Lightbulbs act as resistors. Janine is building a circuit that contains two lightbulbs in parallel. One of the lightbulbs has a resistance of 120 ohms, but the resistance of the second lightbulb is unknown. Therefore, The inverse of Janine's equation is r = -120/(t - 120).
Equation:
An equation is described as a formula that expresses the equality of two expressions, by connecting them with the equals sign. An equation is a formula that expresses that two expressions are equal by joining them with the equal sign =.The word comparison and its cognates in other languages may have subtly different meanings; for example, in French, an equation is defined to contain one or more variables, and in English any well-formed formula composed of two expressions linked by equal signs is an equation.
According to the Question:
In algebra, an equation is a mathematical statement that determines whether two mathematical expressions are equal.
The type of comparison is identity or conditional comparison.
For each potential value, the variable provides an identifier. Only certain combinations of variable values allow conditional comparisons to be true.
In order to find the inverse of Janine's equation, we will to solve for r in terms of t.
First, we can rearrange the equation to get
⇒ t - 120 = 1/r.
divide both sides of the equation by 1/r to get
⇒ t/r - 120/r = 1.
divide both sides of the equation by -120/r to get
⇒ r = -120/(t - 120).
Therefore, the inverse of Janine's equation is r = -120/(t - 120).
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The expression tan(0) cos(0) simplifies to sin(0) . Prove it
Using the definitions of trigonometric functions for x = 0, we have tan(0) = 0 and cos(0) = 1, which simplifies to 0 * 1 = 0, and sin(0) = 0,
therefore tan(0) cos(0) = sin(0).
Define trigonometric.
Trigonometric refers to the branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles. It involves the study of trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant, and their properties and applications in various fields including mathematics, science, engineering, and navigation.
For any angle x, we have the identity:
tan(x) = sin(x) / cos(x)
Setting x = 0, we get:
tan(0) = sin(0) / cos(0)
Since tan(0) = 0 and cos(0) = 1, we can simplify this equation to:
0 = sin(0)
which is true, since the sine of 0 degrees is 0. Therefore, we have shown that:
tan(0) cos(0) = sin(0)
Therefore, the identity tan(0) cos(0) = sin(0) is proven.
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What is the answer to this math problem? I can’t seem to figure it out.
Answer:
X
Step-by-step explanation:
We first must check the total amount of breakfast. Y happens to have 130 instead of 125. Now, we see that W and Z have a majority on strawberries with oatmeal, which is not what we are looking for. The last answer we have is X, where there is a majority of oatmeal + blueberries and there is a total of 125 breakfasts.
Hope this helps!
Tamarisk company began operations on january 2, 2019. It employs 9 individuals who work 8-hour days and are paid hourly. Each employee earns 9 paid vacation days and 7 paid sick days annually. Vacation days may be taken after january 15 of the year following the year in which they are earned. Sick days may be taken as soon as they are earned; unused sick days accumulate. Additional information is as follows. Actual hourly wage rate vacation days used by each employee sick days used by each employee 2019 2020 2019 2020 2019 2020 $6 $7 0 8 5 6 tamarisk company has chosen to accrue the cost of compensated absences at rates of pay in effect during the period when earned and to accrue sick pay when earned
The total cost of compensated absences for Tamarisk Company for the years 2019 and 2020 was $348 + $1,399 = $1,747.
To calculate the cost of compensated absences for Tamarisk Company, we need to calculate the number of vacation days and sick days earned by the employees in 2019 and 2020, and then calculate the cost of the days earned but not taken.
Each employee earns 9 vacation days per year. As they can be taken after January 15th of the year following the year in which they are earned, the vacation days earned by the employees in 2019 can be taken in 2020. Therefore, in 2019, no vacation days were taken by any employee.
In 2020, the employees took a total of 8 vacation days. As there are 9 employees, the total vacation days taken in 2020 were 9 x 8 = 72.
Sick Days:
Each employee earns 7 sick days per year, and unused sick days accumulate. In 2019, the employees used a total of 5 sick days. Therefore, the unused sick days at the end of 2019 were 9 x 7 - 5 = 58.
In 2020, the employees used a total of 6 sick days, and the unused sick days at the end of 2020 were 58 + 9 x 7 - 6 = 109.
To find the cost of compensated absences. The unused sick days and vacation days must be multiplied to get the hourly wage rate in effect in a year.
In 2019, the cost of compensated absences was 58 x $6 = $348.
In 2020, the cost of compensated absences was (72 + 109) x $7 = $1,399.
Therefore, the total cost of compensated absences for Tamarisk Company for the years 2019 and 2020 was $348 + $1,399 = $1,747.
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when the expression -3x^5+6x^2-9x^3-x is written with terms in descending order (from highest to lowest), which list represents the coefficients of the term?
a. 6, -9, -3, -1
b. -3, 6, -9, -1
c. 1, 6, -9, -3
d. -3, -9, 6, -1
Find m ∠ JKL using the picture
The value of m∠JKL is 34°
How to find the value of m∠JKL?An angle formed by a tangent and a secant intersecting outside a circle is equal to one-half the difference of the measures of the intercepted arcs.
Based on the theorem above, we can say:
m∠JKL = 1/2 * (159 - 91)
m∠JKL = 1/2 * 68
m∠JKL = 34°
Therefore, the value of m∠JKL in the circle is 34°.
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Can someone help me with this please? Thank you!
Answer:
a. f(10)= 20*10+14
f(10)=200+14
f(10)= 214
214
Proving Triangle Similarity
The proof is completed using two column proof as follows
Statement Reason
QT ⊥ PT Given
∠ QRP ≅ ∠ SRT = 90 definition of perpendicularity
∠ QPR ≅ ∠ STR Given
Δ PQR is similar to Δ TSR AA similarity theorem
What is AA similarity theorem?The AA similarity theorem, also known as the Angle-Angle Similarity Theorem, states that if two triangles have two corresponding angles that are congruent, then the triangles are similar.
In the given triangle, the two angles given to be equal are
∠ QRP ≅ ∠ SRT = 90 and ∠ QPR ≅ ∠ STRHence the triangles are similar
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Answer:
:)
Hopefully this helps you guys :)
good luck :D
Problem 1 (3 pts). The nearest neighbor method is used with the following labeled training data in a two class, two feature problem. Show clearly the decision boundaries obtained. Indicate all break points and slopes correctly Class1={(0,0)^T,(0,1)^T}. Class2={(1,0)^T,(0,0.5)^T}
Problem 1 (3 pts). The nearest neighbor method is used with the following labeled training data in a two class, two feature problem. Show clearly the decision boundaries obtained. Indicate all break points and slopes correctly Class1={(0,0)^T,(0,1)^T}. Class2={(1,0)^T,(0,0.5)^T}.
The decision boundary is the line that separates the two classes. When it comes to the nearest neighbour method, the boundary of a class is determined by the closest data point in the other class.What is the nearest neighbour method?The nearest neighbour method (NNM) is a type of lazy learning method in which the data is stored and the computation is deferred until the classification phase.
The goal of the nearest neighbor technique is to use the pattern of the closest data point to classify a new sample. It's also one of the simplest non-parametric classification methods, and it's based on the assumption that the feature spaces used by each class are continuous regions.For Class 1, there are two labeled training data points: (0, 0)T and (0, 1)T. Similarly, for Class 2, there are two labeled training data points: (1, 0)T and (0, 0.5)T.
To generate decision boundaries, follow the steps below:Step 1: Plot the given labeled training data. They are shown in the figure below. Step 2: Label the data points according to their class: Class 1 and Class 2.Step 3: Now, we need to find the nearest neighbors. Find the nearest neighbor for each of the labeled training data points from the opposite class. The distances are calculated as follows:For the Class 1 data points, the nearest neighbor is Class 2's (1, 0)T data point.
For the Class 2 data points, the nearest neighbour is Class 1's (0, 1)T data point.Step 4: Connect the nearest neighbour's labeled training data points with a line. These are the decision boundaries. The red line represents the decision boundary between Class 1 and Class 2. The green line represents the decision boundary between Class 2 and Class 1. The slopes of the decision boundaries are -1 for the red line and 1 for the green line. These slopes are the result of the negative reciprocal of the nearest neighbour's slope. The break point for the red line is 0.5, while the break point for the green line is 0. A break point is the point at which the decision boundary intersects the y-axis.
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Part A Which solution do you get when you use the quadratic formula to solve the equation –4x2 – 12x – 9 = 0?
Answer:
A: -3/2
Step-by-step explanation:
-4x²-12x-9=0 First split the b value so that it equals a×c, or -4×-9
-4x²-6x-6x-9=0 Factor by grouping
(-2x-3)(2x+3)=0 Solve for x
x= -3/2
Define a sample space and count the number of sample points in the sample space for each of the following experiments. a. Select at random a set of 5 questions from a set of 15 questions. b. Form by random selection a committee of 5 from a membership of 20.
There are 15C5 or 3003 possible combinations in the sample space.There are 20C5 or 15504 possible combinations in the sample space.
What is number?A number is a mathematical object used to count, measure, and label. Numbers can be represented in many different forms such as natural numbers, integers, real numbers, and complex numbers. They can also be classified as scalar numbers (which have a magnitude or value only) or vector numbers (which have both magnitude and direction). Numbers can be used to represent many different things, including measurements, distances, money, and quantities.
A) Sample Space: The sample space for selecting a set of 5 questions from a set of 15 questions is the set of all possible combinations of 5 questions from 15 questions. There are 15C5 or 3003 possible combinations in the sample space.
B) Sample Space: The sample space for forming a committee of 5 from a membership of 20 is the set of all possible committees that can be formed from 20 members. There are 20C5 or 15504 possible combinations in the sample space.
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The original price of the pearl was 52 euros.
What is price?Price is the monetary value of a product, service, or asset. It is one of the most important factors in a customer's decision to purchase something. Price also determines the amount of profit a business makes on a particular product or service. Price is a key component of the marketing mix, and it can be used to create a sense of value for customers. Price can also be used to differentiate a product from competitors, as well as to indicate quality levels and to create loyalty.
a) One of the cheapest pearls costs 41 euros.
b) This necklace costs 2153 euros, which is the sum of all the pearls.
c) The pearl with the crack originally cost 52 euros. The price was reduced by 1/5, which is 10.4 euros, making the price of the pearl 41.6 euros. The decrease in price of the necklace was 6.5 euros, which means the reduction in price of the pearl was 6.5 euros. Therefore, the original price of the pearl was 52 euros.
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Let θ = 855∘. Complete parts (a), (b), and (c) below. (a) Sketch θ in standard position. (b) Find an angle between 0∘ and 360∘ that is coterminal with θ. (c) Find an angle between −360∘ and 0∘ that is coterminal with θ
Let θ be equal to 855∘. Sketch θ in standard position. θ = 855∘ is in the fourth quadrant of the coordinate plane θ = 855∘
The given angle, θ, is a positive angle. It is measured in the counterclockwise direction from the initial side to the terminal side.Hence, we sketch θ in the standard position with its initial side along the positive x-axis.
Find an angle between 0∘ and 360∘ that is coterminal with θ.
The angle between 0∘ and 360∘ that is coterminal with θ is given by:
θ1 = θ - n × 360∘θ1 = 855∘ - 2 × 360∘θ1 = 855∘ - 720∘θ1 = 135∘
Therefore, an angle between 0∘ and 360∘ that is coterminal with θ is 135∘.Find an angle between −360∘ and 0∘ that is coterminal with θ.
The angle between −360∘ and 0∘ that is coterminal with θ is given by:
θ2 = θ + n × 360∘θ2 = 855∘ + 2 × 360∘θ2 = 855∘ + 720∘θ2 = 1575∘
Therefore, an angle between −360∘ and 0∘ that is coterminal with θ is 1575∘.To learn more about “angle” refer to the https://brainly.com/question/25716982
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You want to measure the height of an antenna on the top of a 125-foot building. From a point in front of the building, you measure the angle of elevation to the top of the building to be 68° and the angle of elevation to the top of the antenna to be 71°. How tall is the antenna, to the nearest tenth of a foot?
The antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.
What is an angle of elevationThe angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.
To get the height of the antenna, we subtract the height of the building from the height from the bottom of the building to the top of the antenna.
we shall represent the distance from the point of observation to the building with x and the height from the bottom of the building to the top of the antenna with y. so that;
tan 68° = 125/x {opposite/adjacent}
x = 125/ tan 68° {cross multiplication}
x = 50.5033
tan 71° = y/50.5033
y = 50.5033 × tan 71°
y = 144.6722
height of the antenna = 144.6722 - 125
height of the antenna = 19.6722
Therefore, the antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.
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Marcus bought a booklet of tickets to use at the amusement park. He used 25% of the tickets on rides, 1 2 of the tickets on video games, and the rest of the tickets in the batting cage. Marcus says he used 23% of the tickets in the batting cage. Do you agree? Complete the explanation.
Answer: Do not agree.
Step-by-step explanation:
To determine if we agree with Marcus, we need to verify if the percentages he used on rides, video games, and batting cage add up to 100%.
Marcus used 25% of the tickets on rides and 1/2 on video games. So, the total percentage of tickets he used is:
25% + 1/2 × 100% = 25% + 50% = 75%
This means that Marcus should have used 25% of the tickets in the batting cage. If he said he used 23% of the tickets in the batting cage, then we do not agree with him.
Brainliest if correct
Answer: a > -1
Explanation is in the image.
Answer:
[tex]a > -1[/tex]
Step-by-step explanation:
1) Write the equation
[tex]-2a+14 < 5a+21\\[/tex]
2) Collect like terms on their corresponding side
[tex]-7a < 7[/tex]
3) Divide -7 from both sides and flip the sign
[tex]a > -1[/tex]
What is the area of the triangle?
Answer:
Step-by-step explanation:
Given:
Side a and Side b are 6 and 5.
The angle C is 131.
This is an obtuse scalene triangle as identified.
Area = ab * sin (C)/2 = 11.32064
QS and TV areparallellines. P Q R S T U V W Which angles are vertical angles?
The required angles ∠SRP and ∠TUW are alternate exterior angles.
What is alternate exterior angles?Alternate exterior angles are a pair of angles that lie on opposite sides of a transversal line that intersects two other lines. Specifically, the angles are exterior to the two intersecting lines and lie on opposite sides of the transversal.
More formally, if two parallel lines are intersected by a transversal, then alternate exterior angles are the pair of angles that are:
On opposite sides of the transversal line.
Outside of the two parallel lines.
Congruent to each other.
These angles are called "alternate" because they are on opposite sides of the transversal and "exterior" because they are outside of the two parallel lines. The congruence of the angles is a result of the parallel lines creating equal corresponding angles.
So,∠SRP and ∠TUW are alternate exterior angles.
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math question please help
Answer:
Step-by-step explanation:
only the 1st and 5th statements are true
Juanita’s Social Security full monthly retirement benefit is $2,128. She started collecting Social Security at age 65. Her benefit is reduced since she started collecting before age 67. Using the reduction percents from Example 1, find her approximate monthly Social Security benefit to the nearest dollar.EXAMPLE 1Marissa from Example 2. What will her monthly benefit be, since she did not wait until age 67 to receive full retirement benefits?SOLUTION Age 67 is considered to be full retirement age if you were born in 1945. If you start collecting Social Security before age 67, your full retirement benefit is reduced, according to the following schedule.• If you start at collecting benefits at 62, the reduction is about 30%.• If you start at collecting benefits at 63, the reduction is about 25%.• If you start at collecting benefits at 64, the reduction is about 20%.• If you start at collecting benefits at 65, the reduction is about 13.3%.• If you start at collecting benefits at 66, the reduction is about 6.7%.Marissa’s full retirement benefit was $1,130.40. Since she retired at age 65, the benefit will be reduced about 13.3%.Find 13.3% of $1,130.40, and round to the nearest cent.0.133 x 1,130.40Subtract to find the benefit Marissa would receive.1,130.40 x 150.34Marissa’s benefit would be about $980.06.EXAMPLE 2Marissa reached age 62 in 2007. She did not retire until years later. Over her life, she earned an average of $2,300 per month after her earnings were adjusted for inflation. What is her Social Security full retirement benefit?
Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.
What is social security benefits retirement age?The age at which a person is qualified to receive their full retirement payment under Social Security is determined by their lifetime earnings history. The complete retirement age for anybody born in 1960 or later is 67. The complete retirement age is steadily lowered for people born before 1960, and is 65 for those born in 1937 or before.
Given that, Juanita started collecting benefits at age 65.
Thus, her benefits reduced by 13.3%.
0.133 x $2,128 = $283.10
Deducting the reduction amount from the total:
$2,128 - $283.10 = $1,844.90
Hence, Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.
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4. What is the solution to 2 + 3(2a + 1) = 3(a + 2)?
Answer:
a=1/3
Step-by-step explanation:
First, expand the brackets by doing multiplication:
2+6a+3=3a+6
Then, move the unknown to the left and the numbers to the right:
3a=6-5
3a=1
a=1/3
The solution to the given equation is -1.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given equation is 2+3(2a+1)=3(a+2)
2+6a+3=3a+2
6a+5=3a+2
6a-3a=2-5
3a=-3
a=-1
Therefore, the solution to the given equation is -1.
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find bases for the null spaces of the matrices given in exercises 9 and 10. refer to the remarks that follow example 3 in section 4.2.
In summary, to find the null spaces of the matrices given in exercises 9 and 10, use the Gauss-Jordan elimination method and refer to the Remarks that follow example 3 in section 4.2 of the text. This will give the dimension of the null space and the number of free variables.
In exercises 9 and 10, the null space of the given matrices can be found by solving the homogeneous linear system of equations. In order to do this, use the Gauss-Jordan elimination method. Refer to example 3 in section 4.2 of the text for a detailed explanation. Afterwards, use the Remarks that follow the example to determine the dimension of the null space and the number of free variables.
The null space of a matrix is the set of all vectors that produce a zero vector when the matrix is multiplied by the vector. Therefore, to find the null space of a matrix, the homogeneous linear system of equations needs to be solved. The Gauss-Jordan elimination method involves adding multiples of one row to another to get a row with all zeroes. After this is done for all the rows, the equations can be solved for the free variables. The number of free variables will determine the dimension of the null space. Refer to example 3 in section 4.2 of the text for more details.
The Remarks that follow the example are important when determining the dimension of the null space and the number of free variables. In the Remarks, it is mentioned that the number of free variables is equal to the number of columns with a zero row. Therefore, after using the Gauss-Jordan elimination method to get the row with all zeroes, the number of columns with a zero row can be counted. This will give the dimension of the null space and the number of free variables.
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Put the steps in correct order to prove that if n is a perfect square, then n + 2 is not a perfect square.1).Lets assume m ≥ 1.2) If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)^2.3) Hence, n + 2 is not a perfect square4) Expand (m + 1)^2 to obtain (m + 1)^2 = m2 + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.5) .Assume n = m2, for some nonnegative integer m
The following is the correct sequence of steps to prove that if n is a perfect square, then n + 2 is not a perfect square:
Step 1: Assume n = m², for some non-negative integer m.
Step 2: If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)².
Step 3: Expand (m + 1)² to obtain (m + 1)² = m² + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.
Step 4: Let's assume m ≥ 1.
Step 5: Hence, n + 2 is not a perfect square.
The first step in the sequence involves making an assumption to start the proof. The second step entails the derivation of the smallest perfect square greater than n. In the third step, we expand the (m + 1)² expression to get n + 2m + 1. The fourth step is an important one, as it shows that m must be greater than or equal to 1.
In the final step, we conclude that n + 2 is not a perfect square.
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The bearing of part A from part B is 074 deg. What is the bearing of part A from part B
The bearing of part A from part B is 254 degrees.
Let X1, X2,..., Xn be i.i.d. random variables from a double exponential distribution with density f(x) = 1/2*λ*exp(−λ|x|). Derive a likelihood ratio test of the hypothesis H0: λ=λ0 versus H1: λ=λ1, where λ0 and λ1 > λ0 are specified numbers. Is the test uniformly most powerful against the alternative H1: λ > λ0?
given the discussion in example 9.4.4, what is the maximum possible length of the repeating section of the decimal representation of 727 1,229 ?
The maximum possible length of the repeating section of the decimal representation of 727 1,229 is 7.
The maximum possible length of the repeating section of the decimal representation of 727 1,229 is 7. The repeating section is comprised of 729.
To calculate this, first consider the prime factorization of 727 1,229. 727 1,229 = 17 × 43 × 137.
Since 17, 43 and 137 are all prime numbers, the prime factorization will not yield a power of 10 as a factor. Therefore, the repeating section must have a length of 7 in the decimal representation of 727 1,229.
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9. Seven more than the quotient of a number b
and 45 is greater than 5.
Any number b greater than -90 will satisfy the inequality. We can express the solution in interval notation as: b ∈ (-90, ∞)
What is inequality?An inequality is a mathematical statement that compares two values or expressions using the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
According to question:Starting from the given inequality:
7 + (b/45) > 5
We can solve for b by first subtracting 7 from both sides:
b/45 > 5 - 7
Simplifying the right-hand side:
b/45 > -2
Multiplying both sides by 45 to isolate b:
b > -2 * 45
b > -90
Therefore, any number b greater than -90 will satisfy the inequality. We can express the solution in interval notation as:
b ∈ (-90, ∞)
For example, x > 5 is an inequality that states that x is greater than 5, while y ≤ 10 is an inequality that states that y is less than or equal to 10.
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A+9 as a verbal expression
Answer:
"9 more than A" is a verbal expression.
.help me additional solve 2 step word problems. All operations
Answer:
1x + 2y = z
Step-by-step explanation:
Here x is the price of jeans and y is the price of T-shirts
z is total money spend
8hr/2days=28hr/?days
Lisa's school is 3 miles west of her house and 3 miles south of her friend Roxanne's house.
Every day, Lisa bicycles from her house to her school. After school, she bicycles from her
school to Roxanne's house. Before dinner, she bicycles home on a bike path that goes straight
from Roxanne's house to her own house. How far does Lisa bicycle each day? If necessary, round to the nearest tenth.
The total distance travelled by Lisa in a day is found to be 10.24 miles.
Explain about the Pythagorean theorem?Pythagoras (born 570 BC) developed a theorem known as the Pythagorean Theorem, which is exclusively applicable to right triangles.
According to the Pythagorean Theorem, a right triangle's hypotenuse square is equal to the sum of its other two sides. The side opposite the right angle is known as the hypotenuse.
Pythagoras theorem:
a² + b² = c²
Given case:
Roxanne's house is 3 miles south of Lisa's school say 'a', which is 3 miles west of Lisa's home say 'b'. Lisa commutes to school by bicycle each day from her home. She rides her bicycle to Roxanne's house after school. She rides her bicycle home before dinner along a bike route that connects Roxanne's home to her own.Here,
a = b = 3 units
Put the values;
3² + 3² = c²
2*9 = c²
c = 3√2
c = 4.24
Total distance = 4.24+ 3 + 3
Total distance = 10.24 miles
Thus, the total distance travelled by Lisa in a day is found to be 10.24 miles.
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Can someone help me with this
Answer:
corn dogs: $1.25fries: $3.50Step-by-step explanation:
You want to know the cost of corn dogs and the cost of chili-cheese fries when 2 dogs and 3 fries cost $13, while 4 dogs and 1 fries cost $8.50.
SetupThe cost of each purchase can be represented by the equations ...
2d +3f = 134d +f = 8.50SolutionSubtracting the second equation from twice the first gives ...
2(2d +3f) -(4d +f) = 2(13) -(8.50)
5f = 17.50 . . . . . . simplify
f = 3.50 . . . . . . . divide by 5
4d = 8.50 -f = 5.00 . . . . use the second equation to find d
d = 1.25 . . . . . . divide by 4
Corn dogs cost $1.25; chili-cheese fries cost $3.50.
__
Additional comments
Many calculators provide a number of methods of solving systems of equations. The use of an augmented matrix of the equation coefficients is perhaps one of the simplest.
The second equation is a good choice for writing an expression for f in terms of d: f = 8.50 -4d. This expression can be substituted into the first equation if you want to solve the system by substitution, rather than elimination. Making that substitution gives 2d +3(8.50 -4d) = 13, and that simplifies to -10d = -12.50 after subtracting 25.50 from both sides.
