Answer:
Step-by-step explanation:
The top and bottom triangles have two congruent sides with different included angles.
- AB = AD and AC is common side.
<u>The greater angle has greater op</u>posite side.
- The ∠BAC is greater than the ∠DAC as opposite side of the first (22) is greater than the opposite side of the second (16).
The ∠DAC must be greater than zero but smaller than 48°.
<u>Required inequality is:
</u>
- 0 < 2x - 12 < 48
- 12 < 2x < 60
- 6 < x < 30
So x has a value between 6 and 30
The two roots obtained for the quadratic equation by quadratic formula are 1.5 and 4.
<h3>What is defined as the quadratic formula?</h3>
- A quadratic equation is just a polynomial with a second degree first term.
- There are several methods for determining the roots, or solutions, of such a quadratic equation.
- Every quadratic equation has two solutions, that might or might not be real numbers.
- The quadratic formula is a simple method for resolving a quadratic equation. whether the answer is a whole number, an irrational number, or perhaps an imaginary number
If the quadratic equation is ax² + bx + c = 0.
Then, the roots are given by x = [-b ± √(b² - 4ac)]/2a.
The quadratic equation is given as; 2x² - 5x - 12 = 0.
On comparing with the standard form;
Put the values in the formula,
x = [-b ± √(b² - 4ac)]/2a.
x = [-(-5) ± √((-5)² - 4×2×(-12))] / 2×2
On simplification,
x = [5 ± 11]/4
There will be two roots of equation,
a; x = [5 + 11]/4
x = 16/4 = 4
b ; x = [5 - 11]/4
x = 6/4 = 1.5
Thus, the two roots obtained for the quadratic equation by quadratic formula are 1.5 and 4.
To know more about the quadratic formula, here
brainly.com/question/1214333
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Formula for the area of a triangle is 1/2bh
b=distance between the two points you gave.
distance between (4,3) and (-1,3) is 5.
1/2 * 5 * h = 15 square units
2.5 * h = 15 square units
h=6
This means the right triangle can be any point that is 6 units higher or lower than the two points you gave.
One of the answers to the question is (4,9). This is because the y value for the point (4,3) was changed by 6. Another possible answer is (4,-3) since distance cannot be negative, so it is still 6 units away from the point (4,3)
To find the third answer add 6 to the y value of (-1,3). The fourth answer can be found by subtracting 6 from the y value of (1,-3). Hope this helps.
Answer:
x= -10
y= -4
Step-by-step explanation:
Given data
3x+1=8y----------------1
11y-3x=-11--------------2
rearange
3x-8y=-1------------------1
-3x+11y=-11---------------2
add 1 and 2
3x-8y=-1------------------1
-3x+11y=-11---------------2
0+ 3y= -12
y= -12/3
y= -4
put y= -4 in 2
11y-3x=-11
11(-4)-3x=-11
-44-3x=-11
-44+11=3x
-33= 3x
x= -33/3
x= -10
