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
Cloud [144]
2 years ago
14

Use algebra to explain how you know that a rectangle with side lengths one less and one more than a square will always be 1 squa

re unit smaller than the square. 2. What is the difference in the areas of a square and rectangle if the rectangle has side lengths 2 less and 2 more than a square? Use algebra or a geometric model to compare the areas and justify your answer. 3. Explain why the method for factoring shown in this lesson is called the product-sum method.
Mathematics
1 answer:
My name is Ann [436]2 years ago
4 0

Answer:

Step-by-step explanation:

1. If a is the length of the side of the square, then a 2 is the area of the square. The rectangle’s side lengths will be (a − 1) and      (a + 1). That product, which represents the area of the rectangle, is a 2 − 1, or 1 square unit less than the area of the square.

2. Using the same logic as for Problem 1, the rectangle dimensions will be     (a + 2) and (a − 2) with an area of a 2 − 4. Therefore, the area of the rectangle is 4 square units less than the area of the original square

3. It is called the product-sum method because you look for the two numbers with a product equal to the constant term of the quadratic expression and a sum equal to the coefficient of the linear term

You might be interested in
The ratio of the side lengths for a triangle is exactly 9:12:15. In another triangle, which is similar to the first, the shortes
AfilCa [17]

Answer: C

Step-by-step explanation:

4 0
3 years ago
The weight of a newborn is 7.5 pounds. The baby gained one-half pound a month constantly for its first year.
iris [78.8K]
Answer is D if the function W is graphed find and interpret the slope of the function
6 0
3 years ago
What type of table has the largest area
Helen [10]

Answer:

The Rectangular Table Has The largest area of 1460 in^2

7 0
3 years ago
Simplify: –3(y + 2)^2 – 5 + 6y
GREYUIT [131]
The answer is -3y^2-6y-17
8 0
3 years ago
Read 2 more answers
Triangle ABC is given where m(angle)A=33 degrees, a=15 in., and the height, h, is 9 in. How many distinct triangles can be made
4vir4ik [10]

Answer:

One triangle

Step-by-step explanation:

Find the measures of the triangle ABC

Let

D ----> intersection point of the height triangle ABC with the segment AB

step 1

Find the measure of angle B

In the right triangle BCD

sin(B)=\frac{CD}{BC} ---> by SOH (opposite side divided by the hypotenuse)

substitute the given values

sin(B)=\frac{9}{15}

using a calculator

B=sin^{-1}(\frac{9}{15})=36.9^o

step 2

Find the length of segment DB in the right triangle BCD

Applying the Pythagorean Theorem

BC^2=DC^2+DB^2

substitute

15^2=9^2+DB^2

DB^2=15^2-9^2

DB^2=144\\DB=12\ in

step 3

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

A+B+C=180^o

substitute the given values

33^o+36.9^o+C=180^o

C=180^o-69.9^o=110.1^o

step 4

Find the length side AC

In the right triangle ACD

sin(A)=\frac{CD}{AC} ---> by SOH (opposite side divided by the hypotenuse)

substitute the given values

sin(33^o)=\frac{9}{AC}

solve for AC

AC=\frac{9}{sin(33^o)}=16.5\ in

step 5

Find the length of segment AD

In the right triangle ACD

tan(A)=\frac{CD}{AD} ---> by TOA (opposite side divided by the adjacent side)

substitute the given values

tan(33^o)=\frac{9}{AD}

AD=\frac{9}{tan(33^o}}=13.9\ in

step 6

Find the length side AB

AB=AD+DB

substitute the given values

AB=13.9+12=25.9\ in

step 7

The measures of triangle ABC are

A=33^o\\B=36.9^o\\C=110.1^o\\AC=16.5\ in\\CB=15\ in\\AB=25.9\ in

so

The measurements of the ABC triangle are unique

therefore

Only one triangle can be constructed  with the given measurements

8 0
3 years ago
Other questions:
  • Select the pronoun that agrees with the antecedent of the sentence below. If my sister or Carol arrives, ask _____ to wait.
    13·1 answer
  • The value given below is discrete. Use the continuity correction and describe the region of the normal distribution that corresp
    5·1 answer
  • An exponential function f(x) is reflected across the y-axis to create function g(x). Which is a true statement regarding
    14·2 answers
  • A construction crew has just finished building a road. the crew worked for 10 days. if they build 2 3/4 kilometers of road each
    11·1 answer
  • 4×9×8^-1×3^-3/6^-1 .Ans is 1 but I want the method.​
    12·2 answers
  • Help please! Will give brainliest
    8·2 answers
  • Solve this equation for x. round your answer to the nearest 0 = ln (x+6)
    8·1 answer
  • Which statement best describes a strategy for estimating the perimeter of the figure below if the grid squares have side
    5·1 answer
  • The ages of Raju and Ravi arw the ratio of their ages will be 4:5 . Find their present ages.
    6·1 answer
  • A teacher surveyed her class after they had taken a vocabulary test. Eighteen of the students claimed they had studied at least
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!