Help meeeee pleaseeeee

In right angle ABC, angle C is the right angle, AC = 3 and AB = 5. Point D is on hypotenuse AB, such that DB = 1. Find the area

Ivan

Look at the picture.

To find the area of triangle DBC we need to find its base, x, and its height, h.

Triangle ABC is a right triangle, so using the Pythagorean theorem we can find x.
$(\hbox{one leg})^2+(\hbox{the other leg})^2=(\hbox{the hypotenuse})^2 \\
3^2+x^2=5^2 \\
9+x^2=25 \\
x^2=25-9 \\
x^2=16 \\
x=\sqrt{16} \\
x=4$

Now look at triangles ABC and DBH. They both are right triangles and have the same angle α. That means they're similar and their corresponding sides are proportional. The ratio of the side opposite to angle α to the hypotenuse is the same in both triangles - so the ratio of h to 1 is the same as the ratio of 3 to 5.
$\frac{h}{1}=\frac{3}{5} \\
h=\frac{3}{5}$

The base x is 4, the height h is 3/5. Calculate the area:

$A=\frac{xh}{2}=\frac{4 \times \frac{3}{5}}{2}=2 \times \frac{3}{5}=\frac{6}{5}$

The area of triangle DBC is 6/5.

4 0

3 years ago

In the triangles, and .

Ratling [72]

The correct answers are:

#1) Angle G is smaller than angle P; #2) The three sides have the same length; #3) The path along XY is longer than the path along ZY, and the path along ZY is longer than the path along AB.

Explanation:

#1) Since the measure of HK is smaller than the measure of MN, this means the angle opposite HK will be smaller than the angle opposite MN. This means ∠G is smaller than ∠P.

#2) Since all of the angles are congruent, all of the sides will be congruent as well.

#3) The side opposite the largest angle will be longest; the side opposite the smallest angle will be shortest. This means the side opposite the 36° angle, AB, will be smallest, and the side opposite the 79° angle, XY, will be largest. ZY will have a length between these two.

8 0

4 years ago

Read 2 more answers

Select the function that represents a parabola with zeros at x = –2 and x = 4, and y-intercept (0,–16). A ƒ(x) = x2 + 2x – 8 B ƒ

Ahat [919]

Answer:

D. $f(x) = 2\cdot x^{2}-4\cdot x -16$

Step-by-step explanation:

Any parabola is modelled by a second-order polynomial, whose standard form is:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

In addition, a system of three linear equations is constructed by using all known inputs:

(-2, 0)

$4\cdot a -2\cdot b + c = 0$ (Eq. 1)

(4, 0)

$16\cdot a + 4\cdot b +c = 0$ (Eq. 2)

(0,-16)

$c = -16$ (Eq. 3)

Then,

$4\cdot a - 2\cdot b = 16$ (Eq. 4)

$16\cdot a + 4\cdot b = 16$ (Eq. 5)

(Eq. 3 in Eqs. 1 - 2)

$a - 0.5\cdot b = 4$ By Eq. 4 (Eq. 4b)

$a = 4 + 0.5\cdot b$

Then,

$16\cdot (4+0.5\cdot b) + 4\cdot b = 16$ (Eq. 4b in Eq. 5)

$64 + 12\cdot b = 16$

$12\cdot b = -48$

$b = -4$

The remaining coeffcient is:

$a = 4 + 0.5\cdot b$

$a = 4 + 0.5\cdot (-4)$

$a = 2$

The function that represents a parabola with zeroes at x = -2 and x = 4 and y-intercept (0,16) is $f(x) = 2\cdot x^{2}-4\cdot x -16$ . Thus, the right answer is D.

6 0

3 years ago

Part A: A graph passes through the points (0, 4), (1, 8), and (2, 10). Does this graph represent a linear function or a non-line

IRISSAK [1]

Part A: In (0,4) and (1,8), as x increases from 0 to 1, y increases from 4 to 8. The slope of the line connecting these 2 pts. is (8-4) / (1-0), or 4. Now do the same thing for the 2 pts (1,8) and (2, 10). You will find that the slope in the 2nd case is different. Thus, the 3 given pts do NOT lie on a straight line. Function is non-linear.

Part B: an example of a non-linear function would be y = 2x^2 - 5. You can tell immediately from that exponent, 2, that this function is non linear.

An ex. of a linear function would include x to the 1st power only: y = 3x - 7.

4 0

3 years ago

Read 2 more answers

Solve the equation for a. 3a+13.61=−9.43

snow_tiger [21]

Answer: a = -7.68

STEPS:

- Subtract 13.61 from both sides

- Simplify

- Divide both sides by 3

4 0

3 years ago