Which mathematical sentence is represented by the diagram?

A) 3^2 + 4^2 = 5^2

B) 3^2 + 5^2 = 4^2

C) 8^2 + 12^2 = 14^2

D) 9^2 + 16^2 = 25^2

Answer:

the answer is 64 sq. in

Step-by-step explanation:

first you need to find the area of the triangle

a =1/2 bh

= 1/2 (4 in) (6 in)

= 12 sq. in

then find the area of the square

area = lw

=(4 in) (4 in)

= 16 sq in.

then add

Surface area = 4 (12 sq in.) + 16 sq. in

= 64 sq. in

To evaluate the integral, rewrite the integrand as

[tex]x^{-x}=e^{\ln x^{-x}}=e^{-x\ln x}[/tex]

Recall that

[tex]e^x=\displaystyle\sum_{n=0}^\infty\frac{x^n}{n!}\implies x^{-x}=\sum_{n=0}^\infty\frac{(-x\ln x)^n}{n!}[/tex]

The leftmost sum is the well-known power series expansion for the function [tex]f(x)=e^x[/tex]. In the rightmost sum, we just replace [tex]x[/tex] with [tex]-x\ln x[/tex].

This particular power series has a property called "uniform convergence". Roughly speaking, it's a property that says a sequence of functions [tex]f_n(x)[/tex] converges to some limiting function [tex]f(x)[/tex] in the sense that [tex]f_n(x)[/tex] and [tex]f_{n+1}(x)[/tex] get arbitrarily close to one another. If you have an idea of what "convergence" alone means, then you can think of "uniform convergence" as a more powerful form of convergence.

Long story short, this property allows us to interchange the order of summation/integration to write

[tex]\displaystyle\int_0^1x^{-x}\,\mathrm dx=\int_0^1\sum_{n=0}^\infty\frac{(-x\ln x)^n}{n!}\,\mathrm dx=\sum_{n=0}^\infty\frac{(-1)^n}{n!}\int_0^1(x\ln x)^n\,\mathrm dx[/tex]

The integral can be tackled with a substitution,

[tex]x=e^{-u/(n+1)}\implies-(n+1)\ln x=u\implies\mathrm dx=-\dfrac1{n+1}e^{-u/(n+1)}\,\mathrm du[/tex]

so that the integral is equivalent to

[tex]\displaystyle\int_0^1(x\ln x)^n\,\mathrm dx=\int_\infty^0\left(e^{-u/(n+1)}\right)^n\left(-\frac u{n+1}\right)^n\left(-\frac1{n+1}e^{-u/(n+1)}\right)\,\mathrm du[/tex]

[tex]=\displaystyle\frac{(-1)^n}{(n+1)^{n+1}}\int_0^\infty e^{-u}u^n\,\mathrm du[/tex]

The remaining integral reduces to [tex]n![/tex], which you can derive for yourself via integration by parts/power reduction.

So we have

[tex]\displaystyle\int_0^1x^{-x}\,\mathrm dx=\sum_{n=0}^\infty\frac{(-1)^n}{n!}\cdot\frac{(-1)^nn!}{(n+1)^{n+1}}=\sum_{n=0}^\infty\frac1{(n+1)^{n+1}}[/tex]

which is the same as

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

and hence the identity.

Answer:

The discount is 179.70

Answer:

$419.30

Step-by-step explanation:

599*.30=179.7

599-179.7

=$419.30

The best answer would give the hight of the shadow without the angle of elevation, not knowing the time of the day the shadow was measured

Answer:

17.33 meters

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The function is f(x) = [tex]6^x[/tex]

we need to find the value of the function when x = 3. We simply plug in 3 into x and solve.

f (3) = [tex]6^3[/tex]

This means 6 multiplied by itself 3 times. So

6 * 6 * 6 = 216

correct answer is A

Answer:

He spent [tex]\frac{23}{40}[/tex] of his allowance

Step-by-step explanation:

The fraction Ebenezer spent on allowance is on Saturday is [tex]\frac{3}{8}[/tex]

The fraction he spent on Sunday is [tex]\frac{1}{5}[/tex]

The fraction of his allowance he spent is the fraction he spent on Saturday plus the fraction he spent on Sunday.

[tex]=\frac{3}{8}+\frac{1}{5}[/tex]

The LCD is

[tex]=\frac{3\times 5+8\times1}{40}[/tex]

[tex]=\frac{15+8}{40}[/tex]

[tex]=\frac{23}{40}[/tex]

It would be similar.

(3x2.5)+(9x12)

7.5+108

115.5

Answer:

3(2.5)+  9(12)=

Multiply

7.5 + 108= 115.5

Step-by-step explanation:

Plzzz brainlist !!!

46:84, it can be simplified to 23:42

A ratio can be written in three different forms and then at that point will you simplify it. 46 width to 84 length, 46:84, 46/84. You can divide 46/84 by 2/2 which will then give you 23/42 or 23:42 or 23 mm wide to 42 mm long. Depends how you choose to express this ratio! Hope that helps

The answer is 392

Volume (for pyramid) = Length(width) Hight/3

Answer:

392 cm³

Step-by-step explanation:

The volume of a pyramid is one third the height times the area of the base.

V = ⅓ h A

The base is a square, so the area is the width times length.

V = ⅓ h wl

Given that h = 6 cm, w = 14 cm, and l = 14 cm:

V = ⅓ (6 cm)(14 cm)(14 cm)

V = 392 cm³

ANSWER

(0,-3)

EXPLANATION

The point which is a solution to the inequality must lie in the solution region ( the shaded region)

Also the boundary line is solid. This means that any point on the boundary line is a solution.

(6,0) zero falls outside the shaded region.

(5,-5) is also not in the shaded region.

(0,-5) is also not in the shaded region.

(0,-3) lies on the boundary line therefore it is a solution.

Answer: is 0,-3

Step-by-step explanation:

Answer:

[tex]\large\boxed{6x^2-4x-5(2x^2+3x)=-4x^2-19x}[/tex]

Step-by-step explanation:

[tex]6x^2-4x-5(2x^2+3x)\qquad\text{use the distributive property}\\\\=6x^2-4x+(-5)(2x^2)+(-5)(3x)\\\\=6x^2-4x-10x^2-15x\qquad\text{combine like terms}\\\\=(6x^2-10x^2)+(-4x-15x)\\\\=-4x^2-19x[/tex]

Answer:

Step-by-step explanation:

I learned to solve these with a box method.

        6x^2     -4x     -5

2x^2  

3x

with this method you add the matching terms

       6x^2     -4x     -5

2x^2  | 1 | 2 | 3

3x      | 2 | 3 | 4

          6x^2     -4x     -5

2x^2 | 12x^4 | -8x^3 | -10x^2

3x     | 18x^3 | -12x^2 | -15x

12x^4 + 10x^3 - 22x^2 - 15x

Answer:

Yes, the sides are in the ratio 2:5.

Can you mark me as the brainliest??

Answer:  The correct option is

(B) Yes, the sides are in the ratio 2:5.

Step-by-step explanation:  We are given to check whether the triangles can be similar based on the side lengths alone.

From the figure, we note that

the sides lengths of the triangle RST are

RS = 3.0 cm, ST = 6.0 cm  and RT = 6.4 cm.

and the corresponding side lengths of triangle XUW are

XU = 7.5 cm, UW = 15.0 cm  and  XW = 16.0 cm.

So, the ratio of the corresponding sides of the two triangles are as follows :

[tex]\dfrac{RS}{XU}=\dfrac{3}{7.5}=\dfrac{30}{75}=\dfrac{2}{5},\\\\\\\dfrac{ST}{UW}=\dfrac{6}{15}=\dfrac{2}{5},\\\\\\\dfrac{RT}{XW}=\dfrac{6.4}{16}=\dfrac{64}{160}=\dfrac{2}{5}.[/tex]

Therefore, we get

[tex]\dfrac{RS}{XU}=\dfrac{ST}{UW}=\dfrac{RT}{XW}=\dfrac{2}{5}=2:5.[/tex]

Hence, the corresponding sides are proportional and they are in the ratio 2 : 5.

Thus, (B) is the correct option.

ln(.0006) = -7.42

Any questions please just ask.

Answer:

Second Option: =  2(y-2x)/(3y-5x)

Step-by-step explanation:

The expression is:

=(2/x-4/y)/((-5)/y+3/x)

Taking LCM in both, numerator and denominator

=  ((2y-4x)/xy)/((-5x+3y)/xy)

Since we know,  

(a/b)/(c/d)=ad/bc

Applying the rule to the given fraction:

=(2y-4x)(xy)/(-5x+3y)(xy)  

xy will be cancelled and we will be left with:

=(2y-4x)/(-5x+3y)

Taking 2 as common:

=  2(y-2x)/(3y-5x)

So the second option is the correct answer. ..

Answer:

See the attachment for a plot

Step-by-step explanation:

I find it convenient to plot lines using their x- and y-intercepts, when those are integers. To find the intercepts, we can divide the equation by the constant on the right:

x/10 +y/5 = 1

This is "intercept form". The denominator in each term is the corresponding intercept:

the x-intercept is 10, point (10, 0)

the y-intercept is 5, point (0, 5)

We can choose another value of y to find a third solution. Let y=2. Then we have ...

-x -2(2) = -10 . . . . . put 2 for y in the original equation

-x = -6 . . . . . . . . . . add 4

x = 6 . . . . . . . . . . . . multiply by -1

A third point is (6, 2)

Answer:

B, f(x) = 2|x - 2| + 6

Step-by-step explanation:

the functions shown have vertical stretches, horizontal shifts, and vertical shifts as a transformation

we do not need to focus on the stretch, and moreso the shifts

the horizontal shift takes place on the x-axis and it is written with the parent function (in this case the parent function is |x|). when the shift is negative (ex: x -2), this means that the x-coordinate would be positive. if the shift is positive (ex: x + 2) the x-coordinate would be negative

the vertical shift takes place on the y-axis and unlike the horizontal shift, is written on the outside of the parent function, like the +6 and -6 in each of the functions we are given. when a shift is positive (ex: +6), the y-coordinate is positive and when a shift is negative (ex: -6) the y coordinate is negative

using this information, we can see that 2|x - 2| + 6 fits this criteria, as we have a positive vertex

therefore the answer is B, f(x) = 2|x - 2| + 6

The function that has a vertex at (2, 6) is:

f(x) = 2|x-2| + 6

To find the function with a vertex at (2, 6), we need to examine the general form of the absolute value function and how it affects the position of the vertex.

The general form of the absolute value function is f(x) = a |x - h| + k, where (h, k) represents the vertex of the absolute value function.

Given the vertex (2, 6), we have h = 2 and k = 6.

Now, let's analyze each given function:

1. f(x) = 2|x-2| - 6

  This function has a vertex at (2, -6), not (2, 6). So, it's not the correct function.

2. f(x) = 2|x-2| + 6

  This function has a vertex at (2, 6), which matches our given vertex. So, it could be the correct function.

3. f(x) = 2|x + 2| + 6

  This function has a vertex at (-2, 6), not (2, 6). So, it's not the correct function.

4. f(x) = 2|x + 2| - 6

  This function has a vertex at (-2, -6), not (2, 6). So, it's not the correct function.

Therefore, the function that has a vertex at (2, 6) is:

f(x) = 2|x-2| + 6

Answer:

x+3

Step-by-step explanation:

1. Use formula for the difference of squares:

[tex]a^2-b^2=(a-b)(a+b)[/tex]

to factor

[tex]x^2-9=(x-3)(x+3).[/tex]

2. Factor [tex]x^2+8x+15:[/tex]

[tex]x^2+8x+15=x^2+3x+5x+15=x(x+3)+5(x+3)=(x+3)(x+5).[/tex]

Now you can see that [tex]x+3[/tex] is the common factor.

Answer:

x + 3

Step-by-step explanation:

x² - 9 ← is a difference of squares and factors as

x² - 9 = (x - 3)(x + 3)

To factor x² + 8x + 15

Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)

The factors are + 5 and + 3, since

5 × 3 = 15 and 5 + 3 = 8, thus

x² + 8x + 15 = (x + 5)(x + 3)

Thus the factor (x + 3) is common to both

Answer:

Option B. [tex]\$1,224[/tex]

Step-by-step explanation:

step 1

Find the area of the playground

The area of the playground is equal to the area of a rectangle plus the area of a triangle

[tex]A=(10)(36)+\frac{1}{2}(36)(24-10)=612\ ft^{2}[/tex]

step 2

Find the number of bags of wood chips needed

by proportion

[tex]\frac{1}{4}=\frac{x}{612} \\ \\x=612/4\\ \\ x=153\ bags[/tex]

step 3

Find the cost

[tex]\$8.00*(153)=\$1,224[/tex]

Answer:

ANSWER IS B

Step-by-step explanation:

YOUR WELCOME ENDGEUNITY STUDENTS

Tim is 20 cm higher on height

Tim's height is 1m 20cm (120cm) and Erica's height is 1m (100cm). The simplified ratio of their heights is 6:5.

To find the simplified ratio of Tim's height to Erica's height, we need to convert both heights to the same unit of measurement (centimeters) before calculating the ratio.

Tim's height = 1m 20cm = 100cm + 20cm = 120cm

Erica's height = 1m = 100cm

Now, we can calculate the ratio of Tim's height to Erica's height:

Ratio = Tim's height / Erica's height

Ratio = 120cm / 100cm

Ratio = 6/5

The simplified ratio of Tim's height to Erica's height is 6:5.

To know more about ratio:

https://brainly.com/question/13419413

#SPJ2

Answer:

[tex]\boxed{100 - 10x}[/tex]

Step-by-step explanation:

The distributive property states that

a(b + c) = a·b + a·c

We can use this property solve your equation.

10(10 – x)

Distribute the 10

10×10 – 10×x

Do the multiplications

[tex]\boxed{100 - 10x}[/tex]

Answer:

7/12

Step-by-step explanation:

Julie and Stefanie shared 1 whole candy bar. Therefore, the candybar can be represented as 1.

To find out what fraction of the candy bar Stefanie and Julie ate, simply add how much each girl ate.

Stefanie ate 1/4 and Julie ate 1/3. 1/4 + 1/3 = 7/12.

Therefore, Stefanie and Julie ate 7/12 of the candy bar. I hope this helps!

7/12

one fourth equals three twelfths and one third equals four twelfths and u add them

Answer:

c because f(x) is x+6 and the bracket means multiply

Answer:

b

Step-by-step explanation:

Given

3y + 15x = - 15

Isolate 3y by subtracting 15x from both sides

3y = - 15x - 15 ( divide all terms by 3 )

y = - 5x - 5 → b

Answer:

B

Step-by-step explanation:

Answer:

the y-coordinate is ±√21

Step-by-step explanation:

Aren't you saying that the point lies ON the circle?

If so:

(x - h)^2 + (y - k)^2 = r^2

This becomes

x^2 + y^2 = r^2 because the center is at (0, 0).

This becomes x^2 + y^2 = 25 because the radius is 5.

Let's substitute -2 for x and find y:

4 + y^2 = 25, or y^2 = 21

Then the y-coordinate is ±√21

Answer:

The answer is B 4.6

Step-by-step explanation:

Its on edgen 2022

Answer:

1/3

Step-by-step explanation:

4 and 5 are two terms

two out of 6 terms is one third

therefore it has a probability of one out of three

Answer:

the answer is 2/6 i just did this test

Answer:

$0.96

Step-by-step explanation:

To find the unit price is to find the price of 1 meter.

9m = $8.64

1 m = 8.64 ÷ 9 = $0.96

Step-by-step explanation:

[tex]\text{Use}\ \dfrac{a^n}{a^m}=a^{n-m}\ \text{and}\ (a^n)^m=a^{nm}\\\\\left(\dfrac{a^x}{a^y}\right)^{x-y}=\left(a^{x-y}\right)^{x-y}=a^{(x-y)(x-y)}=a^{(x-y)^2}\\\\\left(\dfrac{a^y}{a^z}\right)^{y-z}=\left(a^{y-z}\right)^{y-z}=a^{(y-z)(y-z)}=a^{(y-z)^2}\\\\\left(\dfrac{a^z}{a^x}\right)^{z-x}=\left(a^{z-x}\right)^{z-x}=a^{(z-x)(z-x)}=a^{(z-x)^2}\\\\\text{Use}\ a^n\cdot a^m=a^{n+m}\\\\a^{(x-y)^2}\cdot a^{(y-z)^2}\cdot a^{(z-x)^2}=a^{(x-y)^2+(y-z)^2+(z-x)^2}[/tex]

[tex]\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-y)^2=x^2-2xy+y^2\\(y-z)^2=y^2-2yz+z^2\\(z-x)^2=z^2-2zx+x^2\\\\=a^{x^2-2xy+y^2+y^2-2yz+z^2+z^2-2zx+x^2}\\\\\text{combine like terms}\\\\=a^{(x^2+x^2)+(y^2+y^2)+(z^2+z^2)-2xy-2yz-2zx}\\\\=a^{2x^2+2y^2+2z^2-2xy-2yz-2zx}\qquad\text{distributive}\\\\=a^{2(x^2+y^2+z^2)-2(xy-yz-zx)}\\\\\text{From the equastion we know:}\ x^2+y^2+z^2=xy+yx+zx.\\\text{Therefore}\\\\=a^{2(x^2+y^2+z^2)-2(x^2+y^2+z^2)}=a^0=1[/tex]

Answer:

x = 113

Step-by-step explanation:

The corresponding angles in both triangles are congruent

Hence x = 113

Answer:

[tex]\frac{1}{16}[/tex]

Step-by-step explanation:

The experimental probability is based on what already happened.

So we see that both of them found a total of 11 + 3 + 36 + 40 + 134 = 224 coins.

The coins that are worth MORE THAN 10 cents are 11 quarters and 3 fifty-cent pieces (we exclude dimes because we want MORE THAN 10 cents, NOT 10 cents exactly).

So 11 + 3 = 14 coins are worth MORE THAN 10.

So the probability of finding one worth more than 10 cents next is 14/224 = 1/16