A triangle has a perimeter of 18 inches. If one side has length 8 inches, find the length of the shortest side if the other lengths are in the ratio of 2 units : 3 units.

Answers

Answer 1

Answer: $a,b,c-\ sides\ of\ triangle\n\na+b+c=18\ inches\n\na=8inch\n\n(b)/(c)=(2)/(3)\n\n3b=2c\ \ --->b=(2c)/(3)\n\n8+(2c)/(3)+c=18\ |*3\n\n24+2c+3c=54\n\n5c=54-24\n\n5c=30\n\nc=(30)/(5)=6\n\nLength\ of\ shorter\ side\ is\ equal\ to\ 6\ inches.$

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If you have a new deck of shuffled cards, what is the probability you will choose an ace? (52 cards, no jokers) A) 1 13 B) 1 2 C) 1 4 D) 1 6

Answers

Answer:

B 1/2

Step-by-step explanation:

I looked it up.

But I think it'd be C because there would be 4 aces in the deck, and C has 1/4

Answer: 1/13 is the correct answer.

Step-by-step explanation: You put the total amount of aces, which is four, on the top part of your fraction and the total number of 52 cards on the bottom of your fraction. Since four will divide into both numbers, you simplify 4/52 to get 1/13. 4 divided by four is one. 52 divided by 4 is 13. That is how you get your 1/13 from 4/52. Answer was confirmed correct on the test I took. I hope this helps you! Thanks!

Pls help me with this question it’s math look at the pic

Answers

Answer:

youre answer will be the opiton apple juice

if the perimeter of a circular sector is fixed at 100 ft, what values of r and s give the sector the greatest area? ...?

Answers

The sector arc length is just a fraction of the circumference:
Laʀc = (2πR) • (θ ⁄ 2π) = R • θ ... where θ = central angle (of sector)

Ps = R + R + (R • θ) ... perimeter of sector = Ps

Ps = R • (2 + θ) ... Ps = 100 ft

100 = R • (2 + θ)

θ = (100 ⁄ R) – 2

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...

Similarly, the sector area is just a fraction of the circle area:

As = (πR²) • (θ ⁄ 2π) ... area of sector = As

As = R² • θ ⁄ 2 ... substitute for θ

As = R² • [(100 ⁄ R) – 2 ] ⁄ 2

As = 50R – R² ... differentiate

As' = 50 – 2R ... set to zero

0 = 50 – 2R

R = 25 ft ... optimum radius

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...

As = 50R – R² ... evaluate at: R = 25 ft

As = 50(25) – (25)²

As = 625 ft² ... maximum area

Note ... at any other R_value, the sector area is less.

" θ " can be determined using: θ = (100 ⁄ R) – 2

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Final answer:

For a circular sector with a fixed perimeter of 100 ft, the values of radius (r) and arc length (s) that will maximize the sector's area are r=25 and s=50.

Explanation:

The perimeter of a circular sector is composed by the length of the arc (s) plus twice the radius (r). If this sum is fixed at 100 ft, then the length of the arc s is equal to 100 - 2r. The area A of a circular sector can be defined as A = 0.5 * r * s.

Substituting the expression for s into the area formula obtains A = 0.5 * r * (100-2r). Simplifying results in A = 50r - r^2 which is a downward opening parabola.

The maximum value of a parabola occurs at the vertex. For a parabola in the form y=ax^2 + bx + c, the x-coordinate of the vertex is -b/(2a). In this case, a=-1 and b=50, hence r=-50/2*(-1) = 25. Substituting r=25 back into the formula for s obtains s = 100-2*25 = 50. Therefore, the values for r and s that will give the circular sector the greatest area are r=25 and s=50.

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Look at the figures. How can you prove these triangles are congruent?

Answers

By SAScongruence rule Triangles DFE and ACB are Congruent.

What is Congruency?

Twoangles and a non-included side of a triangle are said to be congruent when they are equivalent to the corresponding angles and sides of another triangle.

The measurements of the sides and angles of two or more triangles determine their congruence. A triangle's size is determined by its three sides, and its shape is determined by its three angles. Two triangles are said to be congruent if the pairings of their respective sides and angles are equal.

We have Two Triangles DFE and ACB.

Now, from the triangles we have

AC = DF

BC = EF

< ACB = < DFE

and, the angle which is congruent is in between two congruent sides.

So, by SAS congruence rule Triangles DFE and ACB are Congruent.

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Answer:

You can use the Side-Angle-Side Postulate.

Step-by-step explanation:

The Side-Angle-Side (or SAS) Postulate basically states that if two sides of two triangles and the included angle are congruent, the two triangles are congruent.

at a lunch stand, each hamburger has 50 more calories than each order of fries. if 2 hamburgers and 3 orders of fries have a total of 1700 calories, how many calories does a hamburger have?

Answers

The correct answer is 370. A system of equations can be used, where h represents the number of calories in a hamburger and f represents the number of calories in an order of fries. The equation 2 h plus 3 f equals 1,700 represents the fact that 2 hamburgers and 3 orders of fries contain a total of 1700 calories, and the equation h equals f plus 50 represents the fact that one hamburger contains 50 more calories than an order of fries. Substituting f plus 50 for h in 2 h plus 3 f equals 1,700 gives 2, parenthesis, f plus 50, close parenthesis, plus 3 f, equals 1,700. This equation can be solved as follows:

2 f plus 100 plus 3 f equals 1,700

5 f plus 100 equals 1,700

5 f equals 1,600

f equals 320

The number of calories in an order of fries is 320, so the number of calories in a hamburger is 50 more than 320, or 370.

(3x²y³)(-5xy^{4}z)When multiplying the variables, do you multiply the x by the x next to the y^{4}z, and the y with the y^{4}? I asked my teacher this question for a similar problem and he said not to. When I asked my dad for help with this problem, he said that you do and the answer is -15x^{3}y^{7}z. Which method is correct?

Answers

remember
x^m=x times itself m times

REMEMBER THAT MULCTIPLICATION IS COMMUTATIVE
a(bc)=(ab)c

so basically
(abc)(3ac)=a*b*c*3*a*c=a*a*c*c*b*3=3a^2bc^2
group and regroup and move around

so in your problem
(3x^2y^3)(-5xy^4z)=
(3)(x^2)(y^3)(-5)(x)(y^4)(z)=
(3)(-5)(x^2)(x)(y^3)(y^4)(z)=
(-15)(x^3)(y^7)(z)=
-15x^3y^7z

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