Answer:
12 black beads
Step-by-step explanation:
Given the ration of gold beads to black beads on the short necklace:
![\frac{gold}{black}=\frac{32}{8}=\frac{4}{1}](https://tex.z-dn.net/?f=%5Cfrac%7Bgold%7D%7Bblack%7D%3D%5Cfrac%7B32%7D%7B8%7D%3D%5Cfrac%7B4%7D%7B1%7D)
Since the ratio of 4:1 has 5 total parts, you can take the total amount of beads in the long necklace and divide by 5:
60 ÷ 5 = 12
12 beads represents 1 part of the ratio, so that would be the number of black beads. To check, multiply 12 by 4: 12 x 4 = 48, and set up a ratio:
48: 12 = 4: 1
Answer:
9 years ago.
Step-by-step explanation:
Dotty is 51 years old and Esmerelda is 23 now.
Now, x years ago the age of Dotty was (51 - x) years and the age of Esmerelda was (23 - x) years.
Assume that x years ago Dotty was 3 times Esmerelda's age.
So, we can write the equation as
3(23 - x) = 51 - x
⇒ 69 - 3x = 51 - x
⇒ 69 - 51 = 3x - x
⇒ 18 = 2x
⇒ x = 9 years.
Therefore, 9 years ago Dotty was 3 times Esmerelda's age. (Answer)
The range of the data is 6.
So for a straight line the total is 180 degrees, so angle rpq is 180 - 123 which. makes 57 °. and arc length is just circumference of circle x 57/360. so here, it would be 20πx57/360 so the answer is 9.948..... and round it up 9.9 cm
Answer:
the possible coordinates are -9 and 3
Step-by-step explanation:
coordinates of B=(x2,y2)= (5,1)
Coordinates of A= (x1, y1)= (-3, z)
distance= 10 units
Formula: d=![\sqrt{(y2-y1)^2+(x2-x1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%7D)
substituting the values in the above formula
10=![\sqrt{(z-(-3))^2+(-3-5)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28z-%28-3%29%29%5E2%2B%28-3-5%29%5E2%7D)
10=![\sqrt{(z+3)^2+(-8)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28z%2B3%29%5E2%2B%28-8%29%5E2%7D)
10=![\sqrt{(z^2 +6z+9)+(64)}](https://tex.z-dn.net/?f=%5Csqrt%7B%28z%5E2%20%2B6z%2B9%29%2B%2864%29%7D)
10=![\sqrt{(z^2 +6z+73)}](https://tex.z-dn.net/?f=%5Csqrt%7B%28z%5E2%20%2B6z%2B73%29%7D)
taking square root on both sides
100=![z^2 +6z+73](https://tex.z-dn.net/?f=z%5E2%20%2B6z%2B73)
100-73=![z^2 +6z](https://tex.z-dn.net/?f=z%5E2%20%2B6z)
=0
![z^2 +9z-3z-27=0](https://tex.z-dn.net/?f=z%5E2%20%2B9z-3z-27%3D0)
![z(z+9) -3(z+9)=0](https://tex.z-dn.net/?f=z%28z%2B9%29%20-3%28z%2B9%29%3D0)
![(z-3)(z+9)=0\\z-3=0 ; z+9=0\\z=3 : z=-9](https://tex.z-dn.net/?f=%28z-3%29%28z%2B9%29%3D0%5C%5Cz-3%3D0%20%3B%20z%2B9%3D0%5C%5Cz%3D3%20%3A%20z%3D-9)