A company produces fruity drinks that contain a percentage of real fruit juice. Drink
A contains 20% real fruit juice and Drink B contains 15% real fruit juice. The
company used 100.5 liters of real fruit juice to make 30 more liters of Drink A than
liters of Drink B. Write a system of equations that could be used to determine the
number of liters of Drink A made and the number of liters of Drink B made. Define
the variables that you use to write the system.
Let
System of Equations:

Answer:

6x² - 5x + 3 - (3x² + 8x - 4) = 3x² - 13x + 7

General Formulas and Concepts:

Pre-Algebra

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify given.

6x² - 5x + 3 - (3x² + 8x - 4)

Step 2: Simplify

∴ we have subtracted the two trionomials!

---

Topic: Algebra I

Answer:

3x²-13×+7

Step-by-step explanation:

hope this helps -olive

Answer:

31/14

Step-by-step explanation:

5 1/2 - 1 2/7

By multiplying

5/2 - 2/7

By Elysium

(35-4)/14

31/14

Answer:

[tex]4\frac{3}{14}[/tex]

Step-by-step explanation:

[tex]5\frac{1}{2}-1\frac{2}{7}=\frac{11}{2}-\frac{9}{7}=\frac{77-18}{14}=\frac{59}{14}=4\frac{3}{14}[/tex]

Answer:

8.8 hours

Step-by-step explanation:

Given: Happy Paws charges $20.00 plus $2.50 per hour to keep a dog.

           Woof Watchers charges $9.00 plus $3.75 per hour.

Lets assume the number of hours service provided be "h".

First, writing an equation for Happy paws cost for service.

Total cost of service= [tex]\$ 2.5\times h+ \$ 20[/tex]--- equation 1

Second, writing an equation for Woof watchers cost of services.

Total cost of service= [tex]\$ 3.75\times h+ \$9[/tex]--- equation 2

Now, finding number of hours services provided, when cost of service will be equal for both service provider.

∴ [tex]2.5h+ 20= 3.75h+ 9[/tex]

Solving the equation now to find number of hour.

⇒ [tex]2.5h+ 20= 3.75h+ 9[/tex]

Subtracting both side by 2.5h

⇒ [tex]20= 3.75h+ 9-2.5h[/tex]

Subtracting both side by 9

⇒ [tex]1.25h= 11[/tex]

Dividing both side by 1.25

⇒[tex]h= \frac{11}{1,25}[/tex]

∴[tex]h= 8.8\ hours[/tex]

Hence, 8.8 hours is the number of hours when cost of service will be equal for both service provider.

Answer:

[tex]y = \frac{1}{4}x[/tex]

x  y

4  1

8  2

12  3

16  4

Step-by-step explanation:

Angie makes a spicy salsa by adding red pepper flakes to a chunky tomato mix in proportional amounts. For example, she mixes [tex]\frac{1}{2}[/tex] teaspoon of red pepper flakes to 2 cups of tomato mix.

So, the amount of tomato mix in cups is the independent variable represented by x and the amount of red pepper flakes in teaspoon is the dependent variable represented by y and the relation between them is given by y = kx, as the relation is proportional.

Now, putting x = 2 and y = [tex]\frac{1}{2}[/tex], we get

[tex]\frac{1}{2} = 2k[/tex]

⇒ k = [tex]\frac{1}{4}[/tex]

Therefore, the equation is [tex]y = \frac{1}{4}x[/tex] (Answer)

Now, in table the relation will be given by

x  y

4  1

8  2

12  3

16  4 (Answer)

The relationship between red pepper flakes and tomato mix can be represented by a table showing different quantities matching the ratio, and by an equation, p = (1/4) * t, which expresses the amount of red pepper flakes (p) needed for any given amount of tomato mix (t).

To represent the relationship between red pepper flakes and tomato mix which Angie uses to make her spicy salsa, we will use a table and an equation.

Table Representation:

Red Pepper Flakes (teaspoons)Tomato Mix (cups)1/22141 1/2628

In the table, the amount of red pepper flakes increases proportionally with the amount of tomato mix. This proportional relationship can also be represented numerically.

Equation Representation:

Let's define p as the amount of red pepper flakes in teaspoons and t as the amount of tomato mix in cups. The ratio given is 1/2 teaspoon of red pepper flakes to 2 cups of tomato mix, which simplifies to 1/4 teaspoon per cup. Thus, the equation is:

p = (1/4) * t

This equation states that for every cup of tomato mix, you use 1/4 teaspoon of red pepper flakes. Therefore, if Angie has t cups of tomato mix, she will need p = (1/4) * t teaspoons of red pepper flakes.

Answer:

The equation is already in the standard form.

y

=

1

2

y

=

x

+

2

Step-by-step explanation:

Answer: [tex]m\angle F=140\°[/tex]

Step-by-step explanation:

You know that the sum of the interior angles of an hexagon is 720 degrees.

Based on that and given the figure attached, you can set up the following equation:

[tex](x-60)+(x-40)+130+120+110+(x-20)=720[/tex]

The next step is to solve for "x" in order to find its value. This is:

[tex]x-60+x-40+130+120+110+x-20=720\\\\3x=720-240\\\\3x=480\\\\x=\frac{480}{3}\\\\x=160[/tex]

Now you must substitute the valUe of "x" calculated above, into [tex]m\angle F=(x-20)\°[/tex]:

[tex]m\angle F=(160-20)\°[/tex]

Finally, evaluating, you get that the measure of the angle F is:

[tex]m\angle F=140\°[/tex]

Answer:

114 is the real correct answer

Step-by-step explanation:

May God Bless

Answer:

60 degrees

Step-by-step explanation:

First we need to know how many degrees are in a parallelogram. We can use the formula 180(n-2) (n is the number of sides)

This works out to 180(4-2)=360 degrees.

Now we can set up the following equation as:

2(120)+2x=360 Subtract 240 from both sides to get:

2x=120 Divide by 2 to get:

x=60 degrees

Therefore we know 2 angles are each 120 degrees and the other 2 are 60 degrees.

Answer: 360 cars can park in the parking lot.

40 parking spots x 9 rows = 360 cars

Answer:

B) Both functions have the same domain.

C) Both functions have the same x-intercepts.

D) Both functions are decreasing on the interval (−∞, −2).

Step-by-step explanation:

step 1

Find the vertex of f(x)

we know that

The x-coordinate of the vertex is the midpoint of the roots

we have

x=-1 and x=-3

so

the midpoint is

(-1-3)/2=-2

The y-coordinate of the vertex is -4 (because the range is [−4, ∞))

therefore

The vertex of f(x) is the point (-2,-4)

Is a vertical parabola open upward

The vertex is a minimum

The domain is all real numbers

step 2

we have

[tex]g(x)=2x^2+8x+6[/tex]

Find the vertex

Factor the leading coefficient

[tex]g(x)=2(x^2+4x)+6[/tex]

Complete the square

[tex]g(x)=2(x^2+4x+4)+6-8[/tex]

[tex]g(x)=2(x^2+4x+4)-2[/tex]

Rewrite as perfect squares

[tex]g(x)=2(x+2)^2-2[/tex]

Is a vertical parabola open upward

The vertex is the point (-2,-2)

The domain is all real numbers

The range is the interval [−2, ∞)

Find the x-intercepts

For g(x)=0

[tex]0=2(x+2)^2-2[/tex]

[tex]2(x+2)^2=2[/tex]

[tex](x+2)^2=1\\x+2=\pm1\\x=-2\pm1[/tex]

so

The roots or x-intercepts are

x=-1 and x=-3

Verify each statement

A) Both functions have the same vertex

The statement is false

The vertex of f(x) is (-2,-4) and the vertex of g(x) is (-2,-2)

B) Both functions have the same domain.

The statement is true

The domain is all real numbers

C) Both functions have the same x-intercepts

The statement is true  (see the explanation)

D) Both functions are decreasing on the interval (−∞, −2)

The statement is true

Because the x-coordinate of the vertex is the same in both functions, and both functions open upward

Answer:

The answer is A

Step-by-step explanation:

Answer:

x=45

Step-by-step explanation:

18/4 = x/10

[tex]\frac{18}{4}[/tex] = [tex]\frac{x}{10}[/tex]

use cross-multiplication

10*18=180

180/4=45

x=45

The correct quadratic function represented by the graph is [tex]\(f(x) = 0.5(x + 1)^2 - 2\)[/tex], and doesn't match with any of the options provided.

To find the quadratic function represented by the given graph, we first identify the vertex and then use it to determine the coefficient [tex]\(a\)[/tex] in the quadratic function.

1. Vertex Calculation:

  - The x-coordinate of the vertex, [tex]\(h\)[/tex], is the average of the x-intercepts: [tex]\(h = \frac{1 + (-3)}{2} = -1\).[/tex]

  - Since the focus lies 2 units below the vertex, [tex]\(k = -2\).[/tex]

2. Vertex Form of the Quadratic Function:

  The vertex form is [tex]\(f(x) = a(x - h)^2 + k\)[/tex], where [tex]\((h, k)\)[/tex] is the vertex.

  Substituting [tex]\(h = -1\) and \(k = -2\)[/tex], we get [tex]\(f(x) = a(x + 1)^2 - 2\).[/tex]

3. Determine [tex]\(a\):[/tex]

  Using the x-intercept (1, 0):

  [tex]\[0 = a(1 + 1)^2 - 2\][/tex]

  [tex]\[0 = 4a - 2\][/tex]

  [tex]\[4a = 2\][/tex]

  [tex]\[a = \frac{1}{2}\][/tex]

4. Quadratic Function:

  Substitute [tex]\(a = \frac{1}{2}\)[/tex] into the vertex form:

  [tex]\[f(x) = \frac{1}{2}(x + 1)^2 - 2\][/tex]

Therefore, the correct quadratic function represented by the graph is [tex]\(f(x) = 0.5(x + 1)^2 - 2\).[/tex]

The question probable maybe:

Which quadratic function is represented by the graph?

f(x) = 0.5(x + 3)(x - 1)

f(x) = 0.5(x - 3)(x + 1)

f(x) = 2(x + 3)(x - 1)

f(x) = 2(x - 3)(x + 1)

(Given in the attachment)

Answer:

Step-by-step explanation:

Total game played = 162

Let the games lost be = x

Game won = x + 44

x + x + 44 = 162

2x = 162 - 44

2x = 118

x = 118/2

x = 59

The number of games lost is 59

Answer:

Explanation is given below.

Step-by-step explanation:

Given:

Number of Trumpets = 40

Number of tubas = 35

Carlee says, the ratio of trumpets to tubas = 40 : 35

Danny says,  the ratio of trumpets to tubas = 8 : 7

To explain why the two ratios are equivalent.

Solution:

Equivalent ratios are all ratios which are equal to each other in their reduced to simplest form.

The ratio of trumpets to tubas can be given as = [tex]\frac{40}{35}[/tex]

To reduce the ratio to its simplest form, we divide both numbers by their G.C.F.

The G.C.F. for 40 and 35 is 5.

So, we divide numerator and denominator by 5.

⇒ [tex]\frac{40\div5}{35\div 5}[/tex]

⇒ [tex]\frac{8}{7}[/tex]

Thus, the simplest ratio of trumpets to tubas can be given as = 8:7

This is why both Danny and Carlee are correct with the ratios of trumpets to tubas.

Carlee gave the direct ratio, while Danny gave the simplest ratio.

Answer:

To find that a triangle can be made from these measurements you should know that the sum of two of its sides should be greater than the third side.

lets see if this rule applies...

9+9 = 18 ( greater that 17 ; its third side)

17 + 9 = 26 (greater than 9 ; its third side)

therefore, a triangle can be formed

as two of its sides are equal , it is an isosceles triangle

Answer:

isosceles triangle

Step-by-step explanation:

two of its sides are equal

Answer:

The furthest distance was 2.12 miles from school to the park.

The shortest distance was 1.34 miles from home to school.

The furthest distance was from school to the park, and the shortest distance was from home to school.

In order to determine which trip was the furthest distance and which trip was the shortest distance, we need to compare the distances of each trip. Angel walked 1.34 miles from home to school, 2.12 miles from school to the park, and 1.94 miles from the park back home.

Comparing the distances, we can see that the trip from school to the park (2.12 miles) was the furthest distance, while the trip from home to school (1.34 miles) was the shortest distance.

https://brainly.com/question/33716087

#SPJ2

Answer:

D)

Step-by-step explanation:

3(x-9)=3x-27

Answer:

           [tex]\lim_{x \to 1}\frac{x^2-1}{sin(x-2)}=0[/tex]

Explanation:

Assuming the correct expression is to find the following limit:

         [tex]\lim_{x \to 1}\frac{x^2-1}{sin(x-2)}[/tex]

Use the property the limit of the quotient is the quotient of the limits:

         [tex]\lim_{x \to 1}\frac{x^2-1}{sin(x-2)}=\frac{\lim_{x \to 1}x^2-1}{\lim_{x \to 1}sin(x-2)}[/tex]

Evaluate the numerator:

          [tex]\frac{\lim_{x \to 1}x^2-1}{\lim_{x \to 1}sin(x-2)}=\frac{1^2-1}{\lim_{x \to1}sin(x-2)}=\frac{0}{\lim_{x \to 1}sin(x-2}[/tex]

Evaluate the denominator:

                  [tex]\frac{0}{\lim_{x \to1}sin(x-2)}=0[/tex]

Answer:

# of questions : y = -x + 19

Step-by-step explanation:

if ur only wanting the equation for the number of questions on the test, then it would be :  x + y = 19......y = -x + 19 in slope intercept form.

and if u were wanting the number of points, then it would be :

5x + 10y = 100.....10y = -5x + 100.....y = -1/2x + 10. in slope intercept form

To express the number of questions on Mrs. Morales' test in slope-intercept form, first write the total point equation 5x + 10y = 100, then simplify and solve for y to get the slope-intercept form y = -0.5x + 10.

To write an equation representing the number of questions on Mrs. Morales' test, we must consider the total points possible and the value of each question type. The spelling questions (x) are 5 points each, and the vocabulary questions (y) are 10 points each. The total points for the test are 100, which leads us to the equation 5x + 10y = 100.

However, to put this into slope-intercept form, we solve for y. Dividing the entire equation by 10 gives us 0.5x + y = 10. Then, isolating y yields y = -0.5x + 10, which is now in slope-intercept form where the slope (m) is -0.5 and the y-intercept (b) is 10.

The slope-intercept form provides a way to see how many vocabulary questions (y) can be on the test for a given number of spelling questions (x).

Answer:

Step-by-step explanation:

Let the quantity of milk and water be 40 and 60 respectively.

After removing 50% of solution,

Quantity of milk = 20 and quantity of water = 30

Therefore, the concentration of the solution is reduced from 40 to 20. Hence the solution is reduced by 50%.

Answer:

[tex]In\ 1\ minute\ lawn\ can\ be\ mowed=50\ yd^2[/tex]

Step-by-step explanation:

[tex]Given,\\\\In\ 1\ hour\ lawn\ can\ be\ mowed= 3000\ yd^2\\\\we\ know\ that\\\\1\ Hour=60\ minutes\\\\In\ 60\ minutes\ lawn\ can\ be\ mowed=3000\ yd^2\\\\In\ 1\ minute\ lawn\ can\ be\ mowed=\frac{3000}{60}\ yd^2\\\\In\ 1\ minute\ lawn\ can\ be\ moved=50\ yd^2[/tex]

Answer:

r = 2

Step-by-step explanation:

Given

8 = - 3r + 7r ← combine terms

8 = 4r ( divide both sides by 4 )

2 = r

Answer:

r=2

Step-by-step explanation:

8 = −3r +7r

Step 1: Combine like-terms (-3r + 7r = 4r)

8=4r

Step 2: Divide both sides by 4 to isolate the variable

(8 divided by 4 = 2)

(4r divided by 4 = r)

2=r

Answer: 108

Step-by-step explanation:

18 sandwiches are mad every hour then multiply it by 6 .

Answer:

40%

Step-by-step explanation:

180 - 135 = 45

so, 40%

Answer:

25%

Step-by-step explanation:

135/180= .75

because of 100% - 75% = 25%

Answer:

40,000

Step-by-step explanation:120,000 divided by 30% is 40,00 because 120,000 divide by 30 is 40,000

Answer:84,000 acres is NOT gonna be farm land and 36000 acres will be farm land.

Step-by-step explanation:

The value of y is 64°

Solution:

The image of the question is attached below.

Given two angles of a triangle.

One angle is 79°.

Other angle is 37°.

Let the unknown angle be y.

Triangle sum property:

Sum of all the angles of a triangle = 180°

⇒ y + 79° + 37° = 180°

⇒ y + 116° = 180°

⇒ y = 180° – 116°

⇒ y = 64°

Hence the value of y is 64°.

No, The answer is 120%     and 0.5% = 0.05

Hope this helped!

BTW can I have brainliest

Final answer:

The two numbers are 14 and 19, where one number is 5 more than the other and their sum is 33.

Explanation:

To find the two numbers where one number is 5 more than the other and their sum is 33, we can set up a system of equations. Let's call the first number x, which means the second number would be x + 5 since it's 5 more than the first. Their sum is given as 33, so we can create the following equation:

x + (x + 5) = 33

Now we simplify the equation:

2x + 5 = 33

To solve for x, we subtract 5 from both sides:

2x = 33 - 5

2x = 28

Finally, we divide both sides by 2 to find the value of x:

x = 28 / 2

x = 14

Now that we have the first number, we can easily find the second number by adding 5:

The second number is x + 5 = 14 + 5 = 19.

The two numbers are 14 and 19.

Answer:

[tex]x^{3/5}[/tex]

Step-by-step explanation:

[tex]x^{1/2}*x^{1/5}\\[/tex]

Remember, when multipling common variables by an exponent, add the exponents

[tex]x^{\frac{1}{2} + \frac{1}{5}}\\x^{6/10} = x^{3/5}[/tex]

Final answer:

Scribes in medieval Europe had several important roles:

Explanation:

Scribes in medieval Europe had several important roles: