Find the area of the isosceles trapezoid below by using the area formulas for rectangles and triangles.
a = 10 cm, b = 15 cm, and c = 5 cm

9514 1404 393

Answer:

  undo what is done to the variable

Step-by-step explanation:

As with any "solve for" problem, it is a good idea to take a look at what is being done to the variable you're solving for.

Starting "as is"

Here, the value 2.5 is added to it, and the sum is multiplied by -5 (which we notice is negative).

In general, you want to "undo" what is done to the variable — in reverse order. What was done:

If we adopt that strategy, it means we first need to undo multiplication by -5. That is, we must either (a) multiply both sides by -1/5, or (b) divide both sides by -5. Either choice will require that the sense of the comparison be reversed, so you will have ...

  ( ) < (x + 2.5)

After that, you need to "undo" the addition of 2.5. That is accomplished by adding -2.5 to both sides of the equation.

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Simplifying first

For many problems that have fractions and/or parentheses, it can work well to eliminate both before you start with your "undo" strategy. Here, a first step can be to simplify the inequality, eliminating parentheses. This means you will use the distributive property to multiply each term inside parentheses by the (negative) factor outside.

Having done that, you find the "what was done to the variable" list is slightly different:

As a consequence the "undo" steps are slightly different. Addition is still reversed by adding the opposite. Multiplication is still reversed by multiplying by the reciprocal, or by division (same thing).

As before, (and as always), what you do to one side of the inequality, you must also do to the other side. If multiplication or division by a negative number is involved, the comparison symbol must be reversed.

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About Negative Multiplication/Division

Above, we have noted that multiplication or division by a negative number requires reversal of the comparison symbol. For example, ...

  starting with -1 > -2

multiplying both sides by -1 gives ...

  ending with 1 < 2

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When the (only) variable term has a negative coefficient, there is another strategy you can use that does not require the comparison to be reversed. You can add the opposite of that term to both sides of the inequality. For example, ...

  starting with -5x < -38

we can add 5x to both sides to get ...

  0 < -38 +5x . . . . . now the variable has a positive coefficient

This lets us proceed with the solution without worrying about the sense of the inequality. (Note that the variable will be "greater than" some value.)

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More about solving strategy

The rules that make Algebra possible are the rules of equality. If you look them up, you may find separate versions for addition, multiplication, subtraction, division. If you realize that subtraction is a form of addition, and that division is a form of multiplication, there are really only two—and those can be simplified to ONE RULE: always do the same operation on both sides of the equal sign. The same rule applies to inequalities. You will stay out of trouble if you remember and follow this rule. (There are many "shortcut" versions that go by names like "cross-multiply" and others. They are basically this rule with some steps not shown.)

When it comes to applying functions to inequalities, you need to consider carefully whether the function preserves the ordering relationship (>, ≥, <, ≤). Some functions do not, or have different behavior in different domains, so paying attention is required. Multiplication by a negative number is just the tip of the iceberg here.

answer:

the division property of equality

step-by-step explanation:

5n / 5 = 50 / 5

n = 10

Answer:

Division Property of Equality.

Step-by-step explanation:

In this case, you will use the Division Property of Equality to solve. Isolate the variable, n, by dividing 5 from both sides:

(5n)/5 = (50)/5

n = 50/5

n = 10

~

Answer:

no problem

Step-by-step explanation:

Answer:

you would do

113.04 divided by 3.14 to get 36.

the diameter of the circle is 36 ft

Answer:

Jason can afford 5 more additional lines, making 9 lines total because

175-120=55

55/10=5.5 so He can not afford more than 5 more additional lines.

Step-by-step explanation:

Answer:

B.) 120+ 10x =< 175

Step-by-step explanation:

Answer:

Step-by-step explanation:

x^2 + 6x = 90

x^2 + 6x + 9 = 90 + 9

(x + 3)(x + 3) = 99

(x + 3)^2 = 99

Answer: B

The equation x² + 6x = 90 is also written as (x + 3)² = 99. Then the correct option is B.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Kaylee is building a rectangular nook with an area of 90 square yards. She maintains that the length of the encased region should be 6 yards longer than the width, x. The equation is given below.

x² + 6x = 90

Add both sides 9, then we have

x² + 6x + 9 = 90 + 9

(x + 3)² = 99

The condition x² + 6x = 90 is likewise composed as (x + 3)² = 99. Then, at that point, the right choice is B.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

Answer:

Step-by-step explanation:

Answer:

2. 13

3. 20

4. 28

5. 27

6. 19 1/2

Step-by-step explanation:

Answer:

Think 139 in

Step-by-step explanation: You multiply all the numbers together then square root your final answer

The length of the diagonal [tex]x[/tex] created by the smaller bookend is 7.2 inches.

In this question we have two pairs of books which create two similar triangles, whose formula is an application of the concept of direct proportionality:

[tex]\frac{12\,in}{10\,in} = \frac{x}{6\,in}[/tex]   (1)

[tex]x = 7.2\,in[/tex]

The length of the diagonal [tex]x[/tex] created by the smaller bookend is 7.2 inches. [tex]\blacksquare[/tex]

The figure associated to the question is missing. We included a simplified representation of the figure below.

To learn more on similar triangles, we kindly invite to check this verified question: https://brainly.com/question/25882965

9514 1404 393

Answer:

  6. 15/22

  7. 1/12

  9. 1/16

  10. 0

Step-by-step explanation:

6. 10 of the 12 tiles are "not P", so the probability of a "not P" on the first draw is 10/12 = 5/6. After drawing a "not P" on the first draw, 9 of the remaining tiles are "not P". The probability of drawing one of those is 9/11. So, the joint probability of drawing two "not P" tiles is ...

  (5/6)(9/11) = (5·9)/(6·11) = 15/22

__

7. The probability of drawing a tile worth 3 points is 3/12 = 1/4. The probability of drawing a tile worth 1 point is 4/12 = 1/3. So, the joint probability of drawing a 3-point tile, then a 1-point tile is ...

  (1/4)(1/3) = 1/12

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9. There are 3 of the 12 tiles worth more than 4 points. The probability of drawing one of them  is 3/12 = 1/4. The probability of doing it again is also 1/4, so the probability of doing it twice is ...

  (1/4)(1/4) = 1/16

__

10. The probability of drawing a Z is 1/12. Having drawn a Z, the probability of drawing a 10-point tile is 0/11. The joint probability of drawing a Z twice is ...

  (1/12)(0/11) = 0

_____

Additional comment

We revisited problem 7 because we needed that answer for problem 9.

Answer:

1. 2:5

2. 110 (the total degree of a triangle is 180 so it would be 40+30+x=180)

3. 37 (It's a right angle, 90 degrees so it would be 90-53=x)

Answer:

y=[-2]x[+][5]

Step-by-step explanation:

[tex]\frac{-1-3}{3-1}=\frac{-4}{2} =-2[/tex] m= -2

Using the point (1,3) Find the value of b

3= -2(1)+b

3= -2+b

+2  +2

---------

5=b

y= -2x+5

Answer:

120 cm

Step-by-step explanation:

10 x 6 = 60

60/2 = 30

30 x 4 = 120

Answer: Yes

Step-by-step explanation:

I'm pretty sure it's correct so yes

-96Step-by-step explanation: i-

Answer:

j would be -7

Answer:

number 1 is wrong

Step-by-step explanation:

Answer:

A: tea formation 4

Step-by-step explanation:

Dilating changes the size which makes the shape not congruent

Answer:

transformation 4

Step-by-step explanation:

Answer:

7. 8x^2 + 3y^2

8. 9y^4 -- 8x

9. 5x^2- 2x- 3

Step-by-step explanation:

Answer: question question for you to do a walk on a walk and jog on a walk on a field trip and jog the field of a walk on the walk in a walk on the field and jog jog the

Step-by-step explanation:

Answer:

293

Step-by-step explanation:

2930÷10≈293

Answer:

1. -7

Step-by-step explanation:

-3x - 5 = 16

add 5 to both sides of the equation.

-3x = 16

divide both sides by -3

x = -7

(Sorry, I don't know what 2 is!)

Answer:6,2

Step-by-step explanation:you need to add each step and divide

Answer:

[tex]\huge\boxed{\tt{True}}[/tex]

Step-by-step explanation:

If a parallelogram has at least one right angle, this means that the opposite angles also measures 90 degrees because opposite angles are congruent in a parallelogram. Also, The other angles will then add up to 180 degrees but due to them being equal, they also will measure 90 degrees.

Hence, A parallelogram with at least one right angle is a rectangle.

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

1/16

Step-by-step explanation:

if you do Keep, Change, Flip, you get 1/16. So what you do is you lay out 1/4 divided by 4/1. You KEEP the first fraction, CHANGE the division sign into a multiplication sign, and then FLIP the 4/1 into 1/4. Then all you have to do is multiply 1 times 1, and then 4 times 4. Hope this helps :)

Answer:

560

Step-by-step explanation:

7 x 8 x 10= 560

Answer:

This is what I came up with base on my knowledge please note that I learned this in 4th grade and its been 4 years I am in 8th grade well 7th but I got moved up a grade   Thank You :)

Step-by-step explanation:

7) 56*the other 3

8) 4.6*3 + the other 9.2

:)