What is the solution to the proportion 6-10 = 9-x

Answer:

(A) Similar triangles

Step-by-step explanation:

It is given that AB is parallel to DE, therefore ∠CAB=∠DEC=65°(Alternate angles),

Then from ΔACB and ΔDCE, we have

∠CAB=∠DEC=65°(Alternate angles)

and ∠ACB=∠DCE=50°(Vertically opposite angles)

Thus, by AA similarity, ΔACB is similar to ΔDCE.

Hence, option A that is similar triangles is correct.

C. If x represents the number of bracelets sold at $24 each and y represents the number of rings sold at $38 each, the total sales were $520.

Shakira bowls about 8 games.

Two or more expressions with an equal sign are defined as an equation.

Let Shakira bowl x games.

Since Shakira has to pay $4.75 for each game, she would pay $4.75x for x games.

Shakira also paid $3 to rent shoes, therefore, the total money Shakira spent is:

4.75x + 3

Given that, the total spent is $42, therefore,

4.75x + 3 = 42

4.75x = 42 - 3

4.75x = 39

x = 39/4.75

x ≈ 8

Hence, Shakira bowls about 8 games.

Learn more about equations here:

https://brainly.com/question/10413253

#SPJ2

The partial derivatives of the given function f(x, y) = ax + by / cx + dy with respect to x and y have been calculated, showing how the function changes with each variable while holding the other constant.

For the function f(x, y) = ax + by / cx + dy, the first partial derivatives with respect to x and y are:

These partial derivatives measure the rate of change of the function f(x, y) with respect to x and y while treating the other variable as constant.

                 The number is:

                          1260

We know that the number of ways of arranging n items is calculated by the method of permutation.

If n letters are to be arranged such that there are [tex]r_1,r_2[/tex] items each of the same type.

Then, the number of ways of arranging is:

                   [tex]\dfrac{n!}{r_1!\times r_2!}[/tex]

We are asked to find the number of ways of arranging the letters of "Balloon"

There are a total of 7 words such that 'l' occurs two times and 'o' occurs two times.

Hence, the number of ways of arranging them are:

     [tex]=\dfrac{7!}{2!\times 2!}\\\\=\dfrac{7\times 6\times 5\times 4\times 3\times 2!}{2!\times 2}\\\\=1260\ ways[/tex]

Let us plug-in the values of x to know

> x = 0

f(0) = 3(0) + 1 = 1

g(0) = 3^0 + 1 = 2

> x = 1

f(1) = 3(1) + 1 = 4

g(1) = 3^1 + 1 = 4

> x = 2

f(2) = 3(2) + 1 = 7

g(2) = 3^2 + 1 = 10

> x = 3

f(3) = 3(3) + 1 = 10

g(2) = 3^3 + 1 = 28

Therefore the only answer is:

1

The speed at which the distance is covered by the two vehicles is the sum of their speeds:

... (truck speed) + 1.5×(truck speed) = 2.5×(truck speed)

The time required to cover the distance is inversely proportional to speed, so is

... (2.5 hours)/2.5 = 1.0 hours

It takes 1.0 hours for the vehicles to meet.

_____

The speed of the truck is (145 mi)/(2.5 h) = 58 mi/h

The speed of the car is 1.5 × 58 mi/h = 87 mi/h.

The speed at which they move toward each other is

... 58 mi/h + 87 mi/h = 145 mi/h

So, the time it takes to cover 145 miles is

... (145 mi)/(145 mi/h) = 1.0 h

Answer:

For part A)

Let's make a function for each person, and then combine them to find total calories

Gwen burns 10 cal/min, and had already burned 100 calories when Tristan and Keith started (Yg=100 when x=0)

Yg= 10x + 100

Step-by-step explanation:

I got a 100% on it.

Final answer:

The probability of winning the Powerball jackpot is 1 in 292,201,338.

Explanation:

To find the probability of winning the Powerball jackpot, we need to calculate the probability of selecting the correct five numbers between 1 and 59 and the correct single number between 1 and 39.

The probability for each part is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

For the five numbers, there are 59 possible choices and we need to select 5, so the probability is 1/59 × 1/58 × 1/57 × 1/56 × 1/55.

For the single number, there are 39 possible choices, so the probability is 1/39.

To find the overall probability, we multiply the probabilities of both parts together: (1/59 × 1/58 × 1/57 × 1/56 × 1/55) × (1/39) = 1/292,201,338.

Answer:

x= -2 + and - sqrt 22 /3

Step-by-step explanation:

Her mum ate 31/40 of the cake

Given the weight of the cake to 1 pound

If Carol ate 2/5 of the cake, the remaining fraction of the cake will be 1 - 2/5 = 3/5

If Dima ate 3/8 of the REMAINING cake, then the fraction of cake Dima ate will be:

Dima = 3/8 * 3/5

Dima = 9/40

Fraction of the cake that her mum ate = 1 - 9/40 = 31/40

Hence her mum ate 31/40 of the cake

Learn more here: https://brainly.com/question/24191335

After the first cut, the remaining area represents 70% of the previous area.

Let's assume the initial area of the 10 by 10 grid is 100 square centimeters. After the first cut, a certain percentage of the current area is removed, leaving behind the remaining area. Let's say the remaining area after the first cut is 70 square centimeters.

To calculate the percentage of the remaining area compared to the previous area, we can use the formula:

(remaining area / previous area) * 100

In this case:

(70 / 100) * 100 = 70%

So, after the first cut, the remaining area represents 70% of the previous area.

Learn more about area on

https://brainly.com/question/25292087

#SPJ2

2/3 hours take to mow the​ lawn.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Time taken to mow by push mower= 2 hours

Time taken to mow by riding mower= 1 hours

So, if working together  the time taken

= 1 / (1/2 + 1/1)

=1/ (3/2)

= 2/3

Hence, it will take 2/3 hours.

Learn more about fraction here:

https://brainly.com/question/10354322

#SPJ5

Answer:

b

Step-by-step explanation:

D

This is the plato answer