The formula for the area A of a trapezoid is A=1/2(b1+b2)h, where b1 and b2 represents the lengths of the bases and h represents the height. Which equation can be used to find the height of a trapezoid?
A. h=2A-b1-b2
B. h=2A/b1+b2
C. h=A(b1+b2)/2
D. h=A-2/b1-b2

Answer:

1920 cm^3

Step-by-step explanation:

Divide into the rectangular prism on top, and the one on the bottom. Whole = sum of parts, so you find the volumes of those two separately and add them together to get the total.

V of rectangular prism = l x w x h (length x width x height)

Top:

l = 10

w = 8

h = 14 - 10 = 4

10 x 8 x 4 = 320

Bottom:

l = 10 + 10 = 20

w = 8

h = 10

20 x 8 x 10 = 1600

1600 + 320 = 1920

The volume of the rectangular prism together with subparts is 1920 cubic meters.

The volume of the rectangular prism is the product of the length, breadth, and height of the given prism.

Volume of rectangular prism = (length x width x height)

Divide into the rectangular prism on top, and the one on the bottom.

total volume = sum of parts, so we need to find the volumes of those two separately and add them together to get the total.

Top

l = 10

w = 8

h = 14 - 10 = 4

The volume of the rectangular prism = length x width x height

= 10 x 8 x 4 = 320

Bottom

l = 10 + 10 = 20

w = 8

h = 10

The volume of the rectangular prism = length x width x height

= 20 x 8 x 10 = 1600

The total volume of the shape = 1600 + 320 = 1920

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Answer:

B

Step-by-step explanation:

[tex]5\cdot 21^{5x} = 16 \\\ 21^{5x} = \frac{16}{5} \\\\ 21^{5x} = 3.2 \\\ log 21^{5x} = log 3.2 \\\ 5x\cdot log 21 = log 3.2 \\\ 5x = \frac{log 3.2}{log 21} \\\\\ x = \frac{log 3.2}{5\cdot log 21}[/tex]

I hope I helped you.

Answer:

∠DBC = 40°

Step-by-step explanation:

∠5 = ∠3 + ∠4 = 180° - ∠6 . . . . relationship of angles at a transversal, vertical angles

∠3 = 180° - ∠1 - ∠2 . . . . . . sum of angles of a triangle

Then

∠4 = 180° - ∠6 - (180° - ∠1 - ∠2) = ∠1 +∠2 -∠6 . . . . substitute for ∠3

∠4 = 65° +60° -85° = 40°

∠4 = ∠DBC = 40°

Answer with explanation:

3.19 =There are two digits after decimals.

An integer is set of numbers which includes both positive natural number, Negative Natural number and Zero.

[tex]3.19=\frac{319}{100}[/tex]

Here, 319 and 100 , both are integers.

You can write equivalent form of

[tex]\frac{319}{100}=\frac{319 \times 2}{100 \times 2}=\frac{319 \times 3}{100 \times 3}=........[/tex]

The value 3.19 expressed as a ratio of two integers is :

[tex] \frac{319}{100} [/tex]

Given the decimal :

3.19 which can be expressed as an integer by multiplying with the Number of decimal places after the decimal Point.

To express 3.19 as a combination of two integer values, we divide 319 by 100

Hence, 3.19 = 319 ÷ 100

[tex] \frac{319}{100} [/tex]

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Answer:

61.56/6

10.26

Step-by-step explanation:

For this case we must indicate how much each of the 6 people should pay knowing that the bill is $ 61.56.

For this, we divide:

Let "x" be the amount of money each person must pay, then:

[tex]x = \frac {61.56} {6}\\x = $ 10.26[/tex]

Thus, each one must pay $ 10.26.

Answer:

$ 10.26.

Answer:

The correct answer is D) The rate in which he burns calories

Step-by-step explanation:

We can tell this because the slope is always the change in y value over the change in x value. Since the y value is calories and the x value is minutes, we get the following.

Calories/minute

Which can also be written as calories per minute, which is a rate.

The graph says about the rate of calorie burned.

A plane created by the intersection of two perpendicular coordinate axes is referred to as a cartesian plane. The x-axis is the horizontal axis, while the y-axis is the vertical axis. These axes cross at the origin, whose location is specified as (0, 0). Any location on the cartesian plane is shown as (x, y).

Given the graph between calories burned and time in minutes,

X axis shows the time and Y axis shows the calorie burned,

The ratio of the change in y value to the change in x value is the slope. We obtain the following because the y value is calories and the x value is minutes.

Calories/minute

This is a rate and can also be represented as calories per minute.

Hence Option D is best suitable for condition.

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Answer:

y = ln(x -5)

Step-by-step explanation:

The log function has a vertical asymptote at x=0 and goes through the point (1, 0). This looks like that function translated 5 units to the right. When f(x) is translated right 5 units, x is replaced by x-5. The graph seems to be of the function ...

... y = ln(x -5)

_____

The natural log function will go through the points (2.718, 1) and (7.389, 2), as this curve appears to do.

Answer:

(53.35/11)*4=19.40

Step-by-step explanation:

The cost of 4 key chains is $19.40.

Cost per key chain = Total cost / Number of key chains

                                 = $53.35 / 11

                                   ≈ $4.85

Cost for 4 key chains = Cost per key chain * 4

                                     = $4.85 * 4

                                     = $19.40

So, 4 key chains cost $19.40.

Answer:

x=9     and x=1

Step-by-step explanation:

If 6 is added to the square of an integer, the result is 3 less than 10 times that integer.

x^2 +6 = 10x-3

Subtract 10x from each side.

x^2 -10x +6 = 10x-10x-3

x^2 -10x +6 = -3

Now add 3 to each side.

x^2 -10x +6+3 = -3+3

x^2 -10x +9 = 0

Now we can factor the left side of the equation.

What numbers multiply together to give positive 9 and add together to give -10?

-9* -1 = 9      -9+-1 = -10

(x-9)  * (x-1) = 0

Using the zero product property

x-9 = 0 and x-1 = 0

x-9+9 = 0+9     x-1+1 = 0+1

x=9     and x=1

Answer:

Without an actual drawing to show which side is 74 inches, then the answer could either be the square root of 6052 inches OR 70 inches.  

Step-by-step explanation:

All right triangles follow the rule of the pythagorean theorem, which states that a^2 + b^2 = c^2, where 'a' and 'b' represent the legs of a triangle and 'c' represents the hypotenuse.  The legs of a right triangle are the two sides that come together to form the 90 degree angle and the hypotenuse is the angled line across from the 90 degree angle.  In this case, the height would have to represent one of the legs, while the other 'side' would need to represent either a leg or the hypotenuse (depending on the actual diagram presented which is not shown in the problem posted).  So, if you substitute the values given into our legs, or 'a' and 'b', you would end up with the value of 'c' as the square root of 6052.  However, if the given side is actually the hypotenuse, you would solve by subtracting the c^2 from a^2 to get 'b'=70 inches.  

The height of the right angle triangle is 70 inches

Using Pythagoras's theorem for right angle triangle

c²  = a² + b²

where

c = hypotenuse

a and b are the other 2 legs.

Therefore,

c = 74 inches

a = 24 inches

74² = 24² + b²

5476  = 576 + b²

5476 - 576 = b²

b² = 4900

square root both sides

b = √4900

b = 70 inches

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Answer:

2/(7a) < x < 7

Step-by-step explanation:

The product of roots of ax² +bx +c is c/a. In this case, that means the second root of the equation is ...

... 2/(7a)

Since a < 0, the parabola opens downward and 2/(7a) < 0. The quadratic function will be positive between the two roots, on the interval ...

... 2/(7a) < x < 7

Answer:

r= 3b

Step-by-step explanation:

We can find the slope of the line by using

m= (y2-y1) /(x2-x1)

   = (12-9)/ (4-3)

   = 3/1

The slope is 3

We can use the point slope form for the equation of a line

y-y1 = m(x-x1)

y-12 = 3(x-4)

Distribute the 3

y-12 = 3x-12

Add 12 to each side

y -12+12 = 3x-12+12

y= 3x

let r =y

and x=b

r = 3b

Statement/Reason is a method of presenting your logical thought process as you go from the "givens" in a problem statement to the desired conclusion. Each statement expresses the next step in the solution process. It is accompanied by the reason why it is true or applicable.

For example, if you have an equation that says ...

... x + 3 = 5

Your next "statement" might be

... x + 3 - 3 = 5 - 3

The "reason" you can make that statement is that the addition property of equality allows you to add the same quantity to both sides of an equation without violating the truth of the equality. You know this because you have studied the properties of equality and how they relate to the solution of equations.

In geometry (where you're more likely to encounter statement/reason questions), you know the statements you're allowed to make because you have studied the appropriate postulates and theorems. The "reason" is generally just the name of the applicable postulate or theorem. The "statement" is the result of applying it to your particular problem.

For example, if you have ∠ABC and ∠CBD, you might want to say (as part of some problem solution) ...

... m∠ABC + m∠CBD = m∠ABD

The reason you can say this is the angle addition postulate, which you have studied. It will tell you that the measures of non-overlapping angles with a common side and vertex can be added to give the measure of the angle that includes them both. (Many such postulates seem obvious, as this one does.)

_____

Side comment on geometric proofs

As you go along in geometry, you study and develop more and more theorems that you can use to find solutions to problems. Sometimes, you're required to use a restricted subset of the ones you know in order to prove others.

As an example, in some problems, you may be able to use the fact that the midline of a triangle is parallel to the base; in other problems, you may be required to prove that fact.

I sometimes found it difficult to tell which theorems I was allowed to use for any given problem. It may help to keep a list that you can refer to from time to time. Your list would tell you the name of the theorem, axiom, or postulate, and what the meaning of it is, and where it might be applied.

_____

Which reason fits which statement?

The "reason" is telling how you know you can make the statement you made. It is anwering the question, "what allows you to make that statement?"

How do I form true statements?

The sequence of statements you want to make comes from your understanding of the problem-solving process and the strategy for solution you develop when you analyze the problem.

Your selection of statements is informed by your knowedge of the properties of numbers, order of operations, equality, inequality, powers/roots, functions, and geometric relationships. You study these things in order to become familiar with the applicable rules and properties and relationships.

A "true" statement will be one that a) gets you closer to a solution, and b) is informed by and respects the appropriate properties of algebraic and geometric relations.

In short, you're expected to remember and be able to use all of what you have studied in math—from the earliest grades to the present. Sometimes, this can be aided by remembering a general rule that can be applied different ways in specific cases. (For me, in Algebra, such a rule is "Keep the equal sign sacred. Whatever you do to one side of an equation, you must also do to the other side.")

Answer:

-7(x-5)= y+9

Its kind of hard to explian but...

Hope this helped!! Have a good day c;

Answer:y-6=-7(x-3)

Step-by-step explanation:(3,6) and 5,-8)

Slope= -8-6/5-3

= -14/2

= -7

If your equation started out like this: y-6= then you need to use the point (3,6):

y-6=-7(x-3)

Answer:

<2 = 37.5 degrees

Step-by-step explanation:

Complementary angles add together to equal 90 degrees.

Let < 1 = x  and < 2 = y

x + y= 90

x = y+15

Substitute the second equation into the first equation.

(y + 15) + y = 90

Combine like terms

2 y + 15 = 90

Subtract 15 from each side.

2y+15-15 = 90-15

2y =75

Divide each side by 2

2y/2 = 75/2

y = 37.5

<2 = 37.5 degrees

See the attachment

In this context, "x" stands for "a number". Then 1/2x is "one-half of a number" and 3/4x is "three-fourths of a number."

3/4 - ( ) means "three-fourths minus ..."

( ) + 1/2 means "one-half more than ..." or "the sum of ... and one-half."

Putting these ideas together lets you choose the phrases as indicated below.

See attached graphs.

You are being asked to observe the graphs of the various equations and identify something they have in common. To answer the question, it usually works well to do exactly what the question asks you to do.

a: All three lines have a slope of at least 1 and pass through the origin.

b: These lines all have the same slope. They are parallel.

c: All three lines have a slope less than 1 and pass through the origin.

d: These are all the same line.

e: All of these lines intersect at the point (2, -2).

_____

Comment on the graphs

The number of attachments allowed here is limited, so some graphs have been combined. Where there are 3 lines, the first is red, the second is blue, the third is green.

Graphs for (a) and (c) appear on the same page. The graphs for (c) are shown as dashed lines.

Graphs for (b) and (d) appear on the same page. The graph for (d) is shown in orange (as a dashed line). All threee lines look exactly like this.

_____

Comment on the graphing program

These are graphed using the Desmos on-line graphing calculator. It has a tutorial available and is not difficult to learn for most simple graphing applications. (It prefers the variables x and y.) Graphs can be saved for later. (Here, screen shots are used because Brainly doesn't like external links.)

To find the x-intercept, set y=0 and solve.

... 0 = log(12x +7) -3

... 3 = log(12x +7) . . . . add 3

... 1000 = 12x +7 . . . . take the antilog. (10^3 = 1000)

... 993 = 12x . . . . . . . .subtract 7

... 82.75 = x . . . . . . . . divide by 12

To find the y-intercept, set x=0 and solve.

... y = log(12·0 +7) -3

... y = log(7) -3 . . . . . . simplify

... y ≈ 0.85 -3 = -2.15 . . . . use a calculator for the log function

Answer:

y = 3x-2

Step-by-step explanation:

We can find the slope using the formula

m = (y2-y1)/(x2-x1)

  = (16-4)/(6-2)

  =12/4

 =3

We then use the point slope form of a line

y-y1= m(x-x1)

y-4 = 3(x-2)

Distribute the 3

y-4= 3x-6

Add 4 to each side

y-4+4 = 3x-6+4

y = 3x-2

This is in slope intercept form

Answer:

33

Step-by-step explanation:

I think it would be 33 bc if you subtract 90-66 its 33 but

how did i get 90 bc 90 is a right angel.  

Answer:

D) 15

Step-by-step explanation:

We know the formula for direct variation is  

y=kx

Substituting y=5 and x=4 we can calculate k

5=k4

Divide each side by 4

5/4 =k

Now y= 5/4 x

If x =12

y =5/4*12

y = 15

the second degree term of the expression x^2 + 12x arrowRight the area of the culture banner

the first degree term of the expression x^2 + 12x arrowRight the increase in area of the culture banner to make the sports banner

the monomial, x, a factor of the expression x^2 + 12x arrowRight the width of the sports banner

the binomial, (x + 12), a factor of the expression x^2 + 12x arrowRight the length of the sports banner

The problem statement tells you x is the side length of the culture banner, and also the side length of the sports banner. It also tells you the length of the sports banner is 12 (inches) more than that of the culture banner, a value that can be written as x+12.

Of course, the area of a rectangle is the product of its length and width dimensions. Since the culture banner is a square of side length x, its area will be x^2. Since the sports banner is 12 inches longer and still x inches wide, the increase in area that represents will be 12x.

Answer:

39

Step-by-step explanation:

Let a and b represent the first and second digits, respectively.

... a = b -6 . . . . . . the first digit is 6 less than the second

... a + b = 12 . . . . .the sum of digits is 12 (an even number)

Using the expression in the first equation, we can substitute for a in the second equation:

... (b -6) +b = 12

... 2b = 18 . . . . . . add 6, simplify

... b = 9 . . . . . . . . .divide by 2

... a = 9 -6 = 3 . . . . from the first equation

The number is 39.

1 minute = 60 seconds.

Multiply the speed per second by 60 to get speed per minute:

8 * 60 = 480 miles per minute.

Multiply speed per minute by number of minutes to get total miles traveled:

480 * 6 = 2,880 total miles.

Answer:

"earn"

Step-by-step explanation:

He paid $9 for a box of 24 pens. Selling those 24 pens for $1 each, he sold them for $24. Thus he earned $24 -9 = $15 on each of the 8 boxes he bought.

14.4

This is a special case of the situation where two secant lines intersect a circle. The product of the near distance to the circle and the far distance to the circle from their point of intersection is a constant. A tangent is a degenerate case, where the near and far intersection points with the circle are the same point.

So, ...

... x · x = 9 · (9+14)

... x = 3√23 ≈ 14.4 . . . . . taking the square root

_____

Additional note on the geometry

This rule for the product of segments of secant lines also applies when the secants intersect inside the circle.

Answer:

14.39

Step-by-step explanation:

Theorem 12-15 III

(y+z) y=t squared

(9+14)9=x squared

23•9=x squared

207 =x squared

Square root of 207 is 14.39

Answer:

81

Step-by-step explanation:

width x length = area of a square

in a square width = length

9 x 9 = area

81 = area

Answer:

81 ft²

Step-by-step explanation:

To solve for Square area, note the equation:

Area = side x side

Note that for the rule of square, all sides are congruent, which means they have the same measurements. Therefore, if one side is 9, all the other are 9.

Multiply the base with the height: 9 x 9 = 81

81 ft² is your answer

~

Answer:

12 years

Step-by-step explanation:

r = compound interest rate in percent

t = doubling time in years

t = (72percent years)/(6 percent) = 12 years

As a curious cultural fact, there is a connection between the 72 and the fact that ln(2) = 0.69314718055. The constant is 69.3 for continuous compounding...

Answer:

12 years

Step-by-step explanation: