answer.
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
Brilliant_brown [7]
2 years ago
7

In ΔABC, and m∠ABC = 90°. D and E are the midpoints of and , respectively. If the length of is 9 units, the length of is units a

nd m∠CAB is °.
Mathematics
1 answer:
jok3333 [9.3K]2 years ago
3 0
This is an isosceles right triangle (AB = BC & ∠ B=90° - Given)
Then the angles at the base are equal and ∠ CAB = ∠ ACB = 45°

Theorem: Segment DE, joining the midpoints of 2 sides is:
1st) parallel to the 3rd side and
2nd) equal to half the measurement of the 3rd side
So if the 3rd side (hypotenuse) = 9 units, DE = 9/2 = 4.5 units
You might be interested in
One factor of the polynomial 2x^3 - 3x^2 - 3x + 2 is ( x - 2 ). Which expression represents the other factor, or factors, of the
Georgia [21]

Answer:

Option (D)

Step-by-step explanation:

Given polynomial is,

2x³ - 3x² - 3x + 2

If (x - 2) is the factor of the given polynomial,

By synthetic division we can get the other factor.

2 |  2     -3       -3       2    

 

    <u>         4         2      -2          </u>

     2      1         -1        0

Therefore, other factor of the given polynomial is (2x² + x - 1)

Now (2x² + x - 1) = 2x² + 2x - x - 1

                           = 2x(x + 1) -1(x + 1)

                           = (2x - 1)(x + 1)

Therefore, factors of the given polynomial other than (x - 2) are (2x - 1) and (x + 1)

Option (D) will be the answer.

4 0
2 years ago
Graph the line y = kx +1 if it is known that the point M belongs to it: M(1,3)
tigry1 [53]

Answer:

M(x,y) = (1,3) belongs to the line y = 2\cdot x +1. Please see attachment below to know the graph of the line.

Step-by-step explanation:

From Analytical Geometry we know that a line is represented by this formula:

y=k\cdot x + b

Where:

x - Independent variable, dimensionless.

y - Dependent variable, dimensionless.

k - Slope, dimensionless.

b - y-Intercept, dimensionless.

If we know that b = 1, x = 1 and y = 3, then we clear slope and solve the resulting expression:

k = \frac{y-b}{x}

k = \frac{3-1}{1}

k = 2

Then, we conclude that point M(x,y) = (1,3) belongs to the line y = 2\cdot x +1, whose graph is presented below.

3 0
2 years ago
Wheat contains about 2.5 kcal per gram, and the average U.S. male consumes 2500 kcal per day. How many hectares of wheat are nee
Yuri [45]
First of 30% of 2500kcal is 750kcal
if a male consumes 2.5 kcal then 750kcal / 2.5kcal = 300
but then we would need to know how many wheat are on one hectare of land.
3 0
2 years ago
Read 2 more answers
Leona purchased a $1,000 bond having a quoted price of 99.875. She had to pay a 5.5% brokerage fee (of the selling price). What
Zina [86]

Answer:

The total cost of the bond is none of the given choices.

Step-by-step explanation:

The selling price of a $1000 bond  =   $99.875

The brokerage fee = 5.5 %

Now, 5.5%  of $99.875 =  \frac{5.5}{100}  \times 99.875 = 5.493

So, the brokerage fee = $5.493

Now, to find out the total cost of the bond:

Total Cost  = The selling Price + Brokerage Price

                  = $99.875 + $5.493

                  =  $105.368

or, the total price of the $1000 bond is $ 105.368.

Hence,  the total cost of the bond is none of the given choices.

7 0
2 years ago
In triangle XYZ, XY = 13, YZ=20, and XZ=25. What is the measure of angle Z to the nearest degree?
anastassius [24]
We can use Law of Cosines to solve for the angle of Z. The solution is shown below:
cos C=(a²+b²-c²)/2ab
cos Z = (yz² + xz² - xy² )/2*yz*xz
cos Z = (20² + 25  - 13²)/2*20*25
cos Z = 856 / 1000
Z=31.13°

The answer is angle 31.13°. 
4 0
2 years ago
Other questions:
  • Jessica is buying several bunches of bananas to make dessert for a fundraiser. She can buy 10 pounds of bananas for $14.90 or 8
    15·1 answer
  • The cost of soup, s, varies directly with the number of cans, c. When c is 4, the cost is 3$. Which graph represents the cost of
    14·2 answers
  • If the mean of a symmetric distribution is 170, which of these values could be the median of the distribution?
    12·1 answer
  • 7, 16, 25, 34, 43, ..... nth term is
    15·2 answers
  • Which of the following options best describes the solution process and solution(s) for the quadratic equation?
    14·1 answer
  • Jackson is three times as heavy as Andrew. If the sum of their weight is 360 pounds, find Andrews weight​
    14·2 answers
  • In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass bala
    12·1 answer
  • The temperature in degrees Kelvin is 273 degrees less than the temperature in degrees Celsius. Use the formula LaTeX: C=\frac{5}
    12·2 answers
  • 11.
    12·1 answer
  • Mateo has 7/2 pounds of apples. He needs 3/4 pounds of apples for each batch of applesauce. How many batches of applesauce can
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!