andrea wants to cut a board into three pieces the board is 3 2/3 feet long how long will each piece be

The amount of paint that must be used from can A and can B is 3.86 liters and 5.14 liters respectively to obtain 9 liters of paint which is half blue and half yellow.

Can A has 9 parts of blue paint and 1 part of yellow paint, this can be expressed in percentage as;

Can A = 90% blue, 10% yellow

Similarly,

Can B = 20% blue, 80% yellow

Now consider an algebraic expression as follows;

A + B = 9 liters

90% A + 20% B = 50% [Blue]

10% A + 80% B = 50% [Yellow]

Resolving;

90% A + 20% B = 10% A + 80% B

80% A = 60% B

Solving the equation, A + B = 9, for one variable;

A + B = 9

B = 9 - A

80% A = 60% (9 - A)

80% A = 540% - 60% A

140% A = 540%

A = 3.86 Liters

Now solving for B;

B = 9 - A

B = 9 - 3.85

B = 5.14 Liters

Therefore 3.86 liters should be used from can A and 5.14 liters should be used from can B.

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Answer:

D

Step-by-step explanation:

(14x + 18) and 116 are corresponding angles and are congruent, then

14x + 18 = 116 ( subtract 18 from both sides )

14x = 98 ( divide both sides by 14 )

x = 7

a) We will draw the situation.

b) Considering the theory, the vertex of a parabola is represented in (h,k) where h is the x-coordinate, in this case, if our parabola has an amplitude of x=320feet then h=320/2=160feet, and k is the highest y-coordinate 80 feet. So the equation is:

We have to know the value for a, so we will use a point to replace it in the equation and with that, we will know the value, so in x=0 the y-value is 0 too so:

So the equation is:

c. To know the answer to this question we will have to replace x=280feet with the y value we will know if at the moment the ball can go over the tree or if it would crash into it.

At that point, the ball would be 35 feet up so if it could pass over the tree 5 feet higher.

Answer:

y = -x + 1

Step-by-step explanation:

y =mx + b

It is crossing the y axis at 1 that is the b

The slope (m) is -1.  From one point on the line to another you go down 1 and left 1.  That represents a negative slope of 1

The slope of the line parallel to y = 4  / 7 x + 7 is 4  /7.

The slope of the line perpendicular to y = 4  / 7 x + 7 is - 7 / 4.

The equation of a line can be described as follows:

y = mx + b

where

The equation of the line given is y = 4  / 7 x + 7.

Parallel lines have the same slope.

Therefore, the slope of the line parallel to the given equation of the line is 4 / 7.

A line perpendicular to each other follows the rule below:

m₁ m₂ = -1

where

Therefore, let's find the slope of the line perpendicular to the given equation.

4 / 7 m₂ = -1

cross multiply

4m₂ = -7

m₂ = - 7 / 4

Therefore, the slope of the line perpendicular to the equation is - 7/4

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Answer:

Answer 1: Rajesh: 93/100 Sita: 82/100 (simplest form: 41/50) Rajesh earned more.

Answer 2: 11/100 more marks

Answer 3: Rajesh got an A, while Sita got a B-

Step-by-step explanation:

Put the 93 on top of 100, and do the same for 82.

Rajesh clearly earned more. Subtract 82 from 93 to find out Rajesh score 11 points more.

EXPLANATION

Since we know that the number of hours is represented by a periodic function, the appropriate model is the sine function.

As the average number of daylight hours is 12 with a maximum and minimum of 14.4 and 9.6 respectively.

Furthermore, the period is 365.

Thus, the period is as follows:

The appropiate model is the following:

Now, we need to compute the value of a:

Since the sine function reaches its highest value at t=90° and is represented by 14.4, when t=90°, the value of the function is asin(0.017t) = 1

Therefore,

14.4 = a + 12

Subtracting -12 to both sides:

14.4 - 12 = a

Subtracting numbers:

2.4 = a

In conclusion, the final function is the following:

Since the minimum is at t=0, we want:

In conclusion, the solution is the OPTION C)

For this problem, we are given the following rational function:

We need to determine the horizontal asymptote for this function. In order to determine this, we need to calculate the limit of the function when x approaches infinity. We have:

The horizontal asymptote exists at y= 4/3. The correct option is C.

Given the equations

x + y = 5----------------------(1)

x - 3y = 3-----------------------(2)

Subtract equation (2) from (1)

x - x -3y - y = 3 - 5

-4y = -2

Divide both -4

Substitute y = 1/2 into equation (1)

x + y = 5

Hence, the solution to the equations is

The slope of line through points (-2, 2) and (-4, -1) is 3/2 by using the slope-point formula that tells that change in y divided by change in x.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

A point is a basic concept in classical Euclidean geometry that represents an exact location in space and has no length, width, or thickness. In contemporary mathematics, a point more broadly refers to a component of a set known as a space.

Here,

The points are (-2, 2) and (-4, -1)

m=(y2-y1)/(x2-x1)

m=Δy/Δx

m=(-1-2)/(-4+2)

m=3/2

By dividing the change in y by the change in x, the slope of the line passing through the points (-2, 2) and (-4, -1) is 3/2.

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EXPLANATION

Given the line on the graph, we need to find the slope and the y-intercept.

Considering two ordered pairs, as for instance (x₁,y₁)=(50,-90) and (x₂,y₂)=(80,90)

The slope-equation is:

Replacing terms:

The point-slope form of the line is:

y-y₁= m(x-x₁)

Finally, we need to represent as a point-slope form considering either one ordered pair, as for instance, (x₁,y₁)=(50,-90)

y-(-90) = 6(x-50) [Simplifying terms]

y + 90 = 6(x-50) [ANSWER]

Based on angle relationships, the missing angle measures are:

a = 118° [same side exterior angles]

b = 118° [vertical angles]

c = 32° [Linear pair]

d = 32° [same side interior angles]

Some of the angle relationships that can be used to determine the measures of angles that are formed when two parallel lines are intersected by a transversal are:

Using angle relationships, the following angle measures are determined as follows:

a = 180 - 62 = 118° [same side exterior angles]

b = a [vertical angles]

b = 118°

c = 180 - 148 [Linear pair]

c = 32°

d = 2 [same side interior angles]

d = 32°

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The simplified expression of the perimeter of the triangle is 3.75x - 7.

A triangle is a a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The perimeter of a triangle is the sum of the whole three sides.

Therefore, the simplified expression that represents the perimeter of the triangle is as follows:

Hence, the three sides of the triangle are as follows;

Hence,

perimeter of the triangle = 1.5x - 3 + 1.5x - 3 + 0.75x - 1

perimeter of the triangle = 1.5x + 1.5x + 0.75x - 3 - 3 - 1

perimeter of the triangle = 3.0x + 0.75x - 7

perimeter of the triangle = 3.75x - 7

Therefore, the simplified expression is 3.75x - 7

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The inverse of f(x) will be a relation if the original function's graph contains any location where a horizontal line would cross itself twice, but the inverse of that function won't be a function in and of itself.

Does a function's inverse always represent a relationship?

Essentially, obtaining an inverse is only a matter of changing the x and y coordinates. Although it might not always be a function, this newly generated inverse will be a relation. Sometimes a function's inverse isn't actually a function!

The inverse will also be a function if all horizontal lines only ever intersect one place on the original graph.

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Answer: D) -a

Step-by-step explanation:

a+b=0 , add -a for both side

- a + a + b = 0 - a

we cancel (- a + a) and we get

b = 0 - a => b = -a

Answer:

option d -a

if you take a to the opposite side of the equal mark it's sign is going to change since it's positive it's going to be negative on the other side 0 -a = -a

baam answer

Answer Las raíces de la ecuación x2 − 6x + 7 = 0 son α y β. Encuentra la ecuación con raíces α + 1 β y β + 1 α. Deduzco que α + β = − b a = 6 1 = 6 y que αβ = c a = 7 1 = 7.

Step-by-step explanation:

A. The slope of the function = 1.5.

a = 15; b = 3; c = 3; d = 1.5

B. y-intercept (b) = 7.5

C. The equation of the function is: y = 1.5x + 7.5.

The height in 10 years is approximately 17.5 feet.

The equation of a function can be expressed as y = mx + b, if we know the value of the slope, m, and the value of the y-intercept, b.

Part A:

Using the two points on the graph, we can find the slope of the function as shown below:

The two points are (3, 12) and (5, 15):

Slope of the function = (15 - 12)/(5 - 3)

= 3/2

Slope (m) = 1.5.

Thus, the values that represents each letters would be:

a = 15; b = 3; c = 3; d = 1.5

Part B: The y-intercept of the function

The y-intercept of the function can be defined as the initial tree height which is the point where the line intercepts the y-axis of the graph.

Substitute m = 1.5 and (x, y) = (3, 12) into y = mx + b to find the y-intercept (b) of the function:

12 = 1.5(3) + b

12 = 4.5 + b

12 - 4.5 = b

7.5 = b

b = 7.5

y-intercept (b) = 7.5

Part C: To write the equation of the function, substitute m = 1.5 and b = 7.5 into y = mx + b:

y = 1.5x + 7.5.

Therefore, the initiate tree height is 7.5 feet, and it increases at a rate of 1.5 feet per year.

To find the height in 10 years, substitute x = 10 into the equation of the function, y = 1.5x + 7.5:

y = 1.5(10) + 7.5

y = 10 + 7.5

y = 17.5 feet

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The biconditional statement is "You study for your test if and only if you passed".

What is biconditional statement?

A biconditional statement combines a conditional statement with its opposite expressed in the form of "if and only if."

The given statements are,

"If you study for your test, then you will pass your test"  and "you passed your test then you studied for your test".

The biconditional statement is: "You study for your test if and only if you passed".

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Answer:

y=-5x/3+26/3

Step-by-step explanation:

Because we want the equation to look like y=mx+b, rearrange the terms.

Since 26-5x is the same as -5x+26, rewrite it like that.

3y=-5x+26

Now, since we want the value of y, divide by 3 on both sides.

3y/3=y

-5x/3= -5x/3

26/3= 26/3

The simplest form would look like:

y=-5x/3+26/3

A tall child with an arm span of 120 cm and height of 118 cm was added to the sample used in this study then the correlation will increase whereas the slope stays the same.

Correlation is a relation between two variables, by shifting one independent variable, how the dependent variable will shift, that's the degree of correlation since Correlation can be fitted in any shape or condition. It can be fitted nonlinear, straight or curvy straight, etc whereas slope is related to a straight variety of two variables, it is characterized as the rate of altering of the dependent variable in order with the independent variable. By and large you'll discover equation incline =( y2-y1)/(x2-x1).

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Answer:

sss

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = 0.81x + 6.9

residual value = Measured value - Predicted value

Measured value = actual y-coordinate of the point, y

Predicted value = value of y from the equation, y1

residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)

residual value = y - y1

x y        y1                residual (y-y1)

3 9     9.33                    -0.33

6 9     11.76                    -2.76

5 13     10.95                   2.05

7 13    12.57                    0.43

8 16     13.38                    2.62

8 11     13.38                   - 2.38

Sum of residuals:

sum = (-0.33) +(-2.76)+(2.05)+(0.43)+(2.62)+(-2.38)

B. −0.37; This indicates that the line of best fit is accurate and is an overall good model for prediction.

(Though not very accurate as it should have been if the sum of residuals was equal to 0).

A total discrepancy of -0.37 is not too bad.

Answer:Answer:

B. −0.37;

This indicates that the line of best fit is accurate and is an overall good model for prediction.

Step-by-step explanation:

y = 0.81x + 6.9

residual value = Measured value - Predicted value

Measured value = actual y-coordinate of the point, y

Predicted value = value of y from the equation, y1

residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)

residual value = y - y1

x y        y1                residual (y-y1)

3 9     9.33                    -0.33

6 9     11.76                    -2.76

5 13     10.95                   2.05

7 13    12.57                    0.43

8 16     13.38                    2.62

8 11     13.38                   - 2.38

Sum of residuals:

sum = (-0.33) +(-2.76)+(2.05)+(0.43)+(2.62)+(-2.38)

sum of residuals = -0.37

ANSWER:

B. −0.37; This indicates that the line of best fit is accurate and is an overall good model for prediction.

(Though not very accurate as it should have been if the sum of residuals was equal to 0).

A total discrepancy of -0.37 is not too bad.

Answer:

I don't know if you can use permutations but

(6P2-6)/6=4 ????

When b²−4ac=0 there is one real root.

When b²−4ac>0 there are two real roots.

When b²−4ac<0 no real roots or two complex roots

First equation

-x²-4x+7

b²−4ac>0, then equation -x²-4x+7 has two real roots.

Second equation

-2x²+9x-11

b²−4ac<0, then equation -2x²+9x-11 has two complex roots.

Third equation

3x²-6x+3

b²−4ac=0, then equation 3x²-6x+3 has one root.

The probability that the repair time for an air conditioning unit will be between 29 and 44 minutes is 0.4648

We are given:

u= 38,s = 12

We have to find P(29 < x< 44)

Using the z-score formula, we have:

P(29 <x <44) = P(-0.75 < z <0.5)

Using the standard normal table, we have:

P(29 <x<44) = P(-0.75 < z < 0.5) = 0.4648

Therefore, the probability that the repair time for an air conditioning unit will be between 29 and 44 minutes is 0.4648

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from the question, we were told in 1995, Charter charged a flat rate of

$39.95 for the first twenty hours.

and an additional per hour charge of $5.99

if,

for 20 hours = 39.95

therefore for 1 hour = 39.95/20

so for 18 hours = 39.95/20 X 18.95/20

so for 18 hours = 9

so,

to get the amount Charter bill for 18 hours in 1995 is,

39.95 x 18/20

= 39.95 x 0.9

= $35.955

so Charter bill for 18 hours of internet used in 1995 is $35.955

ould bill for 28 hours is

so, what Charter would

The rule for the given function f /g when the function f(x) = -3x -6 and

g(x) = x² -x - 6 is identified as  f(x) / g(x) = -3 / (x -3).

As given in the question,

Given function are:

f(x) = -3x -6

g(x) = x² -x - 6

Rule to identify for the function f(x) / g(x) we get,

Substitute the value of f(x) and g(x) in the required rule we have,

f(x) / g(x) = (-3x -6 ) / ( x² -x - 6 )

Now simplify the function to get the rule:

f(x) / g(x) = -3(x+2) / (x² -3x +2x -6)

⇒ f(x) / g(x) = -3(x+2) /(x-3)(x+2)

⇒ f(x) / g(x) = -3 / (x-3)

Therefore, the rule for the given function f /g when the function f(x) = -3x -6 and g(x) = x² -x - 6 is identified as  f(x) / g(x) = -3 / (x -3).

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Using linear functions, it is found that:

a) The equation is: y = 2x + 3.

b) The equations are:

c) The systems are consistent independent.

d) The point of intersection is (1, 5).

A linear function is defined in slope-intercept formula by the rule presented as follows:

y = mx + b.

In which:

For Sidewalk 1, it is found that:

Then the rule is:

y = 2x + 3.

For Sidewalk 2, when x changes by 2, y decays by 2, hence the slope is:

m = -2/2 = -1.

The line goes through point (1,5), hence the equation in point-slope form is:

y - 5 = -(x - 1).

Combining the like terms, the slope-intercept form is:

y - 5 = -x + 1

y = -x + 6.

Since the two lines have different slopes, the system is consistent independent.

The x-coordinate of the intersection is:

-x + 6 = 3 + 2x.

3x = 3

x = 1.

The y-coordinate is:

-x + 6 = -1 + 6 = 5.

Hence the intersection point is:

(1, 5).

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Answer: I am I don't know man

Step-by-step explanation: answer is I don't know.

The measure of the numbered angles formed by the common transversal to the two parallel lines are;

[tex] \angle 1 = 113^{ \circ} [/tex]

[tex] \angle 2 = 67^{ \circ} [/tex]

[tex] \angle 3 = 67^{ \circ}[/tex]

[tex]\angle 4 = 113^{ \circ} [/tex]

The relationships between the angles are;

The given angle is 113°

According to corresponding angles theorem, we have;

[tex] \angle 1 = 113^{ \circ} [/tex]

[tex]\angle 1 \: and \: \angle 4 [/tex] are vertical angles

According to vertical angles theorem, we have;

[tex]\angle 1 = \angle 4 = 113^{ \circ} [/tex]

[tex] \angle 3 \: and \: 113^{ \circ} [/tex] are same side exterior angles.

According to same side exterior angles theorem, we have;

[tex] \angle 3 \: and \: 113^{ \circ} [/tex] are supplementary angles. Which gives;

[tex] \angle 3 + 113^{ \circ} = 180^{ \circ} [/tex]

[tex] \angle 3 = 180^{ \circ} - 113^{ \circ} = 67^{ \circ}[/tex]

[tex] \angle 2 \: and \: \angle 3 [/tex] are vertical angles, which gives;

[tex] \angle 2 = \angle 3 [/tex] = 67°

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[tex]-14x^2 \div 3x\implies \cfrac{-14x^2}{3x}\implies -\cfrac{14}{3}\cdot \cfrac{x^2}{x}\implies -\cfrac{14}{3}x[/tex]