Which diagram in the graph at the right is NOT a function?

The equation of the perpendicular bisector of the line segment with endpoints (-7, 2) and (-1, -6) is y = (3/4)x + 1.

To find the equation of the perpendicular bisector of a line segment, we need to determine the midpoint of the line segment and the slope of the line segment. The perpendicular bisector will have a negative reciprocal slope compared to the line segment and will pass through the midpoint.

Given the endpoints (-7, 2) and (-1, -6), we can find the midpoint using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Midpoint = ((-7 + (-1))/2, (2 + (-6))/2)

= (-8/2, -4/2)

= (-4, -2)

The midpoint of the line segment is (-4, -2).

Next, we need to find the slope of the line segment using the slope formula:

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

Slope = (-6 - 2)/(-1 - (-7))

= (-6 - 2)/(-1 + 7)

= (-8)/(6)

= -4/3

The slope of the line segment is -4/3.

Since the perpendicular bisector has a negative reciprocal slope, the slope of the perpendicular bisector will be 3/4.

Now, we can use the midpoint (-4, -2) and the slope 3/4 in the point-slope form of a line to find the equation of the perpendicular bisector:

y - y1 = m(x - x1)

y - (-2) = (3/4)(x - (-4))

y + 2 = (3/4)(x + 4)

y + 2 = (3/4)x + 3

y = (3/4)x + 1.

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Answer:

Step-by-step explanation:

1)

Congruency shortcuts:  

HL, SSS, SAS, ASA, and AAS

where S=side

A=angle

H=hypotenule

L=leg

HL is only for a right triangle

If you can prove sides and angles are congruent according to those 5 rules, you have proven the triangles are congruent

Similarity shortcuts:

AA, SAS, SSS

We have triangle similarity if (1) two pairs of angles are congruent (AA) (2) two pairs of sides are proportional and the included angles are congruent (SAS), or (3) if three pairs of sides are proportional (SSS)

2)

BG ≅ GD              >Given from image

IG ≅ GO               >Given from image

<BGI ≅ <DGO        >Vertical Angles

ΔBGI  ≅ ΔDGO        >SAS            

You have proven that the triangles are congruent because you used the shortcut by proving a side and angle and a side are congruent so SAS makes them congruent

Answer: 12, 30, 162

Step-by-step explanation:

b)  For a regular polygon the central angles will all add up to 360

n= number of sides = 360/30

n=12

d) For exterior angles, the sum of the exterior angles is also 360

n = number of sides = 360/12

n=30

f) for any polygon

interior ange = ((n-2)180) / n

interior angle = ((20-2)180 / 20

interior angle =  (18)(180) / 20

interior angle = 162

Answer:

b. 12

d. 30

f. 162°

Step-by-step explanation:

b. The number of sides of a regular polygon can be found by dividing 360° by the central angle.

In this case, the central angle is 30°, so the number of sides is 360° / 30° = 12.

The polygon is a dodecagon.

d. The number of sides of a regular polygon can be found by dividing 360° by the exterior angle.

In this case, the exterior angle is 12°, so the number of sides is 360° / 12° = 30.

The polygon is a triacontagon.

f. The interior angle of a regular polygon can be found by using the formula  [tex]\frac{180(n-2) }{n}[/tex]where n is the number of sides.

In this case, n=20, so the interior angle is 180(20-2) / 20 = 162°.

There are 182 ways to choose a president and vice president from a class of 14 students using permutations.

To determine the number of ways a president and vice president can be chosen from a class of 14 students using permutations, we can follow these steps:

1: Select the president:

Since we need to choose one student to be the president, we have 14 options available.

2: Select the vice president:

Once the president has been chosen, we need to select one student to be the vice president. Since the president has already been chosen, we are left with 13 remaining students to choose from.

3: Calculate the total number of ways:

To find the total number of ways, we multiply the number of choices at each step. Therefore, the total number of ways to choose a president and vice president is obtained by multiplying the number of choices in Step 1 (14) by the number of choices in Step 2 (13):

Total number of ways = 14 * 13 = 182.

Hence, there are 182 ways to choose a president and vice president from a class of 14 students using permutations.

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7/8 × 2/7

cut 7 on both the sides

=1/4

The answer is:

Work/explanation:

To multiply fractions, simplify them first:

[tex]\sf{\dfrac{7}{8} \times\dfrac{2}{7}}[/tex]

Look what happens now.

[tex]\sf{\dfrac{\diagdown\!\!\!\!7}{8}\times\dfrac{2}{\diagdown\!\!\!\!\!7}}[/tex]

[tex]\sf{\dfrac{1}{8} \times\dfrac{2}{1}}[/tex]

Divide by 2 :

[tex]\sf{\dfrac{1}{4} \times\dfrac{1}{1}}[/tex]

Now if you multiply, you'll get :

[tex]\sf{\dfrac{1\times1}{4\times1}}[/tex]

Which simplifies to 1/4.

Answer:

B

Step-by-step explanation:

The inequality is x < 5

Since there is no equal sign, the circle will be open, and it is smaller than 5, so it will be to the left of 5.

So, B is the answer.

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Using exponential growth formula, the number of bacteria in test tube after 8 hours is  167,772,160

To calculate the approximate number of bacteria after eight hours of growth, we need to determine the number of doubling cycles that occur during that time and apply the exponential growth formula.

Given:

Initial number of bacteria (N₀) = 50 (given as the inoculum)

Doubling time (t) = 20 minutes

Let's first calculate the number of doubling cycles that occur in eight hours (480 minutes):

Number of doubling cycles = (8 hours * 60 minutes per hour) / 20 minutes

Number of doubling cycles = 24 cycles

Now, we can apply the exponential growth formula to calculate the final number of bacteria (N) after eight hours:

N = N₀ * (2 exp (number of doubling cycles))

N = 50 * 2²⁴

Using a calculator or computational tool, we can evaluate this expression:

N ≈ 1.6777216 * 10^8

Therefore, after eight hours of growth, the test tube should contain approximately 167,772,160 bacteria.

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Answer:

+9xy =-13

no

so the answer is c

bro what is the answer is also can say they c optio thanks for point

Answer:

Step-by-step explanation:

4x + 10

C.

4-7(x+5)

4-7x+5

-7x+9

B. 2+5(x-7)

7(x-7)

7x-49

D. 7-3(x - 5)

7-3x-15

-3x-8

its 1,002

Answer:

1 ≤ x ≤ 3

Step-by-step explanation:

4x ≤ x + 3 or 2x ≤ 6

4x ≤ x + 3

3x ≤ 3

x ≤ 1

2x ≤ 6

x ≤ 3

So, the answer is 1 ≤ x ≤ 3

The missing dimensions from the given expression should be completed with the following:

(81.) A) 2

(82.) AD) x

(83.) E) 12

The expression as a product should be written as: DE) 2(x + 12).

In Mathematics and Geometry, a factored form can be defined as a type of quadratic expression that is typically written as the product of two (2) linear factors and a constant.

In this scenario and exercise, we would complete the table above by showing the factored form and expanded form of each of the given expressions as follows;

        x           12

2      2x         24

Note: 2x/2 = x.

         24/2 = 12.

(2x + 24) = 2(x + 12).

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Answer:

x inches = 46 inches

2x inches = 92 inches

(7x - 4) inches = 318 inches

Step-by-step explanation:

The perimeter of the triangle is the sum of all three sides. Therefore,

x + 2x + (7x - 4) = 456 inches

10x - 4 = 456

10x = 460

x = 46 inches

Now, we find the other remaining sides.

2x inches = 2(46) inches = 92 inches

(7x - 4) inches = (7(46) - 4) inches = (322 - 4) inches = 318 inches

So, the final answer is

x inches = 46 inches

2x inches = 96 inches

(7x - 4) inches = 318 inches

Answer:

a. A polygon with 4 equal sides is called a rhombus.

b. A polygon with 4 right angles is called a rectangle.

c. A polygon with opposite sides parallel is called a parallelogram.

d. A rectangle without any design is called a quadrilateral.

Note: It may be different in these cases.

Answer:

Rhombus

Rectangle

Parallelogram

Quadrilateral

Step-by-step explanation:

A quadrilateral is a polygon with four sides and four vertices. It is a closed two-dimensional figure formed by connecting four line segments. The interior angles of a quadrilateral add up to 360 degrees. Quadrilaterals can have various shapes and properties depending on the lengths of their sides and the angles between them. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, rhombuses, and kites.

The first shape has identical tick marks on each side, meaning that each side is equal in length. It does not have any interior angles marked, or any indication if any sides are parallel. Therefore, it is a rhombus.

All interior angles of the second shape are right angles. This means that adjacent sides are perpendicular, and therefore opposite sides are parallel. It does not have any indication of the lengths of the sides. Therefore, it is a rectangle.

The third shape has two sets of arrows on opposite sides, meaning that  each pair of opposite sides is parallel.  It does not have any interior angles marked. It does not have indication of the lengths of the sides, however, as the opposite sides are parallel, this means that the opposite sides will be equal in length. Therefore, it is a parallelogram.

The fourth shape does not have any markings to indicate the length of its sides, the measure of its interior angles, or if any sides are parallel. Therefore, it is a quadrilateral.

The dot plot c represents the data correctly in this problem.

The dot plot gives a dot to each measure for each time that it appears, hence it says the same thing as a table, in a different format.

For this problem, we have that:

Hence the dot plot c represents the data correctly in this problem.

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The volume of the figure is 90 cubic meters

From the question, we have the following parameters that can be used in our computation:

The figure

The volume of the figure is the product of the base area and the height

i.e. Volume = Base area * Height

Where, we have

Base area = 1/2 * 12 * 5

Base area = 30

So. we have

Volume = 30 * 3

Evaluate

Surface area = 90

Hence, the volume of the figure is 90 cubic meters

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The equation X^2/2 - 8 = 2X - 2 has two solutions, X = 6 and X = -2. These are the values of X that satisfy the equation and make both equations Y = X^2/2 - 8 and Y = 2X - 2 intersect on the graph.

To find the solutions to the equation X^2/2 - 8 = 2X - 2, we need to set the two equations equal to each other and solve for X.

The equation is:

X^2/2 - 8 = 2X - 2

To simplify the equation, let's multiply both sides by 2 to eliminate the fraction:

X^2 - 16 = 4X - 4

Next, we rearrange the equation to have all terms on one side:

X^2 - 4X - 12 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case:

(X - 6)(X + 2) = 0

Setting each factor equal to zero gives us two possible solutions:

X - 6 = 0 --> X = 6

X + 2 = 0 --> X = -2

So the solutions to the equation X^2/2 - 8 = 2X - 2 are X = 6 and X = -2.

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Answer: The third one

Step-by-step explanation:

That system has the same equation, but a different solution, meaning the lines can never intersect.

We can also convert it into slope-intercept form.

y = -2x + 9

y = -2x + 5

Different slope and same y-intercept = NO SOLUTION

Answer:

2x + y = 9

2x + y = 5

Step-by-step explanation:

No solutions for 2 lines will only happen when the lines are parallel and never touch.  So there are no solutions.

Lines are parallel when slopes are the same.

The equations cannot be the same just the slopes are the same.  

Let's rearrange this set of equations into y=mx+b so we can see what the slope m is:

2x + y = 9           and               2x + y = 5

y= -2x +9                                 y= - 2x +5

You can see the lines are different but have the slopes so they are parallel and no solutions.

Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

The corresponding monthly expense for the given expenses is approximately $278.34.

We have from the question that;

Monthly automobile insurance expense = $400 / 6 = $66.67

Monthly health insurance expense = $170

Monthly life insurance expense = $500 / 12 = $41.67

Total monthly expense = Monthly automobile insurance expense + Monthly health insurance expense + Monthly life insurance expense

Total monthly expense = $66.67 + $170 + $41.67

Total monthly expense = $278.34

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Answer:

∠ O = 55° , ∠ A = 90°

Step-by-step explanation:

2

the figure has opposite sides parallel and is therefore a parallelogram.

• opposite angles in a parallelogram are congruent, then

∠ O = ∠ Q = 55°

3

the sum of the interior angles of a quadrilateral is 360°

sum the angles and equate to 360°

∠ A + 70° + 110° + 90° = 360°

∠ A + 270° = 360° ( subtract 270° from both sides )

∠ A = 90°

The answer is that the value of f(b) is 4 Times as large as n(b).

Given that d(b) is 2 times as large as n(b) where b is some fixed number, we can express it as:d(b) = 2n(b)Now we are required to find the value of f(b). As f(b) is defined as f(b) = d(b) + 2n(b),

we can substitute the value of d(b) in the expression to obtain:

f(b) = 2n(b) + 2n(b) = 4n(b)

Therefore, the value of f(b) is 4 times as large as n(b).

We can also obtain this result by substituting the value of d(b) = 2n(b) in the expression f(b) = d(b) + 2n(b) to get:f(b) = 2n(b) + 2n(b) = 4n(b)

Therefore, the value of f(b) is 4 times as large as n(b).

Hence, the answer is that the value of f(b) is 4 times as large as n(b).

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The given system of equations does not have a specific value for xy. Therefore, the answer is D) No solution.

To find the value of xy using the given system of equations, we can substitute the value of x from the second equation into the first equation. Let's solve the system step by step:

Given equations:

Y = 4x + 8

x = 2y + 19

First, we substitute the value of x from equation 2) into equation 1):

Y = 4(2y + 19) + 8

Simplifying the expression:

Y = 8y + 76 + 8

Y = 8y + 84

Now, we have a single equation in terms of Y. To solve for Y, we need to eliminate the variable y. Since we know x = 2y + 19, we can substitute this value into the equation above:

Y = 8(2y + 19) + 84

Y = 16y + 152 + 84

Y = 16y + 236

Now, we have an equation in terms of Y only. Since we are asked to find the value of xy, we substitute Y back into equation 2) to solve for x:

x = 2(16y + 236) + 19

x = 32y + 472 + 19

x = 32y + 491

Now, we have equations for x and Y in terms of y. To find the value of xy, we substitute these expressions back into the equation xy:

xy = (32y + 491) * (8y + 84)

xy = 256y^2 + 3664y + 41144

As you can see, the expression for xy is a quadratic equation in terms of y. It does not simplify to a constant value. Therefore, the answer is D) No solution.

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The rate of change of the simple index over one day is approximately 12.78%.

To calculate the rate of change of the simple index over one day, we need to determine the percent change in the total value of the index between Monday's opening and Tuesday's opening.

On Monday, Stock A has 5000 shares at $2.75 per share, so its total value is:

Total value of Stock A on Monday = 5000 * $2.75 = $13,750

Similarly, on Monday, Stock B has 3000 shares at $4.30 per share, so its total value is:

Total value of Stock B on Monday = 3000 * $4.30 = $12,900

The total value of the index on Monday is the sum of the values of Stock A and Stock B:

Total value of the index on Monday = $13,750 + $12,900 = $26,650

On Tuesday, Stock A opens at $3.10 per share, and Stock B opens at $4.85 per share. Both stocks still have the same number of shares as on Monday.

The total value of Stock A on Tuesday is:

Total value of Stock A on Tuesday = 5000 * $3.10 = $15,500

The total value of Stock B on Tuesday is:

Total value of Stock B on Tuesday = 3000 * $4.85 = $14,550

The total value of the index on Tuesday is the sum of the values of Stock A and Stock B:

Total value of the index on Tuesday = $15,500 + $14,550 = $30,050

To calculate the percent change in the index, we use the formula:

Percent Change = ((New Value - Old Value) / Old Value) * 100

Percent Change = (($30,050 - $26,650) / $26,650) * 100 ≈ 12.78%

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Answer:

C

Step-by-step explanation:

12 = - 7x - x² ( add x² to both sides )

x² + 12 = - 7x ( add 7x to both sides )

x² + 7x + 12 = 0 ← in standard form

consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (+ 7)

the factors are + 4 and + 3 , then

(x + 4)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x + 3 = 0 ⇒ x = - 3

solutions are x = - 4 and x = - 3

with a = - 4 and b = - 3

then

a² + b² + a + b

= (- 4)² + (- 3)² + (- 4) + (- 3)

= 16 + 9 - 4 - 3

= 25 - 7

= 18

The Rate of the motorboat in still water is 8 miles per hour, and the rate of the current is 2 miles per hour.

To solve this problem, let's denote the rate of the motorboat in still water as "b" and the rate of the current as "c".

When Juana is going upstream, she is going against the current, so her effective speed is reduced. The formula for the time it takes to travel a certain distance is distance divided by speed. Therefore, for the upstream trip:

Time = Distance / (Boat's speed - Current's speed)

5 = 30 / (b - c)   -- (1)

On the return trip downstream, Juana is going with the current, so her effective speed is increased. Therefore, for the downstream trip:

Time = Distance / (Boat's speed + Current's speed)

3 = 30 / (b + c)   -- (2)

We now have a system of two equations with two variables. We can solve this system to find the values of "b" and "c".

First, let's solve equation (1) for (b - c):

5 = 30 / (b - c)

(b - c) = 30 / 5

(b - c) = 6   -- (3)

Next, let's solve equation (2) for (b + c):

3 = 30 / (b + c)

(b + c) = 30 / 3

(b + c) = 10  -- (4)

Now, we have two equations (3) and (4) that represent the sum and difference of (b + c) and (b - c) respectively. We can solve this system of equations to find the values of "b" and "c".

Adding equations (3) and (4), we get:

2b = 6 + 10

2b = 16

b = 8

Substituting the value of "b" back into equation (3), we get:

(8 - c) = 6

c = 8 - 6

c = 2

Therefore, the rate of the motorboat in still water is 8 miles per hour, and the rate of the current is 2 miles per hour.

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Answer:

range = y values

[-10,0]

Step-by-step explanation:

look at the y axis and see where it goes at minimum to max

Answer:

Step-by-step explanation:

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