Answer: 4 miles
Step-by-step explanation:
If Ashley ran 1 mile 4 times, she ran 1+1+1+1, or 1*4, or 4 miles.
<em>Hope it helps <3</em>
Answer: can I see the choices?
Step-by-step explanation:
Solve for n
Simply both sides 11(n-1)+35=3n
Distribute (11)(n) + (11)(-1) + 35 = 3n
11n+-11+35=3n
Combine like terms (11n)+(-11+35)=3n
11n + 24 =3n
Subtract 3n from both sides
11n+24-3n=3n-3n
8n + 24 = 0
Subtract 24 from both sides
8n+24-24=0-24
8n = -24
Divide both sides by 8
8n = -24
8 8
n = -3
Answer:
The required answer is
Therefore the number in green box should be 7.
Step-by-step explanation:
Given:
AB = 7√2
AD = a , BD = b , DC = c , AC = d
∠B = 45°, ∠C = 30°
To Find:
c = ?
Solution:
In Right Angle Triangle ABD Sine identity we have
![\sin B = \dfrac{\textrm{side opposite to angle B}}{Hypotenuse}\\](https://tex.z-dn.net/?f=%5Csin%20B%20%3D%20%5Cdfrac%7B%5Ctextrm%7Bside%20opposite%20to%20angle%20B%7D%7D%7BHypotenuse%7D%5C%5C)
Substituting the values we get
![\sin 45 = \dfrac{AD}{AB}= \dfrac{a}{7\sqrt{2}}](https://tex.z-dn.net/?f=%5Csin%2045%20%3D%20%5Cdfrac%7BAD%7D%7BAB%7D%3D%20%5Cdfrac%7Ba%7D%7B7%5Csqrt%7B2%7D%7D)
![\dfrac{1}{\sqrt{2}}= \dfrac{a}{7\sqrt{2}}\\\\\therefore a=7](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%3D%20%5Cdfrac%7Ba%7D%7B7%5Csqrt%7B2%7D%7D%5C%5C%5C%5C%5Ctherefore%20a%3D7)
Now in Triangle ADC Tangent identity we have
![\tan C = \dfrac{\textrm{side opposite to angle C}}{\textrm{side adjacent to angle C}}](https://tex.z-dn.net/?f=%5Ctan%20C%20%3D%20%5Cdfrac%7B%5Ctextrm%7Bside%20opposite%20to%20angle%20C%7D%7D%7B%5Ctextrm%7Bside%20adjacent%20to%20angle%20C%7D%7D)
Substituting the values we get
![\tan 30 = \dfrac{AD}{DC}= \dfrac{a}{c}\\\\\dfrac{1}{\sqrt{3}}=\dfrac{7}{c}\\\\\therefore c=7\sqrt{3}](https://tex.z-dn.net/?f=%5Ctan%2030%20%3D%20%5Cdfrac%7BAD%7D%7BDC%7D%3D%20%5Cdfrac%7Ba%7D%7Bc%7D%5C%5C%5C%5C%5Cdfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%3D%5Cdfrac%7B7%7D%7Bc%7D%5C%5C%5C%5C%5Ctherefore%20c%3D7%5Csqrt%7B3%7D)
The required answer is
Answer:
The radius of the inflated spherical balloon is 45 millimeters.
Step-by-step explanation:
Volume of the spherical water balloon = 121,500 pi cubic millimeters
Let the radius of the balloon = r
Now, Volume of a Sphere = ![\frac{4}{3} \pi r^{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D)
⇒![\frac{4}{3} \pi r^{3} = 121,500 \pi](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D%20%20%3D%20121%2C500%20%5Cpi)
On solving for the value of r, we get:
![r^{3} = \frac{121,500\times 3}{4} = 91125\\ \implies r = \sqrt[3]{91125}](https://tex.z-dn.net/?f=r%5E%7B3%7D%20%20%3D%20%5Cfrac%7B121%2C500%5Ctimes%203%7D%7B4%7D%20%20%20%3D%2091125%5C%5C%20%5Cimplies%20%20r%20%20%3D%20%5Csqrt%5B3%5D%7B91125%7D)
or, r = 45 millimeter
Hence, the radius of the inflated spherical balloon is 45 millimeters.