In a food cocktail,the ratio of orange juice to apple juice to coconut milk is 3:2:4, respectively. How much of each do I need to take if I have 5 more oz of orange juice than apple juice

The quotient is 2x^2-5 and remainder is -4

The necessary steps are:

p(x)= 6x^3 + 4x^2 - 15x−14

∴ degree of p(x) is 3.

g(x)=3x+2

∴ degree of g(x) is 1.

∴ degree of quotient q(x)=3−1=2,

and degree of remainder r(x) is zero.

Let, q(x)=ax2+bx+c (Polynomial of degree 2) and r(x)=k (constant polynomial)

By using division algorithm, we have

p(x)=[g(x)×q(x)+r(x)]

=6x^3 + 4x^2 -15x−14 = (3x+2)(ax2 + bx +c)+k

=3ax^3 + 3bx^2 + 3cx + 2ax^2 +2bx+2c+k

∴6x^3 + 4x^2 - 15^x - 14 = 3ax^3 + (3b+2a)x^2 + (3c+2b)x + 2c+k

We have cubic polynomials on both the sides of the equation.

∴ Let us compare the coefficients of x^3, x^2 ,x and k to get the values of a,b,c.

6=a, it is the coefficient of x^3 on both sides

4=3b+2a, it is the coefficient of x^2 on both sides

-15=3c+2b, it is the coefficient of x on both sides

−14=2c+k, it is the constant term on both sides

∴ the quotient is 2x^2 - 5 and the remainder is -4.

learn more about division at

https://brainly.com/question/25289437

The solution of the system of equations is the point of intersection (4, 2), as shown in the graph below.

Caroline bought 4 soda bottles.

Caroline bought 2 juice bottles.

In order to determine the solution to this problem, use the information given to create two equations.

Number of soda bottle = x.

Number of juice bottle = y.

First Equation for the total number of bottle that Kelvin bought

x + y = 6 --> eqn. 1

Second Equation 2 for the total sugar in the soda bottles and total sugar in juice bottles that equals 150 grams of sugar.

30x + 15y = 150

Simplify by dividing by 5

6x + 3y = 30 --> eqn. 2

Rewrite eqn. 1:

y = 6 - x

Solve simultaneously for the variables of x and y, by substituting the value of y into equation 2:

6x + 3(6 - x) = 30

6x + 18 - 3x = 30

3x + 18 = 30

3x = 30 - 18

3x = 12

3x/3 = 12/3

x = 4

Caroline bought 4 soda bottles.

Substitute x = 4 into equation 1 to find the value of y:

x + y = 6

4 + y = 6

y = 6 - 4

y = 2

Caroline bought 2 juice bottles.

The graph below shows the point of intersection, (4, 2), which is the solution.

Learn more about the system of equations on:

https://brainly.com/question/25869125

#SPJ1

Answer:

4/12

Simplest form= 1/3

Step-by-step explanation:

Hope this helps!

5/12-1/12 = 4/12

4/12 divided by 4 = 1/3

The simplest form is 1/3.

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

Given:

5/12- 1/12

Now, we have to subtract the fraction by focusing the numerator as

=5/12 - 1/12

=(5-1)/12

=4/12

=1/3

Hence, the simplest form is 1/3.

Learn more about fraction here:

https://brainly.com/question/10354322

#SPJ2

Answer:

Step-by-step explanation:

Answer: 50°

Step-by-step explanation:

Since angle 3 is in a right triangle we can assume one angle is 90° and then the other missing angle will be 40°

Because you take 180°-140°(the angle next to it) which will equal 40°

Now every triangle must add up to 180°

so lets take the angles we have now

90° +40°=130°

now take that 130°

180°-130°=50°

Now check your work

90°+40°+50°=180°

Angle 3 is 50°

The slope of the line passing the points (1, 1) and (0, 0) is 1

The formula for calculating the slope of a line is expressed as

Slope = y2-y1/x2-x1

Given the coordinate points (1, 1) and (0, 0)

Substitute the given coordinate points

Slope = 0-1/0-1

Slope = -1/-1

Slope =1

Hence the slope of the line passing the points (1, 1) and (0, 0) is 1

Learn more on slope of a line here: https://brainly.com/question/3493733

#SPJ1

branily.com//Httpstesxt

Answer:

9:8:2

Step-by-step explanation:

3/4 : 2/3 : 1/6 Multiply by 12.
9 : 8 : 2

Answer:

a

Step-by-step explanation:

the equation for a circle centered at orgin is x^2+y^2=r where r is the radius. multiplying, adding, or subtracting any numbers to the x and y components such as the other choices here causes the circle to be translated about the graph.

Answer:

They are collinear if they are on the same line

The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

Learn more about system of equation on:

https://brainly.com/question/12526075

To find :

Solving the equation :

\( \longmapsto \sf { \dfrac{4(3x-5)}{1+5} = 13} \)

\( \longmapsto \sf { \dfrac{12x-20}{6} = 13} \)

\( \longmapsto \) 12x - 20 = 6 × 13

\( \longmapsto \) 12x - 20 = 78

\( \longmapsto \) 12x = 78 + 20

\( \longmapsto \) 12x = 98

\( \longmapsto \) x =\( \sf { \dfrac{98}{12} } \)

\( \longmapsto \bf\red { x = \dfrac{49}{6} } \)

Value of x is 49/6.

Answer:

Step-by-step explanation:

\({\underline{\underline{\bf{\red{\:\:\:Given\: Equation\:\:\:}}}}}\)

\(\mapsto\:\:\sf{\dfrac{4(3x-5)}{1+5}=13}\)

\({\underline{\underline{\bf{\blue{\:\:\:Solution\:\:\:}}}}}\\\\\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:\sf\red{\dfrac{4(3x-5)}{1+5}=13}\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:\sf\orange{\dfrac{4(3x-5)}{6}=13}\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:\sf\green{\dfrac{2(3x-5)}{3}=13}\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:\sf\blue{\dfrac{6x-3}{10}=13}\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:\sf\purple{6x-10=39}\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:\sf\red{6x = 39+10}\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:\sf\blue{6x = 49}\)

\(\\\)

\(\qquad:\longrightarrow\:\:\:\:{\underline{\boxed{\sf{\purple{x = \dfrac{49}{6}}}}}}\)

\(\\\)

Answer:

$2247

Step-by-step explanation:

2100+(2100*7/100)= 2100+147=2247

The product of two linear functions having same variables will be a quadratic function where as the The product of two linear functions having different variables will be a linear function.

Linear function is the function whose degree is 1.

Degree of a function is the highest power of the variable of the function.

Let us take two examples.

1. Suppose the two linear functions are -

f(x) = 2x + 3 and g (x) = x + 5

The product of f(x) and g(x) will be

(2x + 3)(x + 5)

=2x (x + 5) + 3 (x + 5)

= 2x² + 10x + 3x + 15

= 2x² + 13x + 15

Here, f(x) and g(x) are the functions having same variables so there product is a quadratic function.

2. Suppose the two linear functions are -

f(x) = 2x + 3 and g (y) = y + 5

The product of f(x) and g(y) will be

(2x + 3)(y + 5)

=2x (y + 5) + 3 (y + 5)

= 2xy + 10x + 3y + 15

Here, f(x) and g(y) are the functions having different variables so there product is a linear function.

To know more about quadratic function here. https://brainly.com/question/27958964#

#SPJ4

Answer:

Step-by-step explanation:

You want to know the number in each party if the total is 100 and there are 8 more Democrats than Republicans.

Let d represent the number of Democrats. Then d-8 is the number of Republicans. The total is ...

  d +(d -8) = 100

Simplifying gives ...

  2d -8 = 100

  2d = 108

  d = 54

  d-8 = 54 -8 = 46

There were 54 Democrats and 46 Republicans.

<95141404393>

Answer:7500

Step-by-step explanation:

Amount of $150,000 represents 42.86% of $350,000.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Danny’s home cost $350,000. The federal government program for flood damage insurance covers only $150,000.

Assume that it represents [x%] percent of the total value. Then, we can write -

x = (150000/350000) x 100

x = 42.86%

Therefore, $150,000 represents 42.86% of $350,000.

To solve more questions on equation modelling, visit the link below-

brainly.com/question/9144182

#SPJ1

Part A: There are 28 green beans in the garden. Part B: There are 80 plants that are either pumpkin or tomato. Part C: There are 52 more corn plants than cucumber plants.

A circle graph, often called a pie chart, is a circular graph with sectors on it, each representing a particular category or set of data. Each sector's area or angle is proportionate to the amount it stands for. In data visualisation, circle graphs are frequently used to show the relative sizes or proportions of several categories or groups within a dataset. They can instantly convey the distribution of data without the need for laborious numerical calculations, which makes them effective for presenting data that is divided into discrete groups. However, if the data is not presented in a clear and simple manner or if the sectors are not precisely drawn to scale, circle graphs may be deceiving.

Part A: The percentage of green beans in the circle graph is 14%.

14% of 200 = 0.14 x 200 = 28

Part B: The circle graph shows:

pumpkin plants and tomato plants is 20% + 20% = 40%.

40% of 200 = 0.40 x 200 = 80

Part C: The corn plants is 36% and the percentage of cucumber plants is 10%.

36% of 200 - 10% of 200 = (0.36 x 200) - (0.10 x 200) = 72 - 20 = 52

Learn more about circle graph here:

https://brainly.com/question/13298277

#SPJ1

Answer: 4.8%

Step-by-step explanation: the total amount of pens in the drawer is (10+12+3)  = 25

the amount of red pens in the drawer is 3

the probability of picking out a red pen from the drawer = 3/25

the amount of blue pens in the drawer is 10

the probability of picking out a red pen from the drawer = 10/25

the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%

Answer:

Step-by-step explanation:

daddy

Answer:

b/2 min

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\)  ( substitute values )

\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

The function has three distinct real zeros.

The correct answer is A.

To determine the statement about the zeros of the graphed function, let's analyze the given information.

We have the following points on the graph:

(0.8, 4), (2, -4), (4.6, 0.5), (6, 0), and (7.5, 8)

Additionally, the function intercepts the x-axis at 1, 4, and 6 units.

To find the zeros of the function, we need to identify the x-values where the function intersects the x-axis.

From the given information, we know that the function intersects the x-axis at 1, 4, and 6 units.

These three x-values correspond to three distinct real zeros of the function.

The correct statement about the zeros of the graphed function is:

The function has three distinct real zeros.

The correct answer is A.

For such more questions on real zeros

https://brainly.com/question/29286241

#SPJ8

Answer:

-38/25

in decimal form: -1.52

Step-by-step explanation:

Answer: -38/25 or -1 13/25 or -1.52

Step-by-step explanation:

-2 is the same as -50/25 because -50/25 is -2

-50/25+12/25

-50+12 = -38

-50/25+12/25=-38/25

-1 13/25

Answer:

The 95% confidence interval for the difference in population proportions is (0.001, 0.079).

Step-by-step explanation:

The (1 - α)% confidence interval for the difference in population proportions is:

\(CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha /2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}\)

The information provided is as follows:

\(\hat p_{1}=0.95\\\hat p_{2}=0.91\\n_{1}=300\\n_{2}=350\\\)

The critical value of z for 95% confidence level is 1.96.

Compute the 95% confidence interval for the difference in population proportions as follows:

\(CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha /2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}\)

     \(=(0.95-0.91)\pm 1.96\times\sqrt{\frac{0.95(1-0.95)}{300}+\frac{0.91(1-0.91)}{350}}\\\\=0.04\pm 0.0388\\\\=(0.0012, 0.0788)\\\\\approx (0.001, 0.079)\)

Thus, the 95% confidence interval for the difference in population proportions is (0.001, 0.079).

The area of the smaller rectangle (KLMN) is 16.

Since rectangles ABCD and KLMN are similar, their corresponding sides are proportional.

Let's assume the length of side AB in rectangle ABCD is x, and the length of side KL in rectangle KLMN is y.

We can set up the proportion:

(x/y) = (20/16)

To find the area of the smaller rectangle, we need to determine the ratio of their areas.

Since the area of a rectangle is given by the product of its length and width, the ratio of the areas will be equal to the square of the ratio of their sides:

(Area of ABCD)/(Area of KLMN) = (x²)/(y²)

We are given that the area of ABCD is 25, so we have:

25/(Area of KLMN) = (x²)/(y²)

To find the area of KLMN, we need to substitute the values of x and y from the proportion:

25/(Area of KLMN) = (20/16)²

Simplifying the right side:

25/(Area of KLMN) = (5/4)²

25/(Area of KLMN) = 25/16

Cross-multiplying:

25 × 16 = 25 × (Area of KLMN)

400 = 25 × (Area of KLMN)

Dividing both sides by 25:

16 = Area of KLMN

Therefore, the area of the smaller rectangle (KLMN) is 16.

Learn more about similarity click;

https://brainly.com/question/26451866

#SPJ1

Vector v can be written as the sum of two vector components, \(v_x = -5i\)  and \(v_y = 6j\)

To write vector v as the sum of two vector components, we need to decompose it into two vectors along different directions.

v = -5i + 6j

w = 3i + 4j

We can decompose vector v into two components, one along the x-axis and the other along the y-axis.

Let's denote the component along the x-axis as \(v_x\) and the component along the y-axis as \(v_y.\)

The x-component, \(v_x,\) represents the projection of vector v onto the x-axis and can be found using the dot product of v and the unit vector i:

\(v_x = v . i = (-5i + 6j) . i = -5i . i + 6j . i = -5\)

Similarly, the y-component, \(v_y,\) represents the projection of vector v onto the y-axis and can be found using the dot product of v and the unit vector j:

\(v_y = v . j = (-5i + 6j) . j = -5i . j + 6j . j = 6\)

Now, we can write vector v as the sum of its components:

\(v = v_x + v_y = -5i + 6j\)

So, vector v can be written as the sum of two vector components: -5i along the x-axis and 6j along the y-axis.

For similar question on components.

https://brainly.com/question/28351472  

#SPJ11

Answer:

11%+12%=23% so $26,450/.23=$115,000.

Step-by-step explanation: