Please complete the proof.

Answer:

8 < f

Step-by-step explanation:

Because it says the cooler could hold less than eight large fish

Less than mean <

So the equation is 8<f

Answer: b  8 < f

Step-by-step explanation:

In the △IGH, the measurement of the angles are m∠G = 114°, m∠H = 49°, and m∠I = 17°.

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Given that,

m∠G = (7x - 5)°, m∠H = (3x - 2)°, and m∠I = x°.

The sum of interior angles of a triangle is 180°.

Therefore,

m∠G + m∠H + m∠I = 180°

Putting m∠G = (7x - 5)°, m∠H = (3x - 2)°, and m∠I = x°:

(7x - 5)° + (3x - 2)° + x° = 180°

Combine like terms:

(7x + 3x + x) - (5 + 2) =180

11x - 7 = 180

Add 7 on both sides:

11x = 187

Divide both sides by 11:

x = 187/11

x = 17

Now putting x = 17 in m∠G = (7x - 5)°, m∠H = (3x - 2)°, and m∠I = x°:

m∠G = (7×17 - 5)° = 114°

, m∠H = (3×17  - 2)° = 49°

m∠I =  17°

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The partial derivative of function f(x, y) = xy/cos(x) is  ∂/∂y [xy/cos(x)] = x sec(x)

In this question we have been given a function y′ = f(x,y) = xy/cos(x)

We need to find the partial derivative of function f(x, y) with respect to y, ∂f/∂y

Consider the partial derivative of function

∂f/∂y = ∂/∂y [xy/cos(x)]

∂f/∂y = ∂/∂y [xy * 1/cos(x)]

we know that 1/cos(x) = sec(x)

∂f/∂y = ∂/∂y [xy * sec(x)]

∂f/∂y = x sec(x)  ∂/∂y (y)

∂f/∂y = x sec(x) * 1

∂f/∂y = x sec(x)

Therefore,  ∂/∂y [xy/cos(x)] = x sec(x)

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The value of x from the triangle CAE is x = 6

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔCAE

Now , the second triangle is ΔCBD

And , ΔCAE ≅ ΔCBD

So , Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

And ,

CE / CD = CA / CB

Substituting the values in the equation , we get

( 30.5 + 12.2 ) / 30.5 = ( 15 + x ) / 15

On simplifying the equation , we get

42.7 / 30.5 = ( 15 + x ) / 15

Multiply by 15 on both sides of the equation , we get

640.5 / 30.5 = 15 + x

15 + x = 21

Subtracting 15 on both sides of the equation , we get

x = 21 - 15

x = 6

Therefore , the value of x is 6

Hence , The value of x from the triangle CAE is x = 6

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The integer that makes the inequality 3(n − 6) < 2(n + 12) false is

The integer that makes the inequality false is solved by substituting the values and solving the inequality

3(n − 6) < 2(n + 12)

for n = -5

substituting the value of n

3(-5 − 6) < 2(-5 + 12)

= -33 < 14

3(n − 6) < 2(n + 12)

for n = 3

substituting the value of n

3(3 − 6) < 2(3 + 12)

= -9 < 30

3(n − 6) < 2(n + 12)

for n = 12

substituting the value of n

3(12 − 6) < 2(12 + 12)

= 18 < 48

3(n − 6) < 2(n + 12)

for n = 42

substituting the value of n

3(42 − 6) < 2(42 + 12)

= 108 < 108 wrong

This is the only wrong solution since 108 = 108

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Answer: [Rational function definition]In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. In other words, it's a function that is the ratio of two polynomials. It is "Rational" because one is divided by the other, like a ratio.

Answer: he reads 52 chapters in 2 hours.

Step-by-step explanation:

Since he reads 26 chapters per hour, multiply the number of chapters by the number of hours which is two.

26 * 2 = 52

he reads 52 chapters in 2 hours.

Answer:

52 chapters

Step-by-step explanation:

Because he reads 26 chapters in 1 hour and his rate is constant (never changing), multiply 26 by 2 to find how many chapter for 2 hours.

26 x 2 = 52

False. Consider a graph with 4 vertices, where there is an edge of weight 8 between the two farthest vertices, and an edge of weight 10 between the two closest vertices.

The highest weight edge (10) would be included in the MST, as it is the only connection between the two closest vertices.The definition of a minimum spanning tree states that it is a subset of edges of a graph that connect all of the vertices without forming any cycles, and with the minimum total weight. If a graph contains an edge with the highest weight, it may still be included in the MST if it is the only connection between two vertices. To illustrate this, consider a graph with 4 vertices, where there is an edge of weight 8 between the two farthest vertices, and an edge of weight 10 between the two closest vertices. In this case, the highest weight edge (10) would be included in the MST, as it is the only connection between the two closest vertices, and thus the minimum total weight is achieved.

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The values of X ∩ Y are 1, 3, 5, and 7.

A set is a collection of items where there are operations such as:

Union of sets, the intersection of sets, complements of sets.

We have,

X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }

Y = {-3, -1, 1, 3, 5, 7, 20}

Now,

X ∩ Y

= The values common to both sets.

= {1, 3, 5, 7 }

Thus,

X ∩ Y = {1, 3, 5, 7 }

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The unit rate of change of flour (y) with respect to sugar (x) will be 2.25.

        r = Δy/Δx

        [tex]\lim_{x \to \;0} (r) = \lim_{x \to \;0}[/tex] (Δy/Δx) = dy/dx

Given is that Melissa made three batches of oatmeal cookies. Her recipe calls for amounts of sugar (in cups) and flour (in cups) in the following ratios as shown in the question.

We can write the rate of change as -

r = Δy/Δx

r = (y₂ - y₁)/(x₂ - x₁)

y₂ = [tex]$6\frac{3}{4}[/tex] = 27/4

y₁ = [tex]$4\frac{1}{2}[/tex] = 9/2

x₂ = 3

x₁ = 2

Using the values -

r = (27/4 - 9/2)/(3 - 2)

r = (27 - 18)/4

r = 9/4

r = 2.25

Therefore, the unit rate of change will be 2.25.

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Answer:

The item that shows what Kenneth has left is [B] Net Worth: $1,050.

Net worth is a person's assets minus their liabilities. In this case, Kenneth's assets include the $2,000 lottery prize and the money he deposited in his bank account. His liabilities include the car payment he paid off and the gift card he bought for his nephew. Subtracting these liabilities from his assets gives us his net worth of $1,050.

Net cash is the amount of cash a person has available, which would not include any assets such as the money in Kenneth's bank account. Net income is the total amount of income a person has earned, which would not include the lottery prize in this case.

Answer: The answer would be 9.125.

Step-by-step explanation:

I can't really find an explanation for it.  Sorry.

The remaining angles are 80 and 30

The sum of angles of a triangle = 180

One angle is given as                 = 70

The sum of the remaining angles= 110

Now we apply the theory of ratios

The ratio between the angles are given as 3:8

So one angle will be 3 parts of 110 and other eight parts of 110

Total number of parts = 3+8 = 11

Angle 1                         = (3*110)/11

                                     =  30

Angle 2                        = (8*110)/11

                                     = 80

So the other two angles are 30 and 70.

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The measure of z on the right triangle shown at the end of the answer is given as follows:

z = square root of 80.

To obtain the measure of z, the first step is obtaining the measure of y, which is obtained using the geometric mean property, as follows:

y = square root of (16 x 4) = square root of 64 = 8.

The Pythagorean Theorem states that the measure of the hypotenuse squared is equals to the sum of the squares of the measures of each side.

For the smaller right triangle, we have that:

Then the length of the hypotenuse z is obtained applying the Pythagorean Theorem as follows:

z² = 4² + 8²

z² = 16 + 64

z² = 80

z = square root of 80.

The triangle is given by the image shown at the end of the answer.

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Answer:

Step-by-step explanation:

Answer:

  10 pounds

Step-by-step explanation:

You want to know the number of pounds of peanuts in a mix of $5/lb peanuts and $6/lb almonds that gives 14 pounds of nuts for $74.

Let p represent the number of pounds of peanuts in the mix. The (14-p) is weight of almonds, and the total cost is ...

  5p +6(14 -p) = 74

Simplifying the equation gives ...

  -p +84 = 74

  10 = p . . . . . . . . add p-74

You should buy 10 pounds of peanuts to make the 14 lb bag cost $74.

__

Additional comment

You notice that simplifying the equation gives p a negative coefficient. If you choose the variable to represent the more expensive contributor, then the coefficient of that comes out positive. (We like positive coefficients, as they tend to reduce errors.)

Here, the problem is requesting the amount of the lower cost contributor, so we used the variable to represent that.

Often, you are asked to solve mixture problems using a system of equations. Those would use a variable for each of the quantities, and the equations would be ...

You notice that substituting for 'a' gives the equation we used above.

Jumping directly to this step saves a bit of written work, though the mental work is the same.

The equation of the line would be 7x - 2y = 6.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                    y - y1 = m(x - x1)

The required line passes through (0, -3) and the slope is 7/2.

By using the slope-point form of the line, we get

          y - (-3) = (7/2)(x-0)

          y + 3 = 7/2x

          2y + 6 = 7x

         7x - 2y = 6

Hence, the equation of the line would be 7x - 2y = 6.

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Question: Find the equation of the line passing through the point (0, -3) having slope 7/2.

Answer:

I believe the answer is y=3

Step-by-step explanation:

If you were to graph y=0, the line would be horizontal through the origin. Since the lines are parallel, you cannot have the answer being x=-3 or x=3 as they would intersect. Now that we have eliminated two answers, we have to choose between y=-3 and y=3. In the question, it says that the line passes through (-3,3). Because of the (x,y) coordinates, you can see that y does indeed equal 3.

I hope this helps!

Answer:

y = 3

Step-by-step explanation:

y = 0(x)

3 = 0(- 3)

y = 3

Answer: 167/30

Step-by-step explanation:

1/6 + 5.4

5.4 = 54/10

So we have 1/6 + 54/10

The common factor is 60

10/60 + 324/60

334/60

167/30

Answer:

1/6 + 5.4 = 167/30 = 5  17/30

Step-by-step explanation:

Conversion of a decimal number to a fraction: 5.4 = 54/

10

= 27/5

a) Write down the decimal 5.4 divided by 1: 5.4 = 5.4/

b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

5.4/1

= 54/10

Note: 54/10

is called a decimal fraction.

c) Simplify and reduce the fraction

54/10

= 27 * 2/5 * 2

= 27 * 2/5 * 2 = 27/5

Add: 1/6 + 5.4 = 1/6 + 27/5 = 1 · 5/

6 · 5 + 27 · 6/

5 · 6

= 5/30 + 162/30 = 5 + 162/30

= 167/30

Answer:

D) $3,264.00

Step-by-step explanation:

I = Prt

I = $1600 × 0.0325 × 32 = $1664

total = $1600 + $1664 = $3264

To find the account balance at the end of the first year, we need to calculate the amount of interest earned. The interest rate is 6%, or 0.06. The initial balance is $6,000, so the interest earned is 0.06*$6,000 = $360.

Adding the interest to the initial balance gives us the account balance at the end of the first year: $6,000 + $360 = $<<6000+360=6360>>6360.

Therefore, the account balance at the end of the first year will be $6360.

Answer:

A. 145 degree

Step-by-step explanation:

A triangle has 180 degree

109 + 36 = 145 degree

180 - 145 = 35 degree

35 degrees is the missing angle of the triangle. This angle must add with angle 1 equal to 180 degrees.

180 - 35 = 145 degree

So, the answer is A

Answer:

ANGLE 1 = 145°

Step-by-step explanation:

Angle 1 is right next to the EMPTY interior angle of the triangle and they are on a straight line!

This means, these two angles (angle 1 and the empty angle next to it) are supplementary angles!

Supplementary angles are angles on a straight line and they always add up to 180°

To find it, we need to find the degrees of the empty angle.
To find it, we need to look at the whole triangle.

Remember, all triangles equal 180°

Let's find this empty angle

180° - 109 - 36 = 35°

The empty angle = 35°

BUT WE ARE NOT DONE!

We are looking for angle 1, not the empty angle.

To find angle 1, we must remember that the empty angle (which we found was 35°) and angle 1 make a supplementary angle (which totals up to 180°)

Let's find angle 1, using subtraction.

180° - 35 = 145°

ANGLE 1 = 145°

The total cost of golf club including shipping and handling is $135.8.

What is cost?

A cost is the value of money that has been expended in the production or delivery of a good or service and is therefore no longer available for use in accounting, retail, research, or accounting. In business, the cost may be one of acquisition, in which case the cost is the sum of the money used to acquire it.

Given:

Rhianna bought a golf club online. It cost $121.25 plus 12% shipping and handling.

The cost of shipping and handling is,

$121.25 x 12% = $121.25  x 0.12 = $14.55

So, the total cost is,

$121.25 + $14.55 = $135.8

Hence, the total cost of golf club including shipping and handling is $135.8.

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To change a greater than or equal to type constraint into an equality constraint, a variable is removed from the left side. It also goes by the name "negative slack variable."

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The unexplained sum of squares measures variation in the dependent variable Y about the estimated Y values. The correct answer is option D.

The unexplained variation is the sum of the squared of the differences between the y-value of each ordered pair and each corresponding predicted y-value. The sum of the explained and unexplained variations is equal to the total variation.

Unexplained variance is also known as error variation or residual variation. It refers to the random fluctuations around the regression line which show as variation. This type of variation is the sum of squared differences among each ordered pair's y-value and the predicted corresponding y-value.

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Answer:

thus: x = 5, y = -3

Step-by-step explanation:

Solve the following system:

{y + x = 2 | (equation 1)

-4 y + 3 x = 27 | (equation 2)

Swap equation 1 with equation 2:

{3 x - 4 y = 27 | (equation 1)

x + y = 2 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{3 x - 4 y = 27 | (equation 1)

0 x + (7 y)/3 = -7 | (equation 2)

Multiply equation 2 by 3/7:

{3 x - 4 y = 27 | (equation 1)

0 x + y = -3 | (equation 2)

Add 4 × (equation 2) to equation 1:

{3 x + 0 y = 15 | (equation 1)

0 x + y = -3 | (equation 2)

Divide equation 1 by 3:

{x + 0 y = 5 | (equation 1)

0 x + y = -3 | (equation 2)

Collect results:

Answer: {x = 5, y = -3

Answer:

y = -3z - 3

Step-by-step explanation:

y=mz+b  ==> slope-intercept form where m=slope

9z + 3y = -9​  

9z - 9z + 3y = -9z - 9  ==> solve for y

3y = -9z - 9

(3y = -9z - 9)/3  ==> divide equation by 3 to isolate y

y = -3z - 3

Answer:

Step-by-step explanation:

y varies directly with x then, y=kx

for x = 2 and y= -10 we get:

-10 = 2k

k= -5

when x = 12

y = -5 * (12) = -60

D

Answer:

5.083

Step-by-step explanation:

[tex]V=\frac{1}{3}Bh=(1/3)(1/2)(1.7)(3.9)(4.6)=5.083[/tex]

Answer:

The expression represents a cubic polynomial with 3 terms. The constant term is -1, the leading term is x^3, and the leading coefficient is 1.

Step-by-step explanation:

Answer: 3a

Step-by-step explanation:

(4a*6a)/8a

24a^2/8a

3a

[tex]4a\times6a[/tex]

[tex]4\times6=24\\4a\times6a=24a[/tex]

[tex]\dfrac{24a}{8a}[/tex]

[tex]=\fbox{3a}[/tex]