainly.com/question/17096268
Given three consecutive odd integers whose sum is 369, find the smallest of the three integers.
Answer:
Step-by-step explanation:
369 = x + (x+2) + (x+4)
369 = 3x + 6
363 = 3x
121 = x
now that we know that x = 121, we can solve the equation by plugging in the variable
369 = x + (x+2) + (x+4)
369 = 121 + 123 + 125
369 = 369
The smallest three integers are 121,123 and 125.
Let, the smallest odd integers be n
Then according to the given condition,
[tex]n+(n+2)+(n+4)=369\\3n+6=369\\3n=363\\n=121[/tex]
So, the numbers are,
[tex]n=121\\n+2=121+2=123\\n+4=121+4=125[/tex]
Learn More:https://brainly.com/question/2254193
Solve the equation for all values of x.
- 2x(x − 8)(10x + 1) = 0
From deltamath.com
Answer:
x=0 x=8 x = -1/10
Step-by-step explanation:
- 2x(x − 8)(10x + 1) = 0
Using the zero product property
-2x =0 x-8 = 0 10x+1= 0
x= 0 x= 8 10x = -1
x=0 x=8 x = -1/10
Find the equation of a line perpendicular to y = (75)x - 1 and has a y-
intercept of 1.
Answer:
6y = -5x + 6
y = -5/6 x + 1
Step-by-step explanation:
y = -5/6 x + b
1 = b
The population of a city is currently 45,000 and is declining at a rate of 2% each year. Give a formula for determining the total population after a period of t years.
Question 4 options:
A)
A = (45,000)e–0.02t
B)
A = 45,000 + e–0.02t
C)
A = (45,000)e0.02t
D)
A = 45,000 + e0.02t
Answer:
Step-by-step explanation:
The general form of this equation is
[tex]A=Pe^{rt}[/tex] where P is the initial population, e is Euler's number (a constant), r is the rate of decay, and t is the time in years.
Therefore, filling in:
[tex]A=45000e^{-.02t[/tex]
9x+5y=34
8x-2y=-2
What are the values of x and y? Please explain the steps.
Answer:
x = 1 and y =5
Step-by-step explanation:
[tex]8x -2y= -2\\Divide by -2\\-4x+y = 1\\add 4x\\y= 1+4x\\[/tex]
Substitute this value of y in the next equation.
[tex]9x+5(1+4x) = 34\\9x+5+20x=34\\29x+5=34\\29x=29\\x=1[/tex]
Solve for y using x.
[tex]y=4x+1\\y=4(1)+1\\y=5[/tex]
Two similar polygons have areas of 4 square inches and 64 square inches.
The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .
Answer:
4
Step-by-step explanation:
The ratio of the area of similar figures is the ratio between corresponding sides squared. This means that 64/4 or 16 is the square of the ratio of corresponding sides. By taking the square root of 16, we get that ratio is 4.
Sand and gravel are mixed in the ratio 5:3
form ballast
a) How much gravel is mixed with 750kg of
sand?
b) How much sand is mixed with 750kg of
gravel?
Answer:
a) 450 gravel b)1250 sand
Step-by-step explanation:
:)
Find the rare of change for the situations , You run 7 miles in one hour and 14 miles in two hours
The rate of change is 7 because its 7 miles per hour
The radius of a circle is 16 ft. Find its area in terms of pi
Step-by-step explanatio
Find the real or imaginary solutions by factoring.
X^4 -3x^2 = -2x^2
Look in the images it is solved.
Which of the following numbers are irrational numbers? Please choose all that apply.
Question 2 options:
−67−−√
13
0.6
π
The rules for two lines are y=x+2 and y=5 - 2x. At what point do they intersect?
Answer:
(1,3)
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
0_____ is
than all negative numbers.
Answer:
is whole number
Step-by-step explanation:
plz mrk me brainliest
Answer:
0 is larger than all negative numbers.
Step-by-step explanation:
When dealing with negative numbers, the number closer to zero is the bigger number. Zero (0) has the unique distinction of being neither positive nor negative.
Item 4
Luis reads the temperature of a solution in a lab experiment. The temperature of the solution is 5.6º F. After 6 hours, he reads the temperature of the solution again. The temperature of the solution is now −1.2°F .
Luis plots the points on the number line to determine the temperature change between these two readings.
What is the temperature change?
ANSWER:____° F
The temperature change after 6 hours is 6.8°F
Initial temperature = 5.6°F
Initial temperature = 5.6°FFinal temperature after 6 hours = -1.2°F
The temperature change can be calculated as the difference in the value of final and initial temperature.
Temperature change = (final temperature - initial temperature)
Temperature change = (5.6 - (-1.2))°F
Temperature change = (5.6 + 1.2)°F = 6.8°F
Hence, temperature change after 6 hours is 6.8°F
Learn more : https://brainly.com/question/15473063
Answer:
6.8
Step-by-step explanation:
k12
Plssss help plssssss
Answer:
True
Step-by-step explanation:
Just compare the numbers to the dots.
I hope this helps!
pls ❤ and give brainliest pls
Answer:
true
Step-by-step explanation:
The answer is true.
