Answer:
Option (1)
Step-by-step explanation:
By the property of alternate segment theorem,
"Angle formed between the tangent and the chord in a circle measures the half of the measure of the intercepted arc"
m(∠EFG) =
× m(minor arc FG)
minor arc FG = 2m(∠EFG)
= 2(76°)
= 152°
Therefore, Option (1) will be the correct option.
Answer:
Step-by-step explanation:
We assume that there are 100 sour candies, Thus-
26 % of candy are grape implies that 26% of 100 candies are grape that is equal to 26
Now remaing candies that are not grape are 100-26 = 74
Based on the rule of multiplication:
P(A ∩ B) = P(A)/ P(B|A)
In the beginning, there are 26grape candies, probability of choosing first grape candy = 26C1 = 26
After the first selection, we replace the selected grape candy so there are still 100 candies in the bag P(B|A) = 100C3 = 100 x 99 x 98 x 97!/3! X 97!
= 50 x 33 x 98
So probability =1/ 50 x 33 x 98 x 26
= 1/4204200
Quadrant is III so, sign would be negative for Sec.
Now, we know, csc = H / P
So, H = 4, P = 3
Calculate for B,
B² = H² - P²
B² = 4² - 3²
B² = 16 - 9
B = √7
We know, sec Ф = H / B = 4 / √7
We can write it as: -4√7 / 7 [ -ve sign for 3rd quadrant ]
In short, Your Answer would be Option B
Hope this helps!
Answer:
x = no. of quarters
3x = no. of dimes
3x + 11 = no. of nickels
2(3x + 11) = no. of pennies
340 quarters
1020 dimes
1031 nickels
2062 pennies
Step-by-step explanation:
x = no. of quarters
3x = no. of dimes
3x + 11 = no. of nickels
2(3x + 11) = no. of pennies
x + 3x + 3x + 11 + 2(3x + 11) = 4453
x + 3x + 3x + 11 + 6x + 22 = 4453
13x + 33 = 4453
13x = 4420
x = 340 quarters
3x = 1020 dimes
3x + 11 = 1031 nickels
2(3x + 11) = 2062 pennies
Check: 340 + 1020 + 1031 + 2062 = 4453
(4, 2) and (8, 1) (option D)
Explanation:
The given equation:
y = 4x - 1
comparing with equation of line:
y = mx + c
m = slope = 4
c = y-intercept = -1
For a line to be perpendicular to another line, the slope of one line will be the negative reciprocal of the other line.
We need to find the option which will give a negative reciprocal of 4.
![slope=m\text{ = }\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=slope%3Dm%5Ctext%7B%20%3D%20%7D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
a) (1, -3) and (2, 1)
![\begin{gathered} slope=\text{ }\frac{1-(-3)}{2-1}=\frac{1+3}{1}\text{ = }\frac{\text{4}}{1} \\ \text{slope = 4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20slope%3D%5Ctext%7B%20%7D%5Cfrac%7B1-%28-3%29%7D%7B2-1%7D%3D%5Cfrac%7B1%2B3%7D%7B1%7D%5Ctext%7B%20%3D%20%7D%5Cfrac%7B%5Ctext%7B4%7D%7D%7B1%7D%20%5C%5C%20%5Ctext%7Bslope%20%3D%204%7D%20%5Cend%7Bgathered%7D)
b) (-4, 7) and (-1, -5)
![\begin{gathered} \text{slope = }\frac{-5-7}{-1-(-4)}=\frac{-5-7}{-1+4}=\frac{-12}{3} \\ \text{slope = -4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7Bslope%20%3D%20%7D%5Cfrac%7B-5-7%7D%7B-1-%28-4%29%7D%3D%5Cfrac%7B-5-7%7D%7B-1%2B4%7D%3D%5Cfrac%7B-12%7D%7B3%7D%20%5C%5C%20%5Ctext%7Bslope%20%3D%20-4%7D%20%5Cend%7Bgathered%7D)
c) (-8, -4) and (0, -2)
![\begin{gathered} \text{slope = }\frac{-2-(-4)}{0-(-8)}=\frac{-2+4}{0+8}=\text{ }\frac{2}{8} \\ \text{slope = }\frac{1}{4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7Bslope%20%3D%20%7D%5Cfrac%7B-2-%28-4%29%7D%7B0-%28-8%29%7D%3D%5Cfrac%7B-2%2B4%7D%7B0%2B8%7D%3D%5Ctext%7B%20%7D%5Cfrac%7B2%7D%7B8%7D%20%5C%5C%20%5Ctext%7Bslope%20%3D%20%7D%5Cfrac%7B1%7D%7B4%7D%20%5Cend%7Bgathered%7D)
d) (4, 2) and (8, 1)
![\begin{gathered} \text{slope = }\frac{1-2}{8-4} \\ \text{slop}e\text{ }=\frac{-1}{4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7Bslope%20%3D%20%7D%5Cfrac%7B1-2%7D%7B8-4%7D%20%5C%5C%20%5Ctext%7Bslop%7De%5Ctext%7B%20%7D%3D%5Cfrac%7B-1%7D%7B4%7D%20%5Cend%7Bgathered%7D)
slope = 4
reciprocal of 4 = 1/4
negative reciprocal = - 1/4
Hence, the option whose slope gives the negative reciprocal of 4 is (4, 2) and (8, 1) (option D)