1. Start with ΔCIJ.
- ∠HIC and ∠CIJ are supplementary, then m∠CIJ=180°-7x;
- the sum of the measures of all interior angles in ΔCIJ is 180°, then m∠CJI=180°-m∠JCI-m∠CIJ=180°-25°-(180°-7x)=7x-25°;
- ∠CJI and ∠KJA are congruent as vertical angles, then m∠KJA =m∠CJI=7x-25°.
2. Lines HM and DG are parallel, then ∠KJA and ∠JAB are consecutive interior angles, then m∠KJA+m∠JAB=180°. So
m∠JAB=180°-m∠KJA=180°-(7x-25°)=205°-7x.
3. Consider ΔCKL.
- ∠LFG and ∠CLM are corresponding angles, then m∠LFG=m∠CLM=8x;
- ∠CLM and ∠CLK are supplementary, then m∠CLM+m∠CLK=180°, m∠CLK=180°-8x;
- the sum of the measures of all interior angles in ΔCLK is 180°, then m∠CKL=180°-m∠CLK-m∠LCK=180°-(180°-8x)-42°=8x-42°;
- ∠CKL and ∠JKB are congruent as vertical angles, then m∠JKB =m∠CKL=8x-42°.
4. Lines HM and DG are parallel, then ∠JKB and ∠KBA are consecutive interior angles, then m∠JKB+m∠KBA=180°. So
m∠KBA=180°-m∠JKB=180°-(8x-42°)=222°-8x.
5. ΔABC is isosceles, then angles adjacent to the base are congruent:
m∠KBA=m∠JAB → 222°-8x=205°-7x,
7x-8x=205°-222°,
-x=-17°,
x=17°.
Then m∠CAB=m∠CBA=205°-7x=86°.
Answer: 86°.
The graph of f(x) opens upward
For the values of x < -5 the function is a line with negative slope, for the values of x > - 5 the function is a line with positive slope.
The two lines intercept in the point (-5,-2). That is the vertex of the function; a minimum value. So, all the other points are above the line y = -2.
The value of x is -3, or x= -3
Answer:
1/12
Step-by-step explanation:
1/6 divided by 2 = 1/12
Answer: 200 bulbs will not be defective.
Step-by-step explanation:
The ratio of defective bulbs to good bulbs produced each day is 2 to 10. This ratio can also be expressed as 1 to 5 by reducing to lowest terms.
The total ratio is the sum of the proportions.
Total ratio = 1 + 5 = 6
This means that if n bulbs is produced, the number of defective bulbs would be
1/6 × n
The number of non defective would be
5/6 × n
Since n = 240, then the number of bulbs that will not be defective is
5/6 × 240 = 200 bulbs
