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3 years ago

You have 25 coins that total $1.45. The only coins you have are quarters and pennies. How many of each coin do you have?

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

5 0

Answer:You have 4 quarters and 45 pennines

Step-by-step explanation:

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Semielliptical Arch Bridge An arch for a bridge over a highway is in the form of half an ellipse. The top of the arch is 20 feet

photoshop1234 [79]

Answer:

the span of the bridge is 73.7 feet

Step-by-step explanation:

The equation of an ellipse with a vertical major axis(i.e major axis parallel to y axis) is given by:

$\frac{(x-h)^{2} }{b^{2} } + \frac{(y-k)^{2} }{a^{2} }= 1$ a>b

where (h,k) are the coordinates of the center of the ellipse, a is the length of the major axis and b is the length of the minor axis

For this problem, the center of the ellipse (h,k) = (0,0)

Therefore:

$\frac{(x)^{2} }{b^{2} } + \frac{(y)^{2} }{a^{2} }= 1$

The top of the arch is 20 feet above the ground level (the major axis), therefore a=20

length of the major axis = 2a= 2*20 = 40

$\frac{x^{2} }{b^{2} } + \frac{y^{2} }{20^{2} }= 1\\\frac{x^{2} }{b^{2} } + \frac{y^{2} }{400 }= 1$

The coordinates of the ellipse (x,y) = (28,13)

$\frac{28^{2} }{b^{2} } + \frac{13^{2} }{400 }= 1$

$\frac{28^{2} }{b^{2} } + 0.4225= 1$

$\frac{784 }{b^{2} } = 0.5775$

b² ≅ 1358

b≅36.85

Length of minor axis (2b) = 73.7 feet.

the span of the bridge is 73.7 feet

7 0

3 years ago

What is the justification for step 2? 4(x-5)= -12 Justification Step 1: 4x-20=-12 Distributive Property Step 2 4x= 8 ? Step 3 x=

matrenka [14]

Answer:

addition property of equality

Step-by-step explanation:

Given the equation 4(x-5) = -12

Expand

4x - 20 = -12

Add 20 to both sides (addition property of equality)

4x-20+20 = -12+20

4x = 8

x = 8/4

x = 2

Hence the value of x is 2

The justification for step 2 is addition property of equality

7 0

3 years ago

Need math help please!!

s2008m [1.1K]

Just by looking at it, 2 seems to be the correct answer. I mean if you think about it, when the triangle is split in two smaller triangles, side LN is longer than LP so that means x needs to be a small number. I could either be 2 or 1. Well if you look at the big picture, side LM is longer than LN so it’s gonna need to be bigger. If you say x=1 then you are saying 2(1) +4 = 6 (therefore LM is 6) but if you say x=2 then you are saying 2(2) +4 = 8 which makes more sense

If x=2 then you can use the Pythagorean’s theorem

a2 + b2 = c2
4^2 + b^2 = 5^2
16 + b^2 = 25
25-16= 9
b^2= 9
b= 3

Now that we know what NP is we can do Pythagorean’s theorem to figure out what side LP is (we already know it but you can do it again to check lol)

So the answer is 2

5 0

3 years ago

Are these fractions equivalent or nonequivalent?<br> 4x/7y 8x/14y

ivann1987 [24]

Answer:

$\frac{8x}{14y} = \frac{ \frac{8x}{2} }{ \frac{14y}{2} } = \frac{4x}{7y} \\$

Hence, they are equivalent.

6 0

3 years ago

Solve the linear equation:<br><br> 3.4 + 2(9.7 – 4.8x) = 61.2

Ganezh [65]

Answer:

- 4

Step-by-step explanation:

(2*(Rationalize(9.7)-Rationalize(4.8x)))==Rationalize(61.2)-Rationalize(3.4)

Rationalize(18.4)-Rationalize(2.8x)

==Rationalize(57.8)

-Rationalize(2.8x)==Rationalize(57.8)-Rationalize(18.4)

x= 38.4÷-2.8

:x= -4

7 0

3 years ago