23) Find the length of the median of each trapezoid.

A) 7.4
C) 5.6
B) 5.8
D) 6.1

Answer:

bro what is the diagonal of second square.

By some properties of logarithms, rewrite the equation as

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

so that

(a - 2b)² = ab

Expand the left side:

a ² - 4ab + 4b ² = ab

Rearrange terms to get a quadratic equation in a/b :

a ² - 5ab + 4b ² = 0

b must be greater than 0, otherwise log(b) doesn't exist, and the same goes for a. So we can divide by b ² to get

a ²/b ² - 5a/b + 4 = 0

Factorize and solve for a/b :

(a/b - 4) (a/b - 1) = 0

==>   a/b = 4   or   a/b = 1

However, if a/b = 1, then a = b makes a - 2b = -b. But we must have b > 0, so we omit the second solution and end up with

a/b = 4

Answer:

the number is 2.66

Step-by-step explanation:

[tex]6.7+5x=20[/tex]

Step 1. Subtract 6.7 from both sides

[tex]5x=20-6.7[/tex]

[tex]5x=13.3[/tex]

Step 2. Isolate the variable

[tex]\frac{5x}{5} =\frac{13.3}{5}[/tex]

[tex]x=2.66[/tex]

The number is 2.66

Answer:

[tex]y=\displaystyle\frac{3}{2}x-3[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x=0)

We're given:

⇒ x-intercept = 2

⇒ y-intercept = -3

1) Determine the slope (m)

[tex]m=\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Given the x- and y-intercepts, we can rewrite them as points:

x-intercept = 2

⇒ (2,0)

y-intercept = -3

⇒ (0,-3)

Plug these points into the equation:

[tex]m=\displaystyle\frac{0-(-3)}{2-0}\\\\m=\displaystyle\frac{0+3}{2}\\\\m=\displaystyle\frac{3}{2}[/tex]

Therefore, the slope of the line is [tex]\displaystyle\frac{3}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\displaystyle\frac{3}{2}x+b[/tex]

2) Plug in the y-intercept (b)

[tex]y=\displaystyle\frac{3}{2}x+b[/tex]

We're given the y-intercept: -3. Plug this into [tex]y=\displaystyle\frac{3}{2}x+b[/tex]:

[tex]y=\displaystyle\frac{3}{2}x+(-3)\\\\y=\displaystyle\frac{3}{2}x-3[/tex]

I hope this helps!

Analyzing the text, we find that the function is decreasing over the following intervals: (0, 1)

-------------------------

Going from maximum to minimum, meaning that between them the function decreases, thus, the first interval it is decreasing is between (0,1).

Going up, increases.

-------------------------

Thus, the function decreases over the following interval: (0, 1)

A similar question is given at https://brainly.com/question/17875907

[tex]\\ \sf\longmapsto \left[{3a+b\atop a-b}\:\:\:{3c-d\atop a+b+d}\right]=\left[{3\atop 5}\:\:\;{6\atop 2d-1}\right][/tex]

Now constructing equations

[tex]\\ \sf\longmapsto 3a+b=3\dots(1)[/tex]

[tex]\\ \sf\longmapsto a-b=5\dots(2)[/tex]

[tex]\\ \sf\longmapsto 3c-d=6\dots(3)[/tex]

[tex]\\ \sf\longmapsto a+b+d=2d-1\dots(4)[/tex]

Adding eq(1) and (2)

[tex]\\ \sf\longmapsto 4a=8[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{8}{4}[/tex]

[tex]\\ \bf\longmapsto a=2[/tex]

Put the value in eq(2)

[tex]\\ \sf\longmapsto a-b=5[/tex]

[tex]\\ \sf\longmapsto b=a-5[/tex]

[tex]\\ \sf\longmapsto b=2-5[/tex]

[tex]\\ \bf\longmapsto b=-3[/tex]

put the values in eq(4)

[tex]\\ \sf\longmapsto a+b+d=2d-1[/tex]

[tex]\\ \sf\longmapsto 2+(-3)+d=2d-1[/tex]

[tex]\\ \sf\longmapsto d-1=2d-1[/tex]

[tex]\\ \sf\longmapsto d-2d=-1+1[/tex]

[tex]\\ \sf\longmapsto -d=0[/tex]

[tex]\\ \bf\longmapsto d=0[/tex]

Put the value in eq(3)

[tex]\\ \sf\longmapsto 3c-d=6[/tex]

[tex]\\ \sf\longmapsto 3c-0=6[/tex]

[tex]\\ \sf\longmapsto 3c=6+0[/tex]

[tex]\\ \sf\longmapsto 3c=6[/tex]

[tex]\\ \sf\longmapsto c=\dfrac{6}{3}[/tex]

[tex]\\ \sf\longmapsto c=2[/tex]

1a. 128

1b. 81

1c. 64

1d. 25

1e. 343

1f. 100000

1g. 64

1h. 0

1i. 13

1j. 1

2a. 243

2b. 64

2c. 36

2d. 625

2e. 1331

2f. 10000000

2g. 81

2h. 0

2i. 17

2j. 1

Answer:

Three more than twice a number is equal to four less than the number. find the number.

Answer:

A) both functions are linear

B) f(x) = 7446.4x + 178713.6 and f(x) = 11000x + 179000

C) House 2 will value $106894.4 more than house 1.

Step-by-step explanation:

A) Value Increase from year 1 to year 2:

House 1: 193,606.40 - 186,160 = 7446.4

House 2: 201,000 - 190,000 = 11000

Value Increase from year 2 to year 3:

House 1: 201,350.66 - 193,606.40 = 7744.26

House 2: 212,000 - 201,000 = 11000

This means that a constant increament in x variable gives a constant increament in both houses vales. Then, both functions are linear.

B) The slope is the same as the value increment from one year to the next one.

slope (m) of House 1: 7446.4

slope (m) of House 2: 11000

General formula of a line:

f(x) = mx+b

Replacing with a known point:

House 1

186,160 = 7446.4(1) + b

b = 186,160 - 7446.4 = 178713.6

equation: f(x) = 7446.4x + 178713.6

House 2

190,000 = 11000(1) + b

b = 190,000 - 11000 = 179000

equation: f(x) = 11000x + 179000

C) Replacing x = 30 into each equaiton:

Value of House 1 after 30 years

f(x) = 7446.4(30) + 178713.6 = 402105.6

Value of House 2 after 30 years

f(30) = 11000(30) + 179000 = 509000

Then, house 2 will value 509000 - 402105.6 = $106894.4 more than house 1.

Answer:

x = 7/2

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj side / hypotenuse

cos 45 = x / 7 sqrt(2) /2

7 sqrt(2)/2 cos 45 = x

7 sqrt(2)/2 (1/ sqrt(2))= x

7/2 = x

Answer:

540°

Step-by-step explanation:

90 revolutions = 360°×90 = 32400°

32400° in 60 sec or 1 min

so, in 1 sec 32400/60 = 540°

Answer:

540°

Step-by-step explanation:  

90 revolutions = 360°×90 = 32400°  

=> 32400° in 60 sec or 1 min  

=> In 1 sec,

=> 32400/60 = 540°

Answer:

133.33

Step-by-step explanation:

Answer:

133 1/3 or 133.33

Step-by-step explanation:

So first let's turn 15% into a decimal. For me personally, its less intimidating that way.

15%=0.15

now, let's say the number we are trying to find is x.

A trick I use for these questions is to look at the words. "Of" is used when something is multiplied. "Is" is used for equal signs. So if 20 is 0.15 of x, our formula is easy to figure out!

20=0.15x

x=133.33333...

x=133 1/3

Answer:

It is a rational number.

Step-by-step explanation:

A rational number is a number that repeats with the same number, or terminates. An irrational number is a number that repeats, but not with a constant number, like pi for example. 3.739 terminates at the end, so it is a rational number.

Hope this helps :)

Answer is: B

Step-by-step explanation: correct answer is B

b  

2

−a  

2

Given, acotθ+bcscθ=p

           bcotθ+acscθ=q

⇒p  

2

−q  

2

=(p−q)(p+q)

                   =[acotθ+bcscθ−bcotθ−acscθ][acotθ+bcscθ+bcotθ+acscθ]

                   =[cotθ(a−b)−cscθ(a−b)][cotθ(a+b)+cscθ(a+b)]

                   =(a−b)(cotθ−cscθ)(a+b)(cotθ+cscθ)

                   =(a  

2

−b  

2

)(cot  

2

θ−csc  

2

θ)

                   =(−1)(a  

2

−b  

2

)[∵csc  

2

θ−cot  

2

θ=1]

                   =(b  

2

−a  

2

)

Step-by-step explanation:

16d-4+5d= -67

21d-4= -67

21d= -67+4

d= -63/21

d = -3

hope it helps

Answer: d = -3

Step-by-step explanation:

⇒16d -(4-5d) = -67

⇒16d -4 +5d = -67

⇒21d = -67+4

⇒21d = -63

⇒d = -63/21

⇒d = -3

Therefore d = -3

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Answer:

$525

x+ y = 975

x - 75 = y

x + x - 75 = 975

2x = 1050

x = $525

Step-by-step explanation:

Answer:

Below!

Step-by-step explanation:

Let x represent the cost of the bench

The cost of the garden table can be represented by this equation:

      x + 75

x + (x + 75) = 975

2x + 75 = 975

2x = 900

Divide both sides by 2

x = 450

The bench costs $450

The garden table costs 450 + 75 = $525

Hope this helps! Best of luck <3

I would really appreciate brainliest if possible :)

Answer:

c = 49

Step-by-step explanation:

Let c = number of cards originally

give away 8 cards

c-8

Now she has 41

c-8 = 41

Add 8 to each side

c-8+8 = 41+8

c = 49

Answer:

49

Step-by-step explanation:

In the end, if she now has 41 cards you have to do inverse operation. Since you subtracted to take away those 8 cards she gave away, you have to add back in 8 cards to the 41 if you want to find what she had before. So, 8 + 41 = 49

Hope this helps! :)

Answer: x= 42.3

Step-by-step explanation:

Sqrt a^2 + b^2 - (2ab)(cos 100)

Sqrt 25^2 + 30^2 - (2)(25)(30)(cos 100)

42.3

Answer:

13 sports books and 10 unknown books is 23 books

Step-by-step explanation:

we already know scott read 23 books total, we also know that he read 10 mystery books.

subtracting 10 unknown books from 23 total books, we get 13 sports books as your answer

Answer:

considering it was simple interest,

We have the formula:

I = PRT ÷ 100

where,

for the first part of the question,

Thus, I = (2160 × 20 × 4)÷ 100

I = Rs. 1728

Now, for the second part,

T = 100×I÷PR

T = 100 × 1728÷(1800 × 12)

T = 8 Years

Answer:

Solution given:

[tex]\sqrt{6-15x} =5x+d[/tex]......(1)

d=?

and

x=-2

Substituting value of x in equation 1.

[tex]\sqrt{6-15*-2} =5*-2+d[/tex].

Solve the like terms

[tex]\sqrt{6+30} =-10+d[/tex].

solve the like terms

[tex]\sqrt{36} =-10+d[/tex].

we have square root of 36 is 6.

6=-10+d

d=16

the value of constant term is 16.

The value of d for the expression [tex]\sqrt{6-15x} = 5x+d[/tex] is 16.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The value of 'd' is calculated as,

[tex]\sqrt{6-15x} = 5x+d[/tex]

Put the value of x =-2,

[tex]\sqrt{6-(15\times -2)}=(5\times -2)+d[/tex]

√36 = -10 + d

6 = -10 + d

d = 16

To know more about Expression follow

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Answer:

The answer for no 2 is x = 3+y or y+3

The actual dimensions of the check out area is 25 m by 35 m.

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Given the scale of:

1 cm = 5 m, hence:

Length = 5 cm = 5 cm * 5 m per cm = 25 m

Width = 7 cm = 7 cm * 5 m per cm = 35 m

The actual dimensions of the check out area is 25 m by 35 m.

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Answer:

#1

The cost to produce 500 helmets:

#5

The break-even point is the price when profit is zero:

#6

There will be a profit as the selling price is greater than the break even point:

Find cost of x=500 helmets

Break even point

So

There is profit as its less than 18

Answer:

x=2,y=2

Step-by-step explanation:

3y-1 = 5

or, 3y = 5+1

or, y = 6/3

y = 2

2x+1 = 3y-1

or, 2x = 3×2-1-1

or, 2x = 4

or, x = 2

[tex]\\ \sf\longmapsto \left[{2x+1\atop 2x+x}\:\:\:{3y-1\atop 3}\right]=\left[{3y-1\atop 4}\:\:\;{5\atop 3}\right][/tex]

[tex]\\ \sf\longmapsto 3y-1=5[/tex]

[tex]\\ \sf\longmapsto 3y=5+1[/tex]

[tex]\\ \sf\longmapsto 3y=6[/tex]

[tex]\\ \sf\longmapsto y=2[/tex]

Put the value in 1st one

[tex]\\ \sf\longmapsto 2x+1=3y-1[/tex]

[tex]\\ \sf\longmapsto 2x+1=3(2)-1[/tex]

[tex]\\ \sf\longmapsto 2x+1=6-1[/tex]

[tex]\\ \sf\longmapsto 2x+1=5[/tex]

[tex]\\ \sf\longmapsto 2x=5-1[/tex]

[tex]\\ \sf\longmapsto 2x=4[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{4}{2}[/tex]

[tex]\\ \sf\longmapsto x=2[/tex]

Answer:

Step-by-step explanation:

B ----> Base Area

Base is triangle

base = b = 10 in

height = h = 6 in

Area of base B = [tex]\frac{1}{2}bh[/tex]

                         [tex]=\frac{1}{2}*10*6\\\\= 5* 6\\\\= 30 \ in^{2}[/tex]

B = 30 in²

H = 15 in

Volume of triangular prism = BH

                                            = 30 * 15

                                            = 450 in³

Answer:

C

Step-by-step explanation:

Answer:

Im not sure what is in the algebra 1 module 4 but for algebra 1 you should study how to graph equations, solve system of equations with substitution and elimination. those topics, at least for e, have been a little tricky

Step-by-step explanation:

Answer:

25/81 is already in the simplest form. It can be written as 0.308642 in decimal form (rounded to 6 decimal places).

Answer:

Step-by-step explanation:

In the coordinate given, x = 3 and y = b. If we plug those into the given equation, we can solve for b:

y = 2x + 9 ---> b = 2(3) + 9 so

b = 6 + 9 and

b = 15

Answer:

b = 15

Step-by-step explanation:

y = 2x+9

Let x = 3 and y=b

b = 2(3)+9

b = 6+9

b = 15