How do I show my work, what do I say?

It will take 28.5 seconds to Makayla to be twice as deep as Jonah.

What is an equation?

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15.

Given,

Jonah is at a depth of -20ft.

Makayla is at a depth of -12.5ft.

at the rate of descending is 0.5.

Given equation is

2(-20+0.25s) = -12.5-0.5s

-40 + 0.5 s = -12.5 -0.5s

0.5s + 0.5s = -12.5+40

1s = 28.5

Hence, the solution of the equation is 1s = 28.5.

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Translating a rectangle involves moving the rectangle.

The coordinate of the image of rectangle QRST is: \(\mathbf{Q' = (-1, 6)}\)    \(\mathbf{R' = (2, 8)}\)    \(\mathbf{S' = (6, 2)}\)   \(\mathbf{T' = (3, 0)}\)

The coordinate points of rectangle QRST are given as:

\(\mathbf{Q = (-6,-1)}\)

\(\mathbf{R = (-3,1)}\)

\(\mathbf{S = (1,-5)}\)

\(\mathbf{T = (-2,-7)}\)

The translation rule is given as:

\(\mathbf{(x,y) \to (x + 5, y + 7)}\)

Apply the above translation rule on point Q

\(\mathbf{Q' = (-6 + 5, -1 + 7)}\)

\(\mathbf{Q' = (-1, 6)}\)

Apply the above translation rule on point R

\(\mathbf{R' = (-3 + 5, 1 + 7)}\)

\(\mathbf{R' = (2, 8)}\)

Apply the above translation rule on point S

\(\mathbf{S' = (1+5, -5+7)}\)

\(\mathbf{S' = (6, 2)}\)

Apply the above translation rule on point T

\(\mathbf{T' = (-2 + 5, -7 + 7)}\)

\(\mathbf{T' = (3, 0)}\)

Hence, the coordinate of the image of the rectangle is:

\(\mathbf{Q' = (-1, 6)}\)    \(\mathbf{R' = (2, 8)}\)    \(\mathbf{S' = (6, 2)}\)   \(\mathbf{T' = (3, 0)}\)

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Answer:

Average rate of change; 1

Step-by-step explanation:

\(g(x) = x^{2} + 10x + 20\)

\(-9\leq x\leq 0\)

1. Find the end-points of the given interval

Input (-9) and (0) into the equation.

Input (-9)

\((-9)^2 + 10(-9) + 20\)

81 - 90 + 20

11

point is; (-9, 11)

Input (0)

\((0)^2 + 10(0) + 20\)

0 + 0 + 20

20

point is; (0, 20)

2. Find the slope

Now find the slope between the two points, the equation for the slope is;

\(\frac{y_{2}-y_{1}}{x_2-x_1}\)

Substitute in the points;

\(\frac{11-20}{0-(-9)}\)

-\(\frac{9}{9}\)

= -1

Answer:

7

Step-by-step explanation:

87 - 80 = 7

Given:

The degree of the polynomial = 3

Leading coefficient = 1

Zeros of the polynomial are 5 and 4i.

To find:

The expanded form of the polynomial.

Solution:

According to the complex conjugate root theorem, if a+ib is a zero of a polynomial, then a-ib is also a zero of that polynomial.

Here, zeros of the polynomial are 5 and 4i. It means the third zero of the polynomial is -4i. So, the factors of the polynomial are \((x-5),(x-4i),(x+4i)\).

The required polynomial is the product of its all factor and a constant which is equal to the leading coefficient. Here, the constant is 1. So, the required polynomial is

\(P(x)=1(x-5)(x-4i)(x+4i)\)

\(P(x)=(x-5)(x^2-(4i)^2)\)

\(P(x)=(x-5)(x^2+16)\)             \([\because i^2=-1]\)

\(P(x)=(x-5)(x^2+16)\)

On further simplification, we get

\(P(x)=x^3+16x-5x^2-80\)

\(P(x)=x^3-5x^2+16x-80\)

Therefore, the required polynomial P is \(P(x)=x^3-5x^2+16x-80\).

The curve of intersection between the cylinder x^2 + y^2 = 1 and the plane y + z = 2 is a circle lying on the plane y + z = 2. The parametric equations for this curve are x = cos(θ), y = sin(θ), and z = 2 - sin(θ), where θ is the parameter representing points on the circle.

To find the parametric equations for the curve of intersection between the cylinder and the plane, we can start by parameterizing the cylinder using the angle θ. Since the equation x^2 + y^2 = 1 represents a circle in the x-y plane with radius 1, we can use θ as a parameter to represent points on this circle.

The parametric equations for the cylinder are:

x = cos(θ)

y = sin(θ)

z = 2 - y

Next, we substitute these equations into the plane equation y + z = 2 to determine the intersection points. By substituting y and z, we have sin(θ) + 2 - sin(θ) = 2, which simplifies to sin(θ) - sin(θ) = 0. This implies that the plane equation is satisfied for any value of θ.

Therefore, the intersection between the cylinder and the plane is the entire cylinder itself, lying on the plane y + z = 2. The parametric equations for the curve of intersection are x = cos(θ), y = sin(θ), and z = 2 - sin(θ).

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Answer:

Unitary cost= $15

Step-by-step explanation:

First, we need to calculate the total cost of the baseball caps:

Total cost baseball caps= 90 - 45

Total cost baseball caps= $45

Now, the unitary cost of each baseball caps:

Unitary cost= total cost / number of units

Unitary cost= 45/3

Unitary cost= $15

Answer:

ef,ge,fg

Step-by-step explanation:

Answer:

D as in dog

Step-by-step explanation:

Given:

Claire is 2 year younger than her sister.

The  sum of ages is no less than 44 years.

To find:

Inequality and find the youngest age Claire can  be.

Solution:

Let the age of Claire be x.

Her sister's age = x+2

Sum of their ages is no less than 44 years. It means the sum ages is greater than or equal to 44.

\(x+(x+2)\geq 44\)

\(2x+2\geq 44\)

\(2x\geq 44-2\)

\(2x\geq 42\)

Divide both sides by 2.

\(x\geq 21\)

It means, Claire age can be greater than or equal to 21. So, the youngest age Claire can  be 21 years old.

Therefore, the required inequality is  \(2x+2\geq 44\) and the correct option is B.

The mortgage payment for a mortgage of $427,550 at an interest rate of 7.66% for 27 years is approximately $3,125.63.

To calculate the monthly payment, first, we determined the down payment as 15% of the purchase price, which amounted to $75,450. Subtracting the down payment from the purchase price, we found the loan amount to be $427,550. Using the formula for calculating the monthly payment on a fixed-rate mortgage, we determined the monthly payment to be approximately $3,125.63.

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Answer:

B

Step-by-step explanation:

We can see that this equation is in point-slope form, which is given by the formula:

\(y-y_1=m(x-x_1)\)

Where m is the slope and (x₁, y₁) is a point.

We have the equation:

\(y-(5)=-3(x-(17))\)

So, we can see that our (x₁, y₁) is (5,17), respectively, and our m is -3.

Therefore, our slope is -3.

Our answer is B.

Answer:

Step-by-step explanation:

y - 5 = -3(x - 17)

y - 5 = -3x + 51

y = -3x + 56

the answer is B

If the business owner wanted to make the case that the workers are paid well, she would use the range of central tendency.

The range, D

You are undoubtedly most familiar with the mean, which is the arithmetic average and a measure of central tendency. It is extremely easy to calculate the mean. Simple addition and division by the dataset's observation count are all that are required to calculate the values. All data values are included in the mean calculation.

Finding a variable's maximum observed value (also known as the range) and deducting its least observed value will yield the range (the minimum).

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The number of students in the telescope club by $x$ and the number of students in the math club by $y$.

$y=2x$Now, suppose there are $z$ students who are members of both clubs. Then the total number of students who are in the math club or the telescope club (or both) is given by:$x + y - z$ Substituting $y=2x$ in the above expression, we get:$x + 2x - z=3x - z$ Hence, the expression for the total number of students who are in the math club or the telescope club (or both) is $3x - z$.b)The number of students who are in the math club but not in the telescope club is given by:$y-z$ And the number of students who are in the telescope club but not in the math club is given by:$x-z$ Adding these two expressions, we get the total number of students who are in the math club or the telescope club but not both:$ y-z+x-z $.

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Answer:

The second graph

Step-by-step explanation:

t is greater than 4 and less than -1 but doesn't include the points 4 and -1 (thus the open circles)

The second graph represents the solution set to t > 4 or t < -1.

In open interval we do not include the point and represented by open circle in close interval we do include the points and represented by closed interval.

According to the given question we have to determine which graph represents the solution set t > 4 or t < -1.

We know when we represent less than or greater than in the number line we represent it as an open circle.

So, t > 4 will be represented by an open circle on the number line starting at 4  but not including which goes to positive infinity and t < -1 will be represented by an open circle at -1 not including which goes to negative infinity.

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To find a function that represents a parabola with the given vertex and passing through the given point, we can use the standard form of a quadratic function:

f(x) = a(x - h)^2 + k

where (h, k) represents the vertex of the parabola.

Given the vertex (-1, 5), we have h = -1 and k = 5. Plugging these values into the equation, we have:

f(x) = a(x - (-1))^2 + 5

f(x) = a(x + 1)^2 + 5

Now, we need to find the value of 'a' using the given point (-2, -3).

Plugging the coordinates of the point into the equation, we get:

-3 = a(-2 + 1)^2 + 5

-3 = a(1)^2 + 5

-3 = a + 5

a = -3 - 5

a = -8

Therefore, the function that represents the parabola with the given vertex and passing through the given point is:

f(x) = -8(x + 1)^2 + 5

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Answer:

A) it increases the mean value of the prizes.

Step-by-step explanation:

The median is resistant to large outliers, so it does not change if there is an especially large or small value. So, we can eliminate choices C and D.

I am actually not sure whether the data in the table count $100 as a large prize or a small one, but I am assuming it is a large prize. So, an extremely large prize would increase the mean value of the prizes.

Hope this helps!

The $100 gift card affect the measure of center of the data by increases the mean value of the prizes.

Option A is the correct answer.

It is the middles value of the given set of numbers after arranging the given set of numbers in an order.

We have,

The $100 gift card has a much larger value compared to the other prizes, and it is only given to one person.

Therefore, adding the $100 gift card to the prizes will significantly increase the total value of the prizes, which will affect the measures of center of the data.

The mean and median are two common measures of center in statistics. The mean is the sum of all the values divided by the number of values, while the median is the middle value when the data is arranged in order.

Adding the $100 gift card will increase the mean value of the prizes, but it will not affect the median value, since the median only depends on the order of the data, not the values themselves.

Therefore,

It increases the mean value of the prizes.

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Answer:

n + 4

Step-by-step explanation:

It´s like a normal sum, but since the number is unknown just put n.

Answer:

x +4

Step-by-step explanation:

it can really be any letter you choose

Answer:

the y-intercept is -5/9

Step-by-step explanation:

(hint, y=mx+b, b= y-intercept)

Example: y=4x-8

b=8

Answer:

Step-by-step explanation:

1.In the equation there is no y-intercept so it will be at 0

2.The slope or rise over run is 3/1 and is positive because there are no negative signs. Going up 3 and to the right 1 is how to mark the points on your graph and the opposite side will be doing a -3 and -1 by going down three from the 0 points and to the left 1.

3.As seen in the graph there are the points given and the line directed on them.

4.We already determined that our slope is positive

m=3

b=0

Answer:

The equation which reveals the minimum value for the equation is  2·x² + 12·x - 14 = 0 is the option;

2·(x + 3)² = 32

Step-by-step explanation:

The given function can be presented as follows;

2·x² + 12·x - 14 = 0

The quadratic equation in standard form is a·(x - h)² + k

Where;

(h, k) is the vertex of the parabola

Given that the coefficient of the x² is positive, the graph is U-shaped and the lowest point is given by the vertex of the graph as follows;

2·x² + 12·x - 14 = 2·x² + 12·x - 14 = 2·(x² + 6·x - 7) = 0

2·(x² + 6·x - 7) = 2·(x² + 6·x + 9 - 7 - 9) = 2·((x + 3)² - 16)

2·((x + 3)² - 16) = 2·(x + 3)² - 32 = 0

∴ 2·x² + 12·x - 14 = 2·(x + 3)² - 32 in vertex form

The minimum value (vertex, (h, k)) for the equation = (-3, -32)

Therefore, the equation which reveals the minimum value for the equation is 2·(x + 3)² = 32

Answer:

2(x + 3)2 = 32

Step-by-step explanation:

I took the test.

The ladder should be about 10.44 feet long (rounded to the nearest hundredth of a foot) for Joseph to reach the window 10 feet above the ground when the ladder is 3 feet away from the wall.

To solve this problem, we'll use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c² = a² + b².

In this case, the ladder acts as the hypotenuse, the distance from the wall to the ladder's base is one side (a = 3 feet), and the height of the window is the other side (b = 10 feet).

Using the Pythagorean theorem:
c² = (3)² + (10)²
c² = 9 + 100
c² = 109

Now, to find the length of the ladder, we'll take the square root of 109:
c ≈ √109
c ≈ 10.44

So, Joseph should use a ladder that is approximately 10.44 feet long, rounded to the nearest hundredth of a foot.

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Ignatius of Loyola, the Spanish priest and theologian who founded the Society of Jesus (Jesuits) in the 16th century, focused on several key issues during the period of the Counter-Reformation.

These issues can be broadly categorized into spiritual, educational, and institutional reforms.

Spiritual Reforms: Ignatius emphasized the importance of personal piety and spiritual discipline. He promoted the practice of spiritual exercises, including meditation, prayer, and self-examination, to cultivate a deep and intimate relationship with God. Ignatius encouraged individuals to reflect on their sins and seek forgiveness through confession and penance.

Educational Reforms: Ignatius recognized the power of education in shaping individuals and society. He established schools and universities to provide a comprehensive education that combined intellectual rigor with spiritual formation. The Jesuits placed great emphasis on academic excellence, encouraging critical thinking, the pursuit of knowledge, and the integration of faith and reason.

Pastoral Reforms: Ignatius focused on improving the quality of pastoral care and religious instruction. He trained his followers to be skilled preachers and spiritual directors, equipping them to guide and support individuals in their spiritual journey. Ignatius also emphasized the importance of catechesis, ensuring that people received proper religious education and understood the teachings of the Catholic Church.

Missionary Work: Ignatius and the Jesuits had a strong missionary zeal. They undertook extensive missionary endeavors, particularly in newly discovered territories during the Age of Exploration. They sought to bring Christianity to non-Christian lands and convert indigenous populations to Catholicism. The Jesuits established missions, schools, and hospitals in various parts of the world, playing a significant role in spreading Catholicism.

Overall, Ignatius of Loyola's reforms aimed to strengthen and revitalize the Catholic Church in response to the challenges posed by the Protestant Reformation. His focus on personal spirituality, education, pastoral care, and missionary work contributed to the renewal and expansion of the Catholic Church during the Counter-Reformation.

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Answer:

-5

Step-by-step explanation:

f(x)=x2-x

f(-5)=(-5)2-(-5)

f(-5)=-10-(-5)

f(-5)= -5

Answer:

23 friends

Step-by-step explanation:

100 - 8= 92

92/4 = 23

HEATHER IS SO POPULAR!!

Answer:

7V3

In triangle ABC, the measure of angle A is 60°, the length of BC is 7V3, and the length of AC is 7V2.

Step-by-step explanation:

Based on the data in the table, if a cow is randomly selected from farm B, the probability that its feed includes seaweed is 0.597 (Option D) and without is 0.57

Note that the total number of feed with sea weed is 74.
And the total number of cows on the farm B is 124.

Thus, the cows whose feed includes seaweed is 74/124

= 0.59677419354

≈ 0.597

The Probability of those whose feed is without sea weed is

Note that the total number of feed without sea weed is 40.
And the total number of cows on the farm B is 76.

Thus, the probability is 40/70
= 0.5714285714

≈ 0.571

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Answer :

55°

Detailed explanation:

The triangles are isosceles (having two sides of equal length and angle).

Hence solve for angle DCE

Angle DCE= 180°-(55°+55°)

=70°

As vertically opposite angles are equal. Thus,

angle ACB=70°.

Hence 180°-70°=110°

As the angles in an isosceles triangle are equal hence;

110°÷2=55°

Hence angle ABC is 55°

Hope this is has been clearly explained!

The measure of angle ABC from the given figure is 55 degree. Therefore, the correct answer is option A.

From the given figure, we have two isosceles triangles DCE and ABC.

In ΔDCE,

Base angle is ∠CED=55°.

Here, base angles are equal

That is, ∠CED=∠CED=55°

By using angle sum property of a triangle, we get

∠DCE=180°-(55°+55°)

∠DCE=70°

Now, ∠DCE and ∠ACB are vertically opposite angles are equal.

So, ∠DCE =∠ACB=70°

In ΔABC, base angles BAC and ABC are equal

So, ∠BAC+∠ABC+∠ACB=180°

∠ABC+∠ABC+70°=180°

2∠ABC=110°

∠ABC=55°

Therefore, the correct answer is option A.

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The shape of the distribution of the number of siblings can vary depending on the specific data set.

However, if we are considering the general case, the most common shape of the distribution is likely to be unimodal and skewed to the right.

This means that the majority of individuals are likely to have fewer siblings,

and as the number of siblings increases,

the frequency of individuals with that number decreases.

The distribution may also have a long tail on the right side,

indicating a few individuals with a significantly larger number of siblings.

However, it is important to note that this is just a general observation, and in specific cases,

the distribution may be different.

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