Select the correct answer.
What is the solution for x in the equation?
-4 + 5x - 7 = 10 + 3x - 2x
A.x=4/21
B.x=21/4
C.x=13/4
D.x=4/13

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.

In 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:

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

Answer:

Gabe is planning to spend $137.89.

Step-by-step explanation:

23.33 + 25.09 + 33.45 + 56.02 = 137.89

Answer:

The answer is

Step-by-step explanation:

Volume of a sphere is given by

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

We have the final answer as

Hope this helps you

Answer:

8.2429

Step-by-step explanation:

Answer:

8.4249

Step-by-step explanation:

Use calculator if you have.

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)

Answer:

32

Step-by-step explanation:

90 = 7y + 27

7y = 63

y = 9

180 = 58 + 7(9) + 27 + $

$ = 32

It might be wrong

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:

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!

Answer:

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 :)

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!

Answer:

48

Step-by-step explanation:

volume=width×length×hight

2×4×6

48

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.

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:

Answer:

5

Step-by-step explanation:

y = 2x - 3

{ x = 4 }

y = 2(4)-3= 8 - 3 = 5

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:

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.

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,

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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

Answer:

26

Step-by-step explanation:

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

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]

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.

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

Answer:

Step-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

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.

Answer:

0.8

The absolute value of 0.8 is 0.8!

Hope this helps!

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.

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

Answer: 8/3

Step-by-step explanation:

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.

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