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Mrac [35]
2 years ago
11

the taco truck sells tacos for $3 and burritos for $4. the number of items sold on a tuesday is 125 with a total income of $430.

how many tacos were sold?
Mathematics
1 answer:
butalik [34]2 years ago
5 0

Answer:

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations:

3 T + 4 B =425

T + B = 125

Where T is the number of tacos sold, and B is the number of burritos sold.

Multiplying the second equation by 3, and subtracting it to the first equation:

3 T + 4 B =425

3T + 3B = 375

___________

B =50

Replacing B in any equation:

T + B = 125

T +50 =125

T =125-50

T = 75

Feel free to ask for more if needed or if you did not understand something.

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Work out the area of abcd.<br><br> please ensure you give workings out too.
ipn [44]

Answer:

\displaystyle A_{\text{Total}}\approx45.0861\approx45.1

Step-by-step explanation:

We can use the trigonometric formula for the area of a triangle:

\displaystyle A=\frac{1}{2}ab\sin(C)

Where a and b are the side lengths, and C is the angle <em>between</em> the two side lengths.

As demonstrated by the line, ABCD is the sum of the areas of two triangles: a right triangle ABD and a scalene triangle CDB.

We will determine the area of each triangle individually and then sum their values.

Right Triangle ABD:

We can use the above area formula if we know the angle between two sides.

Looking at our triangle, we know that ∠ADB is 55 DB is 10.

So, if we can find AD, we can apply the formula.

Notice that AD is the adjacent side to ∠ADB. Also, DB is the hypotenuse.

Since this is a right triangle, we can utilize the trig ratios.

In this case, we will use cosine. Remember that cosine is the ratio of the adjacent side to the hypotenuse.

Therefore:

\displaystyle \cos(55)=\frac{AD}{10}

Solve for AD:

AD=10\cos(55)

Now, we can use the formula. We have:

\displaystyle A=\frac{1}{2}ab\sin(C)

Substituting AD for a, 10 for b, and 55 for C, we get:

\displaystyle A=\frac{1}{2}(10\cos(55))(10)\sin(55)

Simplify. Therefore, the area of the right triangle is:

A=50\cos(55)\sin(55)

We will not evaluate this, as we do not want inaccuracies in our final answer.

Scalene Triangle CDB:

We will use the same tactic as above.

We see that if we can determine CD, we can use our area formula.

First, we can determine ∠C. Since the interior angles sum to 180 in a triangle, this means that:

\begin{aligned}m \angle C+44+38&=180 \\m\angle C+82&=180 \\ m\angle C&=98\end{aligned}

Notice that we know the angle opposite to CD.

And, ∠C is opposite to BD, which measures 10.

Therefore, we can use the Law of Sines to determine CD:

\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}

Where A and B are the angles opposite to its respective sides.

So, we can substitute 98 for A, 10 for a, 38 for B, and CD for b. Therefore:

\displaystyle \frac{\sin(98)}{10}=\frac{\sin(38)}{CD}

Solve for CD. Cross-multiply:

CD\sin(98)=10\sin(38)

Divide both sides by sin(98). Hence:

\displaystyle CD=\frac{10\sin(38)}{\sin(98)}

Therefore, we can now use our area formula:

\displaystyle A=\frac{1}{2}ab\sin(C)

We will substitute 10 for a, CD for b, and 44 for C. Hence:

\displaystyle A=\frac{1}{2}(10)(\frac{10\sin(38)}{\sin(98)})\sin(44)

Simplify. So, the area of the scalene triangle is:

\displaystyle A=\frac{50\sin(38)\sin(44)}{\sin(98)}

Therefore, our total area will be given by:

\displaystyle A_{\text{Total}}=50\cos(55)\sin(55)+\frac{50\sin(38)\sin(44)}{\sin(98)}

Approximate. Use a calculator. Thus:

\displaystyle A_{\text{Total}}\approx45.0861\approx45.1

8 0
2 years ago
The first 5 terms of a sequence are shown below:
nirvana33 [79]

Step-by-step explanation:

To find the formula for the nth term ,

First , find the common difference or common ratio.

Common difference =

T_2-T_1 \\  - 2 - 3 \\  =  - 5

Common ratio =

T_2/T_1 \\  \frac{ - 2}{3}

The common difference applies to the other given numbers for example :

T_3- T_2  =  - 7 - ( - 2) \\  =  - 7 + 2 =  - 5

this proves that it is an arithmetic sequence and the given formula for the nth term of an arithmetic sequence is

T_n =a(n-1)d

Where n = no of terms

a= first term

d= common difference

6 0
3 years ago
Batman uses 5 gallons of gas to drive his Batmobile 140
stepan [7]

Answer:

196 miles

Step-by-step explanation:

if he goes 140 miles with 5 gallons, each gallon lets him go 28 miles.

140miles/5gallons=28miles/1gallon

then 7 gallons lets you go 196 miles

brainliest please :)

7 0
3 years ago
F (x) = 4x + 7. Find the inverse of f(x).
Brilliant_brown [7]

Answer:

C. f(x) = x - 7 all over 4

Step-by-step explanation:

NB: Let f(x) = y

Exchange X and Y

Make y the subject

f(x) = 4x + 7

y = 4x + 7

x = 4y + 7

x - 7 = 4y

x - 7 all over 4 = 4 ÷ 4

y = x - 7 all over 4

6 0
3 years ago
Use the Laplace transform to solve the given initial value problem. y' + 6y = e^4t ; y(0)=2 ...?
TiliK225 [7]
Performing laplace transform of the equation.

sY(s) - y(0) + 6Y(s) = 1/(s-4)
(s+6)Y(s) - 2 = 1/(s-4)
Y(s) = 2/(s+6) + 1/(s-4)(s+6), by partial fraction decomposition
Y(s) = 2/(s+6) + 1/10 * (1/(s-4) + 1/(s+6))
Y(s) = 0.1/(s-4) + 2.1/(s+6)

Performing inverse laplace transform,
y(t) = 0.1e^4t + 2.1e^(-6t)


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
4 0
3 years ago
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