Is the percent increase from 50 to 70 equal to the percent from 70 to 50explain.

Answer:

\(\huge\boxed{\sf Yes.}\)

Step-by-step explanation:

In a right angled triangle, the longest side is called hypotenuse.

So,

Hypotenuse = 13 m

The rest are:

Base = 5 m

Perpendicular = 12 m

Using Pythagoras Theorem to verify:

\((Hypotenuse)^2=(Base)^2+(Perpendicular)^2\)

Put the given data

(13)² = (12)² + (5)²

169 = 144 + 25

Since, both left hand side and right hand side are equal, this means the triangle is a right-angled triangle.

\(\rule[225]{225}{2}\)

Answer:

Step-by-step explanation:

3( -2p +2);  distribute 3 over parenthesis

-6p + 6

Answer:

Step-by-step explanation:

From the information given:

Tank's Capacity = 600 gal

Original content of water = 200 gal

Salt solution = 100 lb

In the tank:

Suppose x(t) = amount of salt at time (t); &

V(t) = volume of water

Then,

V(t) = 200 + t

and \(x'(t) = 3 - \dfrac{2x(t)}{200+t}\)

From the above linear equation, the integrating factor can be computed as:

\(x(t) = \Bigg(e^{\int \dfrac{2}{200+t}} \Bigg)^{dt}\)

\(= e^{2 \ log (200+t)}\)

= (200 + t)²

The general solution can now be expressed as:

\(x(t) = \dfrac{1}{(200+t)^2}\Bigg( \int 3(200+t)^2 \ dt +C\Bigg)\)

We know that C = integrating factor, thus taking the integral:

\(x(t) = \dfrac{(200+t)^3 +C}{(200+t)^2}\)

At the initial condition, x(0) = 100

∴

\(100= \dfrac{(200)^3 +C}{(200)^2}\)

C = ((200)²×100) - 200³

C = -4 × 10⁶

Hence, at any time t, the amount of salt is:

\(x(t) = \dfrac{(200+t^2) - 4\times 10^6}{(200+t)^2}\)

The value of Y when X = 4 in the regression line that has the slope of 2,5 is a) 26

The equation of a straight line with slope m and y-intercept b is given by  :

y = mx + b.

Where

1. y is the dependent variable (i.e., the value of y depends on x)

2. x is the independent variable

3. m is the slope of the line, representing the rate of change of y with respect to x

4. b is the y-intercept, the point where the line intersects the y-axis when x = 0.

This equation can be used to describe the relationship between two variables, and it can be used to make predictions about the value of y for a given value of x, or to find the value of x for a given value of y.

From the question we have the following information :

1. Slope ( or m ) is 2.5

2. The intercept ( y-intercept or b ) is 16

So, using the values given (slope = 2.5, y-intercept = 16), we have:

y = mx + b

y = 2.5x + 16

When X is 4, substituting X with 4 in the equation gives us:

y = 2.5 * 4 + 16 = 26

So the value of Y when X is 4 is 26. Answer: a) 26.

Learn more about equation of a straight line with slope here

https://brainly.com/question/24143133

#SPJ4

Answer:

7

Step-by-step explanation:

7 the numbers drop which would put 7 farthest away from 0

Answer:

None of the above

Answer:

See Below

Step-by-step explanation:

x(2x) - 4(2x) + x(3) - 4(3)

= 2x² - 8x + 3x -12

= 2x²-5x-12

Answer:

G. 0.3

Explanation:

We know that

On April 1: Berry weight = 0.922 grams

On April 12: Berry weight = 0.589 grams

Therefore, the difference in weight is

0.922 grams - 0.589 grams = 0.333 grams

This means that the difference between the weight of the berry on April 1 and April 12 is 0.333 grams.

Now which answer choice is closest to 0.333 grams?

The answer is, choice G is the closest choice.

Hence, choice G, 0.3 grams is the correct answer.

Answer:

y=13

Step-by-step explanation:

divide each term by -7 and simplify

Answer:

y = 13

Step-by-step explanation:

-7y = -91

y = -91/-7

y = 13

Gift brainliest please D: If you hover over this answer, cllck the crown at the bottom.

Answer:

If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16. The average rate of change is 6 over 1, or just 6.

The average rate of change is \(\frac{6}{25}\)

'When we calculate average rate of change of a function over a given interval, we’re calculating the average number of units that the function moves up or down, per unit along the x-axis. We could also say that we’re measuring how much change occurs in our function’s value per unit on the x-axis.'

According to the given problem,

Rate of change formula = \(\frac{f(b) - f(a)}{b-a}\)

y = log3x

⇒ a= 1

   b= 3

Therefore,

⇒ \(\frac{log(3*3) - log(3*1)}{3-1}\)

⇒ \(\frac{log9 - log3}{2}\)

⇒\(\frac{1}{2}\) log\((\frac{9}{3})\)

⇒ \(\frac{1}{2}\) * log 3

⇒ \(\frac{6}{25}\)

Hence we can conclude the rate of change as \(\frac{6}{25}\)

Learn more about rate of change here: https://brainly.com/question/18193470

#SPJ2

Answer:

is it correct please tell

-2.666

Answer:

-1

Step-by-step explanation:

Gradient is another word for slope, and slope can be defined as rise/run.

From the point (0,0) to (1,-1), it moved one unit down and one unit to the right. The slope for this line can be represented as -1/1, which is equal to -1.

Therefore, the gradient of the graph shown is -1.

Answer:

c

Step-by-step explanation:

Answer:

P=19.2 ft

Step-by-step explanation:

ACCORDING TO THE THEOREM,

BC=2(DE)

So BC =2(3.2)

BC=6.4 ft

Now

AB=2(EF)

AB=2(4)

AB=8 ft

Now

AC = 2(DF)

AC= 2(2.4)

AC=4.8 ft

Now we're gonna find the perimeter which is sum of all sides

Perimeter=4.8+8+6.4

P= 19.2 ft

The two bodies are being drawn together by a force of 10812 N, according to Newton's Law of Gravitation.

Every particle in the universe is drawn to every other particle with a force that is directly proportional to the product of their masses and inversely proportional to their separation from one another, according to Newton's Law of Universal Gravitation.

Symbolically, Newton came to the following conclusion on the strength of the gravitational force:

F = G(m₁ × m₂) / r²

F is the gravitational force between two bodies, m1 and m2 are the bodies' masses, r is the distance between their centres, and G is the gravitational constant of the universe.

According to the query,

satellite's mass is m1 = 1100 kg.

mass of earth = 5.98 ×10²⁴ kg

Radius of the earth = 6.37 × 10⁶ m

G = 6.67 × 10⁻¹¹ Nm² / kg²

Force = G(m₁ × m₂) / r²

Substituting the values,

F = 6.67 × 10⁻¹¹( 1100 × 5.98 ×10²⁴)  /( 6.37 × 10⁶)²

=> F = 6.67 × 1100 × 5.98 × 10¹³ / 40.58 × 10¹²

=> F = 43,875.26 × 10 / 40.58

=> F = 10812 N

To know more about Newton's Law here

https://brainly.com/question/15280051

#SPJ4

Answer:

0.4m²

Step-by-step explanation:

use the formular for tripezoid and only substitute a b and h

answer should be A since its by months C would be Y and M be X since its charging per movire

Answer:

x=8

Step-by-step explanation:

Since m and n are parallel, the two given angles are equal (opposite exterior).  Therefore,

7x-2=5x+14

7x-5x=14+2

2x=16

x=8

Answer:

  -23

Step-by-step explanation:

You want the slope of the line whose equation is y -6 = -23(x +6).

The point-slope form of the equation of a line is ...

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k).

Matching the given equation to the above pattern, we see ...

  y -6 = -23(x +6) . . . . . . line with slope -23 through point (-6, 6).

The line's slope is -23.

__

Additional comment

While it is not impossible, it would be unusual for a line to have a slope of -23 in a problem like this. Consistent with equation mangling often seen on Brainly, we suspect the equation is actually ...

  y -6 = (-2/3)(x +6)

and the slope is actually -2/3.

<95141404393>

By evaluating g(x), we conclude that the correct table is:

The correct table is:

x      g(x)

1         2

2         8

3         14

Here we know that:

f(x) = 3x - 4

And function g(x) is defined as:

g(x) = f(2x) = 3*(2x) - 4= 6x - 4

Evaluating g(x) in the values in the tables, x = 1, 2, 3, etc..., we will get:

g(1) = 6*1 - 4 = 6 - 4 = 2

g(2) = 6*2 - 4 = 12 - 4 = 8

g(3) =  6*3 - 4 = 18 - 4 = 14

Then the correct table is:

x      g(x)

1         2

2         8

3         14

Learn more about evaluating functions:

https://brainly.com/question/1719822

#SPJ1

The sum of the infinite geometric sequence is 3 3/4

From the question, we have the following parameters that can be used in our computation:

The geometric sequence

In the geometric sequence, we have

First term, a = 3/5¹⁻¹

a = 3

Also, we have

Common ratio, r = 1/5

The sum of the infinite geometric sequence is calculated as

Sum = a/(1 -  r)

So, we have

Sum = 3/(1 -  1/5)

Evaluate

Sum = 3 3/4

Hence, the sum of the infinite geometric sequence is 3 3/4

Read more about sequence at

https://brainly.com/question/30499691

#SPJ1

1) given

2) given

3) Definition of linear pair

4) If alternate interior angles are congruent, then the lines are parallel.

Answer:

60

Step-by-step explanation:

10 x 6 = 60

Hope this helped! :)

Answer:

x = 18

mZT = 71º

Step-by-step explanation:

Complementary angles total 90º

(3x + 17) + 19 = 90

Subtract 19 from both sides

3x + 17 = 71

mZT = 71º

Subtract 17 from both sides

3x = 54

Divide both sides by 3

x = 18

The cube root of -2i,

⇒ ∛2[ cos(π/6) + i sin(π/6) ]

We can represent -2i in polar form as,

r(cosθ + i sinθ)

by computing its magnitude and angle.

The magnitude of -2i is 2

Since the absolute value of any imaginary number is equal to its magnitude.

To find the angle θ,

We can use the fact that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case,

The opposite side is -2 and the adjacent side is 0.

Therefore, we have tanθ = -2/0, which is undefined.

However,

We can use the fact that the cube root of a complex number is equal to the cube root of its magnitude times exp(iθ/3) to find the cube root of -2i.

So, the cube root of -2i is equal to the cube root of 2 times exp(iθ/3).

Now, we need to find the value of θ/3. Since θ is undefined,

we will represent it as π/2 + 2πn,

where n is any integer.

So, θ/3 = (π/2 + 2πn)/3 = π/6 + 2πn/3.

Therefore, the cube root of -2i is equal to

⇒  ∛2 [ cos(π/6 + 2πn/3) + i sin(π/6 + 2πn/3) ]

Now put n = 0

⇒ ∛2[ cos(π/6) + i sin(π/6) ]

This is the final form of the cube root of -2i in the required form.

To learn more about complex numbers visit:

https://brainly.com/question/27940074

#SPJ1

Answer:

\(x = \frac{2a}{a - 2} \)

Answer:

12(x+3)

Step-by-step explanation:

12 can be factored out from both sides

once you do that your are left with

12(x+3)

Answer:

x = 25

Step-by-step explanation:

Use Pythagoras' Theorem \(a^s+b^2=c^2\)

where a and b are the legs and c is the hypotenuse of a right triangle

\(\implies 7^2+24^2=x^2\)

\(\implies 49+576=x^2\)

\(\implies 625=x^2\)

\(\implies x=\sqrt{625}\)

\(\implies x=\pm25\)

\(\implies x = 25\) only, as distance is positive

Use Pythagorean theorem

\(\\ \rm\longmapsto x^2=24^2+7^2\)

\(\\ \rm\longmapsto x^2=576+49\)

\(\\ \rm\longmapsto x^2=625\)

\(\\ \rm\longmapsto x=25\)

The claim can be said that the proportion of patients taking Lipitor who experience flu-like symptoms is at least 70%.

Opposite: The proportion of patients taking Lipitor who experience flu-like symptoms is less than 0.7.

The test can be said that the one-tailed z-test for proportions that has a significance level of 0.05.  

The test statistic is z =- -1.96

The p-value is: 0.0406.

Based on this we: reject the null hypothesis.

Conclusion:  we can say that there is not enough evidence to support the claim that the proportion of patients taking Lipitor who experience flu-like symptoms is at least 70%.    

The flu-like symptoms  includes fever, chills, headache, muscle or body aches, cough, sore throat, runny nose, and diarrhea.

We can test the  statistic using the formula:

z = (/p  - p) /  √(p x  (1-p) / n)

where /p =  sample proportion = 213/333 = 0.639

p = hypothesized proportion under the null hypothesis = 0.7

n =  sample size = 333

z = (0.639 - 0.7) / √(0.7 * (1-0.7) / 333)

z = -1.96

Learn more about  flu-like symptoms at:

https://brainly.com/question/8153675

#SPJ1