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2 years ago

Amanda buys 4 tickets to the baseball game for $24 each. Which equation

Mathematics

1 answer:

pentagon [3]2 years ago

7 0

Answer:

$96

Step-by-step explanation:

Given that,

The total number of tickets = 4

Cost of each baseball = $24

We need to find the equation that shows the closest estimate of the total amount Amanda spends.

Total cost = No. of tickets × Cost of each baseball

= 4×24

= $96

Hence, the total cost is $96.

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The little Mexican restaurant sells only two kinds of beef burritos mucho beef sandwich Lucho beef last week the restaurant orde

Finger [1]

Answer:

Cost of a single Mucho beef burrito: $\$5.5$

Cost of a double Mucho beef burrito: $\$6.5$

Step-by-step explanation:

<h3> The exercise is: "The Little Mexican restaurant sells only two kinds of beef burritos: Mucho beef and Mucho Mucho beef. Last week in the restaurant sold 16 orders of the single Mucho variety and 22 orders of the double Mucho. If the restaurant sold $231 Worth of beef burritos last week and the single neutral kind cost $1 Less than the double Mucho, how much did each type of burrito cost?"</h3>

Let be "x" the the cost in dollars of a single Mucho beef burrito and "y" the cost in dollars of a double Mucho burrito.

Set a system of equations:

$\left \{ {{16x+22y=231} \atop {x=y-1}} \right.$

To solve this system you can apply the Substitution Method:

1. Substitute the second equation into the first equation and solve for "y":

$16(y-1)+22y=231\\\\16y-16+22y=231\\\\38y=231+16\\\\y=\frac{247}{38}\\\\y=6.5$

2. Substitute the value of "y" into the second equation and evaluate in order to find the value of "x":

$x=6.5-1\\\\x=5.5$

5 0

2 years ago

In AMNO, m = 540 inches, n = 330 inches and o=600 inches. Find the measure of

MaRussiya [10]

Answer: 83.5

Step-by-step explanation:

5 0

3 years ago

Let z=3+i, then find a. Z² b. |Z| c.<img src="https://tex.z-dn.net/?f=%5Csqrt%7BZ%7D" id="TexFormula1" title="\sq

zysi [14]

Given z = 3 + i, right away we can find

(a) square

z ² = (3 + i )² = 3² + 6i + i ² = 9 + 6i - 1 = 8 + 6i

(b) modulus

|z| = √(3² + 1²) = √(9 + 1) = √10

(d) polar form

First find the argument:

arg(z) = arctan(1/3)

Then

z = |z| exp(i arg(z))

z = √10 exp(i arctan(1/3))

z = √10 (cos(arctan(1/3)) + i sin(arctan(1/3))

Any complex number has 2 square roots. Using the polar form from part (d), we have

√z = √(√10) exp(i arctan(1/3) / 2)

and

√z = √(√10) exp(i (arctan(1/3) + 2π) / 2)

Then in standard rectangular form, we have

$\sqrt z = \sqrt[4]{10} \left(\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) + i \sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right)\right)$

and

$\sqrt z = \sqrt[4]{10} \left(\cos\left(\dfrac12 \arctan\left(\dfrac13\right) + \pi\right) + i \sin\left(\dfrac12 \arctan\left(\dfrac13\right) + \pi\right)\right)$

We can simplify this further. We know that z lies in the first quadrant, so

0 < arg(z) = arctan(1/3) < π/2

which means

0 < 1/2 arctan(1/3) < π/4

Then both cos(1/2 arctan(1/3)) and sin(1/2 arctan(1/3)) are positive. Using the half-angle identity, we then have

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1+\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1-\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

and since cos(x + π) = -cos(x) and sin(x + π) = -sin(x),

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{1+\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{1-\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

Now, arctan(1/3) is an angle y such that tan(y) = 1/3. In a right triangle satisfying this relation, we would see that cos(y) = 3/√10 and sin(y) = 1/√10. Then

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1+\dfrac3{\sqrt{10}}}2} = \sqrt{\dfrac{10+3\sqrt{10}}{20}}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1-\dfrac3{\sqrt{10}}}2} = \sqrt{\dfrac{10-3\sqrt{10}}{20}}$

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{10-3\sqrt{10}}{20}}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{10-3\sqrt{10}}{20}}$

So the two square roots of z are

$\boxed{\sqrt z = \sqrt[4]{10} \left(\sqrt{\dfrac{10+3\sqrt{10}}{20}} + i \sqrt{\dfrac{10-3\sqrt{10}}{20}}\right)}$

and

$\boxed{\sqrt z = -\sqrt[4]{10} \left(\sqrt{\dfrac{10+3\sqrt{10}}{20}} + i \sqrt{\dfrac{10-3\sqrt{10}}{20}}\right)}$

3 0

3 years ago

Read 2 more answers

∠CAT and ∠MUD are supplementary. If m∠CAT=11x+16 and m∠MUD=4x+14, find the measure of each angle.

Georgia [21]

Answers:

x = 10
angle CAT = 126 degrees
angle MUD = 54 degrees

=========================================================

Explanation:

∠CAT and ∠MUD are supplementary, which means the angle measures add to 180. They form a straight line.

( m∠CAT ) + ( m∠MUD ) = 180

( 11x+16 ) + ( 4x+14 ) = 180

11x+16 + 4x+14 = 180

(11x+4x) + (16+14) = 180

15x+30 = 180

15x = 180-30

15x = 150

x = 150/15

x = 10

Let's find each angle based on this x value

m∠CAT=11x+16 = 11*10+16 = 110+16 = 126 degrees
m∠MUD=4x+14 = 4*10+14 = 40+14 = 54 degrees

Those two angles add to 126+54 = 180 to confirm we do indeed have supplementary angles, and confirm the correct answers.

8 0

1 year ago

Please help with #12

ExtremeBDS [4]

Answer:

a. 1 1/8 b. 8/9

Step-by-step explanation:

You can set this up as a proportion to solve. For part a. we know that 2/3 of the road is 3/4 mile long. 2/3 + 1/3 = the whole road, so we need how many miles of the road is 1/3 its length. Set up the proportion like this:

$\frac{\frac{2}{3} }{\frac{3}{4} } =\frac{\frac{1}{3} }{x}$