100 Points! Algebra question. Photo attached. Find the missing variable. Round your answers to the nearest hundredth. Please show as much work as possible. Thank you!

a) The deepest that the diver went is of: 432 yards deep.

b) It took 12 minutes for the diver to return to the surface.

c) After one minute, the diver was 132 yards deep.

The quadratic function modeling the diver's height after x seconds is given as follows:

d(x) = 12x² - 144x.

The coefficients are given as follows:

a = 12, b = -144, c = 0.

The x-coordinate of the vertex is given as follows:

x = -b/2a

x = 144/24

x = 6.

Item a:

As a > 0, in item a, the minimum height is given as follows:

d(6) = 12(6)² - 144(6)

d(6) = -432 feet.

Item b:

The roots of the function, in item b, are obtained as follows:

12x² - 144x = 0

12x(x - 12) = 0

Hence:

12 - 0 = 12, hence it took 12 minutes for the diver to return to the surface.

Item c:

After one minute, the depth of the diver, in item c, is given as follows:

d(1) = 12(1)² - 144

d(1) = -132 yards.

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hello

the answer to the question is:

y = a cot(bx – c) + d

a = 1, b = 1/2, c = 0

the midline is y = d, so y = 0

the vertical stretch is 1, so label the y-axis so the inflection point of the curve is 1 above the midline, and the other inflection point is 1 below the midline

the period is:

T = π/b ----> T = 2π

the phase shift is:

PS = c/b ----> PS = 0

and also, there's no amplitude for tangent and cotangent, there is only the vertical stretch that takes the place of an amplitude

Answer:

amplitude does not exist. period = 2π (360°)

Step-by-step explanation:

there is no amplitude for tan θ or cot θ, since there is no limit up or down (positive/negative infinity).

period for cot θ is π (180°)

period for cot 1/2 θ is 2π (360°)

The missing number in the original division problem is 28.

The solution is 113 ÷ 4 = 28.

The given division problem is: 113 ÷ 4 = 2 18.

To find the missing number, we can perform the division calculation step by step.

First, we divide 4 into the first digit of 113, which is 1.

Since 4 cannot be divided evenly into 1, we bring down the next digit, which is 1.

Now we have 11.

Next, we divide 4 into 11.

We can divide 4 into 11 two times, which gives us 8.

We subtract 8 from 11, leaving us with a remainder of 3.

Now, we bring down the next digit, which is 3.

We have 33.

Finally, we divide 4 into 33. 4 can be divided into 33 eight times, which gives us 32.

We subtract 32 from 33, leaving us with a remainder of 1.

So, the complete division is 113 ÷ 4 = 28 remainder 1.

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Answer: x=-7

Step-by-step explanation:

This question is really easy, so I'll just briefly explain axis of symmetry

To find it, it is ((x intercept 1)+(x intercept 2))/2. This is also called the vertex.

Or, the x value of the lowest or highest point. Lowest is it opens up, highest if it opens down.

x=-7 is the answer

For the function  f(x) = 2x + 3 the third iterate x₃  is 37

To find the third iterate, x3, of the function f(x) = 2x + 3, given an initial value of x₀ = 2,

we can apply the function repeatedly.

Starting with x₀ = 2:

x₁ = f(x₀)

= 2(2) + 3

= 7

x₂ = f(x₁)

= 2(7) + 3 = 17

x₃ = f(x₂)

= 2(17) + 3

= 37

Therefore, the third iterate x₃  is 37.

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Answer:x = {-4, 4}

explanation:

Answer:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

Step-by-step explanation:

From the given points (negative 2, negative 1), (0, 1), (2, 3), we can determine the domain and range.

The domain represents the set of all possible x-values of the points, and the range represents the set of all possible y-values of the points.

In this case, we can see that the x-values are -2, 0, and 2, and the corresponding y-values are -1, 1, and 3.

Therefore, the correct answer is:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

Area of triangle A   = 13.5 square units

Area of triangle B   = 10.5 square units

Total area of figure =  24 square units

In the given figure,

It consist of two triangles

Now for triangle A :

Height = 3

Base    = 9

Since we know that,

Area of triangle = (1/2) x base x height

                          = 0.5 x 9 x 3

                          = 13.5 square units

Now for triangle B :

Height = 3

Base    = 7

Since we know that,

Area of triangle = (1/2) x base x height

                          = 0.5 x 7 x 3

                          = 10.5 square units

Now the total are of figure is sum of are of both triangles,

Therefore,

total area of figure,

⇒ 13.5 + 10.5

⇒ 24 square units

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The missing figure of question is attached below:

The correct option is: (x + 3)² = 17; x equals negative 3 plus or minus the square root of 17(x = -3 ± √17) by completing the square

The completing the square method require we move constant term to the right hand side of the equation, divide the middle term and add its square to both sides of the equation as follows:

For the equation;

x² + 6x - 8 = 0

add 8 to both sides

x² + 6x = 8

divide 6 by 2 and add the square of the result to both sides

x² + 6x + 3² = 8 + 3²

by factorization;

(x + 3)² = 8 + 9

(x + 3)² = 17

x + 3 = ± √17 {take square root of both sides}

x = -3 ± √17

Therefore, by completing the square we the equation to be (x + 3)² = 17 and the solution for the value of x = -3 ± √17

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The ascending order of the rational numbers are -1.75 < -1.3 < 0.41 < 1.8

Given are the list of the rational numbers, so,

1 4/5, -7/4, 41% and -1.3

So,

1) The fraction form :-

a) 1 4/5 = 9/5

b) -7/4

c) 41% = 41/100

d) -1.3 = 13/10

2) The decimal form :-

a) 1 4/5 = 9/5 = 1.8

b) -7/4 = -1.75

c) 41% = 41/100 = 0.41

d) -1.3 = 13/10 = -1.3

3) The ascending order of the rational numbers =

You can arrange them by seeing the value and sign,

-1.75 < -1.3 < 0.41 < 1.8

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Does the relation represent a function: C. Yes, because for each input there is exactly one output.

In Mathematics and Geometry, a function can be defined as any mathematical equation which is typically used to define and represent a relationship that exists between two or more variables such as an ordered pair, points on a graph or table.

Based on the mapping diagram, we can reasonably infer and logically deduce that the relation represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).

In this context, we can reasonably infer and logically deduce that the relation represent a function because for each input (independent value) there is exactly one output (dependent variable).

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Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

hello

the answer is:

1)

Sin 28° = x/19 ----> x = 8.91 or 9

2)

tan 41° = x/32 ----> x = 27.8 or 28

3)

Cos 21° = x/26 ----> x = 24.2 or 24

4)

Cos 55° = 8/x ----> x = 13.9 or 14

5)

Sin 33° = 15/x ----> 27.57 or 28

6)

Cos 43° = 36/x ----> x = 49.2 or 49

7)

tan 72° = 25/x ----> x = 8.12 or 8

8)

Cos 64° = x/11 ----> x = 4.81 or 5

The experiment is binomial , probability that 3 out of 14 customers buy a magazine is 0.06 and the expected value is 1.036.

The experiment described is binomial because it satisfies the following conditions:

The probability that exactly 3 out of the first 14 customers buy a magazine. Using the binomial probability formula:

[tex]P(X = k) = (nCk) \times (p^k) \times {q}^{n - k} [/tex]

Where:

n = number of trials (14 in this case)

k = number of successful trials (3 in this case)

p = probability of success (7.4% or 0.074)

q = 1-p

Plugging in the values:

P(X = 3) = (14C3) × (0.074³) × 0.926¹¹

P(X= 3) = 0.0633

The expected number of customers from this sample that will buy a magazine can be calculated using the formula:

E(X) = n × p

Where:

- n is the number of trials

- p is the probability of success

Plugging in the values:

E(X) = 14 × 0.074 = 1.036

Therefore, the experiment is binomial and the expected value is 1.036.

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The value of f(-7) is 172.

To find the value of f(-7) for the given function f(x) = 4x^2 + 6x + 9, we substitute -7 for x in the function and evaluate it.

f(-7) = 4(-7)^2 + 6(-7) + 9

Simplifying the equation:

f(-7) = 4(49) - 42 + 9

= 196 - 42 + 9

= 163 + 9

= 172

Therefore, f(-7) = 172.

By substituting -7 into the function, we obtained the value of 172. This means that when x is equal to -7, the corresponding value of the function f(x) is 172.

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b'

Let the given points be A(3,-5) and B(5,-1).

AB= sqrt of (5−3) ² +(−1+5)²

= sqrt of 4+16

= sqrt of 20

=2 sqrt of 5 units

Answer:(2x+7)+(2x+7)

Step-by-step explanation:

what you do is put 2x on the top and on the side and then seven on the top and on the side and then you got your answer

The logo that fits the requirement is the circle logo i.e. logo 1

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

The figures that represent the logos

For the circle logo, we have

Area = 22/7 * 1/2 * 1/2

Convert units to feet using the scale

Area = 22/7 * 1/2 * 7 * 1/2 * 7

Evaluate

Area = 38.5 square feet

Also, we have

Width = 2 * 1/2 * 7 feet

Width = 7 feet

For the plus-shaped logo, we have

Area = 5 * 1/2 * 1/2

Convert units to feet using the scale

Area = 5 * 1/2 * 7 * 1/2 * 7

Evaluate

Area = 61.25 square feet

Also, we have

Width = 3 * 1/2 feet * 7

Width = 10.5 feet

Hence, the logo that fits the requirement is the circle logo i.e. logo 1

This is because its area is not up to the maximum area (40 square feet) and the width is greater than the minimum width (4 feet)

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y = −(x − 2)(x − 9); the wolf leaped a distance of 7 feet using zeros 2 and 9. Therefore, option B is the correct answer.

Given that, trajectory can be mapped by the equation f(x) = -x² + 11x - 18.

Here, -x² + 11x - 18=0

-x² + 9x+2x - 18=0

-x(x-9)+2(x-9)=0

(x-9)(-x+2)=0

x-9=0 and -x+2=0

x=9 and x=2

Therefore, option B is the correct answer.

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Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

Answer:

3) 50 in²

4)  85 cm²

Step-by-step explanation:

The given figure is composed of 2 triangles, each with a base of 10 inches and a height of 5 inches.

The area of a triangle is half the product of its base and height.

Therefore, the area of the composite figure can be calculated as follows:

[tex]\begin{aligned}\textsf{Area of compositie figure}&=\sf Area_{Triangle\;1}+Area_{Triangle\;2}\\\\&=\dfrac{1}{2} \cdot 10 \cdot 5 + \dfrac{1}{2} \cdot 10 \cdot 5\\\\&=5\cdot 5+5\cdot 5\\\\&=25+25\\\\&=50\; \sf square\;inches\end{aligned}[/tex]

Therefore, the area of the composite figure is 50 square inches.

[tex]\hrulefill[/tex]

The given figure is composed of a rectangle with width of 6 cm and length of 10 cm, and a triangle with base of 10 cm and height of 5 cm.

The area of a rectangle is the product of its width and length.

The area of a triangle is half the product of its base and height.

Therefore, the area of the composite figure can be calculated as follows:

[tex]\begin{aligned}\textsf{Area of compositie figure}&=\sf Area_{Rectangle} + Area_{Triangle}\\\\&=6 \cdot 10+\dfrac{1}{2} \cdot 10 \cdot 5\\\\&=60+5 \cdot 5\\\\&=60+25\\\\&=85\; \sf square\;centimeters\end{aligned}[/tex]

Therefore, the area of the composite figure is 85 square centimeters.

The given fractions representing the conditional probability is P(A | B) = P(AnB)/P(B)

We know that,

Conditional Probability is:

This is the probability that an event has happened given another event. If the two events are A and B, hence;

The conditional probability of A given B is expressed as:

P(A | B) = P(AnB)/P(B)

This given the fractions representing the conditional probability

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Yes, the coefficient of a value can be negative in an exponential function.

A coefficient in mathematics is a multiplicative factor in some term of a polynomial, series, or expression; it is generally a number, although it can be any expression.

Recall that the general form of an exponential function is f(x) = a^(bx + c), where a is the base.

This can be negative or positive. But cannot be equal to zero. A negative exponential function can model the decay of a radioactive substance or, in accounting, depreciation of an asset.

Thus, it is correct to state that , the coefficient a value can be negative in an exponential function.

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The graph of the inverse function is given by the image presented at the end of the answer, and the correct option is given by option 3.

The parent function for this problem is the cube function translated up two units, hence it is defined as follows:

y = x³ + 2.

To obtain the inverse function, first we must exchange the variables x and y on the definition of the function, as follows:

x = y³ + 2.

Then we must isolate the variable y, as follows:

[tex]y^3 = x + 2[/tex]

[tex]y = \sqrt[3]{x + 2}[/tex]

Which has the correct dashed graph given by option 3 on the image given.

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Answer:67/24

hope it helps bye

The expression equivalent to the given numerical expression is 67/24.

The given numerical expression is 2/3 ÷ 2⁴+(3/4 +1/6)÷1/3.

Here, 2/3 ÷ 2⁴+(3/4 +1/6)÷1/3

= 2/3 ÷ 16+(9/12 +2/12)÷1/3

= 2/3 × 1/16 +11/12 ×3/1

= 2/48 + 33/12

= 1/24 + 33/12

= 1/24 + 66/24

= 67/24

Therefore, the expression equivalent to the given numerical expression is 67/24.

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Answer:

To find the slope of a line passing through four points, we can use the formula:

slope = (change in y) / (change in x)

We can use any two points to calculate the slope, but since we need to find the slope for the entire line passing through all four points, we need to make sure that the slope is the same for any two points that we choose.

Let's use the points (-6,7) and (-2,6) to calculate the slope:

slope = (6 - 7) / (-2 - (-6)) = -1/4

Now let's use the points (2,5) and (6,4) to calculate the slope:

slope = (4 - 5) / (6 - 2) = -1/4

Since the slope is the same for both pairs of points, we can conclude that the slope of the line passing through all four points is -1/4.

Step-by-step explanation:

As a result of the seed growing in a field with a different population of plants, we can witness how gene flow works in action.

It will have introduced its alleles into that population once this plant reproduces there. Any movement of people from one group to another—also known as migration—and/or the genetic material they carry is referred to as gene flow. Pollen being carried to a new location by the wind or individuals relocating to new cities or nations are just a few examples of the many different types of events that contribute to gene flow.

Vertical and horizontal gene flow are two different types of gene transfer. Gene flow describes the transfer of genetic material between groups.

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Answer:

35

Step-by-step explanation:

perimeter = sum of the lengths of the sides

In a parallelogram, opposite sides are congruent.

Two sides have length 7.5 cm.

We need the length of the top and bottom sides.

area = base × height

62 cm² = base × 6.2 cm

base = (62 cm²)/(6.2 cm)

base = 10 cm

Two sides have length 10 cm.

perimeter = 7.5 cm + 7.5 cm + 10 cm + 10 cm

perimeter = 35 cm

If the significance level is set at 5%, the probability of the treatment group's mean being greater than the control group's mean by 8 points or more is given as 5%, which is less than the significance level of 5%.

The correct answer is "less than."

The probability of the treatment group's mean being greater than the control group's mean by 8 points depends on the sample sizes, standard deviations, and means of both groups.

These values are used to calculate the t-score or z-score and the corresponding probability or p-value.

The probability can than be compared to the significance level to determine if the result is statistically significant.

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The equation of circle with a center at (9, 5) that passes through (13, 7) is (x - 9)² + (y - 5)² = 20.

we have Center at (9, 5) and passes thorough (13, 7).

To find the equation of a circle with center (h, k) and a point (x, y) on the circle, we can use the standard form equation of a circle:

(x-h)² + (y-k)² = r²

So,  (x - 9)² + (y - 5)² = r

Since the circle passes through (13, 7), then

(13 - 9)² + (7 - 5)² = r²

²4 + (2)² = r²

16 + 4 = r²

20 = r²

So, the equation of circle is

(x - 9)² + (y - 5)² = 20

Therefore, the equation of circle with a center at (9, 5) that passes through (13, 7) is (x - 9)² + (y - 5)² = 20.

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Solution of the given system is,

x = 8

y = 11

The given system of equation

-12x + 5y = 9 ....(i)

    y = 2x - 5  ...(ii)

Now we have to solve it by using substitution method.

So put value of y from equation (ii) into equation (i)

Therefore,

⇒ -12x + 5y = 9

⇒ -12x + 5(2x - 5) = 9

⇒ -12x + 10x - 25  = 9

⇒                    -2x  = 16

⇒                        x  = 8

Now put the values of x into (ii) we get,

⇒ y = 2x8 - 5

⇒ y = 11

Hence,

solutions be ,

x = 8

y = 11

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We are unable to determine the volumes of the individual components and the composite figure due to missing data on the radii and precise component configurations.

We must determine the volumes of the three separate parts—a cylinder, a 1 mm tall cone—in order to get the volume of the composite figure.

The 3 mm tall cone's volume is:

The formula  [tex]V = (1/3)r^{2} h,[/tex]  where r is the radius of the base and h is the height, determines the volume of a cone.

We must determine the radius because the cone's height is 3 mm. We are unable to determine the volume of the 3 mm tall cone without additional information.

Dimensions of the cylinder:

The formula V = r2h, where r is the radius of the base and h is the height, determines the volume of a cylinder.

We are unable to determine the volume of the cylinder without precise measurements for its height and radius.

Volume of the 1 mm tall cone: Once more, in order to calculate the volume of the 1 mm tall cone, we need to know the radius of the base. Without this additional information, we are unable to do so.

The composite figure's volume:

We would need to know the sizes and configurations of the different parts (cones and cylinder) within the composite figure in order to determine its volume.

We are unable to determine the volume of the composite figure without this information.

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