1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kirill115 [55]
1 year ago
15

Original Equation:8 - 7x^2 + 3 = 4x^2 - 1Frist step:11 - 7x^2 = -4x^2 - 1Which property justifies the first step?A. Division pro

perty of equalityB. Commutative property of addition C. Addition of equality D. Multiplication property of equality
Mathematics
1 answer:
Tpy6a [65]1 year ago
7 0

8 - 7x^2 + 3 = 4x^2 - 1

8+3-7x^2 = 4x^2-1

11-7x^2 = 4x^2-1

B. Commutative property of addition

We can swap numbers and obtain the same results.

In this case, we swapped 8+3 and added them.

You might be interested in
The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if paral
Iteru [2.4K]

The answer is really none of the above, because all of these have divisions by difference in x, and there are perfectly fine rectangles where those will mean dividing by zero.

To do the problem the way they want us to, we note segments with the same slope are parallel (or collinear); segments with slopes which multiply to -1 are perpendicular.

Let's figure out what each choice is trying to tell us by translating it into parallel and perpendicular. Remember A is point 1, ...

A. ((y_4-y_3)/(x_4-x_3)= (y_3-y_2)/(x_3-x_2)) and ((y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2))=-1

translated, that's CD║BC and CD⊥BC - contradictory; second half right

B. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and ((y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1))=-1

CD ║ AB and CD ⊥ AB - only the parallelogram half is right

C. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and (y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2)=-1

CD║AB and CD⊥BC - that's TRUE

D. (y_4-y_3)/(x_4-x_3)= (y_3-y_1)/(x_3-x_1) and (y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1)=-1

CD║AC and CD⊥AB - nope

Answer: C

The way I'd get the proper expression is with the dot product.

A parallelogram is a rectangle when adjacent sides are perpendicular. It only takes one right angle to make them all right.

Two sides are perpendicular when the dot product of their direction vectors is zero. All the answers have y_4 - y_3 so one side is CD. The other side must be BC or AD; AD would give y_4 - y_1 terms which don't appear among the answer, so let's go with BC.

The direction vectors are

D-C = (x_4 - x_3, y_4 - y_3)

C-B = (x_3 - x_2, y_3 - y_2)

For perpendicularity we need a zero dot product:

0 = (D-C)\cdot(C-B) = (x_4 - x_3)(x_3 - x_2) + (y_4 - y_3)(y_3 - y_2)

- (x_4 - x_3)(x_3 - x_2) = (y_4 - y_3)(y_3 - y_2)

That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.

8 0
3 years ago
PLEASE ITS DUE SOON HELP AGGGGGGGGGGG IM STRESSING
inna [77]

Answer:

B

Step-by-step explanation:

You have to add 7 to both sides to isolate the variable

4 0
3 years ago
You are building a model of a square pyramid. The side length of the base of the model is 30 cm. The height is 21 cm. What is th
Shalnov [3]

Answer:

Step-by-step explanation:

  1. find the area of the base (square)=900 sq. cm
  2. find area of triangles=1260 sq. cm
  3. total= 2160 sq. cm
6 0
3 years ago
F(x) = x^2 - 4, X is greater/less than 0<br><br> (a) Find the inverse function of f.<br> F^-1(x) =
Natali5045456 [20]

Step-by-step explanation:

f(x) = x² - 4

y = x²-4

x = y²-4

x + 4 = y²

y =  \sqrt{x + 4}

7 0
2 years ago
Is 5x + 12 = 5x + 22 a infinite real solution
Alexus [3.1K]

Answer:

No Solution

Step-by-step explanation:

There is no number that can replace x to make the equation true.

5 0
3 years ago
Read 2 more answers
Other questions:
  • What is the value of n in the equation below
    12·1 answer
  • Nine stuffed animals, all different, are placed along a babies toy shelf.  How many possible  arrangements are there if:  a)  th
    5·2 answers
  • Is 17 feet greater than 804 inches
    5·2 answers
  • Simplify (3x + 5) + (2x - 9) - (4x + 3).
    8·1 answer
  • Which answer best describes the complex zeros of the polynomial function? f(x)=x3+x2−8x−8
    15·2 answers
  • Find the measure of angle 1.​
    14·2 answers
  • Pls help! In the figure below, m∠ABC = 57 degrees and m∠DAB =116 degrees. What is m∠ABC?
    15·2 answers
  • mrs. sing bought a pound of green beans for $1.80. How much will Msr. Tennison pay for 3 1/2 pounds of green beans?​
    14·1 answer
  • YOU BE THE TEACHER Your friend finds the missing length of the triangle. Is your friend correct? 25 ft ² +6² = ² 72+252 = 2 674
    12·1 answer
  • Which expression is represented by the set of algebra tiles below?
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!