Gabriela drank three fourths of her glass of milk and jenny drank six eighths of her glass of milk if the glasses were the same size did they drink the same amount ? Use cross multiplication to prove your answer

Answer:

x = 7, y = 2

Explanation:

equations given:

x + 7y = 21

x + 4y = 15

make "x" the subject:

x + 7y = 21

x = 21 - 7y .........equation 1

x + 4y = 15

x = 15 - 4y .......equation 2

Solving both the equations simultaneously:

15 - 4y = 21 - 7y

-4y + 7y = 21 - 15

3y = 6

y = 6 ÷ 3

y = 2

If y is 2

Then x = 21 -7y;

x = 21 - 7(2)

x = 21 - 14

x = 7

x + 7y= 21

7 goes to RHS = X+ y = 21/7-3

x + 4y = 15

4 goes to RHS= x+y = 15/4 = 3.75

The correct number line that displays the solution `x ≥ 3` would be:

 <------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------>

       -10    -9     -8     -7     -6     -5     -4     -3     -2     -1     0      1      2      3      4      5      6      7      8      9     10

                                   ●------------------------------------------------>

The solution `x ≥ 3` is an inequality that means x is greater than or equal to 3. To graph this inequality on the number line, we mark the point representing the value 3 with a closed circle on the number line and draw an arrow pointing to the right to indicate that all values greater than or equal to 3 satisfy the inequality.

The closed circle at 3 indicates that 3 is included in the solution set, and the arrow to the right indicates that all values greater than 3 also satisfy the inequality. Therefore, any value of x that is equal to or greater than 3 would be considered a solution to the inequality `x ≥ 3`.

It is important to note that if the inequality was `x > 3` (without the equal sign), the closed circle at 3 would be changed to an open circle, indicating that 3 is not included in the solution set, and only values greater than 3 would be considered solutions. In conclusion, the number line provided above correctly displays the solution `x ≥ 3`.

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Answer:

The area of the surface over R is \(\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}\)

Step-by-step explanation:

From this study,

The surface area of f(x,y) is expressed by:

\(A = \iint_R \sqrt{1 +f^2_x+f^2_y}} \ dA\)

where

\(0 \leq x \leq 2 \ and \ 0 \leq y \leq 2\)

Given that:

f(x,y) = 9 - x²

Thus, \(f_x = -2x\) and   \(f_y = 0\)

However, the area becomes:

\(A = \iint_R \sqrt{1+(-2x)^2+0^2} \ dxdy\)

\(A = \iint_R \sqrt{1+4x^2} \ dxdy\)

From above, replacing x with \(\dfrac{1}{2} \ tan \ u\)

then \(dx = \dfrac{1}{2} sec^2 \ udu\)

∴

\(\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint \sqrt{1 + 4u^2 } \ sec^2 \ udu\)

\(\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint sec^2 \ udu\)

\(\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} ( \sqrt{4x^2 + 1x} + \dfrac{1}{2} In \sqrt{4x^2 + 1}+2x)\)

Hence;

\(\mathsf{A = \int \limits ^2_0 \begin {bmatrix} \dfrac{1}{2}(\sqrt{4x^2 +1 x}+ \dfrac{1}{2} In ( \sqrt{4x^2+1}+2x \end {bmatrix}^2_0 \ dy}\)

\(\mathbf{A = 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}\)

Therefore, the area of the surface over R is \(\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}\)

a) Intercepts are the points on the x and y axis

In the graph:

x-int: (-2,0), (2,0)

y-int: (0,1)

b) Domain is the list of x-values and Range is the list of y-values that make this graph true

Interval notations of domain and range

(Square brackets because the circles are closed)

Domain: [3,3]

Range: [0,3]

c) Intervals of increase and decrease: where the graph is increasing and decreasing

Increasing: -2 to 0 & 2 to 3

Decreasing: -3 to -2 & 0 to 2

d)Even, odd or neither

It is an even degree as both of its hands are facing upwards

Hope it helps!

Answer:

2.75 inches

Step-by-step explanation:

City B experienced three times the amount of rainfall than  City A, therefore :

Since both cities received 11 inches of rainfall in total.

We have that:

x+3x=11

4x=11

Divide both sides by 4

x=2.75 Inches

Therefore, we City A received 2.75 inches of rain.

Answer: the awnser is 7

Step-by-step explanation: when numbers are in | ? | and they are negative they just turn positive

The quadratic function that represents the given graph is:

y = ¹/₂(x − 4)² - 1

The general form of a quadratic equation in Vertex Form is expressed as:

y = a(x − h)² + k,

where

(h, k) is the vertex.

From the given graph, we can see that the coordinates of the vertex is (4, -1). Thus, we have:

y = a(x − 4)² - 1

Looking at the four given options from Option A to Option D, we can deduce that only given option that gives us the coordinates of the quadratic curve vertex is option D.

Thus, we can conclude that the quadratic function that truly represents the given parabolic graph curve is:

y = ¹/₂(x − 4)² - 1

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Answer:

12

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

-4x3=-12x

-4x-2=8x

-4x4=-16y

8+-12=-4x

-4x-16y

Answer:

A

Step-by-step explanation:

multiply each thing in the parenthesis by -4

-4×3x = -12x

-4×-2x = 8x

-4×4y = -16

-12x + 8x - 16y

combine like terms

-4x - 16y

Answer:

eeeeee

Step-by-step explanation:

eeeeeeee

Answer:

-7k^2+42k

LOL thats what i got

The search results are unrelated to the question of finding the reflection image of (5, -3) across the y-axis. To find the reflection image of a point across the y-axis, we need to change the sign of the x-coordinate of the point. Therefore, the reflection image of (5, -3) across the y-axis is (-5, -3).

Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

Answer:

(2,6)

Step-by-step explanation:

Google

In the  word problem above, 0 small pizzas, 1 medium pizza, and 5 large pizzas were delivered to the college.

Let  S = number of small pizzas delivered

Let M = number of medium pizzas delivered

Let L = number of large pizzas delivered

We'll start by solving equation 1 for one variable and substituting it into the other equations.

S + M + L = 12

We can rewrite this equation as -

S = 12 - M - L

Now, substitute this value of S in equations 2 and 3 -

4S + 10M + 15L = 109

4(12 - M - L) + 10M + 15L = 109

48 - 4M - 4L + 10M + 15L = 109

6M + 11L = 61

2S + 4M + 13L = 81

2(12 - M - L) + 4M + 13L = 81

24 - 2M - 2L + 4M + 13L = 81

2M + 11L = 57

Now we have a system of two equations with two variables -

6M + 11L = 61 ...(4)

2M + 11L = 57 ...(5)

Subtract  equation   (5)from equation (4) -

(6M +   11L) - (2M +11L) = 61 - 57

4M = 4

M = 1

Substitute the value of M into equation (5) -

2(1) + 11L = 57

2 + 11L = 57

11L = 55

L = 5

Now substitute the values of M and L into equation (1) -

S + 1 + 5 = 12

S + 6 = 12

S = 6 - 6

S = 0

Therefore, the solution is -

S = 0 (no small pizzas)

M = 1 (1 medium pizza)

L = 5 (5 large pizzas)

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Full Question:

Although part of your question is missing, you might be referring to this full question:

a pizza shop delivered 12 pepperoni pizzas to a college on the first night of final exams. the total cost of the pizzas was $109. a small pizza costs $4 and contains 2 ounces of pepperoni. a medium pizza costs $10 and contains 4 ounces of pepperoni. a large pizza cost $15 and contains 13 ounces of pepperoni. the owner of the pizza shop used 5 pounds 1 ounces of pepperoni in making the 12 pizzas. how many pizzas of each size were delivered to the college?

Step-by-step explanation:

The bisection method is a root-finding algorithm that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing. To apply the bisection method to the equation x^3 - x - 9 = 0, you need to find two initial values a and b such that f(a) and f(b) have opposite signs. This means that there is at least one root of the equation in the interval [a, b].

Let’s take a = 2 and b = 3 as our initial interval. We can see that f(2) = 2^3 - 2 - 9 = -1 and f(3) = 3^3 - 3 - 9 = 18, so f(a) and f(b) have opposite signs.

Now we can apply the bisection method as follows:

Calculate the midpoint c = (a + b)/2 = (2 + 3)/2 = 2.5.

Evaluate f© = 2.5^3 - 2.5 - 9 ≈ 5.625.

Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.

Calculate the new midpoint c = (a + b)/2 = (2 + 2.5)/2 = 2.25.

Evaluate f© ≈ 1.765625.

Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.

We can continue this process until we reach the desired level of accuracy.

Answer:

8

Step-by-step explanation:

let x be the number , then

\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )

3x = 108 ( divide both sides by 3 )

x = 36

the number is 36, so

\(\frac{2}{9}\) × 36 = 2 × 4 = 8

The two ninths of the number is 8

We know that Three quarters of a number is  \(\frac{3}{4}\)  times of a number

Hence we will assume the number x ,

                     \(\frac{3}{4} of x = 27\)

                     \(x = 27 X \frac{4}{3}\)

                       \(x = 36\)

Now as we know the number is 36

Therefore , the two ninths of the number assumed as y

We will multiply the number 36 by 2 and then divide by 9

Hence,

                           \(y = 36 X \frac{2}{9}\)

                               \(y = 8\)

Thus, the two ninths of the number 36  is 8                            

Practice more quarters related questions

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Answer:

5

Step-by-step explanation:

As given  

  1/sqrt2=x/5sqrt2

5sqrt2/sqrt2=x                Both sqrt will get cancelled

5=x

Answer:

7

Step-by-step explanation:

1) Subsitute 16 for B

2) 16-9=7

Hope this helps and good luck on your assignment. (please mark me brainliest if possible)

Answer:

No it cannot be

Step-by-step explanation:

Since an obtuse angle is more than 90 degrees, it can't have a complement

Hope this helps!

Answer: 5

Step-by-step explanation:

Since x is directly related to the square of y, we can write the equation:

x = ky^2

where k is a constant of proportionality. We can solve for k using the given values of x and y:

16 = k(2^2) -> 16 = 4k -> k = 4

Now that we know k, we can use it to find y when x = 100:

100 = 4y^2 -> 25 = y^2 -> y = ±5

Since y cannot be negative, the only possible value of y is 5. Therefore, when x = 100, y could be 5.

Answer:

One possible value of y when x = 100 is y = 5.

Step-by-step explanation:

Using the direct variation formula, we know that x = ky^2, where k is a constant. Given that x = 16 and y = 2, we can solve for k:

16 = k(2)^2

k = 4

Now we can use this value of k to find y when x = 100:

100 = 4y^2

y^2 = 25

y = 5 or -5 (since the question only asks for one possible value, we can choose either solution)

Therefore, one possible value of y when x = 100 is y = 5.

Answer:

Step-by-step explanation:

1. Exchange rate = 1 U.S. dollar per 0.9009 foreign currency

i. U.S. Currency (in dollars) = 73.00

   Foreign currency = 81.03

ii. U.S. Currency (in dollars) = 20.00

   Foreign currency = 22.20

2. Exchange rate = 1 U.S. dollar per 1.3699 foreign currency

i. U.S. Currency (in dollars) = 30.00

   Foreign currency = 21.90

ii. U.S. Currency (in dollars) = 50.00

   Foreign currency = 36.50

3. Exchange rate = 1 U.S. dollar per 1.5873 foreign currency

i. U.S. Currency (in dollars) = 25.00

   Foreign currency = 15.75

4. Exchange rate = 1 U.S. dollar per 1.11 Australian dollar

i. U.S. Currency (in dollars) = 72.00

   Equivalent Australian dollar = 72.00 x 1.11 = 79.92

Answer:

?

Step-by-step explanation:

the initial expression is:

and we can operate so:

Answer:

im study about history it was my favourite subject!

Answer:

3.52

Step-by-step explanation:

do 4.40*.20. youll get .88, then subtract .88 from 4.40. pls give brainliest

Answer:

all of the brackets first

Answer:

Step-by-step explanation:

Those consecutive angles must sum to 180 degrees.

7x+9+7y-4=180

7x+7y+5=180

7x+7y=175

x+y=25

x=25-y

We also have

11x-1+2y+5=180

11x+2y+4=180

11x+2y=176, using x=25-y that we found above makes this

11(25-y)+2y=176

275-11y+2y=176

-9y+275=176

-9y=-99

y=11, and since x=25-y

x=25-11

x=14

Finally

z+7x+9=180

z+7x=171

z=171-7x, we found that x=14 earlier so

z=171-7(14)

z=171-98

z=73

So the three values are

x=14, y=11, and z=73 degrees.

The table with the numeric values of the function y = 10x + 1 is given by the image at the end of the answer.

To find the numeric value of a function or of an expression, each instance of the variable in the defined function or in the defined expression must be replaced by the value of the input variable at which the numeric value is to be found.

In this problem, the function is defined by the rule presented as follows:

y = 10x + 1.

The numeric values are found replacing the lone instance of x by the value that we want to find the output at, hence:

The table with these numeric values is given by the image at the end of the answer.

The inputs are missing and are given by the table at the end of the answer.

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Answer:

y = 2x + 10

Step-by-step explanation:

Hi there!

We are given the points (-7, -4) and (-6, -2) and we want to write the equation of the line that passes through these points in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, we need to find the slope (m) of the line

The slope can be calculated from 2 points using the formula \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points

We have everything we need to find the slope, but let's label the values of the points to avoid any confusion & and mistakes

\(x_1= -7\\y_1=-4\\x_2=-6\\y_2=-2\)

Substitute these values into the formula (note: remember that the formula has subtraction in it!)

m=\(\frac{y_2-y_1}{x_2-x_1}\)

m=\(\frac{-2--4}{-6--7}\)

Simplify

m=\(\frac{-2+4}{-6+7}\)

Add the numbers

m=\(\frac{2}{1}\)

Divide

m=2

The slope of the line is 2

We can substitute that in:

y = 2x + b

Now we need to find b

As the equation passes through both  (-7,-4) and (-6,-2), we can use either point to help solve for b

Taking (-6, -2) for example:

Substitute -6 as x and -2 as y into the equation.

-2 = 2(-6) + b

Multiply

-2 = -12 + b

Add 12 to both sides

-2 = -12 + b

+12  +12

___________

10 = b

Substitute 10 as b.

y = 2x + 10

Hope this helps!

Topic: Finding the equation of a line

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Answer:

s = (1/3) t³ - (3/2) t² - 2t + 4

Step-by-step explanation:

v = t² - 3t - 2

s = ∫v dt

= (1/3) t³ - (3/2) t² - 2t + c.

when s=10, t=6.

10 = (1/3) (6)³  - (3/2) (6)² - 2(6) + c

   = 72 - 54 - 12 + c

   = 6 + c

c = 10 - 6 = 4.

s = (1/3) t³ - (3/2) t² - 2t + 4