Answer:
[tex]B = 325[/tex]
Step-by-step explanation:
Given
Total = 900
Singing = 600
Dancing = 500
None = 125
Required
Determine the number of students that participate in both
Representing; Singing with S, Dancing with D, Both singing and dancing with B and None with N;
In Set Notation;
[tex]Total = (S - B) + (D - B) + N + B[/tex]
Substitute 900 for Total, 600 for S, 500 for D and 125 for N
[tex]900 = (600 - B) + (500 - B) + 125[/tex]
Open Brackets
[tex]900 = 600 - B + 500 - B + 125 + B[/tex]
Collect Like Terms
[tex]900 = 600 + 500 + 125 - B - B + B[/tex]
[tex]900 = 1225- B - B + B[/tex]
[tex]900 = 1225- B[/tex]
Collect Like Terms
[tex]900 - 1225 = -B[/tex]
[tex]-325 = -B[/tex]
Multiply both sides by -1
[tex]-1 * -325 = -B * -1[/tex]
[tex]325 = B[/tex]
Reorder
[tex]B = 325[/tex]
Hence, the number of students that do not participate in both is 325
A rectangular prism has a volume of 864 cubic units. How many cubic unit will fill the volume of the solid if they were packed without any gaps or overlaps
Answer: 864.
Step-by-step explanation:
The volume of a rectangular prism has a volume equal to:
V = W*L*H
W = width
L = length
H = height
We know that the volume is equal to 864 cubic units.
This means that if we want to fill the prism such that there is no gap or overlap, we should use exactly 864 unit cubes.
Find the greatest common factor for each of the following expressions, then factor each expression. a. 4p – 4 = ? b. x4 + x3 + x2 = ? c. 8p2 + 9p2q = ? d. x2y2 + 3xy – 4x – 2x4y3 = ? Factor each of the following expressions. a. 4a3 + 28a2 + 4a + 28 = ? b. x3 + 3x2− 2x − 6 = ? c. 8x2− 4xy + 2x − y = ? Factor each of the following, using the difference of perfect squares where possible. a. u2 – 100 = ? b. 4a2 − 49 = ? c. 81 − y2= ? d. 16q4− 16 = ? e. 9c3− 9c = ? f. 48a2b − 12b = ?
Answer:
1. a. Greatest common factor: 4
b. Greatest common factor: x2
c. Greatest common factor: p2
d. Greatest common factor: x
2. a. (a2 + 1)(4a + 28)
b. (x + 3)(x2− 2)
c. (4x+ 1)(2x−y)
3. a. u2 – 100 = (u + 10)(u − 10)
b. 4a2 − 49 = (2a + 7)(2a − 7)
c. 81 − y2= (9 + y)(9 − y)
d. 16q4− 16 = 16(q4 − 1) 16 (q4 −1) = 16(q2 + 1) (q2− 1) = 16(q2 + 1) (q + 1) (q − 1)
e. 9c3− 9c = 9c (c2− 1) = 9c(c + 1)(c − 1)
f. 48a2b − 12b = 12b (4a2− 1) = 12b(2a + 1)(2a − 1)
Step-by-step explanation:
I got it at PennFoster
ALGEBRAIC EXPRESSION 11. Subtract the sum of 13x – 4y + 7z and – 6z + 6x + 3y from the sum of 6x – 4y – 4z and 2x + 4y – 7. 12. From the sum of x 2+ 3y 2 − 6xy, 2x 2 − y 2 + 8xy, y 2 + 8 and x 2 − 3xy subtract −3x 2 + 4y 2 – xy + x – y + 3. 13. What should be subtracted from x 2 – xy + y 2 – x + y + 3 to obtain −x 2+ 3y 2− 4xy + 1? 14. What should be added to xy – 3yz + 4zx to get 4xy – 3zx + 4yz + 7? 15. How much is x 2 − 2xy + 3y 2 less than 2x 2 − 3y 2 + xy?
Answer:
Explained below.
Step-by-step explanation:
(11)
Subtract the sum of (13x - 4y + 7z) and (- 6z + 6x + 3y) from the sum of (6x - 4y - 4z) and (2x + 4y - 7z).
[tex][(6x - 4y - 4z) +(2x + 4y - 7z)]-[(13x - 4y + 7z) + (- 6z + 6x + 3y) ]\\=[6x-4y-4z+2x+4y-7z]-[13x-4y+7z-6z+6x+3y]\\=6x-4y-4z+2x+4y-7z-13x+4y-7z+6z-6x-3y\\=(6x+2x-13x-6x)+(4y-4y+4y-3y)-(4z+7z+7z-6z)\\=-11x+y-12z[/tex]
Thus, the final expression is (-11x + y - 12z).
(12)
From the sum of (x² + 3y² - 6xy), (2x² - y² + 8xy), (y² + 8) and (x² - 3xy) subtract (-3x² + 4y² - xy + x - y + 3).
[tex][(x^{2} + 3y^{2} - 6xy)+(2x^{2} - y^{2} + 8xy)+(y^{2} + 8)+(x^{2} - 3xy)] - [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[x^{2} + 3y^{2} - 6xy+2x^{2} - y^{2} + 8xy+y^{2} + 8+x^{2} - 3xy]- [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[4x^{2}+3y^{2}-xy+8]-[-3x^{2} + 4y^{2} - xy + x - y + 3]\\=4x^{2}+3y^{2}-xy+8+3x^{2}-4y^{2}+xy-x+y-3\\=7x^{2}-y^{2}-x+y+5[/tex]
Thus, the final expression is (7x² - y² - x + y + 5).
(13)
What should be subtracted from (x² – xy + y² – x + y + 3) to obtain (-x²+ 3y²- 4xy + 1)?
[tex]A=(x^{2} - xy + y^{2} - x + y + 3) - (-x^{2}+ 3y^{2}- 4xy + 1)\\=x^{2} - xy + y^{2} - x + y + 3 +x^{2}- 3y^{2}+ 4xy -1\\=2x^{2}-2y^{2}+3xy-x+y+2[/tex]
Thus, the expression is (2x² - 2y² + 3xy - x + y + 2).
(14)
What should be added to (xy – 3yz + 4zx) to get (4xy – 3zx + 4yz + 7)?
[tex]A=(4xy-3zx + 4yz + 7)-(xy - 3yz + 4zx) \\=4xy-3zx + 4yz + 7 -xy + 3yz - 4zx\\=3xy-7zx+7yz+7[/tex]
Thus, the expression is (3xy - 7zx + 7yz + 7).
(15)
How much is (x² − 2xy + 3y²) less than (2x² − 3y² + xy)?
[tex]A=(2x^{2} - 3y^{2} + xy)-(x^{2} - 2xy + 3y^{2})\\=2x^{2} - 3y^{2} + xy-x^{2} + 2xy - 3y^{2}\\=x^{2}-6y^{2}+3xy[/tex]
Thus, the expression is (x² - 6y² + 3xy).
HELP ASAP
What is the distance, in units, between the points [tex](-3, -4)[/tex] and [tex](4, -5)[/tex]? Express your answer in simplest radical form.
Answer:
d=5√2 unit
Step-by-step explanation:
distance between two points d=√(x2-x1)²+(y2-y1)²
two pints (-3,-4) and (4,-5)
d=√(4-(-3)²+(-5-(-4)²
d=√(4+3)²+(-5+4)²
d=√49+1
d=√50
d=√25*2
d=5√2
Answer
[tex] \boxed{5 \sqrt{2} \: \: \:units}[/tex]
Step by step explanation
Let the points be A and B
A ( - 3 , - 4 ) ⇒( x₁ , y₁ )
B ( 4 , - 5 )⇒( x₂ , y₂ )
Now, let's find the distance between these points :
Distance = [tex] \mathsf{ \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }[/tex]
Plug the values
⇒[tex] \mathsf{ \sqrt{ {(4 - ( - 3))}^{2} + {( - 5 - ( - 4))}^{2} } }[/tex]
Calculate
⇒[tex] \mathsf{ \sqrt{ {(4 + 3)}^{2} + {( - 5 + 4)}^{2} } }[/tex]
⇒[tex] \mathsf{ \sqrt{ {(7)}^{2} + {( - 1)}^{2} } }[/tex]
Evaluate the power
⇒[tex] \mathsf{ \sqrt{49 + 1} }[/tex]
Add the numbers
⇒[tex] \mathsf{ \sqrt{50} }[/tex]
Simplify the radical expression
⇒[tex] \mathsf{5 \sqrt{2} \: \: units}[/tex]
Hope I helped!
Best regards!!
Rita got three colors of beads, half of them are pink. She used all her pink beads to make some bracelets. If the number of pink beads she used for each bracelet is one eighths of the total number of beads, how many bracelets did she make?
Answer: she made 4 bracelets.
Step-by-step explanation:
Let x, y, z are the number of three kinds of beads, where x= number of pink beads.
As per given, number of pink beads= half of total beads
[tex]\Rightarrow\ x=\dfrac{1}{2}(x+y+z)\\\\\Rightarrow 2x= x+y+z\\\\\Rightarrow\ x= y+z\ \ \ ...(i)[/tex]
Also, She used all pink beads, Number of pink beads she used for each bracelet= one eighths of the total number of beads
[tex]\dfrac{1}{8}(x+y+z)\\\\=\dfrac{1}{8}(x+x)\ \ \ [ {\text{From (i)}}][/tex]
[tex]=\dfrac{1}{8}(2x)\\\\=\dfrac{x}{4}[/tex]bracelets =
Number of bracelets = (Number of pink beads) ÷ (Number of pink beads used for each bracelet)
[tex]=\dfrac{x}{\dfrac{x}{4}}=4[/tex]
Hence, she made 4 bracelets.
Solve for u.
– 22 = -8u + 6(u-7)
Simplify your answer as much as possible.
Step-by-step explanation:
- 22 = -8u + 6(u-7)
-22 = -8u + 6u - 42
8u - 6u = 22 - 42
2u = -20
u = -20/2
u = -10
Answer:
[tex] \boxed{ \boxed{ \mathrm{ \bold{ \blue{ - 10}}}}}[/tex]Step-by-step explanation:
[tex] \mathrm{ - 22 = - 8u + 6(u - 7)}[/tex]
Distribute 6 through the parentheses
⇒[tex] \mathsf{ - 22 = -8u + 6u - 42}[/tex]
Collect like terms
⇒[tex] \mathrm{ - 22 = - 2u - 42}[/tex]
Swap the sides of the equation
⇒[tex] \mathrm{ -2u - 42 = - 22}[/tex]
Move constant to R.H.S and change it's sign
⇒[tex] \mathrm{ - 2u = - 22 + 42}[/tex]
Calculate
⇒[tex] \mathrm{ - 2u = 20}[/tex]
Divide both sides of the equation by -2
⇒[tex] \mathrm{ \frac{ - 2u}{ - 2} = \frac{20}{ - 2} }[/tex]
Calculate
⇒[tex] \mathrm{u = - 10}[/tex]
Hope I helped!
Best regards!
HELP ASAP
[tex]Given that $33^{-1} \equiv 77 \pmod{508}$, find $11^{-1} \pmod{508}$ as a residue modulo 508. (Give an answer between 0 and 507, inclusive.)[/tex]
===================================================
Work Shown:
[tex]33^{-1} \equiv 77 \text{ (mod 508)}\\\\(3*11)^{-1} \equiv 77 \text{ (mod 508)}\\\\3^{-1}*11^{-1} \equiv 77 \text{ (mod 508)}\\\\3*3^{-1}*11^{-1} \equiv 3*77 \text{ (mod 508)}\\\\11^{-1} \equiv 231 \text{ (mod 508)}\\\\[/tex]
Notice how 33*77 = 2541 and 11*231 = 2541
[tex]2541 \equiv 1 \text{ (mod 508)}[/tex] since 2541/508 has a remainder of 1.
So effectively [tex]33*77 \equiv 1 \text{ (mod 508)}[/tex] and [tex]11*231 \equiv 1 \text{ (mod 508)}[/tex]
3 Question
Select the correct answer.
What is the value of this expression when a = 2 and b = -3?
a3 - 63
5
Hola
O
O
3
Answer:
The qs is not clear.
Simply put values of a and b and you will get the ans.
Step-by-step explanation:
The graph of function f is shown. Function g is represented by the table. Which statement correctly compares the two functions?
Answer:
Option (A)
Step-by-step explanation:
Graph of function 'f' represents,
x - intercept of the function 'f' → (1, 0)
y - intercept of the function → (0, 6)
As x-approaches ∞, value of the function approaches (-2)
Points in the given table is for the another function 'g'
x - intercept of the function 'g' → (1, 0) [For x - intercept, y = 0]
y - intercept of the function 'g' → (0, 3) [For y - intercept, x = 0]
As x approaches ∞, value of function 'g' approaches (-1).
Therefore, x - intercepts of both the functions are same but end behavior are different when x → ∞.
Option (A) will be the answer.
Rory records the percentage of battery life remaining on his phone throughout a day. The battery life decreases as Rory uses the phone, but will increase or stay at 100% while charging. The graph represents the percentage of battery life remaining after a certain number of hours.
A graph titled Phone Battery Life. The horizontal axis shows Elapsed Time (hours) numbered 2 to 20, and the horizontal axis shows Battery Life (%) numbered 10 to 120. A line begins at 100% in 0 hours, to 20% in 8 hours, to 100% from 10 to 12 hours, to 60% in 16 hours, to 100% from 17 to 20 hours.
At which times could Rory's phone have been plugged into the charger? Select three options.
Answer:
9 hours
11 hours
19 hours
Step-by-step explanation:
The graph represents the percentage of battery life remaining after a certain number of hours is attached below.
At which times could Rory's phone have been plugged into the charger? Select three options.
6 hours
9 hours
11 hours
14 hours
19 hours
Answer: From the graph, the line segment with negative slope (that is decreasing value) shows that the phone is not plugged but being used while the line segment with positive slope (increasing value) or stays at 100% shows that the phone is plugged to the charger.
As shown, from 0 to 8 hours their is a decreasing value, the phone is not plugged. From 8 to 10 hours their is an increasing value therefore the phone is plugged also from 10 to 12 hours the phone is plugged since it is constant. From 12 to 16 hours it is not plugged. From 16 to 18 hours it is plugged and from 18 to 20 hours it is plugged.
From the options it is plugged at 9 hours, 11 hours and 19 hours
Answer:
B - 9 HOURS
C - 11 HOURS
E - 19 BHOURS
Step-by-step explanation:
i took the test
Christine, Dale, and Michael sent a total of 71 messages during the weekend. Dale sent 9 fewer messages than Christine. Michael sent 2 times as many messages as Christine. How many messages did they each send?
Answer:
Micheal sent 40 messages, Christine sent 20, and Dave sent 11.
Step-by-step explanation:
Christine, Dale, and Michael sent a total of 71 messages
C + D + M = 71
Dale sent 9 fewer messages than Christine
D = C - 9
Michael sent 2 times as many messages as Christine
M = 2C
Plug-in the numbers.
C + C - 9 + 2C = 71
4C - 9 = 71
4C = 80
C = 20
Now, plug in to other equations for other results.
D = (20) - 9
D = 11
M = 2(20)
M = 40
Micheal sent 40 messages, Christine sent 20, and Dave sent 11.
Verify?
40 + 20 + 11 = 71.
Let f (x) = x – 4 and g(x) = 6 - x
Evaluate g(f(10)).
G(f(10))
First solve f(x) by replacing x with 10:
F(x) = x-4 = 10-4 = 6
Now replace x in g(x) with 6
G(x) = 6-x = 6-6 = 0
So g(f(10)) = 0
answer answer it it it
Answer:
May-June
Step-by-step explanation:
Notice that:
● during April-May period the Badminton memberships rate of increase is greather then Swimming's since the graph of Badminton is showing a faster increase.
● During June-July period, both functions are decreasing so this period does not satisfy our condition.
● During May-June The Swimming memberships growed faster than Badminton's so its rate of increase is greather than Badminton's.
● during August-September period, The swimming memeberships are increasing slower than Badminton's
So the answer is May-June
Answer:
May-June
Step-by-step explanation:
The weight of a box varies directly as the volume of the box. If a 138-pound box has a volume of 23 gallons, what is the weight of a box that has a volume of 25 gallons? A. 31 pounds B. 150 pounds C. 138 pounds D. 29 pounds
Answer:
150 pounds
the weight is directly proportional to the volume. hence:
138/23 = 6
now, 25*6 = 150
Answer:
B. 150 pounds
Step-by-step explanation:
add 2 hours 40 minutes to 11 hours 40 minutes
Answer:
14 hours and 20 minutes
Step-by-step explanation:
11 hours + 2 hours = 13 hours
40 minutes + 40 minutes = 1 hour and 20 minutes
Then you add the answers together
13 hours + 1 hour 20 minutes = 14 hours and 20 minutes
Hope this helps
Answer:
860min or 13:80=14:20=2:20
Step-by-step explanation:
1 hour=60min
2 hours=120min
So, we will add 120min to 40 min
120min+40min=160min
1hour=60min
11hour=660min
So we will add 660min to 40min
660min+40min=700min
160min+700min=860min
2:40
+11:40
13:80
Hope this helps ;) ❤❤❤
1. The cost of buying some books is partly constant and partly varies with the number of books bought. The cost is #4800 when 20 books are bought and #8000 when 40 are bought. Find the cost when 1000 books are bought
Answer:
Step-by-step explanation:
let the cost based on number of book bought be x and the constant be c:
4800 = 20x + c
8000 = 40x + c
c is common in both equations:
c =4800-20x
c = 8000-40x
equate the two:
4800-20x = 8000 - 40x
20x = 3200
x = 160
and c = 4800-20*160
c = 1600
Cost of 1000 books:
160*1000 + 1600
= 161600
Write 1.4888.. in form of p/q
Let x = 1.4888... .
Then 10x = 14.888... and 100x = 148.888..., so that
100x - 10x = 148.888... - 14.888...
90x = 147
x = 147/90 = 49/30
Find an equation of the line: Through the point (2, −4) with a y-intercept of −2 Through the points (4,2) and (3,1) Through the point (3,2) with a slope of −2
Answer and Step-by-step explanation: Equations of line through points and slope can be determined by:
[tex]y-y_{0}=m(x-x_{0})[/tex]
m is slope
Point (2,-4) and y-intercept = -2Y-intercept is point (0,-2)
m = [tex]\frac{y_{a}-y_{b}}{x_{a}-x_{b}}[/tex]
m = [tex]\frac{-4-(-2)}{2-0}[/tex]
m = - 1
Equation:
[tex]y+2=-1(x-0)[/tex]
[tex]y=-x-2[/tex]
Points (4,2) and (3,1)m = [tex]\frac{2-1}{4-3}[/tex]
m = 1
Equation:
[tex]y-2=(x-4)[/tex]
[tex]y=x-2[/tex]
Point (3,2) and slope = -2m = -2
Equation:
[tex]y-2=-2(x-3)[/tex]
[tex]y=-2x+6+2[/tex]
[tex]y=-2x+8[/tex]
Rita makes and sells necklaces. The materials to make each necklace cost $2.75. Last week she made 8 necklaces and wants to make a total profit of $78. Using the equation 8 (x + 2.75) = 78, Rita determined that she needs to sell each necklace for $7 to make a total profit of $78. Which error did Rita make?
Answer:
The error she made was that she was adding x and 2.75. She should subtract 2.75 from x.
Another mistake that she made was that she sold each for $7 assuming that she would make a profit of 78, but she should see each necklace for $12.5 so that she could make a profit of $78.
Step-by-step explanation:
The error she made was that she was adding x and 2.75.
She should write the equation as 8 (x - 2.75) = 78; as she spends $2.75 to make a necklace.
By using the correct equation: 8 (x - 2.75) = 78
=> 8x - 22 = 78
=> 8x = 78 + 22
=> 8x = 100
=> x = 100/8
=> x = 12.5
Another mistake that she made was that she sold each for $7 assuming that she would make a profit of 78, but she should see each necklace for $12.5 so that she could make a profit of $78.
Hope this helps you.
Answer:
C
Step-by-step explanation: Nice
Help please and explain
Answer:
30 ft
Step-by-step explanation:
We can use ratios
3 6
------ = ------------
15 x
Using cross products
3x = 6*15
Divide each side by 3
3x/3 = 6*15/3
x = 30
Answer:
30 ft
Step-by-step explanation:
6/3 = x/15
2 = x/15
2×15 = x
30 = x
The same amount of trash is dumped into a landfill every day. The function below shows the total number of tons of trash n in the landfill after x days:
n = 2000x + 1000
What does the number 2,000 represent?
Answer:
Amount of trash added to the landfill everyday
Step-by-step explanation:
If 2000 represents the amount of trash added to the landfill everyday then 1000 is the starting amount.
I got it right on the test. Hope this helped!
Every time Liliana bakes a batch of brownies, she uses 34 cup of chocolate. If she has 128 cup(s) of chocolate remaining, how many batches of brownies can Liliana make? Input your answer as a whole number.
Answer:
3
MARK BRAINLIEST IF THIS HELPED!
i hope u have a great day.
Plz HELP !!!!! I would appreciate it!!!
Answer/Step-by-step explanation:
a. The sides of ∆ABC can be labelled as follows, taking θ as the reference point.
Adjacent = side AB
Opposite = side BC
Hypotenuse = side AC
b. I. "<B is an acute angle" => FALSE. It is a right angle (90°)
II. "The side opposite to <C is BC" => FALSE. The side opposite to <C is AB.
III. The side adjacent to <A is AB => TRUE
IV. The side opposite to <B is not the longest. => FALSE. It is the hypotenuse and the longest side.
c. Cos θ = [tex] \frac{adjacent}{hypotenuse} = \frac{AB}{AC} [/tex]
Tan θ = [tex] \frac{opposite}{adjacent} = \frac{BC}{AB} [/tex]
d. Sin C = [tex] \frac{opp}{hypo} = \frac{AB}{AC} [/tex]
Cos C = [tex] \frac{adjacent}{hypotenuse} = \frac{BC}{AC} [/tex]
Tan C = [tex] \frac{opp}{adjacent} = \frac{AB}{BC} [/tex]
wyatt uses 3.15 cups of flour in a recipe that makes 9 shortcakes. Cora uses 2.4 cups of flour in a recipe that makes 8 shortcakes. How much more flower per shortcake is needed for Cora's recipe?
Answer:
0.3
Step-by-step explanation:
You have to divide 2.4 ➗ 8
According to the number line, which statement MUST be true? A) A > 1 B) B > 4 C) C < 4 D) D < 0
Answer:
The anwser is C) C < 4
......... .
A blueprint for a house has a scale factor n = 35. A wall in the blueprint is 10 in. What is the length of the actual wall?
29.17 in.
29.17 feet
350 feet
4,200 feet
Answer:
29.17 feet
Step-by-step explanation:
10 x 35 = 350 in. / 12 in/ft = 29.17 feet
The length of the actual wall is 29.17 feet. The correct answer is option B.
What is the scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.
It is given that the blueprint for a house has a scale factor of n = 35. A wall in the blueprint is 10 in.
The length of the actual wall is calculated as:-
L = 10 x 35
L = 350 in. / 12 in/ft
L= 29.17 feet
Therefore, the length of the actual wall is 29.17 feet. The correct answer is option B.
To know more about scale factors follow
https://brainly.com/question/25722260
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Which ppint is the center of the circle?
O point w
O point X
O point Y
O point z
Answer:
??????????????????????????????????????????????????????????????
Step-by-step explanation:
Answer:
where is Point or picture
Find the AM and GM for the numbers 18 and 2
Answer:
Step-by-step explanation:
Solution:
AM =( X_1 + X_2 )/2
=( 18 + 2 )/2
=20/2
=10
Find Geometric mean for data 18,2
Solution:
GM =sqrt( X_1 × X_2 )
=sqrt( 18 × 2 )
=sqrt(36)
=6
Sam ran 63,756 feet in 70 minutes. What is Sam's rate in
miles per hour? (There are 5,280 feet in one mile.)
Step 1: What is Sam's rate as stated?
63,756 feet
63, 756 ft
70 min
70 minutes
Step 2: What factor is used to convert feet per minute into
miles per minute?
Step 3: what factor is used to convert miles per minute to miles per hour
Answer:
10.35 miles per hour
Sam's rate as stated is 63,756 feet per 70 minutes
Divide by 5,280 feet
Divide by 60 minutes
Step-by-step explanation:
1. Find how many feet Sam ran in one minute
63,756 ÷ 70 = 910.8 ft.
2. Find how many feet he ran in one hour
910.8 · 60 = 54,648 ft.
3. Convert the feet to miles
54,648 ÷ 5280 = 10.35
Step 2: There are 5280 feet in one mile. Therefore, you would divide by 5280 feet to convert feet per minute into miles per minute.
Step 3: There are 60 minutes in one hour. Therefore, you would divide by 60 minutes to convert miles per minute to miles per hour.
Answer:
1: 63,756 and 70 mins
2: 1 mile and 5,280 feet
3: 60 mins and 1 hour
4: 10.35
On a coordinate plane, a triangle has points (negative 5, 1), (2, 1), (2, negative 1).
Use the drop downs to answer the following questions about the distance between the points (−5, 1) and (2, −1).
What is the distance of the horizontal leg?
What is the distance of the vertical leg?
Use the Pythagorean theorem. What is the distance between the two points?
Answer:
The answer is below
Step-by-step explanation:
The points of the triangle are (- 5, 1), (2, 1), (2, - 1). The distance between two points is given by:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The horizontal leg is formed by points with the same y axis. Therefore the points that make up the horizontal leg is (- 5, 1), (2, 1). The Distance of the horizontal leg is:
[tex]Horizontal\ leg=\sqrt{(2-(-5))^2+(1-1)^2}=\sqrt{7^2+0}=7\ units[/tex]
The vertical leg is formed by points with the same x axis. Therefore the points that make up the vertical leg is (2 1), (2, 1-). The Distance of the vertical leg is:
[tex]Vertical\ leg=\sqrt{(2-2)^2+(-1-1)^2}=\sqrt{0+(-2)^2}=2\ units[/tex]
The hypotenuse is gotten using Pythagorean theorem. It is gotten by:
Hypotenuse² = (Horizontal leg)² + (Vertical leg)²
Hypotenuse² = 7² + 2²
Hypotenuse² = 49 + 4 = 53
Hypotenuse = √53
Hypotenuse = 7.28 unit
Answer:
The answer are 7, 2 and 53
Step-by-step explanation:
