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3 years ago

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Per single gallon of gas, Gina's vehicle can go 16 more miles than Amanda's vehicle. If the combined distance the vehicles can t

ravel on one gallon of gas is 72 miles, what is the distance that Gina's vehicle travels?A.24 milesB.28 milesC.36 milesD.44 miles

1 answer:

agasfer [191]3 years ago

5 0

The correct answer is c

You might be interested in

Please answer both!

Naya [18.7K]

Answer:

36)12(37)0.67

Step-by-step explanation:

36)A=base×height

A=2×6

A=12

37)A=a+b/2h

A=2+6/12

A=8/12

A=0.67

8 0

2 years ago

Find the exact value of csc theta if tan theta = sqrt3 and the terminal side of theta is in Quadrant III.

WARRIOR [948]

Answer:

3rd option

Step-by-step explanation:

Using the identities

cot x = $\frac{1}{tanx}$

csc² x = 1 + cot² x

Given

tanθ = $\sqrt{3}$ , then cotθ = $\frac{1}{\sqrt{3} }$

csc²θ = 1 + ( $\frac{1}{\sqrt{3} }$ )² = 1 + $\frac{1}{3}$ = $\frac{4}{3}$

cscθ = ± $\sqrt{\frac{4}{3} }$ = ± $\frac{2}{\sqrt{3} }$

Since θ is in 3rd quadrant, then cscθ < 0

cscθ = - $\frac{2}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ = - $\frac{2\sqrt{3} }{3}$

8 0

2 years ago

natita [175]

$\bf (7x-6)\times (3x^2-4x+5)\implies \begin{array}{cllll} 3x^2-4x+5\\ \times 7x\\\cline{1-1} 21x^3-28x^2+35x \end{array}~~ +~~ \begin{array}{cllll} 3x^2-4x+5\\ \times -6\\\cline{1-1} -18x^2+24x-30 \end{array} \\\\\\ 21x^3-28x^2+35x~~+~~(-18x^2+24x-30)\implies \boxed{21x^3-46x^2+59x-30}$

3 0

2 years ago

If 2^n + 1 is an odd prime for some integer n, prove that n is a power of 2. (H

vovikov84 [41]

Step-by-step explanation:

We will prove by contradiction. Assume that $2^n + 1$ is an odd prime but n is not a power of 2. Then, there exists an odd prime number p such that $p\mid n$ . Then, for some integer $k\geq 1$ ,

$n=p\times k.$

Therefore

$2^n + 1=2^{p\times k} + 1=(2^{k})^p + 1^p.$

Here we will use the formula for the sum of odd powers, which states that, for $a,b\in \mathbb{R}$ and an odd positive number $n$ ,

$a^n+b^n=(a+b)(a^{n-1}-a^{n-2}b+a^{n-3}b^2-...+b^{n-1})$

Applying this formula in 1) we obtain that

$2^n + 1=2^{p\times k} + 1=(2^{k})^p + 1^p=(2^k+1)(2^{k(p-1)}-2^{k(p-2)}+...-2^{k}+1)$ .

Then, as $2^k+1>1$ we have that $2^n+1$ is not a prime number, which is a contradiction.

In conclusion, if $2^n+1$ is an odd prime, then n must be a power of 2.

4 0

2 years ago

Jan and Wayne went to the store to buy some groceries. Jan bought 2 cans of corn beef hash and 3 cans of creamed chipped beef fo

yulyashka [42]

Answer:

The system of equations that models the problem is:

$\left \{ {{2*H+3*C=4.95} \atop {3*H+2*C=5.45}} \right.$

Step-by-step explanation:

A system of equations is a set of two or more equations with several unknowns in which we want to find a common solution. So, a system of linear equations is a set of (linear) equations that have more than one unknown that appear in several of the equations. The equations relate these variables or unknowns to each other.

In this case, the unknown variables are:

H: price of a can of corn beef hash
C: price of a can of creamed chipped beef

Knowing the unit price of a product, the price of a certain quantity of that product is calculated by multiplying that quantity by the unit price. So the price for 2 cans of ground beef hash can be calculated as 2 * H and the price for 3 cans of ground beef with cream can be calculated as 3 * C. Jan paid $ 4.95 for those amounts from both cans. This means that the sum of the can prices must be $ 4.95. So: <u><em>2*H + 3*C= 4.95 Equation (A)</em></u>

Thinking similarly, if Wayne bought 3 cans of corn beef hash and 2 cans of creamed chipped beef for $5.45, Wayne's buy can be expressed by the equation:

<u><em>3*H + 2*C= 5.45 Equation (B)</em></u>

Finally, <u><em>the system of equations that models the problem is:</em></u>

<u><em></em></u> $\left \{ {{2*H+3*C=4.95} \atop {3*H+2*C=5.45}} \right.$ <u><em></em></u>

7 0

2 years ago