Answer:
Step-by-step explanation:
1) (3 * 7)(8) =3 (7 * 8)
Associative property of multiplication
It states that product of three or more numbers remains same regardless the way they are grouped
2) (7k)5 = 5(7k)
Commutative property of multiplication
3) 8(x +15) = (8)(x) + (8)(15)
distributive property
A boat travels x miles per hour upstream on the Mississippi River. On the return trip, the boat travels 2 miles per hour faster. How far does the boat travel upstream?
Answer:
Distance = 17.5 miles
Step-by-step explanation:
Note.
Given question is not complete
Given:
Speed upstream = x
Time taken in upstream = 3.5 hour
Speed in return trip = (x+2)
Time taken in return trip = 2.5 hour
Computation:
Distance = speed × time
Distance = x (3.5)
Distance = 2.5 (x+2)
Distance = 2.5x + 5
So,
2.5x + 5 = 3.5 x
1.5 x = 5
x = 5 miles/hour
Distance = x (3.5)
Distance = 5 (3.5)
Distance = 17.5 miles
Evaluate 0 · |-6|. -6 0 6
Answer:
0
Step-by-step explanation:
0 · |-6|
Absolute value means take the non negative number
0* 6
0
The value of the given absolute value equation 0 · |-6| is 0.
Given that an absolute value equation 0 · |-6|, we need to evaluate this.
To evaluate the expression 0 · |-6|, let's break it down step by step:
First, calculate the absolute value of -6:
|-6| = 6
Now, multiply the result from step 1 by 0:
0 · 6 = 0
When you multiply any number by 0, the result is always 0.
In this case, even though |-6| equals 6, multiplying it by 0 will make the overall result 0.
This is a fundamental property of multiplication with zero.
So, the final answer is 0.
Learn more about absolute value click;
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A new firehouse is being built equidistant from three other fire stations. Positioned on a grid, the current fire stations would be located at (3, 7), (−1, −1), and (−4, 8). What are the coordinates of the location where the new firehouse should be built? (PLEASE INCLUDE AN EXPLANATION)
Answer:
[tex](-\frac{3}{22},\frac{185}{22} )[/tex]
Step-by-step explanation:
Step 1: Find out what the question is asking
Because we want the point to be equidistant to all the vertices of the triangle formed we want the circumcenter of the triangle as it is equidistant from all of the vertices, a circumcenter is made from the perpendicular bisectors of the triangle
Step 2: Give the vertices variables
A = (-4,8)
B = (-1,-1)
C = (3,7)
Step 2: Find the Circumcenter
Find the mid point of side AB
MAB
[tex]=(\frac{-4+(-1)}{2} ,\frac{8+(-1)}{2} )\\=(\frac{3}{2},\frac{7}{2} )[/tex]
Find the slope of side AB
mAB
[tex]=\frac{y2-y1}{x2-x1} \\=\frac{8-(-1)}{-4-(-1)} \\=\frac{9}{-3}\\ =-3[/tex]
Solve for 'b'
[tex](\frac{7}{2})=(-3)(\frac{3}{2} ) +b\\\frac{7}{2}=-\frac{9}{2}+b\\\frac{7}{2}+ \frac{9}{2}=b\\b = 8[/tex]
Therefore the equation for line AB is:
y = -3x + 8
Find the midpoint of side AC
MAC
[tex]=(\frac{-4+(3)}{2} ,\frac{8+(7)}{2} )\\=(-\frac{1}{2},\frac{15}{2} )[/tex]
Find slope of AC
mAC
[tex]=\frac{y2-y1}{x2-x1} \\=\frac{8-7}{-4-3} \\=\frac{1}{-7}\\ =-\frac{1}{7}[/tex]
Solve for 'b'
[tex]y=mx+b\\\frac{15}{2} =-\frac{1}{7} (-\frac{1}{2} )+b\\\frac{15}{2} =-\frac{1}{14} +b\\\frac{1}{14}+\frac{15}{2} = b\\b=\frac{53}{7}[/tex]
Therefore the equation for line AC is:
y = [tex]-\frac{1}{7}[/tex]x+[tex]\frac{53}{7}[/tex]
Step 3: Find the P.O.I of the 2 lines
Set both of the equation equal to each other
[tex]3x + 8=-\frac{1}{7} x+\frac{53}{7} \\3x +\frac{1}{7} x=\frac{53}{7}-8\\\frac{22}{7} x=-\frac{3}{7} \\x=-\frac{3}{22}[/tex]
We now know 'x' and we substitute x into any equation to find 'y'
[tex]y = -3(-\frac{3}{22} ) + 8\\y = \frac{9}{22} + 8\\y = \frac{185}{22}[/tex]
Therefore the new firehouse should be built at [tex](-\frac{3}{22},\frac{185}{22} )[/tex]
if 5 + 2root3/7 + root3 = a-root3b find a and b where a and b are rational no
Answer:
a = 29/46
b= - 9/46
Step-by-step explanation:
Given:
(5 + 2√3)/(7 + √3) = a - √3bRationalizing the left side:
(5+2√3)(7-√3)/(7+√3)(7-√3) = (35 + 14√3 - 5√3 - 2√3²)/(7² - √3²) =(35 - 6 + 9√3)/(49 - 3) =(29 + 9√3)/46 = 29/46 + √3 (9/46)Comparing the left and right sides:
a - √3b = 29/46 + √3 9/46a = 29/46b = - 9/46From point A and B on level ground, the angles of
elevation of the top of a building
Are 25 degree and 37degrees respectively
1f AB= 57m calculate to the nearest metre the distance of the top building from A and B if they are both on the same side of
the building
Answer:
Step-by-step explanation:
Call T the top
call G the bottom
T G B is a right triangle
37 at B, 90 at G, thus 53 at BTG
TGA is a right triangle
25 at A, 90 at G, thus 65 at ATG
thus 122 at ABT
law of sines:
sin 25 / BT = sin 12/ 57
so BT = 156 meters (first answer)
now angle ABT = 180 - 12 - 25
= 143
so
sin 143 /AT = sin12/57
AT = 164 meters, second answer
what is reflex?
what is reflex?
Answer:
An action performed without any concious thoughts
The simple definition of reflex is the sudden movement that occurs when it responds to a stimulus in the body. This movement is without any conscious thought beforehand.
For example, you are facing one way and a ball gets thrown toward you from behind. If you have fast enough reflexes, you will sense the ball coming from behind and turn around to catch it.
Best of Luck!
Daniel buys 17 raffel ticket a total of 280 tickets were soldFind the probability that daniel does not win
Answer:
280-17=273
Step-by-step explanation:
because 80-17 equals 73 sooooooo add 200
A plane is flying at a cruising speed of 900 km/h. How far will the plane travel from 11:15 a.m. to 1:30 p.m. on the same day?
Step-by-step explanation:
so the answer must be 2025 km.
The distance of the plane travel from 11:15 a.m. to 1:30 p.m. on the same day will be 2025 km.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
A plane is flying at a cruising speed of 900 km/h.
The distance of the plane travel from 11:15 a.m. to 1:30 p.m. on the same day will be
From 11:15 a.m. to 1:30 p.m., there are 2.25 hours.
Then the distance will be
D = 900 x 2.25
D = 2025 km
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If f(x)=2x+1/x-4, what is the value of f^-1(3)?
Answer:
D. 13.
Step-by-step explanation:
f(x)=2x+1/x-4
let y = 2x + 1 / x - 4
xy - 4y = 2x + 1
xy - 2x = 4y + 1
x(y - 2) = 4y + 1
x = (4y + 1)/(y - 2)
So f^-1(x) = (4x + 1)/(x - 2)
and f^-1(3) = (4(3) + 1) / (3 - 2)
= 13/1
= 13.
PLEASE HELP SUPER URGENT WILLING TO GIVE EXTRA POINTS !!!!! 4-8
somebody please help me on this i’ll mark u the brainliest please don’t waste my answers
Answer:
5 < x < 27 {x - lenght of unknown side}Step-by-step explanation:
If we have triangle of sides: a, b, c, and a < b < c (or b<a<c) then:
for triangle to exist:
a + b > c
So:
if a=11, b=16 then 11 + 16 > c ⇒ c < 27
if a=11, c = 16 then 11 + b > 16 ⇒ b > 5
We don't know if the unknown side (x) is the longest or not, so it has to be greater than 5 and less than 27
5 < x < 27
Which of the following is a correct interpretation of the expression 3 - (-5)?
Chanc 1 answer.
Answer:
8
Step-by-step explanation:
3 - (-5)
This can be rewitten to
3 + 5
Why?
2 negatives cancel each other out to make a positive, therefore:
3 + 5 = 8 or 3 - (-5) = 8
Answer:
8
Step-by-step explanation:3-(-5)=8 because two negatives make a positive so it is like adding 3 and 5 together to get the answer of 8.
NEED HELP ASAP algebra 2
Answer:
b = sqrt(39)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2
5^2 + b^2 = 8^2
25+b^2 =64
b^2 =64-25
b^2 =39
Take the square root of each side
b = sqrt(39)
Answer:
[tex]\sqrt{39}[/tex]
Step-by-step explanation:
Step 1: Find the unknown wide using Pythagorean Theorem
[tex]a^{2}+ b^{2} = c^{2}[/tex]
[tex]a^{2}+ 5^{2} = 8^{2}[/tex]
[tex]a^{2}+ 25 = 64[/tex]
[tex]a^{2}= 64-25[/tex]
[tex]a^{2=39[/tex]
[tex]\sqrt{a^{2}} = \sqrt{39}[/tex]
[tex]a=\sqrt{39}[/tex]
[tex]\sqrt{39}[/tex] cannot be simplified and more
Therefore the unknown side is [tex]\sqrt{39}[/tex]
Does the equation y=3x3+4x2+15x+7 represent a function? Explain. A. No, the equation is not a function because it is a polynomial and polynomials cannot be functions. B. A. No, the equation is not a function because there are multiple terms that contains the variable x. C. Yes, the equation is a function because there is only a single term that contains the variable y. D. Yes, the equation is a function because it is a polynomial and all polynomials are functions.
Your answer would be D, the equation is a function because it is a polynomial and all polynomials are functions.
Step-by-step explanation: I like to remember that polynomials have no negative , fraction exponents and no division. In this case everything is positive so I knew it was a polynomial , and like the answer says all polynomials are functions ! Hope this helped
Calculate 12% simple interest to be paid on a loan of $2000 repaid in 1 1/2 year?
Answer:
1320
Step-by-step explanation:
as
SI=(P×T×R)/100
SI=(2000×12×11/2)/100
SI=132000/100
:.SI=1320
Answer:1320
Step-by-step explanation:2000×12×11/2/100
Two divide by twelve=6
2000÷100=20
20×6×11=1320
A triangle has a base of (3x+7) and a height of (5x-1)a second triangle is drawn with a base that is tripled and its height is doubled. Find the difference between the area of the original triangle and the area of the new triangle
Answer:
The difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2
Step-by-step explanation:
We know that the area of a triangle A = 1/2bh where b = base and h = height.
Let A be the area of triangle 1 with base (3x + 7) and height (5x - 1).
So its area A = (3x + 7)(5x - 1)/2.
Now for the second triangle, the base is tripled, so its base is 3(3x + 7) and its height is doubled, so its height is 2(5x - 1)
So its area is A' = 3(3x + 7) × 2(5x - 1)/2 = 3(3x + 7)(5x - 1)
So the difference between the area of the original triangle and the new triangle is
A' - A = 3(3x + 7)(5x - 1) - (3x + 7)(5x - 1)/2
= (3x + 7)(5x - 1)(3 - 1/2)
= 5(3x + 7)(5x - 1)/2
So the difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2
PLEASE HELP!! Solve the triangle
Answer:
Option D. m<A = 43, m<B = 55, a = 20
Step-by-step explanation:
1. Determination of angle B.
Angle C = 82
Opposite C (c) = 29
Opposite B (b) = 24
Angle B =?
Using Sine rule, we can obtain the value of angle B as follow:
b/Sine B= c/Sine C
24/Sine B = 29/Sine 82
Cross multiply
29 × Sine B = 24 × Sine 82
Divide both side by 29
Sine B = (24 × Sine 82) /29
Sine B = 0.8195
Take the inverse of Sine.
B = Sine¯¹ (0.8195)
B = 55
2. Determination of angle A.
Angle C = 82
Angle B = 55
Angle A =?
The value of angle A can be obtained as follow:
A + B + C = 180 (sum of angle in a triangle)
A + 55 + 82 = 180
A + 137 = 180
Collect like terms
A = 180 – 137
A = 43
3. Determination of side a (Opposite A)
Angle C = 82
Opposite C (c) = 29
Angle A = 43
Opposite A (a) =?
The value 'a' can be obtained as by using sine rule as illustrated below:
a/Sine A = c/Sine C
a/Sine 43 = 29/Sine 82
Cross multiply
a × Sine 82 = 29 × Sine 43
Divide both side by Sine 82
a = (29 × Sine 43) /Sine 82
a = 20
Therefore,
m<A = 43, m<B = 55, a = 20
what does 79 = 61 + v equal
Answer:
v = 18
Step-by-step explanation:
Given
79 = 61 + v ( subtract 61 from both sides )
18 = v
Francesca graphs the function f(x) = 2x - 3, George graphs the function g(x) = 4x2 – 2 – 1, and Harold graphs the function h(x) = 9(f(x)). Which function does Harold graph?
A. Oh(x) = 1622 - 50x + 38
B. Oh(x) = 8x3 - 142++3
c. Oh(x) = 8r2 - 2x - 6
D. Oh(x) = 4x2 - 12x +9
Answer: A. [tex]h(x)=16x^2-50x+38[/tex]
Step-by-step explanation:
Given: Francesca graphs the function [tex]f(x) =2x - 3[/tex], George graphs the function [tex]g(x) = 4x^2 -x - 1[/tex].
Harold graphs the function [tex]h(x) = g(f(x))[/tex].
i.e. [tex]h(x)=g(2x - 3)[/tex] [put value of f(x)]
[tex]=4(2x-3)^2-(2x-3)-1\\\\= 4((2x)^2-2(2x)(3)+3^2)-2x+3-1\ \ [(a-b)^2=a^2-2ab+b^2]\\\\= 4(4x^2-12x+9)-2x+2\\\\=16x^2-48x+36-2x+2\\\\=16x^2-50x+38[/tex]
So, Harold graph [tex]h(x)=16x^2-50x+38[/tex]
Hence, the correct option is A. [tex]h(x)=16x^2-50x+38[/tex]
-5r + 2r = -3
wedaescfsadgfdsfvsd
Answer:
r=1
Step-by-step explanation:
-5r+2r=-3r
-3r=-3
Divide by -3 on both sides
r=1
What is the smallest angle of rotational symmetry for the regular octagon? °
Explanation:
There are n = 8 sides in a regular octagon. The smallest angle of rotational symmetry is 360/n = 360/8 = 45 degrees. Rotating this amount will not change the regular octagon. The before and after will look identical.
ANSWER:
Your answer is 45 Degrees
8.8 + 7.8x = -7.9 - 5.5x
Answer:
[tex]-\frac{16.7}{13.3}[/tex]
Step-by-step explanation:
Step 1: Collect the like terms
8.8 + 7.9 = -5.5x - 7.8x
Step 2: Simplify
16.7 = -13.3x
Step 3: Divide both sides by -13.3
[tex]\frac{16.7}{-13.3} =\frac{-13.3}{-13.3}x[/tex]
[tex]x =- \frac{16.7}{13.3}[/tex]
Therefore the answer is [tex]-\frac{16.7}{13.3}[/tex]
Answer:
x = -1 34/133
Step-by-step explanation:
Given
8.8 +7.8x = -7.9 -5.5x
13.3x = -16.7 . . . . . . . . . . . add 5.5x -8.8
x = -16.7/13.3 = -167/133 . . . . divide by 13.3 and simplify
x = -1 34/133 ≈ -1.25564
Paula invests $600 at a rate of r% per year simple interest. At the end of 10 years, the total interest earned is $90. Find the value of r.
Answer:
1.5%
Step-by-step explanation:
To find Rate in Simple Interest:
R = 100 S.I / T × P
R = 100 × 90/10 × 600
R = 9/6
R = 1.5%
1.5% is the rate.
order Operation
SIMPLIFY : −2b−5z−6+4b−3z
Answer:
2b - 8z - 6
Step-by-step explanation:
Rearrange the equation, so like terms are near each other
-2b+4b-3z-5z-6
Now we add the b's and z's to get,
2b - 8z - 6
Answer:
2b -8z -6
Step-by-step explanation:
−2b−5z−6+4b−3z
Combine like terms
−2b+4b−5z−3z−6
2b -8z -6
Elena has 2 fewer hats than fran. together the have 14 hats.
which equation represents this situation
Answer:
Elena has 6 and fran has 8
Step-by-step explanation:
somebody please help me on this it’s for geometry please don’t waste my answers i’ll mark you the brainliest
Which lists all the integer solutions of the equation |x| = 7? –7 and 7 7 only 0 and 7 –7 only
Answer:
aa
Step-by-step explanation:
Question 11 (1 point)
(01.02)
Given the function f(x) = 4(x+3) - 5, solve for the inverse function when x = 3. (1 point)
а. -21
b. -16
с. -10
d. -1
Answer:
D
Step-by-step explanation:
Insert 3 in place of x in the inverse function.
Josue is running intervals. If he runs high-speed intervals in 16 seconds, and low-speed intervals in 23 seconds, and he runs a combined total of 15 intervals in 4 minutes and 56 seconds, how many of each type of interval did he run?
Answer: He run 7 high-speed intervals and 8 low-speed intervals.
Step-by-step explanation:
Let x = Number of high-speed intervals.
y= Number of low-speed intervals .
He runs high-speed intervals in 16 seconds, and low-speed intervals in 23 seconds, and he runs a combined total of 15 intervals in 4 minutes and 56 seconds.
4 min 56 sec = (4(60)+56) sec = 296 sec [ 1 minute = 60 seconds]
According to the question , we have the following linear equations :
[tex]x+y=15\ ...(i)\\\\ 16x+23y=296\ ...(ii)[/tex]
Multiply (i)by 16 , we get
[tex]16x+16y=240\ ...(iii)[/tex]
Subtract (iii) from (ii)
[tex]7y=56\\\\\Rightarrow\ y=8[/tex]
Put value of y in (i) , we get
[tex]x+8=15\Rightarrow\ x=7[/tex]
Hence, he run 7 high-speed intervals and 8 low-speed intervals.
Based on the areas of the squares, determine whether the triangle shown is a right triangle. side A : 7 square inches side B : 18 square inches side C : 27 square inches It is for. khan acadmey
Answer:
The triangle ABC is not a right triangle
Step-by-step explanation:
For a right angle triangle, we have;
The square of the longest side or leg of the triangle is equal to the sum of the squares of the other two legs
The parameters given from the question, are;
The square of of the length of side A = 7 inch²
The square of of the length of side B = 18 inch²
The square of of the length of side C = 27 inch²
Therefore, the the longest side is side C and the inch² sum of the squares of the other two sides are 7 + 18 = 25 inch² which is less than the square of the length of side C = 27 inch², therefore, the triangle ABC is not a right triangle.
Answer:
Not a right angle
Step-by-step explanation:
Khan academy is never wrong :3