The rectangle below has an area of 81- x^2 square meters and a width of 9 - x meters

Answer:

 112 candles

Step-by-step explanation:

We can simply add up the 5 numbers of candles, or we can take advantage of the invention of multiplication to replace repeated addition. The number of candles altogether is the sum of the numbers of candles in each of the 5 boxes.

  16 + 4×24 = 16 +96 = 112

The total number of candles is 112.

Square B Area = 144cm²

Square B = X

The dimensions of Square A are three times The dimensions of Square B

Square A = 3 * Square B

Square A = 3X

The area of Square A is 1,296 cm2.

Square A Area = (3X)² = 1296

Square B Area = X²

Solve to find X.

(3X)² = 1296

3X = 36

X = 36/3 = 12

Square B Area = 12² = 144

Square B Area = 144cm²

Final answer:

The area of Square B is 144 cm², calculated by dividing the area of Square A (1,296 cm²) by 9, because the area of a square scales with the square of its linear dimensions.

Explanation:

The area of Square A is given as 1,296 cm². Since the dimensions of Square A are three times the dimensions of Square B, we can find the area of Square B by understanding that area scales in proportion to the square of the linear dimensions. This means that if one dimension is three times another, the area will be nine times (3² = 9) larger.

To find the area of Square B, we simply divide the area of Square A by 9:

Area of Square B = Area of Square A / 9

Area of Square B = 1,296 cm² / 9

Area of Square B = 144 cm².

Therefore, the area of Square B is 144 cm².

Add the two numbers in the ratio: 7 +3 = 10

Divide total capacity by 10:

70,580 / 10 = 7,058

Multiply that by the ratio of filled seats:

7,058 x 7 = 49,406

49,406 seats were filled.

3x+4=5x-50

54=2x

27=x

Answer:

x = 27

Step-by-step explanation:

The diagonals of a rectangle are congruent, hence

BD = AC ← substitute values

5x - 50 = 3x + 4 (subtract 3x from both sides )

2x - 50 = 4 ( add 50 to both sides )

2x = 54 ( divide both sides by 2 )

x = 27

[tex]f(x)=\ln(x^2+2x+4)\implies f'(x)=\dfrac{2x+2}{x^2+2x+4}[/tex]

The numerator determines where the derivative vanishes (the denominator has a minimum value of 3, since [tex]x^2+2x+4=(x+1)^2+3\ge3[/tex]).

[tex]2x+2=0\implies x=-1[/tex]

At this critical point, we have

[tex]f(-1)=\ln((-1)^2+2(-1)+4)=\ln3\approx1.099[/tex]

At the endpoints, we have

[tex]f(-2)=\ln4\approx1.386[/tex]

[tex]f(2)=\ln12\approx2.485[/tex]

so [tex]f[/tex] attains a maximum value of [tex]\ln12[/tex] and a minimum value of [tex]\ln3[/tex].

The absolute minimum of the function f(x) = ln(x2 + 2x + 4) is at x=-2 where the value is ln(4) and the absolute maximum is at x=2 where the value is ln(8). There are no critical numbers within the selected interval.

The given function is

f(x) = ln(x

2

+ 2x + 4)

, for which we need to find the absolute maximum and minimum in the interval [-2, 2]. Firstly, we find the derivative of the function:

f '(x) = (2x + 2) / (x

2

+ 2x + 4)

. To find the critical points, we set the derivative equal to zero and solve for x, finding no real solutions, indicating there are no critical numbers within the given interval. Thus, the extrema must occur at the endpoints. So, we find f(-2) = ln(4) and f(2) = ln(8).

The absolute minimum is ln(4) at x = -2 and the absolute maximum is ln(8) at x = 2

.

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Lets say the number is ab. Its value is 10a + b  

When it is reversed it is 10b + a = 12a+1.2b (from the condition its value should increase 0.2 times).  

11 a = 8.8b  

a/b = 8.8/11 = 0.8/1 = 8/10 = 4/5 ( we do this because a and b should be natural numbers less than 10).  

answer is 45.

A two-digit number less than 100 that increases by one-fifth of its original value, when its digits are reversed, can be found by setting up an equation. By defining the tens digit as 'a' and the unit digit as 'b', the equation 6a = 9b is derived. Solving for the digits within their possible values, the number 12 is found.

To find a number less than 100 that increases by one-fifth of its value when its digits are reversed, we need to set up an equation. Let's call the tens digit a and the units digit b. The number can be written as 10a + b. When the digits are reversed, the number becomes 10b + a. The problem states that reversing the digits increases the number by one-fifth of its original value, which gives us the equation:

(10a + b) + \frac{1}{5}(10a + b) = 10b + a

Now solving the equation:

6a = 9b

As a and b are digits, their possible values range between 0 and 9. We find that a = 1 and b = 2 satisfy the equation. Hence, the number is:12

When we reverse the digits, we get 21, which is greater than 12 by \frac{1}{5} of 12, as required.

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Answer: 8

Step-by-step explanation:

 The triangle shown in the image attached is a right triangle.

Therefore, to calculate the missing lenght of the triangle you can apply the Pythagorean Theorem, which is shown below:

[tex]a^2=b^2+c^2[/tex]

Where a is the hypotenuse and b and c are the legs.

The problem gives you the value of the hypotenuse and the value of one leg. Therefore, you must solve for the other leg from [tex]a^2=b^2+c^2[/tex], as following:

[tex]17^2=15^2+c^2\\c=\sqrt{17^2-15^2}\\c=8[/tex]

Therefore, the lenght of the missing side is: 8

Answer:

The value of third side= 8 units

Step-by-step explanation:

It is given a right angled triangle with base = 15 and hypotenuse = 17

We have to find the height of given triangle.

Points to remember

By Pythagorean theorem

Base² + Height² = Hypotenuse²

To find the third side

Here base = 15 and hypotenuse = 17

We have,

Base² + Height² = Hypotenuse²

Height² = Hypotenuse² - Base² = 17² - 15² = 64

Height = √64 = 8 units

Therefore the value of third side = 8 units

Answer:

True

Step-by-step explanation:

To answer this question we must evaluate

y = 0° on both sides of the equation.

For the left side we have:

[tex]sin(0\°) tan(0\°)[/tex]

We know that [tex]tan(0\°) =\frac{sin(0\°)}{cos(0\°)}[/tex]

We know that [tex]cos(0\°) = 1[/tex] and [tex]sin(0\°) = 0[/tex].

Therefore [tex]tan(0\°) = 0[/tex].

Then the left-hand side of the equals is equal to zero.

On the right side we have:

[tex]cos(y)[/tex]

When evaluating [tex]cos(y)[/tex] at [tex]y = 0[/tex]

We have to [tex]cos(0\°) = 1[/tex].

0 ≠ 1

The equation is not satisfied. Therefore y = 0 ° is a counterexample to the equation

Answer:true

Step-by-step explanation:

edge

Answer:

y = 3x^2 + 1/3

Step-by-step explanation:

The first step is the easiest. Find the value of c. That means that all you are left with is c and y because x and a disappear when x = 0.

y = ax^2 + c

Givens

Solution

1/3 = a(0)^2 + c

1/3 = 0 + c

c = 1/3

Second Given

Second Solution

82/3 = a*(-3)^2 + 1/3            Subtract 1/3 from both sides

82/3 - 1/3 = a*(9) + 1/3 - 1/3

81/3 = 9a                              Reduce the left

27 = 9a                                Divide by 9

27/9 = a

3 = a

Answer

y = 3x^2 + 1/3

Answer:

C

Step-by-step explanation:

The equation is y = a(b(x-c))+d

So for it to move right three units, it would be x - 3.

For it to move up 4 unites, it would be x+4.

So the equation would be y = (x - 3)^2 + 4

The correct answer is C

First you would substitute the expression moving it to the left then you change the signs the power function with an even exponent is always a positive or 0 but there is no x intercept.

ANSWER

The distance is 10 units.

EXPLANATION

Let us use the distance formula to find the distance between,

[tex](x_1,y_1)=(1,4)[/tex]

and

[tex](x_2,y_2)=( - 5, - 4)[/tex]

The distance formula is given by,

[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} [/tex]

We plug in the values to get,

[tex]d = \sqrt{( - 5-1)^2 + ( - 4-4)^2} [/tex]

[tex]d = \sqrt{( -6)^2 + ( - 8)^2} [/tex]

[tex]d = \sqrt{36+ 64} [/tex]

[tex]d = \sqrt{100} [/tex]

[tex]d = 10[/tex]

Set [tex]f(x)=2x^3-3x^2+2[/tex]. Find the tangent line [tex]\ell_1(x)[/tex] to [tex]f(x)[/tex] at the point when [tex]x=x_1[/tex]:

[tex]f'(x)=6x^2-6x\implies f'(x_1)=12[/tex] (slope of [tex]\ell_1[/tex])

[tex]\implies\ell_1(x)=12(x-x_1)+f(x_1)=12(x+1)-3=12x+9[/tex]

Set [tex]x_2=-\dfrac9{12}[/tex], the root of [tex]\ell_1(x)[/tex]. The tangent line [tex]\ell_2(x)[/tex] to [tex]f(x)[/tex] at [tex]x=x_2[/tex] has slope and thus equation

[tex]f'(x_2)=\dfrac{63}8\implies\ell_2(x)=\dfrac{63}8\left(x+\dfrac9{12}\right)-\dfrac{17}{32}=7x+\dfrac{151}{32}[/tex]

which has its root at [tex]x_3=-\dfrac{151}{224}\approx-0.6741[/tex].

(The actual value of this root is about -0.6777)

the answer should be C

Answer:

d 7(8 + 3)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

cos(x)=2/3 in Q 4

sin(x/2)=+√(1-cos(x))/2

√(1-cos(x))/2=√(1-[2/3]/2=√(1/3)/2=-√(1/6) because sin is negative in Q 4

Answer:

See below.

Step-by-step explanation:

Because cos x = 2/3 the adjacent side = 2 and hypotenuse = 3 so the length of the opposite side =  

√(3^2 - 2^2) =  -√5 (its negative because we are in Quadrant 4).

So sin x =  -√5/3.

(a) sin (x /2) =  - √ [ (1 - cos x)/2 ]

= -√(1 - 2/3)/ 2)

= -√(1/6).  or -0.4082.

(b)  cos (x/2)  = √ [ (1 + cos x)/2]

=  √ 5/6 or 0.9129.

(c)   tan (x /2) =   ( 1 - cos x) / sin x.

=  ( 1 - 2/3) /   -√5/3

= -0.4472.

We can use the fact that, for [tex]|x|<1[/tex],

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

Notice that

[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{1-x}\right]=\dfrac1{(1-x)^2}[/tex]

so that

[tex]f(x)=\displaystyle\frac5{(1-x)^2}=5\frac{\mathrm d}{\mathrm dx}\left[\sum_{n=0}^\infty x^n\right][/tex]

[tex]f(x)=\displaystyle5\sum_{n=0}^\infty nx^{n-1}[/tex]

[tex]f(x)=\displaystyle5\sum_{n=1}^\infty nx^{n-1}[/tex]

[tex]f(x)=\displaystyle5\sum_{n=0}^\infty(n+1)x^n[/tex]

By the ratio test, this series converges if

[tex]\displaystyle\lim_{n\to\infty}\left|\frac{(n+2)x^{n+1}}{(n+1)x^n}\right|=|x|\lim_{n\to\infty}\frac{n+2}{n+1}=|x|<1[/tex]

so the series has radius of convergence [tex]R=1[/tex].

The Maclaurin series for the function 5(1 − x)⁻² is obtained by applying the binomial series theorem, resulting in the series: 5*(1 + 2x - 2 + 3x² - 3x + 4x³ - 4x² + ...). The radius of convergence for the series is 1.

The function given is f(x) = 5(1 − x)−2. The Maclaurin series of a function f is the expression of that function as an infinite sum of terms calculated from the values of its derivatives at a single point. Here, we can use the binomial theorem as a starting point. It states that (1+x)ⁿ = 1 + nx + (n(n-1)/2!)x² + ..., where n is a real number and -1

Now, f(x) is similar to the binomial series: if we let n=-2, and x become -(x-1), we have f(x) = 5(1 – x)⁻² = 5*(1 + 2(x-1) + 3*(x-1)² + 4*(x-1)³ + ...)

So the Maclaurin series for the function is: 5*(1 + 2x - 2 + 3x² - 3x + 4x³ - 4x² + ...). The next step is to find the radius of convergence. The series has a radius of convergence R such that for all x in the interval -R

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Answer: Actually The Jacksonian Era was characterized by the thought that each individual also equally have right and he or she is important and that all should be able to have a say or participate in any government activities.

All in all i think its actually giving greater right to the common man.

Answer:

Where is the red object?

Step-by-step explanation:

I CANT SEE THE RED OBJECT U DIDNT PUT ITTT

Answer:

0.2312

Step-by-step explanation:

Using the formula given,

[tex]P(x) = p(1-p)^{x-1}[/tex],

we use 0.34 for p and 2 for x:

[tex]P(2) = 0.34(1-0.34)^{2-1}\\\\P(2) = 0.34(0.68)^1\\\\P(2) = 0.34(0.68) = 0.2312[/tex]

Answer:

Three solutions were found :

x = 5

x = 2

x = -1

Step-by-step explanation:

Answer:

d. [tex]x=-1,2,\:or\:5[/tex]

Step-by-step explanation:

The given equation is;

[tex]x^3-6x^2+3x+10=0[/tex]

To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator.

The corresponding function is

[tex]f(x)=x^3-6x^2+3x+10[/tex]

The solution to [tex]x^3-6x^2+3x+10=0[/tex] is where the graph touches the x-axis.

We can see from the graph  that; the x-intercepts are;

(-1,0),(2,0) and (5,0).

Therefore the real solutions are:

[tex]x=-1,2,\:or\:5[/tex]

Answer:

Final answer is approx x=1.27.

Step-by-step explanation:

Given equation is [tex]8^{-x+7}=3^{7x+2}[/tex].

Now we need to solve equation [tex]8^{-x+7}=3^{7x+2}[/tex] and round to the nearest hundredth.

[tex]8^{-x+7}=3^{7x+2}[/tex]

[tex]\log(8^{-x+7})=\log(3^{7x+2})[/tex]

[tex]\left(-x+7\right)\cdot\log\left(8\right)=\left(7x+2\right)\cdot\log\left(3\right)[/tex]

[tex]-x\cdot\log\left(8\right)+7\cdot\log\left(8\right)=7x\cdot\log\left(3\right)+2\cdot\log\left(3\right)[/tex]

[tex]-x\cdot\log\left(8\right)-7x\cdot\log\left(3\right)=2\cdot\log\left(3\right)-7\cdot\log\left(8\right)[/tex]

[tex]x\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)=\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)[/tex]

[tex]x=\frac{\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)}{\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)}[/tex]

Now use calculator to calculate log values, we get:

[tex]x=1.26501646392[/tex]

Round to the nearest hundredth.

Hence final answer is approx x=1.27.

Answer:

She needs 4 more gallons of blue paint than red paint

Step-by-step explanation:

Since the ratio is 3 to 2, 3 + 2 = 5.

The artist needs 20 gallons of purple paint, so 20/5 = 4

The amount of blue and red paint needed is 4x3 to 4x2, or 12 to 8.

She needs 12 gallons of blue paint and 8 gallons of red paint.

12 - 8 = 4

She needs 4 more gallons of blue paint than red paint.

Answer:

ok!

Step-by-step explanation:

blue = 8 gallons

red = 12 gallons

Answer:

[tex]\large\boxed{B)\ 16x^2-25}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ (a-b)(a+b)=a^2-b^2[/tex]

[tex](4x-5)(4x+5)=(4x)^2-5^2=16x^2-25[/tex]

Answer:

wut is it

Step-by-step explanation:

Answer:

a) A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers; b) A series is divergent if it is not convergent. A series is convergent if the sequence of partial sums is a convergent sequence.

Step-by-step explanation:

A sequence is a pattern.  It is an ordered list of objects, such as numbers, letters, colors, etc.

A series is a sum of a sequence.

A divergent series is one that is not convergent.

A convergent series is one in which the sequence of partial sums approaches a limit; this means the partial sums form a convergent sequence.

Answer:

[tex]7;41[/tex]

Step-by-step explanation:

Let

x----> the time it take Ebru to walk to the school

we know that

[tex]x=2(13)=26\ min[/tex]

so

[tex]7;15 +26\ min=7;41[/tex]

Ebru takes 26 minutes to walk to school, twice as long as biking. Leaving at 7:15 AM means she would arrive at school by walking at 7:41 AM.

If Ebru bikes to school, it takes her 13 minutes. Walking takes her twice as long, which would be 26 minutes. If Ebru leaves her house at 7:15 AM, we can calculate the time she will get to school by walking by adding 26 minutes to the departure time.

Therefore, if Ebru walks to school, she will arrive at 7:41 AM.

Answer:

8a - 48

Step-by-step explanation:

An equivalent expression is an expression which is equal to 8(a-6). You can expand or simplify an expression to make an equivalent expression. Apply the distributive property to form a new equivalent expression by multiplying 8 into each term. 8(a-6) = 8*a - 8*6 = 8a - 48. The options listed below do not connect to this problem since they do not use the same variable as the expression.