1. Identify your variables using let statements.

2. Determine the equations for the linear system.

3. Determine the solution to the linear system (point of intersection)

4. Explain the meaning of the solution using a therefore statement.

Chris is mixing 2 different types of fruit juice together for a summer drink. The two types of juices he is using is one that is 30% strawberry concentrate and the other is 55% lemon concentrate. If he wants 2 L that is 40% concentrate of the fruit juices, how much of each should be used to create the drink?

The equation of the line through the point (8,−9) and perpendicular to 3x+8y=4 is given by 8x - 3y = 91.

We are aware that any straight line's equation can be expressed as

y = mx + c,

where m denotes the slope and c denotes a constant.

Also, two perpendicular lines' slopes are the negative reciprocals of one another.

Here, the equation of the given straight line is

3x+8y=4

i.e. 8y = 4 -3x

i.e. y = (4/8) - (3/8)x

Now the negative reciprocal of - 3/8 is 8/3.

Then we can write the equation of the perpendicular line is

y = (8/3)x + c ...(1)

Since (1) passes through the point (8, -9), so we can put x = 8 and y = -9 in (1) to get the value of c.

So, -9 = (8/3)*8 + c

i.e. -9 = 64/3 + c

i.e. c = -9 -64/3 = - (27 + 64)/3 = - 91/3

(1) can be written as

y = (8/3)x - (91/3)

i.e. 3y = 8x - 91

i.e. 8x - 3y = 91

Therefore the equation of the line through the point (8,−9) and perpendicular to 3x+8y=4 is given by 8x - 3y = 91.

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The two values of x best represent where the two functions are equal will be (12,11)

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

Given data;

Linear function passing through;

(1, 2), (3, 4), (6,7) and (8, 9)

Quadratic function passing through

(3, 4), (5, 0), (7, 4) & (8, 9)

Let x be two values of x best represent where the two functions are equal;

The value of the x is obtained from the graph where the two line meets.

The value of x willl be (12,11)

Hence, the two values of x best represent where the two functions are equal will be (12,11)

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Proved Below

[tex]\Longrightarrow x-y = \sqrt{(x+y)^2-4xy}[/tex]

[tex]\Longrightarrow x-y = \sqrt{x^2+2(x)(y)+ y^2-4xy}[/tex]

[tex]\Longrightarrow x-y = \sqrt{x^2+2xy-4xy+y^2}[/tex]

[tex]\Longrightarrow x-y = \sqrt{x^2-2xy+y^2}[/tex]

[tex]\Longrightarrow x-y = \sqrt{(x-y)^2}[/tex]

[tex]\Longrightarrow x-y =x-y[/tex]

Let's check

x-y=√(x+y)²-4xy

Solve RHS

Hence proved

Answer:

the answer to the question is C) 8

The mid-point of the numbers 3.8 and 4.1 will be 3.95.

Let C be the mid-point of the A and B.

C = (A + B) / 2

The numbers are given below.

3.8 and 4.1

Then the mid-point of the numbers 3.8 and 4.1 will be

C = (3.8 + 4.1) / 2

C = 7.9 / 2

C = 3.95

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We can actually deduce here the one that uses the reciprocal property to rewrite  [tex]\frac{x}{6} = \frac{28}{3\\}[/tex]  is: C. [tex]\frac{6}{x} = \frac{3}{28}[/tex].

A reciprocal of a number is defined as the number that when it is multiplied by the number, the result is 1. Thus, we deduce here that the product of a number and its reciprocal gives one.

Thus: x/6 x 6/x = 1

Also, if 28/3 x 3/28 = 1

Thus, we see that they use the reciprocal property.

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Answer:

y=-2/3x-13/3

Step-by-step explanation:

parralel line have the same gradient

y=mx+c is the general straight line equation

m represents the gradient

if the equation is y=-2/3x+3/2

m=-2/3

the coordinates (4,-7)

x=4

y=-7

substitute into equation

-7=-2/3×4+c

-7=-8/3+c

c=-7+8/3

c=-13/3

so the equation is :

y=-2/3x-13/3

Answer:

The vertex is the point of coordinates (-2 , 5)

Step-by-step explanation:

we notice that the equation of the parabola is given in vertex form :

y = -4(x + 2)² + 5

then

y = -4(x − (-2))² + 5

Therefore

The vertex of the graph is the point (-2 , 5)

The expression can be used to find the difference of the polynomials is [10m (–7m)] [(–6) 4]

Difference of polynomials

A polynomial is a function that has a leading degree of 3 and above.

Given the expression below

(10m – 6) – (7m – 4)

Expand

10m - 6 - 7m  + 4

Collect the like terms

10m - 7m - 6 + 4

Simplify

3m -2

Hence the expression can be used to find the difference of the polynomials is [10m (–7m)] [(–6) 4]

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Answer:

Step-by-step explanation:

In this figure of overlapping parallelograms, each angle is related to the others by several different theorems involving triangles, parallelograms, and parallel lines. That is, there are several different ways one can arrive at the answers to this question.

__

∠UTC ≅ ∠UDC = 180° -∠EDU . . . opposite angles of parallelogram; linear pair

∠UTC = 180° -125° = 55°

__

∠UCD ≅ ∠TBC = 180° -∠TBA . . . . corresponding angles; linear pair

∠UCD = 180° -110° = 70°

__

∠BCT ≅ ∠UTC = 55° . . . . alternate interior angles

A mean is an arithmetic average of a set of observations.

The correct option is (A).

A mean is an arithmetic average of a set of observations.

Mean = (Sum of observations)/Number of observations

As, the median is the middle value.

Thus, the median will not be changed.

As, the mean is the arithmetic average.

So, the $100 gift will increase the mean value of the prizes.

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Answer:

A

Step-by-step explanation:

Answer:

C is the answers for the question

Step-by-step explanation:

please mark me as brainlest

The compound inequality can be expressed as "x > -4 or x ≤ 4."

The correct graph of the solution is:

OC. Solution: x > -4 and x ≤ 4

Let's solve the compound inequality step by step:

x + 7 > 3

Subtract 7 from both sides to isolate x:

x > 3 - 7

x > -4

and, we have,

x - 5 ≤ -1

Add 5 to both sides to isolate x:

x ≤ -1 + 5

x ≤ 4

Now, we have two inequalities for x:

x > -4

x ≤ 4

The compound inequality can be expressed as "x > -4 or x ≤ 4."

The correct graph of the solution is:

OC. Solution: x > -4 and x ≤ 4

The graph will include all values greater than -4 (open circle) and all values less than or equal to 4 (closed circle) on the number line.

The correct representation is:

OC. Solution: x > -4 and x ≤ 4

Graph:

-5 -4 -3 -2 -1 0 1 2 3 4 5

+---|---|---|---|---|---|---|---|---|---+

-4 0 4

The open circle at -4 indicates that x is greater than -4, and the closed circle at 4 indicates that x is less than or equal to 4.

The shaded area between -4 and 4 represents the solution to the compound inequality.

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Answer:

This situation of the recipe can be represented as y=x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.

What is the equation for this situation?

It is known the total amount of flour (y) is equivalent to the total amount of whole wheat flour (5.5) added to the total white flour (x). Therefore, the equation is:

y = x + 5.5

The possible values are

x = It is expected x is equalthan 0 or greater to it since the minimum amount of white flour that can be added is 0.

y = It is expected y is equal than 5.5 or greater to it since even if no

white flour is added the minimum total is 5.5.

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Step-by-step explanation:

This situation of the recipe can be represented as equation y = x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

For the given expression

y = x + 5.5

The possible values are

x = It is expected x is equal to 0 or greater to it

since the minimum amount of white flour that can be added is 0.

y = It is expected y is equal than 5.5 or greater to it since even if no

white flour is added the minimum total is 5.5.

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The number of cows and ducks in the garden are 3 and 4 respectively.

Let the numbers of cows be x and the number of ducks is y.

Total number of legs=20

Total number of eyes=14

Linear equation for the total number of legs in the garden,

4x+2y=20 -(1)

Linear equation for the total number of eyes in the garden,

2x+2y=14 -(2)

Solve the system of the two linear equations to find the values of x and y.

Subtract equation (1) from equation (2), and we get,

2x=6

[tex]x=\frac{6}{2}\\[/tex]

x=3

Substitute the value of x in equation (1), and we get,

4(3)+2y=20

12+2y=20

2y=20-12

2y=8

[tex]y=\frac{8}{2}\\[/tex]

y=4

Number of cows=3

Number of ducks=4

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Answer:

46. 135°

47. 225°

47. 270°

48. 3/8

49. 3/4

Step-by-step explanation:

Answer:

46) 135°

47) 225°

48) 270°

49) [tex]\frac{3}{8}[/tex]   (3/8)

50) [tex]\frac{3}{4}[/tex]  (3/4)

Step-by-step explanation:

{the following is if you do not understand my drawing}

There are 4 segments that we can imagine - north, south, east, and west

We can imagine that these lines all meet a circle

There are 360 degrees to a circle. So, if we divide that by 4, we know that each segment is 90 degrees.

(Also, you can probably see that the angles are right angles, or you know that straight lines are 180 degrees, you probably know this information intuitively)

This means that each smaller segment, two in both of our four segments, is 45 degrees.

These 8 sections are each 1/8 of the total circle.

Answer:

-1 and -11

Step-by-step explanation:

"sum" means we're adding.

-1 + -11 = - 12

"product" means we're multiplying.

-1 × -11 = 11

The graph which resembles the graph of f(x)=[tex]2^{x}[/tex] but is reflected over the x-axis is g(x)=[tex]2^{x} +1[/tex]

Given Function f(x)=[tex]2^{x}[/tex].

We have to generate a function whose graph is similiar to the given function and is reflected over the x axis.

If we take first function g(x)=2x-1

put the value of x=-1 then the value of function g(x)=2*(-1)-1=-2-1=-3 means the value of y in this function will be negative means the graph will be under x-axis.

Taking second function g(x)=[tex]2^{x} +1[/tex]

for all the negative values of x it posses a positive value of y so the graph will be over the x axis.

Taking third function g(x)=-[tex]2^{x}[/tex]

In the above function for each value of x the function possess a negative value so the graph will be under x axis.

Taking fourth function g(x)=2x-1

For all values of x less than 1 the function becomes negative which takes graph below the x axis. First graph is for [tex]2^{x}[/tex] and the second is for [tex]2^{x} +1[/tex]

Hence the graph similar to [tex]2^{x}[/tex] and reflected over x axis is g(x)=[tex]2^{x} +1[/tex].

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Answer:

29/10

Step-by-step explanation:

7/2+(-3/5)

7/2-3/5

35/10-6/10

29/10

Answer:

Step-by-step explanation:

All you have to do is add the four sides together and that should be your answer.

(B.) 4√37 units

Good luck! Please rate if this helped! <3

Answer:

The five Platonic solids (regular polyhedra) are the tetrahedron, cube, octahedron, icosahedron, and dodecahedron. In other words the second one.

Answer:

x>0

Step-by-step explanation:

points exist on the right of the graph so the domain is x>0

The point of intersection of two given equations is (0.333, 2.667).

Given that, equation with two variables are y = 8x and y = 2x + 2.

The given equations will intersect at some point where y is the same for both equations.

When you replace y in y = 2x + 2 with y = 8x, we get 8x = 2x + 2.

So, the solution of 8x = 2x+2 will satisfy both equations.

Now, we need to find the solutions to take the integer values of x between -3 and 3.

That is,

x = -3 , then 8(-3) = 2(-3) +2⇒-24 = -6+2

⇒-12 = -4    False.

similarly, for x = -2

8(-2) = 2(-2)+2

⇒-16 = -2   False

For, x = -1

8(-1) = 2(-1)+2

⇒-8= 0   False

For, x = 0

8(0) = 2(0)+2

⇒0= 2   False

For, x = 1

8(1) = 2(1)+2

⇒8= 4   False

For, x = 2

8(2) = 2(2)+2

⇒16 = 6   False

For, x = 3

8(3) = 2(3)+2

⇒24 = 8   False

Therefore, there is no solution to 8x = 2x +2 for the integers values of x between -3 and 3.

The equations can be solved graphically by plotting the two given functions on a coordinate plane and identifying the point of intersection of the two graphs.

The point of intersection is the values of the variables which satisfy both equations at a particular point.

Hence, you can see the graph as shown below, the point of intersection is (0.333, 2.667).

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Answer:

[tex]x > - 3[/tex]

I hope this is helpful

Step-by-step explanation:

The equation of a exponential function is

[tex]a \times (b) {}^{x} [/tex]

where a is the y value of the y intercept, b is the constant rate of change.

Here the y intercept is (0,4), the y value of the y intercept is 4.

So a=4

The graph passes through point (1,2) so

[tex]h(x) = 4 \times b {}^{x} [/tex]

Plug in 1 for x, 2 for h(x)

[tex]2 = 4 \times {b}^{1} [/tex]

Anything to the first power is itself so

[tex]2 = 4 \times b[/tex]

Isolate b.

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

So our function is

[tex]4 \times ( \frac{1}{2} ) {}^{x} [/tex]

Answer:

[tex]h(x)=4\left(\dfrac{1}{2}\right)^x[/tex]

Step-by-step explanation:

Exponential Function

General form of an exponential function:

[tex]y=ab^x[/tex]

where:

From inspection of the given diagram, the defined points on the curve are:

As one of the defined points is the y-intercept (0, 4) then:

[tex]\implies a=4[/tex]

Substitute the found value of a and the point (1, 2) into the general form of an exponential function and solve for b:

[tex]\begin{aligned}h(x)=ab^x & \\\implies h(1)=4b^1 & = 2\\4b & = 2\\b & = \dfrac{2}{4}\\b & =\dfrac{1}{2} \end{aligned}[/tex]

Finally, substitute the found values of a and b into the general formula to complete the equation for the function h(x):

[tex]\implies h(x)=4\left(\dfrac{1}{2}\right)^x[/tex]

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The solution to the complex inequality as in the task content is; -2 < x <= 1.

The inequality in discuss is; -5<4x+3 <= 7.

Hence, solving the inequalities separately; we have;

-5 < 4x +3

-8 < 4x

-2 < x

Also; 4x+3 <= 7

4x <= 4

x <= 1.

Ultimately, the solution to the inequalities is;

-2 < x <= 1.

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