Mark all the relative minimum points in the graph.
See attached!

Answer:

  y = -1/4(x +4)² +4

Step-by-step explanation:

The equation of a parabola with focus (a, b) and directrix y=d can be written using the form ...

  y = 1/(2(b-d))(x -a)² +(b+d)/2

We are given (a, b) = (-4, 3) and d=5. Using these values in the above form gives the equation ...

  y = 1/(2(3-5))(x -(-4))² +(3+5)/2

  y = -1/4(x +4)² +4

The attached image shows the image of A"B"C" after the transformation

The transformation rule states:

A"B"C" = Ro90° (T(-4,3)(ABC))

This implies that one need to rotate the triangle in a 90⁰ clockwise direction, and then one need to translate the triangle.

Using the image shown, the coordinates of ABC are;

A = (-1, 2)

B = (1, 4)

C = (3, -1)

The 90⁰ rule clockwise rotation  will be:

(x,y) -- (y,-x)

So, when translated, it will be:

A' = (2, 1)

B' = (4, -1)

C' = (-1, -3)

Then the translation of the triangle using T(-4,3):

(x, y) -  (x - 4, y + 3)

So, there is:

A'' = (-2, 4)

B'' = (0, 2)

C'' = (-5, 0)

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Answer:

===============

As per given, the missing interior angle is corresponding with 40° angle.

Since corresponding angles are equal, the third interior angle of the triangle is 40°.

Sum of three interior angles is 180°:

Apply angle sum property

The answer is 140

The number of sea stars is 64.

What is a ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other.

In general, a: b, which can be interpreted as "a is to b," is used to denote a ratio between two quantities, let's say "a" and "b."

This ratio is expressed in fraction form as a/b. We utilize the same method for further simplifying a ratio as we use for further simplifying a fraction.

According to the question,

Ratio of sea stars to wolf eels = 4:5

Number of rock fish= 5/8 (Number of sea stars)

Number of wolf eels - Number of rock fish = 40

Using the given information, we get,

Number of sea stars = 8/5 (Number of rock fish)

On simplification,

Number of wolf eels = 80

So, number of sea stars = (4/5)*80

                                          = 64

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The answer choice which is not a step in finding the area of the unknown figure is; Plug all dimensions into the formula: SA=Ixwxh. option B

It follows from the task content that all other steps except Plugging all dimensions into the formula; SA = l×w×h are correct steps.

This is due to the fact that, the formula does not work for all shapes and hence, it can't be generalized for all situations.

The step which is not involved in finding the area of an unknown figure is; Plug all dimensions into the formula: SA=Ixwxh.

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Answer:

B) Plug all dimensions into the formula: SA=Ixwxh.

Step-by-step explanation:

The paddling rate of Alvin is 9km/hr

Given time against the  river current is 10 hours , speed is 3km/hr

and time with the river current given is 5 hours and the speed is 3km/hr

We need to calculate the paddling rate of Alvin

Let us assume that

r =Alvin's average paddling rate in km/hour

y = speed of the current in km/hour

we know that

speed= distance/time

∴ distance=speed*time

Now,

To Campsite against the current

Speed=(r-y)

∴ Speed=(r-3) ---- (1)

Time=8 hours

Distance=(r-3)*10------ (2)

10r - 30

From Campsite with the current

Speed=(r+y)

∴Speed=(r+3)*5

Time=3 hours

Distance=(r+3)*5----(1)

Equate equation 1 and equation 2

5r +15

because is the same distance

5r + 15 = 10r - 30

5r = 45

r = 9

Hence ,The rate of the paddling rate is 9km/hr

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Another rigid motions that maps Δ GHJ to ΔKLM is ΔGHJ winding point J rotates 180° in the counterclockwise direction. It then transits south by 10 units and to the right by two units. See the attached image.

Rigid Motion is any method of moving all the points in the plane in such a way that.

There are four forms of rigid motions:

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The definition of the piece-wise function is:

A piece-wise function is a function that has different definitions, depending on the input.

In this problem, for inputs between -2 and 2, the function is a line that goes through (-2,-4) and (2,6). The slope is:

m = (6 - (-4))/(2 - (-2)) = 2.5.

The y-intercept is of b = 1, hence the rule is:

[tex]f(x) = 2.5x + 1, -2 \leq x \leq 2[/tex]

For x greater than 2 and less than 6, the function is constant at -3, hence the rule is:

[tex]f(x) = -3, 2 < x < 6[/tex].

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The number of years it will take for the world’s population to increase to 8,252,000,000 people is 16

This implies that we calculate the value of x

The equation is given as:

8252=(6080)(1.02)^x

Divide both sides by 6080

1.36 = (1.02)^x

Take the logarithm of both sides

log(1.36) = x * log(1.02)

Divide both sides log(1.02)

x = log(1.36)/log(1.02)

Evaluate the quotient

x = 16

Hence, the number of years is 16

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The expression p% of m changed into an algebraic expression is pm/100

p% of m

= p% × m

= p/100 × m

= (p × m) / 100

= pm/100

Therefore, the expression p% of m changed into an algebraic expression is pm/100

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Answer:

A

Step-by-step explanation:

I. False. Consider y = 3 and x = 4.

II. False. Consider x = 1.

III. False. Consider x = -2.

The regression equation is y =  3.002 + 0.5x and the scatterplot is illustrated.

It should be noted that a scatterplot simply means a type of data that shows the relationship between two numerical variables.

From the information, summation is X is 99, summation Y is 82.5, summation XY is 797.47, and summation X² is 1001.

Now the value of a will be:

= 82.5 - 1001 - 99 - 797.47/(11.1001 - 99²)

= 3.002

b = (11 × 797.47 - 99 × 82.5)/11.1001 - 99²

= 0.5

The regression equation will be:

y = a + bx.

y = 3.002 + 0.5x

There's positive linear correlation between x and y.

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Answer:

The three planes of motion are the sagittal, coronal (or frontal) and transverse planes.

Sagittal Plane: Cuts the body into left and right halves. Forward and backward movements.

Coronal (or Frontal Plane): Cuts the body into front and back halves. ...

Transverse Plane: Cuts the body into top and bottom halves.

The function P(x), for the price of the materials for the pen, is 4.18(800/x + x) + 38.

Based on the information, the function P(x), for the price of the materials for the pen will be:

P(x) = 4.18 (2 × 400/x + x) + 38

= 4.18(800/x + x) + 38.

The dimensions will be:

We'll differentiate the function which will give 20✓2. Therefore, the value for x will be 20✓2 which is 28.28 feet and that of y will be 10✓2 which is 14.14 feet.

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Answer:

  B.  Completing the square

Step-by-step explanation:

Between the first and second steps shown, the square of half the x-term coefficient was added to both sides. That is a value that makes the polynomial on the left be a "perfect square trinomial."

The process of adding the value required to make the left side a perfect square is called "completing the square."

Answer:

angle 8 is congruent to angles 3, 6, and 1

Step-by-step explanation:

If n and q are parallel then corresponding and vertical angles would be congruent. So: angle 8 is congruent to angles 3, 6, and 1.

The graph of the given function, y = 2eˣ, is given below

From the question, we are to determine the graph of the given function

The given function is

y = 2eˣ

The graph of y = 2eˣ is shown below

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Answer:

x = 34

Step-by-step explanation:

The angles x + 12, 100, and x add up to a straight angle, so the sum of their measures is 180°.

(x + 12) + (100) + (x) = 180

x + 12 + 100 + x = 180

2x + 112 = 180

2x = 68

x = 34

Keeping the bases and adding the exponents, the simplified expression is:

[tex]x^{\frac{4}{21}}[/tex]

We keep the bases and add the exponents.

Hence:

[tex]x^{-\frac{2}{3}} \times x^{\frac{6}{7}} = x^{-\frac{2}{3} + \frac{6}{7}} = x^{\frac{-14 + 18}{21}} = x^{\frac{4}{21}}[/tex]

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Answer:

Distribute -1/2 over (x+4)

Step-by-step explanation:

-0.5(x+4) = 6

-0.5x - 2 = 6

-0.5x = 8

x = -16

Answer:

Multiple both sides by -2 or Distribute negative one-half over (x+4)

Step-by-step explanation:

-1/2(x+4) = 6

If I multiple both sides by -2, I am clearing the fraction:

(-2)(-1/2)(x+4) = 6(-2)

x+4 = -12

x = -16

OR

-1/2(x + 4) = 6

-1/2x -2 = 6  Remember, a negative times a positive is a negative.

-x - 4 = 12 multiply both sides by 2

-x = 16

x = -16

Answer: 8/52

2/13=x/52

(2×52)/13=x

104/13=x

8=x

x=8

8 is the equivalent of the fraction using a denominator of 52. 2/13

Equivalent fractions can be defined as fractions that may have different numerators and denominators but they represent the same value. For example, 9/12 and 6/8 are equivalent fractions because both are equal to 3/4 when simplified.

All equivalent fractions get reduced to the same fraction in their simplest form as seen in the example given above. Explore the given lesson to get a better idea of how to find equivalent fractions and how to check if the given fractions are equivalent.

        ⇒[tex]\frac{2}{13} =\frac{x}{52}[/tex]

       ⇒[tex]\frac{2(52)}{13} = x[/tex]

      ⇒[tex]x = 8[/tex]

therefore, 8 is the equivalent of the fraction using a denominator of 52. 2/13

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We are looking for the graph of [tex]y=\sqrt{-x}[/tex]. which is shown in the attached image.

Answer:

$22 * (20) + $18 * (48) = $1304

Step-by-step explanation:

There are 20 reserved seats so it would be: $22 * 20 = $440 for all reserved seats

There are 28 general admission tickets more than reserved seats ticket so number of general admission tickets is: 20 + 28 = 48 (tickets)

Each general admission tickets cost $18, so: $18 * 48 = $864  for all general admission tickets

So the total money was paid for all of the tickets is: $440 + $864 = $1304

Using the normal distribution, the probability is given as follows:

[tex]P(X \geq 10) = 0.0485[/tex].

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the binomial distribution are:

p = 0.5, n = 13.

Hence the mean and the standard deviation are:

Using continuity correction, the desired probability is P(X > 9.5), which is one subtracted by the p-value of Z when X = 9.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{9.5 - 6.5}{1.8028}[/tex]

Z = 1.66

Z = 1.66 has a p-value of 0.9515.

1 - 0.9515 = 0.0485, then:

[tex]P(X \geq 10) = 0.0485[/tex].

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Answer:

x + 4

Step-by-step explanation:

Sine the bases are all the same, I can write the equation:

3x+4 = (x-2) 2^3  When we are adding with logs, that means to multiple.  Also, when we have 3 log 2, that can be written as 2^3 or 8 (2x2x2)

3x+4=(x-2)8

3x+4 = 8x-16

4=5x-16

20 = 5x

4=x

Answer:

a=0, 12

Step-by-step explanation:

a=0 and –12+a=0===> a=12

Answer:

14

Step-by-step explanation:

[tex] {x}^{2} = {4}^{2} \\ = 16\\ 4y = 4 \times - 3 \\ 4 \times - 3 = - 12 \\ 16 - - 12 =16 + 12 \\ - \times - = + \\ 16 + 12 = 28 \\ 28 \div 2 = 14[/tex]

A) The original claim in symbolic form is; p > 0.50

B) The Null Hypothesis is;

H₀: p = 0.50

Alternative Hypothesis is;

H_a: p > 0.50

We are given;

Sample size; n = 576

Sample Proportion; p^ = 59% = 0.59

A) The percentage of 59% represents the proportion of a sample and thus we are making a claim about the population proportion p in the hypotheses.

We claim "most of the adults", which indicates more than 50% or 0.50. Thus, the claim in symbolic form is; p > 0.50

B) The Null Hypothesis is;

H₀: p = 0.50

Alternative Hypothesis is;

H_a: p > 0.50

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