A coordinate map of a college campus gives the coordinates (x,y) of three major buildings as follows: computer center, (3.5,-1.5); engineering lab, (0.5,0.5); andlibrary, (-1,-2.5). Find the equations in slope-intercept form of the lines connecting (a) the engineering lab and the computer center and (b) the engineering lab with the library. Are these two paths perpendicular to each other?
Answer:
a) [tex]y = -\frac{2}{3}x + \frac{5}{6}[/tex]
b) [tex]y = 2x - \frac{1}{2}[/tex]
These two paths are not perpendicular to each other.
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope of the line and b is the y-intercept.
If two lines are perpendicular, the multiplication of their slopes is -1.
(a) the engineering lab and the computer center
Coordinates (3.5,-1.5) and (0.5,0.5)
The slope is given by the change in y divided by the change in x.
Change in y: 0.5 - (-1.5) = 0.5 + 1.5 = 2
Change in x: 0.5 - 3.5 = -3
Slope: [tex]m = \frac{2}{-3} = -\frac{2}{3}[/tex]
So
[tex]y = -\frac{2}{3}x + b[/tex]
Now, to find the y-intercept, we replace one of these points into the equation.
(0.5,0.5) means that when [tex]x = 0.5 = \frac{1}{2}, y = 0.5 = \frac{1}{2}[/tex]
So
[tex]y = -\frac{2}{3}x + b[/tex]
[tex]0.5 = -\frac{2}{3}(0.5) + b[/tex]
[tex]b = \frac{1}{2} + \frac{1}[3}[/tex]
[tex]b = \frac{5}{6}[/tex]
So
[tex]y = -\frac{2}{3}x + \frac{5}{6}[/tex]
(b) the engineering lab with the library.
(0.5,0.5) and (-1,-2.5).
First, we find the slope:
Change in y:-2.5 - 0.5 = -3
Change in x: -1 - 0.5 = -1.5
The slope is: [tex]m = \frac{-3}{-1.5} = 2[/tex]
So [tex]y = 2x + b[/tex]
Now we find b
[tex]y = 2x + b[/tex]
[tex]0.5 = 2(0.5) + b[/tex]
[tex]b = -0.5 = -\frac{1}{2}[/tex]
So
[tex]y = 2x - \frac{1}{2}[/tex]
The multiplication of their slopes, is
[tex]2*\frac{-2}{3} = -\frac{4}{3}[/tex]
Since it is different of one, these paths are not perpendicular to each other.
Which of the following graphs shows a negative linear relationship with a correlation coefficient, r, relatively close to -1?
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answer:graph d
Step-by-step explanation:
I just took the test on a p# x and yea I'm dum and got it wrong
Answer:It’s graph B
Step-by-step explanation:
a) If the perimeter of a circle is 44 cm,
(i) find its radius.
(ii) find its area.
Answer:
[tex]154 \: {cm}^{2} [/tex]
Step-by-step explanation:
Let the radius be = r cm
circumference = 2πr
[tex]44 = 2 \times \frac{22}{7 } \times r[/tex]
[tex]r = \frac{44 \times 7}{44} \times 7[/tex]
[tex]r = 7 \: cm[/tex]
Area of circle =
[tex]\pi {r}^{2} [/tex]
[tex] = \frac{22}{7} \times 7 \times 7[/tex]
[tex] = {154 \: cm}^{2} [/tex]
Hope it is helpful....
The area of the rectangle shown is 66 m2.
4m
x m
Work out the missing length x.
Answer:
16.5 m
Step-by-step explanation:
66÷4=x
x=16.5m
...........
...........
a sweater originally priced at $79 is marked down 20%. What will the sales piece be?
Answer:
$63.20
Step-by-step explanation:
first we have to find how much the sweater is marked down in money. we do this by converting the percentage to decimal form and multiply by the original price.
79•0.2= 15.8
so the sweater is marked down $15.80. now we subtract that markdown from the original price to find the new price
$79-$15.8= $63.20
hope this helps chu <3
Plz help me well mark brainliest if you are correct!
Answer:
the answer is a
Step-by-step explanation:
radius is the diameter divided by 2
Answer:
31.2
Step-by-step explanation:
Triangles 1 and 2 have the angle measures
as shown.
Triangle 1
Triangle 2
1430 186 820
82°
550
Which statement is correct about triangle 1
and triangle 2?
Answer:
C
Step-by-step explanation:
Both triangles have three angles of the same value.
Remember that the angles in all triangles add up to 180°.
Let's use that to find out the unknown angles.
For the first triangle:
180 - 82 - 43 = 55°
55° is also in the second triangle.
Let's check with the second triangle:
180 - 82 - 55 = 43°
43° is also in the first triangle.
Therefore, both triangles are similar as the angles in both triangles are the same - 82°, 43° and 55°.
Hence, C.
Two square garden's are planted. The first has a side length of 12 meters The second garden has a side length of 15 meters.How many square meters greater is the area of the second than the first?
area of first garden
:- side×side
:- 12×12
:- 144m²
area of second garden
:- side×side
:- 15×15
:- 225m²
difference between not square gardens
:- 225-144
:- 81 m²
Need help quick!!! Karl set out to Alaska in his truck the amount of fuel remaining in the trucks tank in liters as a function of distance driven in kilometers is graphed how fast did the truck consume its fuel
Answer:
I think it's 40 . I'm not sure
Answer:
0.6 liter per kilo
Step-by-step explanation:
Kylie is a psychologist who studies memory. She wants to see whether background music affects memorization.
Kylie randomly sorts 40 subjects into two groups. The 20 subjects in one group are given five minutes to memorize a list of words while background music is playing. The 20 members of the other group perform the same task without any background noise. Afterward, Kylie records how many words from the list each subject could remember.
Words memorized with background music
92914927282011132325162226141421131812
Mean: 18.2 words
Words memorized without background music
2824282427261371512276292022262220179
How much lower is the average for the treatment group than the average for the control group?
Answer:
14,96
Step-by-step explanation:
The coordinates of a rectangle are (3,0), (3,-5), (-4,0) and (-4,-5)
a. What is the length of this rectangle? ____ units
b.width? ____ units
c. What is the perimeter of the rectangle? ___ units
d. What is the area of the rectangle? ___ units
PLEASE HELP!! GIVING BRAINLIEST!!!
Answer:
a. 7 units
b. 5 units
c. 24 units
d. 35 units
a) The length of this rectangle is, 5 units.
b) The width of this rectangle is, √74 units
c) The perimeter of the rectangle is,
⇒ 2 (5 + √74)
d) The area of the rectangle is,
⇒ 5√74 units²
What is Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
The coordinates of a rectangle are,
⇒ (3, 0), (3, -5), (-4, 0) and (-4, -5)
Now, The length of this rectangle is,
⇒ Distance between (3, 0) and (3, - 5).
⇒ √ (- 5 - 0)² + (3 - 3)²
⇒ √25
⇒ 5 units
And, The width of this rectangle is,
⇒ Distance between (3, - 5) and (- 4, 0).
⇒ √ (- 4 - 3)² + (0 + 5)²
⇒ √49 + 25
⇒ √74 units
And, The perimeter of the rectangle is,
⇒ 2 (Lenght + Width)
⇒ 2 (5 + √74)
And, the area of the rectangle is,
⇒ Length × Width
⇒ 5 ×√74
⇒ 5√74 units²
Learn more about the coordinate visit:
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Find the value of x.
3
x = [?]
Answer:
12
Step-by-step explanation:
According to Euclidian theorem h^2 = 3*x (h : height)
36 = 3x divide both sides by 3
12 = x
Which term describes the right of a lender to sell collateral to get back the principal if the borrower cannot repay the loan?
Answer:
Lien.
Step-by-step explanation:
A loan can be defined as an amount of money that is being borrowed from a lender and it is expected to be paid back at an agreed date with interest.
Generally, the financial institution such as a bank lending out the sum of money usually requires that borrower provides a collateral which would be taken over in the event that the borrower defaults (fails) in the repayment of the loan.
Lien is a term which describes the right of a lender to sell collateral to get back the principal if the borrower cannot repay the loan. In order to be able to determine whether a borrower would default on the repayment of a loan, lenders usually check the credit score of the borrower.
A credit score can be defined as a numerical expression between 300 - 850 that represents an individual's financial history and credit worthiness. Therefore, a credit score determines the ability of a borrower to obtain a loan from a lender.
This ultimately implies that, the higher your credit score, the higher and better it is to obtain a loan from a potential lender. A credit score ranging from 670 to 739 is considered to be a good credit score while a credit score of 740 to 799 is better and a credit score of 800 to 850 is considered to be excellent.
On a coordinate plane, parallelogram H I J K is shown. Point H is at (negative 2, 2), point I is at (4, 3), point J is at (4, negative 2), and point K is at (negative 2, negative 3).
HIJK is a parallelogram because the midpoint of both diagonals is __________, which means the diagonals bisect each other.
(1,−1)
(1,1)
(1,0)
(0,1)
Answer:
The answer is C.[1,0]
Step-by-step explanation:
HIJK is a parallelogram because the midpoint of both diagonals is (1, 0), which means the diagonals bisect each other.
How to calculate the midpoint of two coordinates?The midpoint is the middle of a line projecting from one end to another.
Given the parallelogram HIJK with the coordinate points
H(-2,2), I(4,3), J (4, -2), and K (-2, -3)
The diagonals are HJ and IK.
Determine the midpoint
M(x, y) = [(-2+4)/2, (2-2)/2]
M(x, y) = (2/2, 0/2)
M(x, y) = (1, 0)
This shows that HIJK is a parallelogram because the midpoint of both diagonals is (1, 0), which means the diagonals bisect each other.
Learn more on midpoint of coordinates here: https://brainly.com/question/18315903
Find the distance between two points (5,10) and (-4,6)
Answer:
Explanation:
The formula for calculating the distance between two points is:
d
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
Substituting the values from the points in the problem gives:
d
=
√
(
−
6
−
−
3
)
2
+
(
−
4
−
−
5
)
2
d
=
√
(
−
6
+
3
)
2
+
(
−
4
+
5
)
2
d = √ ( − 3 ) 2+ 1 2
d = √ 9+ 1
d = √ 10
Or
d = 3.162
rounded to the nearest thousandth
one mile equals approximately 1.6 kilogmeters approximately how many kilometers are in 4 miles
Answer:
6.4
Step-by-step explanation:
multiply
Answer:
6.43
Step-by-step explanation:
You are given:
1 mile = 1.6 kilometers
but you want 4 miles so you multiply both of them by 4 so...
1*4 = 1.6*4
That gives you ------> 4 miles = 6.4 kilometers
Explain how you would find the sum of 0.35, 0.5 and 0.05 giving your answer as a
fraction.
Answer: Here
Step-by-step explanation:ou have learned to think of multiplication by a whole number, such as 3 × 4 or 8 × 0.6, as repeated
addition. However, this concept does not work when neither of the factors is a whole number, as in
0.83 × 1.43 or 2/3 × 7/11. Instead, when you multiply decimals or fractions, think of it as finding
"a certain part of” the other factor. In this sense, the symbol “×” translates to “of.”
Example. 0.1 × 80 means finding one-tenth “of” 80. That is simply 8.
Example. 0.4 × 80 means finding four-tenths “of” 80. Since one-tenth of 80 is 8, then 0.4 of 80 is four times as much, or 32.
Example. 0.02 × 3,000 means finding two-hundredths of 3,000. Since one-hundredth of 3,000 is 30, then 0.02 of 3,000 is two times as much, or 60
Mariah went to the store to buy a coat. The coat originally cost $120.00. Mariah used a coupon
that saves her 20%.
d Marinho hy using the counon?
Answer: $24
Step-by-step explanation:
Mariano saved $24because
120 x 0.2=24
She payed $96
Answer:
$24 dollars i believe
Step-by-step explanation:
hope it helps
For each diagram, choose the correct pair of congruent inscribed angles.
Answer:
1. ∧A and ∧B
2. ∧A and ∧C
3. ∧E and ∧O
in how many ways can you arrange MATHEMATICS if duplication of the arrangement are not allowed?
Answer:
4989600 ways
Step-by-step explanation:
From the question,
The word MATHEMATICS can be arranged in n!/(r₁!r₂!r₃!)
⇒ n!/(r₁!r₂!r₃!) ways
Where n = total number of letters, r₁ = number of times M appears r₂ = number of times A appears, r₃ = number of times T appears.
Given: n = 11, r₁ = 2, r₂ = 2, r₃ = 2
Substitute these value into the expression above
11!/(2!2!2!) = (39916800/8) ways
4989600 ways
Hence the number of ways MATHEMATICS can be arranged without duplicate is 4989600 ways
can someone help me with this?
Step-by-step explanation:
1 in - - > 2 ft
6 in - - > x ft
--------------------
x = 2*6=12 ft
The area of a square is given by:
A=x^2
So,
A=12^2=144ft^2
16=b-3 what is the answer
Answer:
19 is the answer .......explanation is in image.
Answer this question please ASAP
Mauna Loa is one of the most active volcanoes in the world. From 1832 to 1950, the Hawaiian landmark erupted 37 times. What probability distribution will be used to estimate the chance that the next two Mauna Loa eruptions will occur within five months of one another
Answer:
[tex]E \approx \exp(0.31)[/tex]
Step-by-step explanation:
From the question we are told that
Occurrence of volcanoes[tex]x=37 times[/tex]
The number year
[tex]N= 1832-1950\\N=118 years[/tex]
Generally the number of volcanoes occurring is mathematically modeled as
[tex]X \approx Poisson(0.31)[/tex]
Generally the waiting time of the earthquakes will also be modeled with exponential distribution with the same parameters
[tex]E \approx \exp(0.31)[/tex]
Given the following information, find the length of the missing side. Leave your answer as a simplified radical.
Answer:
2√3
Step-by-step explanation:
Given the following information,
Long = 3 = Adjacent
Angle of elevation =30 degrees
Required
Hypotenuse
Using SOH CAH TOA identity
Cos theta = adj/hyp
Cos 30 = 3/hyp
hyp = 3/cos30
hyp = 3/√3/2
hyp = 3* 2/√3
hyp = 6/√3
hyp = 6/√3 * √3/√3
hyp = 6√3/3
hyp = 2√3
Hence the hypotenuse is 2√3
Answer:
2v3
Step-by-step explanation:
PLEASEEEEEEEEE HELPPPPPP
x2−8x+3=−2
Find the roots of the polynomial.
In order to get ANY credit, You must show your work and your steps as best as possible with typing. you can type Sqrt for √
Reduce the answer as much as possible. Take your time.
Answer:
7.31 and 0.685
Step-by-step explanation:
x^2 -8x +5 = 0
use the quadratic formula
- (-8) + √(-8^2 -4(1)(5) / 2(1(
(8 + √(64 -20))/2
(8+√44)/2
8+6.63 / 2
14.63/2= 7.31
+7.31
(8- √44)/2 = 0.685
please help, i will mark brainliest (no links please)
WRITE AN INEQUALITY FOR THE GRAPH
A) n ≥ 3
B) n ≤ -3
C) n > -3
D) n ≥ -3
C
since its pointing towards the positive side frm d negative
1 in
2 in
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
Answer:
[tex]\boxed {\boxed {\sf c \approx 2.2 \ inches}}[/tex]
Step-by-step explanation:
This triangle has a small square in the corner, representing a right angle. This means we can use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
Where a and b are the legs and c is the hypotenuse.
In this triangle, the legs are 2 and 1, because they form the right angle. The hypotenuse, which is opposite the right angle, is unknown.
a = 2b=1Substitute the known values into the formula.
[tex](2)^2+(1)^2=c^2[/tex]
Solve the exponents.
(2)²= 2*2=4[tex]4+(1)^2=c^2[/tex]
(1)²=1*1=1[tex]4+1=c^2[/tex]
Add.
[tex]5=c^2[/tex]
Since we are solving for c, we must isolate the variable. Since it is being squared, we take the square root of both sides.
[tex]\sqrt {5}= \sqrt{c^2} \\[/tex]
[tex]2.2360679775=c[/tex]
We have to round to the nearest tenth. The 3 in the hundredth place tells us to leave the 2 in the tenths place.
[tex]2.2 \approx c[/tex]
The hypotenuse is approximately 2.2 inches.
Erica finds a block of cheese in her
fridge. Originally, the block weighed
126 g, but there is only 60% of it left.
How many 10-g wedges can she cut
from the cheese that is left?
Answer:
7 wedges
Step-by-step explanation:
=60% of 126g
=60 ÷ 100 × 126g
=75.6g
=75.6 g ÷ 10g
=7.56 = 7 wedges
Find the product. Type your answer in the provided space. Do not use spaces in your answer. To demonstrate an exponent, use the ^ key. For example, x2should be typed in as x^2.
3x3y · 5x2y
Answer:
15x²6y² .................
The product of the expression is [tex](3 x 5) x^5y^2[/tex]
We have,
(3x³y) (5x²y)
Now,
Finding the product of the expression.
We add up the exponents of the same base.
[tex]x^3x^2 = x^{3 + 2} = x^5\\yy = y^{1 + 1} = y^2[/tex]
And,
(3x³y) (5x²y)
[tex]= (3 x 5) x^5y^2[/tex]
Thus,
The product of the expression is [tex](3 x 5) x^5y^2[/tex]
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