Ben has 4 dimes and 12 nickels
<em><u>Solution:</u></em>
Let "d" be the number of dimes
Let "n" be the number of nickels
We know that,
value of 1 dime = $ 0.10
value of 1 nickel = $ 0.05
<em><u>Ben had three times as many nickels as dimes</u></em>
Number of nickels = 3 times the number of dimes
n = 3d --------- eqn 1
<em><u>The total value of his coins was $1</u></em>
<em><u>Therefore, we frame a equation as:</u></em>
number of dimes x value of 1 dime + number of nickels x value of 1 nickel = 1
![d \times 0.10 + n \times 0.05 = 1\\\\\text{Substitute eqn 1 in above }\\\\0.10d + 0.05(3d) = 1\\\\\text{Simplify the above expression }\\\\0.10d + 0.15d = 1\\\\0.25d = 1\\\\\text{Divide both sides of equation by 0.25 }\\\\d = 4](https://tex.z-dn.net/?f=d%20%5Ctimes%200.10%20%2B%20n%20%5Ctimes%200.05%20%3D%201%5C%5C%5C%5C%5Ctext%7BSubstitute%20eqn%201%20in%20above%20%7D%5C%5C%5C%5C0.10d%20%2B%200.05%283d%29%20%3D%201%5C%5C%5C%5C%5Ctext%7BSimplify%20the%20above%20expression%20%7D%5C%5C%5C%5C0.10d%20%2B%200.15d%20%3D%201%5C%5C%5C%5C0.25d%20%3D%201%5C%5C%5C%5C%5Ctext%7BDivide%20both%20sides%20of%20equation%20by%200.25%20%7D%5C%5C%5C%5Cd%20%3D%204)
<em><u>Substitute d = 4 in eqn 1</u></em>
n = 3(4)
n = 12
Thus Ben has 4 dimes and 12 nickels
Answer:
- HU ≅ HG
- ∠R ≅ ∠F
- DE ≅ XW
Step-by-step explanation:
It helps to understand what the letters in SSS, AAS, and ASA mean. S stands for <em>side</em>; A stands for <em>angle</em>. The sequence of letters refers to the sequence of sides and angles that must be shown to be congruent in order for that theorem to apply. AAS means two angles and a side <em>not</em> between them; ASA means two angles and the side between them.
To solve these problems, you need to identify the congruences already shown in the diagram, then find the one that is missing to finish out the sequence of sides and angles represented by the abbreviation.
_____
1.
Sides UF and GF are marked congruent. Side HF is congruent to itself. So to use SSS, you need the third sides of the triangles congruent:
HU ≅ HG
__
2.
Side PQ is shown congruent to DQ. We know the vertical angles at Q are congruent. To use AAS, we need an angle not adjacent to the congruent sides, so we need ...
∠R ≅ ∠F
__
3.
A pair of angles in each triangle is shown congruent. To use ASA, the congruent sides need to be between the congruent angles:
DE ≅ XW
Ok so, 8 x 10^9 is in nine days since 1 is x. so 10^9 * 8 so the answer is 8,000,000,000.
<span>Let's assume the mat as a right triangle
Taking length of triangle be x
so height = x-21
and hypotenuse= x+6
for right triangle we can apply pythagoras theorem
so (x+6)^2=x^2+(x-21)^2
expanding we get
x^2 + 12 x + 36 = 2 x^2 - 42 x + 441
solving for x we get
x=9,45
But for length to be 9 height will be negative
So the length of mat will be 45 inches</span>
Answer:
If you are looking for the answer, It will take him 25 miles to walk to school.
Step-by-step explanation: