Answer:
107
Step-by-step explanation:
sum means addition so 3 + 6 = 9 116 - 9 = 107 hope it helps <3
The sum of three consecutive integers is 180. What is the largest integer?
Answer:
61
Step-by-step explanation:
Here's a neat trick when you have an odd number of consecutive numbers.
Call the middle number k
Then the smaller number is k-1
The larger number is k + 1
The two ones will cancel.
k-1 + k + k-1 = 180
3k = 180
k = 180/3
k = 60
Therefore the largest number is k + 1 = 60 + 1 =61
A ranger in a lookout tower spots two fires on the campground below. Fire A is 75 meters east
and 40 meters south of the tower. Fire B is 37 meters west and 64 meters south of the tower.
If there is a fire hydrant located three-fourths of the way from Fire A to Fire B, find the location
of the fire hydrant relative to the tower.
Answer:
the fire hydrant is 9 meters west and 58 m south of the tower
Step-by-step explanation:
Fire A and Fire B can be represented as a point in the Cartesian coordinate with the tower as the origin. Fire A is 75 meters east and 40 meters south of the tower, It can be represented as (75, -40). Fire B is 37 meters west and 64 meters south of the tower, It can be represented as (-37, -64).
If a point O(x, y) divides a line segment AB in the ratio n:m, with A([tex]x_1,y_1[/tex]) and B([tex]x_2,y_2[/tex]), the point O(x, y) is at:
[tex]x=\frac{n}{n+m}(x_2-x_1)+x_1\\ \\y=\frac{n}{n+m}(y_2-y_1)+y_1[/tex]
The fire hydrant (x, y) divides Fire A(75, -40) and fire B(-37, -64) in the ratio 3:1(three fourth), hence:
[tex]x=\frac{n}{n+m}(x_2-x_1)+x_1=\frac{3}{4}(-37-75) +75=\frac{3}{4}(-112)+75=-84+75\\x=-9 \\ \\y=\frac{n}{n+m}(y_2-y_1)+y_1=\frac{3}{4}(-64-(-40))+(-40)= \frac{3}{4}(-18)-40=-18-40\\y=-58[/tex]
The fire hydrant is at (-9, -58). That is the fire hydrant is 9 meters west and 58 m south of the tower
The location of the hydrant relative to the tower is [tex]\left(-9, -58 \right)[/tex] meters.
How to locate the coordinates of the hydrant relative to the towerIn this question we should use the vectorial formula for a line segment to determine the coordinates of the hydrant relative to the tower ([tex]\vec C[/tex]), in meters:
[tex]\vec C = \vec A + r\cdot (\vec B - \vec A)[/tex] (1)
Where:
[tex]\vec A[/tex] - Coordinates of the fire A relative to the tower, in meters. [tex]\vec B[/tex] - Coordinates of the fire B relative to the tower, in meters. [tex]r[/tex] - Distance ratio.Now we determine the location of the hydrant: ([tex]\vec A = (75, -40)\,[m][/tex], [tex]\vec B = (-37, -64)\,[m][/tex], [tex]r = \frac{3}{4}[/tex])
[tex]\vec C = (75,-40) + \frac{3}{4}\cdot [(-37,-64)-(75,-40)][/tex]
[tex]\vec C = (75,-40) + \frac{3}{4} \cdot (-112,-24)[/tex]
[tex]\vec C = (75,-40) + \left(-84, -18\right)[/tex]
[tex]\vec C = \left(-9, -58 \right)\,[m][/tex]
The location of the hydrant relative to the tower is [tex]\left(-9, -58 \right)[/tex] meters. [tex]\blacksquare[/tex]
To learn more on vectors, we kindly invite to check this verified question: https://brainly.com/question/13188123
What are the six trigonometric functions and how are their values determined using the three sides of a right triangle?
Explanation:
Six trigonometric functions are ratio of sides with their angle in right angled triangle.
Six trigonometric functions are:
Sinθ = Perpendicular / Hypotenuse
Cosθ = Base / Hypotenuse
Tanθ = Perpendicular / Base
Cotθ = Base / Perpendicular
Secθ = Hypotenuse / Base
Cosecθ = Hypotenuse / Perpendicular
please answer i need help quick
Answer:
(-2, 6)
Step-by-step explanation:
Since you want a 1 to 7 ratio, you want to divide the line into 2 parts, where one part has a length of 1 and the other has a length of 7. So the total length of the line is 8.
Start by looking at the difference in the X and Y coordinates.
X = | -4 - 12 | = | -16 | = 16
Y = | 7 - -1 | = | 8 | = 8
You could calculate the length of the line using pythagorian's theorem, but that's not needed. Simply use similar triangles. We have a right triangle with legs of length 16 and length 8. We want a similar triangle that is 1/8th as large (to get the desired 1 to 7 ratio). So divide both legs by 8, getting lengths of 16/8 = 2, and 8/8 = 1.
Now add those calculated offsets to point A.
A has an X coordinate of -4 and B has an X coordinate of 12 and the X coordinate for C must be between those limits. So calculate -4 + 2 = -2 to get the X coordinate for C.
The Y coordinate of A is 7 and the Y coordinate of B is -1. And since the Y coordinate must be between then, you have 7 - 1 = 6.
So the coordinates for C is (-2, 6)
What is the first derivative of the following function: f(x) = aexp(-bx)
Answer:
The first derivative of the given function
[tex]\frac{df(x)}{dx} = - ab e^{-b x}[/tex]
Step-by-step explanation:
Step(i):-
Given f(x) = ae⁻ᵇˣ ...( i )
we will use differentiation formula
[tex]\frac{d(e^{ax}) }{dx} = a e^{a x}[/tex]
Step(ii)
Differentiating equation (i) with respective to 'x', we get
[tex]\frac{df(x)}{dx} = a e^{-b x} \frac{d}{dx} (-b x )[/tex]
= -ab e⁻ᵇˣ
[tex]\frac{df(x)}{dx} = - ab e^{-b x}[/tex]
Final answer:-
The first derivative of the given function
[tex]\frac{df(x)}{dx} = - ab e^{-b x}[/tex]
Maya runs 7 miles in 80 minutes. At the same rate, how many miles would she run in 64 minutes?
Answer:
5.6 miles.
Step-by-step explanation:
7/80=x/64 is our equation
Cross multiply to solve for x
x=7*64/80
x=5.6mi
Hope this helps ^-^
Answer:
5.6 miles
Step-by-step explanation:
Let's set up a proportion using the following setup.
[tex]\frac{miles }{minutes}=\frac{miles }{minutes}[/tex]
We know Maya can run 7 miles in 80 minutes.
[tex]\frac{7miles }{80minutes}=\frac{miles }{minutes}[/tex]
We don't know how many miles she can run in 64 minutes. Let's say she can run x miles in 64 minutes.
[tex]\frac{7miles }{80minutes}=\frac{x miles }{64 minutes}[/tex]
[tex]\frac{7}{80}=\frac{x}{64}[/tex]
We want to solve for x (miles in 64 minutes). Therefore, we must isolate x on one side of the equation.
x is being divided by 64. The inverse of division is multiplication. Multiply both sides of the equation by 64.
[tex]64*\frac{7}{80}=\frac{x}{64}*64[/tex]
[tex]64*\frac{7}{80}=x[/tex]
[tex]64*0.0875=x[/tex]
[tex]5.6=x[/tex]
[tex]x= 5.6 miles[/tex]
Maya can run 5.6 miles in 64 minutes.
The expression 36 ÷ 6 · 2 + 1 is equal to _____. 4 18 2 13
Answer:
13
Step-by-step explanation:
We have to use the BODMAS ( Bracket Of Division Multiplication Addition Subtraction) rule here
So first divide
36 ÷ 6 * 2 + 1
6 * 2 + 1
Now multiply
6 * 2 + 1
12 + 1
Now add
12 + 1 = 13
Answer:
13
Step-by-step explanation:
What is the volume of a sphere with a radius of 3 inches? 12π cubic inches 24π cubic inches 36π cubic inches 48π cubic inches
Answer:
The answer is
36π cubic inchesStep-by-step explanation:
Volume of a sphere is given by
[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]where r is the radius
From the question
r = 3 inches
Substitute the value into the above formula and solve for the volume
That's
[tex]V = \frac{4}{3}( {3})^{3} \pi \\ = \frac{4}{3} \times 27\pi \\ = 4 \times 9\pi[/tex]We have the final answer as
36π cubic inchesHope this helps you
Select a counterexample for the conclusion.
The difference between two even numbers is positive.
A
9-13
B
13-9
C
10-2
D
2-10
convert 2 2/3 into an improper fraction
Answer: 8/3
Step-by-step explanation:
If A, B, and C are the vertices of a triangle, find AB + BC + CA.
Answer:
0Step-by-step explanation:
When drawing a triangle, note that the vectors can be drawn either in a clockwise or anticlockwise direction. For a triangle with vertices A, B and C, te vectors are AB, BC and CA
In vector notation CA = - AC (length CA is equal to AC but acting in opposite direction to AC)
and AB+BC = AC
To evaluate AB + BC + CA, we will substitute the vector expression above into the given expression and simplify as shown;
= (AB + BC) + CA
= AC + (-AC)
open the parenthesis
= AC-AC
= 0
Hence the sum of the vector expression AB + BC + CA is a zero vector
Which expression represents the greatest common factor (GCF) of 70 and 112? A. 2 x 2 x 2 x 7 B. 2 x 2 x 2 x 5 C. 2 x 7 D. 2 x 2 x 2 x 3 x 5
Answer:
[tex]\huge\boxed{C. \ \ GCF = 2 * 7}[/tex]
Step-by-step explanation:
Firstly, we'll do prime factorization of these numbers.
70 = 2 × 5 × 7
112 = 2 × 2 × 2 × 2 × 7
So, The Greatest Common Factor can be written as:
GCF = 2 × 7 [Since Only one 2 and one 7 is common]
Hope this helped!
~AnonymousHelper1807Answer:
C
Step-by-step explanation:
I got this correct on e d g e n u i t y thanks to the person above me :)
Canada has a population of 1/10 as large as the United States and Canada population is about 32 million about how many people live in United States explain how many zeros in your answer
Answer:
Step-by-step explanation: If Canada(C) is 32,000,000 and America is A and C x 10 = A then 32,000,000 x 10 = A
And to multiply any whole number by 10 you just add a zero to the end so
320,000,000 is the answer which is pronounced "Three hundred twenty million" And there is 7 zeros in the answer
hope this helps mark me brainliest
Valleywood Golf course offers classes Monday through Saturday. The Saturday classes last 75 minutes. If they offered 705-minutes of classes last week, what was the maximum number of weekday classes?
Answer:
Step-by-step explanation:
To make the problem easier to solve, we will set it up as the equation of the length of time of each class times the number of classes equals the total amount of minutes. However, since we don't know the number of classes, we'll symbolize our two unknowns with two variables.
75x + 45y = 705
(75x + 45y)/15 = 705/15
5x + 3y = 47
y = (47-5x)/3
It looks like we can't simplify the equation any more, so now it is a matter of trial and error. The minimum number of Saturday classes means the maximum number of weekday classes. We first will test for the maximum by assuming there are no Saturday classes, then will work our way up until x is an integer.
If x = 0
(47-5(0))/3 = 47/3 = 15.6666
If x = 1
(47-5(1))/3 = 42/3 = 14
This works. Therefore, the maximum number of weekday classes is 14, or choice b.
-x+7= -6x-13 how do you solve it
Answer:
-4=x
Step-by-step explanation:
Okay, let's do this step-by-step for the best results!
We need to make sure that common variables can be put together first. If you did not know this, look at PEMDAS.
-x+7=-6x-13
We need to add -x and -6x together. If we do that then you would get,
7=-5x-13
Let's add 13 to 7 now.
20=-5x
Lets divide -5 with 20.
-4=x
I hope this helped!
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 4}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ - x + 7 = - 6x - 13}[/tex]
Move 6x to left hand side and change it's sign
[tex] \dashrightarrow{ \sf{ - x + 6x + 7 = - 13}}[/tex]
Move 7 to right hand side and change it's sign
[tex] \dashrightarrow{ \sf{ - x + 6x = - 13 - 7}}[/tex]
Collect like terms
[tex] \dashrightarrow{ \sf{ 5x = - 13 - 7}}[/tex]
Calculate
[tex] \dashrightarrow{ \sf{5x = - 20}}[/tex]
Divide both sides by 5
[tex] \dashrightarrow{ \sf{ \frac{5x}{5} = \frac{ - 20}{5} }}[/tex]
Calculate
[tex] \dashrightarrow{ \sf{x = - 4}}[/tex]
Hope I helped!
Best regards! :D
Calculate the volume of the cube ____ cm³
Answer:
48
Step-by-step explanation:
volume=width×length×hight
2×4×6
48
Which is the best description for the graph below? A graph decreases from (0, 3) to (9, 0). The graph increases everywhere. The graph decreases everywhere. The graph remains constant. The graph increases, then decreases.
Answer:
the graph decreases everywhere
Step-by-step explanation:
the left side of the line is higher than the right side which means its a negative slope so it is decreasing
Answer:B
Step-by-step explanation:
6.9times 1.221 equals
Answer:
8.2429
Step-by-step explanation:
Answer:
8.4249
Step-by-step explanation:
Use calculator if you have.
Is the square root of 900 rational
Answer:
Yes it is rational
Step-by-step explanation:
The square root of 900 is a rational number if 900 is a perfect square. It is an irrational number if it is not a perfect square. Since 900 is a perfect square, it is rational number.
1+6v+4=47
Be quick please :D
Answer:
1+ 6v + 4 = 47
collect like terms
5 + 6v = 47
Subtract the 5 from both sides
6v = 42
divide 6 from both sides
v = 7
Why isn't 0 at the far left of the scales?
Step-by-step explanation:
Why isn't "0" far left of the scales? It's not on the far left side because it wouldn't allow us to be much more precise if it was at the far end. Being where it is, it gives us a closer approximation to the actual distance in the real world.
In the city of Lawrenceville, how many phone numbers are possible using the area code 678? The restrictions for the phone company are listed below. · The first digit of the phone number cannot be numbers 0-5. · The second number cannot be a zero. · The third and fourth numbers cannot be a zero or one · The fifth number cannot be a zero, one or two How many phone numbers are possible using the area code 678? a.2000 b.1,6128 c.1,612,800 d.300
Answer:
Hey there!
If there were no restrictions, there would be 10x10x10x10x10 phone numbers.
The first number can only be a 6-9, so that is four options.
The second number can have nine options.
The third and fourth numbers have eight options.
The fifth number has seven options
4x9x8x8x7=16128.
16128 numbers are possible.
Let me know if this helps :)
what is the absolute value of 0.8
Answer:
0.8
The absolute value of 0.8 is 0.8!
Hope this helps!
plsss help asap!!!! i need it i have a time limit
Answer:
32
Step-by-step explanation:
90 = 7y + 27
7y = 63
y = 9
180 = 58 + 7(9) + 27 + $
$ = 32
It might be wrong
A triangle drawn on a map has sides of lengths 9 cm, 12 cm, and 15 cm. The shortest of the
corresponding real-life distances is 122 km Find the longest of the real-life distances,
Answer:
26
Step-by-step explanation:
Abe has $253.33 in his checking account. He wants to buy items that cost $23.33, $25.09, $33.45, and $56.02. How much is Gabe planning to spend?
Answer:
Gabe is planning to spend $137.89.
Step-by-step explanation:
23.33 + 25.09 + 33.45 + 56.02 = 137.89
in a given year, residents of a country spent approximately $54.7 billion on their pets. Of this amount, $17.6 billion wa for veterinarian bills. What percent of the total was spent on veterinary care?
Answer:
32.176 %
Step-by-step explanation:
(100% / 54.7) x 17.6 = about 32.176 percent
Do the equation yourself for a more precise answer!
The length of a rectangle is four meters less than twice it's width. If the area of the rectangle is 96 square meters what is the width?
Answer: (I'm sorry if this is not the right answer)
The width = 8 meters
Step-by-step explanation:
The length: a (m)
The width: b (m)
We cannot have a negative length and a negative width: a>b>0
Eq. I: a=2b-4
Eq. II: ab=96
Substitute the value of a from Eq. I into Eq. II: (2b-4).b=96
Solve for b:
(2b-4).b=96
2[tex]b^{2}[/tex]-4b-96=0
[tex]b^{2}[/tex]-2b-48=0
[tex]b^{2}[/tex]+6b-8b-48=0
b.(b+6)-8.(b+6)=0
(b+6).(b-8)=0
b=8; b=-6
As mentioned above, b>0. Therefore, b=8
Conclusion: if the area of the rectangle is 96 square meters then its width is 8 meters.
The width of the given rectangle is 8 units.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Let's say the length of the rectangle is L and the width is W
Given that,
The length of a rectangle is four meters less than twice its width.
So,
L = 2W - 4
And,
Area = 96 square meter
LW = 96
Now by substituting
2W² - 4W = 96
W² - 2W - 48 = 0
W² -8W + 6W - 48 = 0
W(W - 8) + 6(W - 8) = 0
(W + 6)(W - 8) = 0
W = 8, -6 since distance cannot be negative so it will be 6 meters.
Hence "The width of the given rectangle is 8 units".
For more about rectangles,
https://brainly.com/question/15019502
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In 2002, a school population was 956. By 2006 the population had grown to 1160. 1) How much did the population grow between the year 2002 and 2006? Correct students 2) How long did it take the population to grow from 956 students to 1160 students? 3) What is the average population growth per year? 4) What was the population in the year 2000? students 5) Find an equation for the population, P , of the school t years after 2000. P = 6) Using your equation, predict the population of the school in 2011. students
Answer:
1) The population grew by 204 students between 2002 and 2006.
2) It took 4 years for the population to grow from 956 to 1160.
3) The average population growth is about 51 students per year.
4) In 2000 the population was 854.
Step-by-step explanation:
Se tiene un conjunto de triángulos equiláteros, cuya medida de lados están en progresión geométrica cuya razón es 2. Si se ordenan los triángulos de acuerdo a su tamaño, se tiene que el primer triángulo mide un 1 cm de lado , ¿cuánto medirá el lado del vigésimo triángulo equilátero?¿cuánto medirá su perímetro?
Responder:
Explicación paso a paso:
Dado el conjunto de un triángulo equilátero con cada uno de sus lados en progresión geométrica, si el primer triángulo mide un lado de 1 cm y una razón común de 2 cm, para obtener el lado del triángulo 29, usaremos la fórmula para calcular el enésimo término de la progresión geométrica. expresado como;
Tn = ar ^ (n-1)
a es el primer término
n es el número de términos
r es la razón común.
Dados los siguientes parámetros
a = 1, r = 2 y n = 20 (ya que estamos buscando el lado del vigésimo triángulo)
Sustituyendo los parámetros dados en la fórmula para obtener el lado del triángulo 20, tendremos;
T20 = 1 (2) ^ 20-1
T20 = 1 (2) ^ 19
T20 = 2 ^ 19
T20 = 524,288 cm
Por lo tanto, la medida de la longitud de un lado del vigésimo triángulo equilátero es 524,288 cm.
Perímetro del vigésimo triángulo equilátero = 3 × 524,288 = 1,572,864cm
Tenga en cuenta que todos los lados de un triángulo equilátero son iguales.